Connection to Holographic Ideas 4/4

3. Emergent Spacetime: If the holographic principle holds, the spacetime geometry inside nested gravastars might be emergent from the information encoded on their boundaries. This could lead to a new understanding of how spacetime emerges from information at a fundamental level.

E: hashtaggies #wolfram #anewkindofscience #coallesence #astrophysics #physics #gravastars #holographictheory #theoreticalphysics #quantummechanics #informationtheory

@gutenberg_org @wikipedia

From https://mathworld.wolfram.com/FermatsPolygonalNumberTheorem.html (ellipses mine):

"Fermat's Polygonal Number Theorem
In 1638, Fermat proposed that every positive integer is a sum of at most three triangular numbers, four square numbers, five pentagonal numbers, and n n-polygonal numbers. Fermat claimed to have a proof of this result, although Fermat's proof has never been found. Gauss proved the triangular case, and noted the event in his diary on July 10, 1796, ... (Duke 1997). More specifically, a number is a sum of three squares iff it is not of the form 4^b(8m+7) for b>=0, as first proved by Legendre in 1798.

Euler was unable to prove the square case of Fermat's theorem, but he left partial results which were subsequently used by Lagrange. The square case was finally proved by Jacobi and independently by Lagrange in 1772. It is therefore sometimes known as Lagrange's four-square theorem. In 1813, Cauchy proved the proposition in its entirety."

8/10
Of (some of) the other e-calcs, #Wolfram does the same as Desmos, #Android and #Excel both forcibly add a multiplication symbol (thus breaking the factorised term), and with the #Windows calculator, any coefficient you type in literally disappears! i.e. type in 8/2(1+3), and it gives you 8/(1+3). #Microsoft MathSolver is the buggiest. If you use ÷ then it essentially does the same as Google, but if you use / it turns it into a fraction and puts the whole 2nd term into the denominator...

@jabberati this is nice actually ;D I had forgotten about #Wolfram #WolframAlpha
https://www.wolframalpha.com/input?i=population+Australia%2C+North+Korea%2C+Sri+Lanka%2C+Taiwan @jikodesu

@kellogh @seldo perhaps because the experts don't even understand how #LLMs work & whether they are thinking, reasoning or even computing.

#Chomsky: human brains are just grammar engines
#Wolfram: LLMs are not even doing computation (much less reasoning or thinking).

#Brains learn statistical models that predict what's going to happen next, so predicting the next word in a convo is a good start ... if your brain "lives" in a fantasy world of Internet words

@jan

Wow, this is the 20th anniversary edition of the book.

It's great that he put it online where anyone can read it. TBH, I thought there would be a more visible effect of this work by now.

The fact that it hasn't is evidence of how compartmentalized & isolated the specialized fields of knowledge have become. Each prefers their own jargon & narrative, and is built on the shoulders of *their* giants, blurring the distinction between communities of religion & science. Newcomers are outsiders, and often ostracized from the in-group.