Smart Remarks 2: Einstein, Noether, Russell, Lockwood, Churchland, Atiyah, Weyl 

In the judgment of the most competent living
mathematicians, Fraulein Noether was the most significant creative
mathematical genius thus far produced since the higher education of
women began.
Einstein Similar light produces, under like conditions, a like sensation of color. Helmholtz Thus
“this is red,” “this
is earlier than that,” are atomic propositions.
Russell & Whitehead
Take some range of phenomenal qualities. Assume that these qualities can be arranged according to some abstract ndimensional space, in a way that is faithful to their perceived similarities and degrees of similarity  just as, according to Land, it is possible to arrange the phenomenal colors in his threedimensional color solid. Then my Russellian proposal is that there exists, within the brain, some physical system, the states of which can be arranged in some ndimensional state space ... And the two states are to be equated with each other: the phenomenal qualities are identical with the states of the corresponding physical system. Lockwood Thus the colors with their various qualities and intensities fulfill the axioms of vector geometry if addition is interpreted as mixing; consequently, projective geometry applies to the color qualities. Weyl
Complete Intersection CalabiYau
Manifolds:
We said at an earlier place, that every difference in experience must be founded on a difference of the objective conditions; we can now add: in such a difference of the objective conditions as is invariant with regard to coordinate transformations, a difference that cannot be made to vanish by a mere change of the coordinate system used. Weyl

How
far does the laser move in color space?
The actual sensedata are neither true nor false. A particular patch of colour, which I see, for example, simply exists: it is not the sort of thing which is true or false. It is true that there is such a patch, true that it has a certain shape and a certain degree of brightness, true that it is surrounded by certain other colours. But the patch itself is of a radically different kind from the things that are true or false, and therefore cannot properly be said to be true [...] We shall say that we have acquaintance with anything of which we are directly aware without the intermediary of any process of inference or any knowledge of truths. Thus in the presence of my table I am acquainted with the sensedata that make up the appearance of the table  its colour, shape, hardness, smoothness, etc. [...] The particular shade of colour that I am seeing may have many things said about it  I may say that it is brown, that it is rather dark, and so on. But such statements, though they make known truths about the colour, do not make me know the colour itself any better than I did before: so far as concerns knowledge of the colour itself, as opposed to knowledge of truths about it, I know the colour perfectly and completely when I see it and no further knowledge of it itself is even theoretically possible. Russell
Discussion so far has been concentrated on the impressive computational power of coordinate transformations of state spaces and on the possible neural implementations of such activity. But it is important to appreciate fully the equally powerful representational capacity of neural state spaces. The global state of a complex system of n distinct variables can be represented by a single point in an abstract ndimensional state space. Churchland, PM
We shall now
recall the data of a classical theory as understood by physicists and
then reinterpret them in geometrical form. Geometrically or
mechanically we can interpret this data as follows. Imagine a
structured particle, that is a particle which has a location at a point
x of R_{4} and an internal structure, or set of states, labeled by elements g of G. Atiyah
The internal
space defined at each spacetime point
Epistemologically it is not without interest that in addition to ordinary space there exists quite an other domain of intuitively given entities, namely the colors, which forms a continuum capable of geometric treatment.
It
seems useful to me to develop a little more precisely the "geometry"
valid in the twodimensional manifold of perceived colors. For one can
do mathematics also in the domain of these colors.
The
fundamental operation which can be performed upon them is mixing: one
lets colored lights combine with one another in space [...]
Weyl 



More smarts 3: Leibniz, Maxwell, Turing, Churchland, Lockwood, Salam, Wigner 