
The Ulam Spiral of Primes - fogus
http://scienceblogs.com/goodmath/2010/06/the_surprises_never_eend_the_u.php?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+scienceblogs%2FCyKN+%28Good+Math%2C+Bad+Math%29
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rgoddard
You are going to see a pattern along the diagonal because every other number
is even and never prime (excluding 2). So the only way for two primes to be
touching is along a diagonal. Given that and our brains tendency to group
items which are closer together as being related, anything along the diagonal
will stand out more and appear to be a pattern. A more interesting picture
would be one where all of the even numbers are omitted.

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inferno0069
All the odds would look like a full checkerboard, not like these diagonals.
The fact that some diagonal lines appear to be favored over other nearby
diagonal lines of odd numbers is still interesting.

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Barnabas
Of course it's interesting. There's no such thing as an uninteresting number.
<http://en.wikipedia.org/wiki/Interesting_number_paradox>

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Dove
From <http://mathworld.wolfram.com/PrimeSpiral.html> :

 _This construction was first made by Polish-American mathematician Stanislaw
Ulam (1909-1986) in 1963 while doodling during a boring talk at a scientific
meeting._

Awesome. My new excuse for all those doodles in my engineering notebook:
valuable, valuable mathematical research.

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mbrubeck
My friend Peter made a poster of the Ulam Spiral that includes the Python code
used to generate it: <http://imprompt.us/2010/ulam-spiral-take-2/>

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crux
That's my friend Peter, too! He's wicked smart.

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jokermatt999
I believe this was also shown briefly in the movie Pi. At least, I think
that's where I recognize it from. Great movie about finding patterns in
numbers and pareidolia.

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dunk010
It really is. One of my favourite movies. Highly recommended.

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shrikant
_[These spirals have] been cited by some religious folks as being a proof of
the existence of God. Personally, I think that that's silly; my personal
belief is that even a deity can't change the way the numbers work: the nature
of the numbers and how they behave in inescapable. Even a deity who could
create the universe couldn't make 4 a prime number._

Amen to that.

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dagobart
So, pushing this thought a little further, I'd say such a (or any) deity and
us have at least this one thing in common: looking in amazement at those
primes.

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CapitalistCartr
We invented the idea of Prime Numbers. They're an arbitrary creation. As are
patterns in them. Random is -NOT- the same as even distribution. Patterns are
inevitable. Las Vegas makes a fortune on people who don't understand that. If
you flip a coin a hundred times, you'll see patterns in the result. People are
good at seeing patterns.

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vecter
This is wrong. Humans _discovered_ prime numbers. They are not an invention.
They fall naturally out of the integers, and would exist regardless of whether
humans did or not. Prime numbers are are some of the most fundamental objects
in all of mathematics, and the fact that you can find them on diagonals in
these graphs probably indicates a pattern that we can't explain yet.

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ascuttlefish
The question of whether math is invented or discovered is far from settled. I
know next to nothing about math, but a quick google search for "math created
or invented" brings up so much controversy I find it unlikely that it's been
decided. See Mathematical Platonism and its Opposites by Barry Mazur (p. 19
in: <http://www.ems-ph.org/journals/newsletter/pdf/2008-06-68.pdf>). He says
it's The Question that won't go away.

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ez77
Indeed. Further, at the risk of soun ding too phiosophical, this
invention/discovery, Platonist/constructivist debate hinges on the fundamental
notion of existence. And, as with most fundamental notions, the obvious soon
ceases to be so.

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borism
if you're like me - more physics than math guy, it's the same Stanislaw Ulam
of Teller-Ulam design fame.

