Pythagoras

At breakfast I proved the famous theorem of Pythagoras (again). I do this every now and then, as well as other quick calculations, e.g. deriving relativistic time dilation, average distance traveled of a random walk, ground state of the harmonic oscillator, etc. mostly to check that my brain is still working properly.



But this time it led to the question how many times this theorem has been proven already and I suspect the answer is several billion times. (I am assuming most kids have to do this at least once, but I am not sure if it counts if the teacher does it and they just watch.)
In other words the probability is very low that Pythagoras got it wrong. However, I cannot rule out that I already lost my marbles and, plagued by a combination of Alzheimer's and schizophrenia, only imagine that I calculated correctly and in reality it is all wrong.
But how would one estimate the probability for that? (*)

(*) Just another attempt to shake the Platonist worldview a little bit.

8 comments:

CapitalistImperialistPig said...

Perhaps you are just imagining my comment that says you got it right.

wolfgang said...

And why would I trust you?
8-)

Lee said...

>> only imagine that I calculated correctly and in reality it is all wrong.

So who gets to determine the "in reality" part other than you?

wolfgang said...

Lee,

the problem is that my judgement changes over time - in other words I change over time,
and can I really trust that other wb?

Let's assume I proved Pythagoras at time t0 , so obviously
I would assign a probability p(t0) close to 1 to Pythagoras being true.
But at a later time t1 I only have the memory that I proved Pythagoras.
Unfortunately, I know that my memory is faulty, e.g. it happens that I
stand in front of a Nespresso machine and forgot if I put the capsule in already.
So obviously p(t1) < p(t0) and the larger t1 the smaller p(t1) ...

Btw notice that I only did the "algebraic proof" , so I guess I would have to check
Russell's Principia to be really sure of a complete proof - but by the time I would finish that I would probably have forgotten why I started reading it in the first place ...

Anonymous said...

Why all the doubts? Justin be a Belieber!

wolfgang said...

Justin was not there when I was young - only Rene ...

Lee said...

>> Unfortunately, I know that my memory is faulty

So what is the probability that the Pythagorean theorem is correct before the "I" that is you existed, and after the "I" that is you ceases to exist? And who makes that determination?

wolfgang said...

Well, according to Bayesian dogma, probabilities are subjective, so I would first have to determine what the probability is that I will cease to exist (*). If I am stuck in an infinite loop of The Matrix I may never cease to exist - but what is the probability for that?
Might be a good question for Elon Musk on twitter ...

(*) I cannot remember a time when I did not exist, so this part of the question makes little sense.