One of the many great things about my readers is how you folks keep me up to date with any new crap that springs up, so that I don’t need to spend so much time hunting down the real good stuff. There’s a beautiful piece of crap on youtube that was pointed out to me by one of you guys. It’s really a wonderful bit of circularity.
Circularity is something that I find beautiful in math. What I mean by circularity is that because numbers are closed, you can run around in circles playing games with that closure. Another post that I’ve got in progress is talking about RSA encryption, which is a beautiful example of circularity. You start with a message, encoded as a number, M. Then you take a particular set of three numbers, N, D, and E. If you raise M to the Dth power modulo N, you get a new number. M’. If you raise M’ to the Eth power modulo N, you get the original M. You’re never taking roots – but the two exponentiations cancel each other out modulo N. It’s beautiful, and astonishing, and yet it makes perfect sense.
That’s a complicated example of circularity. A simpler one, also involving modulo arithmetic, is to look at the tempered music scale. Let A=0, Bb=1, B=2, C=3, Db=4, D=5, Eb=6, E=7, F=8, Gb=9, G=10, Ab=11. Now, start at A, and follow through musical fifths – that is, go from A(0) to E(7). Then E(7) to E+7=14 mod 12 = 2 = B. Then B to Gb(9). Then Gb to Db(4). Then Db to Ab. Then Ab to Eb. Then Eb to Bb. Then Db to F. Then F to C. Then C to G. Then G to D. Then D to A. You’ve taken twelve steps of fifths, and wound up where you started. So by following through one of the natural musical elements of harmony, you’ve got a circle that visits each note exactly once. Looked at mathematically, it’s trivial. But it’s still pretty cool.
It’s pretty easy to trick yourself with circularity of you’re not careful. You can find what appear to be amazing numerical coincidences, because you don’t realize that you’ve created a circle.
The target of this posts isn’t an example of that. It’s a really trivial circle.
This case is a fundie twit who wants to argue that the Bible predicts relativity. How does he do that? Well, he starts with a quote from the New Testament: “But do not forget this one thing, dear friends: With the Lord a day is like a thousand years, and a thousand years is like a day”.
Ok. So – he takes the time dilation equation from relativity. And he plugs stuff into it to see how fast you’d need to go to make time dilation make you move fast enough that a thousand years of non-dilated time is equivalent to one day of dilated time:
Δt = t0/sqrt(1-v2/c2)
1000 years = 1 day/sqrt(1-v2/299,792,4582)
365250 days × sqrt(1-v2/2997924582)=1 day
So after working through it like that (with, apparently, no clue of anything as unimportant as significant figures), he comes up with an answer of how fast you’d need to move to produce that amount of time dilation. And guess what? Miracle of miracles, wonder of wonders, creating a time dilation of approximately 365,000 to 1 requires moving really, really close to the speed of light!
Therefore the bible predicted time dilation and the speed of light. Seriously. From that conclusion, he concludes: “Q.E.D. The BIBLE gives SCIENTIFIC, MATHEMATICAL evidence for the SPEED OF LIGHT and GOD WHO is alpha and omega. (OUTSIDE TIME)”.
Or, in his words, for the layman: “The answer is 299,792,457.99887640380956453724992 m/s. The speed of light is exactly 299,792,458m/s. It strange yields a resultant of 99.999999999625% of the speed of light. This is truly baffling.”
It might be baffling if you’re a moron. It should be obvious what’s wrong here. But for the sake of entertainment and pedantry, I’ll spell it out.
The speed of light is a factor in that equation. The whole rigamarole of the math is just going in circles. You’ve got a huge time dilation factor. You’ve got an equation that increases time dilation as you approach the speed of light. You calculate a speed from the equation that depends on the speed of light, in a way that amounts to taking the speed of light, squaring it, and then taking its square root. And poof! You get the number you started with. Wow! Shocker, huh?
Remember – what he’s doing is asking at what speed will time dilation equal 365250:1. By plugging that into an equation, in which the speed of light is a factor. At what point will 1/(1-v2c2 equal 365250? When v2=(365249/365250)c2. In other words, when v equals roughly 0.999998×c.
So… According to our moronic friend, it’s absolutely baffling that 0.999998×c = 0.999998×C.
What if the speed of light wasn’t roughly 3×108 meters/second. What if it was dramatically faster? Like, say, 5×1013 meters/second. What answer would his process wind up with? Something astonishingly close to 5×1013m/s. In fact, roughly 4.999993×1015.
It’s just a big circle.
To add more cluelessness on top, he goes on: “We should take note of the strange accuracy of the verse. It could result to any random number, but what is truly baffling is that it register a resulting answer digit for digit accuracy of the speed of light except for the last digit before the decimal.”
Yeah, bozo. When you go in circles, you get right back where you started!. It’s amazing! It’s astonishing! It’s a miracle! In fact, it’s so amazing that I think it’s time for you to sell all of your belongings, and use the money to open a church for all of the converts to flock to after they see the brilliance of this proof. You can make the altar round, and then amaze everyone by walking around the edge of it and showing how you got right back where you started!