Thirteen numbers: FINISHED!

I should have stopped with the number list and borne the brunt of your insults.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

Because sometimes, that’s all I gots.

1. One. The identity. Divide or multiply any number by 1, you get that number. Raise any number to the power of 1, you get that number. Cool, eh? And that’s the only number that does something that cool.

Remember those “Great Discovery” books you would read in elementary school? I remember how in more than one of those books, monotheism was listed as “one of the great discoveries of all time.” Even as a faithful li’l Jewish boy, I considered it the height of bogosity to list monotheism as a discovery. I guess the roots of my agnosticism go deep.

2. Zero. The hole in my heart. Not that zero? Oh, yeah: zero the placeholder, without which our numerical system would look like motion picture release dates. Oh, you silly Romans, your empire fell for want of zero.

Nope, can’t prove it. Shut up.

Turns out zero is remarkably recent:

The Mesoamerican Long Count calendar developed in south-central Mexico required the use of zero as a place-holder within its vigesimal (base-20) positional numeral system. A shell glyph — — was used as a zero symbol for these Long Count dates, the earliest of which (on Stela 2 at Chiapa de Corzo, Chiapas) has a date of 36 BCE.

Wanna have some yucks with our number system? Try dividing by zero. If I remember correctly, N/0 (N = any number) is NOT infinity, but “indeterminate.” Meaning, ain’t no such thing.

Speaking of infinity,

3. Infinity. How do you define infinity?

Something which is equal to some of its parts.

Think about it. How many points exist on a million-mile-long line? An infinite number. How many points exist on a one-nanometer-long line? An infinite number. Infinity is equal to a tiny portion of infinity.

But even that’s not a done deal. This source states, “We can’t have numbers be both equal to themselves and not equal to themselves. That’s why we say that infinity does not equal infinity.”

I miss marijuana. Sigh.

4. Googol. Don’t want to crease your brains with infinity, but still hot for a big number? Try googol,

A googol is the large number 10¹⁰⁰, that is, the digit 1 followed by one hundred zeros (in decimal representation).

Just how much is a googol? Well, that Wiki tells us

A googol is greater than the number of particles in the observable universe, which has been variously estimated from 10⁷⁹ up to 10⁸¹

. . .

Seventy factorial, or 70!, is just over a googol, 1.19785717 × 10¹⁰⁰. This means that there are over a googol ways to arrange seventy items (or people) in a sequence (such as a line to a concert).

And if a googol ain’t big enough for you, try

5. Googolplex. From the Wiki,

Googolplex is the number 10¹⁰¹⁰⁰.

. . . or ten raised to the googol power, or one with a googol zeros after it. How much is a googolplex? It’s roughly equal to the number of quantum states in a black hole with a mass equal to the Andromeda galaxy. But a googolplex is still small potatoes compared to

6. Graham’s number. This mofo makes my brain hurt. As the author of that page points out, you can invent numbers far larger than Graham’s number; the significance of Graham’s number is that it’s the biggest mathematically useful number — it was used as part of a proof.

So, yeah, Graham’s number is huge. But it still isn’t infinity.

Hey, let’s get down to earth.

Mmmm. Pi.

7. Pi, the ratio of a circle’s circumference to its diameter. Quick: to how many decimal places do you know the value of pi? If you said anything more than five, you’re a bigger geek than me.

Unlike zero, pi (in an approximate form) goes way back to the Ancient Egyptians and Babylonians.

That’s right — 4000 years of pi.

8. Imaginary number i.

Kids are taught that you cannot take the square root of a negative number. After all, how can the square of any number be negative? (For you math phobic types: a negative times a negative equals a positive.) But, hey, mathematicians can define things however they want and construct vast worlds upon simple, if preposterous, foundations. Such is the case with i.

It’s one thing to invent something provocative, quite another to find uses for it. If a new mathematics has no utility, isn’t it just so much numerowankracy? (Thank protected static for that one.) But imaginary numbers are indeed useful in a variety of scientific and engineering applications — for one thing, we couldn’t understand alternating current without i. Maybe that’s why Edison was so nuts for DC.

9. Euler’s number e.

e is the base of the natural logarithm (ln). e equals the number a, such that ln (a) = 1. And how do you define a natural logarithm? Easy:

Formally, ln(a) may be defined as the area under the graph (integral) of 1/x from 1 to a, that is,

One example of the utility of e: if you want to calculate the value of continuously compounded interest, you’ll need e. But the height of coolness is Euler’s equation

which brings together five of mathematics’ most important numbers. You have to love a pretty equation. Don’t argue with me — you have to love it.

10. The golden ratio, .

which is defined as the ratio of a to b that makes this equation true:

Renaissance dudes liked the golden ratio for its aesthetic properties. But does it have any interesting mathematical properties? Um, yeah:

Those two expressions look cool, don’t you think? And then there’s the significant-if-you-BELIEVE connection to the Mark o’ the Beast.

And you know the pentacle, mark of Satan and all that?

The golden ratio plays an important role in regular pentagons and pentagrams. Each intersection of edges sections other edges in the golden ratio.

Cue Twilight Zone music.

11. Avogadro’s number

If you look at a Period Table of the Elements, you’ll notice a number in the upper left hand corner of each square. This is the element’s atomic weight. Thus, hydrogen (H, the first element in the table) has an atomic weight of 1.00794.

1.00794 grams of hydrogen = one mole of hydrogen.

With me so far?

One mole of hydrogen contains Avogadro’s number of atoms. Thus, Avogadro’s number = the number of atoms in a mole (the molecular or atomic weight, in grams) of any particular substance. But in its purest expression, Avogadro’s number is just a number. You can have Avogadro’s number of peanuts, grains of sand, sucrose molecules, etc.

Speaking of Avogadro’s number of peanuts, you can eat at Avogadro’s Number in Fort Collins, Colorado, and listen to some Bluegrass and Dixieland, too. Hmm. What’s a 20% tip on Avogadro’s Number? I don’t think I want to know.

12. Dirac’s Constant

I was going to list Planck’s Constant, but in deference to my wife, whose hero is P.A.M. Dirac, I give you Dirac’s constant instead. Dirac’s constant (‘h bar’) is

where h = Planck’s Constant,

For you math-haters: this post isn’t getting any better for you, is it? Planck’s Constant is a proportionality constant relating the energy of a photon to its frequency. It’s one of the smallest constants commonly used in physics. Since Dirac’s constant is even smaller, I’ve given it precedence here.

Oh, forget the excuses. Isn’t it enough that I wanted to make Karen happy? Look, Karen! Link to Dirac, link to Dirac!

13. The Fine Structure Constant

Alpha,

Here, let Wikipedia tell you the rest.

where is the elementary charge, is the reduced Planck’s constant [Dirac’s constant, damn you!], is the speed of light in a vacuum [gee. c would have been another great number, huh?], and is the permittivity of free space.

Furthermore,

In the theory of quantum electrodynamics, the fine structure constant plays the role of a coupling constant, representing the strength of the interaction between electrons and photons.

Hah! I worked in QED! Now, if only I can work in some reference to quantum chromodynamics, I’ll get laid tonight for sure!

Now, this truly is a cool number, one of the coolest, which is why I’ve saved it for last. It’s one of those fundamental constants which makes matter possible. Yup, that’s right: if the fine structure constant were much different than what it is, we wouldn’t be here, and the universe itself would be unrecognizable. Quoting Wikipedia again, “For instance, were to change by 4%, carbon would no longer be produced in stellar fusion. If were greater than 0.1, fusion would no longer occur in stars.”

This ties in with the anthropic principle, which, as stated by author Terry Pratchett, demands

that the entire Purpose of the Universe is to make possible a being that will live in England, an island off the coast of France, and spend his time writing Discworld novels.

Gotta love Pratchett.

***

PHEW!

If you think that was painful for you, imagine what it was like for me. Yes, yes, you’ll get your lurve, you lurve-crazed readers. But let me catch my damn breath.

LURVE! FRESH, SLIPPERY LURVE! GET IT WHILE IT’S HOT!

What do my readers have on their plates this weekend?

Microsoar serves up a cold poosicle,

From protected static: Bush Can Has Cheezburger!

Meanwhile, Thorne dishes a cornucopia of lesbian lust, and

Dean provides the Friday Flickr mermaid.

Um, Lyvvie? You’re supposed to get the poo in the toilet, not on the toilet.

SxKitten posts letter requesting head,

Shelbi has a tough choice to make,

While Lyn explores a co-ed Madonna Sanctuary bathroom!

Skinny dipping from Shaina. ‘Nuff said.

Kate brings up a name from my past.

Go light a fire under Carrie. Then come back here and do the same for me.

Yes, Kris, life sucks donkey balls.

D.