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  • way.

  • Writers ready.

  • Watch the gate.

  • This'll be a max bicycle racing.

  • It's basically an acceleration contest.

  • It's not endurance.

  • And so the whole thing is, it's like our drag racing.

  • And let's get going really fast, hold the lead and then carried on through to to to the end.

  • So what you do is you get three opportunities to advance.

  • To call motives.

  • Motor one motor to Motor three.

  • Some other organization have different rules.

  • When I'm talking about a B a American bicycle association, you have eight lanes on a track.

  • And to advance into the next round, you had to win one of the motives.

  • Okay, that means so you get into the first Moto and usually a very good writer would win it.

  • He or she would sit down and then the other seven riders who were going to the second Moto, Then whoever won that would sit down.

  • Then there'd be 1/3 Moto for the third writer.

  • Then those three riders would advance into the next level of competition, and a big meeting could be a finalist.

  • Quarterfinals, semifinals.

  • But you advanced.

  • Okay, so the big issue is to get out of the first round.

  • It's like in basketball getting past the first round of the playoffs.

  • There's eight riders, and so you have eight lanes in Lane eight has always called the one that is part of this from where you turned.

  • So if you turn left, this would be laying eight.

  • If you turn right, this would be lady thing outside Lane, you have to travel further.

  • If all riders were equally talented, you wouldn't win out of lady if they all fell down or if something happened, somebody new.

  • But in general, assuming that all writers are equally, the chances of winning are Delaney are very slim.

  • A lot of people watching might have seen the Olympic Games or running races where we sea staggered lanes.

  • Or we could have a tilted line like an angled start.

  • Like BMX racing doesn't compensate in this way.

  • If you could keep people in their lanes, you know, like you do in track, you say you have to stay for the first lap in your lane.

  • But of course you don't.

  • And what happens if you ever try to do that?

  • Really aggressive riders?

  • Okay, we're just, In other words, if somebody was in front and they saw somebody started to pass him.

  • They would just move in front of them and knocked him down.

  • So you can't give someone an opportunity to be in front of somebody else because we'll move it out and it's gone.

  • So that doesn't work.

  • Years and years ago, when my son started racing, everybody just rushed the gate and noticed that Lane eight Outside is no good and Lane one inside.

  • It's too easy to get so somebody to cut you off for somebody to get boxed in.

  • So good Leans are usually 234 maybe in an extreme case five.

  • But let's say three and four.

  • In the early days, people would rush to the track when they said, We're going Okay, let's start the racing and they'd run and get into 33 or four.

  • So then they said, No, that's not fair.

  • So then they sighted.

  • Okay, What we're gonna do is we're gonna call these rain at random, thought you'd have a deck of cards and they have eight and you just pull the card and that was your link, or they haven't earned with balls in it.

  • And you put one And at least that was fair in the sense that, you know, you had equally likely chance to get anyone of the lanes.

  • So that's how it went on for years and years and years at the start of each moto.

  • Remember, we have three motor, so you have a random draws the starter motor one random draw it to start a motor, too.

  • Random God Starboard three.

  • Now the problem Waas that with that random wrong, there's a reasonably likely chance that you could pull 38 And if you are off somewhere like my son ones was.

  • We were in Shreveport, Louisiana, and he proved 38 Well, he'd road gallantly, okay, but he still didn't qualify into the next round.

  • Hey, hey was unlucky.

  • The curse of Lane eight.

  • The curse of late.

  • So I said, We need a better system we need on where my son can't get 3/8 or to eight and a seven.

  • Ah, colleague of mine who's a statistician?

  • We just started talking and said, Let's fix this, Okay?

  • Were mathematicians were hot shots?

  • Let's fix this system.

  • There were two breakthroughs OK to break through.

  • The first breakthrough was that's not a sign a lane independently, three times.

  • That's instead give you a triple, and your triple would have three numbers.

  • An example.

  • Let's say it had 158 That means you get Lane one in the first Moto Lane, five in the second at eight and and he was another major breakthrough.

  • Instead of working mathematically with the numbers of the lanes like one and two and three, we decided to work with the priorities.

  • Okay, one meant the best link to meant the second best and eight and the worst that has mathematical content.

  • So we put mathematical meaning into it by saying priorities.

  • They're well ordered.

  • Their number.

  • There's a one.

  • It means something on eight.

  • It means something.

  • Those two breakthroughs, triples and priorities.

  • That's kind of subjective.

  • So what you do is you asked a bunch of good writers.

  • Which one is their most desire?

  • It And there's almost total agreement.

  • Almost if you had to say anything and almost always be laying three sometimes before maybe, but it was almost a saint, which were the worst, everybody would say eight.

  • So maybe there's some fuzziness in between, but almost all the good writers would tell you the same thing.

  • So that so That was not a problem.

  • So did you do this?

  • Was that Was that some kind of survey or pole?

  • Yeah, I did.

  • Every time I did it with my son and his friends and they thought that that, you know, sometimes it was the right answer in a wrong answer.

  • Of course I wasn't.

  • So now I had to build a mathematical model that says how I'm going to come up with the very best set of eight triples.

  • There will be the fairest, and then run it on the computer with an elegant Give us the best.

  • So we did.

  • And what we did is we try to say, Look, everybody should have the same.

  • You know, if you summed up priorities like maybe the priorities, like 158 as I said before and you sum them, you're gonna get 14.

  • Well, maybe everybody should have the same sum of priorities.

  • That would be a good fairness country.

  • But you can't do that.

  • They're all gonna be 13 or 14.

  • So you know, you start playing mathematical games about ST A model so soon you start to realize that the best solution is gonna have 4 13 and 4 14 So that's already cutting the data back a lot.

  • You see, it's already saying, Oh, now I don't have to search everything.

  • And so with that constraint that four are going to be 13 and four, we're gonna be 14.

  • You start to do a search, comes ah, situation where you get these optimal eight triples in less than one second, we found 7000 solutions.

  • Okay, so so But that's too many solutions.

  • So does that mean that's you?

  • Could, you know?

  • No, no, no, no, no.

  • You say good things.

  • But in mathematics and physics, when you find too many solutions, that means you didn't put enough information into your mathematical model.

  • The most beautiful mathematics is there exists one solution, and that's why in life we say, Ah, there's one perfect marriage partner.

  • There's one perfect house.

  • There's one perfect.

  • Would I grant you that there's not?

  • But anyway, we like that.

  • So I spend time with a student and we said, Look, if you're an average rider, the third motor is more important than the first and the second, and I'm gonna tell you why because there's always some hotshot and hit and hit.

  • This hotshot is gonna ruin the first race.

  • Then the second hotshot will win the second.

  • So they know in the bedroom.

  • So not in the third race.

  • So now you wanna optimize your chances in the third race.

  • That's when you want the problem.

  • That's when you want the prime lane.

  • So I said, Let's wait that these sums so that not all equal and that a good lane in the third Moto is worth more than a good lane.

  • And we put a little tiny better waiting on there and very simple.

  • I mean, like, the waiting was that maybe in the third motor there's only six riders.

  • So we waited it by maybe 8/6 or something that gave us the unique solution.

  • So we ended up with our optimal solution.

  • I say any reasonable mathematician or intelligent person once you told him.

  • Look, think of priorities and think of triples that come up with our system.

  • That's what I think, Professor.

  • Any problem I see with your system is the priorities are very subjective.

  • And Billy the BMX might prefer Lane one, cause he's good on tight corners.

  • And Sally might like the outside lane because she doesn't like crashes and, like different riders might have different priorities.

  • I'm not Mark your bowl system.

  • I mean, of course you're right.

  • But you're really fine tuning at a level that doesn't exist.

  • Okay?

  • I mean, the bulk of the writer, So, yes.

  • So there's somebody who has some, particularly.

  • Well, they're gonna lose.

  • I'm going to pay a price.

  • Okay, But you're doing this for the bulk of the things and and granted, there's always going to be some kind of a crystal like that.

  • Okay?

  • And and indeed, you could say that.

  • But it's not.

  • It's not a concern.

  • Okay, You say we're going to do this for the bulk of the writers.

  • It's going to take care of bulk of the problems.

  • In certain sense, I wasn't trying to save the world.

  • I was trying to use mathematics in something that would improve the quality of my local life while my son was racing okay.

  • And we did that.

  • And so to me, it was ah, validation of mathematics.

  • Okay.

  • How people Mathematics is not useful.

way.

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A2 BEG lane moto motor racing mathematics bulk

The Curse of Lane 8 - Numberphile

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    林宜悉 posted on 2020/03/30
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