I shall dwell for a moment on this term - 'understanding'. For I must not smuggle in unnoticed this apparently harmless, but in fact sharply controversial word. A powerful movement of critical thought has been at work to eliminate any quest for an understanding that carries with it the metaphysical implications of a groping for reality behind a screen of appearances. Natural science has been taught to regard itself as a mere description of experience: a description which can be said to explain the facts of nature only so far as it represents individual events as instances of general features. And since such representation of the facts is supposed to be guided merely by an urge to simplify our account of them, rival explanations are professed to be merely competing descriptions between which we choose the most convenient. Modern science disclaims any intention of understanding the hidden nature of things; its philosophy condemns any such endeavour as vague, misleading and altogether unscientific.

But I refuse to heed this warning. I agree that the process of understanding leads beyond - indeed far beyond - what a strict empiricism regards as the domain of legitimate knowledge; but I reject such an empiricism. If consistently applied, it would discredit any knowledge whatever and it can be upheld only by allowing it to remain inconsistent. It is permitted this inconsistency because its ruthless mutilation of human experience lends it such a high reputation for scientific severity, that its prestige overrides the defectiveness of its own foundations. Our acknowledgment of understanding as a valid form of knowing will go along way towards liberating our minds from this violent and inefficient despotism.

...I have moved deliberately from facts to values and from science to the arts, in order to surprise you with the result; namely, that our powers of understanding control equally both these domains. This continuity was actually foreshadowed from the moment that I acknowledged intellectual passion as a proper motive of comprehension. The moment the ideal of detached knowledge was abandoned, it was inevitable that the ideal of dispassionateness should eventually follow, and that with it the supposed cleavage between dispassionate knowledge of fact and impassioned valuation of beauty should vanish.

A continuous transition from observation to valuation can actually be carried out within science itself, and indeed within the exact sciences, simply by moving from physics to applied mathematics and then further to pure mathematics. Even physics, though based on observation, relies heavily on a sense of intellectual beauty. No one who is unresponsive to such beauty can hope to make an important discovery in mathematical physics, or even to gain a proper understanding of its existing theories. In applied mathematics - for example in aerodynamics - observation is much attenuated and the mathematical interest often predominates; and when we arrive at pure mathematics, for example, number theory, observation is effaced altogether and experience is alluded to only quite dimly in the conception of integers. Pure mathematics presents us with a vast intellectual structure, built up altogether for the sake of enjoying it as a dwelling place of our understanding. It has no other purpose; whoever does not love and admire mathematics for its own internal splendours, knows nothing whatever about it.

And from here there is but a short step to the abstract arts to music. Music is a complex pattern of sounds constructed for the joy of understanding it. Music, like mathematics, dimly echoes past experience, but has no definite bearing on experience. It develops the joy of its understanding into an extensive gamut of feelings, known only to those specially gifted and educated to understand its structure intimately. Mathematics is conceptual music - music is sensuous mathematics.

And so we could go on extending our perspective, until it took in the entire range of human thought. For the whole universe of human sensibility - of our intellectual, moral, artistic, religious ideas - is evoked, in the way illustrated for music and mathematics, by dwelling within the framework of our cultural heritage. Thus our acknowledgment of understanding as a valid form of knowledge foreshadows the promised transition from the study of nature to a confrontation with man acting responsibly, under an over-arching firmament of universal ideas.