
My Prime Factorization Sweater - ColinWright
http://sonderbooks.com/blog/?p=843
======
ben0x539
Do people often walk up to the OP and start trying to identify country flags?

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Sondy
No, but when people say, "Nice Sweater," and I ask, with a sparkle in my eye,
"Do you want to hear about it?" they often say, "I thought they were flags."

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muyuu
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
73, 79, 83, 89, 97

After just 5 or 6 different colours or so, which happens very soon, it becomes
hard to distinguish them without context. But this is not a big problem thanks
to order consistency. For instance, check 57 and 58, just next to each other
with the tone of 19 (second factor of 57 = 3 _19) looking very similar to the
first factor of 58 (2_ 29). The converse is also true: 3 is a similar tone to
29. But thanks to order consistency it's easy to tell which is which. I'd say
the only problem with this is not being obvious, and also the ordering being
somewhat confusing, as I'd expect normal writing order for numbers.

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Sondy
I have spent so much time looking at graphs, I wanted smaller to be on the
bottom and to the left, as in Cartesian coordinates. Though I know it's a bit
weak. The color differentiation is even worse in the photo than it is with
just the yarn. And it's tricky to find a yarn with enough distinct shades.

~~~
muyuu
That's interesting, because in CompSci screen coordinates (and vector
coordinates when programming graphics) are usually rooted at the top-left, so
we have a more "consistent" natural perception of it - those of us using
mainly left-to-right language scripts.

Anyway, I really don't see graphs as sequences. I have my perception of
cartesian graphs and sequenced lists completely separated.

But the important thing here is the idea :-)

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merraksh
That's an excellent idea for a T-shirt.

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mkopinsky
WAY more geeky/cool to have knitted this yourself than to have just bought it
as a T-shirt.

That said, with varying definitions of hacker, I'd bet she's the least
hacker-y person to make the HN homepage.

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daeken
Not by a long shot. At least once a week we have people talking about how they
"hacked" their focus, or their working hours, or other drivel. This is
genuinely neat.

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mkopinsky
30 year old developer hacks work week, hits HN homepage: common.

50 year old librarian hacks sweater, hits HN homepage: somewhat less common.
But yes, the principle is still the same.

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Sondy
I am NOT 50!!!! (for a few more years, anyway.)

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mkopinsky
Your age isn't on your website, but my calculation (got Master's degree in
1986 at likely approximate age of 24) couldn't have been TOO far off, right?

I guess age is just one of those topics..... :-)

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Sondy
Well, it was farther off two years ago when I posted the picture. And I got my
MA in 1986 on my 22nd birthday. (Later got an MLIS on another birthday.) I put
a math problem in my follow-up post. You should be able to calculate my age
and my son's ages from these clues: <http://sonderbooks.com/blog/?p=10000>

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mkopinsky
My age estimate was from your LinkedIn profile. If I was guessing by pictures,
I would have said 39. (Is that the right answer? (I mean in the sense of Right
Answer to say to someone of how old they are, not mathematically correct. :-)
))

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Poiesis
The Right Answer is to have not brought up the age issue because it is rather
immaterial to the discussion. Can you really say that the authors age, when
considered independently from the article subject, has significant bearing on
the voting?

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martininmelb
I showed this to my 9-year old daughter. After explaining it to her, her first
question was 'Can I have one?'. I told her that it was a one-off. She then
asked me to bookmark the page for her.

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Sondy
I am trying to get the graphics I made for the children's book I wrote with
this concept (not yet published, but now it's time to try) uploaded in a
decent form onto cafepress. I'll post if it comes out okay and I can sell
t-shirts.

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chrisacky
I really wish that I could remember the article/movie/show which I
read/watched but it was talking about creating a universal language.

This would be not just for people living on Earth but also life outside of our
Solar System. It would make sense that if there was a universal language that
it would be based around some mathematical form. At least something which
should be constant through the universe.

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lubutu
The problem is that such a language may have a mathematical basis but that
alone wouldn't be able to convey anything besides mathematics. It can
demonstrate intelligence, as used in Carl Sagan's novel _Contact_ by
broadcasting a sequence of prime numbers — but that doesn't exactly constitute
a language.

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Retric
You could probably move from math to chemistry/physics. Of course all the
'constants' are arbitrary numbers based on the measuring system used, but
going from elements to DNA to cloning to emotion should at least in theory be
possible if you had enough time and intelligence.

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palmtree3000
This is, in fact, solvable; you can use plank units, which result from setting
universal constants to 1. As an example, setting the speed of light to 1 means
that time can now be measured in meters.

<https://en.wikipedia.org/wiki/Planck_units>

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trout
You still have the challenge of choosing a base system. Remember we are base
10 simply because of biology. Our alien friends may be on a different number
base because they have 7 fingers.

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simcop2387
It ought to be possible to deal with that by enumerating each possible digit.
And then showing a representation of some kind of fundamental concept like
PI/TAU that's easy to make a diagram of. Each side shows their digits and
their representation and at that point we can determine conversions between
the bases.

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paduc
I'm wondering. Could this be considered a meta-explanation of what a prime
number is?

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JoeAltmaier
I'd start with zero. Bugs me that the right-hand side is 10 not 9

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JadeNB
0 does not admit a prime factorisation.

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eps
She could've knitted a bit of white noise then :)

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Sondy
I thought about putting in zero, but I'm thinking of this in the mathematical
group Z sub n, the natural numbers. That ring does not include zero, and it's
as if it doesn't exist. One, on the other hand, is the multiplicative
identity, so it is the background color, a factor of all the other numbers.

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JadeNB
Certainly the ring `Z/nZ` has 0, meaning an additive identity (the image under
the natural homomorphism `Z \to Z/nZ` of the 'true' `0 \in Z`). Do you mean
that the group `(Z/nZ)^\times` of units of `Z/nZ` doesn't contain 0?

(I think that it's also confusing to call `Z/nZ`, or `Z_n` or whatever you
like, the group of natural numbers; rather, it is a _quotient_ of the
semigroup (or semiring) of natural numbers by a normal subsemigroup (or
semiideal).)

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Sondy
Okay, you passed me. I knew I should have pulled out my very old Modern
Algebra book. I was thinking in terms of modulo groups. You can show lots of
number theory with the sweater, granted that the number on the end is the
equivalent of zero. I want a group under multiplication. Is that making any
sense?

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gjm11
If you want a group under multiplication, the easy options are: (1) Integers
modulo a prime number, not counting 0 mod p. (2) Integers modulo anything
(call it _n_ ), not counting ones that have a common factor with _n_. (3)
Rational numbers.

In this case you've got 1..100, and 101 is prime. So the numbers on (the front
of) the sweater, mod 101, form a group under multiplication. But of course in
that group you lose all the prime-number structure shown on the sweater -- you
can't really talk about, say, "multiples of 3 (mod 101)" because 101 isn't a
multiple of 3.

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reinhardt
A perfect gift for Sheldon Cooper.

~~~
tripzilch
Hey look everybody, common ground between HN and Reddit! They both dislike
_The Big Bang Theory_ references!

