[_yb2s]

They are demonstrating a fundamental flaw in the logical reasoning behind the original Drake equation, that is robust to specific choices of distributions, or parameters to include or exclude.

Anytime you multiply a large number of uncertain probability distributions, the resulting posterior will have most of the probability mass near zero. This result is not sensitive to which distribution or bounds you choose. The Drake equation is nonsense, because it is effectively assuming certainty about every single term- and that is the only way to produce a result much higher than zero.

When you are multiplying seven unknown together, you can be fairly certain that the result is close to zero without knowing the value of any of the terms, unless you have some real information that none of terms can be near zero.

[jncfhnb]

This is some dumb second order Bayesian reasoning. You’re declaring a prior for arbitrary random variables as if their distributions themselves are sampled from a distribution. They are not.

You cannot be certain that seven random things multiplied together is close to zero. That statement is very obviously wrong.

Further “near zero” is a misleading term at best because it neglects to mention that we are multiplying it by a large number to get an expected value.

[mjburgess]

Distributions are sampled from distributions -- it is this problem which makes global scepticism an even minimally interesting problem.

When faced with "global, recursive" epistemic problems one arrives at an extremely power-law asymmetric distribution where the "bayesian value" of almost all evidence is near zero.

We live our entire lives in this "nero zero" range, and i'd suppose, this makes a "pure bayesian" solution to the problem of knowledge deficient. Since we succeed in knowing, so we succeed in making hyperfine determinations.

This sort of "hyperfine epistemology" works globally to allow us to "know at all", but as you're sensing here -- it's pretty much useless for any local problem.

Perhaps this is just the single up-side of the bayesian approach to the drake eqn: it shows how impossible it is to state such an eqn, let alone evaluate it. We cannot, a priori, make such hyperfine determiniations on such circumstantial matters.

[jncfhnb]

This post is full of fancy word nonsense.

“Distributions are sampled from distributions” is meaningless because you cannot define the meta distribution. But more importantly, the Drake equation is not a RANDOM SAMPLE from a population of distributions. So the idea of sampling distributions is irrelevant even if true. The naive math of multiplying them together is invalid.

[mjburgess]

It really doesnt matter what the "meta-distribution" is, bar trivial ones. My whole point is that we can augment bayesianism by a-priori choosing these meta-distrbutins.

Is my hand in front of me? Is what's in front of me real? Are my perceptions indicative of reality? etc. -- keep recursing

If you're drawing from any sort of epistemically plausible (ie., any plausible model of subjective uncertaintiy) distribution on each of these points, you'll "recurse" to some extreme distribution --- where all possible evidence basically makes no difference.

This is why there cant really be an "evidential" case for realism --- and why bayesianism is an incomplete epistemology.

You have to assert the truth of some basic facts, and thereby focus in on a "region" of this "extreme distribution" which is near-zero. And say only, "simply by being above zero, i'll believe it".

That's the solution to the problem of scepticism.

But this doesn't work for local issues, because locally there really isnt any kind of non-bayesian a-priori analysis which can say, "here, believe the non-zero".

ie., you can 'complete' bayesianism globally by meta-theoretical concerns, but not locally. Meaning that 'from ignorance, only ignorance' everywhere, esp. the drake eqn.

The failure of bayesianism is an indictment of darke-like reasoning -- this only works on genuienly global matters.

eg., "a priori, the world exists, therefore the meta-distributin must be so constrainted..."

[jncfhnb]

Do you read your own writing here?

[mjburgess]

I'm talking to a very rarified audience, for sure. Giving a bayesian gloss on moorean epistemology is not really a project for a hacker news comment.

[karpierz]

There's the bonus problem of: even if you magically have correct priors, you still need to assume that Drake's Equation is a good model for the generation process of civilizations. If the equation is missing terms or has extra terms, no amount of Bayesian reasoning helps correct for that.

It's like thinking that you can use Bayesian reasoning to determine the likelihood of Russell's Teapot existing.

[mjburgess]

Yes, this is essentially what i mean by "distributions are sampled from distributions", ie., there's a subjective uncertainty in the choice of model but also an uncertainty in the very determination of that uncertainty.

You can model a plausible "final stable distribution", after all these recursions, with a power law.

This makes intuitive sense, if you consider how science works: all the confirmatory evidence in the world doesn't help, all the information lies in the single refutative point. This is how power laws work.

So basically we're always operating under a heavily under-determined region with high uncertainty, and we can only improve that by disconfirmatory apparent outliers.

[3abiton]

It's always fun to see frequentists/bayesians infights in HN comments. It's almost a guilty pleasure for me.

[jncfhnb]

Everyone in this thread appears to prefer Bayesian

[_yb2s]

Please try to keep the discourse civil. You have not understood my argument. What you are dismissing as obviously wrong is a well known mathematical fact [1].

Imagine the “space” of all currently unobserved phenomena that require a series of independent hurdles to be overcome a la the drake equation: observable aliens, etc. This space is infinitely big and the probability of each of the hypothetical phenomena is astronomically low as to not even be worth considering. The ones that are worth considering have some evidence that either they have occurred, or that we think we understand the process by which they come about, and all of the series of independent hurdles are likely to be nonzero.

Imagine this simple test: take a random sample of 7+ numbers on [0,1] and multiply them together as the Drake equation does. Repeat this thousands of times to plot a smooth density plot, and you will get a stretched exponential distribution, with the majority of the probability density near zero.

This type of causal process with a cascade of independent filters multiplied together that leads to a stretched exponential is common in a lot of domains[1], and almost always makes positive outcomes very rare. For example, the probability that some random new organic molecule will bind to a specific protein target to be an effective drug is similar in this way, and is close to zero. For a molecule to work as a drug it has to pass a lot of hurdles just as a civilization does in the Drake model: be bioavailable, bind to the right target in the right way, not bind to harmful targets, be metabolized at a reasonable rate, etc.

[1] https://link.springer.com/article/10.1007/s100510050276

[jncfhnb]

No, this is nonsense.

You’re implying that there are many things that could go wrong, and that if we took a random sample of “things” that we would probably find some joint distribution that is small. This is true in the sense that an incalculably small proportion of conceivable things happen.

But this particular thing is not a random sample of things. You don’t get to appeal to the unknown distribution of distributions. Your claim that it “ almost always makes positive outcomes very rare” is completely irrelevant to non randomly chosen and defined processes.

You can’t insert steps into a Bayesian inference until your priors match a desired outcome. It’s as fallacious as inserting an infinite number of steps that are highly likely but technically possible to not be the case as a way to reduce any given prior from basically guaranteed to basically never expected to happen.

Your argument reduces to “I don’t know what decides the probability of alien life but I think the chance is small” which is a fine opinion, but your mathemagics have not strengthened your argument.

Suppose we play a game called “the four game” in which case you have to guess if I’m thinking of the number 4. By your reasoning you would probably guess 0% because you don’t know the rules of generation and there are infinite conceivable ways I could draw numbers from and 1 out of infinite draws will be exactly 4. But when I play the four game I always think of 4. The imagined sampling of unknown distributions is irrelevant because the game itself is not random.

Now, look, the Drake equation tries to do it all, and that’s probably bad. Let’s re imagine it as a function that simply identifies a probability of alien life, by now, on a randomly chosen planet, multiplied by the total number of planets out there right now (let’s ignore the detectable part). Is the probability part really small? Well yeah almost certainly. No math required. Is it small enough that we can provide any confidence on the order of magnitude of the expected value? Nope. The only interesting question, imo, is whether that expected value is greater than or less than one.

The drug example you have provided is a case of exploring a new space. This is not comparable to life appearing on a planet. Because like a novel drug development, we have an example of life originating on a planet. It’s not a random sample either but it’s sufficient to observe that the process to make this happen exists and has happened. Unlike the drug development which largely a test of whether the pattern exists or not.

[_yb2s]

My previous explanation does apply to the Drake equation and all similarly constructed models because of its structure and lack of information.

However, I would agree that there isn’t much support for using the Drake equation as a model for the probability of observing alien life- it assumes too much.