The annual meeting of the British Association was opened at.
Sciuthport on Wednesday, the 19th instant. The President of the year is Professor Cayley, who delivered an address which to the greater number even of scientific men must have appeared' painfully abstruse. It was devoted solely to mathematics, and besides a history of the instances in which mathematical theories have been suggested by questions of common life, or- physical science, contained many recondite, not to say transcend- ental, speculations in pure mathematics, mathematics applied under imagined conditions. The general drift of this part of the address, which was far too full of thought for condensation,. even if we were capable of the fall comprehension neces- sary for such a task, was that the axioms of geometry are abso- lute truths only under imagined conditions, and that conditions: can be conceived of under which they may not be true. For example, the proposition that two straight lines cannot enclose a space is not true of a smooth sphere. Mr. Cayley does not. assert, as Mr. Clifford is supposed to have done, that he cam conceive of four-dimensional space ; but he does assert that he, can conceive of beings to whom three-dimensional space seems- as impossible as four-dimensional space does to us. "It may be at once admitted that we cannot conceive of a fourth dimension of space ; the space as we conceive of and the physical space of our experience, are alike three- dimensional; but we can, I think, conceive space as being two. or even one-dimensional ; we can imagine rational beings- living in a one-dimensional space (a line), or in a two-dimensional space (a surface), and conceiving of space accordingly, and to. whom, therefore, a two-dimensional space, or (as the case may- be) a three-dimensional space, would be as inconceivable as a. four-dimensional space is to us." We suppose, therefore, Mr.. Cayley thinks four-dimensional space or n-dimensional space to be possible, though beyond our intelligence, cramped as it is by our experience. Is not the end of that this,—that final truth is unattainable even in geometry ?
Previous page
