On the Shoulders of Eastern Giants

The Forgotten Contribution of Medieval Physicists

On the Shoulders of Eastern Giants

The Forgotten Contribution of Medieval Physicists

Jim Al-Khalili

Department of Physics, University of Surrey

Jim Al-Khalili

Department of Physics, University of Surrey

A General Interest Seminar at the University of EdinburghDepartment of Physics and Astronomy 10 May 2012

Nathaniel Schmidt, Ibn Khaldun: Historian, Sociologist and Philosopher (New York: AMS Press, Inc., 1967)

Source: Jacob Lassner, Journal of the Economic and Social History of the Orient, Vol. 9, (1966) p.1

Oil painting Julius Koeckert (1827-1918), dated 1864, Maximilianeum Foundation, Munich

Abbasid Caliph Harun al-Rashid and king Charlemagne

Al-Mamun built a new academy:

Bayt al-Hikma

“The House of Wisdom”

6

Indian numerals

179.685

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x +x

10+

x +x

1010

+x +

x

10+

x +x

1010

10= x ⋅

11

10 ⎛ ⎝

⎞ ⎠

3

In this case, x = 135In this case, x = 135

Al-Khwarizmi (c.780 – 850 CE)

The father of algebra.

The Babylonians and early algebra

A typical problem might have been:Find the number if, when added to its

reciprocal, equals a known number.

This is an example of a quadratic equation:

Solved using ‘formula method’ we all learn at school.

But this is not what we regard as real algebra. They did not regard

the unknown (x) as an object in itself, but merely solved specific

problems (instead of developing general algebraic rules).9

Diophantus, wrote Arithmetica and pioneered class of equations involving two or more unknown quantities raised to any power, such that solutions always integers (Diophantine

equations)

Brahmagupta studied particular Diophantine equation –the ‘Pell equation’, which has the general form

10

Algebra or number theory?Algebra or number theory?

He posed the challenge of finding a solution if a =92.

He suggested that anyone who could solve this problem within a year earned the right to be called a mathematician.

Today, this is easy. We have computers!!

Al-Biruni (973–1048)

Persian polymath, regarded as the Da Vinci of the medieval world.

First Biruni measured the

height of a mountain (in

Pakistan)

He then climbed to the top of the mountain and measured the angle of dip to the horizon.

Φ

Φ RR+h

If we know h and Φ then we can find R.

Origin of ‘sine’

Robert of Chester in 12th century gave us the word sine, but how did we get this from the Hindus?

Etymologically, we must begin with the Sanskrit word jya-ardha, which means ‘half the bowstring’(or, geometrically, half the chord of a circle).

Jya-ardha abbreviated to jiva,

transliterated in Arabic as jiba.

When translated to Latin, mistaken to say jayb (‘pocket’).

Latin for pocket is sinus

Hence sine.

Span of two thousand years

Archimedes 3rd c. BCE

Ibn al-Haytham 11th century Isaac Newton

17th century

Greatest Physicists in History

Alhazen’s problemIn optics.

Requires a quartic equation

Solution using conical sections

Latinized first name of ibn al-Haytham: Al-Hassan

Conic Sections

From Ibn Sahl’s On The Burning Instruments (984 AD)

Six centuries before Willebrord Snell wrote down his law of refraction

Was Copernicus first to propose heliocentric model?

No, first proposed by Greek philosopher, Aristarchus (3rd c. BCE); No one believed him (apart from a lone Babylonian called Seleucus );

But, like them, he was just guessing!

Indian astronomers proposed heliocentric modelArab astronomer al-Sijzi (c. 945-1020) also proposed

heliocentric model and was supported by al-Biruni.

Just like these earlier astronomers, Copernicus was

courageous…

Archimedes, wrote: "You know that most astronomers designate by the word cosmos the sphere whose centre coincides with the centre of the earth... But Artistarchus … assumes that the fixed stars and the sun remain stationary, while the earth moves round the sun through the circumference of a circle.”

Archimedes, wrote: "You know that most astronomers designate by the word cosmos the sphere whose centre coincides with the centre of the earth... But Artistarchus … assumes that the fixed stars and the sun remain stationary, while the earth moves round the sun through the circumference of a circle.”

On the other hand, he did turn a philosophical idea into a fully predictive mathematical theory.

Copernicus (1543) Tusi (1261)

Galileo Galilei (1564-1642)

Ibn al-Haytham and Galileo on the frontispiece of Selenographia, a 1647 description of the moon by Johannes Hevelius

The theoretician and the experimentalist

Ibn al-Haytham can and should also be regarded as first person to define the ‘scientific method’:

“We should destinguish the properties of particulars, and

gather by induction what pertains to the eye to be uniform,

unchanging, manifest and not subject to doubt. After which

we should assend in our enquiry and reasoning, gradually

and orderly, criticizing premises and exercising caution in

regard to conclusions – our aim in all that we make subject

to inspection and review being to employ justice, not to

follow prejudice, and to take care in all that we judge and

criticize that we seek the truth and not be swayed by

opinion.”

Mathematical advances in Muslim world

continued into 15th century.

Jamshid al-Kashi (1380-1429) in Samarkand

• Calculated pi to 16 decimal places

• Gave us the ‘Cosine Rule’In France this is still known as théorème d’al-Kashi

a

b

cθ

When it comes to understanding our world through reason AND experimentation…

“The Greeks systematised, generalised and theorised, but the

patient ways of investigation, the accumulation of positive

knowledge, the minute methods of science, detailed and

prolonged observation and experimental enquiry, were altogether

alien to the Greeks’ temperament… What we call science arose in

Europe as a result of a new spirit of enquiry… of the methods of

experiment, observation and measurement, of the development of

mathematics in a form unknown to the Greeks. That spirit and

those methods were introduced into the European world by the

Arabs.”

Robert Briffault, The Making of Humanity (1930)