On the future of Chemistry:
Chemistry is not the preservation hall of old jazz that it sometimes looks like. We cannot know what may happen tomorrow. Someone may oxidize mercury (II), francium (I), or radium (II). A mineral in Nova Scotia may contain an unsaturated quark per 1020 nucleons. (This is still 6000 per gram.) We may pick up an extraterrestrial edition of Chemical Abstracts. The universe may be a 4-dimensional soap bubble in an 11-dimensional space as some supersymmetry theorists argued in May of 1983. Who knows?

A mind that is stretched by a new idea can never go back to its original dimensions.

Absolute space, of its own nature without reference to anything external, always remains homogenous and immovable. Relative space is any movable measure or dimension of this absolute space; such a measure or dimension is determined by our senses from the situation of the space with respect to bodies and is popularly used for immovable space, as in the case of space under the earth or in the air or in the heavens, where the dimension is determined from the situation of the space with respect to the earth. Absolute and relative space are the same in species and in magnitude, but they do not always remain the same numerically. For example, if the earth moves, the space of our air, which in a relative sense and with respect to the earth always remains the same, will now be one part of the absolute space into which the air passes, now another part of it, and thus will be changing continually in an absolute sense.

All the modern higher mathematics is based on a calculus of operations, on laws of thought. All mathematics, from the first, was so in reality; but the evolvers of the modern higher calculus have known that it is so. Therefore elementary teachers who, at the present day, persist in thinking about algebra and arithmetic as dealing with laws of number, and about geometry as dealing with laws of surface and solid content, are doing the best that in them lies to put their pupils on the wrong track for reaching in the future any true understanding of the higher algebras. Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.

Biology is a science of three dimensions. The first is the study of each species across all levels of biological organization, molecule to cell to organism to population to ecosystem. The second dimension is the diversity of all species in the biosphere. The third dimension is the history of each species in turn, comprising both its genetic evolution and the environmental change that drove the evolution. Biology, by growing in all three dimensions, is progressing toward unification and will continue to do so.

For Christmas, 1939, a girl friend gave me a book token which I used to buy Linus Pauling's recently published Nature of the Chemical Bond. His book transformed the chemical flatland of my earlier textbooks into a world of three-dimensional structures.

My soul is an entangled knot,
Upon a liquid vortex wrought
By Intellect in the Unseen residing,
And thine doth like a convict sit,
With marline-spike untwisting it,
Only to find its knottiness abiding;
Since all the tools for its untying
In four-dimensional space are lying,
Wherein they fancy intersperses
Long avenues of universes,
While Klein and Clifford fill the void
With one finite, unbounded homoloid,
And think the Infinite is now at last destroyed. (1878)

Scientists often invent words to fill the holes in their understanding.These words are meant as conveniences until real understanding can be found. ... Words such as dimension and field and infinity ... are not descriptions of reality, yet we accept them as such because everyone is sure someone else knows what the words mean.

The greatest advantage to be derived from the study of geometry of more than three dimensions is a real understanding of the great science of geometry. Our plane and solid geometries are but the beginning of this science. The four-dimensional geometry is far more extensive than the three-dimensional, and all the higher geometries are more extensive than the lower.

Yet I exist in the hope that these memoirs... may find their way to the minds of humanity in Some Dimension, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality.

[S]ome physicists describe gravity in terms of ten dimensions all curled up. But those aren't real words—just placeholders, used to refer to parts of abstract equations.