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The grieving process involves accepting and adapting to a loss, whether it be a loved one, an object, or a situation (Herrera, 2018). It has been observed that children are particularly sensitive to changes and losses. Therefore, according to Herrera (2018), pathological grief in children manifests as a true maladaptation syndrome that can have profound consequences for their development and well-being. What is Pathological Grief in Children? A normal grieving process is defined as a vital stage in which a person reacts to a loss, understands its implications, reorients their life without the presence of the loved one, and accepts the loss (Herrera, 2018). In this process, the memory of the loved one does not provoke significant emotional reactions. The duration of this process is subject to significant controversy. Instead of establishing a temporal criterion, scientists and mental health professionals have agreed on an adjustment criterion. Thus, according to Herrera (2018), it has been established that normal grief should not be a debilitating complication in any case. On the other hand, pathological grief in children is defined as a condition in which the feeling of sadness extends beyond the period considered normal (García, 2018). This feeling of sadness, which is a natural response to loss, can persist for years if not properly addressed with the help of a specialist. Death is a natural process, and grief is an integral part of it. It is crucial to be alert if symptoms persist and to remember that for children, this process can be not only painful but also confusing. Furthermore, in line with García (2018), it is important to note that although grief generally occurs when a close person dies, it can also result from other situations, such as parental separation. Symptoms Pathological grief in children is characterized by intense and prolonged sadness that exceeds the expected duration, affecting the child's normal functioning emotionally, cognitively, physically, and socially (Menéndez, 2018). As a result, the child may show a prolonged inability to perform activities they used to do before the loss. According to Menéndez (2018), as research on pathological grief in children has progressed, it has been recognized that it is uncommon for children to experience extreme grief symptoms that result in persistent distress and impairment in their functioning. Some professionals recommend grouping symptoms into different domains (Menéndez, 2018). According to Menéndez (2018), in the cognitive domain, symptoms may include rumination about the circumstances of the death, frequent disbelief or inability to accept the death, separation anxiety, persistent and intense yearning for the deceased person, frequent feelings of loneliness or emptiness, negative thoughts about life without the deceased or a recurring need to join the deceased, and troubling thoughts about the deceased that impair daily functioning. Regarding feelings, symptoms may include a persistent sense of shock, numbness, or emotional numbness since the death, recurrent feelings of anger or bitterness about the death, difficulty trusting or caring for others since the loss, experiencing pain or other somatic symptoms, hearing the deceased's voice or seeing the deceased person, and intense emotional reactions to memories of the deceased (Menéndez, 2018). Finally, in the behavioral domain, symptoms may include excessive concern or avoidance of places, people, and things related to the death. As a consequence, these symptoms can interfere with the child's normal functioning, causing significant distress in academic, social, and family areas. Additionally, in line with Menéndez (2018), both the intensity and duration of this type of grief are clearly disproportionate. Types of Pathological Grief There are four types of pathological grief in both children and adults (Herrera, 2018). The first is chronic grief, characterized by disabling pain that persists even after a year in adults and six months in children. In this case, the individual has difficulty adapting to their new reality. The second type is delayed grief. Here, the individual initially shows only some emotions after the loss. However, over time, they experience intense emotional burden that had not been previously manifested. The third type is exaggerated grief. In this case, the pain is so overwhelming that the individual resorts to self-destructive behaviors. Moreover, this type of grief can increase the likelihood of developing other psychological disorders. Finally, the fourth type is masked grief. According to Herrera (2018), this type of grief can be difficult to identify, as the individual may present physical and emotional problems without being aware that these problems are a manifestation of their grief. Pathological Grief According to Age It is important to note that symptoms manifest differently and in different proportions depending on the child's age (Menéndez, 2018). In preschool and school-aged children, exaggerated fears, attachment problems with primary caregivers, traumatic play, and persistent regression may be present. On the other hand, in preadolescents and adolescents, risk behaviors, suicidal ideation and behavior, inability to create a narrative about the loss, and a very negative perspective on the future and inability to set goals may be observed. Some studies suggest that, in general, younger children more frequently exhibit fear and attachment problems, while older children more commonly show risk behaviors. According to Menéndez (2018), it is essential to consider these differences to effectively address pathological grief in children. Controversy There is considerable controversy around the concept of pathological grief in children (Herrera, 2018). There are professionals and scientists who reject this diagnostic category, which is included in the DSM-5, arguing that each individual processes, interprets, and manifests their emotions uniquely. For these psychologists, doctors, and psychiatrists, including pathological grief as a psychopathological disorder would be equivalent to labeling a person who is simply sensitive to their loss as sick. However, there is a school of thought that has gained ground against this idea, recognizing the importance of categorizing these particular symptoms. According to Herrera (2018), the goal of this categorization is to obtain more information about the clinical picture, the course, and the prevalence of the problem, as well as to investigate effective treatment. Recommendations Currently, effective psychological treatments are recognized for addressing pathological grief (Herrera, 2018). Therefore, it is advised to establish contact with a psychology professional to treat this condition. However, there are some recommendations that can be followed to help children experiencing pathological grief. Maintaining open communication is essential, providing honest and understanding answers to their questions and concerns. It is important to create a safe and trusting environment where the child can freely express their feelings and thoughts. It is beneficial to provide them with appropriate information about death and the implications of the deceased's absence in their daily life. Additionally, it is useful to ask if they have any doubts, fears, or insecurities and how they can be helped to overcome these feelings. Throughout the grieving process, according to Herrera (2018), it is crucial to show them understanding and patience, providing trust and a secure attachment. References García, F. M. (2018, diciembre 12). El duelo patológico en los niños. Eres Mamá. https://eresmama.com/el-duelo-patologico-en-los-ninos/ Menéndez, M. (2018). Duelo Patológico en Niños: Síntomas y Tratamiento. Psicología Online. https://www.psicologia-online.com/duelo-patologico-en-ninos-sintomas-y-tratamiento-3902.html Peña Herrera, B (Herrera, 2018). (2018, diciembre 26) (Herrera, 2018). Duelo patológico en niños (Herrera, 2018). La Mente es Maravillosa (Herrera, 2018). https://lamenteesmaravillosa.com/duelo-patologico-en-ninos/

The death of a loved one is a delicate subject that requires appropriate communication with children, but many adults are unsure how to approach it (Tarrés, 2023). They are anxious and concerned about discussing serious illnesses, accidents, or death with their children, fearing they will cause them pain and sadness that they believe children cannot handle due to their age and immaturity. Therefore, they often delay such conversations as much as possible (Tarrés, 2023). However, most young children are aware of death, even if they do not understand it (Ehmke, 2019). Death is a common theme in cartoons and television, and some of the child's friends may have already experienced the loss of a loved one. However, experiencing grief firsthand is a different and often confusing experience for children. According to Ehmke (2019), adults cannot protect a child from the pain of loss, but they can help them develop healthy coping skills that will benefit them in the future. Understanding Manifestations Normal grief is characterized by being transient (though its duration is not fixed) and requires emotional processing and a journey, but its manifestations can be mistaken for pathology (Vera Mota, 2023). When a child loses a loved one, they may alternate between crying and playing within minutes (Ehmke, 2019). This does not mean they are not feeling sad or have overcome their grief; children cope with loss differently from adults, and play can be a way to avoid being overwhelmed. Likewise, in accordance with Ehmke (2019), it is normal for them to experience depression, guilt, anxiety, or anger towards the deceased or someone else. In some cases, younger children may regress in their development, such as bed-wetting or baby talk (Ehmke, 2019). These expressions are varied and require careful attention to avoid confusing them with developmental issues (Vera Mota, 2023). Other factors influencing how a child processes grief include previous experiences, the child's age, their relationship with the deceased, preparation time, diagnosis, and planned changes, among others. Grieving a death involves distress and suffering and requires time to accept the loss. According to Vera Mota (2023), helping a child cope with loss does not mean eliminating their pain but helping them express their emotions. What Signs to Look For? Children's reactions to difficult situations can vary greatly, so it is important to pay attention to their emotions, such as sadness, anger, fear, shame, or guilt (Vera Mota, 2023). Changes in behavior should also be observed: some children may become more active or energetic than usual, while others may become more withdrawn, quiet, or talkative. Additionally, according to Vera Mota (2023), they may experience physical pain, decline in school performance, lose interest in play, disrupt their sleep, stop recounting their dreams, reduce their imagination, or ask fewer questions. How to Support Them? The way children understand and engage with death depends on both their developmental stage and family customs and rituals; therefore, each case requires individual evaluation to determine what is best for each child (Vera Mota, 2023). Although talking about death with children is difficult, it is important to introduce it to them as part of life and to provide spaces for them to process their grief, rather than closing or covering it up. According to Vera Mota (2023), it is crucial for adults to articulate and accompany children with words, helping them understand what death means, what has happened, and what has changed, always considering the child's language and age and handling the circumstances of death with care, without providing potentially harmful details in cases of traumatic or violent events. Rituals can be key to facilitating grief (Vera Mota, 2023). Therefore, it is suggested to involve children, as long as someone accompanies them and helps answer their questions. However, some children are not ready for an intense experience like funerals, which can be useful for closure but also very sad and emotional, especially if there is a casket (Ehmke, 2019). Hence, children should never be forced to attend a funeral, and if they want to go, they should be prepared for what they will see and what to expect, considering that their behavior might be unpredictable. If the family decides that the child should not participate in family events, Ehmke (2019) suggests a symbolic farewell ritual at home, such as planting a tree, sharing stories, or releasing balloons, which can offer the child an opportunity for closure. Using alternative resources that address the topic of death can help adults understand how children are processing what happened, such as children's books about grief and death, symbolic play, movies, or stories (Vera Mota, 2023). It is also important to validate children's emotions, recognizing the difficulty of both the loss and the changes that death may bring, and avoiding minimizing their emotions with phrases like: "don't be sad, everything will be fine," "don't worry," "don't be afraid," "don't cry," among others (Tarrés, 2023). Children and adolescents need to feel accompanied and heard, and they should be given space and time to identify and accept their emotions and feelings, including ambivalence (Vera Mota, 2023). For this, according to Ehmke (2019), various means can be used, such as reading books for children about death, drawing, creating a scrapbook, looking at photo albums, or telling stories. Another important aspect of supporting children's grief is the need to teach them to deal with pain and sadness, offering them a real and genuine place to talk about their effects, always adjusting the language to each child's level of understanding (Vera Mota, 2023). Some questions to consider are: Where do we house our pain? What do we do when we are sad? How do we say goodbye to grandpa? How do we talk about fear at home? Lastly, Vera Mota (2023) suggests allowing others to accompany adults in their grief, teaching children to let themselves be accompanied by others in relationships, and to think about their own needs, such as asking, attending, participating, or seeking help (a hug, a gesture, listening, a moment alone, etc.). Finally, it is crucial not to ignore one's own grief, as children often mimic their parents' grieving behavior (Ehmke, 2019). It is important to show emotions, to confirm to children that it is okay to feel sad or upset. However, one should avoid reacting explosively or uncontrollably, as this teaches children unhealthy ways to deal with grief. Additionally, maintaining routines is important, as children find comfort in them (Ehmke, 2019). Despite the importance of expressing sadness over the death of a loved one, it is also important for children to understand that life goes on, and that they should continue their daily activities, such as going to school, doing extracurricular activities, and playing (Tarrés, 2023). According to Tarrés (2023), if daily life becomes difficult after a reasonable and prudent time, it is recommended to consult a psychology professional for advice. References Ehmke, R. (2019, febrero 18). Apoyar a los Niños que Están en Duelo. Child Mind Institute. https://childmind.org/es/articulo/ayudar-a-los-ninos-a-afrontar-el-duelo/ Tarrés, S. (2023, septiembre 7). Acompañar a los Niños en el Duelo. Mamá Psicóloga Infantil; Sara Tarrés. https://www.mamapsicologainfantil.com/acompanar-a-los-ninos-en-el-duelo/ Vera Mota, A. (2023, octubre 25). Duelo en la Infancia: ¿Qué Hacer Cuando un Niño ha Perdido a un ser Querido? Centro de Atención Psicológica; Sens Psicología. https://senspsicologia.com/2023/10/25/duelo-infantil/

Funerary rites refer to the ceremonies performed on the occasion of a person’s death (Oslé, 2021). When a family faces a loss, parents worry about the role children should play in the farewell rituals (mortuary, wake, burial, or funeral) and raise various questions: Is it good for the child to see the sick person in the hospital? What effect will it have on the child to see someone about to die? Is it appropriate for children to say goodbye to the person before death? Is it suitable to take the child to the mortuary or burial? Could visiting the mortuary traumatize the child? (Díaz, 2013). These decisions are very difficult to make as they depend on each child's maturity and development, as well as the beliefs and values of each family. Often, according to Díaz (2013), adults are guided by their own feelings and fears about death, but it is important to consider the needs and wishes of the children, which may differ. At What Age Can Children Participate in Funerary Rites? It is considered that children aged 6 years and older can fully participate in any ritual related to death, as they can understand them better than younger children (Díaz, 2013). This participation benefits their development and usually does not have negative effects on them, as long as the context and the personal situation they are experiencing are taken into account (Benito, 2022). For example, if visiting a sick person in a hospital, the child should be informed in advance and in detail about what they will see, what the place is like, how the relative is, etc. (Díaz, 2013). This way, the child will not be surprised or frightened by what they see, and it will help them prepare for the farewell. According to Díaz (2013), explanations given to the child should be clear and simple, adapted to their level of understanding and emotions. How to Prepare Children for Funerary Rites They should be informed of the death as soon as possible to prevent them from finding out from others (Benito, 2022). The place where they are told should be quiet and intimate, where they can express all their emotions and have the necessary time to process the information they have received. Honest and truthful answers should be given to all their questions. The decision to participate in the funerary rites should be made by the child, who should know if they want to attend the mortuary and the funeral. Before that, some aspects should be clarified: what they will see, what the place is like, where it is, how the room with the deceased in a coffin is (if it is open or closed, if the deceased is wearing their usual clothes, if there are flowers, among other things). Also, in accordance with Benito (2022), they should be explained what condolences consist of, telling them that people will approach to show their affection and sorrow for the death of their loved one. The child should be explained the usual emotional reactions, telling them they will see some people crying, being sad, serious, or angry (Benito, 2022). They should know that all these reactions are normal when losing a loved one, as people become sad knowing they will not see that person again. They should be accompanied at all times. If one of the parents cannot do it, close people should make them feel calm and protected. If the child decides not to go to the mortuary, it should be respected and care taken that no family member makes them feel bad for not wanting to participate. According to Benito (2022), farewells are very important, and participating in the rites is a way to honor the deceased, both for adults and children. When attending a funeral with the child, the cemetery should be described to the child and what they will find there. It should also be explained what will happen during the event, if a grave or niche will be observed, and how the burial process is. They should be given the option to pay tribute to the deceased if they wish and clarified what the possible tributes consist of, such as a prayer, some words, the deposit or collection of flowers, among others. Different situations that may occur during the funeral should also be anticipated. Finally, according to Díaz (2023), the child can be invited to collaborate or participate in the tribute if any is planned (Díaz, 2013). Benefits of Involving Children in Farewell Rites The concept of death should be introduced to children so that they normalize and integrate it from an early age (Benito, 2022). Thus, they will feel included and important in difficult times, when reality overwhelms many people (Oslé, 2021). This feeling of belonging will help them develop a healthy grieving process (Oslé, 2021). On the other hand, if they are isolated from the family core, they will realize that something is happening, but they will not receive the necessary explanations to understand it, which will generate a feeling of exclusion (Benito, 2022). The youngest also need to go through the farewell rituals to develop a healthy grief, as these rituals mark the beginning of acceptance of the loss (Benito, 2022). According to Oslé (2021), William Worden, one of the most recognized authors in the field of grief psychology, funerary rites are beneficial because they help meet three needs of children. They Help Acknowledge the Death of the Loved One The death of the loved one becomes evident with funerary rites, which helps children accept it: people say goodbye to those they will no longer see (Oslé, 2021). By burying or cremating the deceased, children who attend ensure that their loved one will not physically reappear. This builds the grieving process: it begins the adaptation to life without the deceased person. This does not mean that children who do not attend the farewell rites will inevitably have a complicated grief. According to Oslé (2021), it simply means that it is generally beneficial to attend them. They Allow Honoring the Life of the Deceased Person The celebration of the loved one’s life is the basis of many of these rites: anecdotes and love are shown towards them (Oslé, 2021). Speeches and readings about their life and achievements are also made. Additionally, the child’s pain is contextualized with the expressions of grief for their death. According to Oslé (2021), attending the rites is a way to honor the loved one who has passed away: being present to say goodbye. They Establish a Support Network The rituals provide support and comfort to children (Oslé, 2021). Although adults fear the pain these rituals may cause them, they find a space where they can express their emotions without being judged, where they see that others feel similar emotions to theirs, and where they receive comfort from friends and family through hugs, letters, messages, and other gestures. Not only is it advisable for children to attend, but also for their friends who wish to accompany them. Moreover, actively participating in the organization and the rites brings them benefits. According to Oslé (2021), they can collaborate in: organizing the funeral, choosing religious readings, flower arrangements, the deceased’s clothing, music, the coffin, the urn for the ashes, the epitaph text, among others. References Benito, N. (2022, enero 10). ¿Llevo a mi Hijo al Tanatorio y al Funeral? Parcesa. https://parcesa.es/llevo-a-mi-hijo-al-tanatorio-y-al-funeral/ Díaz, P. (2013, febrero 14). ¿Puedo Llevar a los Niños a un Funeral o al Tanatorio? Fundación Mario Losantos del Campo. https://www.fundacionmlc.org/lllevar-a-un-nino-a-un-funeral/ Oslé, D. (2021, abril 15). Por qué es Bueno que los Niños Participen en los Ritos Funerarios. Fundación Mario Losantos del Campo. https://www.fundacionmlc.org/por-que-es-bueno-que-los-ninos-participen-en-los-ritos-funerarios/

The phrase "Cogito, ergo sum," coined by French philosopher René Descartes, has established itself as one of the most iconic statements in the history of philosophy, as documented in his work "Discourse on the Method" (Ortiz, 2020). This proposition has not only achieved considerable fame over the years but also marks the beginning of a new era in philosophical thought known as modern rationalism (Ortiz, 2020). However,what is its meaning? Where does this phrase by Descartes come from? Meaning The famous proposition "I think, therefore I am," originally from the French language as "je pense, donc je suis," was later translated into Latin with the form "cogito, ergo sum," which translates more precisely as "I think, therefore, I am" (Ortiz, 2020). This statement transcends mere literal translation and stands as an indisputable truth, constituting the fundamental pillar of knowledge (Ortiz, 2020). In agreement with Sidali (n.d.), the doubt about one's own existence cannot be deceptive, since the mere act of questioning confirms the reality of the thinking mind; indeed, there must be an entity that thinks. Origin and Explanation To understand the meaning of the famous phrase, it is imperative to consider both the historical context and the philosopher's contributions to rationalism and the genesis of modern philosophy (Ortiz, 2020). Descartes, an itinerant thinker in search of new knowledge, strove to establish the foundations of philosophical knowledge, aspiring to overcome the old notions rooted in tradition or in sensory experience. He maintained that reason is the only path to accurate knowledge and, therefore, the senses are not reliable. He postulated that, as in the natural sciences, philosophy could use a method to obtain indisputable certainties. In this way, he tried to structure philosophy as a science, progressing from simple to complex concepts. To achieve this, according to Ortiz (2020), he formulated four essential rules: the first, to seek clarity and evidence; the second, to proceed through division or analysis; the third, to advance through synthesis; and the fourth, to carry out an exhaustive enumeration or review. The Methodical Doubt The first step in the method proposed by Descartes is, at the same time, the starting point to reach his famous statement (Ortiz, 2020). In his Meditations, he reflects on his erroneous beliefs and proposes to address this problem with the hope of finding a way to ensure that he only has true beliefs and even aspires to scientific research to also produce only truths (Miceli, 2018). To achieve this, Descartes uses methodical doubt, a constructive and provisional approach that contrasts with skeptical doubt, which tends to be more destructive and permanent (Galisteo, 2013). Methodological doubt implies not accepting anything as true without clear evidence, avoiding hasty judgments (Ortiz, 2020). In short, in agreement with Ortiz (2020), trusting the senses can be confusing, and methodical doubt helps us avoid falling into mere intuitions. In Search of an Absolute Certainty For Descartes, certainty is defined as clear and secure knowledge of something, without a doubt (Ortiz, 2020). In his search for a solid foundation for science, he focused on indisputable truths, also known as certainties (Galisteo, 2013).Then, he developed a method to discover these certainties, which would serve as the basis for all knowledge (Galisteo,2013). In this context, he questioned the reliability of the senses, reality itself, and the mind, and pointed out that each certainty is subject to methodical doubt (Ortiz, 2020). Thus, in agreement with Ortiz (2020), he asks himself: does anything really exist that is indisputable? Is there any evidence to challenge this procedure? I Think, Therefore I Am René Descartes, without a doubt, accepted an irrefutable principle, a truth that admits no questioning (Ortiz, 2020). His entire philosophy is built on this basis: "I think, therefore I exist" (Galisteo, 2013). This statement has a double meaning. On the one hand, in the midst of doubt, he realizes that he cannot doubt his own doubt; that is, doubting that he is doubting is, in itself, a form of doubt. Therefore, he has the certainty that he is doubting. Now, since doubting implies thinking, he cannot doubt that he is thinking. The existence of thought implies the existence of a thinking being, since thoughts require a support. In this way, he reaches the unequivocal conclusion that, if there is thought, there must also exist something that thinks (Galisteo, 2013). Consequently, in agreement with Ortiz (2020), the proposition "I think, therefore I am" can be interpreted as the starting point from which Descartes attempted to demonstrate the existence of other entities, based on the knowledge of our own existence. References Galisteo, E. (2013). «Pienso, luego existo» | La guía de Filosofía. La Guía. Recuperado 7 de diciembre de 2021, de https://filosofia.laguia2000.com/el-racionalismo/pienso-luego-existo Miceli, C. (2018). “I think, therefore I am”: Descartes on the Foundations of Knowledge. 1000-Word Philosophy: An Introductory Anthology. Recuperado 27 de noviembre de 2021, de https://1000wordphilosophy.com/2018/11/26/descartes-i-think-therefore-i-am/ Ortiz, M. (2020). Pienso, luego existo: significado, origen y explicación de la frase. Cultura Genial. Recuperado 27 de noviembre de 2021, de https://www.culturagenial.com/es/pienso-luego-existo/ Sidali, D. (s.f.). “I Think, Therefore I Am”. Albert Ellis Institute. Recuperado 28 de noviembre de 2021, de https://albertellis.org/2016/06/i-think-therefore-i-am/

In Descartes' work, freedom emerges as a fundamental thesis, although it often receives less attention than other aspects of his philosophy (Christofidou, 2009). Nevertheless, the treatment and importance that Descartes gives to freedom confer a sense of sublimity to his conception and a certain serenity to his conception of man. According to Christofidou (2009), in this vision, the human being is presented as a rational, autonomous, irreducible, and substantially real being. Free Will Free will manifests as an expression of knowledge that emerges from the understanding of innate ideas, which originate from God (Astore, 2016). René Descartes, the French philosopher, corroborated that the existence of free will is based on the inherent capacity of humans to reject or abstain from actions they perceive as contrary to their nature. Therefore, according to Astore (2016), people exercise their free will by choosing not to do what is unpleasant to them, implying that free will can be considered a faculty at the service of the mind, providing the possibility not only to discern the truth but also to forge a unique, autonomous, and genuine identity. Free will is essential for individuals to recognize their uniqueness, as by being aware of their freedom, they can chart a life path aligned with the truth, which derives from a proper understanding of the cause of their freedom, that is, God (Astore, 2016). He also considered free will to be a fully known concept because, without it, people could not form a notion of their own freedom; however, this is not the case, since humans are aware of their freedom and have the capacity to conceive an idea of it, which, according to Astore (2016), is because God has imprinted the necessary clarity in the human mind to understand free will and has allowed people to know the extent of their freedom, since the innate knowledge of the ability to be free is sufficient for life, being a reflection of divine perfection. Therefore, the perfection of God, as the cause of the human mind and thus the faculty of free will, is not imperfect but directed towards what is true and good (Astore, 2016). In this way, it can be inferred that, for Descartes, free will is intrinsically linked to reason, in the sense that an increase in knowledge can make a person more aware of their capacity to be free. Ultimately, according to Astore (2016), this recognition is achieved through the conscious decision to cultivate the mental ability to reaffirm freedom, acting consistently in a way that reflects an ethical will. Freedom and Will For Descartes, the freedom of the will is a palpable reality, characterized by the capacity to generate one's own will (Astore, 2016). This freedom is based on the mind's ability to make autonomous decisions, provided it understands the cause of its existence. For Descartes, as the knowledge about the nature of the principles that can originate certain phenomena, such as moral acts, deepens, the understanding and capacity to make ethical decisions in a decisive and logical manner are strengthened. In short, Descartes advocates the idea that humans can perfect their ability to be free through the use of reason, which, in turn, increases their potential to act freely (Astore, 2016). According to Christofidou (2009), only through this process is it possible to distance oneself from ingrained customs, habits, lack of reflection, and preconceived notions. Freedom and the Degrees of Freedom René Descartes firmly believed that freedom consists in the power of choice, in the ability to determine oneself to want something without a prior decision; thus, for the philosopher, freedom is manifested in the selection of what the understanding identifies as good and true (Rodríguez, 2019). In this sense, according to Christofidou (2009), Descartes highlights two fundamental and connected aspects in his vision of freedom: the difference between indifference and spontaneity, and the idea that there are various degrees of freedom, a notion that distinguishes his perspective from others. The degrees of freedom are not quantitative but qualitative. Freedom can appear in a greater or lesser degree; the highest degree is reached when clear and distinct perceptions of reason generate an inclination of the will towards truth and good, reflecting its essential nature (Christofidou, 2009). It is in this sense that the freedom of the will becomes evident. For Descartes, freedom at its highest degree is not only fundamental for moral law but also for epistemic responsibility. The act of knowing involves making judgments, and for Descartes, making a judgment requires the participation of both understanding and will, as judging goes beyond merely conceiving; it is an action. According to Christofidou (2009), in the case of clear and distinct propositions, the will assents. On the one hand, he considers that the highest level of freedom is revealed in the theoretical judgments of clear and distinct propositions about the truth (Christofidou, 2009). This highlights the uniqueness of his thesis, as his approach indicates that even from a theoretical perspective, there must be reasons for freedom, whose highest degree is found in its expression and its link to clear and distinct propositions, relating not only to what is good but also to what is true. On the other hand, the lowest level of freedom is expressed in the indifference of the will towards dark or confused perceptions and, therefore, not sufficiently clear and distinct. In such a case, the will can affirm or deny, even in the absence of convincing or sufficient reasons to lean towards one option or another (Christofidou, 2009). According to Margot & Leal (2008), Descartes considers indifference as a consequence of ignorance because if a person knows what is good and true, they cannot remain indifferent. Freedom and Self-Mastery The freedom of spontaneity, closely linked to self-mastery, is achieved through intellectual discipline and self-control, emanations of reason in its theoretical and practical facets (Christofidou, 2009). This self-mastery is not achieved by subduing or isolating rebellious passions and instincts, nor by denying them, as doing so would deny the inherent humanity of each individual. According to Christofidou (2009), two categories of instincts are identified: those inherent to the human being, which are reflected in the natural light of reason and its ability to discern the reality of things; and those of animal nature, which drive people towards the preservation and satisfaction of bodily needs. Self-mastery, therefore, is achieved through the moderation and transformation of passions and instincts of the second category into sensibilities more in line with humanity (Christofidou, 2009). This is accomplished by harmonizing these passions and instincts with the truth and the good, revealed by the reflective capacity of reason. In short, according to Margot & Leal (2008), to achieve autonomy and truly be masters of oneself, it is necessary to exercise control over passions so that behavior aligns with the dictates of reason, avoiding interferences from the body and external elements. Through the transformation seen as essential for self-mastery, a person can achieve autonomy (Christofidou, 2009). Autonomy is characterized by the capacity of rational beings to act not out of fear of punishment or in search of reward, but as conscious beings and agents of their own will. According to Christofidou (2009), in the world, everything acts according to laws and principles, but only a self-conscious individual is capable of also acting from the recognition and clear understanding of the principles and values of truth and good, being distinctively motivated by logical and rational reasons. Self-determination The supreme level of freedom demonstrates that autonomous will is not conditioned by chance or physical causal determinism, but is guided by self-determination that originates from rational motivations (Christofidou, 2009). In this context, human decisions are influenced by an amalgamation of factors that include passions, desires, psychological predispositions, as well as the external environment and social manipulations. These elements are relevant to those who hold that, essentially, all motivations to act are based on calculated interests or for those who question the efficacy of reason. Their interpretation of freedom recognizes these influences but relegates them to a state of indifference and the lowest level of freedom. This level manifests in a range that goes from selfishness to error, fault, and sin. Christofidou (2009) points out that indifference and lack of clarity are constant whenever the opportunity to act incorrectly arises. References Astore, R. A. (2016). Examining Free-Will Through Spinoza and Descartes. Inquiries Journal. Recuperado 27 de noviembre de 2021, de http://www.inquiriesjournal.com/articles/1354/examining-free-will-through-spinoza-and-descartes Christofidou, A. (2009). Descartes on Freedom, Truth, and Goodness. Noûs. Recuperado 27 de noviembre de 2021, de http://people.tamu.edu/~sdaniel/682%20Readings/christofidou%20freedom.pdf Margot, J. P., & Leal, Y. (2008). La libertad de pensamiento en la moral cartesiana. Redalyc. Recuperado 27 de noviembre de 2021, de https://www.redalyc.org/pdf/478/47803004.pdf Rodríguez, A. (2019). René Descartes y la Escuela Cartesiana. Universidad Metropolitana. Recuperado 27 de noviembre de 2021, de https://www.unimet.edu.ve/wp-content/uploads/2019/11/Descartes-ARI-pub.pdf

Christian Wolff (1679 - 1754), a German philosopher and mathematician with a rationalist orientation, is recognized for his outstanding contribution to the historical framework of the Enlightenment (Mitjana, 2020). This movement, which encompassed both cultural and intellectual aspects, had a notable presence in countries such as Germany, France, and England. According to Mitjana (2020), the Enlightenment, as a movement, promoted the use and dissemination of knowledge as fundamental tools with the aim of improving the world in all its aspects. Biography Christian Wolff, whose full name is Christian Freiherr von Wolff, is recognized as a German philosopher who was born in Breslau (Silesia, Poland) on January 24, 1679 (Mitjana, 2020). The son of a craftsman, he received his education at the Maria-Magdalena-Gymnasium, which had a Lutheran-humanist orientation. Here, he had the opportunity to learn from notable teachers such as Christian Gryphius, a Baroque poet and playwright, and Caspar Neumann, whom Wolff credits with introducing him to Cartesian philosophy (Hettche & Dyck, 2019). In 1699, he enrolled at the University of Jena, where he pursued a program of studies in theology, physics, and mathematics. Later, according to Hettche & Dyck (2019), in 1702, he moved to Leipzig, where he obtained his Magister degree and completed his Habilitation in 1703 with the thesis titled "Philosophia Practica Universalis, Methodo Mathematica conscripta." A few years later, in 1706, thanks largely to the recommendations of his colleague Gottfried Wilhelm Leibniz, a German philosopher and mathematician, he obtained the chair of mathematics at the University of Halle (Mitjana, 2020). At this university, he served as a professor of mathematics and natural philosophy. His thought generated controversy, particularly one of his works, "Oratio de Sinarum Philosophica Practica" (1721), which dealt with Chinese philosophy, causing a great stir. As a result of this work, many of his colleagues, professors of theology, accused him of being an atheist, and for this reason, he was dismissed two years after the publication of the mentioned work. However, according to Mitjana (2020), Wolff refuted these accusations of atheism with another of his works: "Theologia Naturalis," where he explains the importance of God as a perfect and real being. As a result of these events, he was exiled from Prussia and his works were banned in 1723 (Mitjana, 2020). Fortunately, he found refuge with the Landgrave of Hesse-Kassel and began teaching at the University of Marburg until 1740. That same year, Frederick II of Prussia, also known as Frederick the Great, the third king of Prussia, called him back to Halle, a German city. Four years later, at the University of Halle, he was appointed chancellor, and two years after that, he was granted the title of baron. According to Mitjana (2020), he remained in Halle until his death on April 9, 1754. Work and Thought Christian Wolff's work is notably extensive, with the publication of up to 67 titles, organized into 23 volumes, in the period between 1703 and 1753 (Mitjana, 2020). His works were written both in German and Latin. The most influential figures in the thought of this renowned philosopher were Gottfried Wilhelm Leibniz and René Descartes. Specifically, according to Mitjana (2020), these two thinkers inspired him to create his philosophical method, which had a mathematical orientation. Christian Wolff's thought was rationalist, which means he considered reason as the main source of knowledge, although this does not imply that he was not a believer (Mitjana, 2020). One of his most notable works was "Logic: Rational Thoughts on the Powers of Human Understanding" (1728), which was based on his idea of society and followed the trend of enlightened despotism. In addition to this book, according to Mitjana (2020), some of his most relevant works include "Philosophia Practica Universalis, Mathematica Methodo Conscripta" (1703), "Dissertationes pro Loco" (1703), "Aërometriae Elementa, in Quibus Aliquot Aëris Vires ac Propietates Iuxta Methodum Geometrarum Demonstratur" (1708), "Elementa Matheseos Universae, IV Vols" (1713-1715), "Lexicon Mathematicum" (1716), "Cosmologia Generalis" (1731), "Psychologia Empirica" (1732), and "Psychologia Rationalis" (1734). Psychology It is understood that the soul, being a simple substance, is part of the world and thus is implicated in the treatment of cosmology (Hettche & Dyck, 2019). However, this does not exhaust what can be known about it, which leads Wolff to treat it as a separate topic from metaphysics. Indeed, Wolff’s psychology constitutes one of his most influential and historically significant innovations. In general, according to Hettche & Dyck (2019), insofar as Wolff seeks to offer a scientific account of the human soul specifically, and indeed with a focus on its cognitive and conative functions, his psychology represents a significant, and clearly modern, deviation from both the treatment of the soul in the context of a generic science of living beings, still prevalent among Aristotelian natural philosophers in seventeenth-century Germany, and the metaphysical treatment of the soul in the context of a pneumatology, or doctrine of the finite and infinite spirit. Moreover, Wolff’s main and most well-known innovation in psychology consists of his clear separation between two distinct investigations of the soul: the first based on the observation of one’s own mind, identified as empirical psychology, and the second which seeks to use reasoning to discover truths about the soul that are not easily revealed by experience, identified as rational psychology (Hettche & Dyck, 2019). Wolff’s distinction between empirical and rational psychology proved to be enormously consequential, but no less important (if less well-attended to) is the fact that these disciplines remain intrinsically connected. For Wolff, in correspondence with Hettche & Dyck (2019), the observations cataloged in the course of empirical psychology serve as principles for the inferences of rational psychology, and the resulting findings from rational psychology serve to guide empirical observation in search of confirmation. Empirical psychology raises a distinctly early modern problem about what can be experienced of the relationship between the soul and the body (Hettche & Dyck, 2019). Wolff notes that people experience some states of the soul that depend on the body (such as sensations), and some states of the body depend on the soul (such as voluntary actions), in such a way that the body and soul are put into a union or commerce. However, in accordance with Hettche & Dyck (2019), Wolff holds that one does not experience the causal power through which the soul influences the body and vice versa, but rather that experience only confirms the general agreement between the states of each without penetrating their ground. Rational psychology also raises the question of what best explains the agreement between the states of the soul and the body (Hettche & Dyck, 2019). In correspondence with Hettche & Dyck (2019), Wolff considers three possible systems that attempt to explain this agreement: the system of physical influx, according to which one substance produces a state in another directly through its own activity; the (Cartesian) system of occasional causes, according to which God modifies one substance on the occasion of something arising in another; and the (Leibnizian) system of pre-established harmony, where the agreement between states of substances is the result of God’s initial activity in creating this world of substances. Wolff provides a series of familiar objections to the first two systems, arguing, for example, that physical influx conflicts with the laws of physics, and that occasionalism relies on what amounts to a perpetual miracle, while defending pre-established harmony from similar criticisms (Hettche & Dyck, 2019). Even so, according to Hettche & Dyck (2019), since no possible explanation can be confirmed or rejected by experience, each of these systems amounts to a mere hypothesis, and Wolff’s conclusion is only that pre-established harmony is a more probable hypothesis than the other two, though he believes there is nothing significant in resolving this contentious issue. The final topic of interest is the most speculative, namely, the demonstration of the soul’s immortality and its state after death (Hettche & Dyck, 2019). It is assumed that immortality presupposes the incorruptibility of the soul, meaning that the soul does not naturally die after the body’s death. However, unlike the Cartesians, Wolff does not believe this is all that is involved. According to Hettche & Dyck (2019), Wolff mentions that any immortality worth having (and that would be consistent with the Scriptures) must also extend to the preservation of the soul’s capacity for distinct perception (i.e., its spirituality) and its awareness that it is the same being in the afterlife as it was before the body’s death (or its personality). The incorruptibility of the soul is derived directly from the fact that it is simple, and therefore incapable of decomposition (Hettche & Dyck, 2019). Inductive reasons are offered in favor of the soul’s preservation of its spirituality (i.e., that the clarity of the soul’s perceptions improves with every “great change”). The soul’s preservation of its personality is demonstrated by reference to the law of imagination, according to which its later perceptions will lead it to remember the earlier ones. In accordance with Hettche & Dyck (2019), the relative merits of these arguments were the subject of intense debate, with particularly notable contributions from Wolff’s colleague in Halle, G. F. Meier, and later from Mendelssohn, and finally Kant. Other Contributions Regarding Wolff's contributions, the development of metaphysical teleologism stands out, a branch of metaphysics that deals with the purposes of objects or beings (Mitjana, 2020). Through this approach, he explained the universal connection and harmony of being as ends established by God. Another significant contribution was the systematization and revitalization of scholasticism, a medieval philosophical and theological current that uses elements of classical philosophy to understand Christianity. In addition, he developed his own philosophical method, which was deductive and rationalist. Through this method, he maintained that all truths of philosophy were reduced to the laws of formal logic. Finally, it is important to recall the extensive dissemination he carried out of sciences considered more "distant" from philosophy, such as mathematics, physics, chemistry, and botany. According to Mitjana (2020), this dissemination demonstrates the versatility and breadth of Wolff's interests and knowledge. References Hettche, M., & Dyck, C. (2019). Christian Wolff. Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/cgi-bin/encyclopedia/archinfo.cgi?entry=wolff-christian Mitjana, L. R. (2020, febrero 25). Christian Wolff: biografía de este filósofo alemán. pymOrganization. https://psicologiaymente.com/biografias/christian-wolff

Does learning occur through experimentation with the environment or through reflection and introspection? This question reflects the main topic that, during the Enlightenment, served as a key differentiator to distinguish between the major types of philosophers: the rationalists, who argued that knowledge is derived through reason, and the empiricists, who believed that the intellect develops through experience (Torres, 2017). Gottfried Wilhelm Leibniz (1646 - 1716), however, did not fit into either of these two categories. Torres (2017) mentions that, despite more than 300 years having passed since his death, his ideas can still serve today to approximately and intuitively understand how reality is experienced. The Monads Leibniz acknowledges that although the unraveling of notions could serve to discover the truth, in practice this proves to be an impossible task, as human rationality does not possess sufficient power to process such a magnitude of information (Torres, 2017). However, this does not imply that every element of the universe is devoid of fragments of the truth. In fact, according to Leibniz, the universe is composed of units called monads, which are metaphysical entities that harbor representations of everything that exists. According to Torres (2017), being true and encompassing the past, present, and future, a monad is identical to any other, as all coincide in containing the truth. Ideas and Knowledge Leibniz's epistemology begins with the distinction between clear and obscure ideas (Glowienka, n.d.). An idea is clear when it allows the recognition of the represented thing, and obscure when it does not. For example, if someone has seen a gerbil, they can have an idea of what a gerbil is. However, if the next time they encounter a small rodent they cannot determine whether it is a gerbil or a hamster, then they only have an obscure idea of "gerbil." Leibniz classifies clear ideas into two categories: confused and distinct. A clear idea is also distinct when all the marks or criteria that distinguish that idea from others can be cataloged. An animal physiologist can differentiate and enumerate the common characteristics of all rodents and the unique ones of gerbils. According to Glowienka (n.d.), a child with a pet gerbil might not be able to do this and thus would have a clear but confused idea. Leibniz further classifies clear and distinct ideas as adequate or inadequate (Glowienka, n.d.). If one has an adequate idea, they have a clear and distinct understanding not only of the idea in question but also of all its parts and components. One has a clear and distinct knowledge "to the end" of the primitive concepts that compose the idea. Leibniz admits that he is unsure if any human possesses an adequate idea, but considers that arithmetic knowledge almost approaches adequacy. According to Glowienka (n.d.), in all other cases where exhaustive analysis to primitive concepts cannot be carried out, one has clear, distinct, but inadequate ideas. At its highest reaches, Leibniz mentions that knowledge is not only adequate but also intuitive (Glowienka, n.d.). Intuitive knowledge is adequate and non-discursive. This means that a person knows clearly and precisely all the components of an idea and understands them simultaneously. In correspondence with Glowienka (n.d.), in the case of all adequate knowledge, intuitive knowledge seems more appropriate for divine knowers than for humans, since the latter cannot think of all the components of a complex concept simultaneously. A consequence of his taxonomy of knowledge is that it provides a means to explain sensory perception (Glowienka, n.d.). Given his idealism, everything that exists in the world are monads and their mental states. Bodies are phenomena and thus are not sources of knowledge. So, what is sensory perception? Is there any difference between sensation and intellect if all ideas arise from the concept of a monad itself, without interaction between monads? Leibniz points out that what is experienced as sensory perceptions are confused ideas. Even if they are clear, sensory perceptions are necessarily confused. Glowienka (n.d.) mentions that although these perceptions arise spontaneously, they express the harmony between a given monad and all others; thus, it is impossible to enumerate all the factors that contribute to the perception of any given sense, most of which fall below the threshold of consciousness. With the category of clear and confused ideas, Leibniz can meaningfully preserve the distinction between sensation and intellection without compromising the basic principles of his idealism (Glowienka, n.d.). His approach to ideas and knowledge distinguishes him in some key aspects from his 17th-century rationalist peers. The division between distinction and adequacy leads him to differentiate between nominal and real definitions. Nominal definitions include distinct knowledge; they sufficiently identify the defining marks of a concept. However, in correspondence with Glowienka (n.d.), they do not guarantee that the concept is possible. It might be that a concept is internally inconsistent, a fact that would be revealed if one had adequate knowledge of all its parts. The Idea of Notions Leibniz was convinced that every component of reality, whether it be an individual, a landscape, or an object, is linked to a concept known as a "notion" (Torres, 2017). A "notion" is understood to be everything that can be asserted as true about the component of reality to which it is associated. To illustrate this concept, Torres (2017) mentions that the color of a raven is black and that the hind limbs of this animal lack feathers, among other aspects. Everything is Connected Leibniz, a thinker deeply influenced by rationalism, held the belief that language should aspire to emulate mathematics, a hermetic system of symbols (Torres, 2017). From his perspective, if something is true, it must be intrinsically connected with the truths of other elements of reality, which are described by their respective notions, at least from a theoretical standpoint. In this way, if the relationships between different notions are discovered, a comprehensive knowledge of reality will be obtained. Essentially, a notion not only contains truths about the element it is associated with, but it also provides information about all the elements it relates to. As an illustration of this concept, Torres (2017) mentions that if a being has feathers covering the fingers of its lower limbs, it cannot be a crow. Innate Ideas Leibniz is typically placed in the camp of rationalists, in opposition to empiricists like John Locke (Look, 2020). Although there are arguments to question this distinction, Leibniz fits the description in two aspects: he is a rationalist to the extent that he adheres to the Principle of Sufficient Reason, and he is a rationalist to the extent that he accepts innate ideas and rejects the notion that the mind is a tabula rasa. Regarding Leibniz's classical loyalties, it is interesting to note that, in the realm of metaphysics, he often expressed his philosophy in Aristotelian and scholastic terms, but in the realm of epistemology, he was quite openly a Platonist, at least in terms of the existence of innate ideas. In fact, according to Look (2020), in the initial passages of his "New Essays on Human Understanding," his commentary on a book about Locke's "Essay on Human Understanding," Leibniz aligns with Plato on the fundamental issue of the origin of ideas. Leibniz has a series of direct metaphysical reasons for rejecting the idea that the mind could be a tabula rasa (Look, 2020). First, since there can be no genuine causal interaction between substances, there could be no way for all ideas to come from experience; in fact, no idea could, strictly speaking, come from experience. But secondly, Leibniz believes that the view that minds are blank slates at birth violates the Principle of the Identity of Indiscernibles. In short, the Principle of the Identity of Indiscernibles works against qualitatively identical physical atoms and against qualitatively identical souls (because they are blank). But how could experience and the senses provide the ideas? Does the soul have windows? Is it similar to writing tablets or wax? Clearly, according to Look (2020), those who have this view of the soul are treating it as fundamentally corporeal. Locke was famous for entertaining the possibility of "thinking matter," and Leibniz found such a thesis abominable (Look, 2020). Throughout his career, Leibniz expressed no doubt that the mind or soul is essentially immaterial, and Locke's skepticism about the nature of substance fundamentally disagrees with Leibniz's deepest philosophical commitments. However, the consequence of this was that Leibniz sought to undermine Locke's position regarding the origin and nature of ideas. According to Look (2020), Leibniz has an argument for the immateriality of the mind or against its mechanism, which referred to the nature of thought and ideas. This is his famous metaphor of a mill, which appears both in the "New Essays" and in the "Monadology" (Look, 2020). Perceptions could not be explained in mechanical or materialistic terms (Look, 2020). Even if a machine were created to which thought and the presence of perceptions were attributed, inspection of the interior of this machine would not reveal the experience of thoughts or perceptions, but only the movements of various parts. However, according to Look (2020), although Leibniz accepted the common way of speaking, that is, as if the senses were causally responsible for some ideas, he had arguments against the empirical claim that the senses were the origin of all ideas. According to Leibniz, while the empirical position could explain the source of contingent truths, it could not explain the origin and character of necessary truths (Look, 2020). Because the senses could never reach the universality of any necessary truth; they could, at best, provide the means to make a relatively strong induction. Rather, it was understanding itself that was the source of such truths and that guaranteed their necessity. Look (2020) mentions that, although people are not aware of all ideas, a fact demonstrated by the function and role of memory, certain ideas or truths were in the mind as dispositions or tendencies. This was what was understood by an innate idea or an innate truth (Look, 2020). In fact, Leibniz believed that the mind had a "special affinity" for necessary truths. On this topic, Leibniz used a distinctive metaphor: a piece of marble had veins that indicated or were arranged to indicate shapes that a skilled sculptor could discover and exploit. Similarly, according to Look (2020), there was a disposition, an aptitude, a preformation, that determined our soul and made necessary truths derivable from it. Truths of Reason and Truths of Fact The existence of monads does not change the fact that individuals are not capable of assimilating their presence, and in practice, they often act as if nothing is certain (Torres, 2017). Although humans can access simple truths through mathematics, this does not allow them to make the leap to a complete understanding of what is true and authentic; they simply remain at that point, with that small portion of reality that establishes that the sum of one and one equals two. That is why, according to Torres (2017), Leibniz makes a distinction between truths of reason and truths of fact. In the case of a truth of reasoning, its reason or explanation can be discovered through the analysis of notions or concepts, resolving into simpler ideas and simpler truths until reaching the primitives (Look, 2020). Ultimately, all truths of reasoning will resolve into primitives or identities, and the Principle of Contradiction is therefore operative. In the case of a truth of fact, on the other hand, its reason cannot be discovered through a finite process of analysis or resolution of notions. However, there must be a reason why some particular fact is so and not otherwise, and, according to Leibniz, this reason is found outside the series of contingent things (Look, 2020). According to Torres (2017), the only entity that has total access to the truths of reason would be the Christian God. Apperception, Memory, and Reason The hierarchy of monads has a corollary in its epistemology (Look, 2020). Monads are more or less perfect depending on the clarity of their perceptions, and one monad is dominant over another when it contains reasons for what happens in the other. However, some monads can rise to the level of souls when, for example, they experience sensations, that is, when their perceptions are very distinct and accompanied by memory. Additionally, some souls are in a position to engage in apperception, that is, to reflect on their internal states or perceptions. According to Look (2020), it is important to distinguish between perception, which is the internal state of the monad representing external things, and apperception, which is the consciousness or reflective knowledge of this internal state, something that does not occur to all souls, nor at all times to a given soul. The point Leibniz wants to make is clearly anti-Cartesian: it is not the case that animals lack souls and are mere machines (Look, 2020). According to Look (2020), there is a continuum from God, angels, and human beings through animals to stones and the opaque monads underlying the dirt and grime of the world; and this continuum should be understood not only in terms of the comparative clarity of the mind's perceptions but also in terms of the types of mental activity possible for a particular being. What makes human beings and higher minds special is the ability, through perception, to formulate a conception of the self (Look, 2020). Indeed, Leibniz suggests that rationality itself derives from the capacity for reflection. Rationality, however, is actually just the ability to form indubitable connections of ideas and follow them to their infallible consequences. In other words, according to Look (2020), animals and most human beings are purely empirical; a rational person, however, is one who can engage in genuine a priori reasoning, moving from the knowledge of a true cause through deduction to necessary effects. Small Perceptions One of the theses of his philosophy is that each substance expresses the entire universe (Look, 2020). In order to incorporate this thesis into his general epistemology and philosophy of mind, he develops his account of "small perceptions" or "tiny perceptions." At every moment, there are countless perceptions in people, unaccompanied by consciousness or reflection; that is, alterations in the soul itself, of which they are not aware because these impressions are very small and quite numerous, or too invariant, so they are not distinctive enough on their own. In other words, according to Look (2020), everything that takes place in the universe is indeed expressed by every finite mind, but the infinite perceptions present in the mind, from the flight of the butterfly in the Amazon jungle to the waddling of the penguin in Antarctica, are often tiny or too indistinct to overcome, for example, the appearance of this computer screen or the sensation of hunger. The infinity of small perceptions is, then, simply epistemological white noise (Look, 2020). The simplicity and unity of the mind still allow for the multiplicity of perceptions and appetites. However, this multiplicity should not only be interpreted as diachronic, but also as synchronic; that is, the mind, despite its simplicity and unity, contains within it at any given moment an infinity of different small perceptions. An individual in a state of wakefulness is aware of particular perceptions, but never of all. In correspondence with Look (2020), the mind is always active, since there are always perceptions present in it, even if those perceptions are tiny and do not rise to a level where people are conscious of them. References Glowienka, E. W. (s. f.). Gottfried Wilhelm Leibniz (1646-1716). Internet Encyclopedia of Philosofy. Recuperado 31 de marzo de 2024, de https://iep.utm.edu/leib-ove/ Look, B.C. (2020). Gottfried Wilhelm Leibniz. En E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Spring 2020). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/spr2020/entries/leibniz/ Torres, A. (2017, julio 18). La Teoría Epistemológica de Gottfried Leibniz. Psicología y Mente. https://psicologiaymente.com/psicologia/teoria-epistemologica-gottfried-leibniz

Gottfried Wilhelm Leibniz (1646 - 1716), the eminent philosopher, physicist, and mathematician, played a crucial role in advancing modern science (Guzmán Martínez, 2018). His legacy endures as one of the pillars of the rationalist tradition of modernity. According to Guzmán Martínez (2018), Leibniz, with his profound knowledge in mathematics and physics, not only explored the mysteries of nature but also the intricate phenomena affecting humanity. Biography Gottfried Wilhelm Leibniz, born on July 1, 1646, in Leipzig, Germany, grew up in a devout Lutheran family during the final years of the Thirty Years' War, which had left the country in ruins (Guzmán Martínez, 2018). His early education at the Nicolai School was complemented by self-directed learning in his father's personal library, inherited from a professor of moral philosophy at the University of Leipzig. According to Guzmán Martínez (2018), by the age of 12, he was already proficient in Latin and studying Greek. In Easter 1661, he enrolled at the University of Leipzig as a law student, where he immersed himself in the thought of revolutionary scientists and philosophers like Galileo, Francis Bacon, Thomas Hobbes, and René Descartes (Belaval & Look, 2024). He aspired to reconcile these modern thinkers with the Aristotelian scholastics. His bachelor's thesis, "De Principio Individui," published in May 1663, was partly inspired by Lutheran nominalism (the theory that universals have no reality but are mere names) and emphasized the existential value of the individual, which should not be explained solely by matter or form but by its entire being. According to Belaval & Look (2024), this concept laid the foundation for his future theory of the "monad." In 1666, he wrote "De Arte Combinatoria," in which he formulated a model that is the theoretical ancestor of some modern computers: all reasoning, any discovery, whether verbal or not, is reducible to an ordered combination of elements, such as numbers, words, sounds, or colors (Belaval & Look, 2024). After completing his legal studies in 1666, he applied for a doctorate in law but was rejected due to his age and subsequently left his hometown forever. According to Belaval & Look (2024), in Altdorf, the university town of the free city of Nuremberg, his dissertation "De Casibus Perplexis" immediately earned him the title of doctor as well as an immediate offer of a professorship, which he declined. During his stay in Nuremberg, he met Johann Christian Freiherr von Boyneburg, one of the most distinguished German statesmen of the time (Belaval & Look, 2024). Boyneburg took him into his service and introduced him to the court of the Elector Prince, Archbishop of Mainz, Johann Philipp von Schönborn, where he dealt with legal and political matters. King Louis XIV of France posed an increasing threat to the Holy Roman Empire. To divert the king's interests elsewhere, the archbishop hoped to propose an expedition to Egypt using religion as a pretext and expressing the hope that the project would promote church reunion. According to Belaval & Look (2024), Leibniz, in view of this reunion, worked on the Demonstrationes Catholicae. His research led him to locate the soul in a point, a new step towards the monad, and to develop the principle of sufficient reason (nothing exists or occurs without a reason) (Belaval & Look, 2024). His meditations on the difficult theory of the point were related to problems encountered in optics, space, and motion; they were published in 1671 under the general title "Hypothesis Physica Nova." According to Belaval & Look (2024), he asserted that motion depends, as in Johannes Kepler's theory, on the action of a spirit (God). In 1672, the Elector Prince sent the young jurist on a mission to Paris, where he arrived in late March (Belaval & Look, 2024). In September, he met with Antoine Arnauld, a Jansenist theologian known for his writings against the Jesuits (Jansenism was an unorthodox Roman Catholic movement that engendered a rigorous form of morality). He sought Arnauld's help for the church reunion. Soon he was left without protectors due to the deaths of Freiherr von Boyneburg in December 1672 and the Elector Prince in February 1673; however, he was now free to continue his scientific studies. In search of financial support, he built a calculating machine and presented it to the Royal Society during his first trip to London in 1673. By the end of 1675, he had laid the foundations of integral and differential calculus. Belaval & Look (2024) mention that with this discovery, he ceased to consider time and space as substances, another step closer to monadology. In his exploration of the concepts of extension and motion, he concluded that they contained an imaginary element (Belaval & Look, 2024). Although the laws of motion could not be discovered by studying their nature, he argued that extension and motion could provide a means to explain and predict phenomena. Contrary to Descartes, he posited that this world could be a well-ordered dream. If visible motion depended on the imaginary element present in the concept of extension, it could no longer be defined solely by local motion; it had to be the result of a force. By criticizing the Cartesian formulation of the laws of motion, he became the founder of a new formulation: dynamics, which replaced kinetic energy with the conservation of motion. Additionally, according to Belaval & Look (2024), he believed that light followed the path of least resistance and could demonstrate the order of nature towards an objective or final cause. Despite not having a revenue-generating position, in October 1676, he accepted employment with Duke John Frederick of Brunswick-Lüneburg, who had converted from Lutheranism to Catholicism (Belaval & Look, 2024). Appointed librarian from February 1677, he applied for the position of councilor, which was finally granted to him in 1678. In his quest for utility, he proposed that education become more practical and advocated for the creation of academies. Additionally, he worked on various mechanical devices, such as hydraulic presses, windmills, lamps, submarines, and clocks. According to Belaval & Look (2024), he devised a windmill-driven water pump, improving the exploitation of mines in the Harz Mountains, where he frequently worked as an engineer from 1680 to 1685. He is considered one of the creators of geology based on his observations, including the hypothesis that the Earth initially melted (Belaval & Look, 2024). In March 1679, he perfected the binary numbering system and proposed the basis for analysis situs, now known as general topology. At the same time, he worked on his dynamics and philosophy, which became increasingly anti-Cartesian. Upon the death of John Frederick on January 7, 1680, his brother Ernest Augustus I succeeded him. At that time, France became increasingly intolerant, with harsh persecutions of Protestants between 1680 and 1682, paving the way for the revocation of the Edict of Nantes on October 18, 1685. Additionally, according to Belaval & Look (2024), threats on the borders increased, as in 1681, despite prevailing peace, Louis XIV took Strasbourg and claimed 10 cities in Alsace. He played a crucial role as a patriot, serving both his prince and the empire (Belaval & Look, 2024). He suggested means to his prince to increase flax production and proposed a process for desalinating water. Additionally, he recommended the classification of archives and wrote a critical pamphlet against Louis XIV in both French and Latin. During this period, he continued to refine his metaphysical system, investigating the notion of a universal cause of all being. His goal was to reach a starting point that would reduce reasoning to an algebra of thought. In the mathematical field, he explored the ratio between a circle and a circumscribed square in 1681 and analyzed the resistance of solids in 1684. According to Belaval & Look (2024), in 1686, he published "Nova Methodus pro Maximis et Minimis," an exposition of his differential calculus. His notable "Meditationes de Cognitione, Veritate et Ideis" defined his theory of knowledge (Belaval & Look, 2024). He argued that the ideas of God and humans are analogously related and that there is an identity between divine and human logic. Similarly, according to Belaval & Look (2024), he criticized the Cartesian version of the ontological argument for the existence of God and presented his own version. In February 1686, he wrote the "Discours de Métaphysique," where he formulated his principle of the identity of indiscernibles (Belaval & Look, 2024). In the March publication of Acta, he revealed his dynamics in a piece titled "Brevis Demonstratio Erroris Memorabilis Cartesii et Aliorum Circa Legem Naturae." Additionally, in an unpublished text written in 1686, he generalized propositions stating that in every true proposition, whether necessary or contingent, the predicate is contained in the notion of the subject. This idea seemed to imply determinism that could undermine human freedom, just like his conception of monads, the individual soul-like substances that compose the universe, as they in some sense "contain" all their pasts and futures. According to Belaval & Look (2024), his proposed solution was to argue that although each monad already contains all its future actions, God can create those actions as "free." In 1685, he was appointed historian of the House of Brunswick, and on this occasion, he was granted the title of Hofrat (Belaval & Look, 2024). His work was to demonstrate, through genealogy, that the princely house had its origins in the House of Este, an Italian princely family, which would allow Hanover to claim a ninth electorate. In search of these documents, he began to travel in November 1687, spending two years in Italy. His main stops were Rome, Florence, Modena, and Venice. On June 3, 1691, he arrived in Vienna, where he tried in vain to obtain a position from the emperor. Upon his return to Hanover, he was not well received. Meanwhile, Leibniz's calculus was attacked by Michel Rolle in 1691 and Jacob Bernoulli in 1692. According to Belaval & Look (2024), in his reply, he generalized the notion of the differential by introducing the difference as a constant ratio. In 1694, in his "Specimen Dynamicum," he completed his system of dynamics, which he compared to the theory of the conservation of force and Newton's theory of gravitational attraction (Belaval & Look, 2024). Furthermore, in 1695, he published "Système Nouveau de la Nature et de la Communication des Substances." In his "Système Nouveau," he developed the concept of the monad, with a hierarchy of levels, from the basic level of perception (subconscious perception) to the higher levels of apperception (conscious perception) (Belaval & Look, 2024). According to Belaval & Look (2024), his universal harmony principle explained how every monad mirrors the entire universe from its unique perspective. Consequently, in 1698, he published his "Tentamen Anagogicum" in the Acta Eruditorum, which summarized his cosmological, physical, and metaphysical theories. During this period, he met Sophia Charlotte, Queen of Prussia, who had just married Frederick I, King of Prussia. From then on, he became one of her confidants (Belaval & Look, 2024). He helped her set up the Berlin Academy of Sciences and was its first president. However, the Hanoverian court was not happy with this situation and criticized his correspondence with the Princess Palatine, his investigation of German law, and his discussions on the reunification of the Church. Leibniz remained faithful to Sophia Charlotte, who was fascinated by philosophy and whom he made read the "Theodicy." She died suddenly in 1705, a blow from which he never fully recovered. Meanwhile, the controversy over the invention of calculus escalated into a dispute between Germany and England. In 1713, the Royal Society took a stand for Newton and declared Leibniz guilty of plagiarism. Leibniz vehemently denied this accusation (Belaval & Look, 2024). His health began to fail in 1714, but he continued to work on his philosophical and scientific projects until his death on November 14, 1716 (Belaval & Look, 2024). Leibniz's passing marked the end of a prolific and varied career that spanned multiple disciplines, leaving a lasting legacy in mathematics, philosophy, and science. Contributions to Philosophy and Science Infinitesimal Calculus Gottfried Wilhelm Leibniz, along with Isaac Newton, is recognized as one of the founders of calculus (Guzmán Martínez, 2018). It is reported that the first use of integral calculus appears in his notebooks from 1675. Leibniz used this calculus to find the area under the function y = x. Additionally, he introduced important notations in the field of calculus, such as the integral sign, an elongated "S" from the Latin "sum," and the "d" from the Latin "differentia," used for differential calculations. These contributions gave rise to Leibniz's Rule, specifically the product rule in differential calculus. He also contributed to the definition of mathematical entities known as "infinitesimals" and defined their algebraic properties, although these definitions presented many paradoxes at the time. However, according to Guzmán Martínez (2018), these definitions were reviewed and reformulated from the 19th century onwards, with the development of modern calculus. Foundations for Epistemological and Modal Logic Gottfried Wilhelm Leibniz, true to his mathematical training, defended the idea that the complexity of human reasoning could be translated into the language of calculations (Guzmán Martínez, 2018). Once understood, these calculations could be the solution to resolving differences of opinion and arguments. For this reason, he is recognized as the most significant logician of his time, at least since Aristotle. Among other contributions, he described the properties and method of linguistic resources such as conjunction, disjunction, negation, set, inclusion, identity, and the empty set, all of which are useful for understanding and making valid arguments and distinguishing them from invalid ones. According to Guzmán Martínez (2018), these contributions constitute one of the main foundations for the development of epistemic logic and also modal logic. Philosophy of Mind and Body In 1695, he published his perspective on the connection between mind and body (Cartwright, 2024). He called his theory the "new system of pre-established harmony." He argued that, although there is no physical connection between the mind and the body, the physical world was created by God in such a way that there is always a link between mental and physical events (experiences), as the mind can dictate an action of the body and vice versa. For Leibniz, "monads," a term derived from the Greek word for "unit," are the ultimate entities of reality. These simple substances combine to produce the world. Monads are the basic, individually isolated elements of reality that are unaffected by each other and are indivisible. According to Cartwright (2024), each monad is complete in itself and contains all the traces of the things that will happen to it. This was a bold and novel theory, but one that proved difficult to fully explain (Cartwright, 2024). Like many other philosophers, Gottfried Wilhelm Leibniz tried to clarify his theory using analogies. He suggested that the body and mind are like two clocks that work independently but are also synchronized. There is a kind of pre-established harmony between these two "clocks." The cause that built the clocks/musicians/monads is God, and He knows everything that is planned for each monad. God is, in fact, the supreme monad and the only one that has a relationship with other monads; otherwise, monads never interconnect with each other. According to Cartwright (2024), this is a fundamental cause upon which all other thoughts of Leibniz's philosophy are built. The Principle of Individuation In his thesis "Disputatio Metaphysica de Principio Individui," which he wrote in the 1660s, he defends the existence of an individual value that constitutes a whole in itself but can be differentiated from the set (Guzmán Martínez, 2018). This thesis represents the first approach to the German theory of monads. By analogy with physics, he argued that monads in the mental realm are what atoms are in the physical realm. They are considered the ultimate elements of the universe and what gives substantial form to being. Among their properties are: they are eternal, do not decompose into simpler particles, are divisible, active, and subject to their own laws. Additionally, according to Guzmán Martínez (2018), they are independent of each other and function as an individual representation of the universe in itself. Referencias Belaval, Y., & Look, B. C. (2024). Gottfried Wilhelm Leibniz. En Encyclopedia Britannica. https://www.britannica.com/biography/Gottfried-Wilhelm-Leibniz Cartwright, M. (2024). Gottfried Wilhelm Leibniz. World History Encyclopedia. https://www.worldhistory.org/Gottfried_Wilhelm_Leibniz/ Guzmán Martínez, G. (2018, octubre 22). Gottfried Leibniz: Biografía de Este Filósofo y Matemático. Psicología y Mente. https://psicologiaymente.com/biografias/gottfried-leibniz Look, B.C. (2020). Gottfried Wilhelm Leibniz. En E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Spring 2020). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/spr2020/entries/leibniz/

It's fascinating to consider how certain individuals have managed to significantly alter the course of history (Sánchez Amador, 2020). A prominent example is Isaac Newton, a polymath who dedicated his life to physics, theology, research, alchemy, and mathematical calculus. While all humans are essential to society in one way or another, there are individuals who have transformed culture and the perception of the world. For a significant number of scientists, Isaac Newton's magnum opus is considered the most relevant scientific publication in history, which is a weighty assertion. Therefore, according to Sánchez Amador (2020), for any reader with a profound interest in scientific knowledge, approaching the figure of Isaac Newton and his contributions to the world of research is fundamental. Biography Isaac Newton (1643 - 1727) was born on January 4, 1643, in Grantham, a town located in Lincolnshire, East Midlands, England, where he spent his early years (Sánchez Amador, 2020). His entrance into the world was marked by adverse circumstances, as his father passed away three months before his birth, and his mother had a premature birth (Sánchez, 2019). Despite being born with very low weight and in a weak state of health, he managed to survive against all odds and was baptized with the name of his father, Isaac. His mother remarried a man named Barnabas Smith, who did not wish to take care of stepchildren, so he was sent to live with Smith's parents, whom he called "grandparents" although they were not really related. According to Sánchez (2019), his relationship with them was very unfortunate, and years later, he would include the desire to burn them alive on a list of his sins. At the age of ten, after the death of his stepfather, he returned to live with his mother and two new step-siblings (Sánchez, 2019). At the age of twelve, he entered a local school where, apparently, he preferred to play with girls and make ingenious toys for them, a precursor to the skill he would later demonstrate in building devices as complex as a refracting telescope (Ordóñez, 2016). During those years, he learned Latin, mathematics, and delved into the study of the Bible (Sánchez, 2019). He was a weak and solitary child who did not excel in class, so he was often relegated to the back row. It is known that he had a stutter, probably throughout his life, and was also sickly. He did not interact much with his peers, and when he did, it was usually to play practical jokes on them or somehow aggress them. However, according to Sánchez (2019), after a fight with a classmate in which he managed to defeat and publicly humiliate him, he decided to become more studious. He spent a lot of time locked in his room, where he began to build mechanical objects, models, and various devices (Sánchez, 2019). He showed great interest in all areas of knowledge and studied a lot. While still very young, he met Catherine Storer, the only woman he possibly had a romance with in his life. He made dollhouses for her as gifts. However, according to Sánchez (2019), the relationship did not transcend, and in fact, it is known that he died a virgin. At the age of 18, he entered the University of Cambridge (Sánchez, 2019). His education took place during a period when the scientific revolution was in full swing across Europe, linked to authors such as Kepler, Galileo, Descartes, Borelli, Hobbes, Gassendi, Hooke, and Boyle, whose works he studied carefully (Ordóñez, 2016). Although he was essentially self - taught, he also found several teachers who expanded his knowledge (Sánchez, 2019). He soon established correspondence with the Royal Society of Sciences, which showed interest in his discoveries and devices. According to Sánchez (2019), it was at this time that the first scientific debates arose, which Newton maintained throughout his life. In 1665, during the productive years of the plague, the University of Cambridge closed due to the disease, and Newton had to return home (BBC News Mundo, 2015). This period turned out to be the most productive of his life. He had always believed that to attain true knowledge, it was necessary to observe more than to read books. For example, instead of relying on texts about optics, he experimented by inserting a blunt needle into his eye to see what effect it had. During this time, he laid the groundwork for his calculus theories and the laws of motion that would later make him famous. However, according to BBC News Mundo (2015), due to his reserved nature, he kept his ideas to himself. In 1671, he continued experimenting in his laboratory, and that combination of theory and practice resulted in many types of discoveries (BBC News Mundo, 2015). His theory of optics led him to reconsider the design of the telescope, which until then was a large and cumbersome instrument. Using mirrors instead of lenses, he created a more powerful instrument that was 10 times smaller. When members of the Royal Society of London for the Improvement of Natural Science learned about his telescope, they were impressed. This encouraged him to tell them about what he described as a "crucial experiment" on light and color (BBC News Mundo, 2015). According to Ordoñez (2016), in 1672, he joined the Royal Society, an institution founded in London in 1660 that brought together English scientists, and that same year he presented to its members a paper titled "New Theory of Light and Colors," in which he explained the relationship between sunlight and the colors of the rainbow. Scholars like Descartes and Huygens argued that light itself was white light, composed of particles that spread out in waves (Ordóñez, 2016). They considered that colors were properties of the surfaces of the material on which the light fell. But through experiments with prisms, Newton concluded that colors were inherent properties of light itself, and that white light was the combination of rays of light of various colors. Therefore, light was not the result of the vibration of any material ether but a substance with properties. These ideas were not well received by Hooke, who had devoted himself to developing the theses of Descartes and Huygens. His criticism of Newton's paper unleashed a enmity that would last for decades. Newton, unforgiving towards Hooke, retreated to Cambridge and severed his relationships with the Royal Society. Ordóñez (2016) mentions that, resentful and relentless, he hastened to erase all traces of Hooke's work, including his portraits. In 1687, at the request of a friend, Newton published the treatise "Mathematical Principles of Natural Philosophy" or "Philosophiæ Naturalis Principia Mathematica" (Sánchez Amador, 2020). The language in which it was written, Latin, indicated the audience it was aimed at: experts in mathematics and mechanics, astronomers, philosophers, and university scholars (Ordóñez, 2016). According to Sánchez Amador (3030), this work is undoubtedly one of the most important in the fields of science in general and physics throughout history. In mid-1693, he suffered a mental breakdown when he suspected that his friends were conspiring against him (BBC News Mundo, 2015). After working for five consecutive nights, he experienced what could be described as a nervous crisis. Later, he apologized to John Locke and Samuel Pepys for wishing them dead. But despite his fragile mental health, his reputation remained intact and he was soon offered a crucial position. As Warden of the Royal Mint in 1696, he found a new vocation. He wanted to make the British pound the most stable currency. In the 17th century, British finances were in crisis. It was found that one in ten coins was counterfeit, and often the value of the metal with which it was made exceeded what it represented. In his role as supervisor, he undertook a project to withdraw the currency in circulation and introduce a more reliable one. According to BBC News Mundo (2015), he kept a database of counterfeiters whom he punished. In 1700, he was appointed Master of the Mint, a position he held for the rest of his life (BBC News Mundo, 2015). In 1703, he was elected president of the Royal Society, and his influence grew to the point of becoming a public figure (Ordóñez, 2016). He maintained control over what happened in Cambridge, and even in Oxford, and his mechanics began to be studied in these universities. His theories spread throughout Europe through books, such as those of his disciple Desaguliers or the Dutch Gravesande. In 1704, he published his Optics, written in English, which collected his corpuscular interpretation of light, a triumph over English Cartesians (Ordóñez, 2016). In 1712, Newton and Leibniz had been in disagreement for years over who had invented infinitesimal calculus (BBC News Mundo, 2015). However, according to BBC News Mundo (2015), Newton finally found a way to snatch victory from his intellectual enemy. In 1713, the Royal Society formed a committee to decide once and for all who had invented it (BBC News Mundo, 2015). The conclusion was that Newton had preceded Leibniz by many years. However, the secret author of the Royal Society's report was none other than Newton himself. Leibniz refused to accept defeat, and the fight only ended when both men were already dead. Today, according to BBC News Mundo (2015), it is accepted that both arrived at calculus independently, so there was no plagiarism. During the last 30 years of his life, he devoted himself to religious studies and occultism (Sánchez, 2019). He considered himself chosen by God to decipher secret messages from the Bible. He predicted that the end of the world would take place in the year 2060. He proclaimed that the Catholic Church was the beast of the Apocalypse and that Moses had been an alchemist. In his final years, he suffered multiple afflictions: moral, due to a heated debate with Leibniz, and physical, due to a serious kidney problem. Isaac left this world at the age of 84 (1727) after several kidney problems, due to a nephritic colic. Despite his strong rivalries, accusations of plagiarism, and evident jealousy with the philosopher and mathematician Gottfried Leibniz, he never lost the respect and devotion of both the general public and the scientific community. According to Sánchez Amador (20202), this recognition culminated in 1705 when he was knighted by Queen Anne. Contributions to Science The Law of Universal Gravitation Bernard Cohen, a renowned historian and contemporary scientist of American origin, has highlighted that Isaac Newton's discovery of the law of universal gravitation represents the culmination of the Scientific Revolution (Sánchez Amador, 2020). This discovery transcends the simplicity of a formula to become the key to understanding most of the physical phenomena observable by the human eye. This law is one of the multiple physical formulations present in the book "Philosophiæ Naturalis Principia Mathematica," which describes the gravitational interaction between bodies with mass (Sánchez Amador, 2020). According to Ordóñez (2016), Newton demonstrated his ability to successfully apply mathematics to mechanical problems, especially regarding the motion of the planets in the solar system. Since Nicolaus Copernicus, it was known that all planets, including Earth, revolve around the Sun, and since then, observations about celestial mechanics had accumulated (Ordóñez, 2016). However, there were still unexplained phenomena. One of them was the curvilinear motion of the planets around the Sun, or the more general problem of circular motion. The works of Kepler demonstrated that the planets revolved around the Sun describing not circular but elliptical orbits, and this with a constant areolar velocity, that is, always sweeping the same surface in the same unit of time. But how were they attracted by the Sun to be able to perform that trajectory? Descartes had hypothesized that the entire universe was filled with particles and that the Sun generated swirls of matter that dragged the planets and led them to describe those elliptical orbits. However, according to Ordónez (2016), it seemed difficult to demonstrate that intuitive image through mathematical calculation. During his time at Cambridge, he found a solution to the problem: he imagined that a force united the Sun with each planet and that this force attracted them in such a way that they were forced to rotate describing orbits (Ordóñez, 2016). Although this might seem only an image, unlike Descartes' proposal, Newton provided a quantitative demonstration of the force in action. In fact, the law of gravity states that the force of attraction between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance separating them (Ordóñez, 2016). In other words, the closer and more massive two bodies are, the more intensely they will attract each other (Sánchez Amador, 2020). In this way, through geometric calculations, he was able to demonstrate that the result of this action was an elliptical trajectory (Ordóñez, 2016). According to Sánchez Amador (2020), this establishes a proportional relationship between gravitational force and the mass of bodies. Newton's Three Laws The Law of Inertia states that an object at rest will remain at rest unless acted upon by a force (Sánchez Amador, 2020). An object in motion will continue moving in a straight line unless acted upon by an external force. The Law of Acceleration posits that an object will accelerate if a force is applied to it. Acceleration is the change in velocity of an object and will occur in the same direction as the force. This idea can also be expressed as force equals mass times acceleration, or F = ma. Finally, the Action and Reaction Law states that for every action, there is an equal and opposite reaction. Sánchez Amador (2020) mentions that, although these postulations may seem obvious today, they were the foundations of classical mechanics, which has allowed for everything from understanding and manufacturing machines to comprehending planetary motion, when combined with the law of universal gravitation. Other Contributions There are many other contributions to the world of science by this figure that the general population is not aware of (Sánchez Amador, 2020). For example, he is credited with the invention of infinitesimal calculus, an important branch of mathematics focused on the study of change and continuity. This invention is also attributed to the philosopher Gottfried Wilhelm Leibniz, whom Newton accused of plagiarism. Additionally, he is credited with the discovery of refractive dispersion, that is, the decomposition of white light into the different colors that compose it (red, orange, yellow, green, blue, indigo, and violet). Thus, he demonstrated that sunlight is composed of the sum of all colors. Sánchez Amador (2020) mentions that, although many more postulations and ideas have been left out, Newton's scientific work can be summarized in establishing the foundations of classical mechanics, various works on light and optics, and the development of infinitesimal calculus in the mathematical field. References BBC News Mundo. (2015, julio 19). El Lado Oscuro del Genio Isaac Newton. BBC. https://www.bbc.com/mundo/noticias/2015/07/150707_isaac_newton_secretos_oscuros_finde_dv National Geographic. (2023). Isaac Newton: Who he Was, Why Apples are Falling. National Geographic. https://education.nationalgeographic.org/resource/isaac-newton-who-he-was-why-apples-are-falling/ Ordóñez, J. (2016, marzo 31). Isaac Newton, científico y alquimista. National geographic. https://historia.nationalgeographic.com.es/a/isaac-newton-cientifico-y-alquimista_10246 Sánchez Amador, S. A. (2020, septiembre 22). Isaac Newton: Biografía y Aportaciones a la Ciencia de Este Investigador. Psicología y Mente. https://psicologiaymente.com/biografias/isaac-newton Sánchez, E. (2019, julio 4). Isaac Newton, biografía de un hombre en claroscuro. La Mente es Maravillosa. https://lamenteesmaravillosa.com/isaac-newton-biografia-de-un-hombre-en-claroscuro/

Robert Hooke (1635 - 1703), renowned in the scientific community for introducing the term "cell," made significant contributions to the development of biology and physics (Arrimada, 2021). His career, marked by a diversity of fields including horology, microscopy, astronomy, medicine, navigation, and architecture, earned him the nickname "the English Leonardo da Vinci." Despite his valuable scientific contributions, Hooke did not receive the recognition he deserved. Additionally, he is known for his notorious feud with Isaac Newton. Arrimada (2021) mentions that this fact, along with his lack of recognition, highlights the challenges scientists sometimes face on their path to discovery and innovation. Biography Robert Hooke was born on July 18, 1635, on the Isle of Wight, the largest island of England (Arrimada, 2021). His parents, Cecily Gyles and John Hooke, an Anglican cleric, were forced to educate their son due to lack of financial resources to enroll him in school. Hooke's life took a dramatic turn when, at the age of 13, he lost his father. As a result, he had to work, taking his first job as an assistant to a popular portrait painter on the Isle of Wight. However, according to Arrimada (2021), the oils and varnishes used in the work caused chest irritation, leading him to abandon the position. After leaving his job, he enrolled at Westminster School, a prestigious educational institution located in London (Arrimada, 2021). During his time there, he attended numerous meetings on science and philosophy, areas of great interest to him. Thanks to his outstanding academic performance, at the age of 18, he received a scholarship as a choirboy at Christ Church College, Oxford, which is the church of the Diocese of Oxford, belonging to the University of Oxford. There, as per Arrimada (2021), in addition to receiving a solid academic education, he had to collaborate in household chores due to his status as a scholarship student. During those years, he focused on his academic development with the aim of improving his future (Arrimada, 2021). He began working as an assistant in a laboratory, where he stood out for a series of discoveries he made. It was at that time when he began to forge his passion for science, showing interest in a wide variety of scientific works (Arrimada, 2021). In 1661, in recognition of his abilities as a scientist, he was appointed "Curator of Experiments" at the newly founded Royal Society, which is still operational today (Sánchez Amador, 2020). The Royal Society of London is the oldest society of scientists in the United Kingdom, officially founded in 1662 (Arrimada, 2021). However, according to Arrimada (2021), even before its official foundation, the founding scientists already held regular meetings. He was a member of the society for 40 years, starting his career as an assistant to the philosopher, chemist, physicist, and inventor Robert Boyle (Arrimada, 2021). His first significant work under Boyle's tutelage was the development of an air pump, designed to compress air and produce a vacuum. According to Arrimada (2021), this pump was instrumental in Boyle's conclusion of his experiment on formulating the law of gases (Boyle's Law), whose main postulate states that the volume of a gas is inversely proportional to its pressure. In 1665, although Hooke was an astronomer, he decided to focus his attention on Earth, specifically on the invisible world (Ennis, 2015). His observations of slices of cork under his microscope revealed that they were composed of small square segments, which he called "cells," as the tiny square structures he observed reminded him of monk cells. After his discoveries, he wrote and illustrated what is considered one of the greatest books of all time: "Micrographia." The incredibly detailed drawings of insects are simply amazing and are unlikely to ever be surpassed. The book made a great impact on the world. According to Ennis (2015), Hooke's invisible world was first made visible to everyone. The massive rebuilding revenues that followed the Great Fire of London in 1666 provided him with the financial freedom to continue his scientific efforts (Cartwright, 2023). In 1675, he participated in selecting a site for a new observatory in Greenwich, and he was also an integral part of the design stage along with Christopher Wren (1632 - 1723). Hooke ultimately supervised the long construction period of the building. Hooke and Wren had already collaborated closely on the design of the new St. Paul's Cathedral, where Hooke provided invaluable assistance in solving the problem of how to build its dome. According to Cartwright (2023), Hooke continued his involvement in London's new and dramatic skyline by designing, again with Wren, the 65-meter (202-foot) hollow column commemorating the dreadful Great Fire. Always pragmatic in his scientific approach, he conducted experiments on gravity and air pressure from the high roof of the old St. Paul's (Cartwright, 2023). He even attempted to install a giant telescope inside the monument to the Great Fire, although unfortunately, he was not successful in this endeavor. Hooke's life came to an end on March 3, 1703, at the age of 67. Throughout his life, he never married or had children. According to Cartwright (2023), in recognition of his contributions, he was awarded a commemorative plaque at Westminster Abbey, although it was not the grand monument awarded to Newton. Contributions to Science Although it took three centuries after his death for historians to recognize him as "the English Leonardo da Vinci," today Robert Hooke's contributions can be summarized into two major pillars: physics and biology (Sánchez Amador, 2020). Arrimanda (2021) mentions that, in addition to the tasks he carried out as Boyle's assistant, Hooke made various significant discoveries. Law of Elasticity In 1665, while serving as Boyle's assistant, Hooke formulated what is now known as "Hooke's Law" (Sánchez Amador, 2020). This law, originally formulated for objects stretched longitudinally, states that the elongation of a spring is directly proportional to the magnitude of the applied force, as long as the spring is not permanently deformed (Sánchez Amador, 2020). This theory opened the door to a series of scientific studies that today allow for various predictions in the fields of engineering and physics (Arrimada, 2021). For example, when designing a bridge, one can calculate the effect that the weight of vehicles passing over it will have on the structure. Thus, according to Arrimada (2021), the necessary materials to build the bridge can be determined so that it can withstand such a load. Capillarity In the work published in 1665, titled "Micrographia," Hooke detailed his discoveries on capillarity (Arrimada, 2021). In it, it is explained that the height to which water, as well as other fluids, rose when exiting through narrow glass tubes was directly related to the diameter of the tube through which they passed. According to Arrimada (2021), this work not only became a scientific bestseller, being the first in history, but also was the first to show drawings of images captured with optical microscopy. Cell Theory and Cells Through the use of a microscope, he identified a series of small cavities with a polyhedral shape on the slide, whose appearance was remarkably similar to that of a honeycomb (Arrimada, 2021). Subsequently, he assigned the term "cell" to each of these cavities, without fully realizing the transcendental relevance that these cavities had in the constitution of living organisms. What he was actually observing were plant cells that were no longer alive. Arrimada (2021) mentions that, thanks to this observation, a few years later, the composition of the tissue of living organisms was discovered, and it also contributed to the postulation of a theory about cell organization. Theory of Planetary Motion Hooke is recognized as the pioneer in the construction of the Gregorian telescope (Domenech, 2019). With this instrument, he managed to observe that Mars and Jupiter rotated on their own axes (Domenech, 2019). For years, he dedicated himself to researching the theory of planetary motion, starting from a mechanical problem, and also explored the law of universal gravitation (Arrimada, 2021). Hooke's work in this field was what triggered his rivalry with Newton. This was because Newton was the one who managed to publish the necessary mathematical proof to demonstrate the theory. Additionally, there are sources that reveal that Hooke investigated the Earth's movement in the form of an ellipse around the Sun (Arrimada, 2021). Hooke is also recognized for promoting the scientific use of microscopes (Domenech, 2019). According to Domenech (2019), the illustrations in his book "Micrographia" marked the beginning of an art that would be perfected by new experts like Anton van Leeuwenhoek. Inventions Hooke is also recognized as a prolific inventor (Arrimada, 2021). Among his creations, instruments stand out which he designed with the aim of recording variations in weather conditions. According to Arrimada (2021), these include an alcohol thermometer, a quadrant barometer, an improved chronometer, an anemometer, a hygrometer clock, and a clock that automatically recorded readings from meteorological instruments. Conflict with Isaac Newton It is recognized that Robert Hooke and Isaac Newton maintained a long battle of egos to be considered the brightest scientific minds of their time (Arrimada, 2021). This competition was quite even while Hooke was alive; however, after his death, Newton continued his scientific work achieving significant advances, which allowed him to obtain greater recognition (Arrimada, 2021). According to Domenech (2019), at the peak of his career in 1679, Robert Hooke began a correspondence with Isaac Newton about gravitation, an idea that Hooke had already assumed years before. The rivalry between them intensified following a publication by Newton in 1687 titled "Philosophiæ Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy), where the universal law of gravitation was discussed (Arrimada, 2021). This scientific idea had already been researched by several scientists for years, with Hooke's contributions during the 1670s being crucial for its development. Despite this, it was Newton who managed to create the rigorous mathematical proof to demonstrate it. After Newton's theory on the law of gravity was published, Hooke became angry, claiming that he had provided the idea to Newton through the letters he wrote to him. Newton, for his part, denied that Hooke had provided him with the idea (Arrimada, 2021). According to Domenech (2019), the highest recognition he attributes is that the letters with Hooke revived his interest in astronomy but did not provide anything new. As a result of this unpleasant conflict, the famous phrase "If I have seen further, it is by standing on the shoulders of giants" by Newton to Hooke arises, in which it is believed that he mocks the scientist's short stature and appearance (Sánchez Amador, 2020). They also had a fairly similar conflict based on the "Corpuscular Theory" published by Newton, in which he claimed that light was composed of very small particles that moved in a straight line (Arrimada, 2021). Aside from the conflicts Robert Hooke had with Isaac Newton, there is no doubt that he was a great scientist with a brilliant mind. According to Arrimada (2021), he is a very representative figure of experimental science, considered one of the fathers of microscopy, physics, and scientific dissemination, so his figure is still remembered to this day. The Mystery of Hooke's Portrait Beyond the brevity of the biography, it is fascinating to discover that almost all knowledge about Robert Hooke comes from the autobiography he wrote in 1696, which, curiously, he never finished (Sánchez Amador, 2020). Robert Hooke's appearance and stature are uncertain, mainly due to the absence of preserved portraits of him (Domenech, 2019). Historically, this lack is attributed to Newton's efforts to eliminate the figure of his great rival. Domenech (2019) mentions that, according to scientific legend, Newton even obtained the only portrait of Hooke and ordered its destruction; another version maintains that he intentionally left it behind when the Royal Society moved to another building. However, Allan Chapman, the most recent biographer of Robert Hooke and a scholar of his figure, dismisses these stories as mere myths (Domenech, 2019). Chapman, along with other historians, has made a great effort in recent years to dignify once again this great genius of science. In 2003, the painter Rita Greer undertook historical research to produce a portrait of Hooke that was faithful to the two remaining written descriptions of him. With his public image thus restored, Domenech (2019) mentions that this tribute portrait by Greer has been used to illustrate numerous articles and documentaries, finally shedding a fairer light on Hooke in the history of science. References Arrimada, M. (2021, diciembre 16). Robert Hooke: Diografía y Aportes de EsteInvestigador Inglés. Psicología y Mente. https://psicologiaymente.com/biografias/robert-hooke Cartwright, M. (2023). Robert Hooke. World History Encyclopedia. https://www.worldhistory.org/Robert_Hooke/ Domenech, F. (2019, julio 31). Hooke, the Genius Whose big Mistake was Confronting Newton. OpenMind. https://www.bbvaopenmind.com/en/science/leading-figures/hooke-the-genius-whose-big-mistake-was-confronting-newton/ Ennis, P. M. (2015, marzo 29). Dr. Robert Hooke. Historic UK. https://www.historic-uk.com/HistoryUK/HistoryofEngland/Dr-Robert-Hooke/ Sánchez Amador, S. A. (2020, octubre 18). Robert Hooke: Biografía y Resumen de sus Aportes a la Ciencia. Médico Plus. https://medicoplus.com/biografias/robert-hooke

The cytoskeleton is an extensive network of filamentous or tubular proteins found in the cytoplasm of cells, with a shape and composition that can vary according to the cell's needs (Laguna & Serrano, 2021). The cytoskeleton is characterized by its three-dimensional shape, which provides structure and volume to both the cytoplasm and cellular organelles, allowing them to carry out their functions (Rothschuh Osorio, 2023). It is a geodesic structure, where the balance of opposing forces maintains the stability of the whole. Additionally, it possesses flexibility and firmness due to the specific properties of the proteins that comprise it. In correspondence with Rothschuh Osorio (2023), the cytoskeleton is composed of four types of structures: microtubules, microfilaments, intermediate filaments, and cilia or flagella, each with a specific function. Functions The function of the cytoskeleton is multiple and fundamental for the cell (Rothschuh Osorio, 2023). On one hand, it organizes the cellular space by serving as the matrix on which organelles are located, ensuring that each of them fulfills its function in the appropriate place. Previously, organelles were thought to be dispersed in the cytosol, the liquid substance of the cytoplasm, but it was later revealed that the cytoplasm also contains a fiber matrix called the cytoskeleton (Rothschuh Osorio, 2023). On the other hand, the cytoskeleton supports the cell by maintaining its shape and rigidity, allowing it to adopt irregular shapes according to its needs (Laguna & Serrano, 2021). According to Rothschuh Osorio (2023), this is especially useful for animal cells, which lack a cell wall like plant cells. Similarly, the cytoskeleton allows ordered movement within the cell, being flexible and facilitating the displacement of small movements that occur within the cell, such as cytoplasmic streaming in plant cells (Rothschuh Osorio, 2023). These movements are called cellular motility. Finally, in correspondence with Rothschuh Osorio (2023), the cytoskeleton regulates biochemical processes within the cell by allowing the flow of components manufactured within organelles, which can then be transported within the cell as part of its vital functions. Structure Cytoskeleton in Eukaryotic Cells Microtubules are the largest cytoskeletal fibers of the three that exist, with a diameter of 25 nm (Khan Academy, n.d.). These fibers are formed by a hollow tube of tubulin proteins, which come in two forms: alpha and beta (Rothschuh Osorio, 2023; Khan Academy, n.d.). Like actin filaments, microtubules are dynamic structures that can grow and disassemble rapidly by adding or removing tubulin proteins, and they have directionality, meaning their ends are different from each other (Khan Academy, n.d.). Microtubules play an important structural role in the cell, as they enable it to resist compressive forces. Additionally, they have other more specialized functions, such as forming tracks for motor proteins kinesins and dyneins, which transport vesicles and other cargo within the cell. According to Khan Academy (n.d.), they also organize into a structure called the spindle during cell division, which is responsible for separating chromosomes. The cytoskeleton is composed of three types of fibers, with microfilaments being the thinnest of them (Khan Academy, n.d.). These fibers have a diameter of 7 nm and are formed by the joining of many monomers of a protein called actin, which are organized in a structure similar to a double helix (Khan Academy, n.d.). For this reason, microfilaments are also called actin filaments (Khan Academy, n.d.). According to Khan Academy (n.d.), actin filaments exhibit directionality, meaning their ends have a distinct structure. Actin filaments perform various functions in the cell, such as serving as tracks for the movement of a motor protein called myosin, which also forms filaments, and participating in many cellular functions that require movement, due to their relationship with myosin (Khan Academy, n.d.). For example, in animal cell division, an actin and myosin ring divides the cell into two daughter cells. Additionally, in correspondence with Khan Academy (n.d.), actin filaments are abundant in muscle cells, where they constitute overlapping filament structures called sarcomeres, which allow muscle contraction by sliding actin and myosin filaments past each other. Actin filaments also function as tracks within the cell for the transport of cargoes, such as vesicles with proteins or even organelles, which are carried by individual myosin motors that "walk" along the actin filament bundles (Khan Academy, n.d.). Actin filaments have the ability to assemble and disassemble rapidly, allowing them to play an important role in cellular motility, such as the movement of white blood cells in the immune system. Finally, according to Khan Academy (n.d.), actin filaments have essential structural functions in the cell, as they form a network in the outermost region of the cytoplasm, which is connected to the plasma membrane by special proteins, giving shape and structure to the cell. Intermediate filaments are fibers composed of different fibrous proteins, the type of which varies depending on the cellular tissue where they are found (Rothschuh Osorio, 2023; Khan Academy, n.d.). For example, keratin is a protein that forms intermediate filaments in hair, nails, and skin (Khan Academy, n.d.). These fibers have a size intermediate between microfilaments and microtubules, with a diameter between 8 and 10 nm (Khan Academy, n.d.). These fibers are only found in animal cells and are the strongest fibers of the cytoskeleton (Rothschuh Osorio, 2023). Unlike microfilaments, intermediate filaments are more stable and have an important structural function in the cell (Khan Academy, n.d.). According to Khan Academy (n.d.), their specialty is to resist tension, and among their functions, they stand out in maintaining cell shape and anchoring the nucleus and other organelles in position. In eukaryotic cells, microtubules are part of three more specialized structures: flagella, cilia, and centrosomes (Khan Academy, n.d.). Flagella are cellular extensions resembling hairs that allow the movement of the entire cell, as in sperm cells. Flagella are scarce, and if a cell possesses them, it usually has one or a few. Cilia are similar to flagella but shorter and more abundant. When motile cilia cover the cells of a tissue, their synchronized movement facilitates the transport of materials over the tissue surface. For example, in correspondence with Khan Academy (n.d.), cilia in the cells of the upper respiratory system help to remove dust and particles towards the nasal passages. Despite their differences in number and size, motile flagella and cilia have a common internal structure. This consists of 9 pairs of microtubules arranged in a circle, with an extra pair of microtubules in the center of the ring. Motile flagella and cilia move thanks to motor proteins called dyneins, which travel along the microtubules generating force. The coordinated movement of dyneins and the structural connections between the pairs of microtubules result in a regular beating pattern. Another characteristic is that the cilium or flagellum has a basal body at its base. The basal body is composed of microtubules and plays a fundamental role in the assembly of the cilium or flagellum. Additionally, the basal body regulates the entry and exit of proteins. According to Khan Academy (n.d.), the basal body is actually a modified centriole. Centrioles are better known for their function in centrosomes, which are structures that act as microtubule-organizing centers in animal cells (Khan Academy, n.d.). A centrosome consists of two centrioles arranged at right angles to each other and surrounded by a mass of "pericentriolar material," which provides anchoring sites for microtubules. The centrosome duplicates before cell division, and the pair of centrosomes appears to have an important function in organizing the microtubules that separate the chromosomes during cell division. However, the exact function of centrioles in this process is still unclear. According to Khan Academy (n.d.), some cells can divide without centrosomes, such as plant cells, which do not have them, or animal cells from which the centrosome has been removed. Cytoskeleton in Prokaryotic Cells The cytoskeleton of prokaryotic cells was unknown until recently, as it was thought that only eukaryotic cells possessed these structures (Rothschuh Osorio, 2023). However, it has been discovered that prokaryotic cells also have a cytoskeleton, which performs similar functions to those of eukaryotic cells but is formed by different proteins. According to Rothschuh Osorio (2023), among these proteins are: MreB and ParM, which resemble actin; proteins of the WACA family, which participate in the biogenesis and assembly of cilia and flagella in unicellular organisms; crescentin, which is equivalent to intermediate filaments; and FtsZ, which is analogous to tubulin. References Khan Academy. (s.f.). El Citoesqueleto. Khan Academy. Recuperado 13 de febrero de 2024, de https://es.khanacademy.org/science/biology/structure-of-a-cell/tour-of-organelles/a/the-cytoskeleton Laguna, M., & Serrano, C. (2021, septiembre 21). Citoesqueleto. Ken Hub. https://www.kenhub.com/es/library/anatomia-es/citoesqueleto Rothschuh Osorio, U. (2023, noviembre 30). Citoesqueleto: Qué es, Características, Función y Estructura. Ecología Verde. https://www.ecologiaverde.com/citoesqueleto-que-es-caracteristicas-funcion-y-estructura-4675.html

The animal cell represents the minimal unit of functionality that constitutes organisms belonging to the category of animals (Torres, 2019). This cell, in particular, is a type of eukaryotic cell that, by combining its elements and occasionally collaborating with other forms of life, such as bacteria forming the intestinal flora, contributes to the formation of tissues and functional organs, which allow the existence and survival of an animal (Torres, 2019). Álvarez (2023) mentions that, given that animals are complex multicellular organisms, the cells composing them exhibit a high level of specialization: depending on the tissue they belong to, these cells perform specific functions that define their morphology, function, and needs. Características All animal cells are part of the taxon of eukaryotic cells (Torres, 2019). These cells are characterized by harboring all their genetic material in a structure called the cell nucleus. Additionally, they present various organelles separated by membranes that envelop them, unlike prokaryotic cells that lack these characteristics and are smaller, with their DNA dispersed in the cytoplasm that fills their interior. Additionally, the animal cell differs from other eukaryotic cells by organizing with others to constitute multicellular organisms that are part of the animal kingdom. Animals, in turn, are living beings of both microscopic and macroscopic dimensions, characterized, among other things, by their ability to move and the presence of nerve cells. According to Torres (2019), the Animalia kingdom constitutes one of the five kingdoms present in the group of eukaryotes. Parts of the Animal Cell Nucleus The nucleus is of utmost importance, as it not only houses a "instruction manual" about the molecules necessary for cell construction and regeneration but also establishes strategies for organism functioning and maintenance (Torres, 2019). In this context, in correspondence with Torres (2019), all information regarding actions inside and outside the cell is contained in this organelle. It stores genetic material in the form of DNA (Deoxyribonucleic Acid) and coordinates various cellular activities, from growth to reproduction (Páez, 2021). Thus, the nucleus operates as a filter to regulate the entry and exit of the zone where DNA is stored, preventing its dispersion and loss (Torres, 2019). Additionally, it strives to minimize the contact of certain molecules with the chromosomes, in order to preserve genetic information (Torres, 2019). Additionally, the nucleus houses a nucleolus, an internal structure composed of the concentration of chromatin and proteins (Páez, 2021). Páez (2021) mentions that, in mammals, there are between 1 and 5 nucleoli in the cell. Cell Membrane or Plasma Membrane The cell membrane constitutes the outermost layer of the cell, encompassing it almost entirely and providing uniform protection to all its parts (Torres, 2019). It is mainly composed of lipids, specifically phospholipids and cholesterol, forming a double lipid layer similar to a sealed bag (Fernandes, 2021). It is worth noting that the cell membrane of animal cells, like those of other eukaryotic organisms, does not exhibit total impermeability; on the contrary, it presents entry and exit points in the form of pores that enable the exchange of substances with the external environment (Torres, 2019). Through these channels or transporters, substances necessary for metabolism enter and ions or waste products exit (Fernandes, 2021). Torres (2019) mentions that, although this process increases the risk of harmful elements entering, it is essential for maintaining homeostasis, which represents the physical-chemical balance between the cell and its environment. Cytoplasm or Cytosol The cytoplasm of animal cells is the space between the cytoplasmic membrane and the nucleus, surrounding all organelles (Páez, 2021). In other words, it acts as physical support for all internal components of the cell (Torres, 2019). It contributes, among other things, to ensuring the constant availability of substances necessary for cell development, regeneration, and communication (Torres, 2019). It is mainly constituted by 70% water, with the rest being a mixture of proteins, lipids, carbohydrates, and mineral salts (Páez, 2021). According to Páez (2021), this environment is essential for the development of cell activity. Cytoskeleton The cytoskeleton represents a set of more or less rigid filaments whose purpose is to confer shape to the cell and preserve its components in stable locations for proper cellular functioning (Torres, 2019). In correspondence with Torres (2019), through its components, such as microtubules, it facilitates the movement of certain molecules along its internal conduits. Mitochondria Mitochondria represent one of the most intriguing parts of the animal cell because they harbor their own DNA, which differs from the nucleus (Torres, 2019). The hypothesis suggests that this structure is, in fact, the vestige of a fusion between a cell and a bacterium (with the mitochondrion being the bacterium integrated into the cell, fused in a symbiotic relationship). During the reproduction process, the duplication of mitochondrial DNA is also carried out to transmit it to the offspring. The main function of mitochondria lies in the production of ATP, the molecule from which animal cells obtain energy, making them crucial components for metabolic processes (Torres, 2019). Their morphology is elongated, and they have two membranes: an inner one that forms crests when folded and an outer smooth one (Páez, 2021). According to Páez (2021), the quantity of mitochondria in each cell varies according to its activity (for example, muscle cells may have a high number of them). Vacuole The organelle, formed by the fusion of a large number of membranous vesicles, undergoes variations in its shape and structure according to the cell's needs (Fernandes, 2021). Inside it, it contains enzymes or water. In correspondence with Fernandes (2021), its main function is to preserve cellular rigidity and favor the cell's enlargement. Golgi Apparatus The Golgi apparatus is mainly responsible for creating molecules from raw materials that come from other parts of the animal cell (Torres, 2019). Its structure, similar to the Golgi complex present in plant cells, consists of three components: membranous sacs, tubules used for sending substances into and out of the cell, and vacuoles (Páez, 2021). Thus, it facilitates the transport, modification, and classification of proteins synthesized in the ribosomes of the rough endoplasmic reticulum (Álvarez, 2023). In accordance with Álvarez (2023), newly synthesized proteins are wrapped with a membrane layer of the rough endoplasmic reticulum, leading to the formation of vesicles. Endoplasmic Reticulum The endoplasmic reticulum is an organelle that adopts the form of flattened sacs and tubules stacked together, sharing the same internal space (Páez, 2021). This organelle is organized into several domains, including the rough endoplasmic reticulum, responsible for protein synthesis and characterized by flattened membranes and associated ribosomes, and the smooth endoplasmic reticulum, responsible for lipid synthesis and having a more irregular appearance, without associated ribosomes (Fernandes, 2021; Páez, 2021). Like the Golgi apparatus, the endoplasmic reticulum is also distinguished by material synthesis, but on a smaller scale (Torres, 2019). Specifically, according to Torres (2019), it is especially involved in lipid creation to maintain the integrity of the cell membrane. Ribosomes Ribosomes, cellular organelles present in the cytoplasm of eukaryotic and prokaryotic cells, are characterized by their globular shape and the absence of a membrane (Rothschuh Osorio, 2022). In correspondence with Fernandes (2021), these organelles are composed of RNA and proteins and play a fundamental role in protein synthesis. Lysosomes Lysosomes represent vesicles containing enzymes responsible for degrading material that enters the cell, called "heterophagy", or material generated internally, known as "autophagy" (Álvarez, 2023). The primary function of this organelle is to carry out cellular digestion, and they are synthesized by the Golgi apparatus (Álvarez, 2023). In short, in accordance with Torres (2019), these microscopic bodies release enzymes with the ability to "dissolve" the components of the animal cell. Centriole It is a cylindrical organelle composed of three triplets of microtubules, which are part of the cytoskeleton (Álvarez, 2023). In correspondence with Álvarez (2023), its function stands out in the transport of organelles within the cell, providing mechanical stability and actively participating in mitosis or cell division processes. Centrosome The centrosome is distinguished in the animal cell by being a cylindrical and hollow structure composed of two centrioles arranged perpendicular to each other (Páez, 2021). In the pericentriolar material, there are complexes of the tubulin protein, essential in creating the mitotic spindle, a set of microtubules that extend from the centrioles during cell division (Páez, 2021; Álvarez, 2023). From this process, Fernandes (2021) mentions that cilia and flagella originate, which are mobile structures present in some cells. Cilia and Flagella The cilia and flagella of the animal cell are appendages formed by microtubules, which provide mobility to the cell (Páez, 2021). These appendages are present in unicellular organisms, playing a crucial role in their locomotion, while in other cells, they perform functions such as removing substances from the environment or participating in sensory function (Páez, 2021). Cilia execute movements similar to oars to move the surrounding liquid to the cell (Álvarez, 2023). Unlike cilia, flagella are characterized by their greater length, acting as propellers that drive the movement of the entire cell (Álvarez, 2023). In terms of quantity, Páez (2021) mentions that cilia outnumber flagella. Peroxisomes Peroxisomes are rounded organelles, delimited by a membrane and with a diameter ranging from 0.1 to 1 micrometer (Sánchez Amador, 2021). Inside these, there are enzymes fundamental for carrying out various metabolic reactions, covering various aspects of cellular metabolism, a process by which each of these functional bodies acquires the necessary energy to carry out its activities. It is estimated that within each peroxisome, there are around 50 different enzymes capable of catalyzing various reactions, depending on the type of cell containing the organelle and its physiological state. Sánchez Amador (2021) mentions that a notable example is that these organelles contain approximately 10% of the total activity of two enzymes involved in the pentose-phosphate pathway, which are closely related to glycolysis, which is the process of glucose oxidation to obtain energy. Types and Functions Epithelial Cells Epithelial cells constitute the cells found on the walls of organs, forming lining tissues (Páez, 2021). They present various specializations depending on the organ they are located in, as this specialization defines their function. Páez (2021) mentions that an example of this is evident in the cells of the epithelium of the small intestine, which develop microvilli with the purpose of increasing the surface area for nutrient absorption. Connective Tissue Cells These cells aim to establish an interconnected structure that, transcending the skin barrier, preserves all internal parts in their corresponding location (Torres, 2019). Torres (2019) mentions that an example is found in bone cells, which, belonging to this category, participate in bone formation, rigid structures designed to keep the rest of the elements in place. Blood Cells They enable all nutrients, vitamins, and molecules necessary for life to circulate through the circulatory system (Torres, 2019). Simultaneously, they prevent the spread of harmful external agents throughout the body. Thus, the activity of these cells is linked to movement (Torres, 2019). Three different types of blood cells are identified: red blood cells (or erythrocytes), white blood cells (or leukocytes), and platelets (Páez, 2021). Red blood cells stand out because they are the only cells in the human body that lack a nucleus. In correspondence with Páez (2021), these cell types primarily move through the bloodstream, performing key functions such as oxygen and CO2 transport and exchange (red blood cells), antibody production for the immune response (white blood cells), or coagulation for maintaining the circulatory system. Muscle Cells Three main types of muscle cells are identified: those belonging to smooth, skeletal, and cardiac muscle tissue (Páez, 2021). These cells have the ability to contract by transforming chemical energy into mechanical energy. The shape of these cells is diverse, and their function is related to the tissue to which they belong. According to Páez (2021), those of smooth muscle show an elongated shape, while those of skeletal and cardiac tissue present striations, with the latter notable for their rhythmic involuntary contraction. Nerve Cells One of the most characteristic types of cells in animal activity is the nerve cell, as animals are distinguished by their ability to move and process various types of information related to constant changes in their environment (Torres, 2019). Nervous tissue is composed of two types of cells: neurons and glial cells (Páez, 2021). Neurons specialize in transmitting nerve impulses through synapses, either between neurons or between a neuron and a muscle cell. On the other hand, glial cells do not transmit nerve impulses but perform support and maintenance functions for neurons. According to Páez (2021), both types have a branched or star-shaped form, thus facilitating communication between them. Adipose Cells Adipocytes, cells of considerable size, perform the function of storing energy in the form of fatty acids inside them (Páez, 2021). Additionally, they are responsible for secreting proteins and hormones, thus playing a crucial role in various biological functions. According to Páez (2921), these cells also serve an important purpose in the thermal and mechanical protection of the organism. Cartilaginous Cells Cartilaginous cells are called chondrocytes, characterized by their flattened and rounded shape, as well as the presence of microvilli (Páez, 2021). In correspondence with Páez (2021), in the human body, they are found in tissues located in the ribs, joints, nose, among other places, and together they perform a support function. Bone Cells Bone cells play a crucial role in the process of bone growth and breakdown (Páez, 2021). According to de Andrade (2019), in this process, they are distinguished into three main categories: osteoblasts, responsible for manufacturing the organic matrix of collagen, which is why they are located on the surface of the bone and in places where new formation is required, such as fracture sites; osteoclasts, a special group of cells responsible for bone resorption; and osteocytes, the most common type of bone cell. References Álvarez, D. O. (2023). Célula Animal - Concepto, Partes y Diferencias con la Vegetal. Concepto. https://concepto.de/celula-animal/ de Andrade, M. (2019). Definición de Células Óseas. Significado.com. https://significado.com/celulas-oseas/ Fernandes, A. Z. (2021, enero 22). Qué es la Célula Animal. Significados. https://www.significados.com/celula-animal/ Páez, J. C. (2021, marzo 1). Partes de la Célula Animal. Ecología Verde. https://www.ecologiaverde.com/partes-de-la-celula-animal-3279.html Rothschuh Osorio, U. (2022, marzo 8). Ribosomas: Función y Estructura. ecologiaverde.com. https://www.ecologiaverde.com/ribosomas-funcion-y-estructura-3795.html Sánchez Amador, S. A. (2021, abril 15). Peroxisomas: Qué son, Características y Funciones. Psicología y Mente. https://psicologiaymente.com/salud/peroxisomas Torres, A. (2019, agosto 1). Célula Animal: Tipos, Partes y Funciones que la Caracterizan. Psicología y Mente. https://psicologiaymente.com/miscelanea/celula-animal