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?

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.

Except that it's not lower than the minimum, but that isn't much.

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?

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.

Yes we do, we know it's the world record. That's the data point.

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.

The world record is not 1 data point, it is a property of all human running in history.

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

It's what he said: Usain Bolt's 100m World Record of 9.58 seconds.

And what can you infer from that?

Given that it's a world record, you can infer that the majority of the species cannot run so quickly.

That is not a "powerful and useful inference", it's not an inference at all. It is simply the definition of a world record.

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.

The global minimum of a distribution is not, in any way, a "single datapoint". It is a property of all the data points that ever were - in this case, it contains information about all humans that have ever run in the history of the species.

It is in no way comparable to knowing how many humans there are, which can't actually tell you anything about how many aliens there could be.

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.

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.

There is no such myth. Nobody is surprised that you can say something about a distribution if you know some facts about the distribution. Using "single data-point" in two completely different ways is just bait and switch.

Any data pertaining to humans would be a single data-point in the true sense, which in itself gives almost zero information. You can't compare that to knowing global properties of the sample or the distribution, it's completely different things.

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.

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.

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.

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.

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...

> 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.

From pure statistical inference, you know precisely 1 more thing than nothing: an individual of the species can run 100m in 9.58s.

Now, adding other kinds of information and reasonable assumption from physics and biology, we can conclude more than that 1 thing, as you say. It's unclear exactly how much those would apply to alien biology, but they might.