Information Beings

Happy Thursday!

One topic I keep circling back to in my /informationbeing research is the Riemann Hypothesis.

Not sure if it’ll ever lead anywhere (a thread I’ve been pulling on since the early 2000s when I first encountered RH), but the way it resurfaces—almost on a clock—is hilarious.

Leaving this trace here… for the ~<0.00001% chance it actually pans out.

math

Aviator, diver, Etherean, nexialist, PhD in aviation ∩ climate science | Host of /diving /ethfinance /eth-staker /geopolitics /science /singapore /thomas

well... in theory.

but i feel the 'simulation' renders otherwise :)

+ @aviationdoctor.eth why the random reply yesterday

+ @aviationdoctor.eth why the random reply yesterday 

https://warpcast.com/zef/0x9c862b03

My recent fixation on the Riemann hypothesis, fueled by John Derbyshire's Prime Obsession (2003), has led me down an unexpected path of reconnecting with math, a subject whose academic dryness I had never enjoyed, and which I had all but left behind since my undergraduate years.

Pulling the thread of complex numbers, I have left the zeta function and arrived at my next stop, chaos theory. James Gleick's Chaos (1987) got me equally fixated on nonlinear dynamical systems, logistic maps / difference equations, and bounded sets / fractals.

I don't claim to understand the finer points (I lack the education for it), but it's a quasi mystical experience for me to witness the emergence of infinite complexity, and such explanatory power over natural phenomena, from such simple rules as iterating z² + c.

Case in point: the Mandelbulb below, a 3D representation of the famous Mandelbrot set in a spherical coordinate system.

I've come to the conclusion that if god exists, then this must be where he lives

There's been a remarkable breakthrough toward proving the Riemann Hypothesis, although it still falls well short of fully resolving the conjecture.

Larry Guth of MIT & James Maynard of Oxford University (Fields medalist and frequent guest on YouTube's Numberphile channel) have co-authored a pre-print (https://doi.org/m7xb) in which they narrow down a previous estimate (known as the Ingham bound, dating back from 1940!) of the maximum number of non-trivial zeros of the zeta function that could lie in the right side of the critical strip (real part greater than 1/2 but not more than 1).

Lay summary: https://www.scientificamerican.com/article/the-riemann-hypothesis-the-biggest-problem-in-mathematics-is-a-step-closer/

Maynard and Guth presenting their results at a recent conference: https://www.ias.edu/video/new-bounds-large-values-dirichlet-polynomials-part-1 and https://www.ias.edu/video/new-bounds-large-values-dirichlet-polynomials-part-2

Thanks! It’s also been a topic of curiosity of mine lately (much more recently than you though)

https://warpcast.com/aviationdoctor.eth/0xbc284332

https://warpcast.com/aviationdoctor.eth/0xf586a2ff

https://warpcast.com/aviationdoctor.eth/0x753d79dd

https://warpcast.com/aviationdoctor.eth/0x9ca50120

i might send you a WIP paper if you have any brain cycles. Localized version of RH with some esoteric applications…