Dorky Poll: Numerical Trivia

Has to be e^(i pi) +1 = 0, really. Even looks good on a t-shirt.

Second is probably the glorious series 1,2,4,8,16,*31*...

Here's one that I realized only recently: sqrt(g) is pi to a few tenths of a percent.

Blast. Ewan beat me to it. But how 1/i = -i

Ack. How about 1/i = -i

Does anyone else find it suspicious that 1*1 =1? Seems a little too convenient.

Actually, the number of seconds in a year is closer to 107.5, but the closeness to π is related to the convenience of having e, π, and the squareroot of 10 being all basically equal to 3.

I like that a light nanosecond is about a foot. :)

One that few seem to know is that e cubed is 20.

1. For an 8-hour day, 5 days a week, there are exactly 2087.1 mean work hours per year, averaged over 400 years. (This is the figure to use when converting between hourly and annual rates. For a laugh, check with HR to see what they use.)

2. Very nearly, the one-way light time from the Sun to the Earth is 499 seconds.

3. Very nearly, the circumference of the Earth is 40 megameters.

4. Back when pocket calculators first came out, pi was very well approximated by 355/113.

My favorite one from when I was young was:
111111111 * 111111111 = 12345678987654321

4=2+2=2*2=2^2=length("four")

Ken, IIRC the fact that the distance from the pole to the equator is 10 million meters is not an accident. It's how the unit was designed.

The meter was supposed to be 10^-7 of the distance along a meridian from the equator to one of the poles, so the circumference of the Earth being 4 10^7 meters isn't a coincidence. It's still cool, though.

My 14-year-old son pointed out on Mole Day that the number of particles in the universe times Avogadro's number is approximately a googol, to within a few orders of magnitude.

Take any 3-digit number, invert it, and subtract the inversion from it (or vice versa if the inversion is larger). Add the result you get and its inversion. You always get 1089.

E.g.: 783-387=396
and 396+693=1089.

Far and away my favorite:

You can use the Fibonacci sequence to convert between miles and kilometers, i.e. F_n miles is roughly equal to F_n+1 kilometers. Why? The ratio between successive Fibonacci numbers tends (rather quickly) toward the golden ratio, which is about 1.6, which is handily also roughly the conversion factor between miles and kilometers.

Asad

I'm not sure what my favorite one is, but one of them is specifically relevant to comments #9-3, #11, #12, but also #2. I like that a "seconds" pendulum is about 1 m long.

The meter was originally defined by the pole-equator distance along the meridian that goes through Paris (not Greenwich, take that you English dogs) as if that detail mattered given the quality of the data at that time. However, I do not think it is a coincidence that a "seconds" pendulum is so close to a meter in length. (Period of 2 s, 1 s per tick, requires L = something between 99.3 and 99.4 cm depending on your local value of g.)

I have long suspected, given the state of clock technology at that time, that the meter was chosen to be close to that length, and they hacked the terrestrial definition to fit that choice. I mean, why use a definition that is so close to a yard, yet slightly better for a pendulum length, rather than a fraction of the earth's diameter or any of many other possible choices?

PS - One useful one is 88 ft/s = 60 mph (exact).

My personal favorite: that ex is its own derivative to any order. There is also the similarly regular higher-order differentiation of natural logarithms, e.g.

d1000/dx1000 = 999!/x1000

Missed "ln x" above. Sorry, it's late.

And I forgot to denote the negative quotient. I'm going away now.

2^10 ~ 10^3 is a very useful one.

Ok I should propose a mass-related one: 6 pi^5. The shortest paper ever published in the Physical Review, probably.

Another one, of which john (e^3 = 20) reminded me. pi^3 = 31

@ CCPhysicist: I have read a claim that the choice of the meter was inspired, in part, by the timekeeping result of a pendulum, but haven't been able to verify it.

Well, since I already did a post about it here, (3/2)12 ~ 27.

A microcentury seems about the right maximum amount of time for a lecture, meeting, between breaks, etc. It's a bit more than 52 minutes.

Quantum Coincidence with Amino Acid Molecular Weight
By
Jonathan Vos Post

Draft 4.0 of 20 April 2007, 8 pp., 3200 words
[submitted to ICCS-2007, withdrawn in favor of revised version at ICCS-2009]

0.0 ABSTRACT:

This reports and speculates on what I presume to be a coincidence: the Mean Molecular Weight of the 20 Standard Human Amino Acids, in Daltons, is within one part in one thousand of the inverse of the dimensionless fine structure constant.

Kip Thorne at Caltech asks: "How do you know that this is a coincidence?" Mere coincidence is suggested by at least 8 factors: (a) different organisms have slightly different amino acids; (b) humans have amino acids altered (methylation) after incorporation in peptides; (c) humans have hydroxyproline as a 21st amino acid, but only in collagen; (d) the mean molecular weight of human amino acids has changed substantially over time by evolution of the genetic code (we calculate this change explicitly); (e) there is no causal connection between amino acids and fine structure constant; (f) there is no consensus mechanism connecting the fine structure constant with the mass of the hydrogen atom;
(g) isotope differences are significant as
second-order (especially Carbon and Oxygen); (h) the fine structure constant may be changing over time.

This is discussed in three contexts: (a) Why this is surely a mere coincidence; (b) Parallels to recent Li and Zhang paper in arXiv; (c) relationship with companion papers by Jonathan Vos Post; (d) distinguishing this from bogus Intelligent Design arguments.

Open questions relate to other organisms, the history of amino acid regulation in the genome, future changes, and the correlations between physical constants and mathematical biology.

1.0 RESULTS

Mean Molecular Weight of the 20 Standard Human Amino Acids = 136.90019 daltons.

1/fine structure constant ~ 137.03599976

ratio 136.90019/137.0359997 = 0.999008949.

Coincidence? You be the judge!

2.0 DATA

Below molecular weights from HMDB (Human Metabolome Database)

89.09318 + 174.20100 + 132.11792 + 133.10268 + 121.15800 + 147.12926 + 146.14500 + 75.06660 +
155.15456 + 131.17291 + 131.17291 + 146.18756 + 149.21100 + 165.18913 + 115.13046 + 105.09258 +
119.11916 + 204.22501+ 181.18854 + 117.14634 = 2738.0038.

Mean 136.90019 = 2738.0038/20

Table 1: The 20 Standard Human Amino Acids (and IUPAC-IUB standard nomenclature)

HMDB Name (alphabetically) Formula Molecular Weight Abbrevs
HMDB00161 L-Alanine C3H7NO2 89.09318 A, Ala
HMDB00517 L-Arginine C6H14N4O2 174.20100 R, Arg
HMDB00168 L-Asparagine C4H8N2O3 132.11792 N, Asp
HMDB00191 L-Aspartic acid C4H7NO4 133.10268 D, Asp
HMDB00574 L-Cysteine C3H7NO2S 121.15800 C, Cys
HMDB00148 L-Glutamic acid C5H9NO4 147.12926 E, Glu
HMDB00641 L-Glutamine C5H10N2O3 146.14500 Q, Gln
HMDB00123 Glycine C2H5NO2 75.06660 G, Gly
HMDB00177 L-Histidine C6H9N3O2 155.15456 H, His
HMDB00172 L-Isoleucine C6H13NO2 131.17291 I, Ile
HMDB00687 Leucine C6H13NO2 131.17291 L, Leu
HMDB00182 L-Lysine C6H14N2O2 146.18756 K, Lys
HMDB00696 L-Methionine C5H11NO2S 149.21100 M, Met
HMDB00159 L-Phenylalanine C9H11NO2 165.18913 F, Phe
HMDB00162 L-Proline C5H9NO2 115.13046 P, Pro
HMDB00187 L-Serine C3H7NO3 105.09258 S, Ser
HMDB00167 L-Threonine C4H9NO3 119.11916 T, Thr
HMDB00929 L-Tryptophan C11H12N2O2 204.22501 W, Try
HMDB00158 L-Tyrosine C9H11NO3 181.18854 Y, Tyr
HMDB00883 L-Valine C5H11NO2 117.14634 V, Val

Total 2738.0038
Mean 136.90019 = 2738.0038/20

3.0 DISCUSSION

[truncated here due to constraints of Blog modality and not wanting to annoy Chad Orzel et al]; [the flights back from the week at ICCS-2007 in Boston rather rough due to Hurricane Noel]