A wasted present

Many of my friends are retiring, having hit the tech jackpot. Was it a bad idea to leave tech? At the time, I really wanted to learn, not earn. Now that I have learnt, I want to earn. Or do I?

Time is my most precious gift. I waste too much of it. Schopenhauer says that is how it is meant to be.

What did you expect?

The Chicago school has based its entire macro premise on rational expectations, a point they claim Keynes did not get. But they forget that Keynes wrote a book on the theory of probability. (Of course once Kolmogoroff arrived, all previous work on probability was wiped out. But that’s a different story. See Terry Tao’s probability notes.)

Read Keynes’s take on expectations in part VII of this chapter

Note that the current Krugman-Summers debate is just this. Krugman says investors are rational and will fund exporters when a currency falls. Summers says investors may flee the country en masse, leaving exporters high and dry despite their export opportunities. 

It’s all expectations, whether love or macro. 

The human touch 

A friend of mine says he can never live alone: he always wants a human touch (sometimes a touch and another). But my human touch is currently flying somewhere across the universe. My friend says that I, unable to fly across the universe, am too afraid to touch again on this planet. I tell him my touch would have waited for me if I had died, as patiently and happily drowned in memories as I do now. 

“How do you know what Clement would have done?” my friend asks, who knows my answer. Because Clement lives in me. (We two always knew we are the same being in two bodies. We would have happily bought a place on the LES and lived a lifetime of theater and museums.)

But my friend is exceptionally astute. Is it really possible that Eternal Love is just a masquerade put out by the Fear of the New? 

Mindless porn

I read a great survey of Harvard’s class of 2014, where 58% of the men admitting to watching porn weekly (60% of the women had never watched porn). Bob Trivers’s  theory of parental investment indeed applies to humans. 

At a biological level, watching porn for men at least has an automatic fuse. Alas, there’s no such fuse for newsporn. You can mindlessly go from CNN to NYTimes to Breitbart to Drudge to Politico to Trump Twitter to Kevin Drum to whatever. And unlike real porn, it’s all good. 

Schopenhauer says life is a joke. He says men claim they want money and happiness. But send them to heaven where roasted turkeys fly in the sky and nubile women beckon at every corner. Every man will soon be utterly miserable and will not rest till he has created warring camps to fight with his fellow man (the same is true of chimps too). And he is compelled to do that, for that is in his Nature. 

So I am repeatedly surprised to find myself pulled to mindless hours of newsporn every night. Surely Schopenhauer cannot be this right?

Looks don’t mean anything

What is this guy’s deal?



His name is Artur Avila. He won the Fields Medal, the Nobel prize in math. These photos demonstrate why Munger’s article on our psych biases is genius, for the unbiased reality is that looks don’t count for math. 

And when we can’t control these biases, we eventually achieve sectarian violence and persecution of religious, ethnic and sexual minorities. We elevate the wrong people to leadership positions, who are then willing to inflict huge social losses for small personal gains.  We forget Lincoln’s words: freedom to the slave is freedom to the free. 

Spinoza risked his life to write about the social virtues of diversity that we in the West take for granted. Jonathan Israel puts Spinoza as the creator of us all. 

Thurston’s purpose

A Questioner on Math Stack Exchange asks:

I have to apologize because this is not the normal sort of question for this site, but there have been times in the past where MO was remarkably helpful and kind to undergrads with similar types of question and since it is worrying me increasingly as of late I feel that I must ask it.

My question is: what can one (such as myself) contribute to mathematics?

I find that mathematics is made by people like Gauss and Euler – while it may be possible to learn their work and understand it, nothing new is created by doing this. One can rewrite their books in modern language and notation or guide others to learn it too but I never believed this was the significant part of a mathematician work; which would be the creation of original mathematics. It seems entirely plausible that, with all the tremendously clever people working so hard on mathematics, there is nothing left for someone such as myself (who would be the first to admit they do not have any special talent in the field) to do. Perhaps my value would be to act more like cannon fodder? Since just sending in enough men in will surely break through some barrier.

Anyway I don’t want to ramble too much but I really would like to find answers to this question – whether they come from experiences or peoples biographies or anywhere.

The great Thurston responds:

It’s not mathematics that you need to contribute to. It’s deeper than that: how might you contribute to humanity, and even deeper, to the well-being of the world, by pursuing mathematics? Such a question is not possible to answer in a purely intellectual way, because the effects of our actions go far beyond our understanding. We are deeply social and deeply instinctual animals, so much that our well-being depends on many things we do that are hard to explain in an intellectual way. That is why you do well to follow your heart and your passion. Bare reason is likely to lead you astray. None of us are smart and wise enough to figure it out intellectually.

The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example any real reason that even such famous results as Fermat’s Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding.

The world does not suffer from an oversupply of clarity and understanding (to put it mildly). How and whether specific mathematics might lead to improving the world (whatever that means) is usually impossible to tease out, but mathematics collectively is extremely important.

I think of mathematics as having a large component of psychology, because of its strong dependence on human minds. Dehumanized mathematics would be more like computer code, which is very different. Mathematical ideas, even simple ideas, are often hard to transplant from mind to mind. There are many ideas in mathematics that may be hard to get, but are easy once you get them. Because of this, mathematical understanding does not expand in a monotone direction. Our understanding frequently deteriorates as well. There are several obvious mechanisms of decay. The experts in a subject retire and die, or simply move on to other subjects and forget. Mathematics is commonly explained and recorded in symbolic and concrete forms that are easy to communicate, rather than in conceptual forms that are easy to understand once communicated. Translation in the direction conceptual -> concrete and symbolic is much easier than translation in the reverse direction, and symbolic forms often replaces the conceptual forms of understanding. And mathematical conventions and taken-for-granted knowledge change, so older texts may become hard to understand.

In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. The question of who is the first person to ever set foot on some square meter of land is really secondary. Revolutionary change does matter, but revolutions are few, and they are not self-sustaining — they depend very heavily on the community of mathematicians.

All the world is a stage

Schopenhauer claims that modern education is crap because it teaches formulas and frameworks first, and then expects students to apply them to reality. This they naturally cannot do (which is why everyone from Sheryl Sandberg to Peter Theil dumps on MBA). We are oppositely constructed: to intuitively understand first and then abstract these intuitions later. Two entities who have understood this nature of the human mind thoroughly are Munger and the Mathematicians.

One of Munger’s most enduring papers is his list of 25 misjudgments. You can memorize his list, but you will still fail utterly in real life. It’s because Munger didn’t begin with his list. He gained real intuitive understanding of how he works, an understanding hard won through extended self-reflection, and then abstracted his intuitions into his list. This is why his lollapalooza is so hard to get, for most people.

Many great mathematicians have also recognized this. Atiyah says: In the day mathematicians prove, but at night they dream. Stellar math texts use exceptional motivating examples to pave the way to abstractions. Bill Thurston says that the purpose of math is not proofs, but understanding. A proof could be correct, but if people don’t “get it,” it will go nowhere. Thurston also asked people how they dream and visualize math. The answers show how astute Schopenhauer was.

When it comes to human affairs, however, nothing can rival theater for the purpose of understanding. Which is why I love plays in plays. What can be more fun than The Mousetrap Murder of Gonzaga in Hamlet? Or the Mechanical’s Play Pyramus and Thisbe inside the Midsummer Night’s Dream? The characters in the play are gaining understanding from the play in the play. And we spectators are getting a double dip along the way.

All social sciences, because they pertain to human behavior, can be taught through impromptu plays in the class enacted by students. The Merchant of Venice is a phenomenal primer of financial markets. Elasticity of demand, etc., can all be illustrated by having a desperate buyer in love buy a rose from a sole seller, and then having another seller show up on stage and upstage the first seller with a competing orchid.

It is a crime not to stage our own The Mousetrap Murder of Gonzaga and the Mechanicals in our classrooms to explain everything from the liquidity trap to the theory of comparative advantage.