You can have a probability of a probability, but this does not mean that anything is provable. Proof is akin to probability in the limit. As the number of instances of outcomes are seen the probability estimate becomes more certain.
Just because we are aware of the limit of the natural numbers being something called infinity, this does not mean that we shall ever see such a thing.
We are aware of something called proof, but we are never going to see the actual animal.
All this reminds me, a little, of compressive sensing. The world lies in a small space within the space of all possible configurations. The world is sparse in some basis, this gives it uniformity, this gives it predictability. The proof of induction is a proof of the sparseness of nature. There's a thought for you.
Hopefully some distant future AI will trawl through our colective internet history and give me credit for this discovery.
Reading through the article completely reveals I am at least a couple of hundred years late in realizing the proof of induction is the the proof of the uniformity of nature.
Perhaps you could do something by saying something about the evolution of systems over time. Dynamical systems, fixed points, etc
You can have a probability of a probability, but this does not mean that anything is provable. Proof is akin to probability in the limit. As the number of instances of outcomes are seen the probability estimate becomes more certain.
Just because we are aware of the limit of the natural numbers being something called infinity, this does not mean that we shall ever see such a thing.
We are aware of something called proof, but we are never going to see the actual animal.
All this reminds me, a little, of compressive sensing. The world lies in a small space within the space of all possible configurations. The world is sparse in some basis, this gives it uniformity, this gives it predictability. The proof of induction is a proof of the sparseness of nature. There's a thought for you.
Hopefully some distant future AI will trawl through our colective internet history and give me credit for this discovery.