My Prime Factorization Sweater | Hacker News Reader

My Prime Factorization Sweater

sonderbooks.com

222 pointsColinWright50 comments

Do people often walk up to the OP and start trying to identify country flags?

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."

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 = 319) looking very similar to the first factor of 58 (229). 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.

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.

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 :-)

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

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.

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.

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.

No. This woman demonstrated intellectual curiosity and real creativity. Most of the "life hacker" type posts I see are self-congratulatory pop-psychology.

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

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..... :-)

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

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. :-) ))

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?

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

Sure, but I didn't say the opposite. I like the idea a lot and knitting this yourself is really great, but I would definitely buy it if it was on a T-shirt.

I would also buy it because I don't knit and it's not really something that's on my list of things to learn.

Agreed. But something still feels wrong with saying, "Nice, you spent 100 hours making something cool? I'd definitely pay $15 for a poor replica thereof."

Again, that is not what I said. What I meant was more along the lines of "You did a great work and I like both the drawing and its meaning. I would love to see that on a T-shirt, and if I were to make that T-shirt it would certainly give you credit for this."

I wouldn't feel like wearing a sweater like that for personal preferences, but I would like this idea to spread. You would definitely have a point if she designed and produced that as a T-shirt and now somebody else started making poor replicas, but hers is probably a unique specimen.

The idea of making a chart from prime numbers is definitely not copywrite-able. So go for it! I got the idea from a knitting magazine where someone described a blanket with a chart of prime numbers that fascinated a student who walked by who was in a remedial math class. They had a small picture of part of the blanket, and I couldn't figure out how their method worked, but I put those ideas into a sweater.

I have attempted to write a children's book about using this idea to make cyphers or just fun art. But I haven't tried to sell it yet. And I did a library program that went over very well with kids. Anyway, if anyone makes a t-shirt let me know -- I'd order one.

Though maybe I should do it -- I've got several colored charts already made from when I was working on my book. Give me some time, and I'll make a cafe press account....

I'm working right now to see if I can get the charts I made into a good enough copy to upload to cafepress and sell t-shirts.

This would make a good quilt pattern (with minimal modification).

Thanks for the idea!

I can see how it's easy to get hooked (sorry) on knitting and maths. You might start off doing visualisations of various sequences. Next, you wonder what happens if Fink and Mao's necktie analysis [1] is extended to an exhaustive analysis of knitting stitches, and end up with all sorts of multidimensional stuff. Finally that becomes too easy and you attempt to use a length of yarn to model the world line of a single electron [2] and accidentally win a Nobel Prize! :-)

[1] http://www.tcm.phy.cam.ac.uk/~ym101/tie/aps97tie.html

[2] https://en.wikipedia.org/wiki/One-electron_universe

I'll be your first customer :-)

No, prime factorization is way more hackish than pickup artistry or startup funding. You're succumbing to stereotypes based on surface appearance instead of looking at the essence of things. That's not very hackish of you.

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.

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.

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.

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.

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.

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

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.

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.

Was it the video of Richard Feynman explaining to a general TV audience how to communicate what "counter-clockwise" meant to aliens?

http://en.wikipedia.org/wiki/Pioneer_plaque

Was it in regard to this?

I misread that as "Pioneer Plague", and envisioned a universe dominated by von Neumann probes launched by intelligences who want to contact someone, but die off before their probes can report back.

Contact?

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

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

0 does not admit a prime factorisation.

I think that's my bottom line reason why I didn't include it. This is all about factorization. 1 is the background color, because anything times 1 is itself. But I don't think 0 would quite fit with the pattern.

What do you think of my plans for a prime factorization scarf? http://sonderbooks.com/blog/?p=10000

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

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.

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).)

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?

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.

A perfect gift for Sheldon Cooper.

Hey look everybody, common ground between HN and Reddit! They both dislike The Big Bang Theory references!

He doesn't believe in gifts. Yada yada, one of the two will die first and the other one will be at a disadvantage.

Reply on news.ycombinator.com