On the Shoulders of
Eastern Giants
The Forgotten Contribution of
Medieval Physicists
Jim Al-Khalili
Department of Physics, University of Surrey
A General Interest Seminar at the University of Edinburgh
Department 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
Abbasid Caliph Harun al-Rashid and king Charlemagne
Oil painting Julius Koeckert (1827-1918), dated 1864, Maximilianeum Foundation, Munich
Al-Mamun built a new academy:
Bayt al-Hikma
“The House of Wisdom”
Indian numerals
6
x
x
x
10
3
x

x


x
11
10 
10
10  x   
x

10
10
10
10
x
In this case, x = 135

179.685
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
Algebra or number theory?
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
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!!
10
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
R+h
R
Φ
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.
Greatest Physicists in History
Archimedes
3rd
c. BCE
Ibn al-Haytham
11th century
Span of two thousand years
Isaac Newton
17th century
Alhazen’s problem
In optics.
Latinized first
name of ibn alHaytham:
Al-Hassan
Requires a quartic
equation
Solution using
conical sections
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 );
 Indian astronomers
heliocentric
model
Archimedes,
wrote:proposed
"You know
that most
 Arab astronomer
al-Sijzi (c.
also
proposed
astronomers
designate
by945-1020)
the word
cosmos
the
heliocentric model and was supported by al-Biruni.
sphere whose centre coincides with the centre of
the earth... But Artistarchus … assumes that the
Just like
these
astronomers,
Copernicus
fixed
stars
andearlier
the sun
remain stationary,
whilewas
courageous…
the
earth moves round the sun through the
circumference of a circle.”
But, like them, he was just guessing!
On the other hand, he did turn a philosophical
idea into a fully predictive mathematical theory.
Copernicus (1543)
Tusi (1261)
Galileo Galilei (1564-1642)
The theoretician and
the experimentalist
Ibn al-Haytham and
Galileo on the frontispiece
of Selenographia, a 1647
description of the moon by
Johannes Hevelius
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
a
c
θ
b
• Gave us the ‘Cosine Rule’
In France this is still known as théorème d’al-Kashi
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)