I do math. Pretty much from sun up to sun down. A lot of people can’t relate to that. Why would a person care so much about a thing like that? Math isn’t going to save the world. The math I do — as is the case for a great many mathematicians — has no practical applications whatsoever. From the “outside view,” it looks like a lot of work that just doesn’t need to be done.
I’ve puzzled over why math might be something worth caring about that much — something worth sacrificing one’s life for. Part of the answer is, art. Math is beautiful. I have been bowled over in aesthetic ecstasy by theorems. I have reacted to proofs and definitions in exactly the same way that I react to a brilliant song or a painting. This isn’t a common experience for those not intimately involved with math; but it is reason enough to justify the funding that math departments get. To keep that experience available to humans is an important social service.
Suppose we were to end war, end poverty, end disease. What then? We would have an awful lot of time to kill, and it would be a sorry situation if we had nothing to beautiful with which to fill that time. Some arts seem to suffer these days from the artists having run out of ideas. But math is not out of ideas.
Despite the outside impression that every mathematical question has been answered, in actual fact we have more open problems than we could possibly begin to approach; and the number only increases as we learn more. I do not doubt that math will continue to keep humans fervently preoccupied until the implosion of the universe. And the indications are that it will only grow more beautiful and more fascinating.
But there are many things of which this could be said. There are many entertaining things other than math; there are many beautiful and fascinating things, other than math. Most of them are more accessible and less stressful to do. What does math uniquely offer to humanity?
I think the unique and central contribution of math is not beauty. It the fact that math is the clearest window which humans have onto the truth. Every academic discipline is a window on the truth; but all agree that math is the brightest and clearest. In math alone, truths can be established beyond all doubt, left to withstand the test of eternity without the possibility of revision or improvement. In all other sciences, truth is tentative and can be overturned by new discoveries and new ways of thinking. In math alone, everything is already perfect, and cannot be any different than it is.
Mathematicians do not disagree for long; every disagreement is quickly resolved, in the direction of the person who is actually right. A totally unknown person can, with no budget, make a mathematical discovery and show it to the top mathematicians in the area. If the result is correct, it will be accepted. There is no room for politics and social games; in math alone, the truth shines so bright that it outshines all of that.
The truths of math usually do not matter, in a worldly sense. But this is, in a sense, beside the point. Humans need truth, independent of all other concerns. We do not need truth only so that we can develop new medicines and navigate the oceans. We need truth simply to know truth and be in relation with reality, and know with assurance that we are in such a relation. Math is the only thing which can provide us with that, with the purity and fullness which it does. And that is why I do it.
Nowadays I am doing my writing over at eh-na.com. I am essentially retiring this blog.
By the way, we are looking for people interested in writing on rational mysticism, to contribute to eh-na.com. Let me know if you are interested in this.
A few pieces of evidence regarding aliens:
- UFO sightings have been regularly reported and carefully recorded for decades.
- Similarly for crop circles.
- Similarly for abduction experiences.
- There are ancient artifacts could not have been constructed by the humans of the time. Who made them?
- The Mexican government has admitted the existence of aliens, and former US government officials have claimed that the US government knows that aliens exist and is not telling anybody.
Of the first four items, each represents a large area of research, with numerous data points and theories. In each case, some of the data points have been debunked; some of them appear very difficult to debunk, with a variety of skeptical explanations definitively ruled out; and the vast majority are ambiguous.
Is there any piece of evidence that “puts the nail in the coffin” regarding aliens? Well, aliens have never landed in the middle of Times Square on a Monday afternoon.
But what does it take to really nail down a proposition? Presumably none of these individual data points are enough by themselves to nail down aliens. But there are millions of them. You can’t say that they’re all hoaxes. Well, you can, but at that point a certain razor needs to step in.
So I ask again, what does it take to really nail down a proposition? What standard of proof do we require? A lot of ideas are widely accepted and credible, on far less evidence than what we here have on offer. Academics accept the DSM, set theory, Martin Heidegger, and so forth, on far less evidence than what we have put forth here.
Infallible proof is talked about more often than it is actually obtained. Compared to the number of ideas that have been floated since the inception of knowledge, the number of ideas that have been truly “nailed down” is miniscule. (It seems like a larger proportion of the total ideas because we keep on teaching those same few ideas over and over to every person who goes through school.) And even those few ideas aren’t nailed down in an absolute sense.
I would put aliens in an epistemic position similar to that of dark matter. We can’t see dark matter, or aliens. But we can deduce, detective-style, that it’s hard to explain how the universe holds together without dark matter, or aliens. Note, not “impossible to explain,” but “hard to explain.” Which in the case of dark matter, is enough to make us believe.
Why do we feel differently about aliens? I think it’s not because the evidence isn’t good enough. It’s not a lack of evidence that makes us reluctant; it’s something else. What?
- The issue is important. If aliens are actually interacting with humans behind the curtains, that has huge implications for the future of humanity and our place in the universe. The more important something is, the more evidence we demand.
- Though there is no lack of evidence, all of the evidence is ambiguous. In some ways, a huge mass of ambiguous evidence is less convincing than a small amount of unambiguous evidence. Statistically speaking, a large amount of ambiguous evidence is probably no less weighty than a small amount of unambiguous evidence; but it’s less cognitively accessible.
- The idea is completely divergent from how we understand the world. Forget quantum physics; forget black holes and dark matter; forget evolving from apes; this is weird. A lot of people feel like aliens are somehow inconsistent with science. They aren’t; they don’t challenge materialism, reductionism, empiricism, or anything else. But there’s still this unshakeable feeling of, this is inconsistent with reality as I understand it. And it is.
 The “ancient aliens” argument has been criticized on the grounds that it is fallacious to infer from an unexplained phenomenon (artifacts that humans of the time could not have built) to the explanation of aliens. But it’s not so fallacious. We can safely say that things like statues and artistic landforms are made by sentient beings. If humans didn’t do it, some other sentient beings did. We know of no appropriate sentient beings, besides humans, that exist on Earth. If they’re not from Earth, they’re from somewhere else.
Lately I’ve been having to get up at six in the morning, for Zen practice. This is bad because I have insomnia and generally terrible sleep patterns. Here are some things I have found that help. Some of them are tips from my master; thanks, Haju!
1. Do not sleep at odd hours! Not under any circumstances!
2. Don’t do stimulating things in the evening. In my case these include: computer usage; eating sugar; intellectually demanding tasks. I try to reserve these activities for the morning or afternoon.
3. Chamomile tea.
4. Self-hypnosis works. I gather that a lot of people use elaborate techniques with visualizations, recitations, etc. to hypnotize themselves. In my case, for this task, I just invoke the feeling of comfortably dozing off, without the use of that sort of formal machinery.
Hey guys, look at all this truth I brought for you!
Oh, you don’t want any of it?
…Not a word?
I shouldn’t need
to dress up my intuitions in math
to make them acceptable to you.
But I’ll do it,
if it means you’ll finally listen.
First I believed everything I was told.
That’s what you do when you’re a child.
As a teenager I began to know things for myself,
and they told me I was wrong.
I was epistemically torn, and beaten, and battered
and bruised until finally I believed
that whoever has the power
is the one who’s right.
I fell for that ancient ruse,
like a rock off a cliff.
I played the game.
I believed only what I could force others to believe.
Damn could I play.
And I took all of this and began calling it “truth.”
But y’know, truth sort of has a different melody
than the one we’re singin’ in school.
I am sick of conspiring
in my own downfall because it’s easier
than standing up.
I can’t help if I contradict myself sometimes. The truth is a very strange place.
Our starvation is a physical manifestation of our inner hunger. Our infections are manifestations of our inner disease. Our wars are manifestations of our divisions within ourselves.
It is for this reason that people in America are depressed. When you remove the physical manifestations of suffering, the suffering does not go away; its spiritual nature simply becomes more obvious. Then we call it depression.
If you want to end world hunger, learn to feel full and happy. If you want to cure cancer, learn to be in harmony with yourself. If you want to fight pollution, learn to think pure and beautiful thoughts.
You can’t remove other people’s pain. But people can’t learn to remove their own pain if they don’t have an example to follow.
That poor man that you refused to help? That suffering animal that you neglected and let die? You are him. You are it. The world is your body; end your suffering and you end all suffering. Save yourself and you save the world.
Things I have found to be helpful for doing math:
2. Don’t guess and check. This can take subtle forms. E.g., “I have no real idea how to prove this theorem, but I think this method might work, even though I haven’t really thought it through; but I’ll try it, since I don’t have any other ideas.”
3. Start by understanding the question. If you really understand the question, usually the answer will be obvious. So you could just spend 95% of your thinking time trying to understand the question, and then the time you spend looking for an answer approaches zero, because it will just come to you.
4. If you have a hard question, try rephrasing it. Find a theorem that’s equivalent to the theorem you’re trying to prove, or find a structure that’s equivalent to the structure you’re studying. Hell, invent a new field of math if you need to (viz. Evariste Galois).
5. Math is about showing that things are the same when they obviously aren’t. Deep similarities behind obvious distinctness. 3 * 7 is the same as 21, a circle is homeomorphic to a square, addition and multiplication both form abelian groups. Usually when I solve a hard problem, 90% of the solution consists of ekeing out some deep similarity that seemingly has little to do with the hard problem, and then the remaining 10% is an easy solution to the hard problem that employs the deep similarity.