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### Major Advance Towards a Proof of the Twin Prime Conjecture

To be pedantic, we still cant conclude the product + 1 is prime, only that it is
a contradiction that it is divisible by no prime (which is all we need anyway). The
GP is correct in that a proof more similar to Euclid's original is given by
considering an arbitrary finite set P of primes, letting N be the product of the
P plus 1, and then concluding that a prime divisor of N must not be in P.

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### Auto-threading Compiler Could Restore Moore's Law Gains

It is important to remember that while a naive approach to functional programming (that is, using the same data structures and idioms as for imperative languages), will indeed be inefficient due to enforced persistence, much of the loss can be mitigated by using better data structures. For instance, Data.Sequence of Haskell supports access and modification time logrithmic in the closest distance to one end of the sequence, and does so in a thread safe (as always) way.

Even in the case where we demand mutable data structures because nothing else is acceptable, we can control the access in a purely functional way using monads (a very cool concept which arent as scary as they first might seem). See for instance, the haskell State monad and mutable data structures.

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### Mathematicians Extend Einstein's Special Relativity Beyond Speed of Light

he postulated tachyons and their properties again?

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### Judge Suggests Apple, Motorola Should Play Nice

A judge who dismisses a case on grounds of 'public interest' and not rule of law is overstepping his authority. As broken as our patent system is, much worse is a judiciary which disregards the checks and balances established for it by our Constitution. Perhaps Apple and Motorola are being childish, but they are acting in a manner they believe benefits their stockholders the most within the confines of the law, which is the extent of the court's authority.

Granted, I havn't read the case materials, and the judge may have a more legitimate legal basis to cancel the jury trial.

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### Re: the debt deal reached Sunday night ...

Well the lowest risk investment you can make these days is in a US Treasury Bond, essentially investing in US debt. One could argue that if the government is trying to create jobs by spending money, giving the government money will lead to job creation. Of course, this depends both on the government being successful at job creation by spending money, and that rich people would actually invest in treasury bonds. The interest rate on treasury bonds is so low right now its actually risky to buy because if the interest rate then increases, the price of the bond you own drops signifigantly (http://en.wikipedia.org/wiki/Interest_rate_risk).

Much more likely for large investments is diversified stocks, possibly managed inside a mutual fund. Diversification mitigates risk of temporal losses of investment value, but the stock market has a much higher historical (average) rate of return than bonds. Stocks give money to companies to spend on their business, which more directly contribute to job creation.

Even if you let your money collect dust in a low-risk savings account in a bank somewhere, the bank's business is to reinvest your money in the above. There are also other investment opportunities, but they all involve your money ultimately getting to companies or the government (but to be fair only mostly US companies and governments).

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### For Texas Textbooks, a Victory For Evolution

To be fair, a 'proof' that is directly experienced and scientific proof are both wholly different from a mathematical proof, which is simply a sequence of deductive steps originating from a stipulated set of axioms and definitions. Given a rational person who also happens to be a creationist, even he would agree that assuming

then B is provable in this system. This is in contrast to scientific inquiry, where there are no axioms. Instead, there are measurements and observations, and hypotheses are created which attempt to explain the measurements and observations. If a hypothesis is successful in its explanatory or predictive power with respect to further measurements and observations, eventually we may call it a theorem. At no point did we prove the hypothesis in the mathematical sense, and in fact if there came along a measurement or observation that contradicted the theorem, it would have to be revised or discarded.

Demanding to see more data before accepting a scientific theory is not an unscientific thing to do, as long as one does it honestly and with intellectual integrity. Obviously the gotcha arguments thrown around by many creationists concerning the inability to directly collect data from before the dawn of man doesn't really fulfill the spirit of science...

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*Anonymous* Creates Its Own Social Network

Talk about an oxymoron.

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### SKA Telescope Set To Generate More Data Than Current Net

Finally a new unit for large amounts of data, appropriate for this new golden age of progress and hyperbole What I want to know is how many library of congresses are in an 'internet-year'...

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### SKA Telescope Set To Generate More Data Than Current Net

...calling your global computing initiative 'theskynet' might be detrimental to your acceptance by the technologically affluent who operate the computers you need help from.

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### I Name My Servers After:

no erroll garner? one of the most mesmerizing stride players i've ever listened to

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### School District Hit With New Mac Spying Lawsuit

The sad thing is that the "Generation Facebook" is not going to go away. Kids are being continually conditioned to accept breaches in their privacy by the facebook model. Around every 2 years or so fb rolls out some opt-out Cool New Feature which causes an initial uproar about its privacy implications. Maybe fb makes a statement or adds some specific privacy features, but eventually people forget and gradually care less and less about the violation of their privacy. Each new feature is only incrementally worse than the previous, never enough to cause enough of an uproar to have it removed (except in a few cases), and so this systematic invasion of privacy continues.

I'm afraid this level of blatant trespassing as you say is only going to get more accepted and mainstream as an entire generation has its opinions on privacy eroded. This gradual desensitization to initially offensive policies is coincidentally the same way the Holocaust started

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### Using Averages To Bend the Uncertainty Principle

Sorry I should have been clear. All I meant was that we wouldnt "see" the interference pattern with just a single electron since it just excites a single atom (talking about wavefunction collapse when it hits the screen). But thats exactly right the electron still interferes with itself and the probability distribution of where we see it is the same as the interference pattern.

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### Using Averages To Bend the Uncertainty Principle

tl;dr

A: why is this so non-intuitive???

B: Quantum mechanics! *winks knowingly*

A: ohhhhh

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### Using Averages To Bend the Uncertainty Principle

I think I can safely say that nobody understands quantum mechanics.

Richard Feynman, in The Character of Physical Law (1965)

That said, I think I can attempt to clarify some of your misunderstandings
from my own understanding. In fact someone set me straight if I have any
issues of my own :)

The entire notion of a point particle is essentially a classical
approximation (as far as geometry goes). In fact, all the spatial information
that can be known (ie not completely transparent to the rest of the universe)
about a particle is completely contained in its wave function, complex valued
defined at every point in space. But the wave function in time must satisfy
the Schrödinger
equation, and it has been shown by people smarter than I that wave
function solutions *must* satisfy the uncertainty principle.

Its easiest to consider what this means in one dimension. Solutions of
the Schrödinger Equation are linear combinations of sinusoidal functions of
all wavelengths and velocities (with the solution for a particular particle
determined like with any differential equation by the spatial and temporal
boundary conditions). This is immediately consistent with the wave description
of light and matter, as a sinusoidal function has a definite velocity but
its position is not defined at all (it looks like a wave :P). So how then
can we get a localized particle, like those we apparently observe enough
to create an entire classical theory around? Well it turns out that taking
linear combinations of waves of differing velocities causes local areas of
destructive and constructive interference, and one can mathematically construct
what's known as a wave
packet. Btw, the time evolution of the wave packet in the picture
on wikipedia is incorrect for solutions to the Schrödinger Equation: particle
wave packets necessarily disperse over time depending on the represented wave
velocities (don't quote me on that). This means the range of represented wave
velocities actually has physical significance. Anyway there's a limit to how
localized a wave packet can get, called a Gaussian wave packet. To achieve
this limit, one has to sum over essentially every possible wave velocity.

So solutions of the Schrödinger Equation can be something with no
localization at all and a perfectly well defined velocity, like a sinusoidal
function, or with a very acute (but not perfect) localization achieved by
an almost infinite range of velocities of component waves. In fact there is a very simple
inequality
expressing the relationship between the smallness of the localization to
the range of velocities (momenta, actually)...

So all that's not that bad. The real strangeness of QM comes with what
observation does to the wave function of a particle. Somehow, the act of observation (something I am not knowledgeable enough to define, but examples of which are hitting it with a photon or having it excite the screen in the double slit experiment, or even covering up a slit thus knowing it must go through the other) "collapses" the wave function of a particle back into its most localized form. The probability distribution of the center of the new localized form is given by the product of the wave function with its complex conjugate just before the observation.

The interference pattern corresponds to the probability distribution of particles when they reach the screen behind the double slit. If I fired only one particle through the double slit, it would cause a single photon (probably) to be emitted from the screen, with its location determined by the probability distribution. We can see an interference pattern because we are firing a beam of particles, not just one at a time. The kicker from the experiment is if we observe the interference pattern (say by collecting billions of data points from electrons fired one at a time), information about which slit each electron went through (in particular) is transparent to the rest of the universe; it cant be determined from say where that electron struck the screen. This seems to be where your misunderstanding lies, at least in part. If we *had* observed which slit the electron went though (by covering up a slit, or by shining light on it and doing what scientists do), then the interference pattern would have disappeared.

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### Disorderly Conduct Charge for Offensive Classmate Ratings

The constitution, as far as I know, cannot be overridden by state laws. That would be absolutely insane, don't you think?

Well consider the actual text of the First Ammendment

*Congress shall make no law* respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

emphasis mine. IANAL, but it looks like a state passing a law limiting speech is technically not addressed in the Constitution.

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