THE PRINCIPLE OF HOPE

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of dimensions ceases at a deeper level; something impossible in three­dimensional classical mechanics can thus be valid, become technologically possible. It can do this
in a way which is at least no longer absolutely out of the question; the utopia which has begun of a non­Euclidean technology already has limits which have been pushed
extraordinarily far forward. In return, of course, there is also the danger cited above of ever greater artificiality, of projecting ever further into a mathematicized no man's
land. And this artificiality is in fact at the same time the Negativum emerging at the end ever more clearly in the break in the graphically physical guideline itself. A
Negativum which indicates likewise at this end a future shift in the expansion of technological space which is so highly important and so highly progressive in itself. Only
this shift will no longer be able to occur on the basis of the bourgeois relation to human beings and to nature, i.e. within that component of the relation to nature which
belongs to bourgeois ideology and thus shares the rest of the abstractness (alienness) of the bourgeois material relation. But just as it manages atomic energies
humanely, a no longer imperialistic society will mediate to itself this material, however non­Euclidean it may be, as one without ultimate alienness. Also connected with
this abstractness is the peculiar pathos of non­graphicness which has filled all non­Euclidean physics up to now. What is meant by this is not non­graphicness in the
simple sense, namely the obvious kind inherent in all occurrences outside three­dimensional visual space. But that other non­graphicness is meant here which is the same
as unmediatedness of the independent object with the thinking subject, of the thinking subject with the independent object. In so far as a non­Euclidean physics, despite
constant recourse to observation, still constructs its world as a mere reification of mathematical symbols, the abstractness has grown so great that subject and object no
longer meet at all, indeed that the non­Euclidean object precisely as real kinetic matter totally drops out of sight. Complete unmediatedness with content thus appears
here — an ideological analogue to the totally alienated, de­realized functional operation of late capitalist society, projected into nature. An idealism of method thus still
increases that whereby even a non­Euclidean technology still towers so strangely into the unmediated and into what is downright disparate to concrete mediation.
Certainly the ideological component is only the one in dehumanized physics, and the other one, irrefutable by ideological analysis, is the dictate of observed nature to do
theoretical justice to it. But neither are both components already sharply separable nor can the real threat of a lack of mediation be overlooked in the whole trenchant
business of