He is a massive crackpot in "pseudohistory", but he is also a decent mathematician. His book in symplectic geometry is probably fine, so unless you are generally depressed by the fact that mathematicians can be crackpots in other fields, I don't think you should be too depressed.
I think this notion of "mathematical maturity" is hard to grasp for a beginning student.
I had a very similar experience. Introduction to (the Russian edition of) Fomenko & Fuchs "Homotopic topology" said that "later chapters require higher level of mathematical culture". I thought that this was just a weasel-y way to say "they are not self-contained", and disliked this way of putting it as deceptive. Now, a few years later I know fairly well what they meant (although, alas, I still have not read those "later chapters").
I wonder if there is a way to explain this phenomenon to those who have not experienced it themselves.
When reading about Transparent Newcomb's problem: Isn't this perfectly general? Suppose Omega says: I give everyone who subscribes to decision theory A $1000, and give those who subscribe to other decision theories nothing. Clearly everyone who subscribes to decision theory A "wins".
It seems that if one lives in the world with many such Omegas, and subscribing to decision theory A (vs subscribing to decision theory B) would otherwise lead to losing at most, say, $100 per day between two successive encounters with such Omegas, then one would wi...
Good, now we are talking.
Shall I contribute to charities promoting assassinations of evil foreign leaders (there are still a few left) and backing democratic coups instead of the blanket pro-peace movements?
This argument is based on completely ignoring future costs and benefit analysis and the available alternatives. To accept this as a (implicit?) axiom seems unnatural. Imagine a powerful lobby group stopped American involvement in the Korean war and all of South Korea ended up like the North. Imagine NATO did not strike Serbia and Milosevic continued to reign. Even the Iraq war did have some positive effect - Hussein was evil, and potentially the new government in Iraq would lead to less suffering, both internally and because of other - local and global - c...
Hm. I can try (depending on how math-y and/or patient you are I may also fail; this is quite long).
In the spirit of Eliezer's dictum "rather than a 3-vector being made out of an ordered list of 3 scalars, a 3-vector was just a pure mathematical object in a vector algebra" the same thing is going on here - the configuration of the photon is given by a complex 2-vector, which we represent as a pair of complex numbers. This means that we have chosen a basis - to quote previous post again "We can represent the polarization of light as a complex... (read more)