The New Renaissance in Mathematical Science

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The New Renaissance in Mathematical Science
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Talking Seals
Tecumseh Fitch http//psy.st-andrews.ac.uk /people
/lect/wtsf.shtml
Partha Mitra http//www.cshl.org/ gradschool/mitra
_.html
Quantum Physics
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Mathematical Modelling
Story-telling with mathematics
Description Plot
Cannonball mass, speed direction
Newtons laws
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Mathematical Modeling
Story-telling with mathematics
Description Plot
Mathematical Metaphor
Physical Laws
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Physics
Limited remit allowed rapid progress
Simplicity/Linearity
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Linearity, Non-linearity, Chaos and Emergence
Linearity 1. Quantitative changes in
conditions lead to quantitative changes in
behaviour 2. The behaviour of the many is a
simple extrapolation of the behaviour of the few.
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Chaos
Small differences in initial conditions lead to
large differences in future motion
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Chaos
Examples

• Driven damped pendulum
• Double pendulum
• Planetary motion
• The weather

Small differences in initial conditions lead to
large differences in future motion
www.nationalsicencecenter.org/FortDiscovery/Roboti
cs/demos/ChaoticPendulumApplet.htm www.physics.ors
t.edu/rubin/nacphy/JAVA_pend/CHAOS/ www.maths.tcd
.ie/plynch/SwingingSpring/doublependulum.html Mat
h.fullerton.edu/mathews/n2003/pendulum/PendulumBib
/Links/PendulumBib_lnk_1.html
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Emergence
More is Different 1972
P.W. Anderson
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Emergence
More is Different 1972
The behaviour of large and complex aggregations
of elementary particles, it turns out, is not to
be understood in terms of a simple extrapolation
of the properties of few particles. Instead, at
each level of complexity entirely new
properties appear, and the understanding of the
new behaviours requires research which I think is
as fundamental in its Nature as any other
P.W. Anderson
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Bob Laughlin
A Different Universe
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Complicated Stories
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Economics
Concrete Metaphor money can be counted!
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Economics
Concrete Metaphor money can be counted!
www.microscopy-uk.org.uk/ dww/home/homebrown.htm
www.federalreserve.gov
Stocks maths worked out by Bachelier
1900 Brownian Motion maths worked out by
Einstein 1905
Economics is fundamentally non-linear.
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Ecology
Concrete Metaphor animals can be counted!
Ecology is fundamentally non-linear.
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Ecology
Concrete Metaphor animals can be counted!
predators
prey
Ecology is fundamentally non-linear.
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Complicated Metaphors
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Computers and the Construction of Mathematical
Metaphor
Mathematical metaphor for beauty
http//perception.st-and.ac.uk/
and apparent intelligence,
and apparent drunkenness
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Complicated World
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Game Theory
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Game Theory
Enormous Successes Social Dynamics in man and
animals Auction of bandwidth, mobile
phones Critical Mass Philip Ball
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Game Theory
The Subtlety of Game Theory

• Relation to world delicate
• Mathematical metaphors not
• that concrete
• Nature of mathematical modelling
• Mimic or Description?

Critical Mass Philip Ball
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Neuroscience and the Relation of Models to the
Real World
Mus silicium (sonoran desert sand mouse)
http//neuron.princeton.edu/ moment/Organism/inde
x.html
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The New Renaissance in Mathematical Science
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Game Theory
Cellular Phones
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Game Theory
Cellular Phones
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Game Theory
Cellular Phones

• Distribute Phone Users to Masts
• Game Theory
• Queuing Theory
• Statistical Mechanics
• (same as spin glass!)
• Same problems in internet etc

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New Renaissance in Mathematical Science?
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