Comment by the__alchemist 17 hours ago
This is why I'm skeptical of theories like Wolfram's: It feels like an overfit based on this: It produces all sorts of known theories (special relativity, parts of QM, gravity etc), but doesn't make new testable predictions, or new fundamentals. When I see 10 predictions emerge from the theory, and they all happen to be ones we already known of... Overfit.
But that means we'd prefer whichever theory our species had landed on first. Basing our preference for a theory on that timing seems kind of arbitrary to me. If they're the same in other respects, I'd take a look at both sides to see if there are other compelling reasons to focus on one or the other, such as which is simpler. Of course if they make different predictions that'd be even better, time to get to testing :)
A positive example would be the periodic table - the pattern to the elements made sense, but also exposed 'holes' in the table which were later filled in as we discovered additional elements. Wolfram may be closer to inventing epicycles to explain orbits - which is interesing and technically challenging and probably tickles his mind, but doesn't actually generate new knowledge.
Not quite apples to apples tho because you have to take into consideration what was known at the time each theory was developed (the input), not just the output.
Theory A: fits 7 known predictions but also makes a not-yet-verified prediction
Theory B: fits 8 known predictions and offers no new ones
In this example wouldn't Theory A be better, because all else equal it is less likely the product of overfitting and required more insight and effort to discover? In other words, Theory A used a different process that we know has a higher likelihood of novel discovery.
(Maybe this is a restatement of the simplicity argument, in that Theory A requires fewer predictions to discover it, ergo it is simpler)
> requires fewer predictions to discover
I don’t think that is implied. It was discovered first, but that doesn’t mean it is necessarily simpler or required less data to discover. Take Newton/Leibniz calculus for example as a clear example of similar discovery time, leading to the same result but using different approaches. Leibniz started after Newton technically, and yet is the preferred way.
Especially if theory B is equivalent to theory A, then using it as a replacement for theory A seems perfectly fine (well as long as there are other benefits).
In some cases it might be pointless though from a scientific standpoint because the goal is “not-yet-known” predictions, but if viewed through a mathematical lens, then it seems like a valid area of study.
Maybe the process behind creating theory A is more generalisable towards future scientific discovery, but that would make the process worthwhile, not the theory.
Jonathan Gorard goes through a handful of testable predictions for the hypergraph stuff here: https://www.youtube.com/watch?v=XLtxXkugd5w
I don't know anything about Wolfram's theory, but one general way to address this is to compare the Akaike information criterion (or similar measures).
The metrics attempt to balance the ability of a model to fit data with the number of parameters required. For equally well-fitting models, they prefer the one with fewer params.
If Wolfram's theory fits as well but has fewer params, it should be preferred. I'm not sure if fewer "concepts" counts, but it's something to consider.