Tower Of Infinity or Endless Depth Of Stupidity
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Recently I challenged my audience to count past Infinity and then showed a very accessible way:
Have a hierarchy of stronger functions like n, n squared, n cubed ... and then consider the function n to the power n.
n
n^2
n^3
...
...
n^n
Then the realization hits you:
The function n to the power n is stronger than any other functions n, n squared, n cubed, ... , n to the billion, n to the power trillion ...
So the moment you give the example of the function n to the power n - you counted past Infinity!!
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Just because you can label 1, 2, 3, ... counting past Infinity, does not convey anything about whether you comprehend the size of Infinity.
Think about the function n to the power (n +1) - this function implies you can count two past Infinity since this function is stronger than n to the power n we just discussed.
Where is all this going?
When you talk about Mathematics in a precise formal language, like raising something to the power of something, you are using a Set Theoretic language. So you can truly say you have comprehended the vast extent of Infinity only if:
you run out of language (expressive power)
That is why the Infinity is formally known as
Inaccessible Cardinals
When you prove that you can count past Infinity - you are still using a given language expressive power. Only when you run out of words then you arrive at the door of Infinity.
Wait - I am not done.
You run out of Words to arrive at the first Inaccessible Cardinal. I did not say
You ran out of Thoughts
Your mind keeps working - and you can formally think of a tower of Inaccessible Cardinals.
How exactly if you wonder it is done - no Words but Thoughts and all while being Formal and Precise - you need to read up on Axiomatic Set Theory.
Now I am done.
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So, you see, the human mind is way too powerful. We run out of words to formally arrive at the very first Infinity and then we continue to Think (not express) about the Tower of Inaccessible Cardinals.
Infinity is an Illogical Concept - that makes all this discourse possible.
The human mind is that powerful ...
Now think about:
The power of Stupidity - the power of Human Mind for the Evil and Inane.
Can AI do anything to counter this collective immense power of Humanity which thought of Tower of Infinity in the first place?
Is it not Stupid to ask this very question?
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9moInteresting perspective on the potential rise of neo-luddites in an AI-driven society. It's crucial for us to adapt and embrace technology while also valuing the unique human touch in creative endeavors.