Simulated Annealing of Opinions


How do brains learn things?  Here’s a Tedx talk about bird brains learning how to sing.  It’s pretty neat.  Check it out.

I’m by no means an expert in this field, but my understanding is that bird brain song learning is pretty generalizable to brain learning in general.  Basically, brains learn through experimentation.  Change some aspects of neural firing: how does it affect the song?  Choose whether or not to adopt the new version of the song.


This learning method is quite similar to Markov Chain Monte Carlo (MCMC).  MCMC is a computational tool for sampling from a probability distribution; in physics, MCMC is used to sample states at a given temperature.

Suppose you have some large number of molecules in a box.  You want to know at a given temperature what the possible positions and momenta of those particles are.  In essence, MCMC provides a way to “move” between configurations of these molecules such that the probability of each state in your simulation is the same as the probability in the system in nature.  Given some configuration of molecules, we’ll call state A, calculate the energy.  Then make a random small change to state A, we’ll call the new state A’.  If the energy of A’ is lower than the energy of A, adopt state A’ with probability 1.  If not, adopt state A’ with some probability <1, depending on the relative energy levels and on the temperature.  At high temperature, adopt higher energy states with high probability.  At low temperature adopt higher energy states with low probability.  Jump in this fashion from state to state for a long time, and you’ll get a set of states that resembles the set of states you would get if you sampled from an actual box of molecules held at that temperature (although the ordering of the samples will be completely different).

At high temperature, this process yields basically random states, as energy plays only a small role in which states to adopt.  The molecules are randomly arranged, like a gas.  At low temperature, the process will strongly favor lower energy states, and can adopt solid crystal structures.

(Of course there are precise equations for all of this, but I’m ignoring the quantitative description in favor of the qualitative because the analogy I’m going to draw won’t have a clear quantitative interpretation).


Okay, let’s assume that we humans use the same method to decide on opinions that song birds use to learn their songs.  This just feels true to me, but I have no evidence beyond my personal experience, so I could be wrong:

We try on opinions.  We make slight modifications to our beliefs, and we try on those modifications to see whether they suit us.  If those modifications are obviously superior (closer to the truth, or socially fulfilling, or …), then we’ll adopt the new set of beliefs.  If they’re inferior, we might adopt them anyway, at least for a time.  Basically, we’re running MCMC on the domain of possible beliefs.

Sounds great so far.  MCMC is proven to give an accurate sampling of a probability distribution, so if we have a community of humans all running MCMC on ideas, with the probability of any opinion weighted by some sort of idea-fitness-function (as a replacement for energy), then that community as a whole should at all times have a broad distribution of opinions, with better opinions appearing more often.

But there is a problem.  One shortcoming of MCMC is the existence of meta-stable states.  We want to know the likely arrangements of a collection of molecules in a box at low temperature.  But if we just choose a random state and evolve it according to MCMC’s rules at low temperature, we might accidentally freeze in the wrong structure: We might end up in an “energy well” that is not the “ground state.”  Metastable states exist in physical systems as well.  If you flash freeze a liquid, you’ll get a glass instead of a crystal.  The glass would “rather” be a crystal (it would be lower energy), but it doesn’t have the energy input to jump over into the crystalline arrangement.

The solution to this “problem” is annealing in physical systems, and simulated annealing in MCMC.  Basically, slowly lower the temperature, so that the system has enough energy to to escape the metastable states, and find the deepest energy well.


So how does nature solve the problem of metastable opinions?  I believe it’s found the same solution as physicists.  Slowly lower the temperature.  Young people are kind of crazy.  Young people will try on all sorts of obviously wrong opinions.   They’ll adopt them for some period of time, and then they might jump to a new crazy idea.

Older people are more ideologically sane.  They’ve settled into their idea-fitness well, and they’re not going to be pushed into some less-fit idea state.

But then, older people are also more stubborn.  They don’t have the temperature to find their way out of a metastable opinion to a more fit opinion.

What is the effect?  In politics, older people are more likely to be conservative, and younger people are more likely to be radical.  In science, paradigm shifts are far more likely to come from younger scientists.

2 comments on “Simulated Annealing of Opinions

  1. -

    Do you know any examples of situations where modulating one’s own temperature is an important strategy? (I feel like increased ideological temperature is a primary effect of certain psychedelics?)

  2. - Post author

    I think people probably modulate their own temperature all the time without consciously thinking about it. There are times when we want to be as correct as possible, like if there’s some short term threat, or if we’re trying to impress someone, or if we’re taking an academic exam. And there are times when we’re more at liberty to be wrong and take risks and improve our beliefs, like if we’re in the shower at home, or on substances with people we trust.

    Song birds adjust their temperature too: When they’re courting, they’re low temperature, singing the best known version of their songs. When they’re alone, they’re high temperature, experimenting and improving.

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