Carl Zimmer's Science Tattoo Emporium

Never Forget Your Inner Mathematician

Robert writes,

Hi Carl,

I like your blog. It inspired me in some way to do the tattoo that I've been thinking of for several years :-)

Here's an explanation:

I have several reasons for choosing a sigma. The simple reason is that I think sigma is really beautiful, especially when using this LaTeX font :-) The tattoo also represents my love of mathematics in general, and of  the beauty of abstract patterns in particular.

I'm studying the fourth year on the clinical psychologist programme and didn't want to forget my roots. Mathematics and computer science has shaped my thinking a lot, in a way that's very functional for me these days. I'm very proud of being a mathematician among the psychologists, or maybe a psychologist among the mathematicians, and I wanted to show this. That's why I made the tattoo.

That About Covers It

MLR writes: "The Tree of Life--carbon, glucose, light, DNA, and the golden rectangle.  A tattoo by Kevin Riley. On the chest of a PhD student in molecular biology."

Catastrophe Math

Angela writes, 

I got this tattoo about a year ago after finishing what turned out to be the magnum opus of my career (so far). Sadly, I am not a scientist, unless one considers sociology and economics to be true sciences, and then only marginally. I'm a grant writer and nonprofit director, and I work to interrupt the patterns of violent human behavior in sub-Saharan Africa. 

This is a tattoo of Salvador Dali's "The Swallow's Tail," the last painting Senor Dali completed before his death. Salvador had a rough couple of years, and through his depression he stumbled upon Rene Thom's catastrophe theory, which inspired him to paint again. This particular painting is a representation of the swallowtail catastrophe (V = x5 + ax3 + bx2 + cx). In four dimensional phenomena, there are seven possible equilibrium surfaces and therefore seven possible discontinuities, and Thom called these the "elemental catastrophes." In bifurcation theory, these are used to predict and model sudden shifts in behavior that result from small changes in circumstances. For a non-scientist, this is about as close to a complete explanation of my job and life as I may ever find. Salvador planned to do a series of all the possible catastrophes, and started with this one. 

Sadly, he died right after he finished it. I'm not typically prone to drawing far-fetched parallels or finding metaphors where none exist, but still, this fact reminds me that my work will never, ever be done.

Endless Additions

Courtney writes:

So, φ, the golden ratio (an honest to goodness irrational number that's equal to 1.618...) appears all over the place and is considered to be the particular ratio associated with beauty. It comes up in discussions about architecture, the spiral on seashells, and the path a hawk in flight takes as it swoops to catch its prey (the vegan in me doesn't like to contemplate that last one).

It's often written as (1+ squareroot(5))/2, but that's not the only way it can be written. Mathematically, it's algebraic, which means it can be written as a continued fraction:

1+1/(1+1/(1+1/(...)))

So in my tattoo, if you start reading at one of the "1+1" parts, you actually read it as "one plus one over one plus one over one plus one over..." -- exactly the infinite fraction!

There's some cool stuff about the golden ratio on wikipedia

en.wikipedia.org/wiki/Golden_ratio (starts off with general information)

en.wikipedia.org/wiki/Golden_ratio#Alternate_forms (writing it mathematically)

My tattoo was done by Jack of Art with a Pulse in Colorado Springs, CO.

Living Squares

Jordan writes, "My tattoo is of the 'glider' formation from John Conway's Game of Life. As a History of Science student I love this geometric arrangement and its promise of self-contained (not viral) reproduction, and travel."

Carl: For more on Conway's primordial artificial life, see here.

Imaginary Tattoo

Euler's Identity: Wikipedia

Does The Golden Ratio Look Less Beautiful As Numbers?

Milad writes, "I am a Mechanical Engineering undergrad at UC Berkeley and I got this tattoo about a month ago. It's the golden ratio in the shape of a rectangle, with the ratio of the sides of the rectangle actually being the golden ratio! I have been obsessed with this number since I heard about it in high school, and it is the reason why I became so fascinated with mathematics. The golden ratio is known to be the closest mathematical explanation of beauty. It has been used a lot in architecture, art, and music around the world, and has some amazing mathematical and geometrical properties." Carl: Like DNA and atoms, the golden ratio is a favorite at the emporium. See these geometrical version.

Fitting the Foundations of Mathematics On One Arm

Mark writes, "This tattoo is the Zermelo-Fraenkel with Choice axioms of set theory. These nine axioms are the basis for ZFC set theory, which is the most commonly studied form of set theory and the most well known set of axioms as well. From these nine axioms, one can derive all of mathematics. These provide the foundation of mathematics, a field that you can likely tell that I love dearly."

Carl: Mark is making an encore appearance at the Emporium. See his Y combinator here...

Fundamental Fluid

Drew, an oceanography graduate student, writes: "This, on my leg, is the incompressible form of the conservation of mass equation in a fluid, also known as the continuity equation. When people ask what it means, I say it defines flow.  Sometimes I say it means you should have studied more physics, but that is only when I am feeling like being funny.  What it means in more detail is that, for an incompressible fluid, the partial derivative of the velocity of the fluid in the three spatial dimensions must sum to zero.  It therefore concisely states the fundamental nature of a fluid.

"My advisor took this picture, and I swear he is obsessed (in a good way) with this tattoo.  He is giving a talk at Woods Hole next week as he is the recipient of an award, and he is planning to show off 'how quantitative scripps students are' which i think is hilarious and only slightly mortifying.  Speaking of mortifying, it is slightly mortifying to be sending this email at all--I have to admit I am a little embarrassed.  It is definitely the most vain thing i have done today.  I do have an ulterior motive which I have no problem admitting: I want to stake a claim on this particular piece.  I guess it might be a little lame to want to claim ownership over something so silly but there it is and I guess at least I can admit it."

Quadratic Vertebrae

"My name is Sharon and I'm an undergraduate math student at Arcadia University. A while ago, I decided that I wanted a tattoo that showed my love for mathematical formulas and equations. I got the quadratic formula on the back of my neck. The quadratic formula has been my favorite equation ever since I learned to sing it to the tune of "pop! goes the weasel." My tattoo is also useful for anyone who happens to sit behind me on an exam!"

Crashing Waves

Aarn writes: "as a student of electrical and mechanical engineering I kept running into sine waves and the unit circle, and came to realize how important it is. After about a year of digging and trying to find the right artist and the right technical drawings to illustrate this concept, I settled on two images which at one time or another were featured in scientific american magazine. The inner arm is a sine wave as it relates to the unit circle, and I continued the wave theme on the whole arm piece with the outer image which is the superposition of two waves. In the background is kind of a broken-out grid that wraps around my arm and onto my shoulder and has other solid and dotted lines in it."

The Surface of Things

Greg writes, "I'm currently a Ph.D. student studying maths in Australia (submitting next week). The the tattoo on the top, I got about three years ago in Berkeley, CA. The other tattoo I got about a year later in Sydney, Australia. Both these tattoos are closely related to the research I've done for my Ph.D., which is in the area of elliptic partial differential equations. The top equation is called the Monge-Ampere equation and is the archetype of the equations I currently study. The bottom equation is called the 'Infinity Laplacian' and was chosen because it is correlated to variational theories which I find to be beautiful. Loosely speaking these equations are correlated to how surfaces (in arbitrary dimension) bend and curve. I figured since I did half my Ph.D. in the US and half in Australia, I would get at least one tattoo in each of those countries. The tattoos are meant to represent a memory of the time I spent in my studies."

God, The Void, and A Tattoo

Helen writes, "I am getting married soon, and I wanted to get a tattoo to commemorate who I was before, something to remember my old name (as I am going to take my future husband's surname when I get married), but I also wanted it to be a secret. So this is what I got..."

Carl: Helen wrote her name in ASCII, the lingua franca of computers. Before ASCII was developed in the 1960s, computers often had no way to send text to one another, with dozens of different systems for representing letters and numbers. Even after ASCII was created, it didn't become common until 1981, when IBM used it for the first personal computers. Now ASCII is ubiquitous--a rare thing for such an old computer technology.

But Helen's hidden name has roots that reach much further back than the Kennedy administration--centuries, in fact. ASCII is a binary code, which can be represented easily by an electric current flipping between two levels, or, numerically, as a string of 1s and 0s. Letters, numbers, and symbols can be represented in ASCII by an eight-digit number. Instead of the base-10 system we are all familiar with, this is a base-two number. (So 3 can be represented by 11 [2+1], for example.) The power of binary codes was understood long ago. The I Ching, for example, is a series of symbols built up from solid and broken bars. In Western mathematics, the father of binary codes was Gottfried Leibniz (1646-1716). Leibniz recognized that turning numbers into binary made them extremely simple to handly mathematically. In fact, he speculated, you could build a machine that would do math based on binary numbers by sifting marbles through slots--a dream of the computers that would come centuries later.

But Leibniz saw a deeper meaning in the binary. "One is enough to derive everything from nothing," he wrote. To Leibniz, 0 represented the void, and 1 represented God. Only by translating nature into binary numbers did Leibniz believe that we attain perfect knowledge of the divine, by seeing its underlying reality and beauty. It was no coincidence that seven--as in the seventh day of creation, when all was created--is 111.

To Leibniz, I'd imagine, a binary code tattoo would not say what we once were, but what will forever be.

(For those of you who want to decode Helen's surname, here's a handy converter.)

Golden Spiral Shell

"here is a pic of my tattoo based on the golden spiral and a nautilus shell. i've wanted to get this done since high school and finally got up the courage to take the plunge earlier this year. it is now a constant reminder that mathematics is the language of nature."--Thom

Fourier Transform

I got this tattoo, which encircles my left wrist, in 2000. The tat is described by this function

(1/n)*sin(nx)

with n from 1 to 6. I had done a lot of work with fourier transforms on the research project I was involved in as an undergrad physics student, and just find the entire concept very beautiful. At the time that I got the tat, I was a master's student in materials science and was taking a class on fourier optics. As music also plays a very large role in my life, the image/concept has a double meaning for me. As an added 'feature', the artist made a small mistake on the inside of my wrist (the n=4 line disappears for a bit). This really bugged me at first until I decided it was a good metaphor for how the messy reality of life is never perfectly represented by our mathematical theories.

--Andrea Grant (now a climatology PhD student in Switzerland, where nerdy tattoos are still pretty shocking....)

The Julia Set

"It is an approximation of the locus of connectedness for the Julia sets of the family of functions f(z) = z^2 + lambda/(z^2) (rotated by pi/2). This is analogous to the standard Mandelbrot set (which applies to the family f(z) = z^2 + c), but holds additional fascination because for lambda values which are in the interior of one of the subdomains of the connectedness locus, the Julia set is a Universal Curve. To me this represents the structure unifying chaos (since Julia sets are chaotic) and order (since Universal Curves act as a sort of catalog of all planar curves)." --Aaron

Y combinator

"I don't quite have a science tattoo, but I have a math tattoo. That's close enough, right?

"Now, for the explanation. This is a formula called the Y Combinator. It is a fixed-point combinator in the lambda calculus and was discovered by Haskell Curry, a rather prolific mathematician and logician whose work helped start Computer Science.

"What this formula does is calculates the fixed point of a function, which in turn allows for recursion by calling on that fixed point; recursion is perhaps the single most important concept in Computer Science. Being a computer scientist and a mathematician, this formula is very important to me and represents the innate beauty of computer science and mathematical logic." --Mark

[Note from Carl: Math is most welcome at the Emporium]

Phi

"This is my science tattoo. It's the greek symbol for Phi, and it represents the golden ratio." --Jeff

Nearly a Golden Spiral

"Here's mine, a rough approximation of the golden spiral... but more accurately a simple logarithmic spiral."--Dave Stroup

source

Koch Fractal

"I'm an evolutionary biologist student at Middlebury College. This tattoo was done at True Love Tattoo in Berkeley CA and is my attempt to show both the beauty and my love of chaos in nature. "--Sam Dakota Miller