- The date: it's 4/4/08, or, as powers of two, it's 2
^{2}/2^{2}/2^{3}. - The timestamp of this post: 4:00 (=2
^{2}) p.m. EDT, or in the 24-hour clock, 1600 (=2^{4}) hours. (Attention my workplace: I created this post in the morning before leaving for work, and used the cool new scheduled posts feature in Blogger in draft.) - Ages: Vinny is one (=2
^{0}), my nephew Byron is 4 (=2^{2}), I am 32 (=2^{5}), and my dad is 64 (=2^{6}). Also, as of tomorrow (i.e., in =2^{0}days) Vinny will be one and a half, which is 2^{0}+2^{-1}. - Events: I've had my new job for half a year now (=2
^{-1}). We've lived here for two (=2^{1}) years. My dad and Marvis have been married for four (=2^{2}) years (although next weekend it will be five). I took my prelim exam almost four years ago. (Maybe those two almost average out.) - Other interesting facts: Four (=2
^{2}) of the digits 0-9 are powers of two (1, 2, 4, and 8). Also, if we wrote out all these interesting numbers in base two, they would all consist of a single 1 followed by a number of zeros equal to the number of the exponent (e.g., 2^{5}= 100000_{2}).

Within the next 64 hours (that's 2 days and 16 hours, for more powers of two!), leave a comment with your favorite/most interesting connection to powers of two. I will select the "best" 2

^{N}of them, where N could be 0 but might be more, and the winner(s) will not only gain fame but also an appropriately themed prize!

Deadline: 8:00 a.m. EDT, Monday, April 7, 2008

Your favorite/most interesting connection to powers of two.

## 11 comments:

The Toonie! It's the Canadian $2 coin. I know that's only 2 to the first (how do you do superscripts here?) -- but where would you be without the original? The coin is surfaced with 2 different colours of metal, it has a picture of Elizabeth II on the back, and it's a very handy and encouraging coin. You'll be feeling all poor, nothing but change in your pockets, and then you'll realize you've got $8, easy.

Cool! Now I have at least 2^0 contestants ;)

(Normally in html, you use the tag sup between less than and greater than brackets to designate superscripts, but the comments don't accept that html tag. So use the carat instead.)

11.00100100001111...

My "lucky" number is 2 and Mike's is 8 (2^3)... er...lame, sorry, but that's all I've got (and it took me a while to find the carat - shows you how often I use it!).

So there I am taking Calc II a thousand years ago, finding infinite series and sums to be mind-bending, tres groovy fun. Don't know if this one converges, but we can bound it by one that I can show does, and so it does. But to what? The mathematician cares not of such trivialities, like the so-called "answer". We've proven there is one, perhaps shown it to be unique, let the peasants waste time determining the actual answer. But still, I wanted to know! So, become a computational scientist, you say, so I did. (Does this mean cs=peasant?)

What were we talking about? Oh, yeah, 2^N. So, the "infinite" sum of 1 / 2^N, N=1, ... proof by picture: take a unit square, black out 1/2, then half of that, ie 1/2^2, then half of that, 1/2^3, and so on. Clear to see that the "infinite" sum appropriates 1. Ah, now I can go back to sleep, surfing the universe and infinity...

Rico

But then again, and just to be ornery, I'm more partial to factors of three:

Our third child, born 090603 at 9:27 (am), 6'15oz...uh, 19 inches. I tried to stretch her out to 21", then scrunch her up to 18", but the doc was on to me...In spite of missing the 3-sweep, she is one incredible critter, living up to her 3rd-ness by taking no nothin' from no body...like her Mom, (3^2)th child (of 11!), born in the 12th month of '63...

my father was a twin, my mother was a twin, and I am a twin.

What does Scott's mean? He's a meaner and wont tell me. (You told him to ruin my life didn't you??)

Though you do realise that in certain mod spaces we can write a great deal more integers as powers of 2.

I got nothing, I just thought of mod space, and the cyclic group U9 which (for all non-math geeks) is the group made up of all integers relatively prime to 9: {1, 2, 4, 5, 7, 8}.

All these numbers can be generated by 2 under multiplication modulo 9: 2^0=1, 2^1=2, 2^2=4, 2^5=5, 2^4=7, 2^3=8.

I geek. I like groups.

"We're okay, we're fine

Baby I'm here to stop your cryin'

Chase all the ghosts from your head

I'm stronger than the monsters beneath your bed

Smarter than the tricks played on your heart

We'll look at it together and we'll take it a part

Adding up the total of a love that's true --

Multiply life by the power of two."

That's a song by the Indigo Girls called Power of Two, and my favorite instance of powers of two!

I couldn't come up with anything good for powers of two. I'll have to start preparing for the next contest on 3/9/27.

Though on a related note, my birthday is 2^2/3^3, but sadly I was not born at 2:56 in the morning to get 4^4 as well.

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