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I don't even understand his main argument, but here's a random, incorrect argument he made. > For example, let's take Usain Bolt's 100m World Record of 9.58 se

I don't even understand his main argument, but here's a random, incorrect argument he made. > For example, let's take Usain Bolt's 100m World Record of 9.58 seconds. Imagine that was the only data point we had regarding human running speed. Wth that one data point we could confidently make a powerful prediction, that anyone we pick from the world population will take more than 9.58 seconds to run 100 metres. This is not true at all. Either he's saying that the "single datapoint" is "Bolt ran 100 m in 9.58 s". If that is the datapoint, we can't draw any conclusions from that, for all we know he could be the slowest human in the world. If on the other hand he means that the single datapoint is "Bolt ran 100 m in 9.58 s and nobody has run faster" then sure, we can conclude that nobody is faster, but that's part of the datapoint so it's not very interesting.

simonh 5y ago
That's the entire point. With the right one piece of data, you can draw powerful and useful inferences. You don't need data on the 100m dash running speed of every single human being on Earth. That one item can be sufficient. It all depends on what the data is and what you're trying to infer. How is that incorrect?
- Grustaf 5y ago
  What is the datapoint in this case? 1. Bolt runs 100m in 9.58s or 2. Bolt runs 100m in 9.58s and he’s the fastest ever
  - simonh 5y ago
    It's what he said: Usain Bolt's 100m World Record of 9.58 seconds.
    - Grustaf 5y ago
      And what can you infer from that?
      - veganomics 5y ago
        Given that it's a world record, you can infer that the majority of the species cannot run so quickly.
        Grustaf 5y ago
        That is not a "powerful and useful inference", it's not an inference at all. It is simply the definition of a world record.
        setr 5y ago
        the point is that a "single datapoint" does not mean the same thing as a "single datapoint", depending on what that datapoint is and the context around it. The myth he was specifically busting in the original paragraph was that you cannot learn anything from a single datapoint, but that's only true if that datapoint is drawn from a random distribution. A single datapoint can tell you a lot, if you know other things about it. In this case, knowing that it's a world record dramatically changes its utility. It's powerful in the sense that it tells you a lot about the overall dataset, not in the sense that it's a novel insight.
        Grustaf 5y ago
        Sure, if you happen to know the global minimum value, then you know a lot. For aliens though, we don't have anything resembling that, so the conclusions we can draw are much less interesting.
        setr 5y ago
        The purpose was debunk that myth so that he can derive further (though less information) about aliens, and then the author goes on to do so. That is, now that you've admitted that a single datapoint does in fact have the potential for providing extreme information in the extreme case, then you should expect to find (some) information in the other cases... so that's what he does. As long as you assume its not a purely random distribution, which he does not.
- simiones 5y ago
  What can you infer from just knowing one human being can run 100m in 9.81s? What if you knew instead that one particular human being can run 100m in 16s?
  - Grustaf 5y ago
    We can’t infer much about how fast others run. Only that it’s possible to run 100m in 9.81s. We don’t know if everyone else can do that, or no one.
    - simonh 5y ago
      Yes we do, we know it's the world record. That's the data point.
      - Grustaf 5y ago
        I would not call it "powerful" that you can infer from "X is the world record" that "nobody is faster than X". It's not even inference, it's simply saying the same thing in different ways. And in any case, it's of course not very relevant for his main argument anyway, since don't don't have any such data-points about aliens. If we knew that "humans are the smallest intelligent beings in the universe" well then yes could "infer" that all aliens are larger. But that is trivial and pointless.
      - simiones 5y ago
        The world record is not 1 data point, it is a property of all human running in history.
- titzer 5y ago
  But that's not what he's doing. He isn't concluding that everyone runs slower than the record (which is almost a tautology), he's trying to conclude things about the average running speed of people. That's extremely deceptive, because you can't actually conclude a damn thing about the average based on the minimum.
  - Grustaf 5y ago
    Except that it's not lower than the minimum, but that isn't much.
jodrellblank 5y ago
You’re missing the point of that claim; he’s refuting “you can’t infer anything from one datapoint” using reductio ad absurdum - if the one datapoint contains in it the information “world record” then you can make a confident prediction that applies to 7 billion people, without measuring anything about their running speed; that’s already included in the one piece of information. That is the absurd case, one piece of data has total information in it. Accept that, and you can then see that a less extreme datapoint can have less extreme amounts of information in it, and can be used to make less confident predictions - but still more confident than guesswork. Really the only point is, if I picked a random person and asked you to bet $1 whether they were slower than Usain Bolt, would you say “ok” or would you say “I can’t infer ANYTHING from only ONE data point”? If you can infer something from only one datapoint, you can infer something about aliens with better than guesswork confidence using humans as one data point.
- Grustaf 5y ago
  If by "data-point" you mean a single sample from an unknown distribution, then no we can't really say anything based on that, definitely nothing interesting. And by that definition the Bolt record is not a data-point, it's a global property of the distribution, namely the minimum value. In his main argument though (and your example here), we just have a single value, and no information at all about the distribution, we don't even know if n>1. In such cases we can hardly say anything at all. So in order to be able to infer something from the single datapoint, we need to make assumptions about the distribution of the values. The problem is that all the interesting conclusions we can draw come from those assumptions, not from the single value itself. To tie it back to Usain Bolt. If you only know his time on 100m, that means nothing. We can of course posit that he's the fastest in the world, and from that we can draw conclusions such as "everyone else is slower", or (somewhat less trivially) that "the average time is above 9.58 s". But we could equally well posit that he is the slowest in the world or that everyone is equally fast, which would lead to completely different conclusions. So we clearly see that all the interesting information comes from the distribution, which sort of makes his arguments pointless.
  - jodrellblank 5y ago

simonh 5y ago

That's the entire point. With the right one piece of data, you can draw powerful and useful inferences. You don't need data on the 100m dash running speed of every single human being on Earth. That one item can be sufficient. It all depends on what the data is and what you're trying to infer. How is that incorrect?

Grustaf 5y ago
What is the datapoint in this case? 1. Bolt runs 100m in 9.58s or 2. Bolt runs 100m in 9.58s and he’s the fastest ever
- simonh 5y ago
  It's what he said: Usain Bolt's 100m World Record of 9.58 seconds.
  - Grustaf 5y ago
    And what can you infer from that?
    - veganomics 5y ago
      Given that it's a world record, you can infer that the majority of the species cannot run so quickly.
      - Grustaf 5y ago
        That is not a "powerful and useful inference", it's not an inference at all. It is simply the definition of a world record.
        setr 5y ago
        the point is that a "single datapoint" does not mean the same thing as a "single datapoint", depending on what that datapoint is and the context around it. The myth he was specifically busting in the original paragraph was that you cannot learn anything from a single datapoint, but that's only true if that datapoint is drawn from a random distribution. A single datapoint can tell you a lot, if you know other things about it. In this case, knowing that it's a world record dramatically changes its utility. It's powerful in the sense that it tells you a lot about the overall dataset, not in the sense that it's a novel insight.
        Grustaf 5y ago
        Sure, if you happen to know the global minimum value, then you know a lot. For aliens though, we don't have anything resembling that, so the conclusions we can draw are much less interesting.
        setr 5y ago
        The purpose was debunk that myth so that he can derive further (though less information) about aliens, and then the author goes on to do so. That is, now that you've admitted that a single datapoint does in fact have the potential for providing extreme information in the extreme case, then you should expect to find (some) information in the other cases... so that's what he does. As long as you assume its not a purely random distribution, which he does not.
simiones 5y ago
What can you infer from just knowing one human being can run 100m in 9.81s? What if you knew instead that one particular human being can run 100m in 16s?
- Grustaf 5y ago
  We can’t infer much about how fast others run. Only that it’s possible to run 100m in 9.81s. We don’t know if everyone else can do that, or no one.
  - simonh 5y ago
    Yes we do, we know it's the world record. That's the data point.
    - Grustaf 5y ago
      I would not call it "powerful" that you can infer from "X is the world record" that "nobody is faster than X". It's not even inference, it's simply saying the same thing in different ways. And in any case, it's of course not very relevant for his main argument anyway, since don't don't have any such data-points about aliens. If we knew that "humans are the smallest intelligent beings in the universe" well then yes could "infer" that all aliens are larger. But that is trivial and pointless.
    - simiones 5y ago
      The world record is not 1 data point, it is a property of all human running in history.
titzer 5y ago
But that's not what he's doing. He isn't concluding that everyone runs slower than the record (which is almost a tautology), he's trying to conclude things about the average running speed of people. That's extremely deceptive, because you can't actually conclude a damn thing about the average based on the minimum.
- Grustaf 5y ago
  Except that it's not lower than the minimum, but that isn't much.

jodrellblank 5y ago

You’re missing the point of that claim; he’s refuting “you can’t infer anything from one datapoint” using reductio ad absurdum - if the one datapoint contains in it the information “world record” then you can make a confident prediction that applies to 7 billion people, without measuring anything about their running speed; that’s already included in the one piece of information. That is the absurd case, one piece of data has total information in it. Accept that, and you can then see that a less extreme datapoint can have less extreme amounts of information in it, and can be used to make less confident predictions - but still more confident than guesswork. Really the only point is, if I picked a random person and asked you to bet $1 whether they were slower than Usain Bolt, would you say “ok” or would you say “I can’t infer ANYTHING from only ONE data point”? If you can infer something from only one datapoint, you can infer something about aliens with better than guesswork confidence using humans as one data point.

Grustaf 5y ago
If by "data-point" you mean a single sample from an unknown distribution, then no we can't really say anything based on that, definitely nothing interesting. And by that definition the Bolt record is not a data-point, it's a global property of the distribution, namely the minimum value. In his main argument though (and your example here), we just have a single value, and no information at all about the distribution, we don't even know if n>1. In such cases we can hardly say anything at all. So in order to be able to infer something from the single datapoint, we need to make assumptions about the distribution of the values. The problem is that all the interesting conclusions we can draw come from those assumptions, not from the single value itself. To tie it back to Usain Bolt. If you only know his time on 100m, that means nothing. We can of course posit that he's the fastest in the world, and from that we can draw conclusions such as "everyone else is slower", or (somewhat less trivially) that "the average time is above 9.58 s". But we could equally well posit that he is the slowest in the world or that everyone is equally fast, which would lead to completely different conclusions. So we clearly see that all the interesting information comes from the distribution, which sort of makes his arguments pointless.
- jodrellblank 5y ago