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Address of Infinity
“Hilbert introduced the Hilbert Hotel paradox in a 1924 lecture. The tale of Hilbert’s Hotel was a profoundly creative way of exploring the concept of infinity in that era. It challenged the minds of mathematicians and laymen alike, and showed them that infinity was not just a number, but a never-ending story waiting to be told.”
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Unlocking the Secrets of Prime Numbers: An Introduction to Factoring
“For example, to determine if the number 13 is prime, we would need to check if it’s divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12. As you can imagine, this becomes increasingly time-consuming and complex as the number gets larger.”
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Conclusion of Everything
“Space-time is like some simple and familiar system which is both intuitively understandable and precisely analogous, and if I were Richard Feynman I’d be able to come up with it.” -xkcd.com
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Quantum Computers
“Our knowledge in the field of computing is extremely limited. We currently employ bits (0/1) at the core of our computers. Dealing with concurrency related issues is a major challenge while representing algorithms. Coming to think of it, the Turing machine itself is a deterministic, single-threaded machine. Can such algorithms ever account for, represent and eventually take the place of the human mind?”
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Artificial Consciousness
“I believe that the real test of a theory of consciousness is to create artificial consciousness. I am not sure whether a simple Turing test would suffice for this, but it does seems inadequate. So is our mind simply an extremely complex computer running a complex bit of software?”
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Cognition and The Theory of Everything
“But either way, it is you who is looking at your computer, moving your eye across this sentence trying to make any sense of it. You do exist. It would be unfair to exclude YOU from the theory of everything. Eventually, you sense this world. Shouldn’t YOU be of greater importance in it?”
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Complexity
Now imagine the universe as a cup of coffee. When the cream and coffee are separate, it’s simple and organized it’s low entropy. When you mix them together, it’s high entropy and everything is disorganized and mixed together. But it’s in the middle, when swirls of cream are mixing into swirls of coffee, that you get this intricate complex structure .
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