The vast majority of you tumblr subscribers have not been with me since the beginning. Here’s a guide to what’s gone on so far at **isomorphismes**.

**PURPOSE**

Mathematics is really, really boring — to *learn*, in school. But it’s a pleasure to know. My goal is to share as much wisdom, perspective, intuition, and interesting tools for thinking about the world as I can, with a minimum of rigour, verbosity, and head-banging frustration.

I actually started this blog for a completely different reason: to prove to RGM Advisors’ HR department that one doesn’t need a fancy degree with letters after the comma to be as educated as someone whose name is followed by titles like PhD or MSc. But that’s neither here nor there. Nowadays I use this platform to share opinions, weird thoughts, art, and mathematical tools. Some of these are meant as aides for students, but most are meant as **imagination**-enhancers for regular people who don’t feel like poring over textbooks and lecture videos—who just want the takeaway.

**What’s with the name? Isomorphisms** map X onto a equivalent, but different-looking form of X. For example you can look at a function normally, look at its Taylor series, or look at its Fourier transform. All three are equivalent, but you see something different with each pair of eyes. Hence the subtitle, **see things differently.**

Here’s some of what I’ve written so far.

**NUMERARY BESTIARY**

- Vectors = anything that can be added together.
- The wind and other vector fields.
- Trigonometry = Navy Coordinates vs City Coordinates
- The simplest example of a functor. Some relations to postmodernism, maybe.
- Groups = verbs.
- What does it mean when a mathematician says “Consider the ordered pair (X, alpha;, Omega;)?”
- Spaces = things + how they should be interpreted. (erm, and you need to have
*everything*to hand. i.e., spaces must be algebraically closed) - Manifolds, racism and self-versus-other.
- Semigroups. (spaces with an associative unary operation)
- Quasimetrics. (and other unidirectional things)
- Convex combinations of beer.
- How I finally understood the Pythagorean Theorem.
- Is calculus a load of crap? (Really I mean is it any good for describing people.)
- Topology = connections between things.
- Noncommutative distances between industries.
- Noncommutative distances between sports. (How do you define “the hardest sport”?)
- Fuzzy logic.
- L_p norms (a well-known family of definitions of distance).
- The point of differential calculus.
- A single image that summarises the calculus.
- Outer product
- How to multiply matrices and other student maths help.
- How to do integration by parts.
- How to tell if a series converges.
- “Half-negative” complex numbers.
- Exercises for thinking in four dimensions. (It’s possible; trust me.)

**WEIRD THOUGHTS THAT ARE ONLY POSSIBLE THROUGH MATHS**

- When Doves Cry Inside A Convex Hull
- The Hotness Scale: 1 to 10, or poset?
- Gender as a maximally separating hyperplane.
- “Feminine” causality (yin).
- My sister isn’t “irrational”; her utility function just has large interaction terms.
- Superpowers I have.
- The “Jesus Norm”
- Emotional / psychological superposition.
- Religious ∞ versus Math ∞.
- My viewpoint on utility theory.
- How come the planets aren’t arranged spherically around the sun?
- How did the zebra get its stripes?
- OK, this is definitely not my idea, but: maybe we live in a 3-dimensional universe literally because three dimensions has the most interesting mathematical properties of all possible numbers of dimensions?
- Jan Koenderink’s view of a cloud.
- Why are US Treasurys considered “risk free”?
- A parable demonstrating that stock prices are
*not*”just an infinite time series”. Addressed to some martingale-imbibing punk on the EliteTrader forum. - There are many kinds of “distance”. Demonstrating that with Circles
- Photons are like the Tralfamadorians from
*Slaughterhouse V*. - 1729 is not a number; it’s a method of calculation.
- Hey Zeno, your little “paradox” is no longer paradoxical. Also we can compute infinite sums in just a few steps now … so, that’s good.
- The universe is a song, singing itself.

**OPINIONS**

- Mestizos are Amerindians, too.
- Native Spanish-speakers should teach high school Spanish. That’s extremely logical, yes? It’s ironic that in the USA, a Mexican could be day-labouring (perhaps even at a high school) while some whitey college grad teaches the language wrong to their kids. Right?
- Regression analysis is only reliable for interpolation — not extrapolation.
- Why a 2d4 oaken staff is better than a 1d8 scimitar. Or, the nerdiest thing that anyone has ever written because I just used a computational “proof” of the Central Limit Theorem in R to prove that the Dungeons & Dragons handbook is wrong.
- “Highly nontrivial” — did you really just say that?
- Somebody is lying here.
- Why I support progressive taxation. (OK, haven’t actually written that yet. #ows)
- Fahrenheit is better than Celsius for talking about the weather.
- I can never express what I think in a political discussion because my interlocutors haven’t read Persson & Tabellini.
- The MBTI oversimplifies people.
- Are mathematicians deliberately obscure? Word-battles with Wikipedians.
- What’s wrong with OKCupid’s matching algorithm.

And, here are some inspiring / awesome quotes by Richard Feynman, Antoine St-Exupéry, Stephen C Stearns, Hal Abelson, Henri Poincare, Stephen J Gould, F J Anscombe, _why the lucky stiff, Ed Leamer, William Tyndale, Glenn Beck, Fidel Castro, Warren Buffett, Sergio the guy who runs the NewBalance factory, John Baez, Kent Osband, James Lighthill, Shing Tung Yau, 1 2 3 4 5 6 7 8 9

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