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Comment I don't think it means what you think it means (Score 1) 633

In 2010, 865 billion was paid into social security and 701 billion was paid out. So ignoring social security and interest on the debt we have 4 major categories of spending, DoD, Medicare & Medicaid, Mandatory and Discretionary. About 150 billion of the discretionary spending is military so we end up with something like Defense: 839 billion, Medicare & Medicaid: 793 billion, Mandatory: 416 billion and Discretionary (non-defense): 510 billion. I don't think "pale in comparison" means what you think it means.

Comment Re:No hw keyboard (Score 1) 252

My initial reaction was "crap, no keyboard" but even with a nice keyboard on my N900 I have to be really bored to do anything more than a very short SMS or an instant message. I'll read an email but generally won't write one unless it is nothing more than "OK", "go ahead" or "thanks".

Comment Re:Missing the point of math... (Score 1) 636

But it's not taught that way.

It's never taught that way in US schools. Ever. It's always taught as an abstraction without ever tying any of it to real life. Ever. (repetition for emphasis)

It is taught that way if you have a good teacher. All my math teachers were excellent so we got lots of practical examples. But just like any skill, there is a lot of what one of my math teachers called "crank and grind" that you have to go through to internalize the skill enough that you can then focus on applying it.

Comment By far the biggest issue I see is ... (Score 1) 396

Many self-taught programmers lack even a basic understanding of algorithmic complexity. This is the single biggest issue I run into in industry and should be one that isn't too hard to fix. Again and again I find people have written some algorithm that just doesn't scale to larger amounts of data because it is n^3 or n^4 instead of linear. After that I would say it is a good grasp of some of the ideas in functional programming particularly recursion. There are a lot of other things I run into but I never noticed that self-taught programmers were more prone to them than others.
Earth

Antimatter In Lightning 169

AMESN writes "The Fermi Gamma-ray Space Telescope, launched last year, detects gamma rays from light years away, but recently it detected gamma rays from lightning on Earth. And the energy of the gamma rays is specific to the decay of positrons, which are the antimatter flavor of electrons. Finding antimatter in lightning surprised researchers and suggests the electric field of the lightning somehow got reversed."

Comment Re:The Amiga Hand? (Score 1) 517

The methodology is the best you can do; proving anything is basically establishing that two descriptions are equivalent.

With formal systems you usually have one definition that written to make it obviously correct and another that is more "pragmatic". In the case of propositional logic the obviously correct formalization is truth tables which are completely untractable to work with for large numbers of variables but are very simple conceptually. The "pragmatic" formalization is the logical connectives like and, or, implication etc that we normally think of as propositional logic. When they prove that propositional logic is sound they mean that all propositions give the same result as a truth table when evaluated and when they prove it is complete they mean that all truth tables give the same result as a proposition and thus propositional logic and truth tables both formalize the same concept.

There is no concept of "correct" in formal systems because it is inherently an informal concept meaning it does what it is supposed to do.

Comment Checking Consistency (Score 1) 517

A machine-checked proof means they are checking that the implementation in C is consistent with the specification written in Haskell. Your confidence that the kernel is correct is exactly your confidence that the specification in Haskell is correct. The C code is 7500 lines, I wonder how big the Haskell code is. This has nothing to do with Godel's incompleteness theorem as correct doesn't mean anything even close the formal definition of complete.

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