Why do we need statistics

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Why do we need statistics?
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If the world is deterministic

• We will have equations describing everything from
  now onward

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For example
Juliet is in love with Romeo. But in this version
of the story, Romeo is a fickle lover. The more
Juliet loves him, the more he begins to dislike
her. But when she losed interest, his feelings
for her warm up. She, on the other hand, tends to
echo him her love grows when he loves her, and
turns to hate him when he hates her. How to model
this love affair?
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See Matlab result. Read the article by Stephen
Strogatz (1988).
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However, in nature

• Non-linear equations are abundant.

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Lorenz equation
See http//www.wam.umd.edu/petersd/lorenz.html Re
ad Ruelles description.
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The butterfly effect
Lorenz, E.N. Deterministic nonperiodic flow, J.
Atmospheric Sci. 20, 130-141, 1963
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This happens everywhere
The above are from http//hypertextbook.com/chaos/
21.shtml
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Even in biological systems and no doubt in the
stock market too
Sensitivity to initial conditions in the
Bak-Sneppen model of biological evolution F.A.
Tamarit1 - S.A. Cannas1 - C. Tsallis1,2 1
Facultad de Matemática, Astronomía y Física,
Universidad Nacional de Córdoba, Ciudad
Universitaria, 5000 Córdoba, Argentina 2
Departamento de Fisica, Universidade Federal do
Rio Grande do Norte, 59072-970 Natal-RN,
Brazil Received 5 November 1997 / Received in
final form 11 November 1997 / Accepted 19
November 1997 Abstract We consider biological
evolution as described within the Bak and Sneppen
1993 model. We exhibit, at the self-organized
critical state, a power-law sensitivity to the
initial conditions, calculate the associated
exponent, and relate it to the recently
introduced nonextensive thermostatistics. The
scenario which here emerges without tuning
strongly reminds of that of the tuned onset of
chaos in say logistic-like one-dimensional maps.
We also calculate the dynamical exponent z.
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Strange attractors

• Sensitive to initial condition
• Solution is strongly influenced by perturbations
• http//www.exploratorium.edu/complexity/java/loren
  z.html
• However, there is an underlying structure

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While we wait for the math to develop for the
underlying structure..
We rely on statistics to describe the
inter-relation between the observations.