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.
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.
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.
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.
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!
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.