Mathematics quote

[JennaW]

Mathematics is inadequate to describe the universe, since mathematics is an abstraction from natural phenomena. Also, mathematics may predict things which don't exist, or are impossible in nature.

-- Ludovico delle Colombe, criticizing Galileo.

"The followers of Ludovico delle Colombe—disgruntled Aristotelian philosophers derisively known as the "Pigeon League"—deserve some blame as well. Galileo's Dialogue on the Two Chief World Systems, published in 1632, shows how little regard he had for these men, whom he publicly ridiculed. It is true, as legend has it, that some contemporaries refused to look into Galileo's telescope, but these were not Church scholars, as is commonly supposed; on the contrary, the Jesuit mathematicians and astronomers, such as Christopher Clavius, had their own telescopes and confirmed Galileo's startling observations for themselves.

Rather, the skeptics were the adherents to Aristotle's doctrines, according to which imperfections in the heavens were impossible. No doubt contributing to his fate, Galileo provoked these philosophers, scoffing at their uncritical reliance on Aristotle's text. When one of them died, Galileo quipped that although the man had ignored the moons of Jupiter during his time on Earth, he might discover them on his way to heaven."

--American Scientist, Trial of the Centuries

[Rodney]

Mathematics is inadequate to describe the universe, since mathematics is an abstraction from natural phenomena. Also, mathematics may predict things which don't exist, or are impossible in nature.

-- Ludovico delle Colombe, criticizing Galileo.

I assume you're disagreeing with this quote, as would I if it is attacking math-based prediction as such. Its logical implication is that concepts (also abstracted) are just as powerless--that the universe cannot be described!

For my full views on the relation of math to reality, I would refer you to the essay in my signature, except that it essentially builds on Rand's ITOE--a book you say confuses you. (I find this a bit surprising, because I experienced the book as basically a description of my own mental operations. In my teens I had arrived at the AR's idea of measurement-omission independently.) But anyone else who is interested in the application of Objectivism to mathematics, is willing to listen to a theory different from that of Ronald Pisaturo and Glenn Marcus, and has $5 to spare, might want to click below.

[BaalChatzaf]

Rather, the skeptics were the adherents to Aristotle's doctrines, according to which imperfections in the heavens were impossible. No doubt contributing to his fate, Galileo provoked these philosophers, scoffing at their uncritical reliance on Aristotle's text. When one of them died, Galileo quipped that although the man had ignored the moons of Jupiter during his time on Earth, he might discover them on his way to heaven."

--American Scientist, Trial of the Centuries

Galileo's nickname was Wrangler. Apparently he was argumentative and pugnacious. He was also a smart-ass of magnitude 1. His portrayal of Pope Urban VII as Simplicio (an Aristotelean dumb-dumb) in G's famous -Dialogues on the Two World System- did not endear him to the upper management of the Church. In fact, his cheekiness put his arse in a meat grinder. Galileo was truly a ba'al chatzaf!

Strangely enough, Mr. G's favorite argument for the rotation of the Earth was completely bogus. G had a theory of tides that was essentially the water sloshing in a moving tub model. G, in his correspondence with Kepler, chided Kepler in thinking that the Moon had something to do with tides. Galileo called such speculation -moonshine-! Well Kepler was right and Galileo was wrong. So even smart-ass cheeky geniuses can be wrong sometimes.

What is even more strange is that Galileo discovered the very instrument with which he could -prove- the Earth rotates about its axis. It is none other than the pendulum. In 1851 Leon Focault displayed his namesake pendulum in Paris proving for damned sure that the earth rotates on its axis (not that anyone at that time doubted it). Galileo had the proof he needed in his hand, but his grasp of inertia was not sound enough for him to make the case.

Ba'al Chatzaf

Edited April 18, 2007 by BaalChatzaf

[BaalChatzaf]

Mathematics is inadequate to describe the universe, since mathematics is an abstraction from natural phenomena. Also, mathematics may predict things which don't exist, or are impossible in nature.

-- Ludovico delle Colombe, criticizing Galileo.

That statement is right as far as it goes. An abstract mathematical formalism -by itself- has no empirical content whatsoever so it cannot describe the world. What is missing? An interpretation. An interpretation establishes a correspondence between the mathematical objects of the system and measurable quantities in the world and operations performed to get the measurements. It is the interpretations that give a mathematical system its physical meaning.

Ba'al Chatzaf

[tjohnson]

In Science & Sanity Korzybski describes mathematics as the only language similar in structure to the world and the human nervous system, which accounts for it's tremendous usefulness. For example, when we observe 'continuously' changing phenomena we translate this via differential calculus into static frames and are able to measure differences from one frame to the next. Similarly, we receive static frames at a rapid speed our nervous system integrates these to a continuous process. Food for thought!

[BaalChatzaf]

In Science & Sanity Korzybski describes mathematics as the only language similar in structure to the world and the human nervous system, which accounts for it's tremendous usefulness. For example, when we observe 'continuously' changing phenomena we translate this via differential calculus into static frames and are able to measure differences from one frame to the next. Similarly, we receive static frames at a rapid speed our nervous system integrates these to a continuous process. Food for thought!

In the 1940's and 1950's when Korzybski wrote very little was known about the brain and nervous system so you can take anything the Count said on that matter con grano salis.

Ba'al Chatzaf

[tjohnson]

With a 'grain of salt'??

Well thanks, but I happen to think that is one of the most unique and creative takes on mathematics around, so no salt is needed. I also don't see how new developments in neuroscience could change that particular point of view, it is extremely general.

Do you have any remarks on the idea itself or just the circumstances surrounding it's appearance?

[BaalChatzaf]

With a 'grain of salt'??

Well thanks, but I happen to think that is one of the most unique and creative takes on mathematics around, so no salt is needed. I also don't see how new developments in neuroscience could change that particular point of view, it is extremely general.

Do you have any remarks on the idea itself or just the circumstances surrounding it's appearance?

The logical mode of mathematics is very atypical of how must people think. That is why most people have a hard time with mathematics.

The intuitive mode is much more "right brained" and related to visual imagination.

A leading physicist, Eugene Wigner wrote an essay on the how effective mathematics is and he essentially punted on the question. No one really knows why mathematics is so effective, but practicing scientists know -that- mathematics is effective. See http://en.wikipedia.org/wiki/The_Unreasona...atural_Sciences

Anything Count Korzybski had to say on the functioning of the brain and nervous system was based on material that has long since been refuted or replaced by modern neurological science. Most of what we know about the brain and nervous system has been discovered in that last thirty or forty years which is after Korzybski's time. Korzybski's main contribution was to show how the misuse of language can distort and confuse our thinking.

Ba'al Chatzaf

Edited June 8, 2007 by BaalChatzaf