[2017-07-13] espresso names

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[2017-07-13] espresso names

Postby shallowandpedantic » Mon Jul 17, 2017 9:55 pm

http://www.smbc-comics.com/comic/espresso

It's not true that all possible espresso-to-milk ratios have Italian-sounding names. The proof relies on 3 assumptions:
1) The possible espresso-to-milk ratios are uncountable (or, to put it more simply, any positive real number could be an espresso-to-milk ratio).
2) Italian-sounding names may be arbitrarily large, but any particular Italian-sounding name must be finite in length.
3) Italian-sounding names are composed from a countable set of characters/phonemes/whatever symbols.

The proof is this: we show that the set of Italian-sounding names is countable, and then assumption 1 necessarily implies that there must exist some ratios without unique, Italian-sounding names. To complete the first half of the proof, consider the following:

Assumption 3 implies that we may write down a list of our "alphabet" of symbols, with each symbol corresponding to a unique, positive integer. It doesn't matter if this list is finite, as long as it is countable. We denote elements of this alphabet by s with a subscript.

Assumption 2 implies that any Italian-sounding name may be written as a unique string S = s1s2s3...sn for some integer n (n depends on the particular string S, of course).

Let pk denote the k-th prime number, ie p1 = 2, p2 = 3, p3 = 5, etc.

The unique factorization theorem implies that f(S) = p1s1p2s2p3s3...pnsn is an injection from Italian sounding names into the natural numbers, and hence that Italian-sounding names are countable.

There can be no injection from an uncountable set to a countable one, so application of assumption 1 completes the proof. QED.

Now, let's analyze the assumptions:
1) is interesting from a physics perspective. If we simply count the whole, fundamental particles composing the espresso and milk as being relevant, then this assumption actually fails. But then again, pi and i are not valid ratios in this case. If we look at volume ratios, then we have to know if space itself is quantized to decide if the assumption is valid. Lacking a quantum theory of gravity, we can only speculate. If we look at mass ratios, then, by E=mγc², we must include the kinetic and potential energy contributions of the espresso and milk's subatomic constituents. In an open system (ie, one coupled to the rest of the universe), the energy spectrum ought to be continuous, and thus any real mass ratio is possible. On the other hand, a perfectly isolated cup of coffee in a Schrödinger's box is composed of bound, disentangled particles, and will therefore have a discrete energy spectrum, rendering the possible mass ratios countable. If I had even less going on in my life, I could probably get a full academic paper out of this question alone.

2): While Italian (or any foreign language) may seem like an endless stream to the untrained ear, if one listens very closely, one will find that every human, no matter how verbose, eventually stops speaking. This cessation may only occur at the point of death, of course, but it inevitably comes. Therefore, an infinite name, while badass, probably doesn't resemble any human language, let alone Italian. Of course, these names can be very long, for example: https://en.wikipedia.org/wiki/Titin#Linguistic_significance

3) The concept of a language composed of an uncountable alphabet is interesting. If spoken, the tone of the signal, for example, would affect meaning out to arbitrary precision. The only way that I can conceive of such a language being understandable is if, past a certain point of accuracy, additional information only conveys nuance rather than dramatically altering the meaning -- that is, the mapping from phonemes to meaning is a continuous function. For example, a particular sound would convey anger, and then the level of anger would be specified precisely by the exact tone of the sound. The problem is that any finite signal, when Fourier transformed, will have a spread in frequency. The only way to emit a pure tone is to have an infinitely long sound, and so we again run into the finite lifespan problem. I am not a linguist, so I will leave further discussion on this matter to them.

This is my first post to the forum, and it took a little while to get registered. Therefore, I apologize for the tardiness of this post. If anyone attempted to open a coffee shop with an uncountably infinite menu over the weekend, I am deeply sorry for your lost investment of time and capital.
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Re: [2017-07-13] espresso names

Postby fungus » Tue Jul 18, 2017 1:03 pm

Wot, no Golden Ratio?

The laws of nature say 1.618:1 must be the best.

Weird that no coffee shop around here sells it.
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Re: [2017-07-13] espresso names

Postby juckto » Wed Jul 19, 2017 12:36 am

I too, made an account to post on this comic and apologise for my tardiness.

However, I'm more interested in funny names than discussing infinites, so here we go:
* Golderiatto 1 : 1.618
* Exponesso, 1 : 2.718
* Fibonatte, 11 : 23.5

... and if I came up with any others, I've forgotten them in the time it took to register :-(
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Re: [2017-07-13] espresso names

Postby GollyRojer » Mon Jul 24, 2017 3:21 pm

juckto wrote:* Golderiatto 1 : 1.618
* Exponesso, 1 : 2.718
* Fibonatte, 11 : 23.5


There needs to be a "like" button for posts like this.
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Re: [2017-07-13] espresso names

Postby Capable Runt » Fri Aug 25, 2017 10:53 pm

In the interest of finding more silly espresso names, I'd like to propose the Decibello (1:10). If you find the ratio a little too strong for you, you can subtract 3dB to achieve the Logarithimo (1:6.9897).

I considered adding 3dB, but it seemed like a latte.
Capable Runt
 

Re: [2017-07-13] espresso names

Postby RyanW » Tue Aug 29, 2017 9:10 pm

I immediately thought of the L'Hospiccino: A zero to zero ratio.
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Re: [2017-07-13] espresso names

Postby Theseetor » Fri Sep 01, 2017 10:09 pm

Il Cesare 3:15
Protestantto 15:17
Primo 19:14
Secundo 19:39
Finito 19:45
Brasiliano 1:7
Currento 20:17.
That last one sounds like a fun idea actually. It gains a part of espresso each year, but every one hundred years all espresso is removed and milk gains one part forever more.
Theseetor
 

Re: [2017-07-13] espresso names

Postby dreycow » Thu Sep 14, 2017 3:17 pm

I think the assumption that the number of Italian sounding names is countable is incorrect.

Let addition be assumed to concatenate characters together
Let p(x) = n, where n is any combination of characters representing a sound made by a human that sounds Italian.
Let q(n) = "mia" + n
q(n) + "mia" = "mia" + "mia" + n = q(n + "mia")

In short, miamiamiamiamiamiamiamiamiaespresso is probably the best ratio, though miamiamiamialatte is good too.
dreycow
 


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