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Models and reality
1. Models and reality
A model is an abstraction of reality.
Essentially, all models are wrong, but some are useful. George Box, Statistician.
The best material model of a cat is another, or preferably the same, cat. Norbert Wiener (and A. Rosenblueth).
A model is a useful fiction.
A
model is an abstraction of reality.
As a representation of reality, models are often used to answer or predict specific questions about that reality.
The purpose of data science, for example, is insight.
2. Models: simple
Here is a simple way to think about a model.
A
model is an abstract representation of the real world with a postulated
mapping between the real world and the model (and between the model and the real world).
3. Models: refined
Here is a more refined way to think about a model.
4. George Box
Essentially, all models are wrong, but some are useful. 1976, 1978. George Box, Statistician.
A model is a useful fiction.
5. Norbert Wiener
The best material model of a cat is another, or preferably the same, cat. Norbert Wiener (and A. Rosenblueth).
6. Mathematics and reality
Do whole numbers exist?
Do integer numbers exist?
Do real numbers exist?
Does infinity exist?
7. Infinite things
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe. Albert Einstein's (Physicist)
8. Reality
Albert Einstein (English): "
As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality". (Albert Einstein, 1879-1955).
Albert Einstein (German): "
Insofern sich die Sätze der Mathematik auf die Wirklichkeit beziehen, sind sie nict sicher, und insofern sie sicher sind, beziehen sie sich nicht auf die Wirklichkeit" (Albert Einstein, 1879-1955).
9. Map of the world
Is a one to one (1 to 1) model useful?
What would make a good 1 to 1 map of the world?
When the map (model) does not match the world (reality) what do you change?
Which of the following might you do?
Change the map to fit the reality of the world.
Change your understanding of the world to fit the map. That is, be willingly ignorant.
10. Implications of a model
A model is said to faithfully reflect the real world if implications of the model (usually derived via mathematical calculations), when mapped back into the real world, are a sufficient approximation of truth in the real world to be useful.
Models can be deceptive.
11. Day the universe changed
James Burke, science historian, did an interesting video series in the 1980's entitled "
The Day the Universe Changed: A Personal View by James Burke".
The title comes from the philosophical idea that the universe essentially only exists as you perceive it through what you know; therefore, if you change your perception of the universe with new knowledge, you have essentially changed the universe itself. Wikipedia,
http://en.wikipedia.org/wiki/The_Day_the_Universe_Changed
12. Average ocean depth
A model is a simplified representation of something (e.g., a reality).
Models can be deceptive. Take, for example, the depth of the ocean.
13. Average ocean depth
The average ocean depth is over
2 miles deep (
12,200 feet).
On a model globe, the oceans (and highest mountains) would be about the thickness of a piece of paper.
14. On the earth
To see this, consider the following calculations. On the earth:
12,000 feet ocean depth
--------------------------------- = 0.000284 (depth/diameter)
(5,280 feet/mile) * (8,000 miles)
15. On a globe
On a 12-inch globe, this thickness would be as follows.
0.000284 * 12 = 0.0034 inches
16. Ream of paper
Now consider a ream of paper and the thickness of 500 sheets of paper.
(1.5 inches/ream)
----------------- = 0.003 inches/sheet
(500 sheets/ream)
So on a model globe, the oceans (and highest mountains) would be about the thickness of a piece of paper.
17. Descriptive or predictive
Models can be classified as descriptive or predictive.
18. Descriptive models
To describe something is to talk about the attributes/properties of something.
A descriptive model is a model that talks about the attributes/properties of something.
Marketing models tend to be more descriptive than predictive.
19. Predictive models
To
predict something is to claim that something will happen before it actually happens.
If you predict and you are wrong, you lose credibility.
20. Predicting the future
A
predictive model is a model that can claim what will happen in that model before it actually happens.
The best way to predict the future is to invent it. Alan Kay (American computer scientist)
21. Assumptions
An assumption is something that is to be true for the desired conclusions to be drawn.
A predictive model should clearly state the assumptions under which the model correctly predicts what will happen.
Engineering models tend to be more predictive than just descriptive.
22. End of page
