Can random experimental choice lead to better theories?
journals.sagepub.com
journals.sagepub.com
They are analyzing a toy model of science. The details and in figure 1. They have a search space that has a few Gaussians like
f(x,y,z) = A0 * expt(-(x-x0)^2-(y-y0)^2-(z-z0)^2) + A1 * expt(-(x-x1)^2-(y-y1)^2-(z-z1)^2)
but maybe in more than 3 dimensions and maybe with more than 2 Gaussians.
They want the agents to find all of Gaussians.
It's somewhat similar to a maximization problem that is easier. There are many strategies for this, from gradient ascent to random sampling to a million more of variants. I like simulated annealing.
They claim that the best method is random sampling, that only work when the search space is small. But it breaks quite fast for high dimensional problems, unless the Gaussians are so big that cover most of the space, and perhaps I'm beeing too optimistic. Add noise, overlapping Gaussians and the problem gets super hard.
Let's get to a realistic example, all the molecules with 6 Carbons and 12 Hydrogens. Let's try to find all of them and their stables 3D configuration. This is chemistry from the first year in the university, perhaps earlier, no cutting edge science.
You have 18 atoms, so 18 * 3 = 54 dimensions, and the surface of -energy has a lot of mountains ranges and nasty stuff. Most of them very sharp. Let's try to find the local points of maximal -energy, that is much easier than the full map. These are the stable molecules, that (usually) have names.
* There is a cycle one with 6 Carbons, where each Carbon has 2 Hydrogens, https://en.wikipedia.org/wiki/Cyclohexane Note that it actually has two different 3D variants.
* There is one with a cycle of 5 Carbons and 1 carbon attached to the cycle https://en.wikipedia.org/wiki/Methylcyclopentane
* There are variants with shorter cycles, but I'm not sure how stable they are and Wikipedia has no page for them.
* There is also 3 linear versions, where the 6 Carbons are a s wavy line, and there is a double bound in one of the steps https://en.wikipedia.org/wiki/1-Hexene I'm not sure why the other two version have no page in Wikipedia, I think they should be stable, but sometimes it's not a local maximum or the local maximum is to shallow and the double bound jump and the Hydrogen reorganize.
* And there may be other nasty stuff, take a look at the complete list https://en.wikipedia.org/wiki/C6H12.
And don't try to make the complete list when of molecules that includes a few Nitrogen, because the number of molecules explodes exponentially.
So this random sampling method they propose, does not even work for an elementary Chemistry problem.
Moreover, both random and all other experimentation strategies we examined require constructing a bounded experimental space, a challenge that lies beyond the scope of the current work (see Almaatouq et al., 2024, for further discussion).
For molecules, 10 Armstrong away is probably as good as infinite.
For how many bananas should you eat per week to become the chess world champion, you can ask Wolfram Alpha to convert 2400kcal * 7 to bananas and get an upper bound.
I think everyone agree that with infinite time a resources a brute force search is better in case there is a weird combination. But for finite time and resources you need to select a better strategy unless the search space is ridiculous small and smooth.
How many points do you need to find it by brute force searching all of them? It looks like a 10m*10m square is good enough, perhaps 100m*100m is enough. That is 5E12 or 5E10 points.
Anyway, you need all of them to detect all the mountains and oceanic trenches.
Most of the times, the terrain is quite smooth and you can interpolate like in their example with the Gaussians. Well, except the Colorado Canyon, the Niagara Falls and a long list of sharp features.
Also, if you want to detect also buildings, you need like x100 more points.
And this is just a 2D problem. When you add dimensions, the problem grows like grid size ^ dimensions and the brute force approach is not feasible. There are a few ideas that are very nice in 1D, but in 100D they are just impossible in a sensible amount of time.
The first commercial antibiotics (Sulfa drugs) were found by systemically testing thousands of random chemicals on infected mice. This was a major drug discovery method up until the 1970s or so, when they had covered most of the search space of biologically-active small molecules.
But they choose chemical reactions that are usual in the lab, so they guess they will be able to make it work in the lab, and they keep most of the structure without changes. So it's closer to what they classify here as look nearby the known good points instead of a true random search.
An interesting concept they mentioned was this idea of "injected serendipity" when they were screening for novel materials with a certain target performance. They proceed as normal, but 10% or so of the screened materials are randomly sampled from the chemical space.
They claimed this had led them to several interesting candidates across several problems.
It also:
* Bakes in the assumption that there are no internal mechanisms to be discovered ("Each environment is a mixture of multivariate Gaussian distributions")
* Ignores the possibility that their model of falsification is inadequate (they just test more near points with high error).
* Does a lot of "hopeful naming" which makes the results easy to misinterpret as saying more about like-named things in the real world than it actually does.
You can ask many people to propose hypotheses and choose one at random, and perhaps with a good sample you get better experiments. You can query a Markov chain until it produces an interpret-able hypothesis. But the people or Markov chain (because English itself) has significant bias.
Also, some experiments have wider-reaching implications than others (this is probably more relevant for the Markov chain, because I expect the hypotheses it forms to be like "frogs can learn to skate").
https://www.wired.com/2010/06/ff-sergeys-search/
He went backwards and started with just collecting an absurd amount of data. Later while talking to a researcher he could confirm years of research with a "simple" search in his database.
Counter example is the decades that amyloid cascade hypothesis was the only allowed / funded research of Alzheimer disease.
> "We find that agents who choose new experiments at random develop the most informative and predictive theories of the world. "
https://www.goodreads.com/book/show/25670869-why-greatness-c...
Incidentally, the author works at OpenAI these days.
One, in a sufficiently advanced field of study, an idea's originator may be the only person able to imagine an experimental test. I doubt that many physicists would have immediately thought that Mercury's unexplained orbital precession would serve to either support or falsify Einstein's General Relativity -- but Einstein certainly could. Same with deflected starlight paths during a solar eclipse (both these effects were instrumental in validating GR).
Two, scientists are supposed to be the harshest critics of their own ideas, on the lookout for a contradicting observation. This was once part of a scientist's training -- I assume this is still the case.
Three, the falsifiability criterion. If an experimental proposal doesn't include the possibility of a conclusive falsification, it's not, strictly speaking, a scientific idea. So an idea's originator either has (and publishes) a falsifying criterion, or he doesn't have a legitimate basis for a scientific experiment.
Here's an example. Imagine if the development of the transistor relied on random experimentation with no preferred outcome. In the event, the inventors at Bell Labs knew exactly what they wanted to achieve -- the project was very focused from the outset.
Another example. Jonas Salk (polio vaccine) knew exactly what he wanted to achieve, his wasn't a random journey in a forest of Pyrex glassware. It's hard to imagine Salk's result arising from an aimless stochastic exploration.
So it seems science relies on people's integrity, not avoidance of any particular focus. If integrity can't be relied on, perhaps we should abandon the people, not the methods.
Science relies on replication. And any real gain society gets that comes from science is a form of replication in itself.
Integrity can't be relied on. But then, complete reliability is not necessary, just enough to make replication work.
And also, science is in a crisis due to the lack (or really large delay) of practical use. We actually don't have any other institution that ensures replication happens.
> Science relies on replication.
If that were true, then extraterrestrials would be real, because people repeatedly report sightings. The fact that most such sightings are misinterpretations of natural phenomena would be swept away by the sheer number of events, i.e. by replication, not interpretation.
> And also, science is in a crisis due to the lack (or really large delay) of practical use.
That's not a crisis in science, because science doesn't care whether an idea can be applied, only whether it can be verified, whether it resists falsification.
When Maxwell constructed his electromagnetic theory, it had no practical application -- none whatever. But much of modern technology relies to a greater or lesser degree on Maxwell's work, 175 years later. Because of Maxwell's theory with no practical application, Einstein regarded him as a scientist on a par with Newton.
Richard Feynman correctly called science "The pleasure of finding things out," with no consideration given to science's applications, if any. Science is judged, not based on its utility, but on its accuracy.
Science asks, "Is this true?" It doesn't ask, "How can we sell this?" That's not science, that's marketing.
(This problem is not just limited to social scientists. I think you could, for example, construct a plausible objection to dark matter as an "explanation" that just "saves appearances" on the same basis.)
What’s interesting about this paper is the suggestion that perhaps empiricism could do with a soft blur.
One might even invoke KJ Healy’s “Fuck Nuance” here as well.
Grounded theory is probabilistically correct. Deduction if correct, is actual reality.
Don't get me wrong, I want to love induction, I have William James of Pragmatism on my wall... but the problems with induction hurt me to my core. I know deduction has problems too, but the Platonic Realist in me loves the idea of magic truths.
I suspect that the 21st-century will continue to show better and more evidence for “mess” being the right cognitive container (or just garbage can à la James March). I don’t think induction will win but deduction will require more epicycles.
Use both?