The author of the Wikipedia entry also tells us - and I find this really interesting - that Plato's interest in the regular highly symmetrical solids that have come to bear his name was connected with his speculations about the nature of matter.

To wit:

Plato wrote about them in the dialogue Timaeus c.360 B.C. in which he associated each of the four classical elements (earth, air, water, and fire) with a regular solid. Earth was associated with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron. There was intuitive justification for these associations: the heat of fire feels sharp and stabbing (like little tetrahedra). Air is made of the octahedron; its minuscule components are so smooth that one can barely feel it. Water, the icosahedron, flows out of one's hand when picked up, as if it is made of tiny little balls. By contrast, a highly un-spherical solid, the hexahedron (cube) represents earth. These clumsy little solids cause dirt to crumble and breaks when picked up, in stark difference to the smooth flow of water. The fifth Platonic solid, the dodecahedron, Plato obscurely remarks, "...the god used for arranging the constellations on the whole heaven". Aristotle added a fifth element, aithêr (aether in Latin, "ether" in English) and postulated that the heavens were made of this element, but he had no interest in matching it with Plato's fifth solid.

Modern scientists of course, find the whole business of the "elements" being earth, wind, water, and fire rather quaint, but looking at the article one sees that actually the idea - given that nothing was understood about matter at the time - is in the best tradition of science.   It was an example of observing phenomena and then constructing a theory consistent with the observations.    A theory relying on observation - what Plato's speculations in fact were - may be proved wrong ultimately by other observations, experimental or otherwise, but the exercise in itself advances knowledge, which is, I guess, why Plato is still around:  His ideas mattered.

The more popularly applauded greek idea, the one that ultimately proved to be true, that matter was composed of atoms - the idea of the philosopher Democritus - was, to my knowledge at least, more mystical than observational.  The idea was not seriously connected with the actual properties of matter until at least the 18th century, beginning with the work of John Dalton and others.   The existence of atoms was not really incontrovertibly proved until Einstein proved it with his famous paper on Brownian motion in the early 20th century.  

Some of Democritus's ideas about matter, for instance the notion that atoms are immutable and everlasting, are simply false.   On the other hand, some of the ideas Plato discussed are still very important.    An example of the importance of Plato's ideas is that it turns out that geometry plays a central role in understanding matter, and the nature of platonic solids is critically involved.    The most important example of this case is what is called the "tetrahedral" nature of many, but not all, carbon compounds.    This tetrahedral symmetry is the subject of all introductory organic chemistry classes and is generally discussed in the very first meeting of the class.   The bonds of a molecule of methane all point to the corners of tetrahedron, and this fact, roughly approximated by many billions of organic carbon containing compounds, plays an vital role in understanding the chemistry of everything from life itself to the nature of diamonds to the properties of plastic toys.   Further many inorganic compounds exhibit cubic symmetry in their crystal shape, and many other inorganic compounds have octahedral symmetry.   These factors very much effect their properties.

Because symmetry - including the properties Platonic solids - plays such an important role in chemistry, research chemists have gone off on some esoteric quests involving it.    For instance, chemists have made a compound of carbon and hydrogen where all eight corners of a cube are occupied by carbon atoms.   The compound, unsurprisingly, is called "cubane."   It wasn't an easy trick.   Normally carbon, which again most often has its bonds directed at the corners of a tetrahedron, has a bond angle of 109.6 degrees.   In cubane of course, the angle must be 90 degrees.   The difference in the angle which chemists call "angle strain" gives rise to one of the few technological uses of cubane derivatives:   As an explosive.    Similarly chemists have tried, but failed, to make a compound called "tetrahedrane" where instead of being directed at the corners of the tetrahedron, the carbons are all  located at the corners of a tetrahedron.    This effort has lead to interesting innovations in chemistry and has helped the advance of the science, so on some level it's all been worth it but most people think that tetrahedrane will never be made - it will just blow up before it can be isolated.

This quest for the synthesis of highly symmetrical compounds in chemistry, which has theoretical utility as well as artistic/scientific implications  has been sort of in the news in the past.   In 1996 three chemists, Harold Kroto, Richard Smalley, and Robert Curl were awarded the Nobel Prize in Chemistry for their discovery of "buckminsterfullerene," dubbed by the media - along with all sorts of futuristic commentary about what technology they would cause to be developed - "buckyballs."   The compound is actually another allotrope - or form - of carbon, joining diamond and graphite which are also (ignoring impurities) pure carbon.    Buckyballs are not actually platonic solids - they have two different kinds of faces, hexagons and pentagons, whereas platonic solids have only one type of face.   Buckyballs represent a class of solids discovered by the man who may well have been the greatest scientist who ever lived - Archimedes.   They are known as truncated iscosohedrons, and they are very, very, very, very cool.

The synthesis of "buckyballs" was a rather elaborate quest, and involved all sorts of esoterica, things called pericyclic reactions, thermal vs photochemical rearrangements, metathesis reactions, condensations of corannulenes, blah, blah, blah.    Their were lots of failures in this quest, and probably a lot of graduate students who had to punt.   The actual discovery of buckyballs however was not actually deliberate, it was a sort of serendipitous thing that nonetheless involved elaborate instrumentation.   The discovery resulted molecular beam experiments that were not explicitly related to "buckyballs."   The scientists who discovered them were trying to do something else, and then they noticed them.   It was good that they were skilled at recognizing things, and they were justly awarded prizes and honors.

People all over the world began to study "buckyballs" and characterize their chemistry, their derivatives and their properties.  Once people learned all about these things an interesting thing happened:

People discovered that people had been making buckyballs all the time, for many thousands of years.   People had been making buckyballs before anybody knew about atomic theory, or chemistry, or the scientific method, or even about writing.

Almost all of the NNadir diary entries at DKos are about energy, usually about nuclear energy, and this one is too.   What does nuclear energy have to do with buckyballs?   I'll get to this in a minute, but first I'd like to refer to my most recent diary entries which were about  radioactive iodine and radioactive hydrogen, also known as tritium.   Over the years I've heard lots of comments from lots of people who want to tell me all about things like tritium and radioiodide.   Many people, even people with very low levels of scientific understanding, can get quite passionate about these subjects.  Routinely people curse me out for the ways in which I discuss matters like tritium and related subjects - which is almost wholly dismissive.   (For the record, there are some people who disagree with me who are scientifically sophisticated and very scientifically literate - and frankly often challenging - but 90% of the critical responses I receive to writings like this one are scientifically nonsensical.)

I'm on some kind of quest, I guess.   Many people try to assert that my quest is about money, or bribery or meaness or an inflated sense of intellectual superiority, but I claim it isn't.   I claim my quest to minimize the risks of nuclear energy is about something that has me very upset:  

Climate change.  

Whether or not I am telling lies about my motivations, I should admit that I may have very little impact.  It's not like the members of Greenpeace are going read my entries and suddenly send in their resignation letters to that silly organization.    Maybe my quest is as quixotic as trying to make buckyballs from pericyclic reactions or corranulenes.  

Let me be honest:  If you ask me whether I believe that nuclear energy will actually help to solve the vast problem of climate change, I would have to say "not really."   I believe it is now impossible to avoid very tragic consequences from climate change.   I don't believe that humanity will build enough nuclear reactors to control it.   it could, maybe, but it won't.    Moreover I believe that a great deal of the damage and tragedy related to climate change has already occurred, and a great deal more is in the immediate future and in the long term future inevitably.    In short, to put it more crudely, I think we're fucked.   On the other hand, it is my strongly felt opinion that nuclear energy is the best shot we have at mitigating any of the consequences.

So what do I find myself doing?   I find myself writing long elaborate diary entries about every damn constituent of nuclear fuel.   I must do this exhaustively, in great detail, trying to prove that trillionths of a gram of I-129 in thyroids around the world don't mean a hill of beans on the general scale of the massive problem of energy and energy waste.

So back to the buckyballs.   Yes, they are a form of carbon, and yes, carbon is an international problem of vast magnitude and yes people have been making buckyballs for thousands and thousands of years using very primitive technology.    

What is that primitive technology?   Burning things, that's what.

It turns out that buckyballs are a common constituent of soot, of lampblack.   Nobody realized this until they had made buckyballs in other ways.   Once they did, though, once they could recognize them, they found them all over the place.   They're one of the pollutants.

I certainly don't read the majority of diary entries at DKos and I am not familiar with everything that is written as this very fine website, whose value I appreciate greatly.   Still, I'm quite sure that very few people here have felt themselves compelled to write long articles here about soot, exhaustively describing the properties and risks of every single constituent.   I on the other hand will be writing long articles here about technetium and about cesium and about strontium and radioactive zirconium.   People will be very upset with me.   Some of them will secretly hope I die.   Even so, it turns out that people, even very sophisticated people who have been awarded the Nobel Prize for scientific achievement, still don't even know, in general, what soot is.   Nevertheless, billions of tons of coal, billions of tons of oil, billions of tons of biomass are burned every day, and the number of people who are calling for "soot phaseouts" with the same passion as people who are calling for "nuclear phaseouts," is vanishingly small.   There are even people who are now arguing that soot is a sort of a good thing, as poorly understood as it really is, since it helps mitigate the consequences or the other major consequence of burning things, the annual addition of billions of tons of carbon dioxide to the atmosphere.

This latter matter, carbon dioxide, has made us afraid of our own sun.  Believe it or not, we are now running around wondering to ourselves if we should try to block out the sun.