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If your high school math would only consist of working through the various books of Allen Downey you would get a very rigorous, basic introduction to: programmi

by wjnc 3y ago

If your high school math would only consist of working through the various books of Allen Downey you would get a very rigorous, basic introduction to: programming, computer science, statistics, computational and Bayesian thinking and a lot more. You could write and compare simple to intermediate programs in many programming languages, where you’d have experience in implementing the same structures in different languages. Distributions and sampling wouldn’t scare you. It would beat high school math (at least mine in the 90s) by a million miles. Did I mention I think Allen is totally great yet?

tgv 3y ago
This article is bollocks, though. It's a fit of highly unrepresentative data, not even a good one, but worse: it doesn't explain anything. If you take that model seriously, Usain Bolt could have been anybody in the entire history of mankind.
- wjnc 3y ago
  There’s two types of people in the world: those that build models and those that complain about the models than have been built. Seriously though, Allen is an instructor. These are educational pieces to bring a spark of understanding and creativity to students. I don’t think he is aspiring on modeling the absolute truth in these posts. This piece has a learning about the working of non-normal distributions in sampling and reasoning about cut-off points.
- dilawar 3y ago
  "All models are wrong, some are useful." Heard it so many times during my Ph.D.
- codeflo 3y ago
  > If you take that model seriously, Usain Bolt could have been anybody in the entire history of mankind. No model is perfect, but I don’t have the slightest clue why you think that would follow.
  - tgv 3y ago
    Because it fits by multiplying random variables. It cannot explain why records are improving, i.e. why Usain Bolt didn't live 100 years ago.
    - suavesito 3y ago
      It can explain it. Better training and better equipment are (at least) two variables that improve people timings. Maybe a century ago there was an Usain Bolt, just didn't had neither the proper training, nor equipment, and those low factors avoided better timings.
      - iLoveOncall 3y ago
        And nutrition of course.
      - tgv 3y ago
        Except the model was fitted on people from the same period in the same region. Also, Ethiopian runners would be a counterargument. It's just reading way too much in a model that probably was there before the data. Seeing how everybody defends it as "learning", the example was sought to be described by the model.
- NavinF 3y ago
  > If you take that model seriously, Usain Bolt could have been anybody in the entire history of mankind Wat. His model says that many factors have to be perfect for someone to be as fast as Usain Bolt. If anything, it implies the opposite of what you said
_Microft 3y ago
Is this a reasonable comparison? I‘m unfamiliar with these works but would someone be able to work through them without the basic math knowledge that they acquired in school? If not then they are not an alternative to math in school?
- wjnc 3y ago
  I can say I’ve worked through four of his books from front to cover. You’re right. The learnings are on top of (some) math. In my case actually quite a lot of math post-high school. But I think a 14 year old could finish the books as well, or at least 90%. My eldest is 10. He is good at math because we do math games all the time. I can’t get algebra to sink in properly yet. Doesn’t really click in the time we have and with the teacher he has (me). But in Python he is giving variables a name all the time. Perhaps there is something about programmatic math that helps, not hinders education.
  - OJFord 3y ago
    > can’t get algebra to sink in properly yet. Doesn’t really click in the time we have and with the teacher he has (me). But in Python he is giving variables a name all the time. Perhaps there is something about programmatic math that helps, not hinders education. On the hinders side though, I can understand it being confusing to try to grasp: y = x + 2 As being sort of 'constantly updating', referring to x in abstract, when you've just learnt that Python will assign (once) the result of computing x (at that time) + 2 to y. You could def y as being x() + 2, but you might just be delaying the confusion to when you try to introduce functions in math and find yoursel saying 'no no that was just a hack to get python to behave more like algebra'. Is there any language that allows this I wonder? Where you can do something like: y = &(*x + 2) That is, y is a pointer to the result of adding 2 to the value pointed to by x, and this is somehow kept up to date, by tracking references like garbage collection perhaps, or at compile time by inserting the code to update y whenever x is updated. (Names would need to be globally unique I suppose, or else x transformed in to some kind of struct that could contain y and other dependents I suppose, and then also a link from y to x so you can remove that if y definition changes.. but that's a lot of load for the humble assignment operator!)
jmmcd 3y ago
I'm a big fan of Downey but this article is quite far from his best. 1. The data he fits is for distance (10k), and the conclusion ("why you can't beat the Freeze") concerns sprinting. 2. The claim that speed is a multiplicative model is fine and I agree based on the 10k data. But the people running against the Freeze aren't uniform from the population, so the argument is missing a step about what distribution (what percentile of the background distribution) they might be from. 3. There are some interesting numbers about how the high school girl is x% faster than Downey, the boy is y% faster than the girl, etc, but they don't link to the stats later in the article.
- Aeolun 3y ago
  To be fair, you don’t really need any of the numbers in the article. If the only thing you know about the freeze is that he’s 1.5 seconds slower than Ursain Bolt on the 200 meters you can conclude that he’ll win basically any race he runs.
  - jefftk 3y ago
    I do think you need the discussion of distributions and variance: for all I know the 200m tends to be won by fractions of a second and there are millions of people just a second slower than Bolt.
    - Aeolun 3y ago
      To some extend. If there’s millions of people that are nearly as fast you’d have encountered them on your school or university course, but what you see there doesn’t even come close (aside from the odd one out like the article describes). Since I haven’t, I can make a reasonable assessment of the likelihood someone is nearly as fast. Of course I might be wrong (maybe people in my general area are just incredibly slow)? But I’d have some confidence in the assertion anyway.

by wjnc 3y ago

tgv 3y ago

This article is bollocks, though. It's a fit of highly unrepresentative data, not even a good one, but worse: it doesn't explain anything. If you take that model seriously, Usain Bolt could have been anybody in the entire history of mankind.

wjnc 3y ago
There’s two types of people in the world: those that build models and those that complain about the models than have been built. Seriously though, Allen is an instructor. These are educational pieces to bring a spark of understanding and creativity to students. I don’t think he is aspiring on modeling the absolute truth in these posts. This piece has a learning about the working of non-normal distributions in sampling and reasoning about cut-off points.
dilawar 3y ago
"All models are wrong, some are useful." Heard it so many times during my Ph.D.
codeflo 3y ago
> If you take that model seriously, Usain Bolt could have been anybody in the entire history of mankind. No model is perfect, but I don’t have the slightest clue why you think that would follow.
- tgv 3y ago
  Because it fits by multiplying random variables. It cannot explain why records are improving, i.e. why Usain Bolt didn't live 100 years ago.
  - suavesito 3y ago
    It can explain it. Better training and better equipment are (at least) two variables that improve people timings. Maybe a century ago there was an Usain Bolt, just didn't had neither the proper training, nor equipment, and those low factors avoided better timings.
    - iLoveOncall 3y ago
      And nutrition of course.
    - tgv 3y ago
      Except the model was fitted on people from the same period in the same region. Also, Ethiopian runners would be a counterargument. It's just reading way too much in a model that probably was there before the data. Seeing how everybody defends it as "learning", the example was sought to be described by the model.
NavinF 3y ago
> If you take that model seriously, Usain Bolt could have been anybody in the entire history of mankind Wat. His model says that many factors have to be perfect for someone to be as fast as Usain Bolt. If anything, it implies the opposite of what you said

_Microft 3y ago

Is this a reasonable comparison? I‘m unfamiliar with these works but would someone be able to work through them without the basic math knowledge that they acquired in school? If not then they are not an alternative to math in school?

wjnc 3y ago
I can say I’ve worked through four of his books from front to cover. You’re right. The learnings are on top of (some) math. In my case actually quite a lot of math post-high school. But I think a 14 year old could finish the books as well, or at least 90%. My eldest is 10. He is good at math because we do math games all the time. I can’t get algebra to sink in properly yet. Doesn’t really click in the time we have and with the teacher he has (me). But in Python he is giving variables a name all the time. Perhaps there is something about programmatic math that helps, not hinders education.
- OJFord 3y ago
  > can’t get algebra to sink in properly yet. Doesn’t really click in the time we have and with the teacher he has (me). But in Python he is giving variables a name all the time. Perhaps there is something about programmatic math that helps, not hinders education. On the hinders side though, I can understand it being confusing to try to grasp: y = x + 2 As being sort of 'constantly updating', referring to x in abstract, when you've just learnt that Python will assign (once) the result of computing x (at that time) + 2 to y. You could def y as being x() + 2, but you might just be delaying the confusion to when you try to introduce functions in math and find yoursel saying 'no no that was just a hack to get python to behave more like algebra'. Is there any language that allows this I wonder? Where you can do something like: y = &(*x + 2) That is, y is a pointer to the result of adding 2 to the value pointed to by x, and this is somehow kept up to date, by tracking references like garbage collection perhaps, or at compile time by inserting the code to update y whenever x is updated. (Names would need to be globally unique I suppose, or else x transformed in to some kind of struct that could contain y and other dependents I suppose, and then also a link from y to x so you can remove that if y definition changes.. but that's a lot of load for the humble assignment operator!)

jmmcd 3y ago

I'm a big fan of Downey but this article is quite far from his best. 1. The data he fits is for distance (10k), and the conclusion ("why you can't beat the Freeze") concerns sprinting. 2. The claim that speed is a multiplicative model is fine and I agree based on the 10k data. But the people running against the Freeze aren't uniform from the population, so the argument is missing a step about what distribution (what percentile of the background distribution) they might be from. 3. There are some interesting numbers about how the high school girl is x% faster than Downey, the boy is y% faster than the girl, etc, but they don't link to the stats later in the article.

Aeolun 3y ago
To be fair, you don’t really need any of the numbers in the article. If the only thing you know about the freeze is that he’s 1.5 seconds slower than Ursain Bolt on the 200 meters you can conclude that he’ll win basically any race he runs.
- jefftk 3y ago
  I do think you need the discussion of distributions and variance: for all I know the 200m tends to be won by fractions of a second and there are millions of people just a second slower than Bolt.
  - Aeolun 3y ago
    To some extend. If there’s millions of people that are nearly as fast you’d have encountered them on your school or university course, but what you see there doesn’t even come close (aside from the odd one out like the article describes). Since I haven’t, I can make a reasonable assessment of the likelihood someone is nearly as fast. Of course I might be wrong (maybe people in my general area are just incredibly slow)? But I’d have some confidence in the assertion anyway.