2nd entry from PROMYS
Jul. 10th, 2003 06:44 pmWell, I've already managed to teach a bunch of people Chrononauts and SoC, but I have yet to teach them Gnostica.
You know, being told that you have to *prove* induction - yes, *prove* induction - is certainly rather annoying. Apparently it's not a basic logical principle, like deduction or proof by contradiction (which has become something of a running joke: "How do you prove that proof by contradiction works? Well, first you assume that it doesn't...").
Well, at least I finally managed to rigorously prove that 0*a=0, if a bit more complexly than I had to.
Specifically, my proof was:
1*0=0
(1+1)*0=1*0+1*0=0
(2*0)*a=0*a
2*(0*a)=0*a+0*a
0*a=0*a+0*a
0*a=0
Then Fan pointed out you could just do
0+0=0
0*a=(0+0)*a
And thus arrive directly at my second-to-last line.
Also, I am now officially a dolphin, and not a swordfish as you may have thought. My name is still Sniffnoy the Swordfish, but I am a dolphin.
Hm, some of the people decided to name this useful and apparently true conjecture that I thought of after me (despite the fact that it almost certainly is already proven and has a name) - specifically, since it's a method, they decided to call it The Altman Maneuver, after the Chinese Poker tactic they've named after me (ie stupidly playing all your 2s early). What the two have to do with each other, I don't know.
Without my spam filters, my bergen.org address is certainly filling up quickly. Thank you, Fan.
On another note, we somehow can't seem to get away from the topic of modular buildings. Not buildings where walking straight brings you back to the same place - you just make a big enough ring and spin it really fast - but one in which moving far enough *vertically* takes you back to the same place. Someone pointed out that this violates conservation of energy - drop a ball down the elevator shaft, and it'll just keep accelerating. We finally settled on making the building a spinning ring, but a constantly accelerating - or rather, increasingly accelerating - one. Whether this can be made to work, I don't know, but it sort of makes sense and at least it gets around the conservation of energy problem. But someone noted that centrifugal force will interfere at high velocities - this is why someone pointed out that it has to be increasingly accelerating - although if it's increasingly accelerating, that doesn't make for a very good sort of gravity, does it? I have no clue. I don't know this sort of thing.
Hm... if we generalize that the noun form of something ending in "ous" is to change the "ous" to an "osity" (ie "generosity", "obviosity", "mysteriosity"), this gives us such words as "dangerosity", "rigorosity", and a whole bunch of other funny ones that I can't be bothered to remember right now.
And finally, to restate the obvious: These problem sets are hard!
You know, being told that you have to *prove* induction - yes, *prove* induction - is certainly rather annoying. Apparently it's not a basic logical principle, like deduction or proof by contradiction (which has become something of a running joke: "How do you prove that proof by contradiction works? Well, first you assume that it doesn't...").
Well, at least I finally managed to rigorously prove that 0*a=0, if a bit more complexly than I had to.
Specifically, my proof was:
1*0=0
(1+1)*0=1*0+1*0=0
(2*0)*a=0*a
2*(0*a)=0*a+0*a
0*a=0*a+0*a
0*a=0
Then Fan pointed out you could just do
0+0=0
0*a=(0+0)*a
And thus arrive directly at my second-to-last line.
Also, I am now officially a dolphin, and not a swordfish as you may have thought. My name is still Sniffnoy the Swordfish, but I am a dolphin.
Hm, some of the people decided to name this useful and apparently true conjecture that I thought of after me (despite the fact that it almost certainly is already proven and has a name) - specifically, since it's a method, they decided to call it The Altman Maneuver, after the Chinese Poker tactic they've named after me (ie stupidly playing all your 2s early). What the two have to do with each other, I don't know.
Without my spam filters, my bergen.org address is certainly filling up quickly. Thank you, Fan.
On another note, we somehow can't seem to get away from the topic of modular buildings. Not buildings where walking straight brings you back to the same place - you just make a big enough ring and spin it really fast - but one in which moving far enough *vertically* takes you back to the same place. Someone pointed out that this violates conservation of energy - drop a ball down the elevator shaft, and it'll just keep accelerating. We finally settled on making the building a spinning ring, but a constantly accelerating - or rather, increasingly accelerating - one. Whether this can be made to work, I don't know, but it sort of makes sense and at least it gets around the conservation of energy problem. But someone noted that centrifugal force will interfere at high velocities - this is why someone pointed out that it has to be increasingly accelerating - although if it's increasingly accelerating, that doesn't make for a very good sort of gravity, does it? I have no clue. I don't know this sort of thing.
Hm... if we generalize that the noun form of something ending in "ous" is to change the "ous" to an "osity" (ie "generosity", "obviosity", "mysteriosity"), this gives us such words as "dangerosity", "rigorosity", and a whole bunch of other funny ones that I can't be bothered to remember right now.
And finally, to restate the obvious: These problem sets are hard!
