bo1024

Of course it's tempting to reply "don't install random extensions". But a bigger point here is that browsers have grown so massively complex that it's almost impossible to build one, so we don't have an ecosystem where you can choose your browser for safety and I can choose mine for freedom. Of course, Google has had a big incentive and hand in making it this way.

A variant:

> Don't encounter the hard ones

For example, with the simplex method for linear programming, we don't do anything about disallowing the hard instances. We just solve the problems as they come in and none of the ones we get asked to solve ever turn out to be hard. (Generalizing, of course.)

Yes, and I have the same problem with Cloudlare’s “we are checking the security of your connection” page that is now popping up for me everywhere.

Thanks for making sure I’m secure enough to read your three-paragraph news article…

The pacers have to obey the same rules as every other runner. They start at the starting line, they can't run inside the lines, etc.

One of the reasons that Eliud Kipchoge's "Breaking 2" marathon wasn't a legal world record was that teams of pacers would rotate in, take a break, then rotate in again. This way he could have pacers with him almost the entire way. But in a real world record attempt, the winner is always running by themselves in the last part of the race because all of the pacers have been left behind or dropped out -- by definition of a world record, they can't keep up to the end.

What is the political goal behind this directive? I assume there is some completely non-subtle purpose, but I can't tell what it is.

Qwen3.5-122B is actually Qwen3.5-122B-A10B. The A10B means that this is a "mixture of experts" model where only 10B parameters are activated at a given time. Whereas Qwen3.6-27B is a "dense" model where all 27B parameters are activated all the time. So for many tasks, you'd expect the 27B dense model to be better than the 122B-A10B model.

Plus, this is more fuel for Anthropic's God complex.

Is it much different in other countries?

What is the policy and guidance you gave the students regarding LLM use?

There are basically two kinds of applications. One is where you want to correctly solve the problem at least 99 out of 100 times. LLMs generally don't (and not everybody realizes that) so there are a lot of debates and research around how useful and reliable they are or how to make them so.

The other kind of application is where you can try 100 times and you only need to be right once. Solving a mathematical research problem is like that.

There are about 2^64 more 64-bit integers than 32-bit integers.

What's wrong with a 20% tax? We who make a living from labor instead of capital pay more than that.

Paul tries to frame it as an increase of 20% in the tax rate, but in reality the increase is from 0% to 20%, and it's hard to see why that's unfair.

The reason I say it's currently 0% is of course that for the wealthy most of these 5% gains are unrealized (e.g. inflation in the value of their assets) and untaxed.

Your current understanding also seems a bit warped. The US government provides the source of a lot of research funding but historically exerts little "control". Generally grant applications are evaluated by panels of researchers who don't work for the federal government.

Also, this government funding supports fundamental innovations that private companies wouldn't fund because it's too general and too far from monetizable. But after those breakthroughs happen funded by public research, private industry benefits enormously. This includes most health and medical advances and the science underlying most technological advances. So government funding doesn't conflict with the work being necessary or important, on the contrary, it is possibly more important long-term.

Disclaimer? The government funds some of my research.

It's much easier than it seems.

* There are axioms, there are models, and there are theorems.

* A model is a particular structure with objects and relationships. The "standard model of arithmetic" is just the natural numbers 0, 1, 2, ... with normal rules of addition and subtraction and so on. A different model could be the real numbers, or one that includes infinitesimally small numbers, or so on.

* A set of axioms are rules about how a model can work. For example, we can have an axiom for any set of objects called "numbers" with an operation called "addition" that the operation must be commutative (x+y = y+x). The standard model above is one model that satisfies this axiom.

* A theorem is a fact that can be true or false about a given model. For example, "the model has infinitely many objects." If we can prove a theorem from a set of axioms, then that theorem is true for every model that satisfies the axioms. However, there can also be theorems that are true for one model that satisfies the axioms but false for a different model.

Godel's completeness theorem says that if a theorem is true for every model that satisfies a set of axioms, then one can prove that theorem from the axioms.

Godel's first incompleteness theorem says that in any axiomatic system (sufficiently complex) there are theorems that are neither always true nor always false. In other words, there is a theorem that is true for some model of the axioms but false for some other model of the axioms.