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Dec17-03, 06:18 PM
Sci Advisor
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marcus's Avatar
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now I see better what you mean, hellfire, and if I understand you
correctly I think you have a good point.
just talking about SCIENCE it seems to me that
there has been a real shift towards mathematical description and

and not merely a shift towards emphasizing quantities
but a shift towards more sophisticated algebra and even subtle geometry

Kepler circa 1618 is often for me the test if something is true.
For over 15 centuries before him they had the Ptolemaic system which had plenty of quantities! It had all the radiuses of all the spheres! It had all the time periods of all the cycles! So if one just focuses on SCIENCE as you suggest you have them using lots and lots of QUANTITIES for 15 centuries and making very good quantitative predictions.

Kepler made a couple of subtle changes. It was not to be circles anymore, instead it was to be ellipses. You could even say it was a QUALITATIVE change that he made, to go from circles to ellipes and to get rid of all the extra spheres.

[the Copernicus model goes back to 250 BC and Aristarchus, and it does not actually work because it uses circles, so mars will not fit.
the really new thing was not Copernicus but Kepler, and it was a qualitative change]

Another change was Kepler discovered that the planet's distance from sun was not merely straigt-line proportional to its year-period. He found a relation that is SUBTLY DIFFERENT from a straight line. He discovered the distance from sun is 2/3 power of the period.

Both these moves are in the direction of more sophisticated math----circle changing to ellipse---linear, square, cube algebra moving to more subtle 2/3 power algebra.

One of the main goals in improving a scientific model is to get rid of numbers.
One sees the same progress in 20th century particle physics and in the replacement of Ptolemaic model. In the Ptolemaic model one had to specify more than twice as many number. Radii for all the spheres AND time periods for them to turn. Starting in 1618 more than half those numbers went away because you only had to list the periods of the planets and they would imply the distances from sun.

The smarter the model, the fewer numbers it needs to have input before it can start to run and make predictions

(Well there are other criteria of elegance too, but that is one of the main ones.)

So I would not call the trend, since 1618, one from qualities to quantities----I would see it as one from verbal explanation to mathematical modeling.
I see mathematical models as highly qualitative and capable of subtlety. there is a rich diversity ways to model things
and even seemingly little differences, like between circle and ellipse
can make a change

or between the 1/2 power (the square root) and the 2/3 power

before 1618 one had verbal classifications of materials to try to explain why some would burn, why some would melt or vaporize, and others would not, alchemy.
eventually there is an atomic model which roughly predicts which reactions happen readily and which combinations are possible, chemistry.
the chemical model uses numbers----numbers of electrons in the outer shell, for the most part, and associated valences.
there is less ad hoc stuff to remember and more that is predicted just by the atomic number, or the electron shell.
Carbon is Mr. 6, Nitrogen is Mr. 7, Oxygen is Mrs. 8. You almost can forget their antique names and just call them 6,7, and 8. And then these number-names will tell you things about how they behave.

Yes, I see a trend away from verbal classification and towards mathematical modeling----and also a process of qualitative refinement within the mathematical models. a process models of getting more varied and predictive and less clunky.

maybe this is so obvious to people it doesnt need to be said!
I will post it and erase later if it seems superfluous.