Vi Hart Pi Day rant 2016: best one yet

[datathief]

@awfulhorrid

I prefer the format which @dragonfrog mentioned for my file system, but 14-MAR-2016 for day to day purposes.

This is the One True Way, at least until the world realises how much sense %Y-%m-%d makes.

[HMSGoose]

Her videos about the superiority of tau are actually exceedingly rational and well-founded in a philosophy of mathematical elegance, efficiency and simplicity. She just wraps it in a sweet swaddle of unique charm to help the medicine go down.

@datathief

This is the One True Way, at least until the world realises how much sense %Y-%m-%d makes.

I’ve blown many a mind in my office when I show them that if they append drafts with a Y-m-d date, they can use a-z/z-a sorting to order them.

[Donald_Petersen]

Heh. Nerd.

[anon33466019]

Takes one to know one

[chenille]

@logruszed

Not a mathematician but she’s saying tau is superior to pi? Is that true? Do people actually feel sentimental about irrational numbers to the point that they cling to them when a superior alternative exists?

Sort of, but it’s not just sentimentality. In a vacuum, sure, it’s more elegant and understandable to assign a symbol to a full-turn than to a half-turn. In practice, though, the constant π is universally recognized throughout mathematics, science, engineering, even philosophy and art. There are very few symbols with such constant meaning across so many disciplines.

And the constant τ, well…the symbol is clever, but even in geometry books it’s already as likely to stand for the golden ratio. It stands for various times and torque and torsion. There are after all so many Greek letters; π is special in having been largely reserved, and it’s a hard sell to use up another to not write 2π.

[daneel]

[Vert]

@chenille

π is special in having been largely reserved, and it’s a hard sell to use up another to not write 2π.

There must be a symbol that would make sense that hasn’t already been reserved by some branch of math?

edited to add: ® for “radians per revolution”?

[mdavis]

@chenille

And the constant τ, well…the symbol is clever, but even in geometry books it’s already as likely to stand for the golden ratio. It stands for various times and torque and torsion. There are after all so many Greek letters; π is special in having been largely reserved, and it’s a hard sell to use up another to not write 2π.

Not really. π is used frequently to mean other things, notably the projection maps associated with a product in category theory, and more generally anywhere products are used. Circles definitely don’t have a monopoly on π. And the golden ratio is more commonly written ф. I don’t think you’ll find a single-letter symbol that isn’t overloaded in mathematics.

Admittedly, it’s perhaps one of the most ubiquitous and widely-recognized symbols, but in math more than anywhere else, truth and elegance will ultimately win out. It might take a long time to gain acceptance, but I think τ will eventually win this battle.

[chenille]

@Vert

There must be a symbol that would make sense that hasn’t already been reserved by some branch of math?

There are lots! Many scripts have barely been mined at all. Maybe you could use other versions of the letter t that look less similar to ours like Arabic ت, or a logogram like Chinese 周 for cycle, or since that’s inconvenient to write 开 since it looks like one π on to of another. The trick is still in getting them accepted, though.

@mdavis

Not really. π is used frequently to mean other things, notably the projection maps associated with a product in category theory, and more generally anywhere products are used.

Sure, projection maps and the prime-counting function, but if you see lowercase π used as a number you can typically be all but certain of its meaning with no explanation. My point that τ so often stands for other things is less that the symbol is taken and how very far it is from that from working like that.

The golden ratio is usually written φ, but to most people aside from Dan Brown it isn’t “phi”, it’s the “golden ratio”. We use that as a common symbol for it, and τ as a less common one, but you don’t need to those to mention the number. Whereas most people genuinely do avoid π as a variable because the constant is very common and has no other name. That’s an accident of history I don’t think you can engineer your way into. Even e can cause confusion.

So I’d argue it is a misstep to name pi’s double nothing more than “tau” as if it were already that kind of standard. It means that so long as the symbol τ commonly means other things, the only way to introduce it is to say “you know, the number 2π”. And then most people are happy to get by calling it exactly that, because they’d really like to worry about larger things.

@mdavis

Admittedly, it’s perhaps one of the most ubiquitous and widely-recognized symbols, but in math more than anywhere else, truth and elegance will ultimately win out.

I mean, I like elegance as much as the next person, but sometimes a sub-optimal standard is a small price for shared history and understanding. Electricians still draw their arrows opposite the electron flow, and even pure mathematicians still write with base 10, because while arbitrary, they let us move on together.

[mdavis]

@"chenille

I mean, I like elegance as much as the next person, but sometimes a sub-optimal standard is a small price for shared history and understanding. Electricians still draw their arrows opposite the electron flow, and even pure mathematicians still write with base 10, because while arbitrary, they let us move on together.

Your point about current direction is well-taken. Base 10, I’m not as convinced - it’s only used for writing down constants, really, it doesn’t actually play a role in the theory itself. Base 2 is arguably more natural but completely impractical for that purpose.

Things do change in mathematics, though. Much of the mathematics written, say, 150 years ago looks absolutely archaic without the notation and generality in common use today. π may have particularly deep roots but I don’t think even that is insurmountable given enough time.