Calculating God?

I don't believe that the God of any earthly religion is the creator of the Universe.

But I really dislike a lazy and innumerate argument commonly used to "prove" the non-existence of God, which can be summarized in the following false dichotomy:

Either there is no God and the universe just 'poofed' into existence, or there's an infinite number of Gods, because the plane of existence for each God has to be created by a higher-level God.

This is a false dichotomy: it could well be that our universe was created by a powerful being from a higher-order universe, but that universe poofed into existence without a creator. Or maybe it did have a creator, whose universe poofed into existence; or that third universe may have had a creator...

Hey, this looks like dynamic programming. I know dynamic programming.

Let's say that universes are recursively nested until one of them just poofs into existence. Of course we can't see outside our universe, but we can build simple models.

So, our universe either poofed into existence (say with probability $p$) or it was created by some higher being (with probability $1-p$). Now we iterate the process: 'level 2' universe either poofed into existence (with some probability $q$) or was created by a 'level 3' universe being (with probability $1-q$); and so on.

Time for a simplifying assumption, or as non-mathematicians call it, making things up. Let's assume that all these universes share the poofed/created probabilities, so that for any 'level $k$' universe, it poofed into existence with probability $p$ and was created by a being from a 'level $k+1$' universe with probability $1-p$.

Note that it's still possible to have an infinite number of universes, but with this formulation, the probability of a 'level $k$' universe (with us being 'level 1') being the last level is

$p (1-p)^{k-1}$.

This probability gets small pretty quickly, which suggests the 'infinite regress of universes' argument gets thin very fast.

Now we can compute the expected number of universes as a function of $p$:

$\mathbb{E}(n) = p + 2(1-p)p + 3 (1-p)^2 p + \ldots N (1-p)^{N-1} p + \ldots$

or

$\mathbb{E}(n) = p/(1-p) \times ( \text{ sum of series } N (1-p)^N )$

The sum of series $N (1-p)^N$ is $(1-p)/p^2$, so

$E(n) = 1/p$

Therefore, if we believe that the probability of a universe poofing into existence is 0.1, there are an expected ten universes; for 0.2, five universes; for 0.5, two universes.

Very far from 'turtles all the way down.'

Of course, these calculations were unnecessary, because as we know from the revelations of the prophet Terry Pratchett, it's four elephants on the back of the Great A'Tuin swimming in the Sea of Stars.

Thoughts inspired by a science joke

Another day, another science joke. Not a very funny one, but enlightening.

When I say "science joke," I mean one that involves a modicum of science knowledge. Which makes this yet another post against the scientistologists that are all in favor of science as long as they don't have to learn any. They like the idea and the image of science, but are not willing to do the work necessary to learn it.

Last sunday I tweeted: According to my alarm clock, the computer & phone spent two hours moving at almost 90% of speed of light. That's one explanation.

Since that was the end of Daylight Savings Time, what that tweet says is that clocks which get a synchronization signal from the internet were one hour behind those that I have to reset manually. The twist is that I calculated what speed would compress time 1:2, $v = 0.8660254 c$, and included that in the joke.

(By the way, this time compression is an example of the twins "paradox," which is not paradoxical at all.)

As for the people who "love science" (as long as they don't have to learn any), well, many of them have a vague notion that I was referring to relativity, but no idea whether the 90% number was right, wrong, or random. Science is something they believe in, without actually knowing any of the details.

More and more people are falling into this trap of believing in science as opposed to actually learning it. That is a very bad trend in a technology-dependent society.

My phone is just as smart as you guys!

Dunning-Kruger Effect, the internet is your multiplier.

Anyone can search for anything, which makes knowing what to search for and how to interpret the results more important than ever. The comoditization of information increases the value of knowledge.

Early on in the most recent episode of The Big Bang Theory (season 7, episode 5, "The Workplace Proximity" *), Amy, Bernadette, and Penny are in Penny's apartment drinking wine and talking about Amy's temporary move to Caltech:

Amy: "I'm leading a study to see if deficiency of the monoamine oxydase enzyme leads to paralyzing fear in monkeys"

[Bernadette lets slip that she might have done that research with death row convicts, which she quickly denies because it would have been unethical.]

Penny: "Not many people know this, but the monoamine oxydase [mispronounced as "oxidize"] enzyme was discovered by a woman, Mary Bernheim.

[Bernadette and Amy are stunned.]

Penny: "That's right. My phone is just as smart as you guys."

And this captures a common confusion between knowledge and information. Note the pathologies illustrated in that vignette:

1. Who discovered MAO is irrelevant for the work Amy will be doing. Like Penny, many people pluck some vaguely related fact from the internet to interject into a discussion, in the illusion that they will appear knowledgeable. This behavior is becoming more and more common, especially with smartphones, but knowledge is a lot more than a simple collection of facts.

2. Penny searches for MAO because someone else brought up the topic. Without a framework of knowledge to integrate facts, people who depend on search don't know what to search for. In other words, the input for a meaningful search requires knowledge.

3. Even if Penny found useful MAO information, for example the mechanism by which it catalyzes the oxidation of monoamines and affects mood, she wouldn't be able to interpret the biochemistry and neuroscience involved. In other words the output of the search only gets meaning through knowledge.

Yes, I understand it's a joke. But this attitude that learning substantive material is passé, made unnecessary by the existence of search engines — an attitude that sadly can be found even among educators — is corrupting, corrosive, and counterproductive.

Without knowledge, information is useless. More people making knowledge-poor searches leads to more random facts being flung haphazardly into discussions; this makes having the knowledge to select and interpret the important facts more valuable than before.

Knowledge is power, the power to use information. Pity so few people know that.

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* Even though the general arc of the show has become a soap opera, there are still some good jokes in each episode, and the final joke in this one is among the best.