Platon - Science topic

There is another issue of interest with your challenging question, Prof. Scott Mavers,

In crystal physics, we know about 1-fold, 2-fold, 3-fold 4-fold, and 6-fold symetries. But what about 5-fold symmetry?

n-fold refers to the way an axis is rotated to get the same structure (n = 1,2,3,4 or 6) please refer to * for a very pedagogical introduction, but n = 5? Well, n = 5 are the so-called quasicrystals widely mentioned, in such a case, Prof. Kepler tried the so-called Kepler’s Pentagon Tiling **

* https://www.tulane.edu/~sanelson/eens211/introsymmetry.htm

** https://www.pnas.org/content/93/25/14271

Best Regards.

Dear Professor James Doran ,

I thank you very much for your proposing this discussion.

It is not easy to give an answer: I think that the Timaeus is and will remain of interest for interpreting Plato's strategy, since in Timaeus many elements of Plato's vision of reality are exposed. Plato's positions can be interpreted as a beginning of an intelligent design assumption.

Dear Noor U Din Reshi

As for "magic numbers" there is a good paper https://www.researchgate.net/profile/Alexander_Schmidt7/publication/225876498_Concept_of_magic_number_clusters_as_a_new_approach_to_the_interpretation_of_unusual_kinetics_of_the_Heck_reaction_with_aryl_bromides/links/0046353361f888daf4000000/Concept-of-magic-number-clusters-as-a-new-approach-to-the-interpretation-of-unusual-kinetics-of-the-Heck-reaction-with-aryl-bromides.pdf

At the same time the crystal structure of Ruthenium is hexagonal close-packed (hcp) but in the above-mentioned paper presented the equations for number of atoms for cubic lattices.

Maybe it will be better to calculate the surface of nanoparticle and divide it on the surface of atom (π*r_{{Covalent radius}}²).

With kind regards,

Liliya

What issue re you pointing at? Convergence?

What a collection!

In inteligence tests you are supposed to see a pattern, not anything goes.

If the test is not good, perhaps we can interpret the pattern of a sequence in more than one way.

Rings instead of normed division algebra can be anything dimensional. Complex nos. just one example.

Try something like x+ty+ttz with ttt=1 or -1

or x+ty with tt=0 or 1

No norm here, just a determinant of a representation. Cannot divide by any nonzero element, but by most.

If you see the world as something constantly changing, you will be unable to to grasp the nature of things. Greek philosophers believe that time is a constant line of events. However this view is object-centered, meaning, that here we just take a look at the object and from this we try to say something about the history, present state and future. This is not a good idea and it tells us nothing about correlations and choices which have been made.

Events are rather like fields of influences. A plant only grows at daytime and when night comes the plant rests. When we only look at the plant we will never know why it grows. Likewise certain fields of influence allow growth, others do not. And other fields make it necessary to make changes.

In your own interest I would suggest to let the Greek view go and rather concentrade on a more Jewish view. The Greek view is outdated and also wrong in many ways. Heraklit was not able to grasp the deepth of the topic. Also did the available knowledge not allow him to translate his ideas into correct concepts sharp enough, but he stranded on the island he tried to build here up. The concept of wisdom goes way deeper (don't confuse it with the idea of wisdom like defined in a Greek way), but it needs to be studied extra. Lewin might be a good introduction, also he had problems too and was restricted. Then I also recommend to read the book of Proverbs and Ecclesiastes (especially chapter 3). They talk about time rather like states, comparing it to seasons.

We need a complete other language here to describe a different concept. For this we must go back to the roots and take a look at what we have missed.

Also watch this to get a feeling for the problem: https://www.youtube.com/watch?v=KSqyvvoHmAw

For an overview about the books watch this: https://www.youtube.com/watch?v=Gab04dPs_uA

Got it from: http://www.chem.gla.ac.uk/~louis/software/platon/

Interesting question as ever Gianrocco - and of course a full analysis would be very long, I'll just try and contribute a couple of thoughts.

First, I'd be very leery of 'usefulness' as a criterion. Very many arrantly wrong 'theories' have historically been very useful in serving a specific purpose (the belief in the godhood of the emperor heightening the fighting ability of kamikazes, for instance, and so on.)

Second - very many theories can actually be modeled mathematically, although we seldom realize this, and the truth tends to lie in the numbers. To model successfully of course we need to 1- establish the suitably of math within the given domain where modeling will be used to approach the truth and 2- we need to be very good at math modeling which can be sneakily difficult (the biggest traps being overlooked variables and unrecognized implicit assumptions and/or cognitive bias - a typical issue in economic modeling, for instance), but it's worth a try. If done properly, mathematical modeling can at the very least show whether a theory is self-consistent (if not, it's very likely wrong.) 

Sometimes, math modeling shows that an answer is in principle non existent, or some variable is a non-observable - which is very useful because it suggests that perhaps the question is hiding a deeper one which should be looked at instead. 

Most of the crystallographic questions posted here suggest that a lot of people think that to do structural crystallography one just needs a diffractometer and proper software. Sorry, but crystallography is a complex subject and without attending dedicated courses one never will be able to overcome the problems are met in crystallographic research.

Dear Ferenc Hörcher:

"On the whole I think Aristotle's practical philosophy makes sense only if distinguishable from his mater's one. However, I go with Gadamer, who claims that there are strong Platonic building blocks in this theory"

Of course, as soon as one wishes to determine the relationship between Aristotelian thought and Platonic philosophy, one runs immediately into two fundamental problems. The first is that each author seems to have left us diametrically opposed, or at least opposite, literature. For Aristotle, we have something akin to his lecture notes: material intended for the Academy and students. We lack the more formal composition that was "literature" vs. letters, mandates, court scripts (Antiphon's likely fictional oratory I'd count as literature, but in general prepared defenses that come down to us I wouldn't as they were not meant to be and were not considered to be).  For Plato, all we have is his literary works (and maybe a couple of letters admit the pseudepigrapha. Aristotle himself was one of the first to demarcate writings into genre and analyze the importance and nature of each category (περὶ ποιητικῆς αὐτῆς τε καὶ τῶν εἰδῶν αὐτῆς/”concerning literature both itself and the many forms it has…” Poetics 1447a). Plato not only dealt with genre but with the dangerous power literature and/or oral history/tradition had. I think that their recognition of genre as in some sense a medium both fixing and dictating the content of composition renders the distinctions between the 'kind of writing left to us by each all the more important when it comes to interpretation.

Then there's the Socratic problem. Whatever influences Plato had on Aristotle, Aristotle's works were his own. On the most superficial and inaccurate interpretation, Plato just repeated the teachings of Socrates. This is, I think, clearly wrong, but it is quite likely that Plato didn't just use Socrates as a mouthpiece, especially in his earlier works.

So we have Aristotle writing a different kind of literature for a different kind of audience, and the works of Plato which are not only literary (Aristotle was first tell us of τούς Σωκρατικούς λόγους as a genre of sorts), but also tied quite directly to what Socrates taught in ways that are impossible to wholly separate.

In short, I guess I would just agree that such a broad view of both philosophers' thought can't be of much help here. It is within the text and secondarily the corpus that we have our best chance of understanding the usage here. The problem then becomes partly a matter of the Greek language (not that Greek was or is alone here). In the Romance languages (even Latin itself to some extent) and English that we find (like the use of a numerical "alphabet" which differs from the written) a large influx and coining of technical terms using classical languages. One need look no further than German to see what a difference this can make. Greek is harder, as technically there weren't any technical words. Just technical contexts. 

You can additionally consult the manual for PLATON here: http://www.cryst.chem.uu.nl/platon/