
Is e Normal? - lisper
https://www.mathpages.com/home/kmath519/kmath519.htm
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ccvannorman
It's fascinating how little we know about everyday numbers like pi and e, it's
widely assumed that they are normal but there is no proof for this (and it's
extremely difficult to do so). In fact we believe the fast majority of numbers
are transcendental and normal but we only actually know of a single normal
number, and it is a manufactured number.

Numberphile has an excellent video on the numbers we know about and the quest
to find / define normal numbers:
[https://www.youtube.com/watch?v=5TkIe60y2GI](https://www.youtube.com/watch?v=5TkIe60y2GI)

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empath75
> It’s widely believed that the two most naturally occurring transcendental
> numbers, p and e...

Not really germane to the larger topic of the essay, but I don’t think it’s
true that those two numbers occur naturally very frequently except that they
make it easier to calculate systems with cycles or exponential growth. It’s
almost certainly exceedingly rare that someone would measure exactly pi or e
in nature, and even in calculations they’re generally multiplied by some
constant or other.

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infradig
I would say the ratio of a circle circumference to its diameter is naturally
occurring.

~~~
coldtea
Are there circles in nature?

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sverige
(Looks at sun, closes eyes.) Yes.

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billpg
That's an ellipse.

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sverige
Really? You can tell that by looking at it with the naked eye and no
scientific instruments? Are such instruments 'natural'? Wherever did we get
the idea of 'circle' from then?

~~~
coldtea
> _You can tell that by looking at it with the naked eye and no scientific
> instruments?_

How is that relevant?

We didn't ask if someone can consider or see with naked eye something that
looks like a circle, but whether circles do exist in nature.

And we have the "scientific instruments" to check up on the sun (which has a
very small, but existing, buldge in the equator, and which also has an uneven
exterior with flares and all kinds of motion).

> _Wherever did we get the idea of 'circle' from then?_

From objects resembling circles, like cut tree trunks, the moon at night, and
so on.

Same place we got the idea of line, while there are no lines in nature (for
one, because everything we see line-like, is just a line segment: lines extend
to infinity).

~~~
sverige
So, and really just for the sake of argument, if we could look at the sun with
one of its poles at the center, it would still be elliptical?

Or if we could somehow see cross-sections of atoms are elliptical and not
circular too?

If so, how do you know that?

~~~
coldtea
> _So, and really just for the sake of argument, if we could look at the sun
> with one of its poles at the center, it would still be elliptical?_

Missed the part where the sun's surface also isn't seamless, but an"uneven
exterior with flares and all kinds of motion"?

> _Or if we could somehow see cross-sections of atoms are elliptical and not
> circular too?_

I seriously doubt it, as from what we know atoms don't look like little balls
and aren't solid objects themselves -- they consist of electrons, protons, and
neutrons, in orbits, and are "fuzzy". They're drawn as little balls for
illustration purposes.

