mlechha

Whenever this comes up, I think about the conjunction fallacy https://en.m.wikipedia.org/wiki/Conjunction_fallacy. The observation that human subjects seem to assign higher probability to joint events than a single event. Which is weird because the probability of two events at the same time (conjunction) is always less than or equal to the probability of a single event on its own.

How does the Bayesian brain hypothesis deal with this fallacy? It seems to me that nothing based on classical probability can explain this fallacy. So either the observation that humans can assign higher probability to joint events is wrong or human decision making isn't exactly probabilistic (in the classical sense, can't rule out exotic probabilistic approaches).

EDIT: As several folks have commented that the conjunction fallacy can be explained away by different arguments based on interpretation and semantic issues. Indeed, the original Linda problem was susceptible to these issues. However, since then several researchers have tried to study this effect more carefully and it seems to still persist. An example that I'm aware of is the following https://link.springer.com/article/10.3758/BF03195280 where the authors used unambiguous language and a betting paradigm, but still found the effect. Again, this is most likely not fool proof. Regardless, I do not think the fallacy can be trivially explained away as an effect of ambiguous language.

Atiyah says, Hirzebruch named and defined the function. Why not look for it in the work of Hirzebruch that Atiyah cites at the end?

I just went through the preprint and I do not understand your comment. What specifically ticked you off? The preprint is well written, arguments are clear and there's enough background for an expert to work things out.

As Atiyah says in the preprint. The magic is the Todd function and the Mathematical framework that comes with it. It seems Atiyah has developed a new framework (which he calls Arithmetic Physics) and a side product of the framework you get a simple proof of RH. I don't know if the proof is correct. But I don't see any signs of crackpottery in the preprint.

Finally, this is in the style of Atiyah. He is known to be a "theory builder" rather than a "problem solver". True to that, he's claiming a whole new way of looking at number theory. So even if the proof turns out to be false. Mathematicians still get some new ideas.

They're probably the most fundamental kind of reinforcement learning algorithms. Understanding bandit algorithms is crucial to developing a good understanding of RL.

Here are some basic things, the predictability of which most people in the developed world enjoy.

1. Clean water 2. Roof over the head and the sense of safety that comes with it. 3. Basic food.

A sense of community and friendship is probably the only basic human necessity that is not certain in the developed world.

Now imagine a world where none of this is can be taken for granted. You live under a constant threat from various sources (disease, wild animals, other humans out there to steal, loot from you etc) , there's not enough food, water and on top of that you're lonely. Religion is one driving force that helps people through these.

It's not about being an atheist per se, but about believing. The others I'm sure strongly believed in something, which kept them going. Landau for example had physics to occupy him and keep him sane.

7. I saw that the only group of people able to preserve a minimum of humanity in conditions of starvation and abuse were the religious believers, the sectarians (almost all of them), and most priests.

This, to me is the point of religion. We need religion when things are hard and unpredictable. In a world where most things are certain and predictable, religion has no value.

Not a very good abstract. It doesn't tell me anything about Feynman's contribution to molecular biology.

Search for Wulfram Gerstner's courses and books. You'll find most elementary (and advanced) topics in there.

When making a decision as to whether something is small, large, or tiny one needs a scale. What's the scale here? For example, if the rest of the world combined has had 12 mass k-12 shootings, then American accounts for 40% of the total shootings which is a huge fraction. So in my original question I was trying to find the right scale.

Edit: In a comment below, this article was linked https://qz.com/37015/how-school-killings-in-the-us-stack-up-.... Indeed, on this scale we see a very different picture!

Shouldn't the comparison be made against school shootings world wide? Or at least be normalized for overall crime rate or something?

Nobody eats a tablespoon of turmeric! We usually use 1/4 teaspoon for a 4 person meal. Source: I'm Indian.

Number of samples depends on the effect size. e.g. You only need n=1 to claim a dog can talk.

All of Reinforcement Learning :)

Well it depends on what you mean by quality. On Quora the discussion is meant for the general public, and terms like diophantine equations are defined in common language before delving into their mathematical details. While mathoverflow is for mathematicians, for a layman it's mostly gibberish. So imho it's unfair to even compare the two, they're different things and both have their place.

I find this discussion pointless as driverless cars that can drive on Indian roads are a long way from becoming a reality.

How do you know whether something is a hyperbole? When the author claims something is not a hyperbole.

It was a simulation from the data they already had. It's near impossible to do that with a real monkey colony.

Exactly! 2000 in 8 is fucking ridiculous! For some context, there have been only 8 Chinese and 7 Indian Nobel Laureates. That's two of the most populated countries in the world!

Wow! Thanks for this. Adhell is awesome.

Those who find connecting quantum mechanics and the brain repulsive should check out Quantum Cognition https://en.m.wikipedia.org/wiki/Quantum Cognition.

For some reason the mathematics of QM is extremely good at explaining counter intuitive phenomena that classical probability theory cannot (necker cube is a good example, where the mental state can be said to be in a superposition of the two cube orientations).

Mind you, this doesn't say anything about the actual mechanism. It could or couldn't be quantum but we'll never know if we just shrug the entire thing off as crackpottery.

There's a new topology video out! As cool as the first one!

In applied machine learning not so much. They feel ancient! But some use them to study the physics of computation. They were used to make the connection between renormalization group (RG) and machine learning. RG is one of the main workhorses of quantum field theory and condensed matter physics. The fact that there's a mapping from RG to RBMs means that we can understand how deep learning works by using the same techniques that modern physicists use to understand the world! Here's a nice article on this topic if you're interested https://www.quantamagazine.org/20141204-a-common-logic-to-se...

Haha I'm not sure if you're being sarcastic so I'll try to unpack the comment. Hopfield networks were one of the first models of associative memory. They themselves were based on a model of simple magnets called ising model (generalized). Basically a group of binary units, each connected its nearest neighbors with a coupling strength. Each unit prefers to be like their neighbors. Hopfield developed a clever method to change the coupling so that the networks can store and retrieve patterns of activity. In the Hopfield network everything is deterministic, Hopfield himself realized that if this constraint was relaxed this model could become a very powerful computational machine. Which means that if instead of being always on or off, the units had a probability of being on or off the networks could perform very general computational tools [1]. Unfortunately, training these general stochastic systems was not easy. With their Boltzmann machines Sejnowski and Hinton proposed a possible solution. The activity of stochastic binary units effectively encodes a probability distribution, so all they had to do was make sure that the probability distribution being encoded by the activity of the units was the same as that of the input. They did this by changing the connection strengths between the units such that the activity pattern minimized something called the Kullback-Leibler or KL divergence, which is a measure of how close two probability distributions are (the one encoded by the network activity, or the dream activity of the network and the probability distribution of the real data e.g. a set of natural images). If two distributions match exactly then the KLd is zero and if not it's large. When they wrote out the math it turned out that the algorithm required two phases, an awake phase where the connections were changed according to the real data, and the sleep phase where the connections were pruned by the spontaneous activity of the network without any input (or dreams). This analogy got a lot of people excited, including Francis Crick and several others tried to test this idea in real brains, but we are still waiting for a convincing result.

They weren't. They were a generalization of the Hopfield networks. Boltzmann machines are a stochastic version of the Hopfield network. The training algorithm simply tries to minimize the KL divergence between the network activity and real data. So it was quite surprising when it turned out that the algorithm needed a "dream phase" as they call it. Francis Crick was inspired by this and proposed a theory of sleep.

It's been a great era for condensed matter physics though. And the recent revolutions in nonequilibrium thermodynamics (fluctuation theorems and generalizations of the second law) promise an exciting time ahead!

Exactly!!! To me this is the obvious consequence. Another thing is Fermat's principle, if time doesn't exist then what is light minimizing as it moves through space?

Interesting. I'm curious as to why you make that connection? What reminded you of predator prey systems?

That's another option and there are people who do that https://blog.inf.ed.ac.uk/insectrobotics/.

To be honest, the wiring diagram is a bit of a distraction from the really big questions. It has its uses for sure, and is really essential in many situations but overall it gives this illusion that we understand something important about the system, where in reality we don't. Understanding a biological system from its wiring diagram is something like understanding a city by studying its road map.