Month: January 2020

Fluid Equation Singularity

In the same way that eddies in a stream alter downstream currents, Elgindi’s work itself prompted a new round of mathematical discovery. In October 2019, Hou and Jiajie Chen adapted some of Elgindi’s methods to create a rigorous mathematical proof of a scenario closely related to the one in the 2013 experiment. They proved that in this slightly modified scenario, the singularity they’d observed forming in the Euler equations really does occur.

“They took Elgindi’s ideas and applied them to the scenario from 2013”. The circle was complete.

There’s still more work to be done, of course. Hou’s new proof has some technical qualifications that prevent it from establishing the existence of the singularity in the exact situation he modeled in 2013. But after a remarkable 6-year run and with renewed momentum, Hou believes he’ll soon surmount those challenges, too. “I think we’re very close”.

2022-04-12:

Now another group has joined the hunt. They’ve found an approximation of their own — one that closely resembles Hou and Luo’s result — using a completely different approach. They’re currently using it to write their own computer-assisted proof. The team’s answer looked a lot like the solution that Hou and Luo had arrived at in 2013. But the mathematicians hope that their approximation paints a more detailed picture of what’s happening, since it marks the first direct calculation of a self-similar solution for this problem. “The new result specifies more precisely how the singularity is formed. You’re really extracting the essence of the singularity,. It was very difficult to show this without neural networks. It’s clear as night and day that it’s a much easier approach than traditional methods.”

US Transit growth

This growth was driven almost entirely by an influx of subway, commuter rail, and bus trips in the New York City region, as well as subway trips on Washington, D.C.’s Metro. Both cities, which have the nation’s 1st- and 3rd-highest shares of transit commuters, have weathered major reliability and maintenance crises in recent years and hemorrhaged riders as a result.

Intellectual Progress

the single most important thing I discovered this decade (due to a random comment in the SSC subreddit!) was the predictive coding theory of the brain. I started groping towards it (without knowing what I was looking for) in Mysticism And Pattern-Matching, reported the exact moment when I found it in It’s Bayes All The Way Up, and finally got a decent understanding of it after reading Surfing Uncertainty. At the same time, thanks to some other helpful tips from other rationalists, I discovered Behavior: The Control Of Perception, and with some help from Vaniver and a few other people was able to realize how these 2 overarching theories were basically the same. Discovering this area of research may be the best thing that happened to me the second half of this decade (sorry, everyone I dated, you were pretty good too).

Psychedelics are clearly interesting, and everyone else had already covered all the interesting pro-psychedelic arguments, so I wrote about some of my misgivings in my 2016 Why Were Early Psychedelicists So Weird?. The next step was trying to fit in an understanding of HPPD, which started with near-total bafflement. Predictive processing proved helpful here too, and my biggest update of the decade on psychedelics came with Friston and Carhart-Harris’ Relaxed Beliefs Under Psychedelics And The Anarchic Brain, which I tried to process further here. This didn’t directly improve my understanding of HPPD specifically, but just by talking about it a lot I got a subtler picture where lots of people have odd visual artifacts and psychedelics can cause slightly more (very rarely, significantly more) visual artifacts. I started the decade thinking that “psychedelic insight” was probably fake, and ended it believing that it is probably real, but I still don’t feel like I have a good sense of the potential risks.

In mental health, the field I am supposed to be an expert on, I spent a long time throwing out all kinds of random ideas and seeing what stuck – Boorsboom et al’s idea of Mental Disorders As Networks, The Synapse Hypothesis of depression, etc. Although I still think we can learn something from models like those, right now my best model is the one in Symptom, Condition, Cause, which kind of sidesteps some of those problems. Again, learning about predictive processing helped here, and by the end of the decade I was able to say actually useful things that explained some features of psychiatric conditions, like in Treat The Prodrome. Friston On Computational Mood might also be in this category, I’m still waiting for more evidence one way or the other.

Gauge CNN

going beyond the Euclidean plane would require them to reimagine one of the basic computational procedures that made neural networks so effective at 2D image recognition in the first place. This procedure, called “convolution,” lets a layer of the neural network perform a mathematical operation on small patches of the input data and then pass the results to the next layer in the network. Gauge CNNs can detect patterns not only in 2D arrays of pixels, but also on spheres and asymmetrically curved objects. “This framework is a fairly definitive answer to this problem of deep learning on curved surfaces”

this has been applied to proteins:

Correia’s system, called MaSIF (short for molecular surface interaction fingerprinting), avoids the inherent complexity of a protein’s 3D shape by ignoring the molecules’ internal structure. Instead, the system scans the protein’s 2D surface for what the researchers call interaction fingerprints: features learned by a neural network that indicate that another protein could bind there. “The idea is that when any 2 molecules come together, what they’re essentially presenting to 1 another is that surface. So that’s all you need,. It’s very, very innovative.”

Chinese & Their Government

Why do so many people feel that the Chinese can’t possibly be OK with their government or society? It seems that many in West deem the current Chinese government/society as wrong and that any “right-thinking” person would agree and join in the fight.

First, I’ll look at the gap in political culture between China and the liberal Western democracies, especially the United States. I’ll argue that there is little appreciation among most WEIRD individuals — that is, Western, Educated people from Industrialized, Rich, and Developed nations — for just how highly contingent political norms they take for granted really are from an historical perspective. I’ll sketch the outlines of the major historical currents that had to converge for these ideas to emerge in the late 18th century. Then, I’ll compare this very exceptional experience with that of China, which only embraced and began to harness those engines of Western wealth and power — science, industrialization, state structures capable of total mobilization of manpower and capital — much later. And late to the game, China suffered for over a century the predations of imperial powers, most notably Japan. Hopefully, I’ll show why it was that liberalism never really took hold, why it was that Chinese intellectuals turned instead to authoritarian politics to address the urgent matters of the day, and why authoritarian habits of mind have lingered on.

Next, I’ll argue that a lot of unexamined hubris lies not only behind the belief that all people living under authoritarian political systems should be willing to make monumental sacrifices to create liberal democratic states but also behind the belief that it can work at all, given the decidedly poor record of projects for liberal democratic transformation in recent years, whether American-led or otherwise. It’s important to see what the world of recent years looks like through Beijing’s windows, and to understand the extent to which Beijing’s interpretation of that view is shared by a wide swath of China’s citizenry.

Finally, I’ll look at the role of media in shaping perspectives of China in the Western liberal democracies and in other states. A very small number of individuals — reporters for major mainstream media outlets posted to China, plus their editors — wield a tremendous amount of influence over how China is perceived by ordinary Anglophone media consumers. It’s important to know something about the optical properties of the lens through which most of us view China.