
How to fit an elephant (2011) - Kristine1975
https://www.johndcook.com/blog/2011/06/21/how-to-fit-an-elephant/
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oddeyed
I can't help but feel like a complex number is two parameters (real&imag /
mod&arg) - so really this is 8 parameters.

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Y_Y
Cantor showed that these sets have the same cardinality. You can represent a
complex (in the form of two reals) by interleaving digits or using a space-
filling curve for example.

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wolfgke
> Cantor showed that these sets have the same cardinality. You can represent a
> complex (in the form of two reals) by interleaving digits or using a space-
> filling curve for example.

But this (set) isomorphism between R and C is not continuous. Indeed one can
show that there exists no continuous epimorphism f: R^n -> R^m, where m > n,
since for every such continuous map f the image f(R^n) has a measure of 0 with
respect to the Borel measure in R^m.

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Y_Y
Sure, but did we need continuity? Also, if you want to be awkward, you can get
around this by using the discrete topology, I don't think we needed the metric
structure of R^n.

~~~
wolfgke
> Sure, but did we need continuity? Also, if you want to be awkward, you can
> get around this by using the discrete topology

This is indeed possible - but this is clearly not the topology that "ordinary
people" and physicists mean when talking about continuity of functions from
R^n to R^m.

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pvg
The only thing missing here is a little anecdote about how Von Neumann, when
challenged on this, did it in his head and started rattling off the
parameters. For arbitrary animals.

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scott00
Source please. Must learn more.

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pvg
Von Neumann was renowned for his great prowess at mental maths. A famous (if
also not entirely serious) story:

"When posed with a variant of this question involving a fly and two bicycles,
John von Neumann is reputed to have immediately answered with the correct
result. When subsequently asked if he had heard the short-cut solution, he
answered no, that his immediate answer had been a result of explicitly summing
the series (MacRae 1992, p. 10; Borwein and Bailey 2003, p. 42)."

From
[http://mathworld.wolfram.com/TwoTrainsPuzzle.html](http://mathworld.wolfram.com/TwoTrainsPuzzle.html)

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mamon
The article you linked to provides a trivial solution:

"the trains take one hour to collide (their relative speed is 100 km/h and
they are 100 km apart initially). Since the fly is traveling at 75 km/h and
flies continuously until it is squashed (which it is to be supposed occurs a
split second before the two oncoming trains squash one another), it must
therefore travel 75 km in the hour's time."

So if von Neumann was solving it by explicitly summing the series, as the
anecdote claims, then he was doing it wrong :)

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xelxebar
Well, if you're familiar with sums, then the "shortcut" isn't all that much
faster; it's mostly a function of how quickly you can grok the salient points:

The fly travels 3/2 times the speed of a train, so every bounce the fly
travels 3/5 of the remaining track and leaves 1/2 * 2/5 = 1/5 track to travel,
so we just compute the geometric sum

    
    
        3/5 * \sum 1/5^r = 3/5 * 1/(1 - 1/5)
                         = 3/5 * 1/(4/5)
                         = 3/5 * 5/4
                         = 3/4.
    

One nice thing about this sum is that it encodes a bit more insight about the
fly's flight path than the shortcut method.

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rkroondotnet
How do you fit an elephant?

One parameter at a time.

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triclops200
Now can you add one more and make him wiggle his trunk?

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dEnigma
In the actual paper they do exactly that

[https://www.google.at/url?sa=t&source=web&rct=j&url=https://...](https://www.google.at/url?sa=t&source=web&rct=j&url=https://publications.mpi-
cbg.de/Mayer_2010_4314.pdf&ved=0ahUKEwiqzNeRmuvWAhWFb1AKHXVsBDYQFggtMAI&usg=AOvVaw1AmrjYniYTf8n9dYp405VW)

