This essay largely labours to clarify the above question, as first strictly considered by John Locke in Book 2, Chapter 27 of On Identity and Diversity. None of what is written here is intended to be a rigorous read but rather an effort to entertain contraries for the sake of contemplation.

The measure of identity in the diachronic sense is revealed by comparing the existence of a person existing at a certain time, with that which exists in another time. Thus, an essay concerning the dimensions of congruence between one’s present and past self must inadvertently first seek to clarify the nature of this self. The problem of personal identity stands central to this.

Reid maintains that identity “is too simple a notion to admit of logical definition” [1]. Hume claims that the question of personal identity is “impossible to answer without a manifest contradiction and absurdity” [7]. Reid’s and Hume’s arguments, prima facie, explore the nature of personal identity without dealing with it directly; they go insofar as rendering it simple and unanalyzable. Locke, uniquely, identifies that “consciousness makes personal identity” [9]. But the abstractness of consciousness, a priori, is an unsuitable clarification too since it calls upon more problems than it really solves. Therefore, we must deal with the problem in logical divisions that are analytical:

I. What is the nature of personal identity?
II. What is the arbiter for continued existence of the above?
III. To what degree and in what senses can personal identity be defined?

To firmly assess in what sense I am the same as some arbitrary point in the past presupposes an answer to the questions “what am I?” and “what makes me who I am?” The union of these questions can be reduced to a problem of personal identity. The second question deals with the problem of persistence. In other words, what does it take for a person to persist from one time to another? Without knowing how existence subsists over time, the ways in which it remains the same cannot be answered. The third question then builds on the results of the second. We consider an argument inspired by the Ship of Theseus. We then contend that propositions of identity resolve into matters of contingency where it is not possible to offer a definitive resolution but rather only a relative one.

I. What is the Nature of Personal Identity?

Identity is the relationship that a thing bears to itself, as compared to other objects [15]. Personal identity is viewed by Locke as the product of consciousness over time, i.e., “sameness of the rational being.” Thus, it follows that our identity only persists so far as our consciousness does. However, it can be equally argued that by consciousness, Locke actually meant memory [9], but the faculties of consciousness and memory differ in that the former translates to knowledge of the present while the latter is that of the past. So, Locke’s argument may be reformulated in saying that personal identity consists in episodic memory. Yet I contend that present consciousness of the past is not necessary to our personal identity, for our personhood does not cease in those instances we cannot remember. In other words, to say that memory constitutes personal identity or at the very least is necessary for us to be the same is to say that persons have only existed through the times they can remember. This is a manifest absurdity.

Contrary to Locke’s views, Hume held persons as a bundle of different perceptions that succeed each other with “an inconceivable rapidity” [7]. In this sense, successive rapid changes often allow one to confound diversity with the notion of identity. I would, however, contest that to say identity is an illusion offends common sense since it implies I am in no ways the same as the person I was yesterday. This is an absurd result. I believe that our understanding of identity is in accordance with the proportion of changes relative to the body that suffers those changes, just as how the addition or diminution of a leaf would not be sufficient to bestow diversity upon a tree.

II. What is the Arbiter for Continued Existence of the Above?

For clarity, I will reformulate the persistence question as follows: if a person A exists at a time t1 and a person B exists at another time t2, under what conditions can we argue that they are the same? It is worth noting that diachronic identity is a controversial notion since time is itself identified by change. Heraclitus’ dictum that one could not step foot in the same river twice captures this, along with Hume’s idea of identity being a fictional concept.

The Memory and Bodily Criteria

It is apparent that Locke’s theory confounds evidence of personal identity with the very idea of personal identity; this is also reflected in Reid’s criticisms [1]. Episodic memory is merely a yardstick to gauge that I exist but not a yardstick to gauge that I exist continuously. For logically, if A at a time t2 > t1 remembers an event at time t1, then it is sensible to say A existed at time t1. However, while memory of an event at time t1 entails that A existed then, it does not necessarily mean that the intelligent agent viewing the event at t1 is identical with the agent that exists at t2. Thus, I contend that memory is a very fallible metric for persistence.

Further, Reid and Locke both agree that mental faculties such as memory are not continuous and that personal identity supposes a continued existence [2]. The result is a manifest contradiction, allowing us to discard the memory criterion. As far as any brute-physical relation is concerned, we may not identify as different persons even after having suffered losses of bodily faculties. In saying that a man has lost a limb, we do not mean that the man is now a different person. So, I contest that personal identity is not ascribed to parts of the body, or the body as a whole. This discards any brute-physical relation.

Anticriterialism

Most philosophical views (be it those of psychological continuity or those of brute-physical relations) agree that there is a criterion responsible for our persistence; this is challenged by anticriterialism, which is the thesis denying the existence of any such criteria for diachronic identity. Anticriterialism supposes that psychological and physical continuity are evidence for persistence but do not always guarantee it [13]. In other words, there are no metaphysically informative necessary and sufficient conditions for the persistence of persons.

The general consensus is then understood as any proposed criterion for personal persistence will be uninformative, unnecessary, or insufficient [4]. The motivation in espousing anticriterialism stems from the results of criterialism; namely, the thesis that obtaining one contingent state of affairs necessarily implies obtaining another distinct contingent state of affairs is unacceptable [13]. It has been shown, however, that in some cases, espousing anticriterialism leads to absurd results [4]. This, however, is still subject to modern debate [14, 18].

Aristotelian Changes

In circumventing the above problems, I propose that we may distinguish between “accidental” and “essential” changes in the Aristotelian sense. Accidental changes are assumed as ones which do not manifest any changes such that an object’s core nature remains the same. Essential changes, on the other hand, are those that do not preserve the identity of a being [6]. In distinguishing between the two, one may argue that it is certainly possible for a changing being to remain the same thing before and after the change so long as the only changes suffered are accidental. This is extended with relative relations of identity wherein we cannot simply say that two bodies are identical; instead, we require a sortal yardstick that serves to tell us in which sense the two bodies are identical.

III. To What Degree and in What Senses Can Personal Identity Be Defined?

Let’s momentarily propose that persons are, in some senses, like the Ship of Theseus, with ideas and virtues refurbishing themselves. We then ask whether the person who has suffered those experiences is the same as the one who has not. In other words, as we refurbish or discard ideas and perceptions, at what point do we stop bearing personal identity with our past selves? In answering this, I contend that refurbishment only affects one’s accidental properties. It is easy to see this since persons do not lose their personhood (an essential property) through time. Therefore, at no point in this process may we contest that a person has ceased being a person or is now a different person.

Further, I argue that one is the same as their past self in all the essential senses. As far as the accidental senses are concerned, I contend that when a succession of such changes occur, we are not hesitant to attribute identity since the alterations are trivial. However, this perspective resolves into a matter of contingency depending on one’s notions of essential properties, identity, and diversity.

We have now shown that facts concerning personal identity are relative to the framework and are not overarching and valid to every theory addressing identity but only to those whose fundamental descriptions are the same. We have shown some manifest absurdities and contradictions, allowing us to narrow the metatheory of personal identity. Further, we argue that the question resolves into a matter of contingency and therefore, one may arrive at different answers depending on the foundational ideas one chooses to begin with. One of the reasons we may be reluctant to accept such a conclusion about the arbitrariness of personal identity is because our personal experiences imply a continuity which might well be no more than an illusion of coherence. Ultimately, the determination of sameness between my present self and my ten-year-old self depends on the sense in which the question is posed, rendering it relative to the framework applied.

1. Bailey, Patrick. “Concerning Theories of Personal Identity” (2004). USF Tampa Graduate Theses and Dissertations. Available at: https://digitalcommons.usf.edu/etd/945
2. Copenhaver, Rebecca. “Reid on Memory and Personal Identity,” The Stanford Encyclopedia of Philosophy (Winter 2018 Edition), Edward N. Zalta (ed.).
3. Descartes, René. The Philosophical Writings of Descartes, Vol. II, trans. John Cottingham, Robert Stoothoff, Dugald Murdoch. Cambridge: Cambridge University Press, 1995.
4. Deutsch, Harry and Pawel Garbacz. “Relative Identity,” The Stanford Encyclopedia of Philosophy (Winter 2022 Edition), Edward N. Zalta & Uri Nodelman (eds.).
5. Duncan, Matt. “A Renewed Challenge to Anti-criterialism,” Erkenntnis, Vol. 85 (2020), pp. 1–18. DOI: 10.1007/s10670–018–0023–7.
6. Gallois, Andre. “Identity Over Time,” The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.).
7. Hume, David. A Treatise of Human Nature. Edited by L. A. Selby-Bigge, 2nd ed., Oxford University Press, 1978.
8. Langford, Simon. “A Defence of Anti-criterialism,” Canadian Journal of Philosophy, Vol. 47, №5 (2017), pp. 613–630.
9. Locke, John. An Essay Concerning Human Understanding (Ed. R. Woolhouse), Penguin Classics, 1998. DOI: 10.1604/9780140434828.
10. Merricks, Trenton. “There Are No Criteria of Identity Over Time,” Noûs, Vol. 32, №1 (1998), pp. 106–124. Available at: http://www.jstor.org/stable/2671929.
11. Olson, Eric T. “Personal Identity,” The Stanford Encyclopedia of Philosophy (Summer 2023 Edition), Edward N. Zalta & Uri Nodelman (eds.).
12. Parfit, Derek. Reasons and Persons. Oxford: Oxford University Press, 1984.
13. Piccirillo, R. A. “The Lockean Memory Theory of Personal Identity: Definition, Objection, Response,” Inquiries Journal/Student Pulse, Vol. 2, №08 (2010). Available at: http://www.inquiriesjournal.com/a?id=1683.
14. Reid, Thomas. Essays on the Intellectual Powers of Man. Edinburgh University Press eBooks, 1785. DOI: 10.1093/oseo/instance.00106533.
15. Shoemaker, Sydney. “Against Simplicity,” in G. Gasser & M. Stefan (Eds.), Personal Identity: Complex or Simple? (2012), pp. 123–136. Cambridge: Cambridge University Press.
16. Zalabardo, José L. Introduction to the Theory of Logic. Boulder, Colorado: Westview Press, 2000.
17. Zimmerman, Dean. “Criteria of Identity and the ‘Identity Mystics’,” Erkenntnis, Vol. 48 (1998), pp. 281–301.

On Identity was originally published in Atlas Wept on Medium, where people are continuing the conversation by highlighting and responding to this story.

This essay largely labours to clarify the above question, as first strictly considered by Saint Augustine in The Literal Meaning of Genesis. None of what is written here is intended to be a rigorous read but rather an effort to entertain contraries for the sake of contemplation.

The established theological tradition of creation has run from Plato’s transcendental demiurge and Plotinus’ Neo-Platonic God into the Abrahamic creation narrative and Spinoza’s metaphysical position of pantheism. In dealing with these theses, interalia, we may make two primary distinctions. Creatio ex nihilo, the view which holds that the material world and all matter within it is not eternal and was created by a divine act of God. Creatio ex nihilo nihhil fit, an antithesis to the above, primarily rooted in not supporting the existence of a creator deity and instead postulating that the Universe was formed from endless, primordial, formless matter.

Creation here is broadly understood as the effort by which God causes an object to exist. Therefore, creating the cosmos necessarily implies bringing it from a state of non-being into one of being, which does not permit a transformation of pre-existing substances production ex materia where the word creation would then be inappropriate. Then, it is clear that the question presupposes a logical basis primarily grounded in ex nihilo theologies since any theory of eternal matter posits that God did not, strictly, create the Universe. Instead, one would rather consider him as a divine architect of some sort (Plato’s demiurge, for example). Answering this question then obviously presupposes the statement “God created the cosmos.” However, there exists sufficient debate to support that there is no clear answer to the problem of cosmic origin. Then, we may not concede so easily that God did indeed create the cosmos. In showing otherwise, we reduce the question to a matter of redundancy for if God were not the Creator, then the Abrahamic question falls prey to absurdity.

Granted the rigor, precision, and interconnectedness of theological and metaphysical views concerning creation, we will consider them, to the fullest extent possible, in a linear fashion. It must be subsequently noted that the answer to the question is not an absolute one since it largely depends on individual interpretation of translated scripture and is incomplete at the expense of contingent views. It is nonetheless our aim to consider the full theological treatment of creation theories to, at the very least, provide a relative resolution to the question.

Ancient views of creation

The dogma of ex nihilo creation is not reflected in early Sumerian or Bablyonian mythologies. The Sumerian Creation of the Pickax supports this eternal matter view, proposing the origin of the cosmos in the separation of the heaven from the Earth. The Babylonian creation epic Enûma Eliš similarly supposes an eternal chaos consisting of Abzû (fresh-water) and Tiamat (salt-water) from which the diety Marduk created Heaven and Earth. Unlike the Sumerian epic, Enûma Eliš goes further in its active consideration of what happened before the divine act of Marduk: a conflict between Marduk and the forces of chaos unravels to result in the production of the cosmos. As far as the ancient Egyptians are concerned, study of Papyrus Leiden I 350 and Utterance 80 of the Coffin Texts, show that they did not have a concept of matter as the later Greeks did but there still remains no evidence of any ex nihilo thought arising here.

Whether primordial matter with the Pre-Socratics, the notion of the δημιoνργoς (Artificer of the Universe) in Plato’s Timaeus, or Prime Matter in Aristotle’s Metaphysics, the Greeks all demonstrate a marked idea of some ex materia creation of the cosmos. It is almost a truism to contest that the process of creation described in the Timaeus is not to be conceived in the sense of time. Rather, the demiurge appears as some form of an Eleatic unity. It is also worth recognizing that it is not strictly correct to conflate the demiurge with the idea of God Himself since he is not omnipotent but is rather limited in creating the cosmos from pre-existing chaotic matter. However, because Plato’s demiurge is a striking parallel to the Judeo-Christian God, I will concede this transgression for the sake of theological argument. Further, Plato notes that as beings incapable of divine knowledge and transcedence, we may not possibly know the answer to this question. This is similar to some Gnostic views developed later.

Timaeus: And amid the variety of opinions which have arisen about God and the nature of the world we must be content to take probability for our rule, considering that I, who am the speaker, and you, who are the judges, are only men; to probability we may attain but no further.

In the Timaeus, the cosmos is thought to be the result of self-evolution of some absolute thought wherein there can be no discernibility between mind and matter for all that exists is the mind. Plato’s system then ends in a distinct form of pantheism, and any attempt to consider notions of “before the cosmos” is futile since creation appears to be a process independent of both time and space. Similarly, Aristotle’s exploration in Physics Book I shows a manifest contradiction ultimately concluding that the cosmos has existed eternally. Parmenides’ dictum ex nihilo nihil fit first appears in the same work and similar views were expressed by Lucretius in De Rerum Natura: “that nothing’s brought Forth by any supernatural power out of naught… Nothing can be made from nothing.” Lucretius also remarks tanta stat praeidta culpa in support of the same argument, maintaining that were the world to have been made by gods, there would not be so many things wrong with it. It is worth noting, however, that Aristotle’s work deals with teleological analysis and it was not he who was tasked with converting this into a cosmogony of any sort — -that was the work of the reception. This position of eternalism does not offer one the privilege of invoking any notion of God or creation. In all theological polemics, perhaps, the Epicureans were most likely to concern themselves with the eternalist view. Epicurean physics rejected any divine involvement in the creation of the cosmos since any evidence of it is derived from senses of the mind; so, as Epicurus notes, “if nothing existed, no concept of the world would be found in the minds of the gods.”

These creation theses go insofar as demonstrating how the earliest views of what one may consider ancient theology were grounded in the basis of primordial eternal matter and the concept of “something out of nothing” was foreign; it may be argued by the creationists that the infancy of cosmogonies relating to the early civilizations further suggests that theological thought was not sufficiently sophisticated to provide a rigorous and precise answer concerning our question. To this, I contest that the views of the Greeks were built in a manner to appease to logic. The Abrahamic creation narrative seems to be host to sufficient inconsistencies for us to side with the Greeks for now.

The Judaeo-Christian Narrative

According to the tafsirs (the exegises) of the Quran, Islam acknowledges three types of creation. ex nihilo in time, emanation, and productio ex materia. Given the rigor and grandness of the arguments supporting all three views, we do not wish to indulge ourselves in the problem of which one is accurate. So, instead, we will restrict ourselves to the Judaeo-Christian concept of God and interpretation of the Genesis.

In the beginning, God created the heaven and the Earth
Bereshit bara Elohim et hashamayim ve’et ha’aretz.

Genesis 1:1 forms the basis of ex nihilo thought emerging in Judaeo-Christian doctrine of creation. Some scholars still support this view, while others believe, on exegical grounds, that the Book of Genesis is not strictly concerned with the origin of matter. The problem of interpreting the transliteration is not of immediate concern here. Instead, we espouse the views of the former (as done by Aquinas and St. Augustine, along with other Christian Fathers) in saying that the Genesis supposes an ex nihilo creation.

Some people, in order to discover God, read books. But there is a great book: the very appearance of created things. Look above you! Look below you! Note it. Read it. God, whom you want to discover, never wrote that book with ink. Instead He set before your eyes the things that He had made. Can you ask for a louder voice than that? Why, heaven and earth shout to you: “God has made me!”
 — Sermon 126.6, Saint Augustine

Inspired from Plotinus’ Enneads and Plato’s Timaeus, it can be contested that the question, even in the Judaeo-Christian sense, remains improper since one could equally argue that time was itself created at the beginning of the cosmos. In fact, our understanding of time only dates to as far as back the Universe existed, for one cannot subsist without the other. This can be credited to the very nature of time being rooted in an experience of change; as Aristotle notes in Physics, time is “a number of change with respect to the before and after.” So, the lack of a “before” is sufficient in determining the lack of time, since the existence of both a before and an after are necessary for our experience of time. My view is contested by those that believe the question itself is a futile effort since Man is restrcted by divinity. Similar to Plato’s views, this is reflected in Adverses Haereses by Irenaeus:

If, for instance, anyone asks, “What was God doing before he made the world?” we reply that the answer to such a question lies with God himself. For that this world was formed perfect by God, receiving a beginning in time, the Scriptures teach us: but no scripture reveals to us what God was employed about before this event.

This emphasis on unknowability and incomprehensibility of the divine is reflected throughout Gnostic, Christian, and Jewish theology. The question then dissolves into a manner of incapability and is not satisfying to the theologist. This is, in some senses, a trivial resolution. Perhaps, as is noted by some earlier thinkers, one could say God was resting before creation. However, if one does concede that God had rested before creating our cosmos, why did He not continue to rest? To this, I would argue, as done by Origen in Book III of the Peri Archon, “it is alike impious and absurd to say that God’s nature is to be at ease and never move.” Further, unlike Irreaneus’ admission of impropriety, Origen does pursue an answer in saying that before creation of this world, there existed others and God may have been presumably involved in them. However, it could be rather easily be contested that this is solely a product of his own speculation as there appears no record in Scripture of worlds before or after ours.

In all, I contend that even espousing the Judaeo-Christian narrative of creation only leads one to either an inability to answer or an answer that suggests time could not have existed before the cosmos. If considering an ex materia view, it is then also apparent that the question is a manifest absurdity since God did not create the cosmos and so it is futile to ask what He did before it. So, I concede that the question remains futile not because we cannot know but because it is grounded wrongly in the presumptions that either, God created the cosmos, or time existed before the ex nihilo creation of the cosmos.

As always, thank you for reading!

On God and Creation was originally published in Atlas Wept on Medium, where people are continuing the conversation by highlighting and responding to this story.

Philosophy is notorious for raising more questions than it answers: if this is held to be true, it is perhaps more true of aesthetics, the branch of philosophy that examines all that which humans hold to have aesthetic value.

Every form of expression possesses in virtue of its capacity to elicit pleasure when experienced. The quantity qualifying this — more precisely, the quantity qualifying the ability to make valid judgments about an object’s aesthetic value — can be naively thought of as taste. First commanding philosophical attention in the 18th Century, the concept of taste labored to correct the school of rationalism, which held the position that beauty is determined by reason. The aesthetic rationalism view was largely championed by Les Géomètres, a group of theorists who aimed to bring to literary criticism the mathematical rigor that Descartes had brought to physics. It was against this that alternative theories of taste were developed. These antitheses find their fountainhead in the idea that judgments of beauty are not (or at least not canonically) mediated by inferences from principles or applications of reason, but rather have all the immediacy of straightforwardly sensory judgments. It is the idea, in other words, that we do not reason to the conclusion that things are beautiful, but rather “sense” that they are — that one’s cognitive ability is not responsible for the recognition of beauty. The wise and foolish man will have similar accounts on the aesthetic value of some expression. Kant expands on this in his Critique of the Power of Judgment.

If someone reads me his poem or takes me to a play that in the end fails to please my taste, then he can adduce Batteux or Lessing, or even older and more famous critics of taste, and adduce all the rules they established as proofs that his poem is beautiful… . I will stop my ears, listen to no reasons and arguments, and would rather believe that those rules of the critics are false … than allow that my judgment should be determined by means of a priori grounds of proof, since it is supposed to be a judgment of taste and not of the understanding of reason. — (Kant 1790, 165)

In other words, we never conform to reason in discerning whether a Caesar salad is good or bad. We don’t need to define the qualities of each ingredient, we don’t then need the salad to settle into the reasonable principles of taste, and we certainly don’t need to examine the proportions of its mixture in order to decide whether it’s good or bad. This is never practiced. We have a sense given to us by nature to distinguish whether something has been created in accordance to the principles of its art. Even those unacquainted with the rules of the salad will be able to tell whether it’s good or not. Dubos, in his Critical Reflections on Poetry, Painting, and Music, echoes a similar sentiment, proposing that the same immediacy thesis may be applied to human productions.

But aesthetics would not have reigned over much of the eighteen century, nor would it continue to now be a studied field, if it lacked resources to counter an obvious rationalist objection. There is a wide difference — so goes the objection — between judging the excellence of a Caesar salad and that of a poem. More often than not, poems and plays — and whatever such productions of the human mind may be called — admit a degree of complexity. In assessing and comprehending such complexities, one requires substantial cognitive work. The examined literary work, as some would contest, is far more profound in its beauty than the unexamined. Judging the aesthetic value of poems and plays, then, is evidently not immediate and so not a matter of taste.

We now meet a paradoxical understanding. The chief way of meeting this objection was first to distinguish between the act of grasping the object preparatory to judging it and the act of judging the object once grasped, and then to allow the former, but not the latter, to be as concept- and inference-mediated as any rationalist might wish. This is fairly convoluted but Hume expresses this idea with his characteristic clarity as follows.

[I]n order to pave the way for [a judgment of taste], and give a proper discernment of its object, it is often necessary, we find, that much reasoning should precede, that nice distinctions be made, just conclusions drawn, distant comparisons formed, complicated relations examined, and general facts fixed and ascertained. Some species of beauty, especially the natural kinds, on their first appearance command our affection and approbation; and where they fail of this effect, it is impossible for any reasoning to redress their influence, or adapt them better to our taste and sentiment. But in many orders of beauty, particularly those of the fine arts, it is requisite to employ much reasoning, in order to feel the proper sentiment. (Hume, 1751, Section I)

Alternatively, one could contest that maybe, as Plato suggests, beauty is tantalizingly obvious; we’re all drawn to it, and we all recognize it when we’re confronted with it. Like the Sirens themselves, beauty calls out to us. Now, obviously, there will exist art that looks like it was scribbled by a five-year old but still enjoys a privileged place in the confines of a reclusive billionaire’s room. But these fringe cases are constructed for the exact purpose of challenging our intuition of what we think beauty is. We use our capacity to recognize beauty, even though we can’t recognize it perfectly. In this view, we are forced to believe that the subjectivity of beauty is an illusion.

Alternatively, when people look at beautiful statues, explore drop-dead gorgeous gardens, or listen breathtaking music, they enjoy all these things for their intrinsic virtue and not for their incidental capacity to bring forth associations. As Aristotle mentions in Nicomachean Ethics III, a lion can enjoy seeing a gazelle only as a potential meal and never for its beauty. Aristotle’s ideas point to what we today call aesthetic disinterestedness, a brainchild of Kant. The word disinterested should not be perceived to mean a lack of interest exhibited by being indifferent. Instead, its focus is on the artwork itself, which speaks to finding satisfaction in the way the work of art appears; for its own sake. When individuals find satisfaction of an aesthetic nature in an object of art using disinterestedness, they are essentially seeing the object in or for itself; the enjoyment is being extracted from the object in its own right as opposed to what the purpose of that project is. And in another passage from the Nicomachean Ethics, Aristotle clearly implies this:

A virtuous person, as a virtuous person, takes pleasure in [others’] actions that express moral virtues, and is upset by actions caused by moral vices, just as a musician enjoys beautiful songs but finds bad ones painful.
(Nicomachean Ethics IX)

When we take to the evolutionary approach, as the world has post-Darwin, we recognize that much of the physical beauty we’re drawn to serves some sort of evolutionary advantage. Why do we think bi-lateral symmetry is more beautiful than radial? What if your face possessed rotational uniformity? Historically, the point, although fairly hand-wavy, is there seems to be some sort of advantage to beauty. If that’s true, then we’d all agree largely on what is beautiful — which we seem to. It’s the same reason we prefer pesto over soap and salads over dirt. We’ve evolved to appreciate some things a lot more than others — Monet over a stick figure, Van Gogh over me, and Shakespeare over your English teacher. On this view it’s the objectivity of beauty that’s an illusion — beauty is completely subjective, it just happens that our respective subjectivities happen to coincide as a consequence of evolution.

Of course, beauty meets the same problem as morality. We, more often than not, know what is right and what isn’t — when faced with having to exercise our morality and duty, we usually know what to do even if we don’t do it. Similarly, beauty can be recognized viscerally and we know what it is even if we can’t define it. You can exercise your judgement on something you cannot fully comprehend. But without a concrete definition, it’s hard to say whether it’s an objective or subjective concept. Maybe certain things that we create, or certain features of the world, are in some sense objectively beautiful, and some other things we call beautiful are subjectively so because they appear to mimic those objective things to some people. I’m just rambling here, because I don’t have a conclusive definition of “beauty” and I’ve seen enough failed attempts to put me off trying.

I hope I’ve shed some light on the field of aesthetics here, though this is hardly a conclusive answer. Beauty appears, at times, objective and subjective, because we all recognize it but none of us can exhaustively describe it. As always, thank you for reading!

On Aesthetics, Caesar Salads, and Taste was originally published in Atlas Wept on Medium, where people are continuing the conversation by highlighting and responding to this story.

Dynamics is the science of how things move. The fundamental principles of classical mechanics were laid down by Galileo and later Newton in the 16th and 17th centuries. In writing Principia, Newton gave us three laws of motion and one law of gravity. Fundamentally, this pretty much wraps it up for classical mechanics. Given a collection of particles, acted upon by a collection of forces, you draw nice little arrows, subject the system to the infamous F = dp/dt and call it a day. All you need is patience, some physics, and a sufficiently powerful computer. But as Tong notes, from a modern perspective, this is a little unsatisfactory. It’s sometimes messy and sometimes hard to deal with problems that are large, not to mention those that aren’t ideal.

In what follows in the next articles, we will describe the advances that took place during the centuries after Newton by some of the most important giants of mathematical physics: Lagrange, Euler, Hamilton, and Jacobi. It’s maybe fascinating to note that the mathematical methods and ideas developed in classical mechanics follow through most of physics — every theory of Nature, from electromagnetism and general relativity, to the standard model of particle physics is best described in the language this field develops. We will fly through most of high school physics but on a more nuanced level.

In this article, we will introduce the mechanics Newton handed us. For the more interested reader, I’d direct you to these notes by Stephen Siklos on Dynamics and Relativity but most of what we cover here should suffice.

Newtonian Mechanics

Classical mechanics concerns itself with the motion of particles. To clarify the situation, we begin with a definition.

Definition. A particle is an object of insignificant size.

It perhaps doesn’t sit right to leave things at “insignificant” but we truly do mean exactly that; particles are usually understood in the one-dimensional sense, that is, their property of being points. In questions concerning mechanics, you sometimes treat electrons, nuclei, and even spherical cows as particles. We admit this logical transgression since (as we’ll show later), we can effectively treat most objects through their center of mass. The validity of this statement, of course, depends on the situation; in computing the Earth’s orbit around the sun, we may treat it as a particle but in understanding Earth’s angular velocity, we treat it as an extended object.

Describing particles

To describe the position of a particle we need a reference frame; a choice of origin and a set of Cartesian axes which can describe the particle’s position, r, in some space. The particle’s motion is described by r(t) and consequently its velocity is denoted as

A comment on vector differentiation.
If a vector is denoted as r = (x₁, x₂, x₃) then its derivative is

Geometrically, the derivative lies tangent to the path r(t). In studying classical mechanics, we will be working with vector equations — three, coupled, differential equations where each corresponds to a component in the vector space (x, y, or z). We will frequently come across situations where we need to differentiate vector dot-products and cross-products. They are as follows. For two arbitrary vector functions r(t) and y(t)

As usual, it doesn’t matter what order we write the terms in the dot product, but we have to be more careful with the cross product because the cross product of two vectors a and b is negative of the cross product of b and a. Vector functions will often be embedded in what we call equations of motion. The complete behaviour for a system is not given to us outright, but rather is encoded in these differential equations. The study of classical mechanics primarily concerns itself with this precise quantity; it is the method by which equations of motions are obtained and solved.

Laws of Motion

Aristotle held that objects move because they are somehow impelled to seek out their natural state. Thus, a rock falls because rocks belong on the earth, and flames rise because fire belongs in the heavens. To paraphrase Wolfgang Pauli, such notions are so vague as to be “not even wrong.” The earliest sufficiently rigorous framework was developed by Newton. This is usually presented in three axioms. The laws of motion are as follows.

• A body remains in uniform motion unless acted on by a force.
• The force acting on a body is equal to its rate of change of momentum.
• For every action there is an equal and opposite reaction.

While it is worthy to try to construct axioms on which the laws of physics rest, Newton’s attempts fall somewhat short. For example, on first glance, it appears that the first law is nothing more than a special case of the second law. (If the force vanishes, the acceleration vanishes which is the same thing as saying that the velocity is constant). But the truth is somewhat more subtle. Newton’s First Law states that a particle will move in a straight line at constant (possibly zero) velocity if it is subjected to no forces. Now this cannot be true in general, for suppose we encounter such a “free” particle and that indeed it is in uniform motion, so that r(t) = r₀ + vt. Now, if we instead chose to measure it in a different coordinate system whose origin moves as O(t) then in this frame of reference, our particle’s position will be

and if the acceleration of this origin is non-zero (again, perfectly plausible; consider bodies interacting gravitationally), then by merely shifting frames we’ve rendered Newton’s laws false — a free particle does not move in uniform rectilinear motion when viewed from an accelerating frame of reference. Therefore, to maintain consistency, together with Newton’s Laws comes an assumption about the types of reference frames we permit. We call these inertial frames. A transformation from one frame κ to another frame κ’ which moves at a constant velocity relative to κ is called a Galilean transformation. In fact, this is not the only Galilean transformation. There exist ten such transformations under which inertial frames remain inertial.

• Three rotations: κ → Aκ where A is a 3x3 orthogonal matrix.
• Three translations: κ → κ + c for some constant vector c
• Three velocity additions: κ →κ + vt for some constant velocity v

You can convince yourself of these by considering the effect each of these transformations have on the relationship between the two reference frame. For more on this, check out my previous article which delves into the Galilean group more rigorously.

Classical Dynamics: Appreciating Reference Frames

A note concerning orthogonal matrices. Forgive me being pedantic but a square matrix with real numbers or elements is said to be an orthogonal matrix if its transpose is equal to its inverse matrix. Or we can say when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix. For the more casual reader, an orthogonal matrix, when used as a transformation, does not change the length or angles of vectors in a coordinate system. In other words, it is a special type of linear transformation that preserves the geometry of the space.

The tenth transformation does not consider the reference frame in a spatial sense — a time translation is also considered Galilean, t → t’ where t’ is some constant different from t. The equations of motion of classical mechanics are invariant (do not change) under Galilean transformations which make up the Galilean group. There exists another (but quite trivial) transformation which is κ → λκ for some scale factor λ; this is to say that we can measure different reference frames using different units (eg. meters and parsecs) and still maintain our intertial-ness.

Translations tell us that there is no special point in the Universe. Rotations tell us there is no privileged direction. And boosts tell us there is no special velocity. Physics is the same regardless (within classical limits, of course). The first two are fairly unsurprising: position is relative; direction is relative. You define your position and direction with respect to other bodies. In itself, it means little to say I live four kilometers. You must specify from where and in which direction. The “no special velocity” rule (yes, the speed of light is special but we’re working within the framework of classical mechanics which never did admit for such a case) tells us that there is no such thing as absolute stationariness. You can only be stationary with respect to something else.

We have already mentioned that Newton’s laws are to be formulated in an inertial frame. But, importantly, it doesn’t matter which inertial frame; notice that’s why I say “an” intertial frame. In fact, this is true for all laws of physics: they are the same in any inertial frame — something we know call the the principle of relativity. The earth’s surface, where most physics experiments are done, is not an inertial frame since it’s subject to centripetal acceleration about the sun. In this case, not only is our coordinate system’s origin — somewhere in a laboratory on the surface of the earth — accelerating, but the coordinate axes themselves are rotating with respect to an inertial frame.

That’s all from me. Thank you for reading and have a great day!

Introduction to Dynamics: Inertial Frames was originally published in Quantaphy on Medium, where people are continuing the conversation by highlighting and responding to this story.

The first major philosopher to call himself an idealist was Kant. He asserted (if not clearly in the first edition of his Critique of Pure Reason (1781) then in his Prolegomena to Any Future Metaphysics (1783)) that idealism does “not concern the existence of things”, but rather identifies that our “modes of representation” of them are not “determinations that belong to things in themselves”. Instead, they are features of our own minds. In a desperate effort to prevent confusion with Berkeley’s ideas, Kant labored to distinguish his position as empirical realism combined with transcendental idealism—industry jargon for the proposition that space and time are ineliminable properties of our experience but not real properties of things as they are in themselves. In other words, the view that reality is merely a formal feature of how we perceive objects — that it’s not, as we’d like to believe, something existing absolutely. Rather, it’s a pure form of human intuition contributed by our own faculty of sensibility.

In the Fourth Paralogism, Kant clarifies the following.

To this [transcendental] idealism is opposed transcendental realism, which regards space and time as something given in themselves (independent of our sensibility). The transcendental realist therefore represents outer appearances as things in themselves [Dinge an sich selbst], which would exist independently of us and our sensibility and thus would also be outside us according to pure concepts of the understanding. — The paralogisms of pure reason (A), A369

He expands on this in the Critique.

We have sufficiently proved in the Transcendental Aesthetic that everything intuited in space or in time, hence all objects of an experience possible for us, are nothing but appearances, i.e., mere representations, which, as they are represented, as extended beings or series of alterations, have outside our thoughts no existence grounded in itself. This doctrine I call transcendental idealism. — The Antinomy of Pure Reason Section Six, Transcendental idealism as the key to solving the cosmological dialectic, A491 / B 519

Transcendental is a term that deserves special clarification. By this, Kant means that his philosophical approach goes beyond mere consideration of sensory evidence and requires an understanding of the mind’s innate modes of processing that sensory evidence.

In his work, Kant neither denies the existence of things independent from our representations of them nor asserts that these things must be mental in nature; the transcendental idealist part of his position cannot be straightforwardly identified with idealism as he understood it or as we are understanding it here, namely, as the position that reality is ultimately mental in nature. While Kant thinks that he has given a sound argument for the transcendental ideality of space and time, he holds that there is no reason at all to question the existence of things independent from our representations of them. That’s where I find, he fails. Kant was close and so was Berkeley but Schopenhauer nailed it.

There are two parts to this story: the object and the subject. The object can be thought of as the collective set of all things perceivable; it’s the entire world as we know it. Now, the existence of a perception necessitates a perceiver, the one to whom the perception belongs. This is the subject, the haver of the idea — the being that exercises agency. The sentence you are now reading is the object and you, the subject. What’s perhaps worth noting is that these are inseparable. You can’t have one without the other — there’s no thought without a thinker, and you’re not thinking if you don’t have thoughts. Any attempt to separate “object” and “subject” into truly different things, rather than parts of the same idea, heralds failure.

But that’s not enough nearly enough. We aren’t happy being told that reality lies beyond our grasp. Those before Schopenhauer had admittedly approached the problem from the outside looking in, rendering any effort at understanding reality pointless. But Schopenhauer realized that we are in the world as much as anything else; our bodies are objects just like the laptop I’m writing this on. What sets my hand apart from the cup of coffee it holds? What if my body were just the object I’m closest to, and I had no more control over it than your body, which is also an object to me?

So, if objects encompass all perceivable states, and these states don’t exist absolutely, what is innate to our reality? Schopenhauer’s resolution was the Will. Schopenhauer argues that the world we experience exists solely as “representation” (Vorstellung, German for perception) dependent on a cognizing subject, not as a world that can be considered to exist in itself (i.e., independently of how it appears to the subject’s mind). One’s knowledge of objects is thus knowledge of mere phenomena rather than things in themselves.

Schopenhauer identifies the thing-in-itself (Ding an sich selbst)— the inner essence of everything — as the Will: a blind, unconscious, aimless striving devoid of knowledge, outside of space and time, and free of all multiplicity. The world as representation is therefore the “objectification” of the Will. Oddly enough, the thing-in-itself is an idea introduced by Kant in his Prolegomena. It is worth noting that Kant offered no resolution here. Schopenhauer's methodic approach nailed a problem that neither Kant nor Berkeley could. He led us to the Will.

And we indeed, rightly considering objects of sense as mere appearances, confess thereby that they are based upon a thing in itself, though we know not this thing as it is in itself, but only know its appearances, viz., the way in which our senses are affected by this unknown something.— Prolegomena, § 32

Schopenhauer’s philosophy holds that all nature, including man, is the expression of an insatiable will. It is through the will, the in-itself of all existence, that humans find all their suffering. The desire for more is what causes this suffering. He argues that only aesthetic pleasure creates a momentary escape from the will. Schopenhauer’s concept of desire has strong parallels in Buddhist thought. Buddhism identifies the individual’s pervasive sense of dissatisfaction as driving craving, roughly similar to what Schopenhauer would call the will to live. Both assert that remedies for this condition include contemplative, ascetic activities.

Schopenhauer says that our Will is all that sets our body apart from any other object; the Will manifests itself in the movement of the body. Emotions? Just violent movements of the Will, as these too cause the body to react, whether the heart races, the hands sweat, or the breathing slows. Only the Will allows us to take the body beyond an object of perception. Aesthetic experiences release one briefly from an endless servitude to the Will, which is the root of suffering. True redemption from life, Schopenhauer asserts, can only result from the total ascetic negation — the indefinite renunciation of all instinct and desire — of the “will to live” (Wille zum Leben). The will to live is an idea Schopenhauer put forth, but similar instances can be found in Freud’s pleasure principle. Schopenhauer described it as an irrational “blind incessant impulse without knowledge”. There is a fundamental agreement between his philosophies and those of Plato and the ancient Indian Vedas.

What sets man apart is his ability to reason, to replace perception with abstract ideas — not only do we perceive individual things, but we can categorize them and reason about them. No lower being could succeed in such an exercise. The idea behind every abstract idea, the highest idea, is pure unadulterated Idea— the idea of being an object for the subject. It may sound like nonsense rambling at this point but this is the crux of most reason. This Idea is the ultimate reality — Idea itself. But the Idea rests on notions of object and subject and if we strip this away, only one thing remains: the Will, which is the thing-in-itself that Kant thought we couldn’t know.

If the whole world as representation is only the visibility of the will, then art is the elucidation of this visibility, the camera obscura which shows the objects more purely, and enables us to survey and comprehend them better. It is the play within the play, the stage on the stage in Hamlet. — Schopenhauer, The World as Will and Representation, Vol. 1, Book III, §52

This was arguably one of the more philosophically convoluted articles I’ve written and neither Kant’s nor Schopenhauer’s works are straightforward for the amateur reader. Please let me know if there are any errors here and I’d be happy to correct them. Thank you for your time and have a great day!

On Cognition, Knowledge, and Nature was originally published in Atlas Wept on Medium, where people are continuing the conversation by highlighting and responding to this story.

Newton’s discovery of universal attraction in the 17th Century dramatically changed our understanding of the motion of celestial bodies. His law masterly reconciles two profound physical principles: the principle of inertia, put forward by Galileo and Descartes in terrestrial mechanics, and the laws of Kepler, written down in Astronomia Nova.

Newton, in computing the orbital quantities of planets, realized that his law of gravitation wasn’t entirely accurate. The unforeseen consequence of Newton’s discovery was to question the belief that the solar system is stable: it was no longer obvious that planets kept moving immutably, without collisions or ejections. This started a two-century long competition started between astronomers, who made more and more precise observations, and geometers, who had the status and destiny of Newton’s law in their hand. At the heart of this, was the N-body problem.

In what follows, we will create a simulation of N particles interacting through a common gravitational potential. Poincare and Bruns proved that the differential equations of this system cannot be generally be integrated in closed form (that is, in terms of elementary functions instead of infinite series). So, if we want any meaningful attempt at a simulation, we must rely on numerical methods.

The system is set up as follows. We will assume N particles indexed i = 1, 2, …, N, with masses m_i, positions rᵢ = [ xᵢ, yᵢ, zᵢ ], and velocities vᵢ = [vxᵢ, vyᵢ, vzᵢ ]. Following Newton’s law of gravitation, each particle feels a force

where G=6.67×10^-11 m³/kg/s² is the Gravitational constant. To obtain the acceleration of our masses, we will compute getAcceleration as follows.

function [a] = getAcceleration(pos, mass, G, softening)
%   pos  is an N x 3 matrix of positions
%   mass is an N x 1 vector of masses
%   softening is the softening length
%   a is N x 3 matrix of accelerations

x = pos(:,1);
y = pos(:,2);
z = pos(:,3);
dx = x' - x;
dy = y' - y;
dz = z' - z;

% matrix that stores 1/r^3 for all particle pairwise particle separations
inverse = (dx.^2 + dy.^2 + dz.^2 + softening.^2).^(-3/2);

ax = G * (dx .* inverse) * mass;
ay = G * (dy .* inverse) * mass;
az = G * (dz .* inverse) * mass;

% pack together the acceleration components
a = [ax ay az];
end

The softening term is added to prevent two particles being abysmally close to each other, in which case the acceleration from the gravitational law goes to infinity.

The above code is vectorized. Although storing intermediate calculations in matrices requires a lot of memory, it’s incredibly useful with interpreted languages; this can sometimes lead to a speedup in the order of tens.

To validate our code, we rely on energy conservation — we know that this quantity should be constant through the time evolution.

The first term is the kinetic energy, defined as the momentum squared over twice the mass. The second term is the gravitational potential energy. Our code computes these quantities and keeps track of the total energy, ensuring validation of our approximations.

function [Ek, Ep] = getEnergy(pos, vel, mass, G)

% Kinetic Energy:
KE = 0.5 * sum(sum(mass.* vel.^2));

% Potential Energy:
% positions r = [x,y,z] for all particles
x = pos(:,1);
y = pos(:,2);
z = pos(:,3);

% matrix that stores all pairwise particle separations: r_j - r_i
dx = x' - x;
dy = y' - y;
dz = z' - z;

% matrix that stores r for all particle pairwise particle separations 
r = sqrt(dx.^2 + dy.^2 + dz.^2);

% sum over upper triangle, to count each interaction only once
PE = G *  sum(sum(triu(-(mass*mass')./r,1)));
end

To specify the initial conditions to our system, we’ll randomly choose values from a Gaussian distribution. You can set this up using the randn function in MATLAB.

For numerical integration, we use a leapfrog scheme which employs a kick-drift-kick form.

The evolution is performed in the code using a for-loop.

for i = 1:Nt
    vel = vel + acc * dt/2;
    pos = pos + vel * dt
    acc = getAcceleration(pos, mass, G, softening);
    vel = vel + acc * dt/2;
    t = t + dt;
end

The separation of the acceleration calculation onto the beginning and end of a step means that if time resolution is increased by a factor of two (Δt →Δt/2), then only one extra (computationally expensive) acceleration calculation is required.

There are two primary strengths to leapfrog integration when applied to mechanics problems. The first is the time-reversibility of the Leapfrog method. One can integrate forward n steps, and then reverse the direction of integration and integrate backwards n steps to arrive at the same starting position. The second strength is its symplectic nature, which sometimes allows for the conservation of a (slightly modified) energy of a dynamical system (only true for certain simple systems). This is especially useful when computing orbital dynamics, as many other integration schemes, such as the Runge–Kutta method, do not conserve energy and allow the system to drift substantially over time.

Finally, we use another for loop, for i = 1:ceil(end_t/dt), we run the leapfrog integrator and save the energies and positions for a plotting trail. Below is a result of the our simulation.

Find the GitHub repository here. That’s all from me. Thanks for reading and have a great day!

The N-body Problem was originally published in Quantaphy on Medium, where people are continuing the conversation by highlighting and responding to this story.

Kant’s Groundwork for the Metaphysics of Morals, Chapter 1

It’s impossible to think of anything at all in the world, or even beyond it, that could be considered good without limitation except a good will. Anything else is up for abuse. Understanding, wisdom, judgment, courage, resolution, perseverance, whatever such talents of the mind may be called, are undoubtedly good and desirable but they can also be extremely evil and harmful if the will with which they’re used isn’t good.

History stands as a testament to this. Hitler’s perseverance, the Manhattan Project’s collective genius, Genghis Khan’s leadership; crusades, colonialization, slavery. Any oppression of the greater human project has resulted from somebody’s extraordinary capabilities. It’s only the presence of a good will that prevents chaos.

For the coolness of a scoundrel makes him not only far more dangerous but also immediately more abominable in our eyes than we would have taken him to be without it. — Kant, Groundwork for the Metaphysics of Morals. Chapter 1

Kant’s ideas are largely based on subjective consequentialism, championing the value of intention over that of an act itself. Consequences aren’t what make a good will good; it’s inherently good. Taking a few minutes out of your day to help the old lady cross the road is a good act. Now, if you get her run over, things get a little blurry. Kant, unlike objective consequentialists, argues that your goodness is founded in your intention of helping the old lady; that neither usefulness nor fruitlessness can change the goodness of your act.

In the natural constitution of an organized being, Kant assumes as a principle that there is no faculty for an end other than what the organism’s end is itself. In other words, there is no part of any sensible design that serves a purpose different from the design’s ultimate purpose — to include an accelerometer in a laptop is insanity. So, if we must consider that the highest good — the ultimate function of man — is happiness (pretty reasonable), we must also concede that Nature or God or whoever’s in charge has seriously screwed up in gifting us with reason. Instinct is beyond enough to achieve pleasure and happiness; to be victims of reason serves no real purpose to our “highest good”. Galileo’s efforts made him nonetheless happier than the colonial British who rejoiced in India’s depredations. Van Gogh was manically depressed, Boltzmann killed himself, Ehrenfest took a bullet to his own head, Woolf was an insomniac, Kafka lived a tormented life, Darwin was unhappy, and Hemingway was riddled with paranoia. It’s not often that you find those whose functions align entirely with their happiness. So, why did any of them commit to their own purpose? Answer: to produce that good will you’ve already heard so much about. We must use our reason to drive our good will.

Now, this does not mean that reason should be the ultimate arbiter of life. Those who have experimented with reason, if only they are candid enough to admit it, fall prey to a certain degree of misology. In allowing reason to govern, you find that it has in fact only brought upon more troubles than it has brought happiness. You then finally envy rather than despise the more common run of people, who are closer to the guidance of mere natural instinct and don’t allow reason much influence on their behavior. We must admit then that reason is founded in a far worthier purpose of our existence, to which, therefore, and not to happiness, we destine ourselves.

It is reasonable to believe that Nature has everywhere gone to work purposively in distributing its faculties and capacities and so there must be a function for reason in the human experience; if this function is not that of happiness, which we hold to be the supreme good, the true vocation of reason must be to produce a will that is good, not perhaps as a means to other purposes, but good in itself for which reason is absolutely necessary. That, however, doesn’t translate to discarding happiness; it’s in the fundamental nature of man to pursue pleasure and pleasure he pursues. That’s reasonable too (pun intended). But how exactly does reason help good will? Enter: duty. We all know what duty is. It takes a strong reason to determine one’s duty, and a good will to execute it — these are right actions, actions that are ends in themselves, and actions done because we have an obligation to do them. Duty, like morality, lies in some implicit understanding of the mind. We can’t quite tell what duty itself is unless confronted with the problem of exercising our duty.

To be benevolent where one can is a duty. But many are so sympathetically attuned that, without any ulterior motive of vanity, they find inner satisfaction in spreading joy around them. Kant asserts that although such an action conforms to duty, it nevertheless has no true moral worth and is on the same footing with other inclinations; the inclination here being that of inner satisfaction.

Suppose, then, that the mind of this philanthropist were overclouded by his own grief, which extinguished all sympathy with the fate of others, and that while he still had the means to benefit others in distress their troubles did not move him because he had enough to do with his own; and suppose that now, when no longer incited to it by any inclination, he nevertheless tears himself out of this deadly insensibility and does the action without any inclination, simply from duty; then the action first has its genuine moral worth. — Kant, Groundwork for the Metaphysics of Moral, p. 12

After all, helping somebody because they offered you a fiver isn’t all that great anyway. Kant champions the view that we have an obligation to ignore our inclinations, even if they point us in the right direction. An action is only truly worthy when one does it because they must, because they have a duty to do so, and not because of some greater inclination to honor, fame, or satisfaction. Help people out even if nobody’s watching, donate to charity even if the world doesn’t hear of it, and be a good man even if it doesn’t make you feel good. The only worthy actions are those that come from a place of duty.

That’s character, doing the right thing when you don’t want to — doing it solely out of the virtue that it’s right. We’re not commanded to love our enemy. That’s insane. You can’t command love. But you can command the act of it — we’re commanded to act with love, good will, and respect to even the most atrocious people.

For, love as an inclination cannot be commanded, but beneficence from duty — even though no inclination impels us to it and, indeed, natural and unconquerable aversion opposes it — is practical and not pathological love, which lies in the will and not in the propensity of feeling in principles of action and not in melting sympathy; and it alone can be commanded — Kant, Groundwork for the Metaphysics of Morals, p.13

Only actions done from duty have moral worth. I’ve said that a dozen times now. Simple enough. But more than that, they have worth because we will them from duty, never because of some aim we attain or even intend. As Kant puts it, the worthiness of an action lies in the maxim in accordance with which it is decided upon. So, it doesn't depend on the realization of the object of the action but rather only upon the principle of volition in accordance with which the action is done. Do we have a duty to help little children and caterpillars and old ladies cross the road? Yes, but those actions aren’t right because somebody is being helped, they’re right because we are rightly motivated. This motivation comes from duty.

Having spoken so much about duty, it’s important to consider where it comes from. Kant holds the stand that duty comes from respect for the law. What law, you might be wondering? Roman law? Immigration law? International maritime law? No.

All so-called moral interest consists simply in respect for the law. I ought never to act except in such a way that I could also will that my maxim should become a universal law. — Kant, Groundwork for the Metaphysics of Morals, p.15

That’s the law we’re talking about. We want to always act in a way such that we wish everyone would act. This doesn’t necessarily mean acting in a way that yields the outcome everybody wants (since, clearly, outcomes don’t matter). This also doesn’t mean acting from those desires we think everybody should or does possess (since, again, inclinations don’t matter). Kant means that we must be guided by a principle that supersedes our desires and the outcomes, such that our guiding principle is a universal one, and was it the case tomorrow that a pigeon gained reason, it would know our law as well. If your actions held true for yourself and for others, would the resulting inconvenience still justify your moral transgression? Respect for the law is an estimation of a worth that far outweighs any worth of what is recommended by inclination and that the necessity of action from pure respect for the practical law is what constitutes duty. You can’t “never lie except when it’s convenient”, “keep promises unless they have bad consequences”, or “only help people when you feel like it”. Any such maxim is to be repudiated because its universality is detrimental.

If lying is wrong, it’s wrong for everyone. If theft is wrong, it’s wrong for everyone. If killing is wrong, never do it. If something is wrong, it is wrong whatever the consequences. Kant holds that even in situations where benefits to the majority might ensue, wrong things are wrong and you must fall back on virtue because duty calls.

If adversity and hopeless grief have quite taken away the taste for life; if an unfortunate man, strong of soul and more indignant about his fate than despondent or dejected, wishes for death and yet preserves his life without loving it, not from inclination or fear but from duty, then his maxim has moral content. — Kant, Groundwork for the Metaphysics of Morals, Chapter 1, p.11

Now, it’s never easy to abstract away from our inclinations and desires. We’re instinctively driven to satisfy these. And sure, we have some intuition about what’s right and what’s wrong but it’s easy to say that conflicts between morality and desire result in our transgressions of the law. That’s what makes philosophy so important — to restore our sense of duty, to remind us of reason, and to allow us our morality. We’re then sorted in the long run. Probably.

As always, thank you for reading!

On Reason, Morality, and Duty was originally published in Atlas Wept on Medium, where people are continuing the conversation by highlighting and responding to this story.

Aristotle’s Nicomachean Ethics, Book 1

Every art and every inquiry, and similarly every action and pursuit, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim. — Aristotle, Nicomachean Ethics/1.

Nicomachean Ethics is undoubtedly Aristotle’s most profound teleological work: the science of the good for human life, that which is the goal or end at which all our actions aim. It is the canonical text of virtue ethics and much of what is published today makes extensive references to the work of Aristotle either as a foundation or a foil.

We don’t do things for no reason. We have our motivations, whatever these motivations may be. We don’t bumble through life arbitrarily with no hopes or desires. Instead, we seek goods instrumental to some other goods, like steps on a ladder. This implies the existence of some final good; some good that we desire for its own sake, with everything else being desired for the sake of this. If such a good did not exist, we would be victims of some infinite causality, seeking instrumental goods would be an end in itself. This is a manifest absurdity. Clearly, then, there must be a chief, final good.

Everyone pretty much agrees that this ultimate good is happiness — serotonin, oxytocin, dopamine, endorphins, call it whatever you’d like. The problem is, not everyone agrees on what happiness is or how to get it. The many do not give the same account as the wise. The general account of happiness is that it remains some plain, obvious thing like pleasure, honor, or wealth. But often the same man identifies it with different things — pleasures conflict all the time. The hungry man and the sick man will disagree on what happiness means. This is certainly not the right answer.

You could equally contest that happiness lies in honor and we should seek that. But honor is instrumental to virtue and to value honor means to value virtue more; honor is only an incidental achievement. This remains somewhat incomplete since the possession of honor does not afford one a privileged reference frame; honor is sweet but it cannot be the end at which all our actions aim.

Now, the Platonic resolution is to concede and admit that we are after the Form of the Good and not chief goods themselves, whatever that means. The definition of the Good, as Plato saw it, is a perfect, eternal, and changeless Form, existing outside space and time. Aristotle argues Form of the Good does not apply to the physical reality for Plato leaves “goodness” unassigned to anything in the existing world. Since Plato’s idea does not explain human behavior nor arises from it, we do not have any reason to believe that such a form exists and thereby its purpose is irrelevant to human ethics.

Plato, however, did have a defense. Through Socrates in The Republic, Plato acknowledges the Form of the Good is an elusive concept that should be appreciated as a hypothesis, rather than criticized for its weaknesses. The only alternative to accepting a hypothesis is to refute all its propositions, which is counterproductive to the process of contemplation.

If good can be attributed to specific virtues or just the property of being virtuous, then it must be something common we can account for in different experiences, just as how white characterizes both snow and paper and heat characterizes both the desert and the summer. But of honor, wisdom, and pleasure, just in respect of their goodness, the accounts are distinct and diverse. We can then firmly conclude that the Form is not very productive to our exploration of the good.

Aristotle clarifies that when we say final good, we mean it without qualification; that which is always desirable in itself and never for the sake of something else. So, happiness isn’t some other thing we need to identify and seek — it’s the reason we do things. It’s certainly not a good instrumental to some other greater good. Nobody wants to be happy because being happy makes them feel anything other than, well, happiness. It’s the aim of all our activities, we’re always seeking it, and it’s self-sufficient. Here, we mean, as Aristotle does, self-sufficiency in the sense that “which when isolated makes life desirable and lacking in nothing”. Happiness is always the final good. That conversation is short. “Why do you want to be happy?” “Because… it’s happiness, genius.”

But let’s entertain a contrarian perspective and say happiness isn’t the final good; that there is something else, something more “final” than happiness. Aristotle says that for all things that have a function or activity, the good is thought to reside in the function. So, in our Nicomachean efforts, this would require us to first ascertain the function of man. Everything has a purpose, and good things accomplish their purpose well. A good writer writes well and a good singer sings well. Anybody that has ever been good at any other thing has characteristics that allow them to pursue their function “well”. Then, we must ask what makes a good human. Aristotle proposes that what sets us apart in our sentience is our soul: our ability to recognize virtue.

What makes people happy? Being good at what they’re supposed to be good at. When has an A on a test ever disappointed you? When has being the best at something ever been a miserable experience? And when has doing something well made you unhappy? Aristotle attests that our highest purpose is virtue and to be happy, we have to perform this function well.

Human good turns out to be activity of soul in accordance with virtue.
 — Aristotle, Nicomachean Ethics/11.

“But Aristotle, virtue is hard. It doesn’t make me happy to be virtuous. Why do you say that? What’s virtue anyway?” Well, anything worth doing is difficult, and being the best at something is always hard. Virtue is an acquired habit of excellence. Nobody has the privilege to just sit around and be happy because they deem themselves virtuous. It’s your word against mine; have fun arguing that in court. You want to win the Olympics? You have to work for it. The Oscars? Work for it. A Nobel Prize? Work. Any mark of excellence in one’s function requires sweating it out and putting in the hours. How do we distinguish the best from the second best? How do we know the fastest and the strongest? It’s the hours they’ve put in.

And as in the Olympic Games it is not the most beautiful and the strongest that are crowned but those who compete, so those who act win, and rightly win, the noble and good things in life — Aristotle, Nicomachean Ethics/13.

At the heart of the Nicomachean Ethics is the question about what it means to be an excellent human being — what it means to perform the function of a human well. We know what it means to be a good writer, a good scientist, and a good driver, but what about a good human? Aristotle argues that a good human is one who is virtuous, which is a person who knows the good, wants the good, and acts for the good. Now you may want to attack the Aristotelian approach for championing the subjectivity of “good” but let’s be real here, more often than not, we know what’s good. There’s always an innate understanding of what we’re doing. There is some morality in us. This defines our humanity. This is a good rule of thumb for most of life. We don’t need to get down into the specifics of what being virtuous means; we know what it does.

Virtue is difficult. A virtuous man enjoys his virtue and virtue has to be learned but it cannot be taught. For what good is a virtuous life if it conflicts with the ordained pleasures of life? It’s not a switch you flip and oh, now I’m virtuous so I must be happy. Pleasure is a state of soul, and to each man that which he is said to be a lover of is pleasant; a horse is pleasant to the lover of horses, a hamster to the lover of hamsters, and justice to the lover of order. This is in the same way virtuous acts are pleasant to the lover of virtue. The man who does not rejoice in noble actions isn’t noble himself. Therefore, virtuous actions must be in themselves pleasant. Aristotle says “Happiness then is the best, noblest, and most pleasant thing in the world.”

Aristotle says it is worth recognizing that happiness isn’t something achieved momentarily. True happiness takes a lifetime, or however long it takes for one to become a lover of virtues and a disciple of virtues. Ask the dead man. He’ll know whether he’s happy because happiness isn’t something you do, it’s an end you achieve. It’s the end you achieve.

“But Aristotle, what about those situations governed by chance? What about the misfortunes life brings?” Yet even in these nobility shines through, when a man bears with resignation many great misfortunes, not through insensibility to pain but through greatness of soul.

If activities are, as we said, what gives life its character, no happy man can become miserable; for he will never do the acts that are hateful and mean. For the man who is truly good and wise, we think, bears all the chances life becomingly and always makes the best of circumstances, as a good general makes the best military use of the army at his command and a good shoemaker makes the best shoes out of the hides that are given him; and so with all other craftsmen. And if this is the case, the happy man can never become miserable; though he will not reach blessedness — Aristotle, Nicomachean Ethics/16.

And since all of this starts with the soul, it must end with it as well; we have to know the soul, both the rational and the irrational dimensions of it. When we allow the irrational part to govern us, things get out of hand. I mean, they really get out of hand. Yes, it feels good to fulfill our most innate desires. Yes, Schopenhauer was right about the will to live. And yes, Freud said the same about the id ego. But when shit (excuse the profanity) hits the fan, you’re left bogged down in the consequences of your actions. Is it ever worth it? No, not if you’ve abandoned virtue — this is a road to misery. There’s nothing wrong in living the life of a hedonist as long as you remain true to your virtues and morals. Without it, we’re horses mindlessly trotting. The only resolution lies in being virtuous both of mind and of character. And as you learn these, Aristotle bets you become wise and temperate and happy.

As always, thank you for reading.

On Happiness, the Function of Man, and Virtue was originally published in Atlas Wept on Medium, where people are continuing the conversation by highlighting and responding to this story.

20th-century physics says everything is made up of point particles with a bunch of different properties. But where do these properties come from and where does gravity fit in?

Particle physics is a bit of a misnomer — modern understanding suggests these particles are excitations in quantum fields. So, really, field physics is more appropriate — this is incomplete too since we fail to explain gravity. Turns out, we can get a self-consistent explanation of all particles and gravity if we concede that they’re tiny little strings. The way these strings vibrate determines their properties and ultimately, the particle. Instead of points tracing out lines (as in Feynman diagrams), these strings trace out two-dimensional surfaces as they move through space and time. This is how we describe interactions between them.

As for the nature of these strings, it turns out they can be both open and closed loops and their vibrational mode defines their characteristics. Now, the unification of particle physics and gravity is certainly a victory so what’s wrong with string theory? Well, for the theory to even begin working, you’d need upwards of 11 dimensions, and then some exotic ideas follow through. Bosonic string theory is 26-dimensional, M-theory is 11 while superstring theory only requires 10.

We only experience three spatial dimensions and one temporal dimension. So, we have to think of ways these other dimensions are hiding. Compactification is one way of modifying the number of dimensions in a physical theory. We assume some of the extra dimensions are “closed up” on themselves to form circles. A standard analogy for this is to consider a multidimensional object such as a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. However, on approaching the hose, you’d discover that it contains a second dimension, its circumference. So, an ant crawling on the surface of the hose would move in two dimensions while we’d only perceive one.

And finally, to make matters worse, It doesn’t help that we’ve had no experimental triumphs vindicating this theory because strings are theorized to be in the domain of Planck lengths; the smallest theoretical length.

As always, thank you for reading and have a great day (or night)!

String Theory in Three Minutes was originally published in Quantaphy on Medium, where people are continuing the conversation by highlighting and responding to this story.

Communism, Exploitation, and Revolutions

For my digital footprint, it would be wise to preface this. No, I’m not a communist.

Communism is a lot more than just pigeons in a parliament nodding in unison, yelling “yes, comrade!” In fact, the Manifesto is perhaps one of the most profound accounts of sociopolitical theories but it’s often alienated under the misguided judgement that reading communism makes one a communist. No, it doesn’t.

“A spectre haunts Europe — the spectre of communism. All the powers of old Europe have entered into a holy alliance in order to lay this spectre: pope and tsar; Metternich and Guizot; French radicals and German police.”
 — Karl Marx. Chapter 1, the Communist Manifesto.

Humanity has always been one large class struggle. That’s all we really are: victims of the sentient ego. Our unimportance has us building systems to differentiate ourselves on some vaguely unimportant features. Ancient Rome was maybe our most primitive effort at keeping the poor, poor, and the rich, rich. The patricians and the plebians, a historical first. Of course, feudalism followed and was largely just a knockoff, besides its glorified decentralization. Slavery — well, obviously we know how that goes. Soon came capitalism with the bourgeois and the proletarians, a modern second. Through all of this and everything else, however, oppression has always looked the same — it’s all just the rich trying to be rich, dividing us into the cans and the cannots, the able and the unable. And we always end in revolution, except it never ends. We build problems and then throw solutions at them, only to find that our solutions bring more problems than we had to begin with.

And back in the day, oppressors at least pretended to have more noble, ominously virtuous reasons for all the — excuse the profanity — crap they pulled. Divine mandate, the greater good, social contract, whatever. But in Marx’s time, the struggle was not between those who could convince and those who could get convinced. The class struggle was between those with capital and those without: the bourgeois and the proletariat. There was no “divine purpose”. It’s money. What’re you going to do about it? Either you’re in or you’re out, either you can exploit or you’re exploited. This was the capitalist’s creatively rousing and honest defense.

It’s worth noting that the communist agenda, at its core, isn’t natural. It’s not the general inclination of human behavior to achieve a communist state — no, the impetus for communism comes from the failures of capitalism. It’s to say “Hey, this doesn’t work. It has some insanely awful consequences. Try this instead”. But what exactly is the problem with capitalism anyway? Why should you care?

As a species, we aren’t getting anywhere. There is no greater goal. We’re a machine that serves no purpose. Occasionally a riot breaks out; sometimes a union forms, real problems hit the Wednesday afternoon news headline, and people talk about things. But nothing is really changing. Think of the grandest of things humanity can achieve. Think of space revolutions, ambient-pressure superconductivity, solving housing crises, and fixing poverty. Think of harmonizing a species. None of that will be achieved under a capitalist state — the sole purpose of capitalism is not to make the human experience better, but rather to throw money at it. The aggregate suffering of humanity has only increased with time and the turn of the industrial revolution stands a testament to that.

This problem, albeit on a more microeconomic scale, was largely recognized by Marx and the likes of him. The Manifesto proposes a solution through the abolition of private property.

Communism isn’t as scary to understand as we think it is. The theory of the communists may be summed up in a single sentence: abolition of private property. Now, the modern man would obviously contend that he worked hard for his property and that his fathers and forefathers struggled. Why should anyone take it away? Who is anybody to say what can be owned and what cannot? But the modern man fails to recognize that the idea of private property has been destroyed.

Does wage-labour create any property for the labourer? Not a bit. It creates capital, i.e., that kind of property which exploits wage-labour, and which cannot increase except upon condition of begetting a new supply of wage-labour for fresh exploitation. Property, in its present form, is based on the antagonism of capital and wage labour.
 — The Manifesto, Chapter 3

Here’s the crazy thing that often goes unnoticed. Nine-tenths (a severe euphemism) of the population have already had their private property abolished. No one has anything, except the tenth that has everything; the communists only hope to equalize those conditions. The 85 richest in the world have as much wealth as the 3.5 billion poorest, giving them the freedom to disregard the human condition.

“But Marx, why is communism such a violent experience?” There is no greater state that protects the proletariats. There’s no reason to be a part of some social allegiance beyond one that unites their cause. And so, they turn to political revolution, to take back capital. It is only owning the means of production that affords one the privilege of disregarding others. Marx recognized this.

Communism doesn’t inherently have a problem with capital. There’s no conflict here. The only conflict is the oppression that arises as a result of capital. So yes, revolutions and radical changes will be draconian. And yes, they have to be. There is no other way. You cannot fix the capitalist system. You must replace it entirely. The Manifesto predicted that proletariats would one day rise up in a revolution and its materialization is often seen as one of communism’s largest failures. But there is no way we can do it peacefully because we have been lulled into complacency for so long. We find ourselves comfortable in mediocrity. A sleeping species.

As always, thank you for reading!

On Marx and Engel’s Manifesto of the Communist Party was originally published in Atlas Wept on Medium, where people are continuing the conversation by highlighting and responding to this story.