Archive for the ‘Pattern Recognition’ Category

Humans are relatively good at induction and relatively poor at deduction; computers are just the opposite

December 21, 2007

Induction is reasoning from a limited number of observations toward a general conclusion. A classic example: After observing that 2 or 10 or 1,000 ravens are black, you may decide that all ravens are black.

Another way of thinking about induction is that it is reasoning by pattern recognition – we fill in the gaps of missing information.

With deduction you start with a set of possibilities and reduce it until a smaller subset remains. For example, a murder mystery is an exercise in deduction. Typically, the detective begins with a set of possible suspects — the butler, the maid, the business partner, and the widow. By the end of the story he has reduced this set to only one person: “The victim died in the bathtub but was moved to the bed. Neither woman could have lifted the body, nor could the butler with his war wound. Therefore, the business partner must have committed the crime.”

Humans are relatively good at induction and relatively poor at deduction. Any of us is capable of instantly recognizing a face (an inductive task), yet most of us would have a tough time quickly doing the deductive calculation:

(239.46 x 0.48 + 6.03) / 120.9708

Computers are relatively poor at induction and relatively good at deduction. A simple pocket calculator can quickly and perfectly do the calculation, while it is a very hard programming challenge to get even a powerful computer to accurately recognize a face.

The Origin of Wealth by Eric D. Beinhocker and Logic for Dummies by Mark Zegarelli

Similarity is not Sameness … Dangers of Misused Metaphors

August 15, 2007

“Human beings are skilled pattern recognizers and use metaphors to help them understand and reason about the world. Saying that something resembles or has qualities of something else enables us to quickly, and in just a few words, grasp the essence of a complex phenomena. Shakespeare could have given us a long passage about how Juliet was central to Romeo’s life, brought him happiness, and so on. Instead, with the simple phrase “Juliet is the sun!” Shakespeare conveyed those meanings in a far richer and more powerful way.

Science uses metaphor as well, both to inspire creativity and to help communicate complex ideas. For example, the metaphor of tiny, vibrating loops of string has helped inspire the physicists who are developing string theory (an attempt to unify the fundamental forces of the universe and explain the origins of subatomic particles) to think in radically different ways from their predecessors. Likewise, the phrase loops of string helps metaphorically communicate the key ideas of string theory to a lay audience more easily than does “eleven-dimensional Calabi-Yau space.”

But while the metaphor is useful in inspiring and communicating science, science itself is based on more than metaphor. Scientific theories do not merely make claims that one thing resembles another. Scientists make claims that something literally is a member of a universal class of phenomena.

Similarity is not sameness. When a cosmologist says our sun is a star, the scientist doesn’t just mean it is similar in some way to a star. Rather, our sun is a member of a universal class of phenomena, which are called stars, which share certain empirically observable characteristics.

When you see a similarity of one idea to another you may be inspired to use the tools and techniques from one field in another. Danger! Is the similarity a metaphor or science? That is, does the one idea genuinely share the same properties as the other, or is there merely a superficial similarity? If there is merely a superficial similarity but you treat it as the same then you are headed for erroneous results.

Example: in the nineteenth century was an economist by the name of Walras. He was eager to put economics on a mathematical basis. He observed the physicists and noted that they had created mathematical equations to describe equilibrium in nature. He thought, “Hmm, we have a similar situation in economics: prices seem to converge to equilibrium, supply and demand seem to converge to equilibrium.” So Walras hijacked the mathematical equations from the physicists and applied them to economics. The problem is with the word “similar”, i.e. “we have a similar situation …” He mistook a metaphor for science. Prices converge to something that approximates equilibrium, but doesn’t really attain equilibrium. Supply and demand converge to something that approximates equilibrium, but doesn’t really attain equilibrium. The consequence of Walras mistaking metaphor for science is that he placed the whole field of economics on a wrong footing.

— Extracted from The Origin of Wealth by Eric D. Beinhocker