02 May 2016

If you hadn't noticed last time I wrote about my reading, I enjoy reading old books, and books about old things.  One of the interesting, to me, things about math/science/engineering is that it is incremental.  Each generation builds on what the preceding generations learned or accomplished.  Related truth is that I can read some of the best work from all people, across all of time.  Books are my time machine.

Richard J. Gillings, Mathematics in the Time of the Pharoahs, Dover Books.

Ed. T. L. Heath, The Works of Archimedes, Dover Books.

Tacitus, The Agricola and the Germania, Penguin Classics.

Craig Martin, Renaissance Meteorology: Pomponazzi to Descartes, Johns Hopkins University Press.

A. S. Kompaneyets, Theoretical Physics, Dover Books.

Michael W. Shaw, Kids and Teachers, Tardigrade Science Project Book, Fresh Squeezed Publishing.

A few thoughts.  One is, I do like Dover books (www.doverpublications.com).  In keeping with my interests across all time and topic, Dover re-publishes books across time and topic.  Also, they make relatively inexpensive editions, which makes my wallet happy.  They also have many other types of publication, including crafts, children's books, literary classics, coloring books, and others.  Alas, I don't get commission.  I'm sure that's an oversight on their part.

Math in the Time of the Pharoahs, well, mathematicians 3000+ years ago were quite good.  I'm not surprised myself.  The pyramids, and, more so, the kingdom's accounting and surveying, required a significant knowledge of mathematics.  In Gillings' book, you get a view of the work the ancient Egyptian mathematicians did, and how they did it.  People who aren't fond of fractions might appreciate the Egyptian solution to their existence -- have to have fractions, but all (except 2/3) fractions are written as 1 over something.  You then deal with fractions by way of some tables on how to add, for example, 1/3 plus 1/6 (which is the special 2/3).

More significantly, the conception of proof was different then versus today, or with the classical Greeks (call it 1000-2000 years more recent, something like 400 BC).  This is something to spend some time appreciating.  When I was a college Freshman, I laughed some at a course a friend was taking, titled something like 'standards of proof in mathematics'.  But then he explained how this gets to be a challenging mathematical and philosophical issue.  Does the fact that the Egyptians of ca. 2000 BC had a different idea of what constituted a proof than the Greeks of 400 BC mean that they didn't 'really' 'prove' anything?  Some moderns seem to think so, but read the book.  I think Gillings makes a good case that the Egyptians were making solid proofs millennia before the Greeks.

Speaking, however, of the Greeks, one of the greatest of the classical Greek mathematicians, and of classical Greek scientists, was Archimedes of Syracuse.  In this book, you have a chance to see him executing his ideas in his own way.  It's a very different manner than you'd see similar topics addressed today, which is one of the challenges in reading him fairly.  But, it's well worth making the effort.  As you do, you'll see a truly inventive mind executing very creative mathematics.  One item I'll be taking up as an independent post is Archimedes' use of Eudoxus' method of exhaustion, or, as I'll take it, method of successive approximations.  In different vein, making proofs about three dimensional objects (spheres, cones, ...) using two dimensional methods.

Having written documents for things is rather a restriction.  Or at least insisting on it is.  One of the few sources on who was about in non-Roman Europe during the period of the Roman Empire is Tacitus.  You'll see some familiar names, but some fluidity in representation.  For the Romans, any of the non-Romans were 'Germania'.  You might want to translate that as Germans, but the Lithuanians (Fenni in Tacitus) aren't what we'd consider Germans.  Still, an insight to the historiography and knowledge of the time.  Neither are what we consider today.

In the Renaissance Meteorology, you have a chance to approach the questions and issues of what is meteorology and what would be evidence or proof about ideas regarding weather.  One of the crucial issues was, in the early period, since God is responsible for weather; what would be evidence against God?  This got solved, in time, by reframing the issue as one of what was evidence about the natural world (meaning the world as God allowed it to evolve in this very Christian western Europe).  Even then, weather being what it is, what kinds of things could be evidence, and how much could you trust them?

Last two books are far more modern, and wildly different.

In Theoretical Physics, you've got a nice summary of theoretical physics.  Interesting and comprehensive.  But you want to be comfortable with your multivariate calculus and partial differential equations.

The Tardigrade book is suitable for parents and children, as you might hope from the title.  I'm carrying out some of the experiments myself.  I currently have a Tardigrade farm on my desk.  Or is that Tardigrade herd?  Sloth?  Anyhow, some microphotographs might be showing up.  (Microscope attachment for phone cameras is a wonderful thing).

Alastair said...

Hi Bob,

I took your advice and read some original papers and books. Not only that, I have followed William Connolley's example and translated some (Swiss) French into English, viz. Chapter 35 of H-B de Saussure's "Travels in the Alps", and his letter to the Journal de Paris which can be found here: https://sites.google.com/site/saussureproject/

I've also read several Dover books including:
Chandrasekhar, S. Radiative Transfer. New York: Dover Publications Inc., 1960. http://archive.org/details/RadiativeTransfer which you recommended, but Spencer Weart says "It was too subtle and complex for meteorologists.(7)They mostly ignored the astrophysical literature and worked out their own shortcut methods, equations that they could reduce to a sequence of arithmetic exercises to get rough numerical results."
Menzel, Donald Howard. Selected Papers on the Transfer of Radiation. Dover Publications, 1966 which contains Schwarzschild's derivation of his equation of radiative transfer, which is still used in all models today. It also contains E. A. Milne's explanation of LTE.
Planck, Max. The Theory of Heat Radiation. Translated by Morton Masius. 2nd ed. New York: Dover Publications, Inc., 1959. https://www.gutenberg.org/files/40030/40030-pdf.pdf. which describes Kirchhoff's universal law, used by Schwarzschild and by Chandrasekhar, and how it needs a speck of carbon to make it work!

All very useful in my investigations into radiative transfer. Thank you.

Robert Grumbine said...

Thanks for the references Alastair. Looks good. I'll look forward to Saussure in translation.

Weart is more negative about meteorologists than warranted. It was from that community that I discovered Chandra in the first place, and that was 30 years ago.