To paraphrase, you can't be too rich, too thin, or have too many bits of precision in a calculation. With single precision you have to be enormously careful not to drop digits even in comparatively modest loops; with double precision you can many digits before you run out. You can see it in almost any computations involving trig and pi -- single precision pi degrades in series much faster than double precision pi. It isn't just a matter of not using forward recursion to evaluate bessel functions, which is unstable in any precision (or for that matter, using book definitions of e.g. spherical bessel functions in terms of trig functions) or reordering series to avoid subtracting big numbers and running small to big instead of big to small -- there is simply a big difference between cumulating a random walk with a random digit at the 16th place and one at the 8th place.

A second problem is the exponent. 10^38 just isn't "big" in a modern large scale computation. It is easy to overflow or underflow a single precision computation. 10^308 is a whole lot closer to big, even expressed in decibels. One can concentrate a lot more on writing simple code, and a lot less on handling exponent problems as they emerge.

A final problem is random numbers. This is actually a rather big problem, as lots of code (all Monte Carlo, for example) relies on a stream of algorithmically random numbers that (for example) do not have a period less than the duration of the computation and that do not have significant bunching on low dimensional hyperplanes or other occult correlations. It is much more difficult to build a good random number generator on fewer bits, because the periods of the discretized iterated maps scale (badly) with reduced numbers of bits and it is more difficult to find acceptable moduli for various classes of generators from the significantly smaller discretized space. You can watch this problem emerge quite trivially by building a Mandelbrot set generator in float and rubberbanding in -- oops, you hit bottom rather quickly! Rebuild it in double and you at least have to work to rubberband in to where it all goes flat. You have to build it in a dynamically rescaleable precision to rubberband in "indefinitely" as the details you wish to resolve eventually become smaller than any given finite precision. This actually illustrates the overall problem with single precision quite nicely -- the emergent flat patches in an graphical representation of an iterated map are isomorphic to the establishment of unintended correlations in long runs of iterated maps in a random number generator and the clipping of the graphical representation of small numbers illustrates the problems with mere underflow in real computations of interest.

Personally, I dream of default quad precision and 128 bit processors. 34 decimal digits of precision means that a random walk with n unit steps (which accumulates like \sqrt{n}) require (10^30)^2 = 10^60 steps to get to where I don't still have 4 significant digits. Even a rather large cluster running a rather long time would have a hard time generating 10^60 add operations. In contrast, with only (say) 8 decimal digits a mere 10^16 operations leaves you with no digits at all, assuming you haven't overflowed already. I've run computations with a lot more than this number of operations. I also like the idea of having overflow around 10^5000. It takes quite a while adding numbers at the overflow of double precision to hit overflow, and one basically could add overflow scale single precision floats forever and never reach it. That gives me comfort. It would also make writing a Mandelbrot set explorer tool where one would be likely to give up before rubber banding all the way to the "bottom" -- there are a whole lot of halvings of scale in there to play with that still leave you with much more resolution than needed on the screen.

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I like to make sure that the wires are very slightly tipped when I talk so that the electrons go downhill into my phone. Otherwise the wire gets clogged.

Isn't that why the phone lines run overhead? Otherwise the people on the second floor couldn't use the phone!

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...with laser beams! Radical!

Shades of a bad science fiction novel. Or even several bad science fiction novels.

Next up on the news at 9 -- replete from eating Fukashima, Godzilla shows up from the trenches off of Japan to eat the Independence before marching on San Francisco, plates a-glowing...

...and this isn't even the first journal to do this. It's probably happening now because an entire book has just come out walking people how universally abused p-values are as statistical measures.

http://www.statisticsdonewrong...

The book is nice in that it does give one replacements that are more robust and less likely to be meaningless, although nothing can substitute for having a clue about data dredging etc.

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Donations are already taxed for most non-profits. Tax-exemption for donations isn't the same thing as not paying a corporate tax. Bear in mind that it is trivial to set up non-profit organizations and easy-peasy to use them to pass absolutely obscene not-profits straight through to the corporate officers as salaries, who just happen to be the folks that founded the not-for-profit and who own its not-for-profit shares that, in the event that those same officer/owners convert it over to for-profit, will become disgustingly valuable in an instant (see the history of Blue-Cross-Blue-Shield, for example). My wife worked for just such a non-profit until about a year ago. The company president of this not-for-profit company was knocking down seven digit salaries plus seven digit bonuses at the same time they were cutting her income to pay for an IT transition that they mandated. Her "donation" to the company was indeed not taxed -- it wasn't even voluntary. Non-profits need substantial tax revision almost as badly as religions.

You seem confused about the constitution, the bill of rights, and taxation in general, and nobody has suggested taxing people for exercising a civil liberty (certainly not me). What is being suggested is not giving people a tax deduction for money donated to a club. I'd oppose giving a tax deduction for dues paid to the Shriners, the Benevolent and Paternal Order of the Elks, the Masons, the Knights of Columbus, etc on the same basis, even though in some cases some of those organizations do some charitable works some of the time. I'm even borderline comfortable with tax breaks for donations to things like the Salvation Army whose primary focus is charity, although I am most unhappy with the way they pay their corporate officers and don't like the idea that those that they help get the help only at the cost of proselytizing. I could see clear to similar rules for genuine charities stripped of the missionary component set up by religious groups as well.

But the pass-the-hat donations to churches, used primarily to pay to maintain the infrastructure and personnel of the church, no. Taxing that isn't taxing your right to exercise a civil liberty -- nothing in the world is preventing you from belief or worship. It is taxing the money you are giving to a club designed to promote your belief in yourself and others and to support a huge formal infrastructure that yes, absolutely, exercises a substantial amount of power. We have similar laws regulating donations to things like political action committees and candidates for office -- if those laws were fairly applied to many churches they would not meet the criteria for 527 status because they often advocate for specific candidates or positions and are knee-deep in issue advocacy.

Some churches do good stuff some of the time. My niece is a Methodist minister; so was my grandfather. My grandfather, from all accounts, was a sharpster who ran his household until he ran out of money and then went and held a tent revival somewhere to refill his coffers. My niece works in Palestine trying to bring justice for the Palestinians and peace in a land that has almost never known it. But if you donate money to the Methodist church in church, almost all of that money goes to support the church itself and the minister that preaches to you on Sunday. That's the money I don't think should be deductible, because the government has no business subsidizing the support of churches, synagogues, mosques, temples, or the people that run them, "cult" or not, and tax breaks are a de-facto subsidy.

If at some time you want to talk about the religious beliefs or lack thereof of our founding fathers, I'm happy to direct you to their own writings in which it was made perfectly clear that most of them were anything from atheists to deists. Jefferson's personal ambition was to establish a state free from religion, not a religious state, a state where one did not have to profess belief in a God at all in order to exercise political rights.

If you look up above, you can see precisely where that plan has been run awry by your own words. You are quite right. Even for atheists like Abraham Lincoln and Jefferson and John Adams and George Washington and Thomas Paine, it was necessary to hide their (lack of) beliefs in a world where political power was solidly in the grasp of the churches. It still is. One cannot get elected as an atheist. Which all by itself says that something has gone very, very wrong with the founding fathers' ideal of religious freedom -- freedom from religion, especially in politics. All you are doing is confirming my reasons for wanting to oppose it -- you suggest that anybody "godless" must be "totalitarian" (bullshit!) or that simply actually enforcing the separation of church and state that the bill of rights requires and getting nonsense like "In God we Trust" off of our currency is somehow threatening to our civil liberties rather than actively enforcing them.

I really do suggest that you consider studying the Bible before you suggest that our rights were endowed by a Creator. The Bible makes it clear that humans have no rights whatsoever. For example, it explains that I can beat my slaves almost to death, or rape my neighbor's daughter as long as I pay her father 20 shekels of silver afterwards and marry her. Numbers 21 is another really excellent passage describing the genocidal slaughter of women, children and old men except for the young virgin women in the Midianite crowd who were given to the troops to rape and enslave as part of the booty -- by Moses, who was surely a righteous man, somebody Jesus was perfectly happy to walk around with up on the mount. Consider that at no time in the history of the world has God enforced a single human right. No injustice, no matter how it cries out to the sky for correction, has ever been repaired by a divine act. Every day acts of unspeakable horror occur -- plenty of them as the result of so-called acts of God -- without any hint of divine rescue or retribution.

No, human rights were invented by humans -- in particular by Thomas Hobbes, John Locke, and Thomas Jefferson, especially by Jefferson who gave them a compelling poetic appeal, one that could rouse passion in the human heart. The declaration of independence is a statement of what the world should have been if God had in fact been on the job, and an acknowledgement that since he's not, since there is no such thing, it is high time that we as human beings pick up the burden for ourselves. If you want heaven, if you want justice, you'd better put your shoulder to the wheel and make it happen here on Earth because there is no divine heaven or hell or cosmic justice before, during, or afterward.

I can do no better than close with a nice quote from Thomas Paine, one of our good old founding fathers:

All national institutions of churches, whether Jewish, Christian or Turkish, appear to me no other than human inventions, set up to terrify and enslave mankind, and monopolize power and profit.

That, my friend, is the common attitude of the founding fathers, most of whom were sufficiently adept at concealing the depth of their antipathy to organized religion that they could continue to hold political power in a world where mankind was already enslaved, where the church(es) already held the monopoly on profit and power. It has taken hundreds of years to break that monopoly. The work isn't finished yet. But the age of reason that Paine called for is gradually bringing it about, because -- and I know you won't like this, but it is simple truth and you should think about it -- reason and religion are fundamentally incompatible. You cannot consistently accept a dual standard for determining probable truth, one for "scientific" facts deduced using observation and consistently applied reason in the actual world and another for "truths" supposedly stated by people whose primary goal was the establishment of a stable religious hegemony that conferred upon them substantial power and wealth and tribal status, which have no observational basis and which cannot ever be verified or disproven by observation or reason.

That's why you are reduced to making up stuff about Creators and trying to tie it into what might have caused the Big Bang or other observed aspects of the visible Universe. Nobody can prove you wrong, to be sure. You could assert that the big bang was the hatching of a giant egg (Hindu), or the expression of certain bodily fluids (Greek) or that it can be mapped in some improbable way into the absurdities at the beginning of Genesis and nobody can possibly prove you wrong. In fact, you can make up a literally infinite number of stories for what might have gone on beforehand. You can support them by means of antique scriptures or just invent them. There really isn't any difference.

Physicists (I am a physicist, BTW) do the same thing -- they try to imagine what might have been going on beforehand. The difference is that their guesses and imagination are tempered by the need for absolute, rigorous consistency with the body of knowledge we have gradually built up that can be verified at any time by any person interested in doing so by the means of performing various experiments or observations, and that physicists do not assert their hypotheses as truth . Physical laws are expressed as probable truth -- in the case of some things, very, very probable truth -- but we always maintain the mental flexibility to change our minds in the event that an experiment comes along that disproves a belief or demonstrates that the belief is not complete.

Where is there any evidence of that rational process in religion? Physics is humble and skeptical where religion is arrogant and certain. In science there is no revealed truth, only truth as we can best discern it when we work very hard and in a completely open and collaborative way. In religion it is exactly the opposite -- all truth is revealed truth, and (with the exception of perhaps the Quakers) such truths are held to be immutable and unchallengable. For most of human history, to openly challenge a supposed revealed truth was to invite torture and death.

You like the idea of freedom. So do I. And the most basic freedom is the freedom to think, to challenge the system of beliefs you were force-fed as a child and indoctrinated in to the point where you find it difficult to challenge them. I suggest that you use it.

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Not at all. I'm perfectly happy for people to believe anything they like. However, I absolutely object to giving them tax breaks on the basis of their belief system or to support an organized supernatural belief system. For one thing, as has been pointed out it clearly violates the separation of church and state (as do many other silly things, such as the references to God on currency, and yeah, I oppose those too because they do not speak for me or for a Hindu who believes in Gods, not (the Judeo-Christian) God, or for a Buddhist, or for many others. The state has no business even obliquely endorsing belief in the supernatural, especially given the lack of evidence for anything supernatural to sensibly believe in.

You clearly seem to have Obama on the brain, BTW. Curious, since this discussion isn't really about Obama -- it is a conservative principle to not force religious belief down people's throats and there was never any constitutional reason to give religions of any sort tax breaks (as I said, the Bill of Rights directly and specifically prohibits mixing church and state).

As for judging organizations about being a cult or not being a cult -- that's what is done NOW, when the Federal Government has to decide whether or not any given group of people who adhere to some absurd belief constitute a religion or a cult. The only rule that is consistently applied is that "old" absurd belief systems are grandfathered in and try to stomp on "new" absurd belief systems with hobnail boots, so anything new is a cult, anything old is a religion. So Jehovah's Witnesses, who were never anything but a cult and remain so today, are part of a religion in spite of the fact that some of their religious practices with their children actively endanger those childrens' lives. Ditto Mormanism. Ditto some of the other offshoots of Christianity with their tinhorn messiahs (there are a bunch of them out west and across the south). But Islam or Methodism or Catholicism aren't cults, because a lot of people believe in them instead of only a few. There's no more evidence for any world religion than any other -- zero equals zero -- but numbers apparently matter.

I disagree. I don't want to distinguish a religion from a cult at all. I want none of them to have any sort of legal protection or legal persecution, provided that they obey the common secular law, which includes taking care of your children and giving them blood-based products (like plasma or a blood transfusion) if they need them medically and so on. Including tax protection.

Look, if you wanted to join a chess club, you wouldn't try to deduct your dues. Why should you get to deduct your dues if you join a God club?

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I'm an acolyte of the Don't Make Up Stupid Theories About Everything Coming From Nothing Because a Big Guy In The Sky Made It So Without Evidence. Especially don't try to sell them as revealed truth (without evidence) in contradiction to all of the other equally absurd and related theories that are sold as revealed truth (without evidence) that were invented by unbelievably primitive cultures to establish political-religious hegemony. As for "all human wisdom that existed in the past is foolishness" -- quite a lot of it was. Not all of it. You know how we can tell which is which?

I didn't think so, but a big hint is this -- NOT because it is written in scripture, NOT because it is believed by a large or small fraction of the human population, NOT because they are the words of somebody famous, NOT even because the "wisdom" isn't overtly inconsistent and hence isn't a priori impossible.

In the meantime, I'm not a big fan of the everything came from nothing theory simply because it isn't terribly consistent with physics. I much prefer everything came from everything, or if you prefer, the gobsmackingly obvious observation that "nothing" is not a state that has ever been observed or that can reasonably be inferred from observations of that which we can measure. But whether or not you yourself think that everything came from nothing (ex nihilo) because there wasn't really nothing, there was God, and God, while not really something, was enough to make something out of nothing or whatever tangled web of irrational logic you want to make up or accept as "ancient wisdom" concerning "creation" in a Universe with an apparent empirical law of conservation of mass energy, otherwise known as the "we have never, ever, seen an act of creation" law) I am highly allergic to giving the name "God" to my own ignorance, allowing it to fill the gaps in my understanding as the easy way out.

What happened before the alleged Big Bang? Was there "nothing"? Was there "something"? Is the visible Universe part of a much larger structure of existence, most of which we simply cannot see? Sure, all of these are perfectly lovely questions and I have no answers to them. How could I? We simply cannot see, and until we can there is no good reason to prefer one "answer" (otherwise know as "hypothesis" since they are only provisional answers) over another and only silly people would spend a lot of time arguing over the enormous range of possible answers, let alone fighting wars and blowing themselves and others up when people refuse to accept one particularly silly hypothesis without evidence or any reasonable hope of obtaining evidence.

But do as you like.

And BTW, I don't have an iPhone. Honestly, I'm not even sure what your implication is when you assert that I do. Are iPhones satanic atheist instruments? Does the fact that Ask Siri is more likely to reveal an evidence-supported truth than Ask the Old Testament grate on you?

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Let's repeal the tax-exempt status of all religions! There isn't the slightest good reason that they should be tax exempt in the first place. For one thing, they are organizations devoted to coercing and conditioning the young to believe in absurdities. For another, they wield political power and influence and I don't want my own tax dollars making up the deductions taken by those individuals who are directly or indirectly supporting political positions I don't agree with. For a third, it is semantically and epistemologically impossible to differentiate a "religion" from a "cult". All religions began as cults and are cults still -- they both consists of a group of people who claim special and absurd knowledge of things that cannot be independently and objectively verified or observed and who want to convince others that accepting this "knowledge" as true will grant them equally special status promised, curiously enough, only as a part of the knowledge that must be accepted.

The two words refer to the same thing, at most separated by a scale factor. Either we make pastafarianism a tax-exempt religion or allow special tax concessions to any Subgenius preacher claiming to spread the word of J. R. "Bob" Dobbs, or Methodism and Judaism and Islam and Catholicism and Scientology and... (the list continues, and continues) should all have all forms of special status revoked. Religion can be a tax-paid-dollar supported club all it wants, but the idea that money paid into a kitty to be given to somebody to support a building and employee whose sole purpose is to promise people ludicrous rewards or tortures and to believe in magic should some how have the same status as money given to (say) UNICEF or Care is absolutely ridiculous.

So please, sign this petition. If we make Scientology financially untenable, maybe then we can tackle the next 100 cults on the same list.

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Continuous commanding and telemetry with a slight delay...

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Mod up for a great reply. Oh, wait. No mod points again. Wish there was a kitty so that I could save a handful for when I need them.

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If I had mod points today, I'd mod you up. Personally I'm skeptical that CO_2 will lead to a climate disaster, but either way burning all our oil and coal is incredibly stupid as they are the base stock for pretty much all organic chemistry synthesis, and while sure, if/when we master fusion or get off of our backsides and start burning thorium and drop PV solar to the point where it can interpolate or provide industrial daytime energy in suitable locations we can work comparatively inefficient magic with other materials, aside from methane the carbon itself is likely to be entropically downhill from where we'd like it to be and it will cost us a lot of energy to reverse that. I'm pretty skeptical, however, of electric cars -- maybe a bit less so of biofuels -- I don't think people realize that it would require 100% of an entire day's worth of clear-sky production of their $20,000 5 KW rooftop solar system to not-quite replace 1 single gallon of gasoline. No matter how you amortize that, it isn't going to be pretty. Biofuels have the same issue, they just get to the gallon via different route -- a lot of land surface, water, human effort, and capital investment per gallon equivalent of fuel.

Fusion is really the critical technology. If we master D-D commercially scalable fusion, as long as we can don't lose the knowledge and can bootstrap a single fusion plant we can "reboot" civilization. The problem we're soon going to be facing, however, is that all of our knowledge is going to be stored in a volatile form that will be absolutely unreadable post-apocalypse, and in another generation or two humans will get so lazy and dependent on instant access to information they had to at one time internalize that a collapse will lose nearly everything we know in a single generation. Paper isn't a perfect medium for preserving knowledge, but it does have the advantage of lasting for as long as centuries with reasonable care and not requiring any particular technology to read from it, and only very modest technology to produce it and print to it.

So let's all sing a canticle for Liebowitz and imagine a post-apocalyptic world in which priests are running around conserving -- usb sticks, old dvds, ancient hard drives, or little tiny chips of plastic with tarnished brass that individually could contain a good chunk of Wikipedia but are as useless as a boar's teats without a mountain of technology too high to imagine any primitive culture surmounting in any amount of time.

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This is curious, given that UV is so strongly scattered by the atmosphere that it would have almost no range. Even blue light has comparatively little range. They must have used hellaciously bright UV lights and/or just communicated over very short distances in clear air. One wouldn't expect even people with artificial lenses or corneas to have much sensitivity in the UV, as well.

Rayleigh scattering of UV light of (say) 300 nm wavelength is over 16 times stronger than the scattering of red light. It's one reason that runway lights intended to be seen by planes only after they've landed are typically blue, while markers intended to be seen from far away are typically red.

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So here I am, building my death drone fleet, thinking "Gee, I'll be sure to leave in the transponder and radar reflectors. After all, even though there are no government regulations requiring them, I want my victims to see them coming."

As for 911, a) the economic impact of air travel and freight is difficult to equate to the net productivity of a small-payload drone fleet at any level; b) the "solution" to the problem turned out to be literally locking the pilots into the front of the plane so passengers would have to cut through a solid bulkhead in order to reach the cockpit, which would at the very least require time and make the enterprise not worth the risk. There might be more measures we don't know about as well. This is possible because airplanes are an enormous capital investment in addition to being a core feature of our economy in ever so many ways. Adding security features to an airplane doesn't double its cost or halve its productivity.

With a drone, that is not the case. Security measures added to a drone do significantly increase its cost and lower its productivity (which is probably marginal anyway, given its small payload). And there is no way that I can imagine to add security features that somebody can't just turn off or remove or trivially suborn without massive government intervention.

It's sort of like the various assault rifles being sold that can have a single part or two removed or replaced and they are magically transformed from being "semi" to "full" automatic. Marvelously effective at preventing honest citizens from owning fully automatic assault rifles, not so good at preventing full automatic assault weapons from showing up all over the place in the hands of the less honest or fringe militias.

But hey, now the fringe militias will be able to add another weapon to their repertoire! Full automatic rifles, vans full of homemade TNT and an explosives-laden drone fleet. I can't wait!

And yes, we'll get this in spite of the government trying to slow it down. I'm betting we'll first see it in drones built and delivered by personality disordered borderline high school students who by some means manage to lay their hands on real explosives. That sounds like so much fun I'm tempted myself...

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It's also perfectly reasonable to assert "That is never, ever, going to be legal, so why bother to permit then to develop something we aren't going to allow." Admitting that this isn't quite what has been said, it is probably at the heart of the denial.

As you suggest, there will probably be little we can do about preventing people from doing this with drones already and/or in the near future -- the barn door already done been opened and the horses are long gone -- but at least we can arrange a world where ANY drone, autonomous or not, is illegal and hence a candidate for defensive measures.

It is, sadly, yet another case of the tragedy of the commons. Drones could be everything from fun to enormously useful, but once they are in "the commons" and available to everyone, it only takes a few butt-holes to make them a liability that exceeds any possible benefit. At the same time, it is virtually impossible to put techno-genies back into the bottle. I can hardly wait for the day somebody figures out how to make a compact 20 kt+ nuclear device out of commonly available materials and using nothing but garage-shop tools. There have been a very few SF stories written about such things, and none of them have happy endings.

Maybe this is the answer to the "Where are they?" paradox. Any time a civilization rises above a certain technological threshold, it becomes possible for anybody to destroy it, and there is always somebody that does. Maybe it becomes possible to build a fusion device that doesn't require a fission trigger, for example, or maybe it becomes possible to bio-engineer a doomsday virus with a "perfect" epidemiological profile and nearly 100% mortality in your basement.

Fully anonymous drone-delivered murder and mayhem may not qualify as doomsday, but it will certainly create some serious challenges to the concept of personal freedom vs public safety and the abuse of the commons.

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And who knows, maybe they'd add a radical "new" idea or two to Windows (just to enable playing games). Like, I dunno, multiple desktops. So you can have your Excel spreadsheet up on desktop 1 and WoW up in desktop 2 and switch with a keystroke when the boss comes in.