Thursday, April 23, 2009

A World Without Math - None I'd Choose to live in

Take a close look at the image of our planet, seen from space. It shows as no other the isolation of our little orb against the vast blackness of the cosmos - and that we are all passengers (crew) on Spaceship Earth.

Now, consider this: In a world without mathematics we'd never have been afforded such a view. It would have been impossible. It is mathematics (specifically differential calculus) that enabled us to engineer the rockets that attained an altitude to snap our world from space.

A world without math, featuring creatures evolved with no left-brain abilities to quantify or analyze, would be impoverished indeed. Truthfully, we'd not even be aware that our planet is spherical -curved and not flat, since the geometry necessary to attain that awareness (as performed by Eudoxus, Eratosthenes etc) would never have existed.

It is math that has opened the doors to the level of analysis needed to expose facets of the world and universe otherwise invisible.

Consider just trigonometry. No trig and no ability to plot altitudes or find heights! No ability to find distances between different levels. Think of a humdrum skyline for our cities, as opposed to the exotic and geometrical spires that populate most of the world's urban centers, from London to Paris, to Seattle to New York.

Calculus! No differential calculus or differential equations, and no ability to do celestial mechanics - which is the basis for actually sending a rocket from Earth to any other planet! Indeed, the equations of celestial mechanics from Kepler's equation: E - e sin(E) = n(t - t_o)

to the energy integral: r' x r" = - u/ r^3 [r' x r]

to the angular momentum defined for a 3-body system:

h = r x r’ = r x dr/ dt =

(y z’ - z y’)
(z x’ - x z’) = (C1 C2 C3)
(x y’ - y z’)

so (r x r’) = (C1/ h, C2/ h, C3/h)

is the whole basis for not only predicting the future positions of planets, but for launching spacecraft to other worlds, and landing them. Minus such advanced math, we'd have no close-up images of Saturn, or Neptune, or Uranus - nor would there be any Mars Rover plodding the dusty surface of that planet and sending back surface images.

In a world without math, most new medical devices would never have emerged. There'd be no MRI machines, no stereoscopic machines, no x-ray machines or radiotherapy-brachytherapy cancer treatment machines, or software.

There would be no computers, nor any software to run them, since the latter requires math-based code, and the former a level of engineering that makes use of everything from quantum tunnelling to quantifying thermal processes and inputs.

No telescopes would exist, or microcopes, or TV sets.

A world without mathematics would be so barren, so devoid of richness, it would be nearly impossible to imagine.