Posted in Numbers, Unquantified fragments of numbers

Is mathematics natural?

The Heretical Philosopher

While perusing the Uncommon Descent blog, I noticed a post

This seemed a strange thing to say.  It perhaps even involves what Gilbert Ryle would have called “a category mistake”.  Browsing through that post, I saw that it referred to an article in Aeon magazine

Clearly, professor Franklin and I have very different ways of looking at mathematics.  And that’s what I will be discussing in this post.

Mathematics and naturalism

Let’s start with that reference to “naturalism”.  Franklin adopts a philosophy that he describes as Aristotelian realism.  And it is in relation to that philosophy, that he makes his comment about naturalism.

Aristotelian realism stands in a difficult relationship with naturalism, the project of showing that all of the world and human knowledge…

View original post 1,318 more words

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Posted in Ancient Greece, Ethnobotany, Language, Music, Music History, Numbers, Uncategorized

CICADA: EveryWHere

Image of Molting cicada

The prototypes of strong sensation: blazing lights, red earth, blue sea, mauve twilight, the flake of gold buried in the black depths of the cypress; archaic tastes of wine and olive, ancients smells of dust, goat dung and thyme, immemorial sounds of cicada and rustic flute.

Please listen whilst you read:    http://www.youtube.com/watch?v=lR4iTS0Y5ro

θέλω λέγειν Ἀτρείδας,
θέλω δὲ Κάδμον ᾄδειν,
ἁ βάρβιτος δὲ χορδαῖς
Ἔρωτα μοῦνον ἠχεῖ.
ἤμειψα νεῦρα πρώην
καὶ τὴν λύρην ἅπασαν·
κἀγὼ μὲν ᾖδον ἄθλους
Ἡρακλέους· λύρη δὲ
Ἔρωτας ἀντεφώνει.
χαίροιτε λοιπὸν ἡμῖν,
ἥρωες· ἡ λύρη γὰρ
μόνους Ἔρωτας ᾄδει

I, too, wish to sing of heroic deeds
(about the Atreides, and about Kadmus),
but the lyre’s strings
can only produce sounds of love.
Recently, I changed the strings,
and then the lyre itself,
and tried to sing of the feats of Hercules,
but still the lyre kept singing songs of love.
So, fare well, you heroes!
because my lyre sings only songs of love.

and

Δαιμόνια Νύμφη – Δαίμονος

Δαίμονα κικλήσκω μεγάλαν ηγήτορα φρικτόν,
μειλίχιον Δία, παγγενέτην, βιοδώτορα θνητών,
Ζήνα μέγαν, πολύπλαγκτον, αλάστορα, παμβασιλήα,
πλουτοδότην, οπόταν γε βρυάζων οίκον εσέλθηι,
έμπαλι δέ τρύχοντα βίον θνητών πολυμόχθων:
εν σοί γάρ λύπης τε χαράς κληίδες οχούνται.
τοιγάρ τοι, μάκαρ, αγνέ

πολύστονα κήδε’ ελάσσας,
όσσα βιοφθορίην πέμπει κατά γαίαν άπασαν,
ένδοξον βιοτής γλυκερόν τέλος εσθλόν οπάζοις.

Latin transcription:

[Daimonos]

Daimona kiklisko megalan igitora frikton,
meilichion Dia, paggenetin, biodotora thniton,
Zina megan, polyplagkton, alastora, pambasilia,
ploytodotin, opotan ge bryazon oikon eselthii,
empali de trychonta bion thniton polymochthon:
en soi gar lypis te charas kliides ochoyntai.
toigar toi, makar, agne

polystona kide’ elassas,
ossa biofthoriin pempei kata gaian apasan,
endoxon biotis glykeron telos esthlon opazois.

[To the Daemon]

Thee, mighty-ruling, Dæmon dread, I call,
Mild Jove, life-giving, and the source of all:
Great Jove, much-wand’ring, terrible and strong,
To whom revenge and tortures dire belong.
Mankind from thee, in plenteous wealth abound,
When in their dwellings joyful thou art found;
Or pass thro’ life afflicted and distress’d,

The needful means of bliss by thee supprest.
‘Tis thine alone endu’d with boundless might,
To keep the keys of sorrow and delight.

 

ORIGIN

late Middle English: from Latin cicada, cicala.

The earliest explicit reference to the cicada occurs in one of the first works in all of Western literature – the Iliad of Homer, a long epic narrative of events which are set within the framework of the Trojan war. At one point the elders of the besieged city are described standing and conversing on the great fortification wall. The poet likens the old men to cicadas, perched in their trees and singing with voices that are described by the Greek adjective leirios. Now every dictionary of the ancient Greek language tells us that this adjective means “lily-like.” From one perspective that seems entirely plausible, for the adjective is presumed to have been formed from the noun leirion which means “lily”. (At least it does sometimes, though most Greek botanical nomenclature is rife with redundancies and inconsistencies.) And so virtually every translation of the Iliad and every learned annotation on the passage tells us that the cicadas to whom the old men are compared have “lily-like voices.”

 

To continue reading about this most fascinating insect please follow: http://www.insects.org/ced3/cicada_ancgrcult.html

 

Prime numbers and cicadas:

Mathematical Locusts

This may be hard to believe, but there’s a special class of numbers that influence many things in the modern world, including cryptography and the behavior of locusts. As to the first, a popular encryption scheme uses prime numbers to create a very good level of security (but one that may erode in the future because of a new kind of computer). As to the second, locusts aren’t mathematicians, but nature makes them pay attention to prime numbers anyway.

It is well-known that a certain kind of locust (actually a cicada) spends most of its time in hiding, only reappearing to mate every 13 or 17 years (13 years in the southern U.S., 17 years in the north). This reproductive pattern has been noted by many, but until recently no one understood why. Obviously by hiding so long, these cicadas sacrifice opportunities to eat and breed, which leads one to ask — what do they get in return?

To continue, follow: http://arachnoid.com/prime_numbers/index.html#Mathematical_Locusts

 

And Finally…

If you are really, really, really interested (glad you are reading up to this point ):

Emergence of Prime Numbers As the Result of Evolutionary Strategy:

http://www.cicadamania.com/cicadas/68/