HILBERT SPACE

How many dimensions can we draw in?  If we are within Hilbert Space, then the number of dimensions is infinite.  David Hilbert was a great mathematician working in the early part of the 1900s.  And his contributions to and creations of new ways of understanding space that he developed during that time remain useful today to mathematicians.

What I find most applicable to our purposes is that while the space of his imagination allowed for infinite numbers of dimensions, the resulting constructs, (dare I use the words form or enclosure?), are measurable.  They are real and they resolve.

I ran across this painting by James March in which the artist applied their knowledge of Hilbert Space to what that could look like.  Of course, they used opaque blobs of paint on a canvas as their selected method with which to get at this multidimensional spacetime.  Of course, employment of transparency did not occur to them.  So of course, I wonder what I can generate on my paper, using the same geometry, transparently?

My drawing, using transparency, results in something that is actually buildable.  That is to say, you could certainly construct an arrangement of forms, and from one spot, it would look like my drawing.  That cannot be said for the painting.  In the painting, some of the slots dissolve from their opacity: this is not constructable.

So Hilbert mathematized a multidimensional spatial understanding that was measurable.  An artist, using opaque paint blobs, depicts this spatial understanding in a non measurable way.  A transparent drawing cuts thru the artifice and superficiality of opacity which results in a measurable spatial construct of Hilbert Space.

1.  Link to the website of James March, in which this painting can be purchased.