Comment by jiggawatts | Hacker News Reader

Comment by jiggawatts | Hacker News Reader

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> at a certain point the incidental complexity is eating you alive.

I had a similar deep insight when studying both theoretical physics and computer language / compiler design: for some areas of human endeavour, the only limit is the human brain. The machines ceased being the limiting factor a long time ago, but the human brain is essentially unchanged over the timescale of millennia.

In areas like this, incidental complexity is the key limit holding us back.

Once you've reached 100% of the brain's capacity, the only way to "get more out of it" is to waste less of its capacity on non-useful things.

You mentioned pi as a significant advancement. Yes, it is. But tau would be better. Every time I (or anyone) mentions this, there's dozens of people coming out of the woodwork saying that it doesn't matter, that it's just notation, that there's an established standard, blah, blah, blah.

Meanwhile, basically nothing in trigonometry really clicked for me until I saw Vihart's rant about why we should use tau. None of it. Not really, because the pi notation is nonsense, an accident of history, nothing more. It filled my brain with incidental complexity: that factor of two everywhere that made no sense to me.

> …for some areas of human endeavour, the only limit is the human brain. … But tau would be better. … [people dismiss this because “it’s just notation”…]

The case for me of this is current flowing from - to +. Franklin didn’t know better and had a 50/50 chance of getting it right, but happened to get it “backwards”.

A small thing but one that always makes me skip a beat while following a circuit.

> In areas like this, incidental complexity is the key limit holding us back.

> Once you've reached 100% of the brain's capacity, the only way to "get more out of it" is to waste less of its capacity on non-useful things.

Queue modern day social media... It has its uses, but I feel like the brainrot and lessening of attention span it induces (and not to mention everything else like polarization, cult-like behaviours etc) is basically not worth the small amount of benefit it actually provides.

Tau is better for some equations (most of them?) and worse for some others. It would probably be a net positive to adopt it if you discount the huge chore of transitioning during decades. But what this fails to account is that most mathematicians regard 2pi as an important quantity on its own already; it's not a single symbol but it's close enough. So 2pi is expected to appear in many equations and any other value, like 3pi, looks fishy.

Really, the only problem with 2pi is that if you multiply it by a constant, it disappears. so people might write 2*2pi as 4pi. Sometimes you may not want to do that.

Anyway you don't need to fully transition to tau in order to benefit from it. Just like the planck constant has a reduced planck constant (which is probably more useful), and both are used, tau can be already used when it makes sense, without ever fully replacing pi.

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