John Cuthber
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how do you get the sine of an angle without calculator?
John Cuthber replied to calculot's topic in Mathematics
I have seen the longhand method for calculating square roots, but I never learned it. To calculate the third order coefficient I have to multiply 2 by 3 to get 6 and take the reciprocal. That's not especially taxing. The more time consuming part is cubing 0.3372986 to give 0.038374578279565321256 (I cheated and used a calculator but ten or twenty minutes with a pen and paper would also work: I wouldn't calculate all the digits of course. ) Then I divide that result by 6 to give 0.00639576304659422020933333333333 and subtract that from 0.3372986 to give 0.33090283695340577979066666666667 which is pretty close to 0.33093912096425615102766149161188 What steps are involved in your route? (Incidentally, As I now have x^2 and x^3 calculating x^5 is just one more long multiplication. Division by 5! and addition won't take as much effort as getting the cubic term did, and the same applies to higher order terms if I needed them) -
WMAP balance of the universe using 3D electromagnetic forces
John Cuthber replied to acsinuk's topic in Speculations
Why? -
If there's no S, do you mean "Wikunde" ?
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And again, "Perhaps you would like to point out the factual errors in this analysis" Incidentally, even if I were unconcerned by the death toll from Chernobyl (I'm not, of course) then perhaps you would like to explain why you are unconcerned about a bigger number of people killed by coal. "We are not dysfunctioning Chinese coal burners and miners, "
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how do you get the sine of an angle without calculator?
John Cuthber replied to calculot's topic in Mathematics
That would make a different set of the values in your table redundant. I'd calculate cos of (pi/2)- 1.337... The small angle formula says it's 1 (the true value is .973) so I'm already pretty close My guess is the 2nd order term would get me within 1% Incidentally, without a calculator, how do you calculate the square roots in your table? I know it's possible, but it isn't trivial. More interestingly, how do you do the interpolations? Linear interpolation won't be very accurate (unless you are prepared to calculate a lot of square roots). There are two different problems here, and we are each addressing one of them. If you need sin(x) for any one particular value of x then calculating that value is less effort than constructing a table. If, on the other hand, you are going to need the value of sin(x) for many values of x, the table will save you some effort. However, it only makes sense to calculate the values for an eighth of a circle because you can use the trigonometric identities to find the other values. -
how do you get the sine of an angle without calculator?
John Cuthber replied to calculot's topic in Mathematics
For 0.3372986 rads the sin x=x approximation is within 2%. If you wanted to know it more accurately, the third order term would help a lot. However most of the entries in your proposed table would be redundant. Or, you could construct the angle (possibly easier said than done) and measure the ratio of the sides of the triangle. -
So, in respect of my earlier invitation "Perhaps you would like to point out the factual errors in this analysis" , I can take that as I can't" (save to the extent you did),.. BTW, "Why is he, and by link you, even bothering to total up the coal deaths in China, for example? " because we have to get energy from somewhere. BTW, I'm intrigued by this false assertion "If anyone cares (and you don't) the death toll from Chernobyl," Would you like to try to justify that?
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How good is your understanding of maths? If you have not waltzed through science wondering how people ever struggled with maths, don't do physics
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Fair enough, how many do you want to add to the nuclear power death toll to account for those? Unless it's comparable with the death toll from Chernobyl, it's not going to make any real difference is it? Of course, you should have realised that but...
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Does pyramid power make time stop or go backwards?
John Cuthber replied to Windevoid's topic in The Lounge
ACG55 is stuck in a pyramid and is posting from the future. -
The comparison is entirely relevant. The additional radiation dose to everyone who isn't close to the source is tiny compared to the background dose. So the additional risk is tiny. Let me know when this stops being true. "The article still says 'In fact, the fly ash emitted by a power plant—a by-product from burning coal for electricity—carries into the surrounding environment 100 times more radiation than a nuclear power plant producing the same amount of energy.' which is the point I was making " Until then, anything you say about it isn't worth reading. " through the events and risks of Fukushima the entire nuclear power industry. " Clearly bollocks since I cited a much worse example of nuclear waste emissions. Perhaps you would like to point out the factual errors in this analysis http://nextbigfuture.com/2011/03/deaths-per-twh-by-energy-source.html (I know- it's not quite the same issue as it includes things like the direct use of coal for heat, rather than for electricity generation) Delbert, they are already drawing up plans to strip the radioactive material out of the water so they can dump the clean water. Of course, that still means storing the radioactive material- but they were planning to do that anyway.
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Must Evolution [read: abiogenesis] and the Big Bang be taken on faith?
John Cuthber replied to Didymus's topic in Religion
He didn't assume your ignorance. He demonstrated it. Care to guess how many debates you will win by not understanding that difference? -
You can't have it both ways. It is a complicated issue. So it's impossible to say that the risks are "the same". But you try to berate me for saying they are comparable. Rather than complaining about my choice of words ( though it's not much of a choice in the circumstances) why don't you actually either accept that I'm right or show that I'm wrong? Also, in saying that the affected area "will include some rather far flung regions of the Pacific, if the models are even close." you are proving my point about the dilution into much of the Pacific. If I wait long enough, will you accept all the points I have made? And, BTW, I cited the sci am article to show what the article said. The article still says "In fact, the fly ash emitted by a power plant—a by-product from burning coal for electricity—carries into the surrounding environment 100 times more radiation than a nuclear power plant producing the same amount of energy." which is the point I was making so your claim that "does not support his assertion in the thread." is more than a bit fishy.
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1000 Facts you probably didnt know!
John Cuthber replied to *puffy* japanisthebest's topic in The Lounge
I think most of us can be described as functioning computers rather than just data stores. -
1000 Facts you probably didnt know!
John Cuthber replied to *puffy* japanisthebest's topic in The Lounge
About 7 billion such computers have been built without needing that much power in aggregate, never mind individually. Not only that but they were produced fairly cheaply and usually by unpaid labour. -
No, a fairly simple one. The biological damage produced by equal activities of potassium and caesium is comparable, so the threat from the two is also comparable. Now, can you refute it? If not then the fact that the sea has (on a Bq/litre basis) a lot more potassium in it that Cs is vitally important in terms of addressing the additional risk from the Cs. On a local basis, this is a disaster, but on a global scale the only impact is likely to be via the disruption to Japan's economy. Exagerating the threat from the leaks will make that effect worse.
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How many people need to ask you before you realise it's a valid question? Anyway, imagine we were having this conversation a couple of thousand years ago (I think- history isn't my forte) in Scandinavia. The usual viewpoint there would be "everyone knows that Odin created the world". Similarly, a bit earlier in Egypt "everyone" knew that the world was created by Ra, the Sun God. Did the origin of the world change or was it just that people's best guess changed? Clearly, it has changed again and now most people believe there's just one "God". But that may change again. So what most people believe isn't valid evidence. Now, can you please show why your God is any different from the fleets of Gods that the Romans or Norsemen had? Once you realise that you can't, you might understand why you are equally unable to distinguish your God from iNow's Dragon. And maybe then you will realise that there's no real evidence for any of them. iNow's point is that , in order to convince us of the validity of your God, you need to provide evidence which is as good as that required to convince you of the pet dragon. The system is symmetrical and the "number of supporters" doesn't change that.
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No, but there are many people who actually believe that some creature made the universe. Is there some reason why that's any less absurd?
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1 is true by tautology and therefore pointless. 2 clashes with your assertion that "I don't see how my personal views are relevant to this discussion." 3 Occam's razor says that you shouldn't invent any more things than you need to. There is no scientific need for God so you shouldn't invent Him. 3.5 is a strawman: God clearly isn't part of "objective" reality. 4 Yes it is: the sound-bite version is "do unto others as you would have others do unto you": Strictly, it's the enforcement of morality that's self interest, but without enforcement it doesn't amount to much. Animals like this http://www.telegraph.co.uk/earth/wildlife/5373379/Animals-can-tell-right-from-wrong.html show morality and they didn't get it from any holy book. 5 nobody said it wasn't objective- it's even measurable. You can measure levels of neurotransmitters and hormones etc and get a pretty good idea of when someone falls in love. So, that's a strawman too. Love is, however, consistent with ordinary biology- there's no need for any God and also, as I pointed out, the idea of God is love doesn't stand up to analysis. 6 What you put on your list was "That love has objective reality and has its source in God." yet God's love seems to have nothing to do with reality. 7 My question was "Perhaps you'd like to tell us what a scientist might have a religious view about (If it conflicts with the evidence, it's ruled out)" Now there are answers to that- the existence of God per se is one of them, but only if you redefine God to essentially doing nothing. The God described by any religion I have heard of doesn't exist. because, if He did, his actions would be observable. The number of angels that can dance on the head of a pin is another thing about which you can have a religious view point. One thing these have in common is that they are useless. 8 Science is a bit reductionist and materialistic- had you not spotted that? 9 ask anyone who has ever had appendicitis- or look at the design of the human eye- it's a cockup. This is clearly not the output of some mind.
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If it's as simple as "good vs bad" why no invasion of Uganda or the Congo?
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Psychology of insults [NSFW - Language]
John Cuthber replied to Tridimity's topic in Psychiatry and Psychology
I was always puzzled by the idea that calling someone a wanker is perceived as an insult when it's very likely to be a statement of fact. -
"This language has the power to alter our environment in terms of altering the weather " No it doesn't. "The great pyramid puts out a frequency that is thought to be beneficial to the earth." No it doesn't. "antennas that put out over 10hrtz that cause people and animals to go stir crazy. " No it doesn't. "Zephaniah 3:9-20 New King James Version (NKJV) “For then I will restore to the peoples a pure language, That they all may call on the name of the LORD, To serve Him with one accord. " old books are not evidence.