qwafafew models behaving badly derman u 2011

7/17/2019 QWAFAFEW Models Behaving Badly Derman U 2011

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1

Emanuel Derman

Columbia UniversityPrisma Capital Partners

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2



3

The Trouble With Finance

!

The fundamental theorem of arithmetic: Every natural number greater than 1 can be written as a

unique product of prime numbers.

! The fundamental theorem of algebra: Every polynomial equation of degree n with complex

number coefficients has n complex roots.

! Economists don’t understand the difference between theorems and laws.

!

Economists have fallen in love with mathematics, rigor and formalism for their own sake,

irrespective of their efficacy. It’s not their fault that they can’t find better models; economics is a

social science and people are difficult to theorize about. It’s their fault that they don’t understand

the difference.



4

Metaphors!

“Sleep is the interest we have to pay on the capital which is called in at death; and the higher the

rate of interest and the more regularly it is paid, the further the date of redemption is postponed.”

- Arthur Schopenhauer

! Periodicity of sleep and coupons is the common element of the metaphor.

!

Metaphors are an insight that state that something is something else.

!

But metaphors also extend our understanding:

!

Analytic continuation of the factorial function.

!

Much of our knowledge is a layer of metaphors.

!

Metaphors and language build on our physical nature:

-

Elation/depression

-

Light/dark

5

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6

Why Is A Model A Model?

! A model is not the thing in itself: there is a gap between the model and the system.

-

It is a caricature.

- It focuses on parts.

- It is a metaphor with limited applicability.

- It is a fetish, and therefore attractively dangerous.

! Models transform consciously learned knowledge into unconscious visceral knowledge.

!

One must digest previous metaphors to move up the hierarchy to wider ones.

! Models are labor-saving devices, allow you to avoid thinking/working for yourself.

-

Feynman diagrams, like silicon chips, bring computation to the masses.

!

Models reduce dimensionality

!

Models extrapolate or interpolate

! Sometimes it’s time to make unconscious knowledge conscious again.



Why Is A Theory A Theory?

7

!

Models are analogies and relative. Theories are the real thing.

! A theory is the ultimate non-metaphor: I am that which I am.

!

Theories tell you what something is. Models tell you what something is more or less like.

!

The Dirac equation for the electron:

!

Maxwell’s Equations

!

Why is the Dirac equation a theory?

!

A theory provides non-metaphorical insight, deals in absolutes; hence often uses math.

!

Theories are deep, models are shallow. Nothing wrong with that.

!

A correct theory is almost indistinguishable from the world.

Feynman’s Nobel Prize Lecture:

Many different physical ideas can

describe the same physical reality.

Thus, classicalelectrodynamics can be described by

a field view, or an action at a

distance view, etc.

Originally, Maxwell filled space with

idler wheels, and Faraday with fields

lines, but

somehow the Maxwell equations

themselves are pristine and

independent of the

elaboration of words attempting a

physical description.



An Example: Spinoza’s Theory of Emotions …

8

! Spinoza’s treats emotions like Euclid treats geometry: emotions are derivatives.

-

Primitives are Desire, Pleasure, Pain.

! Good is everything that brings pleasure, and Evil is everything that brings pain.

! Love: Pleasure associated with an external object.

!

Hate: Pain associated with an external object.

!

Envy: Pain at another’s Pleasure.

! Hope: Expectation of future Pleasure tinged with doubt.

!

Fear: Expectation of future Pain.

!

Cruelty: Desire to inflict Pain on a someone Loved.

! Three more primitives:

-

Vacillation, Wonder, Contempt.

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Intuition

10

! It takes intuition to discover the nature of the world.

-

Kepler, Newton, Ampere, Maxwell.

!

Intuition may sound casual but it takes intimate knowledge of the world acquired by careful

observation and painstaking effort.

!

Keynes on Newton:

“I believe that the clue to his mind is to be found in his unusual powers of continuous concentrated

introspection! His peculiar gift was the power of holding continuously in his mind a purely

mental problem until he had seen straight through it.”

!

Maxwell on Ampére

“We can scarcely believe that Ampere really discovered the law of action by means of the experiments which hedescribes. We are led to suspect, what, indeed, he tells us himself, that he discovered the law by some process

which he has not shown us, and that when he had afterwards built up a perfect demonstration, he removed all

traces of the scaffolding by which he had built it.”

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18

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19

qwafafew models behaving badly derman u 2011

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