Fecund Universe and The Blind Universemaker

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Imagine that there are many universes, not just the one we live in, and that they can reproduce; that one universe can have many children. If there is some mechanism that universes can use to pass on their “genes,” we would expect universes to evolve.

Think of it this way. Say we start with two universes, one who births four universes and one who births twelve. These universes would in turn reproduce, passing on some of their “genes.” The very fertile universes would in turn produce many fertile children who would produce many fertile children and so on, until most of the universes are very fertile universe.

Or, to put it in terms of humans, imagine a world where stupid people have many more children than smart people and that stupid people tend to have stupid children. Given that this is the case, the earth will soon come to be populated by stupid people.

This idea was proposed in 1992 by Lee Smolin, who speculates that universes reproduce via black hole formation; each black hole contains the seed of a new universe. If this is the case, we would expect that most of the universes in the multiverse are fertile ones, ones selected for black hole formation. Thus this theory is pseudo-testable. If it’s true, we would expect our universe to be tuned for black hole formation.

This speculative theory leads to the intriguing hypothesis that intelligence is selected for because it somehow aids black hole formation. Maybe the reason that we look up into the night sky and fail to observe alien life monopolizing the universe’s resources is that they’re busy producing black holes.

You can read more about it here. There’s also a book on the theory called The Life of the Cosmos.

An Argument Against An Agument Against Nihilism

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Skepticism, while logically impeccable, is psychologically impossible, and there is an element of frivolous insincerity in any philosophy which pretends to accept it.
—Bertrand Russel

The standard argument against nihilism – the notion that life is an affair devoid of meaning – goes something like this: Nihilists don’t actually believe anything they’re saying because they still act as though the world is ordered. They still value something, like freedom from pain, and this is revealed through their actions.

The implication, then, is that nihilism is bullshit. If people believed it, they would act differently, so you need to pay no attention to nihilism, because no one really believes it anyways.

This is not a satisfying refutation. The argument relies on the notion that one’s beliefs and one’s actions need to be aligned. If Andy says that he believes your pet Burmese python, Handsome, is harmless, but is hesitant to hold him, then Andy is a fucking liar.

But that’s brain damaged. You can believe something on one level while not accepting it on another. You can believe that the odds of being attacked by a shark are nigh non-existent, but still be afraid to swim in the ocean. You can believe that you really ought to stop eating unhealthy food and keep eating it anyways. I know that the Earth is hurtling around the sun at 67,000 miles per hour, but it sure doesn’t feel like it.

The behavior of those who hold a belief doesn’t speak to the accuracy of that belief. There are a lot of stupid atheists, but that’s not evidence either way as to whether or not there is a God. There are a lot of utilitarians failing to live up to the moral standards they set for themselves, but this doesn’t mean they don’t really believe it, and whether or not someone really believes something doesn’t speak to the truth of that belief.

If humans are incapable of being perfect nihilists, this is a fact about human capabilities, not about the truth of nihilism.

Categories for the Working Philosopher

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Elaine Landry is working on putting together a book, Categories for the Working Philosopher. The list of topics that various contributors are working on is broad, including model theory, special relativity, quantum mechanics and ontology, biology, computer science, foundations, and more.

John Baez has posted an excellent abstract of his planned contribution. It talks about what happens when we attempt to formalize intuitive notions of equality. Some exciting relationships fall out, such as understanding equivalence as a path between two points in a topological space.

In short, by formalizing the concept of sameness using isomorphisms instead of equality, we bring group theory, geometry and topology closer to the foundations of mathematics, giving them a kind of inevitability that they might not otherwise seem to possess. We also see that these three subjects are tightly connected. A lot of important mathematics, and also theoretical physics, flows from this realization.

I recommend checking out the entire thing. John mentions in the comments that there is a (less exciting) paper in the same vein here, and all of this ties into the recent work on homotopy type theory.

Epsilon-Delta Proof Intuition

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There’s a nice question on MathOverflow about the mental experience of mathematics. I tend to lean heavily on bodily sensations of motion and mental imagery when working on something mathematical: stretching, compressing, and movement. Proofs and algebraic manipulation often seem like a sort of flowing. (Something I’ve covered before in my post on reading math.)

But, anyways, here’s an excerpt from one of the responses that I think is particularly valuable. On epsilon-delta proof intuition and understanding:

One specific mental image that I can communicate easily with collaborators, but not always to more general audiences, is to think of quantifiers in game theoretic terms. Do we need to show that for every epsilon there exists a delta? Then imagine that you have a bag of deltas in your hand, but you can wait until your opponent (or some malicious force of nature) produces an epsilon to bother you, at which point you can reach into your bag and find the right delta to deal with the problem. Somehow, anthropomorphising the “enemy” (as well as one’s “allies”) can focus one’s thoughts quite well.

What’s deadlier: HIV or Smallpox?

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The annals of history are strewn with smallpox-infested corpses. The idealist thinks, “Ah, the past. What a barbaric era!” The cynic thinks, “Open your eyes. We have traded smallpox for the horrors of HIV/AIDs.”

To which we respond, as always, show me the numbers: smallpox killed an estimated one-third to one-half a billion people, while AIDs has killed 30 million people, a tenth as many. Terrible-future proponents would be better off scaring children with scenarios where tobacco use doesn’t peak and fall off in the developing world (India, China, and others) like it has in the USA, in which case we could see staggering death tolls, with one WHO report projecting as many as a billion tobacco-related deaths by the end of the century.

Further Reading

  • If you find this kind of reasoning compelling, you’ll probably enjoy Peter Singer’s talk here.
  • If you actually want to do something about it, check out GiveWell.
  • In the vein of preventing a terrible future, Nick Bostrom has a neat paper here.

Feynman on the Supernatural

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The nurse recorded the time of death, 9:21 P.M. He discovered, oddly, that the clock had halted at that moment —just the sort of mystical phenomenon that appealed to unscientific people. Then an explanation occurred to him. He knew the clock was fragile, because he had repaired it several times, and he decided that the nurse must have stopped it by picking it up to check the time in the dim light.
—from James Gleick’s biography of Richard Feynman

I was sitting in my chair a couple of days ago when it started to shake. I googled earthquakes. Nothing. Was there a cat beneath my chair? Didn’t find anything. A couple of hours later, the news reports that a nearby quarry blast caused a seismic event.

So bring me the supernatural in a jar and we’ll find out that it is made out of quarks (or whatever quarks are made of).

Bad at math? Have you tried steroids?

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Men with lower T performed better than other groups on measures of spatial/mathematical ability, tasks at which men normally excel. Women with high T scored higher than low-T women on these same measures.1

Our findings are the first that present the relationship between testosterone and the broad range of general IQ in childhood. The boys of average intelligence had significantly higher testosterone levels than both mentally challenged and intellectually gifted boys, with the latter two groups showing no significant difference between each other.2

Deliberately reducing testosterone levels in men, however, harms cognition, as evidenced by testosterone suppression in those with prostate cancer.3 If anything, the relationship seems to be reversed, with increasing testosterone improving cognition:

Significant improvements in cognition were observed for spatial memory (recall of a walking route), spatial ability (block construction), and verbal memory (recall of a short story) in older men treated with testosterone compared with baseline and the placebo group, although improvements were not evident for all measures.4

But wait! Another study found that boosting test levels among healthy men reduced spatial ability while improving verbal skills.5 One study speculates that the effects of testosterone on cognition are fixed after puberty, in which case, alas, there is still no royal road to geometry.6

Sources


1. Gouchie, Catherine, and Doreen Kimura. “The relationship between testosterone levels and cognitive ability patterns.” Psychoneuroendocrinology 16.4 (1991): 323-334.

2. Ostatníková, Daniela, et al. “Intelligence and salivary testosterone levels in prepubertal children.” Neuropsychologia 45.7 (2007): 1378-1385.

3. Green, Heather J., et al. “Altered cognitive function in men treated for prostate cancer with luteinizing hormone‐releasing hormone analogues and cyproterone acetate: a randomized controlled trial.” BJU international 90.4 (2002): 427-432.

4. Cherrier, M. M., et al. “Testosterone supplementation improves spatial and verbal memory in healthy older men.” Neurology 57.1 (2001): 80-88.

5. O’Connor, Daryl B., et al. “Activational effects of testosterone on cognitive function in men.” Neuropsychologia 39.13 (2001): 1385-1394.

6. Hier, Daniel B., and William F. Crowley Jr. “Spatial ability in androgen-deficient men.” New England Journal of Medicine 306.20 (1982): 1202-1205.

Sir John Harington on Treason

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I thought about titling this as “Sir John Harington on Selection Effects,” but treason seemed more compelling.

Treason doth never prosper: what’s the reason?
Why, if it prosper, none dare call it treason.

—Sir John Harington

How To Get Started With Anything

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A complex system that works is invariably found to have evolved from a simple system that worked. The inverse proposition also appears to be true: A complex system designed from scratch never works and cannot be made to work. You have to start over, beginning with a working simple system.
—Gall’s law

All life is an experiment. The more experiments you make the better.
—Ralph Waldo Emerson

The point of the post is this:
1. Try the dumbest thing that could work.
2. Start experimenting as soon as possible.

That’s it. Now I’m just going to go through examples to hammer the point home.

Get start with anything: Concrete examples

How do you train a dolphin to perform a backflip? You reward it for the right behaviors, which reinforces those, until you can chain it all together and get a backflip.

Thanks to Darwin, we know that humans are animals, too, and we know that a lot of the infrastructure our minds run on is shared with other animals. This means that a significant part of what makes you you is also what makes a chimpanzee a chimpanzee.

The takeaway, then, is that humans can be trained in a similar way to every other animal, with rewards for behavior. That’s positive reinforcement.

Okay, so here’s the scenario. You want to learn more math and intend to do this through solving math problems. You enjoy this once you get started, but you’re lazy. Your brain protests when you pull out the textbook. It just wants to watch television. So, you decide to use positive reinforcement to help reinforce studying behavior.

How do you do it? What reinforcer are you going to use? What are you going to reinforce? What if you reinforce the wrong behavior? Who’s going to dole out the rewards? Start thinking like this and you will become overwhelmed and implement nothing.

Try the dumbest thing that could work. Buy a bag of M&Ms and eat one whenever you solve a problem. If that doesn’t work, iterate and try something different.

Waking up in the morning

Getting out of bed in the morning is the bane of humans everywhere. What’s a guy to do? Informed by this post, you know the answer. What’s the dumbest thing that could work?

Download one of the dozens of Android alarm clock apps and try that. If that doesn’t work, iterate. Reduce caffeine in the evening or increase it in the morning (via caffeine pills). Install bright lights. Fast after dinner. Try melatonin.

Building a chess bot

Want to write a program that plays chess? It’s only overwhelming when you’re thinking: how can I write a program that wins at chess? Wrong goal! First write a program that loses at chess every time. It could pick a move at random, or always move a pawn. Then, iterate from there.

Learning math

Maybe you want to learn more math, but you don’t know where to start. Doesn’t matter. Go find a book about math and start reading, or start working through Khan Academy, or watch some video lectures. Don’t like it? Find another book or something else. Keep experimenting.

Memorizing stuff

Or it seems like a lot of people have trouble getting started with Anki. They wonder: what should I memorize? What should I use this for? It’s a hard question so they get stuck. Waste of time. Just add anything that you want to remember or learn. Keep adding, keep experimenting. You’ll figure out what works as you go along.

By the way, don’t miss the writeup of my experience memorizing more than 10,000 flashcards with Anki.

Exercise

In general, a little bit of data is going to be more enlightening than just thinking about it. Maybe you want to start exercising more, but you’re not sure whether or not you want to run or lift weights. Go out and start running. Don’t like it? Okay, try something else.

The alternative is that you spend a bunch of time googling and trying to figure out which is better for you or which you think you’ll enjoy more. Don’t worry about it. Just go try something. See what sticks.

Reading Math: Tips and Heuristics

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Reading math is tough. So tough that even Fields Medal winner Bill Thurston wrote about his near-constant confusion. To make it a bit easier, try out these heuristics.

The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.
—G.K. Chesterton

Visualize it: Build a mental image. Lines, triangles, donuts. Add one thing at a time. A significant amount of your brain mass is devoted to imagery. Repurpose it for mathematics. Don’t understand what a function does? It takes an input and produces an output, but that’s too vague. It makes mathematical sausage.

Do I contradict myself? Very well, then I contradict myself, I am large, I contain multitudes.
—Walt Whitman

Metaphorize it: Walt Whitman contains multitudes. So does the number line. Walt Whitman is the number line. The number line is made of numbers. Walt Whitman is made of molecules. Numbers are molecules. Every number can be uniquely factored into a set of primes. Each of Walt Whitman’s molecules can be constructed out of atoms. Prime numbers are atoms.

What did your face look like before your parents were born?
—Zen koan

Kinethesticize it: Grab it, stretch it, tear it, move it, bend it. Zoom in on it. Stack one number line on top of another line. Shift the bottom number line. Compress the line on top of itself. Motion. Feel the equation. What does a summation feel like? What is its original face?

Debug it: Debug yourself. What step does not make sense? What can you not follow? Make it concrete. What’s the simplest case? Plug in numbers. Write it down.

Don’t just read it; fight it!
—Paul Halmos

Fight it!: Unwieldy definitions, holds for all numbers but zero, bah! Why does the author show me something so grotesque? Why can’t I divide by zero? Find out.

What do you know?: You know something like this! What is it?