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> Less sardonically, there is a lesson here: systems which intermediate between cultures are useful. Intermediating between cultures is a thing the world urgently needs and is extremely prepared to pay for.
https://www.bitsaboutmoney.com/archive/financial-systems-tak...
I don't think decentralized currency will actually solve the issues travelers have with this, at least without reproducing much of the infrastructure already in place for traditional currencies.
This symbol for it may be useful, but it's the concept that matters.
You can read it at https://fivethirtyeight.com/features/disaster-politics-can-g... .
Admittedly, Python, Bash, Perl, and Ruby use # for comments, so you do have a point, especially since Python is such a common teaching language.
> Gibraltar is adjacent to known drug trafficking and human smuggling routes, but the territory is heavily policed on land and at sea due to the risk of these activities occurring within its borders or territorial waters
https://www.state.gov/j/inl/rls/nrcrpt/2014/supplemental/227...
All throughout the talk there were statements like "Let p be an odd prime and…"
My friend asked, “what is an odd prime?”—thinking it must be special in some way. The answer back was: not 2.
from https://rjlipton.wordpress.com/2009/05/18/boolean-solutions-..."To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries" (Emphasis added)
[1] https://www.constituteproject.org/constitution/United_States...
You can see the analysis at http://projects.fivethirtyeight.com/flights/. The explanation, linked to at the top of that page, is at http://fivethirtyeight.com/features/how-we-found-the-fastest....
In particular, the two most consonant (best-sounding) intervals are the octave and the fifth. The frequencies of the two pitches in an octave have a ratio of 2.0, and the frequencies of the two pitches in a pure fifth have a ratio of 1.5.
We would like the pitches we obtain from powers of these two ratios (stacking these intervals on top of each other) to be the same. However, since the integers are a unique factorization domain, they will never be (except for 2^0 = 1 = 1.5^0, of course). [1]
Thus, we pick powers of the two that are 'close enough' and call those the same pitch. The following Python (3) code subtracts the log-base-two of the powers of 1.5 from the integer they round to in order to find the closest ones:
from math import log
fifth = log(3/2, 2.0)
print(0, 0.0)
minDist = 0.08
for i in range(1,100):
pow = i* fifth;
dist = abs(pow - round(pow))
if dist < minDist:
minDist = dist
print(i, pow, dist)
This has output: 0 0.0
5 2.924812503605781 0.07518749639421918
12 7.019550008653875 0.019550008653874684
41 23.983462529567404 0.01653747043259557
53 31.003012538221277 0.003012538221277339
From this, you can see that 12 is the closest that the powers of 2.0 and of 1.5 come being equal until 41. This is a primary reason why we use a chromatic scale with 12 notes.(As an aside, a scale with 5 notes is also common around the world, called the pentatonic scale [2])
[1] For an explanation of this, see http://blogs.scientificamerican.com/roots-of-unity/the-sadde...
"'I have discovered something else,' I continued. 'By flipping the pages at random, and putting my finger in and reading the sentences on that page, I can show you what’s the matter – how it’s not science, but memorizing, in every circumstance. Therefore I am brave enough to flip through the pages now, in front of this audience, to put my finger in, to read, and to show you.'"
One can use this to show that pairs of integers have the same cardinality as natural numbers.
Further, since one can sum the binary representations of two numbers and get the representation of the result, this is homomorphic under addition. I have never before seen a pairing function with that property (not that I have seen many).
[1] https://en.wikipedia.org/wiki/Pairing_function#Cantor_pairin...
https://rjlipton.wordpress.com/2015/11/04/a-big-result-on-gr...
https://rjlipton.wordpress.com/2015/11/09/the-world-series-o...
https://rjlipton.wordpress.com/2015/11/11/a-fast-graph-isomo...
I expect he will post more as he gets more information.