These three questions are phrased as alternative-history questions, but my real

Question

These three questions are phrased as alternative-history questions, but my real intent is to understand better how well different modeling approaches fit the phenomena they are used to describe; see 1 below for more discussion of that point.

Short "informed opinion" answers are fine (better, actually).

If Dmitri Mendeleev had had access to and a full understanding of modern group theory, could have plausibly structured the periodic table of chemistry in terms of group theory, as opposed to the simpler data-driven tabular format that he actually used?

If Mendeleev really had created a group-theory-based Periodic Table, would it have provided any specific insights, e.g. perhaps early insights into quantum theory?

The inverse question: If Murray Gell-Mann and others had not used group theory concepts such as SU(3) to organize particles into families, and had instead relied on simple grouping and graphical organization methods more akin to those of Mendeleev, is there any significant chance they could have succeeded? Or less speculatively, is it possible to create useful, concise, and accurate organizational structures (presumably quark based) that fully explain the particle data of the 1970s without making any reference to algebraic structures?

1 Background: My perspective on the above questions is to understand the interplay between expressive power and noise in real theory structures. One way to explain that is to note that mathematical modeling of data sets has certain strong (and deep) similarities to the concept of data compression.

On the positive side, a good theory and a good compression both manage to express all of the known data by using only a much smaller number of formula (characters). On the negative side, even very good compressions can go a astray by adding "artifacts," that is, details that are not in the original data, and which therefore constitute a form of noise. Similarly, theories can also add "artifacts" or details not in the original data set.

The table-style periodic table and SU(3) represent two extremes of representation style. The table format of the periodic table would seem to have low expressive power and low precision, whereas SU(3) has high representational power and precision. The asymmetric and ultimately misleading emphasis on strangeness in the original Eight-Fold Way is an explicit example of an artifact introduced by that higher power. We now know that strangeness is just a fragment -- the first "down quark" parallel -- of the three-generations issue, and that strangeness showed up first only because it was more easily accessible by the particle accelerators of that time.

Explanation / Answer

No, the elements of the periodic table don't form any representation of a group or, more precisely, any irreducible representation. Even more precisely, the real insights by Mendeleev

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.