Taxonomy of Theories in Theoretical Physics

[Auto-Didact]

It goes without saying that theoretical physics has over the years become overrun with countless distinct - yet sometimes curiously very similar - theories, in some cases even dozens of directly competing theories. Within the foundations things can get far worse once we start to run into different interpretations of the same theory, such as is the case with the interpretation of QM.

It would therefore be quite enlightening if there was some kind of taxonomic classification of the properties of the main fundamental objects of different theories within theoretical physics. This would enable both a better conceptual understanding of the theory itself as well as a relative comparison between theories and classes of theories. Currently used taxonomies like PACS and PhySH clearly don't seem to be sufficient for such a task.

Incidentally, it is often argued by physicists that group theory already provides us with such a classification scheme of theories based on their symmetry groups. Group theory as is however, as far as I can tell, is nowhere near sufficient for carrying out the above task; this shouldn't be surprising, seeing that classification of course isn't the main aim of group theory.

The problem with group theoretical taxonomies of physical theories is that they essentially presuppose that all theories in question share the same fundamental nature i.e. the fundamentality of the group; this while it seems to be obvious that physical theories in practice can fundamentally differ in much more subtle ways that aren't necessarily captured - or even fully capturable - by the group concept.

Those that insist that group theory can and must be used in this way, do not do so by reason and demonstration, but instead by order of fiat. Two other contenders which seem much more appropriate for carrying out the task of taxonomy of physical theories are network theory and category theory. Such a taxonomy, being non-static, would of course have to be updated at least every few years, therefore another very nice solution would be if AI could solve this problem for us like described here: https://arxiv.org/abs/1611.03890

In any case, seeming such a simple task which could teach us so much, I presume that such a project of creating a taxonomy of extant and stagnant/dead physical theories is already being undertaken by various institutes (such as the APS or the Royal Society), but a quick search turns up pretty much empty. Does anyone have any references for such a project being carried out?

 

[jedishrfu]

Its not clear that these groups such as the APS would be interested in doing this. Usually as one becomes proficient in one's field of research you are aware of past and current attempts for the problems of the field and can navigate through them accordingly.

I think any taxonomy might tend to confuse folks more than help them as they attempt to decide on a given theory's relevance to their work. This is why things get rediscovered after some thought is put into developing a new idea.

For physics theories in particular, the notation might be different, the mathematics might be different and in using the taxonomy you might be led astray.

I can only compare this to doing programming where I might search for how someone did an algorithm and find it in another language and so I try to use it as a template only to discover one its wrong or there's some specialized feature or api that is used that brings in so much more code that it might be better to simply start from scratch. I'm sure these same thought processes occur while investigating past and current theories.

 

[Auto-Didact]

Its not clear that these groups such as the APS would be interested in doing this. Usually as one becomes proficient in one's field of research you are aware of past and current attempts for the problems of the field and can navigate through them accordingly.

I don't doubt that at all. The same is true for example in clinical medicine, where those who have become proficient i.e. experts tend to make the exact point you are making. Luckily for everyone else, explicitly making such taxonomies eventually got forced down the experts' throats in favor of educational didactics and of course patient safety; there is a point to be made that any simple academic instrument capable of increasing the efficacy and efficiency of young researchers is in the favor of not wasting tax payer money, by actively challenging the band wagon effect.

I think any taxonomy might tend to confuse folks more than help them as they attempt to decide on a given theory's relevance to their work. This is why things get rediscovered after some thought is put into developing a new idea.

It could but it might also turn out different; I don't see why we have to choose. The amount of theories has become vast and in such cases a taxonomy is a natural choice to help make order out of chaos. Such a taxonomy has multiple purposes, e.g.

• for experts: a way to empirically ground folk wisdom (and folk theorems) among practitioners and so possibly transform them into new theories
• for all researchers: meant to clarify which kind of theory one has created, i.e. what is physically fundamental in the theory and what is merely mathematics (and vice versa), instead of merely relying on your own interpretation
• for funding instutions and administrators: demonstrate which branches of theories are extant, productive, stagnant and explicitly show in what way (which fields) they are productive, providing all kinds of new measures of the potency of a theory and of a theorist
• for students: an empirically based guide through the zoo of theories and how they relate to various research programmes, potentially also giving the student some more academic guidance such as clarify where they would want to go to do their degree

Finally, it should be made clear to non-experts that such a taxonomy is meant as a tool to help the researcher, not some kind of performance measure to which one must necessarily adhere.

 

[jedishrfu]

So are you trying to develop such a taxonomy?

I think in physics people knowledgeable of the subject would not want to waste time on it. Those that might want it don’t have the field knowledge to make it so or to properly train some AI to do it.

One other point is I don’t think there’s a large enough population of theories to even make this viable.

 

[jedishrfu]

Lastly, here's a video from the Domain of Science showing a taxonomy of fields:



One way this AI version of a taxonomy could be developed would be by using archive papers and journal papers. I've heard of folks wanting to do that sort of thing but then running into terms of use walls where the journals don't want their papers downloaded and stored in data warehouses for data mining exercises.

I think we've covered everything here and so I'll close the thread before we veer into philosophy or original research.

 

[Auto-Didact]

That map is a nice starting point for students, but hardly reflective of the extent of theory occurring in the practice of theoretical physics.

For physics theories in particular, the notation might be different, the mathematics might be different and in using the taxonomy you might be led astray.

One might, but this is easily pointed out and corrected, since which notation and which mathematics would all explicitly be described in the taxonomy; and as I said before a change of interpretation of the mathematics might naturally also lead to a new theory.

I can only compare this to doing programming where I might search for how someone did an algorithm and find it in another language and so I try to use it as a template only to discover one its wrong or there's some specialized feature or api that is used that brings in so much more code that it might be better to simply start from scratch. I'm sure these same thought processes occur while investigating past and current theories.

I agree, but more importantly, that statement is a testable hypothesis. To make your analogy with programming complete: it might benefit programmers in wasting less time if there already was a taxonomy (condensed into a handbook if you will) of each algorithm in each language listing all the ways in which the algorithm is better or worse in completing (a list of) specific tasks.

So are you trying to develop such a taxonomy?

On the contrary, I'm trying to avoid the task. I have some experience in doing this type of research: it is a real headache. I am therefore really hoping that someone else will do it or already has started doing something like this. From my experience, it isn't clear what the practical value is of AI this early in the scenario; usually AI is much more helpful after the human work has at least been carried out successfully.

I think in physics people knowledgeable of the subject would not want to waste time on it. Those that might want it don’t have the field knowledge to make it so or to properly train some AI to do it.

Of course, this would need to be done by a large highly interdisciplinary team (consisting of at the very least data scientists, linguists, cognitive researchers, sociologists, philosophers and historians of physics, and of course physicists and mathematicians) comprising a truly enormous research programme.

To actually carry such a project out to completion requires multiple lines of research being carried out: questionnaires, interviews, expert panels, textual analysis, conversation analysis all under the guidance of a data scientist who has preferably been trained in theoretical physics.

One other point is I don’t think there’s a large enough population of theories too even make this viable.

On the contrary, the population of theories is so vast that I'm thinking that the collection of theories in such a project would need to be limited to the 20th and 21st century theories first, before the researchers get swamped in data.

I also think it might be best to start from Newton and then work forward towards the present. The swamping in data definitely starts once we start to count abandoned or "dead" theories, and especially once we start counting interpretations as well; we of course have to count these as well.

For numerical comparison, the amount of theories in theoretical physics is much larger than the typical amount of conditions "belonging" to most single medical specialities (e.g. like Alzheimer belonging to neurology); just like single conditions, a single theory can express itself in a variety of ways. All of this development would need to be quantified and classified.

It is only after enough data has been collected, i.e. after each member of the expert panel of theorists and mathematical physicists decide (independently in successive randomized reliable runs) that the resulting data exhausts the body of theories in theoretical physics as a whole, that the next phase of research can begin.

This is where the actual analysis begins: identifying all the core recurring themes. I suspect that with a team of say 100 researchers working full time, that this part would still take at least five years to complete for a century worth of theories. And it is only after the analysis is done that the actual construction of the taxonomy can begin.
Therefore, I think such a project is definitely best left to large instutions like the Royal Society or the APS, or some novel instution.

 

[jedishrfu]

Thanks @Auto-Didact, I think we covered the idea and it’s attendant issues. Now we’ll just have to inspire someone to do the work or at least start it in a meaningful way.

Closing thread now.