Question

Until one of you googles this and finds out the person that discovered this before me, I'm calling this the mhchen paradox:

Suppose there are 2 ways to solve a problem.
The first way takes A-time to finish.
The second way takes B-time to finish

We wish to know if we should use the first way, or the second way based on whichever time is smaller.

But calculating which one is faster also takes up time, and suppose we have a choice of whether to calculate the most efficient way, or randomly choose a way. We'll denote this time as C

So far my options are:
A or B or C+min(A,B)

Now I wish to find out whether randomly choosing A or B is faster or C + min(A,B) is faster.

Denote this extra time as D.

We construct a decision tree for visualization:

Answer 1

Now we apply induction:


thus you will never find out what the most optimal way of completing a task efficiently is, given 2 possible decisions

Answer 2

Here's where the phrase "Just Do It" comes into play.

Answer 3

Also if I guess just doing A, doesn't that solve the problem of ending up in an infinite calculation? xD

Answer 4

It would but you wouldn't know if it was the fastest way

Answer 5

I mean, I'm introducing humanity to a mathematical thought experiment which kind of betrays the spirit of it a bit, but through experience humans can approximate the timely scenario.