A Failure of Inspiration and Knowledge

• Imperial Rome.

• The Middle Ages.

• Science in the East.

• Beginning of science in the West.

1

“... men go on to search out the hidden

powers of nature ..., which to know profits

not, and wherein men desire nothing but

knowledge. ... nor care I to know the

courses of stars ...; all sacrilegious mysteries

I detest.”

St. Augustine of Hippo (354-430).

Confessions X, XXXV, 55 and 56.

2

The Crusader attack on Constantinople,

from a Venetian manuscript of Geoffreoy

de Villehardouin’s history, ca 1330.

3

De rerum natura by Lucretius (ca 95-55

BCE). This manuscript was copied by an

Augustinian friar for Pope Sixtus IV in 1483.

4

This is not what I mean by a portable

sundial!

5

“Those impostors then, whom they style

mathematicians, I consulted without

scruple; because they seemed to use no

sacrifice, nor to pray to any spirit for their

divinations; which art, however, Christian

and true piety consistently rejects and

condemns.”

St. Augustine of Hippo (354-430).

Confessions, IV, XXX, 4.

6

12th century copy of Gerbert’s De geometria.

7

15th century European portrait of

Geber (721-815). Born Abu Musa

Jabir ibn Hayyan.

8

Brahmi numerals.

1 2 3 4 5 6 7 8 9

10 20 30 40 50 60 70 80 90

100 200 500 1,000 4,000 70,000

9

The first ten Indian or Gwalior numerals

appeared sometime(?) around 800 and

included zero.

1 2 3 4 5 6 7 8 9 0

10

From a tablet in the temple at Gwalior.

50

270

11

1 2 3 4 5 6 7 8 9 0

The first ten East Arabic numerals included

a zero.

The first nine West Arabic or Gobar

numerals. Gobar numerals first appeared in

Europe around 976 in the Codex Vigilanus.

The first ten Indian or Gwalior numerals.

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9 0

12

Clock on the Cairo Metro

Modern-day Arab

telephone keypad

with two forms of

numerals; European

and East Arabic.

13

Page from the Latin translation begins ...

Dixit algorizmi

(“So says Algorizmi ...”)

14

Al-Khwarizmi’s book, al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala (Calculation

by Completion and Balancing) was written in

830. In 1145 it was translated into Latin with

the title Liber algebrae et almucabala, later

abbreviated to simply ‘algebra’.

15

Gobar numerals appeared in a few documents

in the 10th century; for example, in the

Codex Vigilanus in the year 976. It was

commemorated in a Spanish stamp in 2006.

16

A page from Fibonacci’s Liber Abaci ,published in 1202.

17

Al-Battani (ca 853-929):

• Determination of the length of the solar year.

• Discovered the direction of the Sun’s eccentric was changing.

• Catalogued the positions of 489 stars.

• Determined the inclination of the Earth’s axis to be 23! 3 ! 5 and that it took23,600 years to complete a precession.

• Introduced the trignometric sinefunction and developed equations for calculating tangents and cotangents.

18

ibn al-Haytham (965-ca 1040), as pictured on an Iraqi 10,000-dinar note. His Latinized name was Alhazen. His most notable work was a 7-volume treatise on optics, Kitab al-Manazir (Book on Optics), written between 1011 and 1021.

19

A beam of light from a source (on the left)

is directed into a glass block. The light is

‘bent’, i.e., refracted, as it enters the block.

It is also ‘bent’ when it exits the block but

in the opposite direction. The emerging

beam is parallel to the incoming beam.

20

Camera obscura

Using different colored lamps Alhazen

concluded light travels in straight lines,

explaining how a camera obscura worked.

images sources

small hole

21

A possible likeness of Hamid al-Ghazali (ca 1058-1111). He wrote more than 70 books

on science and Islamic philosophy. His

book, Tahafut-Al-Falasifah (The Incoherence

of the Philosophers), marked a turning point

in Islamic philosophy through its vehement

rejections of Aristotle and Plato.

22

Statue of Roger Bacon (ca 1214-1294) in the Oxford University Museum of Natural History.

23

Refraction of light by a spherical glass

container full of water. From the Opus Majus

(Greater Work) by Roger Bacon, a 840-page

treatise sent to Pope Clement IV in 1267.

24

“Bar charts” from Tractatus de latitudinibus

formarum by Nicole Oresme (ca 1323-1382).

25

Left: Figure 49 from Dialogues concerning

the Two New Sciences by Galileo, 1638; the

Third Day.

Right: More familiar “modern” graph of the

same data.

Time

Speed

26

The earliest known 2-dimensional chart

showing changes in latitude (vertically) and

time (horizontally) of the Sun, Moon and

planets. The scribe used the horizontal and

vertical lines as aids, i.e., they are not a true

scale in the sense we know today. From MS

Munich 14436, an 11th century manuscipt.

27