The Naming of Names by Anna Pavord: a book review

Some time ago, I read the beautifully illustrated The Naming of Names by Anna Pavord. This book tells the story of botany, beginning with the pioneering work by Theophrastus, the Vienna Dioscurides, and other works. The Naming of Names is gloriously adorned with botanical illustrations such as this:


Blackberry plant, from the Vienna Dioscurides (text is in Greek)

I also found Pavord’s book to be an enjoyable read, with interesting historical snippets (though, I think, a misunderstanding of Augustine), and quotations from ancient writers such as Theophrastus: “Other [plants] are found in fewer forms, as strykhnos which is a general name covering plants that are quite distinct; one is edible and like a cultivated plant, having a berry-like fruit, and there are two others, of which the one is said to induce sleep, the other to cause madness, or, if it is administered in a larger dose, death.” – Enquiry into Plants, Vol II, Book VII, Ch XV.

English Protestant preacher and botanist William Turner had this to say about the poisonous Oleander plant: “I have sene thys tre in diverse places of Italy but I care not if it never com into England, seying it in all poyntes is lyke a Pharesey, that is beuteus without, and within, a ravenus wolf and murderer.

Pavord takes her history up to Linnaeus, and his binomial naming system which finally gave standardised names to plants: Glycyrrhiza glabra, Allium sativum, and so forth.


Plants as they truly appear: “Das große Rasenstück” by Albrecht Dürer (1503)

Overall, an enjoyable book, although the illustrations are its greatest strength. It would be worth buying just for those. See also this review by Ursula Le Guin.


The Naming of Names by Anna Pavord: 3.5 stars

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The Monterey Bay Aquarium


Rear of the Aquarium (photo by “Meij.kobayashi,” public domain)

Continuing the museum theme, one of the world’s best aquaria is the Monterey Bay Aquarium in Monterey, California.


Kelp forest exhibit (photo by “Daderot,” public domain)

One of the highlights of the Aquarium is an 8.5 metre tall tank which houses a kelp forest exhibit.


Sea nettles (photo by “Omegacentrix”)

For those who cannot travel to Monterey, there are several live web cams providing views of some of the star exhibits.


The sea otters are among the most popular exhibits (photo by Fred Hsu)

National Museum of Natural History, Washington, D.C.


View of the National Museum of Natural History, photo by “Amanda”

Although I’ve never been to this museum in London, one of the places I have been fortunate enough to visit is the National Museum of Natural History in Washington, D.C.


The elephant in the Rotunda, my photo

This museum has a wonderful collection of items, and is very well-curated. Floor plans are online, as are some virtual exhibitions.


Photo by “Daderot,” public domain

This is certainly one of the world’s best science museums. And it’s free!

Shells

The study of shells leads to many wonderful images. This one, by H. Zell, is part of a gallery of shells on Wikimedia Commons. Udo Schmidt also has a great collection online.

…Building their beauty in three dimensions
Over which the world recedes away from us,
And in the fourth, that takes away ourselves
From moment to moment and from year to year
From first to last they remain in their continuous present.
The helix revolves like a timeless thought,
Instantaneous from apex to rim
Like a dance whose figure is limpet or murex,
cowrie or golden winkle…
” – Kathleen Jessie Raine

Why study mathematics?

Like John Allen Paulos, I am often asked why mathematics is worth studying. In his book A Mathematician Reads the Newspaper (Basic Books, 1995), Paulos gives an excellent answer:

As a mathematician, I’m often challenged to come up with compelling reasons to study mathematics. If the questioner is serious, I reply that there are three reasons or, more accurately, three broad classes of reasons to study mathematics. Only the first and most basic class is practical. It pertains to job skills and the needs of science and technology. The second concerns the understandings that are essential to an informed and effective citizenry. The last class of reasons involves considerations of curiosity, beauty, playfulness, perhaps even transcendence and wisdom.

The second and third answers are reflected in the words inscribed on the door of Plato’s Academy: “Let no one ignorant of geometry enter” (Ἀγεωμέτρητος μηδεὶς εἰσίτω):

ΑΓΕΩΜΕΤΡΗΤΟΣ ΜΗΔΕΙΣ ΕΙΣΙΤΩ

The first answer relates to the critical importance of mathematics in several fields of human endeavour, including science, engineering, medicine, and finance. For example:


A stressed ribbon bridge is strong if its shape is that of the mathematical curve called a catenary.


The spread of an infectious disease can be predicted by a set of three differential equations, relating three variables: S, I, and R (left). Real-world disease outbreaks show a similar pattern (right).

Many people list this as the only reason for studying mathematics, but it only applies to a minority of students – those keeping open the option of entering those fields. The second answer relates to the importance of mathematics in decision-making by ordinary citizens, and this applies to everybody. Some of those decisions by citizens require quantitative thinking. For example, which groceries are the best value for money? If two studies on 20 people report that a certain vegetable causes cancer, and one study on 1,000 people report that it doesn’t, is the vegetable safe? More subtly, training in mathematics helps in thinking clearly even about non-quantitative issues. Plato seemed to think that mathematics was essential training, and I would agree. Bertrand Russell put it this way: “One of the chief ends served by mathematics, when rightly taught, is to awaken the learner’s belief in reason, his confidence in the truth of what has been demonstrated, and in the value of demonstration.


What is the best value for money – the melons at $5 each, the grapes at $4 per kg, or the blueberries at $3 per punnet?


This classic book has applications to more than mathematics.

The third answer relates to a famous remark of Debussy – “La musique est une mathématique mystérieuse dont les éléments participent de l’infini” (“Music is a mysterious mathematics whose elements partake of the Infinite”). It works the other way around too. Mathematics is a mysterious and beautiful music that puts one in touch with the Infinite. As Plato would have said, mathematics reminds us that more things exist than just the finite and physical. This particularly applies to those parts of mathematics which relate to infinity, such as the number π, or the Mandelbrot set:

π = 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989 …
Some of the (infinitely many) digits of π.


The Mandelbrot set contains an infinite amount of detail (click for zoom animation).

Rudy Rucker’s little book The Fourth Dimension and How to Get There is also a great mind-stretcher. And, of course, having one’s mind stretched like that is a lot of fun.

Geometry 1900 years ago

Papyrus Oxyrhynchus 29 (not to be confused with New Testament Papyrus 29) is a papyrus from the Oxyrhynchus collection, containing the statement of Proposition 5 of Book 2 of Euclid’s Elements, with an accompanying diagram. In modern notation, the proposition is ab + (ab)2/4 = (a+b)2/4. Euclid states the proposition as follows (the first paragraph is on the papyrus):

If a straight line be cut into equal and unequal segments, then the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half.

PROOF: For let a straight line AB be cut into equal segments at C and into unequal segments at D; I say that the rectangle contained by AD, DB together with the square on CD is equal to the square on CB.

For let the square CEFB be described on CB, and let BE be joined; through D let DG be drawn parallel to either CE or BF, through H again let KM be drawn parallel to either AB or EF, and again through A let AK be drawn parallel to either CL or BM.

Then, since the complement CH is equal to the complement HF, let DM be added to each; therefore the whole CM is equal to the whole DF.

But CM is equal to AL, since AC is also equal to CB; therefore AL is also equal to DF. Let CH be added to each; therefore the whole AH is equal to the gnomon NOP.

But AH is the rectangle AD, DB, for DH is equal to DB, therefore the gnomon NOP is also equal to the rectangle AD, DB.

Let LG, which is equal to the square on CD, be added to each; therefore the gnomon NOP and LG are equal to the rectangle contained by AD, DB and the square on CD.

But the gnomon NOP and LG are the whole square CEFB, which is described on CB; therefore the rectangle contained by AD, DB together with the square on CD is equal to the square on CB. Therefore etc. Q. E. D.

The papyrus is in Greek capitals; in modern letters it reads like this:

Modern scholars date the fragment to AD 75–125. It is not of great quality, with poor handwriting, spelling errors (μετοξὺ for μεταξὺ, and τετραγώνου for τετραγώνῳ on the last line), and missing labels on the diagram (making it of limited use, and perhaps explaining why it was found in an ancient trash pile). However, unlike the New Testament with its hundreds of manuscripts, there is not much of Euclid before AD 900, which makes this fragment historically very significant. It contains one of the oldest extant Greek mathematical diagrams.

See more here.