You have, as has been pointed out, failed to understand the purpose of my comment. You will notice I never stated anything about this paper merely some basic guidelines to follow for determining if the paper is worth the effort to read, if one doesn't have significant knowledge of the field within which the paper was written.

I apologize if my purpose was not clear, but your comment is completely irrelevant and misguided.

EDIT: This is not an evaluation of the particular paper in question merely some general evaluation guidelines which are useful.

Drop dead easy way to evaluate the paper without reading it: (Not a standard to live by but it works)

1.) look up the authors if they are professors or experts great if its a nobody or a student ignore and discard or take with a grain of salt

2.) was the paper published and where (if on arxiv BEWARE it takes really no skill to get your work posted there anyone can do it)

Criteria: If paper written by respectable authorities or ones who's opinion can be trusted or where you have enough knowledge to filter for mistakes

If the paper was published in a quality journal or you have enough knowledge to filter

Then if both conditions are met, I find you can do a good job filtering the papers not worth reading.

"On one hand, Eliezer writes extremely good explanations. I'm learning from his style a lot."

Yeah, but they are rather verbose he tends to use 5 words when 2 would do.

"On the other hand, many people have pointed out that he doesn't publish novel rigorous results, which kinda detracts from the aura."

If you want to be in science this is a big issue unless your trying to pull a Wolfram and we all know how that turned out.

"On the third hand, he often finds and corrects non-obvious mathematical mistakes made by other people, including me, and he's turned out right every time that I know of."

But the math on this site what little there is tends to be toy problems and very simple. Let's see him find and correct a mistake in some higher order fluid mechanics equations. I would personally like to see him solve a non-trivial second order non-linear partial differential equation.

"On the fourth hand, I've seen multiple cases where he made math mistakes of his own, and have discovered a couple of those myself. But that could be attributed to the fact that he publishes so much, and his error frequency is certainly many times lower than mine."

That's horrifying if you're going to do science you have to control your error rate and that is where peer review comes in. (I recently submitted a paper where I was sloppy on some rounding of some of my results and I got slammed for it, science is all about precision and doing it right) If you don't do the peer review then you may think your idea is good when if you actually had someone else look at it you'd see it was total trash.

"On the fifth hand, he has published novel non-rigorous arguments on real world topics that I don't completely agree with but find pretty important. Biggest of them is the idea of Friendly AI."

But for science and AI this is essentially meaningless since if your goal is to make an FAI then math and rigor is necessary. The ability to write non-technical papers arguing for some idea that is technical is trivial. The challange is getting the technical detail right. This is where I would like to see Eliezer submit some of his work on decision theory show that he is actually making a theory that is properly rigorous.

I think the worst thing would be if people here just wait for Eliezer and he shows up at the end of 10 years with an extremely long non-technical paper that gets us no closer to a real FAI.

But those are just my thoughts.

Oh I get it. I would make the same point either way especially when the idea comes from a non math person. Whenever a non math person says this kind of thing it should make anyone who has done their due diligence cringe.

If you can't do the math so for the physics if partial differential equations are beyond you then you shouldn't be talking about physics. There are many fields where knowing the "drop-dead" math is not sufficient to qualify one to talk about it.

Now I know you will all vote me down, I am rocking the boat.

Ok, I have to be honest this entire idea makes me cringe, it seems a bit to much like a cheap get out of learning the math idea. Maybe I am biased because I actually am a mathematician but these kind of ideas I think are dangerous since you take away an important bar of admission to fields like physics. If you don't understand why the math is an important bar of admission look at the google groups physics group.

To be honest I think someone would be better off spending their time learning calculus at minimum then trying to read this kind of general overview. I think what is likely to happen is that either the math will be to simple and muddles the field to the point of being useless or its so complex that nobody can follow it. A good case and point you can understand quantum physics if you understand algebra but your going to be hopeless in a discussion about it without understanding things like the differential equations. Of course there are other fields which you have to know the math, from some of my own experience, fluid mechanics.

For my own part I think required math should include at minimum: Advanced Calculus (not that "calculus class" you took in high school it doesn't count) Differential Equations Linear Algebra Abstract Algebra Set Theory (basic at least) Number Theory

I think with these you probably can figure a lot of the more complex math out.

I am sure I am leaving a couple out but you get the idea.

Why re-invent the wheel this has already been done if I understand correctly for example in a bit of a more specific case "Fundamental Formulas of Physics".