500-year-old maths problem turns out to apply to coffee and clocks | Hacker News Reader

500-year-old maths problem turns out to apply to coffee and clocks

newscientist.com

120 pointsgumby27 comments

In "An Introduction to Mathematics", by A. N. Whitehead, he makes a wonderful argument for the "usefulness" of pure math. With many fascinating examples like this he describes how when people work to solve purely mathematical problems without any "real-world application," they actually end up having incredibly useful applications in real life situations down the road. But where people are limited only to seemingly useful, "practical" math problems, they don't end up making the progress that brings great practical advances in the end.

I just finished G. H. Hardy's celebrated "A Mathematician's Apology". He describes "useful" math such as calculus as "on the whole, rather dull", and contrasts it with the "real" math of Euler, Fermat, and Gauss, which he finds "almost wholly 'useless'"; he adds that the great achievements of applied math--relativity and quantum mechanics--are "almost as useless as number theory".

He was prudent to add "at present [1940], at any rate": the phone on which I am typing wouldn't work at all without number theory, relativity, and quantum mechanics!

I have a vague sense that mathematicians take some pride in the uselessness of their discipline, even when it's the exact opposite of useless. Maybe because the more useless the mathematics appears to be, the more it must be motivated by the pure love of the subject?

With regard to the "pride in uselessness" thing, I caution you against generalizing here. Different people get into math for different reasons, but I would say that all the pure mathematicians I know of are motivated principally by interest in the problems they care about, and don't think too much about questions of purity.

There's a nice quote from Courant in his "Introduction to Calculus & Analysis" where he warns against "smug purism", exhorting students to draw inspiration and insight from other fields because it will make them better mathematicians. I think this is the attitude that I encounter most frequently among mature, pure mathematicians.

Chebyshev in particular was known not only for working on problems that had engineering applications, but for using methods and techniques from engineering to inform his approach to pure math problems. As the founder of the St. Petersburg school of mathematics, this approach had broad impacts on (later) Soviet mathematics and global mathematics as students brought up in this tradition went on to train later generations of mathematicians around the world.

Here is an amusing related phenomenon: if you look at dynamical system induced by multiplication by 3/2 on the binary digits of a seed and cut a fixed window, you get the following graph family: https://ykonstant1.github.io/images/trans_limit.png

More generally, exponential maps on finite structures produce these reflection-like envelopes.

Epicycloid -> Antikythera gearing -> planetary epicycles

https://digitalrepository.unm.edu/cgi/viewcontent.cgi?articl...

The mathematics of the epicycloid : a historical journey with a modern perspective

See the Wikipedia page for satisfying proofs of the Cycloid's Involute, Arc Length, Area, and Pendulum properties. The involute property has a particularly neat proof, and it gives us a neat proof of the arc length property, and a shockingly elegant construction for the pendulum motion:

https://en.m.wikipedia.org/wiki/Cycloid

The article about cardioids has a very elegant proof of coffee cup caustic reflection property:

https://en.m.wikipedia.org/wiki/Cardioid

The butt pattern.

Finally, a mathematical solution to why coffee makes me poop. It's clearly subliminal messaging.

I always assumed despite the slight laxative effect of coffee, the real reason is most people are just morning poopers and morning coffee drinkers.

I noticed years ago while feeding my newborn that she would chug some delicious warm milk and fill up that diaper. Since then I always figured the coffee phenomenon was related.

Drinking plain warm/hot water can trigger the same response so it is arguably not just coffee.

I vary my routine a lot, so I am pretty sure that it is the liquid coffee here that is the trigger. Not just caffeine because I normally use caffeine pills instead.

It's a pretty strong effect for me, but IIRC there are multiple causes, like that it's hot + acidic + caffeinated.

It's hard to discount other factors but I certainly notice a difference switching from water to coffee.

I can drink as much coffee as I want and I experience no laxative effects. But if I eat some chilli peppers next morning I feel like I am going to explode.

On some days I'm 8-10 times a day coffee drinker and on the same days I turn out to be 4-5 times a day pooper. I suspect there is some connection.

I think it's because it pulls water into the intestines, which helps you poop easier.

As it's a diuretic I'd say it pushes water, but yeah.

Correlation <> causation.

Most people tend to poop around the same each day. Largely because we tent to eat around the same time each day.

Most people tend to drink coffee at the same times each day. Naturally for a bunch of folk one will co-incide with the other, at least some days a week.

The added factor is that most people (who drink coffee) drink multiple times per day, allowing for more correlation opportunities.

But mostly what causes pooping is eating (he says, speculating, with no data to back it up.)

All stimulants cause this, it is well known.

Why is it a maths problem and not a math problem?

> Why is it a maths problem and not a math problem?

Because what Americans call 'math' is called 'maths' in many parts of the English-speaking world.

Thanks for the clarification. Maths sounds inherently terrible to me - maybe i infer US instagrammers using maths to sound hip and they don’t really use math. Glad to know its normal use in UK.

Similar in US we typically say 'the University' however on HN I frequently see just 'University'.

(Note I had the same thought as you but assumed (w/o a search) it was for the reason stated by your reply).

"maths" is British English for "math" in US English.

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