Sunday, March 18, 2018

Bayesian inference doesn’t mean there must be a planet Earth for each fraction of curly-haired people.

Speaking of communicating complex issues in science well,  Sabine Hossenfelder's post on what's wrong with the multi-verse theories is the best I've ever read, especially this, her third point about why Sean Carroll's resort to Bayesian probability doesn't do a thing to promote the reality of the multiverse.

3. Ok, then. So it’s neither falsifiable nor sound logic, but it’s still business as usual.

The gist of this argument, also represented in Sean Carroll’s recent paper, is that we can assess the multiverse hypothesis just like any other hypothesis, by using Bayesian inference. 

Bayesian inference a way of probability assessment in which you update your information to arrive at what’s the most likely hypothesis. Eg, suppose you want to know how many people on this planet have curly hair. For starters you would estimate it’s probably less than the total world-population. Next, you might assign equal probability to all possible percentages to quantify your lack of knowledge. This is called a “prior.”

You would then probably think of people you know and give a lower probability for very large or very small percentages. After that, you could go and look at photos of people from different countries and count the curly-haired fraction, scale this up by population, and update your estimate. In the end you would get reasonably accurate numbers.

If you replace words with equations, that’s how Bayesian inference works. 

You can do pretty much the same for the cosmological constant. Make some guess for the prior, take into account observational constraints, and you will get some estimate for a likely value. Indeed, that’s what Steven Weinberg famously did, and he ended up with a result that wasn’t too badly wrong. Awesome. 

But just because you can do Bayesian inference doesn’t mean there must be a planet Earth for each fraction of curly-haired people. You don’t need all these different Earths because in a Bayesian assessment the probability represents your state of knowledge, not the distribution of an actual ensemble. Likewise, you don’t need a multiverse to update the likelihood of parameters when taking into account observations. 

So to the extent that it’s science as usual you don’t need the multiverse.

I can't help but cite that quote beloved of atheists, when Laplace answered Napoleon's question of where God fit into his theory,  "I had no need of that hypothesis." 

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