Information is Real & Information is Physical.
The Bit and the Pendulum http://www.amazon.com/gp/product/0471399744/
The Pythagoreans ...having been brought
up in the study of mathematics, thought
that things are numbers ...and that the
whole heaven is a scale and a number...
--Aristotle
Answering Thales' original question, (are all things water?) http://tinyurl.com/obn4m Pythagoras and his followers held that all things are numbers. His study of the mathematical ratios of musical scales and planets led Pythagoras to believe that quantitative laws of nature could be found in all subject matters. He further expected such laws to have the simplicity of those governing music.
Origins of the Concept of [FORMS]
THE CONCEPT of form and the Greek word eidos, which finally came to express that concept, have a rather complicated history.
At first, eidos meant "the look of a thing"
or "the face" as it does in Homer,
when Achilles furious at Agamemnon
calls him "kyneidos!" ("dog-faced one!").
Eidos in medicine had the sense of "the
look of a patient" his physical type,
relevant to diagnosis and treatment.
In mathematics, eidos was a near synonym
for schema ("shape") and referred to the
mathematical structure.
The medical use, relating "the look" of
the patient to health and disease, merged
with the idea of "good form," important
in athletics and dancing, to suggest
that form is a standard of value.
Plato and Aristotle tried in different ways to bring these two senses of form, the mathematical and the ideal, together.
The philosophical ideas characteristic of the Pythagoreans can be summed up in the two phrases:
["Numbers are things"] & ["Things are numbers."]
The first precept extends the notion of reality well beyond the Milesian idea that, "To be is to be material"; it reflects the discovery of pure mathematics made by the school. The second expresses a notion that grew from another discovery of the Pythagoreans, namely, that;
mathematical formulas can be applied
to explain the physical world. From
this discovery, they generalized to
the philosophic thesis that the
ultimate nature of reality is
mathematical...
The development of pure mathematics seems to have been Pythagoras' own doing. Recent studies of the history of science show that in Egypt there was a civilization and technology where science and pure mathematics played no part. The Babylonians had developed some techniques of computation, but were not curious about the nature of number and figure as such. But it is just such a curiosity that is needed to lead to the discovery that numbers, figures, and relations have a kind of reality of their own and to the philosophical doctrine that numbers are things.
Pure mathematics requires a remarkable step of generalization.
Instead of thinking and counting sets
of things, so that a different form
of the number two results from adding
together pairs of pigs or pebbles,
one must pay attention to the number
two itself, as just "two," and not
as two this or two that.
In most, if not all, primitive languages, we find these ["numerary_adjuncts"] words indicating the kind of thing being counted.
English still has some: we speak of
"two pieces of bread," "two head of cattle,"
Japanese has many more:
"two round-shaped pencils,"
"two flat-shaped sheets,"
These are relics of a mental state
where numbers were used only as
numbers of something,
...so that if one said, "Two," his hearers would ask him, ["Two what?"] It is only possible to recognize that "numbers are things" when two or any other quantity has been separated from this dependence on numerary adjuncts.
The Pythagoreans found they could
think about shapes in the same way.
Instead of thinking of particular pieces of land that were triangular in shape, they could think about [triangularity] about any triangle, or any right triangle.
It is hard for us today, familiar as we are with pure mathematical abstractions and with the mental act of generalization, to appreciate the originality of this Pythagorean contribution. And, in fact, some aspects of Pythagorean mathematics strike us as rather odd. In the first place,
Numbers had shapes and even personalities.
Summarized From; The philosophers of Greece
by Robert S. Brumbaugh
http://www.amazon.com/gp/product/0873955501/
http://en.wikipedia.org/wiki/Pythagoras
http://en.wikipedia.org/wiki/Pythagoreans
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