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Comment by morpheos137 | Hacker News Reader

Mathematics may be made up in the sense of what we use for notation or symbology but the underlying relations are timeless and superuniversal.

In any universe or species pi defined as the ratio of the path length traced by a set of coplanar points equidistant to a common point to the path traced by a set of points in a different plane intersecting exactly two points in the first path and the aforementioned common point will be the same as our pi.

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I think you are oversimplifying in a way that eludes the point OP was trying to make.

Or rather two points. First that the process of actually creating mathematics is messy and largely made up as it goes along. I can create a new mathematical structure that turns out to not be very useful, etc. Secondly that the way math is taught typically hides this, and creates a very linear "greatest hits" approach which is misleading.

You are correct that one of the things that has come out of centuries of studying mathematics are clear definitions of abstract objects that almost have to have been found; but the day-to-day isn't that.

On the other hand, how something is taught and how it is practised often aren't that close to each other. Part of the reason the pedagogy looks the way it does is to distill centuries of thought and argument into a few credit hours.

if anyone gave a crap about your second sentence they'd point out that its impossible to parse without punctuation or rewording or something, but the fact that everyone already knows what you're saying despite an inscrutable explanation really pokes a hole in the idea that you are bringing up anything remotely novel

Is this still true in hyperbolic geometry, where the circumference of a circle of radius r is greater than 2.pi.r?

Never used the word circle in my definition of pi. If planes curve in another geometry then no. I think these would called surfaces rather than planes. You could define a plane as simply the set of points sharing a common normal vector not intersected more than once by lines oriented in directions that have a non-zero normal component (i.e. parallel planes are unique).

In hyperbolic and elliptical geometry ratio of radius and circumference of a circle is not a constant. You can't define pi there as such.

Anyway, pi comes up in various fields of math with no relation to the geometry of space we live in.

Ironically, pi comes from geometry (land measurement), and the land they measured has elliptical geometry.

For Pi to have any meaning requires a universe with at least two dimensions. Whether Pi would exist without a universe is a matter of debate.

> For Pi to have any meaning requires a universe with at least two dimensions

There is no such requirement. Mathematical constructs have meaning even outside of their most immediately obvious manifestation (such as the application of geometry to the understanding of physical space). Even a one-dimensional intelligent being, if such a thing is even possible, would eventually encounter pi, alongside the basics of euclidian geometry, as soon as they start doing math on datasets measuring more than one feature, as such datasets are embedded in n-dimensional spaces, where n is the number of independent features, even if physical space has less than n dimensions.

So if I tree falls in a forest and nobody hears it it doesn't make a sound?

Pi never has existed in a material sense.

It exists as a logical potential consequent of abstract definitions regardless whether the universe does or not.

Your definition of pi gives incorrect values of pi...

("a set of points in a different plane" is not constrained to be a straight line.)

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