Six maps that will make you rethink the world. Not only are the maps beautiful, but the interview is pretty interesting too.
The math behind computational learning is hard, but Christopher Olah makes understanding it really easy. Every article of his is worth reading.
Forty-four percent of the way through the complete Sherlock Holmes works on Kindle and Mycroft is finally introduced:
“My dear Watson,” said he, “I cannot agree with those who rank modesty among the virtues. To the logician all things should be seen exactly as they are, and to underestimate one’s self is as much a departure from truth as to exaggerate one’s own powers. When I say, therefore, that Mycroft has better powers of observation than I, you make take it that I am speaking the exact and literal truth.”
“You wonder,” said my companion, “why it is that Mycroft does not use his powers for detective work. He is incapable of it.”
“But I thought you said—”
“I said that he was my superior in observation and deduction. If the art of the detective began and ended in reasoning from an arm-chair, my brother would be the greatest criminal agent that ever lived. But he has no ambition and no energy. He will not even go out of his way to verify his own solutions, and would rather be considered wrong than take the trouble to prove himself right. Again and again I have taken a problem to him, and have received an explanation which has afterwards proved to be the correct one. And yet he was absolutely incapable of working out the practical points which must be gone into before a case could be laid before a judge or jury.”
From the chapter on Leonardo da Vinci in Visari’s Lives:
Da Vinci would buy and the immediately release birds…
He was so pleasing in conversation, that he attracted to himself the hearts of men. And although he possessed, one might say, nothing, and worked little, he always kept servants and horses, in which latter he took much delight, and particularly in all other animals, which he managed with the greatest love and patience; and this he showed when often passing by the places where birds were sold, for, taking them with his own hand out of their cages, and having paid to those who sold them the price that was asked, he let them fly away into the air, restoring to them their lost liberty. For which reason nature was pleased so to favor him, that, wherever he turned his thought, brain, and mind, he displayed such divine power in his works, that, in giving them their perfection, no one was ever his peer in readiness, vivacity, excellence, beauty, and grace.
Was it karma? In another story, a Prince had commissioned a work from da Vinci, but da Vinci was not working on it, and the Prior grew worried…
Leonardo, knowing that the intellect of that Prince was acute and discerning, was pleased to discourse at large with the Duke on the subject, a thing which he had never done with the Prior: and he reasoned much with him about art, and made him understand that men of lofty genius sometimes accomplish the most when they work the least, seeking out inventions with the mind, and forming those perfect ideas which the hands afterwards express and reproduce from the images already conceived in the brain.
What can history teach us? From Chapter 1 of Hegel’s Introduction to the Philosophy of History:
Rulers, statesmen, and nations are told that they ought to learn from the experience of history. Yet what experience and history teach us is this, that nations and governments have never learned anything from history, nor acted in accordance with the lessons to be derived from it. Each era has such particular circumstances, such individual situations, that decisions can only be made from within the era itself. In the press of world events, there is no help to be had from general principles, nor from the memory of similar conditions in former times—for a pale memory has no force against the vitality and freedom of the present. In this respect, nothing is more trite than the repeated appeal to Greek and Roman examples, which was so commonplace at the time of the French Revolution. No difference could be greater than that between the nature of those ancient peoples and our own time.
The translator, Leo Rauch, footnotes an interesting quote from Hume:
See Hume’s Enquiry Concerning Human Understanding, Section VIII, Part I, “Would you know the sentiments, inclinations, and course of life of the Greeks and Romans? Study well the temper and actions of the French and English. … Mankind are so much the same, in all times and places, that history informs us of nothing new or strange in this particular.”
It’s worth noting that Hume lived in rather extreme poverty until he published a multi-volume history of England, after which he skyrocketed to fame and fortune in the intellectual atmosphere of his time. Surely such a deep study of history helped to inform his other writings.
The case for using computer algebra
Many academics and researchers get annoyed when students use computer algebra programs such as Mathematica to evaluate simple integrals that they maintain should be done by hand. The question I ask is “At what point do you expect your students to switch over to using a computer?”. Most mathematical examples are artificial in that closed form expressions exist. However, in nearly any real problem, this is not the case.
I learnt mathematics using slide rules and tables, then calculators, then computers, then symbolic algebra. To me, this is a valid progression — but not one that everyone should have to go through. I feel that the only way true progress can be made is if we don’t have to learn a whole set of rules. If we had to do calculus using Newton’s geometrical constructs then progress would be very slow. The real question is what are the essential tools and lessons. To me, knowing what a derivative and integral mean “physically” is far more important than knowing how to compute a specific integral.
Many people feel that reliance on computer algebra means that students can’t do calculus by hand and hence they really don’t understand what’s going on, just how to get the answer by computer. Calculus concepts are subtle. However, just knowing the mechanics of computing an integral or derivative does not imply understanding. I believe that it is possible to have true understanding without computation.
From a list of pet peeves of Paul Abbot, physics professor at University of West Alabama.
We learn nothing from those who say: ‘Do as I do.’ Our only teachers are those who tell us to ‘do with me’, and are able to emit signs to be developed in heterogeneity rather than to propose gestures for us to reproduce. In other words, there is no ideo-motivity, only sensory-motivity.
—Gilles Deleuze, Difference and Repetition, page 23
“I know that I am mortal by nature, and ephemeral; but when I trace at my pleasure the windings to and fro of the heavenly bodies I no longer touch the earth with my feet: I stand in the presence of Zeus himself and take my fill of ambrosia”
― Ptolemy, Ptolemy’s Almagest
My friend Carl and I recently had a short conversation about zen meditation. He brought up some points that all basically referred to the end goal of meditation: health and mindfulness benefits, etc. To which I replied that meditation is necessarily a goalless endeavor. Yes, meditating will make you think clearer and harmonize your body with your mind and all that, but if you go into meditation trying to do these things, then you will not achieve these things. That’s the paradox of meditation. And here’s a quick psychoanalytical explanation of why I think that is from a paper:
The “self” and the “ego” must not be confused to be the same. Instead we must understand the ego to be an element within the self, a device for the self’s cognition. The self creates a cognitive framework in which the ego may recognize (re-cognize) self from non-self, in which the ego may create its home, thereby completing the individual’s identity in what Levinas calls the “I.” The ego moves outward toward the world in understanding, adequating the world around it and reducing other to same: thus the ego is the totalizing element within the self. In order to totalize, the ego must be self-referential, it must return to itself in its process of adequation; thus the ego assumes a teleological structure.
This teleological structure is exactly the same as any goal-oriented task. You say “I want to accomplish X, and I will do Y to get it.” After doing Y, you have X. This posits the end, X, before acting out Y, thus it is teleological. This structure is absolutely related to the totalizing movement of the ego, so it could be called an egoism, for better or for worse.
Our society largely follows this general teleological trend, which may have been why Carl wasn’t used to the idea of a goalless endeavor (which he admitted to). Now, I’ve been doing zazen meditation for 4 years, and I’ve studied the Japanese Kyoto School of philosophy, so I should have a good understanding of this idea. Today I meditated for the first time in about 6 or 8 weeks, and I noticed that my mind was racing, all over the place. You’re supposed to let go of your thoughts, but I couldn’t – they just kept racing, it was terrible. Reflecting on that later, I realized what happened: I had been so entrenched in goal-oriented thinking (eg. programming, problem solving, generally trying to figure out life) over the past few weeks that my mind had conditioned itself to work teleologically: I was constraining my thinking to a known end goal. As soon as I removed that end goal by meditating, my mind unleashed it’s pent-up creative chaos and went every which way.
This release is a great thing! Since this morning, I’ve had a few good ideas relating to a paper I’m writing, and I’ve been super productive. But I have two important points to make:
- Even if we have an intellectual understanding of this goal-oriened framework and the downsides that come with it, the natural tendency of our ego is to revert back to it. The ego is a powerful structure in the psyche, it’s quite overbearing at times, and it takes continual practice to let it go. This is something that meditation accomplishes. Regression is possible: if you stop meditating, you may go back to egoism. And, because it is so powerful, it tends to manifest itself in multiple layers of our society, from the way we structure businesses (greed and power) to the way we approach relationships (why are you really friends with/dating this person? for the things you get out of it?).
- The mind is decidedly not consumed by the ego. It can release the ego when necessary, such as during meditation, or during the pop-psychology state of “flow.” And, when the mind is not consumed by the ego, it is allowed to freely produce. It can be creative to its fullest capacity. The immense ability for creativity is one of humanity’s greatest assets and something that should be sought after. Ay, this egoless, creative state, achievable and practicable via meditation, certainly should be valued.
I’m not saying meditation is the only way to go about egolessness, but it is a quite effective one, with little barrier to entry. Martial arts, painting and drawing, practicing mathematics, reading literature, playing sports; these can all be goalless endeavors.
From the little reading I had done I had observed that the men who were most in life, who were moulding life, who were life itself, ate little, slept little, owned little or nothing. They had no illusions about duty, or the perpetuation of their kith and kin, or the preservation of the State… The phantasmal world is the world which has never been fully conquered over. It is the world of the past, never of the future. To move forward clinging to the past is like dragging a ball and chain.
—Henry Miller, Sexus pages 262, 430; as quoted in Anti-Oedipus, pages 27-8