Colorful Science

This rather pretty diagram is my result on the Farnsworth Munsell 100 hue test. I took it because a friend who is a scientist was discussing with me the inevitability that my 61 year old eyes had yellowed and that I must have lost my ability to discriminate finely between colors. That possibility was a terrible shock to me, especially as I consult with people about color. I felt that if my color vision was skewed I had better know about it, hence the test. The result is very reassuring "My guess is that your color discrimination is substantially better than 99% of normal people of any age. So do not worry" says my friend who scored it.

I won't! 

There is something so elegantly beautiful about the circular chart. Color is a paradox to me. It is a thing we who have color vision simply assume as part of the physical world. It seems so empiric, so definite, yet it so subjective. We experience it as a quality of the objects around us yet it exists only in our brains. Just this morning the old question about a tree falling in a forest came up. If no one is there to hear it, is there any noise? The same question applies to color- is the field green if there is no one there to see it? The answer to both these questions is no. When the tree falls the event will send mechanical waves through the medium of the air, and an ear and brain working together interpret those waves as what we call sound if they each them, but that is in our heads, not in the forest.

When we "see," electromagnetic waves which are reflected off of a surface reach our eyes and are interpreted as a representational "vision." The sun shines upon the field, showering it with the remnants of energy waves that have not been blocked by the atmosphere. The sun, in it's seeming endless roiling of atomic explosion radiates on the fragile atmosphere which envelopes this tiny planet. The atmosphere fragments it into the glow of blue that we call sky. The energy that now has substance to interact with becomes visible as light as it energizes the air and irradiates the grass to give it the energy of life, and those wave lengths that the grass doesn't take in are reflected to our eyes and we experience a wave length, one that is not absorbed by the grass, and we have decided, as a group, a culture, to call that sensation green.

It seems to me that this agreement is rather like the "as if" approach to religion. Some of my friends in our theology discussion group will recognize what I am referring to. That we agree to participate "as if" it is all true. In the case of color, we agree to name it "green" as if we are all experiencing the same thing, but in fact all we know is that we each of us has that wavelength available to us if we are observing under the same conditions. It has passed through the air, been bounced off the grass, passed through more air, some glass perhaps, and now passes through our very probably yellowed cornea, thence to stimulate a now motley collection of much worn rods and cones and then the resulting stimulus winds it's way through the rather quirky maze of the individual brain to create that experience that we call green, which we treat as if it were identical for us all.

We can never know if the experience is the same for all of us- all we know is that when we see that wavelength we recognize it's sameness to the other occasions on which it is visible to us. I am wearing a sky blue sweater, it is the color of the sky, the egg of a robin. I say it is the color of the sky "Blue" and you say"oh yes! the color of the sky, like the egg of a robin, your sweater is that lovely, light, and slightly greenish blue." But really, beyond the fact that this sweater is showering you with the same wavelength as a clear sky on a cool summer morning, and so you make that pleasant association, the experience is completely within yourself, and you are profoundly isolated within your reactions to the wavelength of light, as I am within mine, and it is only the consistency of our individual experiences that enables us to shout across the gulf of sensual interpretation that separates us, and allows us to talk "As If" the field were green, and the tree crashes loudly, and the beauty of the world around us makes us one with creation.

We are dealing with, not the wavelengths that are in the grass, but those that are not in the grass. One could say that the grass is every color except green. It has rejected the greeness, thrown it back to us. This is another aspect of the paradox, that the color the thing is "is" exactly the color it "isn't." The grass gives our eyes "green" as the left over of it's feast on the sun's life giving energy. And we see it with pleasure.

Evolving Polygons,DNA, and the Renaissance

I would like to dedicate this to my friend Doctor Q at Q-optical in Boston.

This morning my rss feed from Slash Dot led me to this very interesting post by Roger Alsing in which he demonstrates the generation of a copy of the Mona Lisa comprised of 50 polygons. I can not pretend to understand the technical aspects of his process, but what I find interesting 

is the similarity to calculus. From the point of view of computer science this may be stating the obvious, but what I suspect is less obvious to those who have not studied the development of pictorial perspective is the way all this relates to the process of creating a perspective image on a two dimensional surface. I am speaking specifically of drafted, or measured perspective

This process can be very complicated geometrically and is without question a "scientific method."

This image was drawn by Paulo Uccello, a florentine artist of the late 14th- early 15th century. It is particularly good for illustrating the way that the volume of the object is reduced to many polygons. I will try to explain briefly what you are seeing here.  The various circles which in fact form the shape of the chalice - it's foot, the rings, the stem, the rim etc. have been drawn as circles on a separate drawing and then projected into ellipses by the method shown in the wikipedia article linked above. But this only gives the broad outlines. Say for instance a decorative pattern  circles the chalice, how do you locate the intervals of the pattern as they turn around the circumference? This is very likely the exact problem Uccello was addressing in this study. 

The way one locates the points turning around the circumference is to return to the plan view (the view from directly above), of the actual circles, and divide their circumference into the number units required. The circles of the plan are easily drawn with a compass and they are easily divided with a protractor. These constructions are often called "Projections" in this case we are creating a "perspective projection." Refer to the article, this is a "One point perspective projection" The term "Projection" is used because what we do at this point is to project, using the vanishing point, those divisions of the circumference of the circle in plan onto the circle drawn "In Perspective" (the ellipse.) The trickiest part of this is the fact that when viewed from above those divisions are even, but when projected they diminish as the approach the edge.

I have done a quick drawing to show this.  (forgive me, but the Uccello image jumped right into this post where I wanted it and my own drawing is stuck at the top of the post out of sequence- sorry) 

The circle in my drawing is divided into 12 equal segments. Slices of a pie- A pie chart, another connection- perhaps this is also used to convert pie charts into graphs in power point- all these things are done on the same principle. Above the "Pie chart" and centered exactly is the ellipse that represents the circle receding in space. What is very interesting is that the ellipse acquires the appearance of a receding circle only by it's context- it is of course a two dimensional ellipse but we understand it as a three dimension circle receding on a plane by comparing it to the circle. I have raised lines (this is the projection) from the points on the circumference to the analogous points (analogous-algorithm) on the ellipse. Notice the way that the space between the lines diminishes as they move away from the center. The Uccello drawing is doing this same thing in an incredibly elaborate way. Imagine this process turned 90 degrees and dealing with rectangles and you have the method of representing a checkerboard pattern receding in space; again, the way the squares diminish is determined by a geometric projection.

What now become obvious (at least to me) is the connection between the studies of Uccello, Brunelleschi, and Leonardo on the one hand, with the method of calculating surface area employed in the calculus on the other.

Of course that diminishing of the divisions can be calculated using algorithms, which is what calculus and computers do, and thereby we have a direct connection between the studies of Uccello and Roger Alsing - is it a reducio ad absurdum to propose that they have done the same thing, just used different tools?

As another student of this art, L.B. Alberti said "Art without science is nothing."