"If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one." -John Barrow
Image credit: Codex Vindobonensis 2554 (French, ca. 1250), in the Österreichische Nationalbibliothek.
Image is from the front cover of the most important medieval picture bible to survive. But the caption is all my fault. Anyone can fool some of the people some of the time, but to enrage all of the people all of the time, that takes talent. Don't worry, I've got no future in comedy; I'll stick to the astrophysics.
Also, for those of you who want something fun to puzzle over, try this fun math fact.
102 + 112 + 122 = 132 + 142. Is there an explanation? Or is it just a coincidence?
Have a good weekend!
I found the second integer solution, but shouldn't there be an infinitude of non-integer solutions?
It's not "God did it", is it? Because that's such a cop-out.
*runs from the Fundies*
I'm not sure what sort of "explanation" is needed. If one is looking for 3 consecutive squares which have the same sum as the next two consecutive squares, that boils down to a quadratic equation x^2+(x+1)^2+(x+2)^2=(x+3)^2+(x+4)^2, which when expanded, simplified, and factored, is equivalent to (x-10)(x+2)=0, implying that 10^2+11^2+12^2=13^2+14^2 and (-2)^2+(-1)^2+0^2=1^2+2^2 (this last one's a bit trivial, though) are the only solutions.
Is that an explanation? A coincidence? I dunno.
Looking at this sequence more generally, you have:
0^2 = ??? (added for completeness)
The first number appears to be the nth triangular number where n is the number of terms on both sides of the equals sign (the 1st triangular number is 0, and there are 1 terms in 0^2=???, the 3rd triangular number is 3, and there are 3 terms in 3^2+4^2=5^2, etc).
reading the quote you posted by john barrow, if religion is a set of unprovable ideas, and math can 'prove' itself to be a religion, then by contradiction, its not a religion !
> if religion is a set of unprovable ideas
It's not though, it's defined to *contain* unprovable ideas. The definition leaves room for provable ideas.
A religion can claim to be a religion though, and still satisfy the definition. The definition also leaves room for incorrect ideas, so it's possible for a religion to claim that it proves itself to be a religion, or to claim anything at all really!, and still satisfy the definition of religion.
I laughed. But that picture of Jesus intelligently designing the world creeps me out. His gaze is just a little too intense. And the inside of the sphere looks like a drug trip.
I prefer the Spaceman Spiff crashing planets together to get the math answer or the Dirk Derringer series, where Calvin gets beat up by goons, which leads him to the conclusion that it's a numbers game. The only number big enough to pull it off, of course, is Mr. Billion.
The inside of the sphere isn't a drug trip; it's obviously an indication of Jesus' use of fractals, in the creation of he universe. As for the intense gaze, you would prefer or would join those that accuse God of not paying attention, when creating said universe.
As for numerical coincidence: Numbers are what they are, no more no less; therefore, it would be hard, if not impossible, to prove that there is any coincidence to inherent properties. Though, as an astrophysicist should well know, that doesn't mean that the universe is deterministic, by any stretch of the imagination (okay, maybe you could stretch your imagination that far). bc
for more about the numbers Blaise is talking about:
Blaise Pascal - you are right :)
Ethan special case equation "10^2 + 11^2 + 12^2 = 13^2 + 14^2." got me thinking.
It sort of looks like a special case of an expanded pythagorean theorem. hmm, yes.
You know 3^2 +4^2 = 5^2 is a special case of the pythagorean theorem x^2 + y^2 = r^2 in two Euclidean dimensions.
So what is Ethan's equation a sp[ecial case of?
Well in 3-dimensions, pythagoreans theorem is =
x^2 + y^2 + z^2 = r^2
But for any r^2 there are two orthogonal numbers h and g such that
r^2 = h^2 + g^2 aah.
So Ethan's special equation is a special case of the general expansion of pythagorean theorem to any number of dimensions.
x1^2 + x2^ 2 +...xn^2 = r^2 = y1^2 +y2^2 +... ym^2
where x1, x2, x3 ... xn are all orthogonal to one another
and where ya, y2, ... ym are all orthogonal to one another
and n and m are respective numbers of euclidean dimensions.
So what we have is a special case of pytharogean theorem comparing 3 versus 2 dimensions
Of course, the pythagorean theorem is valid in any number of dimensaions. Fun.
"People are entirely too disbelieving of coincidence." - Isaac Asimov
"Is not all this an extraordinary concatenation of coincidence?" - Isaac Asimov, from Foundation’s Edge
That Bill Watterson from Calvin and Hobbes is the strangest character he just stopped drawing those cartoons and has disappeared as if he was sucked into a Black Hole ... no information is coming out ever-since ... it's too weird 4 me.
Even weirder is as an anagram:
ELEVEN+TWO is the same as TWELVE+ONE...
We will never know whether Fermat's Last Theorem was a joke....
Ian, as best we can tell, FLT was proven several years ago.
That's a hoax! God on that picture uses compass to shape a Mandelbrot set, which certainly was not known in medieval times! :-)
The irony? Atheism IS a religion,,, aka,, a "belief in things unseen" (see panel 3). To believe that the double helix (20 in the simplest life we know) magically floated together, delicately and cogently, only to destroy itself to replicate?,, aka,, ABIOGENETIC ORIGIN OF LIFE,,, is a leap of "faith", the odds of which are almost infinite.
Nope, atheism is no more a religion than not collecting stamps is a hobby.
"aka,, a “belief in things unseen” "
The belief in God is a belief in things unseen.
"ABIOGENETIC ORIGIN OF LIFE,,, is a leap of “faith”, the odds of which are almost infinite."
Yet over the course of a billion years, that dice gets rolled again and again. After a while, it turns up the right number.
Unless the odds against it ARE infinite, abiogenesis requires no faith.
"aka,, a “belief in things unseen” (see panel 3)"
For "unseen" substitute "for which there is no evidence". There is evidence besides being able to see. Maybe you were just being brief, but I thought I should straighten that out.
"... aka,, ABIOGENETIC ORIGIN OF LIFE,,, is a leap of “faith”, the odds of which are almost infinite."
We have pretty good evidence that there was a point in time at which there was no life on Earth, and a time later than that when there was. This is evidence that abiogenesis occurred.
That it occurred is a different question that identifying the mechanism by which it occurred.
Given our experiences, there is no reason to specify supernatural intervention as the default answer for any phenomenon for which we have no identified mechanism, if only because there is no previous example where, after investigation, that turned out to be the case. We just don't see magic occurring.
Ben Vost. Love the anagram.
Harry from Tennessee: Bravo. The math for evolution doesn't add up. Even billions of years is not long enough to go from single cells to the incredible complexity of today's living organisms. Where are the transitional creatures? Why aren't we still changing, becoming more complex? God as Creator, Word of God as truth, seeing how the evidence fits those stories brilliantly: Why is that so hard? Why the knee-jerk reaction of that not being scientific thinking?
3^2+4^2=5^2 = 25
3^3+4^3+5^3=6^3 = 216
10^2+11^2+12^2=13^2+14^2 = 365
With all the infinity of numbers and the higher order infinity of how to combine them,you can get any pattern you wish to see by "proper" selection of the values you assert need to be looked at.
IOW if you look for patterns until you get one this is no more than the texas sharpshooter fallacy.
"Even billions of years is not long enough to go from single cells to the incredible complexity of today’s living organisms. "
It's VASTLY more time than strictly necessary.
You can get from "patch of skin that is minimally light sensitive" to "full human eyes with humous and varifocal lens" in 30,000 generations.
Because any useful change is kept, it's not a random walk to "having eyes" (or "making a hippopotamus") but a progresstion from "not having eyes" (or "being a simple RNA replicator") to the any advanced product via incremental change without direction, but keeping those elements that are useful.
"There is evidence besides being able to see"
A shadow from the sky much too big to be a bird
A screaming crashing noise louder than I've ever heard
It looked like two big silver trees that somehow learned to soar
Suddenly a summer breeze and a mighty lion's roar
"God as Creator,"
God doesn't exist. Prove me wrong.
"Word of God as truth,"
cf "If you eat of the fruit of the tree of life, you will surely die". A HUGE porkie pie there from the mystic Pinocchio. Not to mention the bats aren't birds.
"seeing how the evidence fits those stories brilliantly"
If by "brilliantly" you mean "really crappily and only after the fact". Um. No. Not even then. They don't fit the stories. See bats' "kind" (hint: it's not "bird kind").
Not "the fruit of the tree of life", but "the fruit of the tree of .knowledge" no porkie there!
@Keith #26: Not "the tree of knowledge" (i.e., keeping humans in ignorance), but "the tree of knowledge of good and evil" (i.e., keeping humans innocent). See Gen 2:17.
"Not “the fruit of the tree of life”, but “the fruit of the tree of .knowledge” no porkie there!"
nope, still huge porkie pies.
Adam and Eve ate the fruit, didn't die from eating it.
PS that tree was really "knowledge you're a slave". Not to mention that god's being portrayed as a huge dick there. Put the damn tree in hell or underneath a huge mountain and put a label on it "NO EATING". Totally avoiding the need to kill himself later so he can kid on he cares for us.
"Not to mention that god’s being portrayed as a huge dick there"
No doubt. Threatening adam and eve with death when they had no concept (if you buy the mythology) is one of the largest bit of dickery.