First Letters Represented

Do note that quite a few of these can change over time. The set of countries used for this chart is the standard {UN recgonized+Taiwan+Palestine+Kosovo}. If you recognize the independence of the Sahrawi Arab Democratic Republic, then there would be a country capital starting with E.

lettersRepresented

A Lament on the State of Chinese Pronunciation

(A warning in advance: this post assumes Pinyin transliteration. I will not attempt to untangle the mess that is Wade-Giles.)

Here’s one thing that I’ve gathered to be nearly universally true about Chinese people: they don’t correct others that pronounce their names incorrectly.

I used to be one of them. I thought I was helping to be considerate of people who don’t get how Chinese, as transliterated, is pronounced (transliteration itself being a problem due to the various methods by which it happens). Quite a few events, however, most notably when I overheard a conversation in my high school office in which someone said something along the lines of “…and it’s another Chang (?), you know, there’s so many ways to spell that last name.” It was, of course, pronounced incorrectly, for any of the various definitely different Chinese last names that she may have meant. And I decided I did not want to help spread the ignorance. Thus I have increasingly tried to contribute to proper (or at least close-to-proper) Chinese pronunciation. So at the risk of making certain Chinese names and words sound weirder in an English context, I’d like to take a moment to lament how Chinese is pronounced, by the populace in general, but more importantly by Chinese people helping to let it continue to happen.

Here’s a chart.

chinesePronunciationIntuition

Congratulations, you’ve been pronouncing the blue ones correctly (up to tone, at least)! That’s the set of Chinese words and names that go along with intuition. (This is of course excepting those that haven’t yet absorbed the general standard of “ai” being a long “i” and “ei” being a long “a”.) The green ones are ones most people have been getting close enough for it to be acceptable (due to nuances in certain sounds between Chinese and English), so that’s also pretty good. The red ones, unfortunately, are the ones that nearly everyone mispronounces, and are the subject of today’s lament. Look at how many of them there are! Now, the ones with a cyan background involve sounds or sound patterns that do not exist in English, so it is quite understandable if someone who only speaks English natively does not pronounce them correctly, but there’s all of the other ones such that people that do not pronounce them properly can be politely corrected as to their pronunciation. I know it can happen, because the orange ones are words and names I’ve heard a significant number of people pronounce correctly, but not most. The teal names and words are those for which the general Pinyin transliterations, due to the fact that people tend to not resolve between the two different Chinese u’s in transliteration, are actually still ambiguous, and for which an additional query is typically needed for proper pronunciation.

By the way, feel free to go over to the pronunciation guide for Chinese I wrote earlier in this blog to see how those red words and names are supposed to be pronounced.

Note/Erratum: A small number of actually existent valid words and names have been left out of the table.

Sorry, but You’re Still Wrong: A Partly Corrected Pi Day

I may take it as a good sign that people are questioning the arbitrarity of conventions, but this article hasn’t properly fully baked the idea. The article claims that the celebration of Pi Day on March 14 is “an archaic and local convention”, and suggests alternative dates for celebrating π. Unfortunately, these alternative dates are founded upon artificial and arbitrary conventions still, although I will give kudos for at least thinking beyond the normal line of thought.

First of all, picking the day that happens to be January 1st is artificial: there is nothing naturally special about that date for the start of the year and is only an aged human convention; a significant transition of the moon or an apsis (I would argue for aphelion) is a much less arbitrary date to perform year partitioning at. If you decide that using days to measure pi instead of the SI seconds is inferior, why do you not consider measuring against January 1st to be inferior to measuring against an apsis?

Speaking of which, do you think SI is actually the proper way to measure pi? Don’t you think a power of ten times pi (speaking of which, powers of ten…) periods of caesium-133 ground state hyperfine transition radiation is actually based on a natural rather than an artificial standard? Those numbers like 9192631770 in the definitions of SI units are human-decided. I agree that days are from the experimental view not “suited to the dignity of science”, but your propositions are not suited to the dignity of mathematics, as you have not fully embraced the elegance of simplicity. And π is a mathematical constant, not a number of seconds in a natural phenomenon.

One last note: there is substantial evidence that tau, rather than pi, is the proper circle constant. Fortunately, the degree to which tau is better to use than pi is rather negligible, so there’s nothing wrong with being friendly with both. But if you decide to bash tau as utter heresy, then I’m afraid you’re just reflecting that you have not looked all the way through the problem with an eye for unjustified convention.

Happy birthday, Albert Einstein.

“This Is How Your Brain Works”

Video

(You probably want to watch it before reading the rest of this post, for reasons having to do with spoilers.)

This was a very interesting video, although I would insist on noting that at least not all brains work that way, because I, for one, had several different results.

First of all, it took me longer to figure out that the woman is angry than to solve the multiplication exercise. Seeing that she’s blonde was instant, as a direct visual cue, but figuring out that the woman is angry took first noticing that her facial expression is not usual, wondering what such a facial expression is usually correlated with, and eventually noting within the category of emotions that angry seems to fit. In my mind, 19 times 26 was instantly converted to 520 minus 26, followed by a non-instant but short amount of time to perform the carry subtraction.

I’ve seen the optical illusions before, so I’m biased.

I did notice that the numbers to the side changed. In fact, because they changed, I was unsure if we were actually supposed to be mentally performing the operation on both piles. I did not notice the color changes.

I actually misheard “the bat cost ten cents more than the ball,” thus coming up with an answer of 50 cents for the ball. This is very interesting; did I actually take the unintended outcome and repipe it into the problem, or was this just a fluke mishear?

How many animals did Moses take on the ark? Zero. I actually never until revealed noticed that it said Moses instead of Noah, but Noah also took zero animals onto the ark. Until someone actually presents to me historical evidence that there was a Noah that notably took a set of animals onto the ark, I will insist that the answer is zero, because, well, it’s what looks much more convincing to be true.

I read that as an A, a 1, a 3, and a C. I then considered the possibility that the 1 and the 3 are a B in stencil.

I did envision Ann approaching a bank of money, soap, and soup.

State of My Trivia Knowledge

Largest Three Cities per US State: 132/150
Largest Three Cities per Canadian Province or Territory: 19/39
Largest Cities of California: 80/200
Largest Five Cities per Decade in US History: 115/115
Olympic Host Cities: 31/49 [1]

[2]
States of India: 10/28
Provinces of Indonesia: 29/34
States of Brazil: 3/27

Flags of US States: 16/50 [3]
Flags of the World
: 197/197

Elements: 117/118 [4]
Main Amino Acids: 20/20

Moons of Jupiter: 26/50
Moons of Saturn: 53/53
Moons of Uranus: 24/27
Moons of Neptune: 13/13

Fifty Brightest Stars of the Night Sky: 43/50
Brightest Stars of Constellations: 31/41 [5]

[6]
Generation I Pokémon: 51/151
Generation II Pokémon: 14/100
Generation III Pokémon: 49/135
Generation IV Pokémon: 20/107
Generation V Pokémon: 11/156
Generation VI Pokémon: 0/69 [7]

Most Mentioned Harry Potter Characters: 14/200

MIT Majors: 32/32 [8]

Notes:
[1] The amount I actually know is slightly lower than listed here, as a few I got on the quiz by accident.
[2] Note the lack of a “Provinces of China” here. You probably know why.
[3] Note that the flags have state names that are on flags redacted. If it weren’t for those, then my performance would be slightly higher.
[4] Since 2012, this is the lowest percentage-wise that it has been for me since 2003, as I have never bothered to remember flerovium. Darn.
[5] Note that some constellations that have named brightest stars are not included in this quiz, for instance Libra (with brightest star Zubeneschamali).
[6] Note that I have never owned a Pokémon game (although I have played a bit of a Generation II game on someone else’s game boy), and have never read a Harry Potter book.
[7] As you can see, I am doing rather well at pretending that nothing beyond Generation IV in Pokémon exists.
[8] Note that some majors that exist at MIT are not in the quiz, like WGS (Women and Gender Studies), and of course Course 19.

Round Numbers

When someone says “a nice round number, like 1000,” what are they really saying? What about a number makes it round?

The most reasonable explanation is probably that it is has very few non-zero digits, thus giving it properties like being easy to remember, easy to put in bundles, and easy to divide up. But if one thinks a bit deeper about these qualities of round numbers, one can find that typically-considered round numbers are really not the optimally round ones to find.

1000, for example, is only round because we use base ten, which is only because we happen to have ten fingers. If would also be round if we used base five or twenty, not so round if we used base two, and not round at all if we used base nine (not that nine is that reasonable of a base to use).

We can satisfy properties of being easy to put in bundles and being easy to divide up much better, and be more correct about few non-zero digits by a theoretical viewpoint, by looking for numbers that are the original definition of round…in a particularly large number of bases: numbers with many factors. How would we elegantly define this type of having a lot of factors?

Here, I will propose a new definition for a round number: it is a number n with the property that for all pairs of primes p and q, with e_p and e_q being the respective powers of p and q in the prime factorization of n, if q>p, then e_q \leq e_p, or in other words, e_2 \geq e_3 \geq e_5 \geq e_7 \geq e_{11} \geq ....

Here are some properties of round numbers as defined, with all variables in the statements below being positive integers:

-1 is the only odd round number.
-If n is round, then n^m is round.
-If \sqrt[m]{n} is an integer, then if n is round, then \sqrt[m]{n} is round.
10^n is not round.
-All round numbers are abundant, except for 6 and the powers of 2.

We can also define barely round numbers as numbers that just barely qualify for being round: the boundary cases where all prime factors are 2 or exactly one factor of each prime factor involved exists, namely, the powers of two and the primordials. Note that if a round number is not barely round, then it is necessarily abundant.

Here is a list of round numbers less than 65537, by the new definition:

1
2
4
6
8
12
16
24
30
32
36
48
60
64
72
96
120
128
144
180
192
210
216
240
256
288
360
384
420
432
480
512
576
720
768
840
864
900
960
1024
1080
1152
1260
1296
1440
1536
1680
1728
1800
1920
2048
2160
2304
2310
2520
2592
2880
3072
3360
3456
3600
3840
4096
4320
4608
4620
5040
5184
5400
5760
6144
6300
6480
6720
6912
7200
7560
7680
7776
8192
8640
9216
9240
10080
10368
10800
11520
12288
12600
12960
13440
13824
13860
14400
15120
15360
15552
16384
17280
18432
18480
20160
20736
21600
23040
24576
25200
25920
26880
27000
27648
27720
28800
30030
30240
30720
31104
32400
32768
34560
36864
36960
37800
38880
40320
41472
43200
44100
45360
46080
46656
49152
50400
51840
53760
54000
55296
55440
57600
60060
60480
61440
62208
64800
65536

This post has 430 words, or, when rounded, 432.