Spirals are found throughout the nature at all scales:
Saturday, May 18, 2024
The Ulam Spiral and the non-random distribution of prime numbers
An analogy for the brain as a computer
Friday, May 17, 2024
Tuesday, May 14, 2024
Solving the AI Hand Problem
The reason why AI struggles to create images of hands is because it cannot understand the three-dimensional nature of hands from two-dimensional input. To overcome this, AI needs to be paired with a 3D printer so it can get proper feedback. A human can determine which output hands are best, and that in turn can be used to improve the algorithm and training data.
Hands are complicated, and even artists struggle to draw them. This is the reason cartoon characters often wear gloves.
Manifestations of the Riemann Function in Nature & Scientific Discoveries from Dreams
The Collatz Conjecture, Primes, and The Nautilus Shell
Monday, May 13, 2024
The best analogy for artificial intelligence (AI)
AI is basically the same as a room full of monkeys and typewriters eventually producing Shakespeare. There is a funny clip from The Simpsons along those lines:
https://www.youtube.com/watch?v=loMEF18Ir4s
Interestingly enough, this experiment was tried in real life on a small scale. It resulted in several damaged keyboards and several pages consisting entirely of the letter s.
Today's computers are descended from the code-breaking machines of WW2. Those too could be described as a room full of monkeys and typewriters.
The process of using a room full of monkeys and typewriters to create something sensible is better known as a brute force search. For example, if you are trying to guess a 4-digit passcode, there are 10,000 possible combinations (10 x 10 x 10 x 10 = 10^4). This can be narrowed down in various ways given that some passcodes are more popular than others.
The computing power of a typical smartphone could guess all 10,000 passcodes in much less than a second. Thus, devices which are accessed by other devices need much longer "passcodes" to be secure. Today, that process is called RSA and relies on the fact that as of today there is no efficient way to factorize (find the prime factors) very large semiprime numbers (numbers with only two prime factors). That could change in the future.
To make another analogy, there has always been an arms race of better locks and lock-pickers. In the same way, there has been a race between better codes and better codebreakers.
Sunday, May 12, 2024
A math video that synchronizes with every song
Watch this video on mute while playing any song simultaneously in another tab. It will appear to synchronize.
https://www.youtube.com/watch?v=Ey-W3xwNJU8
Rihanna's Diamonds syncs up rather well, as does Only Love Can Hurt Like This.
Art, music, nature, and math are all different forms of the same thing.
Wednesday, May 1, 2024
"Don't Be Too Proud of this Technological Terror You've Constructed."
A destroyed US Abrams main battle tank displayed near Moscow:
"Don't be too proud of this technological terror you've constructed."
-Darth Vader, military commander and philosopher