- May 26, 2005
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As a mathematician, I am fascinated by an idea of introducing negative numbers where negative numbers aren't typically used. For example, floors are typically labeled with positive numbers. But I had an idea of labeling with 0 and negative numbers ground and basement floors. As it turns out, its not really my idea: thats how they do it in Europe. But, as someone who was raised in Russia and then migrated to US, I haven't seen it, since neither Russia nor US does it. So I came up with my own original idea of floor number 0, floor number -1, etc. and was fascinated by it. And then eventually when I visitted Europe I realized I rediscovered the wheel.
My other idea of negative numbers is with running competition. Conventionally, they take photos of the fastest runners in order to make them proud. But my idea is that they should also take photos of the slowest runners to make them ashamed. And they should make it symmetric. For example, if its a race of 100 people, and they take photos of 5 fastest runners, they should also take photos of 5 slowest runners. Thus, the other 90 are neither fastest nor slowest and thus their photos aren't taken.
And here is an irony. While, clearly, my idea will humiliate the bottom 5, it will also take humiliation AWAY from the 90 runners in the middle. Because you see, according to the conventional race, those 90 in the middle will say they lost by the virtue of not winning the prize. But I say no, they didn't lose: they weren't those 5 at the bottom. Instead, they had a draw!
So this would also change the dynamics of a race in two ways:
a) In conventional race, everyone is stressing because they have to be at the top to avoid losing. My race will take stress AWAY from most people. As long as they know they aren't horrible, they know they aren't going to lose. Yes, they would have to push in order to win. But not winning is not the same as losing (separating out slowest runners that do lose would make this point very clear). So they won't be "in a crisis mode" so to speak.
b) In conventional race, the runners at the bottom typically give up, they aren't even trying any more since by the time they get to the finish line the crowd disperses anyway. But in my variation of the race, the ones at the bottom will be trying extra hard, since they will be trying to avoid being at the bottom 5. And the crowd won't be dispersing: it would be eagerly waiting to see who is at the bottom 5 that they will be taking picture of.
This should be reflected financially too. In conventional race, everyone pays entrance fee, and the winners get a prize. Thus, people that aren't at the top lose a little bit of money, by paying entrance fee and not getting a prize, while people at the top gain a lot of money by getting a prize that is a lot more expansive than the entrance fee that they have paid. But in the version of the race that I propose, there is no entrance fee, to reflect the fact that most people do NOT lose. Instead, the people at the very bottom pay money to the people at the very top.
So lets say the race has 100 people. In conventional setting, they might take 5 dollar entrance fee from each person, then pay 250 dollars to the first place, 150 dollars to the second place and 100 dollars to the third place, and they don't punish the people at the bottom in any way. But the way I propose it is different. I propose that there is no entrance fee. Instead, the slowest runner hands 250 dollars to the fastest runner, the second slowest runner hands 150 dollars to the second fastest runner, and the third slowest runner hands 100 dollars to the third fastest runner.
This can also be done publicly. So, after the race is completely finished, all the runners sit on the chairs. Then they call out the fastest runner to stand in front. They announce his time and the crowd makes thumbs-up sound. As the top runner stands, they call out the slowest runner to stand next to him. They announce his time and the crowd makes thumbs-down sound. Then they announce that the slowest runner will pay 250 dollars to the fastest runner. He pays, right in front of the audience, and they clap. Then they repeat the same thing for second top runner and second bottom runner with 150 dollars, and then they repeat it for third top runner and third bottom runner with 100 dollars.
And here is something interesting about it. With conventional races, as mentioned earlier, by the time the slowest runners come, the crowd already disperses. And the fastest runners aren't typically associated with slowest runners (unless they have something else in common): they are typically associated with runners that are also fast, although perhaps not as fast as them. But in my version of a race, the fastest runner will specifically meet the slowest runner in that money transaction, which would make it unusual, thus fascinating.
Now, while I am at it, here is another version of a race. What if, instead of only 3 or 5 people winning or losing, what if I will make the whole top half win and the whole bottom half lose. For example, we can set a rule that everyone gets 5 dollars for each person they beat and loses 5 dollars for each person that beat them. So, again, lets look at the race of 100 people. The person at the top beat 99 of them (he didn't beat himself, obviously). So he got 99*5=495 dollars. The person at the second place beat 98 people and was beaten by 1 person. So he gains 98*5-5=985. The person at the third place beat 97 people and was beaten by 2 people, so he gains 97*5-2*5-975, and so forth. Then the person at the 49-th place beat 50 people and was beaten by 48 people, so he gains 50*5-48*5=10 dollars. The person at the 50-th place beat 48 people and was beaten by 50 people, so he "gains" 48*5-50*5=-10 dollars: and gaining -10 dollars is the same as losing 10 dollars. But its really cool to say "gaining -10 dollars": remember my fascination with negative numbers to designate basement floors? Then the person at the 51-st place gains -20 dollars (or loses 20 dollars) and keep going all the way to the person at the bottom gaining -495 (or losing 495) dollars.
Within this context, money transfers will be private rather than public, because the first 3 or first 5 won't stand out from the rest plus nobody has time to watch 50 different transfers.
So, lets call conventional model, with 5 winners and 95 losers, model 1, the model I described earlier with 5 winners, 5 losers and 90 people in between model 2, and lets call the model with 50 winners and 50 losers model 3. So I already talked about the differences in dynamics between model 1 and model 2 (see a and b above). But now lets compare model 3 to them:
c) In model 1, there is huge pressure at the top, moderate pressure in the middle, and no pressure in the bottom. In model 2, there is high pressure at the top and bottom, and low pressure in the middle. In model 3, there is even pressure throughout
d) In model 3, the winners don't get special acknowledgement they get in the other two models. Yet, at the same time, other people at the top half get acknowledged for being at the top half. So lots of people get a chance to feel like they won. Let me give you a personal story. When I was in cross country team in high school back in good old 1997, I was at the top half but never the top. So if they were to do it with model 3, I would be winning every time. But unfortunately they did model 1 instead of model 3 so I was losing instead of winning. And no, money wasn't involved in high school races: the whole thing about entrance fee is what I remember from a different race I ran as an adult. But anyway you get a point.
And then we can also combine model 2 and model 3, which we will call model 4. So according to model 4, there would be two sets of transactions taking place on top of each other: model 2 transactions and model 3 transactions. Thus, the fastest runner will win 250 dollars from model 2, 495 dollars from model 3, making it total of 745 dollars (and likewise the slowest runner will lose 745 dollars). The second fastest runner will win 150 dollars from model 2, 485 dollars from model 3, making it total of 635 dollars (and likewise the second slowest runner will lose 635 dollars). The third fastest runner will win 100 dollars from model 2, 475 dollars from model 3, making it total of 575 dollars (and likewise the third slowest runner will lose 575 dollars). But then the 4-th fastest runner will not gain anything from model 2 and will only gain 465 dollars from model 3, so he will gain 465 dollars total. The 5-th runner will gain 455 total, the 6-th runner 445 total, etc. So if you look at 4-th runner, 5-th runner, 6-th runner spaced only 10 dollars apart, while 1-st, 2-nd and 3-rd are ahead by a lot more than that, then again it makes sense to strive to be at the top. Yet, at the same time, other runners don't feel overlooked either. So within this framework, model 2 transactions will be made public (as described earlier) while model 3 transactions will take place privately afterwords. Likewise, the three runners in the bottom get humiliated publically, while others in the bottom half lose money privately.
And here is another interesting idea. So, back when I was going to Junior High back in 1994, the detention room was 134. So for bad behavior the student was first sent to the office, and then from the office they were sent to room 134 (and office was a separate room). Now, I had an idea of making it more symmetric: if they were sending people for bad behavior to the room 134, they should be sending people for good behavior to room 143 (143 comes from switching around 3 and 4). Also, the opposite to "off" is "on". So, if for bad behavior the students were sent to the office, then for good behavior they should be sent to the onice. So I came up with an idea of calling room 143 an "onice" and sending students there for good behavior. I remember, back in 1994, I wrote a note, pretending as if its a teacher who wrote it, that said that I behaved really well, and so I should go to onice 143. Actually there was no room 143, but I didn't know it. So I kept asking different teachers where is the room 143. And one of them took my hand and said "maybe 134" and I was like "no no, 143" and shown her that note. I don't remember what was her response.
Now, going back to races: it would be really cool to send 5 top runners to the onice and the bottom 5 runneres to the office. I had that idea too back in Junior High. So my family knew Galen Rowell, who was a famous photographer but unfortunately died in a plane crush. He was also a runner. So me and my father were regularly running with him. Usually my father was slow, so me and Galen had to wait for him. Anyway, one of those times we ran, Galen said he went to a race and won. I asked him "did you wait" (in reference to my idea of being sent to the onice after the race). He responded "if I were to wait I wouldn't win the race" (thinking I was talking about waiting for other runners in the middle of a race, similarly to how we wait for my dad). And I was like "no no, did you wait AFTER the race, not during". Galen was confused. My dad said "he is joking".
And here is yet another idea. If someone cheats on a race, instead of saying he didn't finish, they should say he finished, but he took infinite amount of time. Thus, he ran with infinitesimal velocity and, accordingly, takes the last place. So if you humiliate 5 people at the bottom then in case of 1 cheater you will humiliate only 4 people besides him, since he is counted as one of the 5. This idea is fascinating because it introduces infinities and infinitesimals.
My other idea of negative numbers is with running competition. Conventionally, they take photos of the fastest runners in order to make them proud. But my idea is that they should also take photos of the slowest runners to make them ashamed. And they should make it symmetric. For example, if its a race of 100 people, and they take photos of 5 fastest runners, they should also take photos of 5 slowest runners. Thus, the other 90 are neither fastest nor slowest and thus their photos aren't taken.
And here is an irony. While, clearly, my idea will humiliate the bottom 5, it will also take humiliation AWAY from the 90 runners in the middle. Because you see, according to the conventional race, those 90 in the middle will say they lost by the virtue of not winning the prize. But I say no, they didn't lose: they weren't those 5 at the bottom. Instead, they had a draw!
So this would also change the dynamics of a race in two ways:
a) In conventional race, everyone is stressing because they have to be at the top to avoid losing. My race will take stress AWAY from most people. As long as they know they aren't horrible, they know they aren't going to lose. Yes, they would have to push in order to win. But not winning is not the same as losing (separating out slowest runners that do lose would make this point very clear). So they won't be "in a crisis mode" so to speak.
b) In conventional race, the runners at the bottom typically give up, they aren't even trying any more since by the time they get to the finish line the crowd disperses anyway. But in my variation of the race, the ones at the bottom will be trying extra hard, since they will be trying to avoid being at the bottom 5. And the crowd won't be dispersing: it would be eagerly waiting to see who is at the bottom 5 that they will be taking picture of.
This should be reflected financially too. In conventional race, everyone pays entrance fee, and the winners get a prize. Thus, people that aren't at the top lose a little bit of money, by paying entrance fee and not getting a prize, while people at the top gain a lot of money by getting a prize that is a lot more expansive than the entrance fee that they have paid. But in the version of the race that I propose, there is no entrance fee, to reflect the fact that most people do NOT lose. Instead, the people at the very bottom pay money to the people at the very top.
So lets say the race has 100 people. In conventional setting, they might take 5 dollar entrance fee from each person, then pay 250 dollars to the first place, 150 dollars to the second place and 100 dollars to the third place, and they don't punish the people at the bottom in any way. But the way I propose it is different. I propose that there is no entrance fee. Instead, the slowest runner hands 250 dollars to the fastest runner, the second slowest runner hands 150 dollars to the second fastest runner, and the third slowest runner hands 100 dollars to the third fastest runner.
This can also be done publicly. So, after the race is completely finished, all the runners sit on the chairs. Then they call out the fastest runner to stand in front. They announce his time and the crowd makes thumbs-up sound. As the top runner stands, they call out the slowest runner to stand next to him. They announce his time and the crowd makes thumbs-down sound. Then they announce that the slowest runner will pay 250 dollars to the fastest runner. He pays, right in front of the audience, and they clap. Then they repeat the same thing for second top runner and second bottom runner with 150 dollars, and then they repeat it for third top runner and third bottom runner with 100 dollars.
And here is something interesting about it. With conventional races, as mentioned earlier, by the time the slowest runners come, the crowd already disperses. And the fastest runners aren't typically associated with slowest runners (unless they have something else in common): they are typically associated with runners that are also fast, although perhaps not as fast as them. But in my version of a race, the fastest runner will specifically meet the slowest runner in that money transaction, which would make it unusual, thus fascinating.
Now, while I am at it, here is another version of a race. What if, instead of only 3 or 5 people winning or losing, what if I will make the whole top half win and the whole bottom half lose. For example, we can set a rule that everyone gets 5 dollars for each person they beat and loses 5 dollars for each person that beat them. So, again, lets look at the race of 100 people. The person at the top beat 99 of them (he didn't beat himself, obviously). So he got 99*5=495 dollars. The person at the second place beat 98 people and was beaten by 1 person. So he gains 98*5-5=985. The person at the third place beat 97 people and was beaten by 2 people, so he gains 97*5-2*5-975, and so forth. Then the person at the 49-th place beat 50 people and was beaten by 48 people, so he gains 50*5-48*5=10 dollars. The person at the 50-th place beat 48 people and was beaten by 50 people, so he "gains" 48*5-50*5=-10 dollars: and gaining -10 dollars is the same as losing 10 dollars. But its really cool to say "gaining -10 dollars": remember my fascination with negative numbers to designate basement floors? Then the person at the 51-st place gains -20 dollars (or loses 20 dollars) and keep going all the way to the person at the bottom gaining -495 (or losing 495) dollars.
Within this context, money transfers will be private rather than public, because the first 3 or first 5 won't stand out from the rest plus nobody has time to watch 50 different transfers.
So, lets call conventional model, with 5 winners and 95 losers, model 1, the model I described earlier with 5 winners, 5 losers and 90 people in between model 2, and lets call the model with 50 winners and 50 losers model 3. So I already talked about the differences in dynamics between model 1 and model 2 (see a and b above). But now lets compare model 3 to them:
c) In model 1, there is huge pressure at the top, moderate pressure in the middle, and no pressure in the bottom. In model 2, there is high pressure at the top and bottom, and low pressure in the middle. In model 3, there is even pressure throughout
d) In model 3, the winners don't get special acknowledgement they get in the other two models. Yet, at the same time, other people at the top half get acknowledged for being at the top half. So lots of people get a chance to feel like they won. Let me give you a personal story. When I was in cross country team in high school back in good old 1997, I was at the top half but never the top. So if they were to do it with model 3, I would be winning every time. But unfortunately they did model 1 instead of model 3 so I was losing instead of winning. And no, money wasn't involved in high school races: the whole thing about entrance fee is what I remember from a different race I ran as an adult. But anyway you get a point.
And then we can also combine model 2 and model 3, which we will call model 4. So according to model 4, there would be two sets of transactions taking place on top of each other: model 2 transactions and model 3 transactions. Thus, the fastest runner will win 250 dollars from model 2, 495 dollars from model 3, making it total of 745 dollars (and likewise the slowest runner will lose 745 dollars). The second fastest runner will win 150 dollars from model 2, 485 dollars from model 3, making it total of 635 dollars (and likewise the second slowest runner will lose 635 dollars). The third fastest runner will win 100 dollars from model 2, 475 dollars from model 3, making it total of 575 dollars (and likewise the third slowest runner will lose 575 dollars). But then the 4-th fastest runner will not gain anything from model 2 and will only gain 465 dollars from model 3, so he will gain 465 dollars total. The 5-th runner will gain 455 total, the 6-th runner 445 total, etc. So if you look at 4-th runner, 5-th runner, 6-th runner spaced only 10 dollars apart, while 1-st, 2-nd and 3-rd are ahead by a lot more than that, then again it makes sense to strive to be at the top. Yet, at the same time, other runners don't feel overlooked either. So within this framework, model 2 transactions will be made public (as described earlier) while model 3 transactions will take place privately afterwords. Likewise, the three runners in the bottom get humiliated publically, while others in the bottom half lose money privately.
And here is another interesting idea. So, back when I was going to Junior High back in 1994, the detention room was 134. So for bad behavior the student was first sent to the office, and then from the office they were sent to room 134 (and office was a separate room). Now, I had an idea of making it more symmetric: if they were sending people for bad behavior to the room 134, they should be sending people for good behavior to room 143 (143 comes from switching around 3 and 4). Also, the opposite to "off" is "on". So, if for bad behavior the students were sent to the office, then for good behavior they should be sent to the onice. So I came up with an idea of calling room 143 an "onice" and sending students there for good behavior. I remember, back in 1994, I wrote a note, pretending as if its a teacher who wrote it, that said that I behaved really well, and so I should go to onice 143. Actually there was no room 143, but I didn't know it. So I kept asking different teachers where is the room 143. And one of them took my hand and said "maybe 134" and I was like "no no, 143" and shown her that note. I don't remember what was her response.
Now, going back to races: it would be really cool to send 5 top runners to the onice and the bottom 5 runneres to the office. I had that idea too back in Junior High. So my family knew Galen Rowell, who was a famous photographer but unfortunately died in a plane crush. He was also a runner. So me and my father were regularly running with him. Usually my father was slow, so me and Galen had to wait for him. Anyway, one of those times we ran, Galen said he went to a race and won. I asked him "did you wait" (in reference to my idea of being sent to the onice after the race). He responded "if I were to wait I wouldn't win the race" (thinking I was talking about waiting for other runners in the middle of a race, similarly to how we wait for my dad). And I was like "no no, did you wait AFTER the race, not during". Galen was confused. My dad said "he is joking".
And here is yet another idea. If someone cheats on a race, instead of saying he didn't finish, they should say he finished, but he took infinite amount of time. Thus, he ran with infinitesimal velocity and, accordingly, takes the last place. So if you humiliate 5 people at the bottom then in case of 1 cheater you will humiliate only 4 people besides him, since he is counted as one of the 5. This idea is fascinating because it introduces infinities and infinitesimals.
