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| David Hilbert |
Spectral Theory
To understand Spectral Theory, one must have some working
knowledge of Vector Mathematics and a number of esoteric mathematical terms and
concepts. Or at least that is what this blog contributor has gathered. As it seems the theories themselves
cannot be explained concisely without being incomplete, or without the proper
context, I will begin by laying down some basic facts.
Spectral Theory was initially developed by David Hilbert, a
Prussian-born mathematician whose work spanned many facets of mathematics. One of his legacies includes his
efforts in the axiomatization of mathematics. That is, at the age of 38, he proposed a list of unsolved
mathematical problems to the mathematicians of the world, challenging them to
take on these long-standing problems.
Spectral Theory was coined by Hilbert while developing his
Hilbert Space Theory. Hilbert
Space is essentially an extension of the Euclidean two-dimensional plane and
three-dimensional space to spaces with any number of dimensions. Spectral Theory itself is certainly an
abstruse concept, but it can be explained as a collection of theories dealing
with multidimensional space and corresponding linear algebraic equations.
For the purposes of this study, we will simplify the concept
to a mathematical theory that begins to explain in a concrete, quantifiable
way, how vectors are able to move in multidimensional planes or spaces.
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| A Hilbert Space-filling Curve |
Significance in Against the Day
The most obvious part Spectral Theory has played thus far in
ATD has been its initial place of mention on page 324. Professor Vanderjuice tells Kit about
Hilbert, and his work with Spectral Theory at Gottingen. Shortly after this, Kit, after also
speaking with Tesla, procures the means from S. Vibe to study abroad at
Gottingen. His intention is to
study the concept of infinite dimensions.
However, there are times at which this concept of multiple
dimensions, moving through infinite plane, occurs. The Chums of Chance move through the sky, away from the
“flat” plane of the earth. They
also travel through time, and the layers below the surface of the earth. In this way, these multitude of
previously uncharted, unexplored territories are now being experienced. On page 327, while talking to Kit,
Tesla states, “Underground, therefore, lies an entire unmapped region, a
carrying into the Invisible of geography, and—one must ask—why not of other
sciences as well?” This is in a
time when science was beginning to theorize about what a world with multiple dimensions
could be like.
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