Powers of two

[ciphergoth]

I can't remember what made me think of this, but there's a bit in Snow Crash about powers of two, and I wondered if things had changed, and that people deal in higher level stuff than this these days. And it's just striking and a bit weird anyway that some people have had occasion to memorize this stuff, I wondered if you had...

[Poll #1217360]

Update: The "powers of two" are just 1+1 = 2, 2+2 = 4, 4+4 = 8, 8+8 = 16 and so on.

Update: it seems like it isn't clear from the above, so for the avoidance of doubt, no-one should feel that they should know this off by heart!

Comments

It's easy

[babysimon]

0x00000001
0x00000002
0x00000004
0x00000008
0x00000010
etc

;)

Re: It's easy

[uke.livejournal.com]

What's wrong with

1
10
100
1000
10000
100000
1000000
...

?

[alextiefling.livejournal.com]

All except the one that's got the form 32xxx; I can calculate that it must in fact be 32768, but I always forget it when listing them.

[valkyriekaren.livejournal.com]

No, I get stuck somewhere in the mid-hundreds, but that's dyscalcula for you - I can't cope with numbers more than two digits long.

[damerell.livejournal.com]

Almost. "Ha, he means 65535, what a... no, wait."

[stgpcm.livejournal.com]

no, 16Ki and 32Ki escape me

[olethros.livejournal.com]

Admittedly, I go a bit fuzzy after 4096.

[kimble.livejournal.com]

Have to stop and think for a second to get the last two, but basically, 'yes'.

[wildeabandon.livejournal.com]

Apparently I can only do up to 12 completely off the top of my head, although the time lag between recalling from memory and calculating the other four is scant seconds.

[thekumquat.livejournal.com]

I'd probably only recognise up to 4096. Although once when I was about 6 I set out with vast reams of computer printout paper to calculate how many grains of rice went on the final square of the chessboard. I think I got up to square 40 or so before getting bored of multiplying by two by hand...

[elsmi.livejournal.com]

16384 is my only shaky one.

I note that right now the poll responses look like: 15, 7, 1. Which is nice.

But does anyone know 2^17?

[phantas.livejournal.com]

I can tell you that 2^17 - 1 is not a prime

ETA: arg, sorry, shouldn't make claims of (non) primality at 1h30AM.

[selectnone.livejournal.com]

I get fuzzy after 8192.

Textures for games usually have power-of-two resolutions, and that'd be at the silly end of the image-sizes I'm likely to touch.

(actually, 64x64 is a largish texture for the game I'm working on right now)

[phantas.livejournal.com]

Computational Number Theory does that to you. I also know or can quickly compute in my head way to many squares, primes, factorisations and square-roots. Back in my teens I computed square-roots with <1% error by head as a party trick (really, it's *way* more easy than it sounds)

[mskala.livejournal.com]

There's an amusing story in one of the Feynman autobiographies about a human-versus-abacus cube root contest.

[marnanel.livejournal.com]

To my alarm I find I don't:

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 163oh dammit, 32768, 65536.

The others I can reel off like telephone numbers. Better change my vote.

[ephermata.livejournal.com]

I can recognize more easily than I can generate, but the lower ones up to 4096 I know reasonably well. They just seem to pop up all over the place, that's all.

[dennyd.livejournal.com]

IAWTC.

[aster13.livejournal.com]

I don't know what one is. :(

I was an oddity in high school - top sets for science (extra classes and everything!) and third set for maths. No one else was in anything less than top set for maths.

[ciphergoth.livejournal.com]

1+1 = 2, 2+2 = 4, 4+4 = 8, 8 + 8 = 16 and so on.

[wechsler.livejournal.com]

At this time of day I stop at 16384, although I feel I should be able to get to 65536 normally.

[keirf.livejournal.com]

One of my telephone interview questions is "tell me what 2^10 is" - it's amazing how many candidates claiming to have mathematics or computer science degrees get it wrong. About 7 out of 10.

[andrewducker]

I don't know them off by heart, but I can calculate them in my head up to 8192 - and I'd recognise 16384, 32768 and 65536 instantly.

[martling.livejournal.com]

Up to exactly that, yes. I also happen to know 2^24.

But I do a lot more low-level stuff than most.

[alextiefling.livejournal.com]

How do you know 16777216 by heart? (I do too, obv.)

[otterylexa.livejournal.com]

I get fuzzy after 4096, though I'd recognise the higher ones as "looking like a power of two" and then have to check.

[jhg.livejournal.com]

I do up to 1,024... after that I have to think about it!

[ergotia.livejournal.com]

Why would I? I dont need that information in my professional life or my personal life.

[ciphergoth.livejournal.com]

No indeed - it's not something anyone *should* memorize, it's just striking how many folk have...

[yoyoangel.livejournal.com]

I don't need to do this in my head: I have a pooter.
This leaves more room in my head for the important things, like what to have for breakfast.

[ajva.livejournal.com]

You bastard. Now I'll have to memorise them.

[adjectivemarcus.livejournal.com]

I know up to 1024, and then I switch to calculating them, and then to not being bothered to do the maths. Actually, I calculate 2048 and then my brain loses interest immediately, so I don't get to the next one...!

Uploaded textures to Second Life are fitted by the system automatically into powers-of-two dimensions (128x512 and so on), so I do actually use them when making textures in graphics programs. But there's no way I'd need any bigger than 1024.

[ladycat.livejournal.com]

I'm afraid I'm not quite sure I even understand what it means?

[ciphergoth.livejournal.com]

Have updated with a brief explanation.