Alfred
Russel Wallace : Alfred Wallace : A. R. Wallace :Russel Wallace : Alfred Russell Wallace ( sic)Supposed "Dimensions" of Spaceas Possible Realities ( circa October 1894)Editor Charles H. Smith's Note: A very interesting essay probably written around October 1894
(while a discussion on this subject was running in the journal Light: see S502a), but apparently
never published. The nine page handwritten manuscript from which this transcription is drawn is
part of the Alfred Russel Wallace collection at the Natural History Museum (London), item
WP7/116(1). The outside cover of the manuscript (WP7/116(1), 1 of 10) gives a slightly different
title: "The Supposed 'Dimensions' of Space (shown to be a verbal quibble with no possible
relation to actual and possible facts)." The original manuscript contains various edits (strike-outs and corrections) by Wallace himself; I have reproduced what appears to be his final version
of the paper. To link directly to this page, connect with:
http://people.wku.edu/charles.smith/wallace/Supposed_Dimensions.htm
Space is defined to be "extension as distinct from material substances", but this is hardly general enough, and I think it would be best defined as "that which contains all things both actual and possible," or words to that effect. This is certainly what we all understand when we speak of the necessary infinity of space. It has been tersely said, "space is nothing, but it contains all things"; and again--"space is a sphere whose centre is everywhere and circumference nowhere". With such a conception of space as this, the idea that it is of three, or any other number of
"dimensions", is absolutely unmeaning, if not absurd and self-contradictory. The so-called "three
dimensions" Let us take another example. We can assume a straight line to be of any length in feet or
miles &c. Let us call this length aaa is a^{3}^{}; and a multiplied by a three, or any number of times, is said to be raised to the fourth fifth or any higher power of a determined by the number of a's multiplied together.
The result will be purely arithmetical, though expressed by a different formula. If we apply these
higher "powers" to geometry, we must return to the original arithmetical form. Thus a, will
either give us the number of superficial feet in a rectangular surface ^{3}aa feet long by a feet wide,
or of solid feet in a cube of a feet long wide and high. So a will give us the area of a square ^{4}aa
feet x aa feet, or in a parallelogram a feet x aaa feet, or of a solid figure (a parallelepiped) a
wide, a high, and aa long. So, a is a mere number, but it will also give us the solid feet in a
parallelepiped ^{5}a feet wide, a feet high and aaa feet long, or of one aa feet wide aa feet high and
only a feet long. And so, for any power of a, it may give us either a superficial area or a solid
area of rectangular figures whose dimensions multiplied together make up any special power,
which we may term a.^{n} But according to the mode of reasoning of the mathematicians from their very convenient
method of defining curved lines or surfaces, the mere fact that, while a to measure a solid, therefore ^{3}a must be the measure of
something that is to a solid, as a solid is to a surface or a surface to a line. And if this argument is
sound it implies that there are, or may be, as many distinct categories of bodies or forms
(differing in nature as do lines, surfaces, and solids) as there are powers of numbers--in other
words that they are infinite.^{4} Returning now to the alleged different The attempt to popularise the argument by supposing intellectual beings to live within
surfaces and lines from which they have no senses that enable them to perceive outer space is a
ludicrous begging the question. A line or a surface, having by definition The extraordinary looseness of reasoning of even good writers is shown by the following
words in the article The last four words embody a statement as to the nature of space itself, derived from one
purely technical formula used by mathematicians to determine the forms or the dimensions of
certain I have now shown that all assertions as to the "dimensions of space" (whether two, three,
four, or infinite) rest upon confusion as to the meaning of words and deriving results from such
incorrect or illogical meanings. Space is said to be, actually, of one, two, or three dimensions;
whereas the first two are in no sense space, or even portions of space, but only the limits or
surfaces of portions of space. The third, is only a term applied to the mode of determining the
shape and size of certain portions of space, and is wholly inapplicable to Space as a general term,
which is by definition immeasurable. The other confusion of meaning is as to the word
dimension; which, as popularly used refers to the size of any object; but, as used by
mathematicians, refers to the varying lengths of one, two, or more co-ordinates as measured from
imaginary rectangular axes anywhere Alfred R. Wallace
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