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Duality principles
1. Duality principles
2. Duality principles
There are areas of study where there is more than one way to view things.
In ancient China, the yin and yang symbol represents a philosophy of how opposite ideas may be complementary or in some way connected.
The literal meaning of the Chinese symbol for yin yang is "
陰陽" and is composed of "
dark light"..
Some of the same ideas or found in the writings of Greek philosophers including Aristotle.
A modern expression of this idea is a duality principle.
3. Perspective
Alan Kay (American computer scientist) . Talk at Creative Think seminar, 20 July 1982.
A change in perspective is worth 80 IQ points.
Perspective is worth 80 IQ points.
Point of view is worth 80 IQ points
Kay uses the example of solving problems using polar coordinates rather than Cartesian coordinates. Each works better in certain circumstances. Kay developed (invented) object-oriented and user interface ideas that changed computer science and led to the modern window interface with icons, the mouse, etc.
Principles of duality in many fields allow the same problem to be addressed from two seemingly different points of view.
4. Duality in computation
There are two ways of looking at computation.
Operational view: Turing machine - how computation works (bottom-up view)
Declarative view: Church lambda calculus - what computation does mathematically/functionally (top-down view)
The good computer scientist needs to understand both views and how to switch between them as needed.
5. Colors and color models
Two ways of looking at colors: (Note: there are other useful color models)
RGB additive model (light, added to black/screen)
(black) + red + green + blue = white
CMYK subtractive model (pigments, print, subtracted from white/paper)
(white) - cyan - magenta - yellow = black
Each model is correct. In many cases, one way may be easier to work with or use than the other model.
6. Views of the same thing
Glass half-empty or half-full
Type 1 and type 2 errors in statistics
7. Wave particle duality in physics
There are two correct ways of looking at physics:
wave model
particle model
Heisenberg Uncertainty Principle applies. A good physicist needs to know and use either.
8. Different views of the same thing
Trinitarianism and Modalism
9. Duality in statistics
Statistics has two correct ways of looking at reality. Both are correct. One may work better in a given situation.
Frequentist statistics (null hypothesis, confidence intervals, etc.)
Bayesian statistics (inverse probability, probability of causes, etc.)
Many statisticians disagree over both frequentist and Bayesian statistics being correct ways of looking at reality.
10. Problem solving
In problem solving, a top-down design approach can be contrasted with a bottom-up design approach.
11. Counting
Six of one
Half dozen of the other.
12. Bubbles
In beer, one can see bubbles going up or beer going down.
13. Heat and cold
In temperature as a measure of energy, one can feel heat going out or in or could going out or in.
14. Electricity
Electricity can be viewed as electrons going one way or holes (no electron) going the other way.
15. Longest common subsequence
|
nematode-knowledge
empty-bottle
emt-ole
|
The
LCS = Longest Common Subsequence problem is a dual problem of the
SED = Shortest Edit Distance problem.
The solution to these problems are used in open source file comparison tools such as WinMerge and DiffMerge.
In 1974, Hirschberg published a reasonably space and time efficient solution to these problems.
16. Colors and color models
Two ways of looking at colors: (Note: there are other useful color models)
RGB additive model (light, added to black/screen)
(black) + red + green + blue = white
CMYK subtractive model (pigments, print, subtracted from white/paper)
(white) - cyan - magenta - yellow = black
Each model is correct. In many cases, one way may be easier to work with or use than the other model.
17. Wave particle duality in physics
There are two correct ways of looking at physics:
wave model
particle model
Heisenberg Uncertainty Principle applies. A good physicist needs to know and use either.
18. Statistics
Two ways of looking at statistics:
frequentist model (human use for static decisions due to historical factors)
Bayesian model (computer use for dynamic decisions due to it works)
Each model is correct. In many cases, one way may be easier to work with or use than the other model.
19. The Art of Statistics
The good news is that the Bayesian approach opens fine new possibilities for making the most of complex data. The bad news is that it means putting aside almost everything you may have learned in this book and elsewhere about estimation, confidence intervals, P-values, hypothesis testing, and so on. David Spiegelhalter,
The Art of Statistics: How To Learn From Data (p. 305)
Note: This comment is made on page 305 of a very interesting and popular book on statistics.
20. Business
The Bayesian approach is used, behind the scenes, by many top companies.
Those top companies do not talk about it much.
It is a competitive advantage, so, as someone once said (I have heard this from several people in different industries about cutting-edge techniques), If they tell you about it, it means that they are not using it any more.
... more to be added ...
21. End of page
