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Comment: Re:Astronomy: Astrology for Physicists (Score 1) 141

by Red Jesus (#46228079) Attached to: Oldest Known Star In the Universe Discovered
Oops, correction to the car analogy: The rubber sheet is 6000 miles long when the car starts driving, is 46.6 billion miles long when the car stops driving, and the car itself thinks it has driven 13.7 billion miles relative to the sheet. (If space behind you expands, you don't have to redrive that extra distance.) Replace miles with light-years and we have a description of the photon traveling from this star to the Milky Way galaxy: they started 6000 light-years apart, they ended 46.6 billion light-years apart, and the photon thinks it spent 13.7 billion years in flight because it traveled 13.7 billion light-years with respect to the background of expanding space.

Comment: Re:Astronomy: Astrology for Physicists (Score 2) 141

by Red Jesus (#46227621) Attached to: Oldest Known Star In the Universe Discovered

The phrasing is a bit misleading. The star was 6000 light-years away when it first emitted the light, but the empty space between stars (and galaxies, now) has been expanding continuously (but at a nonconstant rate) since then. Imagine a car driving along a rubber sheet that's stretching. The sheet *starts* 6000 miles long and the car drives at one mile per hour, but since the sheet is growing as the car drives along it's 13.7 billion years long by the time the car reaches the other end.

So we're seeing the star as it looked 13.7 billion years, ago, not as it looked 6000 years ago, the current physical distance between us and the star is actually a whopping 46.6 billion light-years, and the 6000 light-year number corresponds to the distance between us and the star when the light was first emitted. (The universe was much smaller then.)

Note that this goofy universe-expansion correction factor doesn't apply to such short distances nowadays. The center of the Milky Way galaxy is 30000 light-years away, but since space itself isn't expanding so rapidly today, we see the center of the galaxy the way it looked about 30000 light-years ago, as expected. The most ridiculous rates of expansion took place shortly after the Big Bang.


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Comment: It's not hard (Score 1) 154

by Red Jesus (#45730043) Attached to: 'Approximate Computing' Saves Energy


To determine if a/b is greater than 1, it is sufficient to check if a > b.

To determine if a/b is greater than c, it is sufficient to check if a > bc.

Multiplication already consumes less time and energy than division on modern computers. I do not see why they needed to modify their instruction set to realize such gains.

Comment: Re:Solved problem (Score 2) 226

by Red Jesus (#45487219) Attached to: Ask Slashdot: How Reproducible Is Arithmetic In the Cloud?
Not quite. IEEE754 mandates correct rounding for addition, subtraction, mutiplication, division, and square roots, but it only requires "faithful rounding" for the transcendental functions like sin, cos, and exp. That means that, for example, that even the floating point number nearest arcsin(1) is above it (i.e. correct rounding in this case requires that you round up), a math library that rounds arcsin(1) *down* is still compliant. The only requirement is that it round ot one of the two nearest floating point numbers.

Comment: Re:You need to know some numerical analysis (Score 4, Interesting) 226

by Red Jesus (#45487183) Attached to: Ask Slashdot: How Reproducible Is Arithmetic In the Cloud?

While that's true in many cases, there are some situations in which we need . Read Shewchuk's excellent paper on the subject.

When disaster strikes and a real RAM-correct algorithm implemented in floating-point arithmetic fails to produce a meaningful result, it is often because the algorithm has performed tests whose results are mutually contradictory.

The easiest way to think about it is with a made-up problem about sorting. Let's say that you have a list of mathematical expressions like sin(pi*e^2), sqrt(14*pi*ln(8)), tan(10/13), etc and you want to sort them, but some numbers in the list are so close to each other that they might compare differently on different computers that round differently, (e.g. one computer says that sin(-10) is greater than ln(100)-ln(58) and the other says it's less).

Imagine now that this list has billions of elements and you're trying to sort the items using some sort of distributed algorithm. For the sorting to work properly, you *need* to be sure that a < b implies that b > a. There are situations (often in computational geometry) where it's OK if you get the wrong answer for borderline cases (e.g. it doesn't matter whether you can tell whether sin(-10) is bigger than ln(100)-ln(58) because they're close enough for graphics purposes) as long as you get the wrong answer consistently, so the next algorithm out (sorting in my example, or triangulation in Shewchuk's) doesn't get stuck in infinite loops.

Comment: Your chances are pretty darned good (Score 5, Informative) 226

by Red Jesus (#45486489) Attached to: Ask Slashdot: How Reproducible Is Arithmetic In the Cloud?

Mathematica in particular uses adaptive precision; if you ask it to compute some quantity to fifty decimal places, it will do so.

In general, if you want bit-for-bit reproducible calculations to arbitrary precision, the MPFR library may be right for you. It computes correctly-rounded special functions to arbitrary accuracy. If you write a program that calls MPFR routines, then even if your own approximations are not correctly-rounded, they will at least be reproducible.

If you want to do your calculations to machine precision, you can probably rely on C to behave reproducibly if you do two things: use a compiler flag like -mpc64 on GCC to force the elementary floating point operations (addition, subtraction, multiplication, division, and square root) to behave predictably, and use a correctly-rounded floating point library like crlibm (Sun also released a version of this at one point) to make the transcendental functions behave predictably.

Comment: Re:Pointless posturing (Score 5, Informative) 200

by Red Jesus (#44782961) Attached to: New Jersey Congressman Seeks To Bar NSA Backdoors In Encryption

Whoa, now. While it's true that the NSA has a history of disregarding the law, it's bad to fall into the trap of believing that there's no point to creating such laws at all.

What do you want Congressman Holt do? Rip off his shirt and physically attack James Clapper? That's not going to help curtail the powers of the NSA and you know it. Congress creates laws. That's what they're supposed to do. If you think the law is a good idea, then proposing the law isn't "pointless posturing," it's Congress' job.

It's easy to get so lost in cynicism that you stop believing that forward progress is possible. But it's an ugly fact that many of the NSA's recent activities have had explicit Congressional approval. Revoking that approval is an essential step to fixing the situation, and Congressman Holt should be applauded for attempting to do so.

Comment: Pardon my troll, but... (Score 5, Interesting) 120

by Red Jesus (#44624031) Attached to: Google Chrome 29 Is Out: Omnibox Suggestions, Profile Resetting

I hate to troll what could be a pleasant discussion about a new release of a popular web browser, but Chrome sends lots of extra data to Google and Google sends lots of extra data to the NSA. I therefore do not trust Chrome.

I understand that this is irrelevant to the current topic. If I don't want to use Chrome, I should just use another web browser, right? Like how I didn't want to use GMail, so I got a Lavabit account in 2009. (Seriously!) But Lavabit is gone now. And when I updated my friends with my new email address, I sullenly noted that well over half of them use GMail because the convenience outweighs the loss of privacy.

So... I'm tired and afraid. Google is integrating more features into the browser that are based on the "recency of the websites visited"? That information will almost certainly be radioed back home to Google. And when the NSA is finally forced to answer for their sins before Congress, they'll point to how many people downloaded Google Chrome 29 and they'll say, "People don't mind being tracked! They sign up for this stuff voluntarily!" Regardless of whether that's a good reason for the NSA to be able to read my email, it's going to come up repeatedly in the inquiry, and that one fact might be enough to allow the program continue.

I have no choice but to see the existence of Google Chrome 29 as a threat to my freedom. I wish I could be more reasonable about it, or at least keep my stupid opinions to myself, but being reasonable about Snowden wasn't enough to save my email account.


Comment: Re:Concrete reality (Score 5, Insightful) 771

by Red Jesus (#44516485) Attached to: Encrypted Email Provider Lavabit Shuts Down, Blames US Gov't









Comment: Concrete reality (Score 5, Interesting) 771

by Red Jesus (#44515323) Attached to: Encrypted Email Provider Lavabit Shuts Down, Blames US Gov't





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--Anthony Coulter, a.k.a. Red Jesus

Comment: From Isaac Asimov's "Foundation" (Score 5, Insightful) 657

by Red Jesus (#36378022) Attached to: Could the US Phase Out Nuclear Power?

And you men and half of the Internet as well are just as bad. We sit here, considering Wikipedia the all-in-all. We consider the greatest end of science is the classification of past data. It is important, but is there no further work to be done? We're receding and forgetting, don't you see? Here in the America they've lost nuclear power. In Japan, a power plant has undergone meltdown because of poor repairs, and the Chancellor of the Empire complains that nuclear technicians are scarce. And the solution? To train new ones? Never! Instead they're to restrict nuclear power.

--Salvor Hardin, paraphrased
