Tag Archives: Math

Suppose your mind is really nothing more than the sum of a bunch of physical processes. If so, this can be simulated on a computer (albeit a much more powerful computer than any we currently have).

When you get right down to it, computer programs are just a bunch of ones and zeroes. Every single one of them, from Plants vs Zombies, to the browser you’re reading this on, is just a really, really long number.

We’re pretty sure that π contains all finite number sequences. Your mind as a computer program is a finite number sequence. π contains that number.

Consider digital-you once more, running inside the computer. I think we can agree that he’s conscious.

What if we remove the computer? On what basis do we privilege a physical substrate, when really we’re only already interested in what it is representing in the abstract. Remove the computer, and you just have the number. From the inside, the number itself is conscious. This number feels exactly like you do right now.

And so π is not only conscious, it is teeming with minds (same goes for e and √2). Every version of every person that ever has or will exist, and infinitely more who haven’t, live within it.

This is the metaphysics of Max Tegmark.

I find it incredibly seductive, escapable only by denying the supposition in sentence 1.

Papal Probability

This article contained some numbers which led me off on a tangent.

Pope Francis is the 266th pope. There have been 37 false popes.

Therefore, 37/(266+37) = 12.2% of papal claimants are antipopes.

The average Pope serves for 7.3 years (John Paul II, it turns out, had the second longest reign in history).

Now, the average US life expectancy is 79.8.

Therefore, on average, an American will see ceiling(79.8/7.3) = ceiling(10.93) = 11 popes in their lifetime.

So, given an antipope rate of 12.2% and 11 popes in a lifetime, what are the odds that you will see an antipope in your life?

My probability is very rusty, and I wasn’t exactly great at it back in school, either, but I’m pretty sure this boils down to a classic Probability Mass Function

f(k;n,p) = Pick(n k)(p^k)(1-p)^(n-k)

So, the probability of exactly one antipope in a lifetime:

f(1;11,.122) = Pick(11 1)(.122)^1(1-.122)^(11-1)
= 0.36534

In other words, the odds of you living through exactly 1 antipope are a little over 1 in 3.

But wait, there’s more!

What are the odds of at least 1 antipope in your lifetime? At this point, the maths get pretty long and repetitive, so let’s cheat using the internet:

Probability of success on a single trial: 0.122
Number of trials: 11
Number of successes (x): 1