# Circling Around The Speed of Light

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

v=299792457.99887640380956453724992.

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!

## 0 thoughts on “Circling Around The Speed of Light”

1. Alex Besogonov

1 == 1 – the greatest identity EVER.
However, sometimes it comes handy: http://arxiv.org/abs/0810.4446 – this is a story about how the equivalence of 20kEv of kinetic energy of energetic elementary particles and 20kEv of kinetic energy of slow-moving protein molecules allowed to use the same equipment to detect them!
PS: I want to apologize for my inflammatory comment on your previous post.

2. jeff

Thanks for bringing these asinine pices of work to our attention. No doubt this video will soon be circulated around our town as “proof”. This is better than the one about the the relationship of the height of the Great pyramids and the distance to the sun.

3. dreikin

I don’t really see the circle in this (not the type you defined previous to it) – are you sure you’re not using two different definitions here? (or maybe I’m just not seeing what you’re talking about).
Of course, the guy’s still off – it takes only a bit over 33 years to have a v = c-1, which given the size of c, is still a huge percentage.
I’m also pretty sure they weren’t using the modern calendar (leap years and all) back then…

4. Jonathan Harford

If I make a Bible that says “But do not forget this one thing, dear friends: With the Lord a day is like ten thousand years, and a ten thousand years is like a day” will this guy want to join my church?

I agree with dreikin’s comment that I don’t think this is a circle the way you defined it in your previous example. Here’s a better take down:
If you take the time dilation equation and solve it for the velocity ratio squared, you get
(v/c)^2 = 1 – (dt/dt’)^2. Now in this ridiculous example, dt/dt’ = 1/365250, which is very nearly zero. As dt/dt’ approaches zero, v/c approaches one. So shockingly, surprisingly, as delta-t ratio gets smaller, v approaches c! Baffling! It’s proof of God’s word! If that biblical verse said that a day were like a ten years, then the difference between the velocity and the speed of light would be about 11.24 m. One hundred years? 11.24 cm. A thousand years? 1.124 mm. Ten thousand years? 12 micrometers or zero basically. I calculated the time ratio for the difference in velocities to be one meter. Turns out it’s 12,240:1. So as long as one day were like (at least) 33.5 years, the resulting calcuations would appear that that gawd was moving at the speed of light (to within one meter) and the bible was correct! Baffling!

6. Anonymous

He could have just argued that the existence of time dilation is something that is postulated in the bible. (am i in a circle too? ARG). Of course, his calculation was wrong, but I think the idea itself that a concept of time dilation exists might be something he could catch unto.

7. Chris

I tried to look at the video but all I got was:
“This video is private. If you have been sent this video, please make sure you accept the sender’s friend request.”
You meanies! You made him hide it from critical eyes.
😉

8. Jonathan Vos Post

Music of the Spheres…
“You’ve taken twelve steps of fifths, and wound up where you started.” Yes, but the Cycle of Fifths works because 5 is relatively prime to 12, so performing the group operation 12 times orbits you through all elements, giving you the Cyclic group of order 12. You take the same operation, inverted, and raise that to the 12th power and you’re running through the same elements in the reverse order, also known as the Cycle of Fourths.
That is, because 5 is the unique integer less than half of 12, and relatively prime to 12, you have 4 ways to cycle through the 12 notes: chromatically up, chromatically down, Cycle of Fifths up, Cycle of Fifths down.
If we divided the octave into 30 microtones, we’d have the chromatic up, chromatic down, Cycle of Sevenths up, Cycle of Sevenths down, Cycle of Elevenths up, Cycle of Elevenths down, and there would be too many possibilities for the untutored human brain. The balance between surprising and inevitable in a good melody would be missing.
Some other cultures have a prime number of microtones in an octave, so that there is only the chromatic scale.
Good Math, and good listening, all in one package.

9. mpj

Another thing you could’ve demonstrated: change the verse to
“a day is like a month”
and
“a day is like a million years”
and see that both are very close to c, with a million years even closer than the original!

10. MarkusR

I think to fix the italics by us non-site admins we would need to correct the settings in the top container…Don’t think it’ll work due to security settings, and I’m rusty with DOM anyways.

11. Ambitwistor

That’s possibly even stupider than the guy I ran across who advanced the following proof that the speed of light isn’t constant:
E = mc^2
c = sqrt(E/m)
E is a variable: it can take on any abitrary value. Same for m. Since E can be anything and m can be anything, then so can c: it can take on any value. Therefore it can’t be a constant.
I used circumference = pi*diameter to similarly “prove” that pi isn’t a constant, but it failed to impress him.

12. Morgan

Another thing you could’ve demonstrated: change the verse to
“a day is like a month”
and
“a day is like a million years”
and see that both are very close to c, with a million years even closer than the original!

Exactly. Because of how time dilation works, any significant ratio would require a speed very close to c, and it will asymptotically approach c but never overshoot, so you can name any poetically large number and it will always come out as very close to c.
If an ancient prophet wanted to impress future generations with his knowledge of the speed of light, he should have talked about the heavens being n leagues across and angels taking x years to cross them, providing such figures that angels would be found to travel at lightspeed. That would be cool. This is just idiocy.

13. tinyfrog

I’ve seen this same type of argument used by Muslims as well. It seems to be much more widespread in Islam. There seems to be a large movement in Islam to claim that the Koran predicts lots of modern science – it is similarly bad logic, but they’re probably more effective at pulling the wool over the eyes of Muslims (since a smaller percentage of Muslims have higher educations). Google ‘koran speed of light’.

14. Mark C. Chu-Carroll

tinyfrog:
I don’t think that it’s more widespread in Islam. I’ve seen several variations of this from christians, like the one in this post. The silliest one was this one. I’ve also seen a couple of Jewish versions (one of which I wrote about here. I’ve also done the Muslim version of it, here. And I’ve got a Hindu variation waiting in the wings.
I think that fundamentalists of all stripes want to find a way of justifying their religion using science. Since relativity is the most famous theory of modern science that they don’t reject outright, they naturally want to justify their religion using it. And since just about any religious text is going to, at some place or other, contain a poetic metaphor involving time, they home in on those, and try to connect it to relativistic time dilation.
Jews do it using the way that things don’t spoil on the altar. Christians find phrases about how time passes in the presence of God. Muslims find bits of text talking about how fast angels can fly. Hindu’s find reference to the speed of the Garuda bird carrying one of their gods. Buddhists find references to time passing sitting at the foot of the Buddha.
It’s everywhere.

15. SteveM

So God is travelling close to the speed of light? Wouldn’t it make more sense for God to be travelling at the speed of light? Then, like a photon, from His perseptive he would be everywhere at the same time.
Anyway, to change the subject almost completely. I’ve been wondering recently why we don’t adjust the meter so that the speed of light would be exactly 300,000 newmeters per second? I mean, what is so special about the current length of the meter?

16. EliteLC

The computations are basically correct. The explanation is wrong. The author should have stuck with Time Dilation having to agree with that Bible verse instead of getting excited about the Speed of Light magically encoded in the Bible. It is pretty obvious that whatever value you put on c, and in the case of extremely dilated time, it will result to 99.999% +++ of c forever.
It’s not actually going in circles though, I fail to see that viewpoint here. Because if v=c, then its zero at the speed of light at infinity. You get zero forever. Its like stopping a parked car. You can’t stop it even more.
He also forgot to include Gravitational Time Dilation, because that verse also have the other component, if you guys didn’t notice.
If someone could compute for GTD, that would be great because I haven’t taken general relativity yet. Here’s basically the run down:
According to hyperphysics, the time dilation due to gravity is
T= To/Squareroot( 1- 2GM/Rc^2)
It looks pretty much like gamma to me, but replace v with GM/R. The units still work out to be that of v^2.
An equivalent expression in terms of gravitational field rather than as it appears above could be
T=To/sqrt(1- 2gR/c^2)
which in the end is going to be more helpful since the problem is asking for the gravitational field.
Pull out some algebra and solve.. and we find that
g= c^2/2R * (1- (To/T)^2)
or GM/r = c^2( 1-(To/T)^2)/2
Plug in the numbers and you get a gigantic number.
If I am right, that would be just a hair away from becoming a black hole, if 1day:1000years. Near the speed of light on one end, and near the singularity, at the other end. Otherwise, you can no longer measure time at both infinities.
If an object were to escape that, it will have to travel near the speed of light at, you guess it, at 99.999++++ of the speed of light.
Just my 2 cents.

17. carl

I think what needs to be realized in order to understand the inanity of this connection is that for any considerable time dilation you must travel close to the speed of light so this result is NOT SPECIAL. That is, *many many different magnitudes* of dilations will all yield a necessary velocity close to c. Nothing special in the result.

18. Rob

The funny thing is I believe the joke is on all of us. The guy that made the video could have better logic and preciseness, but while we’re all calculating his errors we’re missing the point of the scripture he mentioned.

The point of the verse is say that God can time travel, and is outside of the restraints of time. “A day is as a thousand years, and a thousand years is as a day” is just the method to getting that point across. It could have just as easily said 10,000 years or a billion years; doesn’t matter. If God exists as the Bible states, He most definitely would travel at the speed of light, as he is said to be omnipresent in other scriptures.

What we know about special relativity does not rule out the existence of this God. It doesn’t prove Him as the video presenter says either, but it is compatible with the abilities He is described to have. Anything beyond that is a matter of faith.