The Official Uncertain Principles Cosmic Jackpot Giveaway Contest was even more popular than I expected, with 122 comments (at the time of this writing) each trying to pick the "best" number.
As promised, the winner will be announced today, but this really comes down to deciding which number is the best. So, what's the best number?
The "best" number should obviously be something with intrinsic fundamental importance. Numbers like 7 and 37 and 206 (I liked that entry a lot) are interesting, but not all that fundamental. Constants of nature like h, c, or even the fine-structure constant alpha are important for physics, but not important as numbers.
The requirement of fundamental importance cuts the list down to five candidates: 0, 1, e, i, and π They each have their merits:
- π is, of course, the ratio between the circumference of a circle and its diameter, and is critically important for geometry.
- i is the square root of negative one, and the basis for the entire field of complex numbers, which makes it possible to do a vast range of calculations that are impossible with real numbers alone.
- e is Euler's number, a number that is critical for all sorts of calculus and differential equations. The function ex is its own derivative, and its the basis for the natural logarithms.
- 1 is the multiplicative identity, any number multiplied by one is itself, any number divided by itself is one.
These are all worthy candidates, but ultimately, the best number is:
0 (zero).
Obviously, zero has a bunch of very nice properties. You can add zero to anything, and it doesn't change the original number. More importantly, you can multiply any number by zero, and you get zero, and zero divided by anything is also zero.
In the end, though, the reason it's the best number is that roughly 50% of the effort expended on physics problems is spent trying to get things to equal zero-- cross terms in quantum probabilities, decoherence rates due to external interactions, vacuum energy contributions. We love zero in physics, and theorists get very cranky when things are almost but not quite zero-- see, for example, the cosmological constant.
For those reasons, the winning number in the pick-a-number contest is zero, and the winner of the contest is mollishka, at comment #6. Send me an email (orzelc at steelypips dot org) with a shipping address, and which version of the book you'd prefer (the paperback proof copy, or the final hardcover version), and I'll send you a copy of The Cosmic Jackpot.
Many thanks to everyone who entered. This was fun.
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Zero also has an alias, '12', on a 12-hour clockface, where the hour is modulo-12, and thus noon is zero hours post meridiem, aliased to '12 p.m.'.
When I was in school, solving equations was always tricky, until a math-type showed me that setting everything to zero put all the remaining terms on the same side where it was easier to do bookkeeping on them.
I've worked in spacecraft tracking, where the ultimate goal was to predict everything perfectly, differing the observations and the expectations to produce a residue as near as was possible to zero.
Yeah, I like zero, too. It's been a good friend to me.
So, Mister Smarty Pants, I have a question for you:
I note that #34 in this contest listed infinity over zero as his/her number. Now, what I want to know, and I might need a math geek for this, not a physics geek, but I'm asking here anyway, is that since x/0 goes to infinity, does that make infinity over zero equal to one?
Huh? DOES IT!? DOES IT!?!?
Yes, after spending a week at the House of the Mouse, I am feeling a bit silly.
Hi, Jamie,
Infinity over zero doesn't equal anything. Nor does x over zero, actually. This points to the difference between
lim x -> a (f[x])
and
f[x]
That is, function can approach its limit with no hope of ever achieving, i.e. equaling, that limit. The function y/x, for instance, will approach infinity as x approaches zero, but will never actually reach infinity. Infinity is not a number.
Hope that helps.
Daniel
Uh...perhaps I can't convey tone very well in text, but I'm pretty sure that in this particular instance it was clear, as I stated it explicitly, that I was being silly.
Well, I guess I'll have to settle for the 206 booby prize. I tried my best on the non-obvious number route.
A neglected copy of Wolfram's A New Kind of Science sounds about right. I can pick it up at your office sometime. It would probably cost you $20 to ship that one.
Infinity is not a number in the real number sense, but it is a number in the sense of floating point numbers ... where +/- Inf are the endpoints of the number line and generate unique results when used in arithmetic. [See, for example, the IEEE-754 choice commonly encountered in modern computers.] Crucial knowledge when doing any computational, as opposed to mathematical, physics.
Zero?! Oh, some nihilist had his thumb on the scale for this one.
In an equation where a combination of some terms equals zero, it's not zero that's the interesting part. It's that those other terms are so perfectly balanced. Otherwise all there is is nothing. That won't do. I need at least a rubber band to play with.
i, e, or 1 would have been fine. I'll buy their CD's, but not zero's. Yuck. This is the problem with looking for fundamental meaning instead of aesthetics. The latter would let me go for numbers like 343 or some very large, pretty integer. To each his own, of course, but choosing zero is just so dark. Play Darth Vader's theme.
I like the choice of zero, because it generates the fewest objections compared to all other possible choices.
Consider the CD produced by 1. It would be very boring if there were no zero bits to create interest. On the other hand, the CD produced by 0 would have similar properties but would be considered performance art because of the clever consistency of its name and contents. ;-)
Sweet!!! I can't believe I actually managed to resist the nearly overwhelming urge to say "17," which is truly the correct answer. Mod 17, of course.
Hey, just because Phi has no physical significance doesn't mean it isn't fundamental... ^_^
Did I at least get any brownie points for using latex notation? Oh, and my number evaluated to zero in sane number systems as well! (#39)
Heehee, zero.
"Zero" is the best number??
I demand a recount....