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By Root 638 0

high level of difficulty does not allow many consistent formulations; so far, after all, no completely satisfactory form has been found. On the other hand, consistency conditions are usually difficult to evaluate, and so the concept of beauty as an additional criterion often enters the stage. Beauty is easier to spot than consistency, for it is based on an emotional process even for theoretical physicists, who are often seen as rather prosaic. However, mathematical beauty does not reveal itself to the untrained eye. More critically, even in mathematics, beauty is in the eye of the beholder; and so various research directions emerge, all following different ideals and often communicating with each other only with difficulty. Above all, one loses sight of reality: “There is no doubt, the veracious one, in that bold and final sense as the belief in science requires it, affirms therewith a world different than that of life, of nature, and of history; and insofar as he affirms this ‘other world,’ what? is he not, by just this, led to its counterpart’s, this world’s, our world’s—negation?”1

Once one arrives at such an intimate relationship with mathematics, one can easily confuse mathematical objects with reality. John Stachel, in this context, speaks of the “fetishism” of mathematics: “I designate as the ‘fetishism of mathematics’ the tendency to endow the mathematical constructs of the human brain with an independent life and power of their own.”2 Occasionally, the words already indicate what criteria (scientific or otherwise) are used to develop certain theories. In some branches of quantum gravity research, the language often appears overblown, manifesting itself, for instance, in descriptions of mathematical facts as “magical” or “mysterious.”3

In all these considerations, it is important to remember what the aim of science is: to describe Nature; and Nature has her own sense of beauty. Nature alone can decide which theories best describe and predict her behavior. What too strong an insistence on human concepts of beauty can lead to in the exploration of Nature was Faust’s experience in the following passage and its continuation:

SPIRIT: Who calls me?

FAUST: (turning aside) Dreadful shape!

SPIRIT: With might,

Thou hast compelled me to appear,

Long hast been sucking at my sphere,

And now—

FAUST: Woe’s me! I cannot bear thy sight!

SPIRIT: To see me thou dost breathe thine invocation,

My voice to hear, to gaze upon my brow;

Me doth thy strong entreaty bow—

Lo! I am here! —What cowering agitation

Grasps thee, the demigod! Where’s now the soul’s deep cry?

Where is the breast, which in its depths a world conceiv’d

And bore and cherished? which, with ecstasy,

To rank itself with us, the spirits, heaved?

Where art thou, Faust? whose voice I heard resound,

Who toward me press’d with energy profound?

Art thou he? Thou, —who by my breath art blighted,

Who, in his spirit’s depths affrighted,

Trembles, a crush’d and writhing worm!

FAUST: Shall I yield, thing of flame, to thee?

Faust, and thine equal, I am he!

SPIRIT: A constant weaving

With change still rife,

A restless heaving,

A glowing life—

Thus time’s whirring loom unceasing I ply,

And weave the life-garment of deity.

FAUST: Thou, restless spirit, dost from end to end

O’ersweep the world; how near I feel to thee!

SPIRIT: Thou’rt like the spirit, thou dost comprehend,

Not me!

(Vanishes.)

—GOETHE, Faust

Turning away from Nature, symbolized by the Earthly Spirit, did have unfortunate consequences not only for Faust, who afterward made a fateful pact with Mephisto and his magic, but also for several others initially uninvolved. Faust gains more and more power, but loses sight of the essential.

ABUSE OF INFINITY:

THE DIRTY TRICKS OF PHYSICS

The moving moves neither in the space where it is, nor where it is not.

—ZENO OF ELEA, Fragment

The concept of infinity is a dangerous weapon in certain mathematical arguments, and so it comes as no surprise that it is sometimes abused. As the discoverer of the power of infinity we may identify Zeno,