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Why math?

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.

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A Relocation

Nowadays I am doing my writing over at I am essentially retiring this blog.

By the way, we are looking for people interested in writing on rational mysticism, to contribute to Let me know if you are interested in this.

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Aliens? Aliens!

A few pieces of evidence regarding aliens:

  1. UFO sightings have been regularly reported and carefully recorded for decades.
  2. Similarly for crop circles.
  3. Similarly for abduction experiences.
  4. There are ancient artifacts could not have been constructed by the humans of the time. Who made them?[1]
  5. 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?

  1. 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.
  2. 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.
  3. 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.

[1] 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.

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I can’t help if I contradict myself sometimes. The truth is a very strange place.

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My eventual graduate thesis will be on the inconsistency of mathematics, and its implications. Topics will include:

  • A proof of the inconsistency of all theories of mathematics in first-order logic.
  • The equivalence of truth and provability, via Tarski’s truth schema.
  • The equivalence of all first-order theories of mathematics, via the truth schema.
  • The consequences of na├»ve set theory:
    • Properties of the set of all sets, including the combinatoric indescribability of its cardinality.
    • Infinitely deep sets, and a proof of the continuum hypothesis.
    • The existence of various large cardinals.
    • The existence of indefinable sets.
  • Whatever I figure out about the “singularity point” of mathematics: the location of the border between consistency and inconsistency in the hierarchy of increasingly strong theories.
  • My philosophy of mathematics, including mathematical nondualism: the view that every statement is ultimately true and false. As well as the view that formal proof does not solely dictate what propositions we are to accept.

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Why I do math

Lately I’ve been spending inordinate amounts of time doing math. From sun-up to sun-down it sometimes seems, learning and understanding and deriving. Why am I compelled to do this? I ask myself that a lot. It takes a more explicit form: why am I doing that instead of meditating?

I think the answer is that math is easy and rewarding. Not as rewarding as meditation, but quite a bit easier. Math easy? Esoteric graduate-level math, easy? Compared to meditation, yes. Meditation makes abstract algebra and topology seem like child’s play.

With the qualifier, of course, “for me.” I don’t think there’s some absolute scale of task-difficulty, where meditation is six levels higher than abstract algebra. I’m sure there are lots of people more enlightened than me, but less intellectually adroit, for whom abstract algebra would be quite a lot harder than meditation.

But still, for me abstract algebra is child’s play compared to meditation. And I don’t think this is just a fact about me. I feel comfortable saying that, in some general sense, meditation is immensely harder than math. It’s not just that I happen to find math really easy. Sure, I’m better at math than most people. But I’m also better at meditation than most people. It’s gotta balance out somewhat.

What makes math easier than meditation? No doubt a complex question, but I think the biggest factor is this: meditation is lonelier.

Let’s think about math. When I do math, nobody will tell me I’m wrong. (Except when I occasionally am. But that doesn’t upset me; they’re just bringing me back to the truth.) There are people I know who will actually talk about it with me, and we can actually understand each other, and actually agree with each other. I can ask them questions, and they’re delighted to teach me. I can teach them things, and they’ll learn something. And they’re impressed as hell with me because I’m so damn good at math.

I can even make a god damn career out of talking to people about math! I can get paid money to do this thing I love! There’s a shortage of me! I’m in huge demand!

Compare to meditation. It’s “weird” to be a mystic. It’s not socially accepted. I can’t share my experiences with anybody. Nobody will recognize my achievements. Nobody will appreciate my work. Nobody will even *know* what I achieved. I can have the most earth shattering mystical experience ever, and nobody will ever see that. Nobody will ever pat me on the back. And you can bet your ass that nobody will pay me to do it! Being a mystic is a lonely, lonely, lonely experience.

And I think that’s the reason I spent three hours doing math today, instead of spending three hours meditating. And this aching empty void is still sitting inside me because I didn’t spend enough time with God today.

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The Death of God: Pros and Cons

I have mixed feelings about Christianity losing its grip over the Western world. It’s not hard to see the reasons why it did. Christianity was forced upon the world: disagreeing with the Church could get you killed. And this is obviously doubly bad in the cases where the dictums being forced upon the world are arbitrary.

Using force on people rarely produces good results, and so I suspect that the compulsory Christianity was not terribly good at helping people to become more enlightened. Similar to how people go through twelve years of school and then forget it all, whereas if they had voluntarily sought teaching out of a pure passion for learning that wouldn’t happen.

I think that the illusion of people believing in Christianity probably exceeded the reality. That is, people professed belief in the various dictums of the Church, without believing them in their hearts. No doubt there was genuine belief also. But the more force you apply to people, the more people are going to start faking it.

So in that sense, I’m glad that Christianity has lost its grip over the Western world. But there’s another side to the issue.

I’ve pointed out, in the past, that it isn’t necessary to hold any particular propositional beliefs in order to be enlightened. And it isn’t necessary to be part of an organized religion in order to be enlightened.

It isn’t necessary, but it’s helpful. What it boils down to, I think, is that it’s difficult to value things other people don’t value, think things other people don’t think, and do things other people don’t do. There’s this incredible pressure to fall in line.

So if you’re living in a situation with no organized religion, it’s harder to be enlightened. This isn’t any remarkable fact. It would be hard to be a mathematician if universities had no mathematics departments; it would be hard to laugh in a society that was always serious; it would be hard to keep a heavy metal band going in a society where all music was mellow and relaxed.

This problem shows up for lots of things besides religion. Every marginalized activity becomes harder to do. In our society these marginalized activities include art, music, poetry, and being a woman.

So here’s the issue with having an atheist society. All of a sudden pursuing God is hard. And that’s a problem, because the religious need is at the heart of all human needs.

When we don’t have a broad consensus on what the meaning of life is, it creates a sort of a moral void, an existential ennui, where we’re just randomly floating through life with no direction or purpose. (Nietzsche, incidentally, predicted this, with his declaration that God was dead.) That’s what it’s like to live in an atheist society.

So do I think we should reinstitute compulsory Christianity? No. I think we need to find our way to a new societal religion — whatever the word “religion” might mean in this case. One that turns the clock forward rather than turning it back. One that isn’t a forced consensus, but something resembling a genuine consensus. One that integrates not only what we learned from Christianity, but what we learned from science, feminism, secularism, the New Age movement, existentialism, music, drug culture, modern art, Islam, Buddhism, Hinduism, Taoism, Judaism, occultism, martial arts, science fiction, capitalism, communism, activism, environmentalism, TV and movies, the invention of birth control, the Internet, abstract algebra, the dating scene, and on and on and on. One that is a cornerstone of our lives which resonates beautifully with the whole, rather than being awkwardly tacked on every Sunday morning.

We are one of few societies to have ever existed which did not have a religion. Some would tout this as a great innovation. I suggest that it is actually a form of poverty.

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On the Large and the Small II

When the scientists made a map of the universe
They measured the skies and said,
“Look! The Earth is so small compared to empty space!
The universe is almost entirely void!”

But when God made his map of the universe,
the very same void was shoved into a tiny corner,
and the Earth was giant and looming.
God did not measure his universe in meters and hectares.
God measured it in love, in suffering, in understanding.

As God measures it, the Earth where humans live and suffer
is orders of magnitude larger than the empty space around it.
The miles of empty arctic tundra
Are smaller than the one-person mattress on which I lay with my lover.
The birth of one human counts larger
than a thousand rearrangements of celestial gas clouds.
The shame that a person carries inside them
is heavier than the cargo which the freight train so effortlessly pulls along.
And one wild, implausible dream
carries more weight than a thousand mundane realities.

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Idealism and Materialism

Prior to the 20th century, there were two dominant positions in Western philosophy about the nature of existence: materialism, and idealism. Materialism holds that the world is made of matter: the stuff of the Earth, molecules and atoms. Idealism holds that the world is made of ideas: the world is precisely our experience of a plenitude of subjective images dancing before our consciousnesses.

Rationality is in support of materialism; all the evidence of science points towards materialism. Hence, with the rise of scientism in the 20th century, materialism has become the overwhelmingly dominant position in Western philosophy. But the materialism/idealism debate more or less lives on, with different vocabulary, in the form of the so-called “mind/body problem,” or the “hard problem of consciousness.”

Rationality speaks of materialism. Our mystical intuitions, on the other hand, speak to us of idealism. They tell us that the existence of the experienced is predicated on the experiencer; that all the multiudinous, dancing phenomena emerge from, and are grounded in, a numinous, immanent Self.

I would like to say that idealism is ultimately true. Materialism shallowly admits only the existence of that which we can see with our eyes. It fails to give the self its due. It notices everything outside, but never stops to look within and see the infinity that lies there. It is the sort of shallow, self-assured, fake wisdom that is typical of skeptics and scholars.

We can formulate the idealist thesis like this: existence is experience. This statement is an equation, unifying two fundamental philosophical concepts. Unifying equations are often important in science. Think of the unifying of light, magnetism, radiation, and electricity into the single concept of electromagnetism. Think of the unification of matter and energy. Similarly, I suggest the unification of existence and experience. (Not that this will constitute a scientific hypothesis.)

This equation mends a hole in our ontology: it tells us the ontological position of consciousness. The mind/body problem asks, in essence, “how does consciousness fit into everything?” It is a deep puzzle that is currently confounding some of our best philosophers. With our equation, the question melts away; consciousness is everything.

But I think that there is another sense in which we do not need to reject matter. Every experience we have, in this material world, is a duality split between matter and consciousness. A consciousness experiences matter. For instance, I (a consciousness) look at a table (matter). And it is always like that. So in this sense we say that materialism and idealism each have half of the picture, and we arrive at an ontology like Cartesian dualism.

We can then extend our mind/matter duality into a trinity: spirit/mind/matter. Spirit is the I, the most subjective. Matter is the “it,” the most objective. Mind is the middle ground in between them, both subjective and objective, the point where “I” and “it” meet.

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I used to spend a lot of time meditating. For a few months I meditated around three hours a day, while attending college. I don’t meditate any more.

I’m not any less enlightened than I was then. The difference is just that I don’t have my enlightenment regimented to occur at specific times in my day. What I didn’t realize then is that it’s all meditation, if you let it be. I don’t ever sit down and say to myself, “now I am going to meditate.” But that doesn’t mean that meditation isn’t happening. Like breathing or sneezing, it just happens, without me asking it to.

I had to get past several different thoughts. I had to get past the idea that I am naturally impure, and need to do something special to be enlightened. I had to get past my skepticism about my spirituality, which needed some observable, measurable indicator of my spirituality in order to believe in it. I had to get past the idea that it is a good idea to use force on myself to become more enlightened.

In retrospect, I think the need for a measurable indicator was the biggest reason that I meditated so much. The need for proof has a very powerful sway over me.

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