What Cheer, Netop?

mmcirvin, who guessed 5,271,009. The actual mean of all the guesses was approximately 168,350,168,350,168,350,168,350,168,350,168,350,168,350,168,350,168,350,168,350,168,350,168,350,168,350,168,350,168,350,168,355,203.093093. There were 33 guesses. Matt, if you email me your mailing address, I'll mail you my five dollars.

If we had been using the median, the correct answer would have been 44, and the winner would have been either katrinkles or plant_geek, both of whom guessed 44.

Nobody guessed a negative number. Also, nobody guessed a transcendental number (like pi or e or 1.01001000100001...). Two people expressed their entries as fractions (thirty-three and one third and seven and a half); these were also the only entries written out. Four people picked decimals (7.5, 7.6, 50.1, and 83.76). With those exceptions, everyone else picked a positive integer.

The smallest guess was 0, while the largest was 5,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555,555. (I almost disqualified that latter guess, as it came close to violating my request regarding not submitting entries that make me do complicated calculations, but dividing it by 33 wasn't that bad. If I had disqualified it then annarama would have won with her guess of 1999.)

The most common number picked was 7, which was picked by three people. The closest non-identical guesses were 7.5 and 7.6.

The smallest ten entries were in the range 0-16; the next ten were in the range 27-72; the next ten were 73-1508; and the top three were 1999, 5271009, and the big honkin' list of fives.

( raw data )

Discuss! Or not.

I suppose that theoretically some of you might disagree with that. Anyway:

( If I were a Springer-Verlag Graduate Text in Mathematics, I would be ... )

Last night, after many phone calls and some thought, it was decided that Craig (who's visiting for the weekend and is sleeping on my futon couch) and I would go to Federal Hill to pick up some Sicilia's pizza and some desserts from Pastiche, and then would head over to Keeney Quad (one of Brown's dorms; during reunion weekend visiting alumni are allowed to rent a dorm room to stay in) to pick up my friend Greg, and we would then head back to my apartment to watch videos, eventually to be joined by a few other people.

When we picked Greg up he suggested stopping by a convenience store to get some diet caffeinated soda (he's diabetic), so we stopped by the East Side Mini Mart. It turned out that a bunch of people in my knitting group happened to be in front of the Mini Mart just then, so I was greeted with hearty shouts of "Jake!", "Hey! We were just talking about you!" "Hey, Jake, we were just talking trash about you!" and "Jake! I am sooooo absurdly drunk right now!" Craig and Greg were confused and befuddled by the commotion and retreated into the store to get soda while I stayed outside and chatted with the knitting folk for a few minutes, until they suddenly announced that it was "time for phase two" and disappeared as quickly and mysteriously as they appeared. Craig and Greg emerged from the store and asked, "Who were those people?" All in all, it was extremely awesome.

We then returned to my apartment and watched a bunch of videos. Craig recently bought a DVD and has been capturing little bits of teevee ephemera that he thinks are funny or particularly notable; possibly the best (for the crowd of mathematicians and engineers that collected at my apartment anyway) was a late-night ad for the Forever Shaker Flashlight, which starts out normally enough with an illustration of the problem with regular flashlights but then at a key moment says, "Based the Faraday Principle of Electromagnetic Induction!" and flashes something like the following equation on the screen:

∮Eds = -∬BdA

It was pretty much the only time I've seen a double integral used in a late-night advertisement. (Or a path integral for that matter.) Edit: The equation on the screen is actually slightly different from the above. Pictures under the cut.

( Pictures of the ad )

We then watched two episodes of the new Doctor Who: the Dalek one and the one with the crashing flying saucer. At that point it was like quarter to two in the morning so everyone went home.

Now I am in my bedroom typing away (thanks, wireless network!) waiting for Craig to wake up so we can embark on today's adventures.

As near as I can remember, this is something I devoted an afternoon of thought to back when I worked at a miniature golf course and essentially spent the whole day in a gazebo by myself with very little to do.

I had read some stories (maybe in science fiction books, maybe in comics, probably both) in which time stops for everyone except one person or group of people.

The two standard approaches to this situation are:

1) Time flows normally for you and you can basically do whatever you do normally while everyone around you appears to be frozen. (So you can breathe, gravity appears to be normal, you can pick up and move around objects that you would normally be able to move, etc.)

2) You're unable to change anything, so you can just walk around and observe things. In extreme versions of this you can't even move air, so you are stuck in place and suffocate. (I think Borges had a story where a guy who is about to be executed is frozen in time, so that even his body is completely immobile, but his thoughts are able to continue.)

I decided that the second version was more reasonable for various reasons. One of the ideas I came up with (or borrowed from somewhere -- it isn't the most original idea, but then few if any of my ideas are) is the situation where instead of time stopping it slows down for you. At or near the extreme this has a similar effect to scenario (2) above, but there should be some point at which your muscles are able to handle the (to you) increased inertia of everything around you, so that you can breathe, move things, and so on. (See, F=MA, and A=S/T2, so if 1 minute of your time = 2 minutes of the outside world's time, then you have to exert four times as much force [as far as you're concerned] to move the same amount of mass the same distance as if your times matched up, which to you feels like the object has four times as much mass. Right?)

Another thing that a sped-up person would notice would be that it was suddenly cooler. Air molecules would seem to be moving slower, and of course that corresponds to a lower temperature. If you were sped up enough you could be frozen to death at room temperature. [In my original post I got this backwards, because I am a dope.]

Of course, there's no particular reason that this time-speeding process should be restricted to living beings, so I next thought about what would happen if you modified a glass of water so that time for it passed twice as quickly as the outside world. How could you distinguish it from a normal glass of water? The previous discussion indicates that one method I thought of is that they would boil and freeze at different temperatures.

Then I started thinking of what would happen if you mixed sped-up water with normal water and eventually I realized that it was all more work than it was worth, even if it did let me pass the time at the old miniature golf course. There may be a way to make a nifty science fiction story out of this, but I don't know what it is.

[I thought about this whole thing again recently because this week's New Yorker contains an article by Oliver Sacks about people whose subjective senses of time differ from the norm. (Unfortunately it doesn't appear to be in the online edition.) The article doesn't have anything to do with any of the junk discussed above, of course.]

I started reading John Brunner's Meeting at Infinity. Early on in the book we encounter that hoary old bit of science fiction nonsense, the inconstant π:

Pi, it seemed, was invariant. However, certain deductions from curved-space mathematics indicated conditions under with it would assume values different from the familiar 3.1416. It would remain an irrational number of course. But the physical conditions for altering its value could be described.

So the guy creates a machine that creates an area where the value of π is different, and this turns out to be a way to reach alternative universes whose history differs from Earth's proportionately to the difference between its value of π and ours.

I think that this sort of thing comes from a misunderstanding of noneuclidean geometry (or, I suppose, a desire to annoy mathematicians). There are geometries where if you measure the circumference of a circle and divide it by the diameter you'll get a number other than 3.14159265... This doesn't change the value of the number π, though, and it has nothing to do with π's irrationality. It makes about as much sense to posit a universe where 2 has a different value.

Anyway!