3 ms·

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. A

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
If I asked you to predict an alien time to cover 100 meters would you assign equal probability to every millisecond between 0 (teleport) and infinity (plants can’t move)? And if I then told you one example alien covered 100m in 9.58 seconds would you not change your estimate at all from learning that information? You wouldn’t assign less probability to nuclear powered teleporting aliens or crawling vine plant aliens or insect sized slug aliens because “you can’t say anything without knowing the distribution”? No that would be silly; you would put a lot more weight on times around 9.58 seconds, because that tells you something. Saying “it doesn’t tell you much” is right but it’s told you something, there is non-zero amounts of information there.
- tsimionescu 5y ago
  There are a priori arguments that can tell you that 0 and infinity are bad estimates. If you find out that one individual of this species can run 100m in 9.58s, there are biological intuitions that suggest certain possibilities for the entire species. Crucially, those intuitions could be entirely wrong for alien biology - they are not statistical reasoning, they are intuitions built from Earth biology. From pure statistical reasoning, or even taking into account basic physics (e.g. speed < c) and biology (e.g. speed > 0, almost certainly speed << c), you can't conclude anything about the average speed of an alien species by finding out that one individual can run as fast as Usain Bolt.
  - jodrellblank 5y ago
    Yes those intuitions could be entirely wrong. You're reading it as I'm saying "if we know one individual can cover 100m in 9.58 seconds then we can confidently understand everything about the alien species, their biology, their origin, the world they live on, with 100% accuracy" and saying no we obviously can't. I agree we obviously can't say all that. It's the other way round, we start with a blank slate and can say absolutely nothing about their origin, biology, world, etc. But when we find out one member can cover 100m in 9.58 seconds then we can say ever so slightly more than nothing about them, a non-zero amount more than nothing. Maybe not much more. But definitely more. And not with 100% confidence, we can't conclude anything. But there is information there, and we would be daft to ignore it completely because it isn't conclusive. We should adjust our predictions. > "you can't conclude anything about the average speed of an alien species by finding out that one individual can run as fast as Usain Bolt." If you know that a sloth takes 6min40s to cover 100 meters, a giant ant takes 1min40s to do it, and you run it in 30 seconds and a cheetah can do it in 5.1seconds. I say "I'm thinking of a creature, what is it?" your answer has to be "I don't know". If I say "an example of the creatures I'm thinking of takes 9.58 seconds" you ought to be thinking "slow cheetah or fast human" not "could be a sloth because ackchyewally the distribution of sloth speeds could be very wide so we don't know". You could assume the individual was the fastest of their species, but why would they be? You could assume the individual was noteably slow, a famous creature to be laughed at. With no way to know which is the case, you may as well assume the creature is a typical example - not because you know they are, but because if they aren't you have no way to know which way they aren't. Before we knew nothing, now we have more information than nothing. We ought to update our predictions based on this information, even if it's not much information and we can't know for sure. We ought to think the alien is less likely to be an immobile plant or silicon intelligence, less likely to typically move at the speed of a sloth. Not impossible, but this isn't meant to be a trick question where we get a deliberately wildly misleading time. 9.58 seconds is more like (cheetah, human, giant ant, jellyfish) than it is like (panda, mushroom, saltwater snail, sentient light beams). And yes, there might be nothing like those creatures at all, but "we could be wrong" is no reason not to adjust our best available guess. [1] https://www.newscientist.com/article/2220211-desert-ant-runs-so-fast-it-covers-100-times-its-body-length-per-second/ https://www.newscientist.com/article/2220211-desert-ant-runs...

jodrellblank 5y ago

If I asked you to predict an alien time to cover 100 meters would you assign equal probability to every millisecond between 0 (teleport) and infinity (plants can’t move)? And if I then told you one example alien covered 100m in 9.58 seconds would you not change your estimate at all from learning that information? You wouldn’t assign less probability to nuclear powered teleporting aliens or crawling vine plant aliens or insect sized slug aliens because “you can’t say anything without knowing the distribution”? No that would be silly; you would put a lot more weight on times around 9.58 seconds, because that tells you something. Saying “it doesn’t tell you much” is right but it’s told you something, there is non-zero amounts of information there.

tsimionescu 5y ago
There are a priori arguments that can tell you that 0 and infinity are bad estimates. If you find out that one individual of this species can run 100m in 9.58s, there are biological intuitions that suggest certain possibilities for the entire species. Crucially, those intuitions could be entirely wrong for alien biology - they are not statistical reasoning, they are intuitions built from Earth biology. From pure statistical reasoning, or even taking into account basic physics (e.g. speed < c) and biology (e.g. speed > 0, almost certainly speed << c), you can't conclude anything about the average speed of an alien species by finding out that one individual can run as fast as Usain Bolt.
- jodrellblank 5y ago
  Yes those intuitions could be entirely wrong. You're reading it as I'm saying "if we know one individual can cover 100m in 9.58 seconds then we can confidently understand everything about the alien species, their biology, their origin, the world they live on, with 100% accuracy" and saying no we obviously can't. I agree we obviously can't say all that. It's the other way round, we start with a blank slate and can say absolutely nothing about their origin, biology, world, etc. But when we find out one member can cover 100m in 9.58 seconds then we can say ever so slightly more than nothing about them, a non-zero amount more than nothing. Maybe not much more. But definitely more. And not with 100% confidence, we can't conclude anything. But there is information there, and we would be daft to ignore it completely because it isn't conclusive. We should adjust our predictions. > "you can't conclude anything about the average speed of an alien species by finding out that one individual can run as fast as Usain Bolt." If you know that a sloth takes 6min40s to cover 100 meters, a giant ant takes 1min40s to do it, and you run it in 30 seconds and a cheetah can do it in 5.1seconds. I say "I'm thinking of a creature, what is it?" your answer has to be "I don't know". If I say "an example of the creatures I'm thinking of takes 9.58 seconds" you ought to be thinking "slow cheetah or fast human" not "could be a sloth because ackchyewally the distribution of sloth speeds could be very wide so we don't know". You could assume the individual was the fastest of their species, but why would they be? You could assume the individual was noteably slow, a famous creature to be laughed at. With no way to know which is the case, you may as well assume the creature is a typical example - not because you know they are, but because if they aren't you have no way to know which way they aren't. Before we knew nothing, now we have more information than nothing. We ought to update our predictions based on this information, even if it's not much information and we can't know for sure. We ought to think the alien is less likely to be an immobile plant or silicon intelligence, less likely to typically move at the speed of a sloth. Not impossible, but this isn't meant to be a trick question where we get a deliberately wildly misleading time. 9.58 seconds is more like (cheetah, human, giant ant, jellyfish) than it is like (panda, mushroom, saltwater snail, sentient light beams). And yes, there might be nothing like those creatures at all, but "we could be wrong" is no reason not to adjust our best available guess. [1] https://www.newscientist.com/article/2220211-desert-ant-runs-so-fast-it-covers-100-times-its-body-length-per-second/ https://www.newscientist.com/article/2220211-desert-ant-runs...