
Near-miss math provides exact representations of almost-right answers - dnetesn
http://nautil.us/issue/49/the-absurd/the-impossible-mathematics-of-the-real-world
======
vumgl
It's always fascinating to think about how few people realize the near miss
(better called lucky approximation) of 2^7/12 ~ 3/2, which is the basis of the
equal-temperament musical system, i.e. music as we know it.

~~~
endymi0n
A great further read:

"The saddest thing I know about the integers"

[https://blogs.scientificamerican.com/roots-of-unity/the-
sadd...](https://blogs.scientificamerican.com/roots-of-unity/the-saddest-
thing-i-know-about-the-integers/)

------
GlenTheMachine
Is there a body of literature that one can use to bootstrap yourself into
these ideas? I've seen it written up in the popular scientific press a couple
of times over the last few months, but I've never found a tutorial or textbook
or body of papers accessible to AI researchers or engineers. Pure math papers
are often not written to be understandable to dabblers.

------
tectec
This page is referenced in the article, but I didn't see a link provided:
[http://www.orchidpalms.com/polyhedra/acrohedra/nearmiss/near...](http://www.orchidpalms.com/polyhedra/acrohedra/nearmiss/nearmiss.htm)

------
GuB-42
Interesting,

Does it makes sense to do statistical analysis on near-misses like it is done
in experimental science in order to find if it is just a coincidence or if it
warrants more attention?

For example: estimate the entropy of a formula and compare it to the error
margin.

~~~
TeMPOraL
I'd say it doesn't, and that's precisely why it might be a fertile ground for
new mathematics. Like it was with e.g. complex numbers, aka. "let's assume
that this thing, which clearly doesn't make sense, exists, and let's consider
how it behaves".

------
strictnein
The two triangles and blocks are kind of mind bleep, before it's explained to
you.

Check it out here, without the spoiler:

[http://static.nautil.us/12472_4c78f7b58f4de12ed2cab9bcb9ec0b...](http://static.nautil.us/12472_4c78f7b58f4de12ed2cab9bcb9ec0ba0.png)

------
jfaucett
How can any irrational number x be close to a rational number y? as long as x
is irrational it seems to me it would still be infinitely far away from y.
What notion of proximity are they talking about?

~~~
bmm6o
There is a rigorous notion about how well an irrational can be approximated by
a rational, related to its continued fraction representation (
[https://en.wikipedia.org/wiki/Continued_fraction](https://en.wikipedia.org/wiki/Continued_fraction)
). I'm having trouble finding a better description than the note in that WP
page, but the idea is if the cf representation has a "surprisingly large"
value, then the rational number you get by truncating the sequence there will
be a very good approximation, like 355/133 is for pi (see the comment in
[https://math.stackexchange.com/questions/435668/finding-
the-...](https://math.stackexchange.com/questions/435668/finding-the-value-of-
a-continued-fraction)).

~~~
user51442
Continued fraction approximations p/q have |x-p/q| < 1/q²

------
mangix
Uhhhhh I'm pretty sure near miss is the wrong term.

Near hit sounds about right.

~~~
raattgift
Close call?

