Have you ever seen a color picker widget anywhere which shows the entire spectrum of all possible colors in one single image? I mean, sometimes there are separate hue, saturation, brightness selectors, sometimes just two out of these three. The selection of the intended color always requires some interactivity by way of dragging some sliders, or clicking in an image which changes dynamically based upon the selected position in another image. If you have seen anything anywhere which avoids the above by showing all the colors in one single static image, please let me know. There are some clever attempts out there to minimize the number of clicks and the number of elements in the widget, but none of them includes both black and white and all the shades of grey along with all the colors in a logical manner in the same image.

The nature of this problem arises from the familiar difficulty we face in so many other things: there are 3 primary colors, but the computer screen has only two dimensions. We can create all possible colors by combining the three basic colors(red, green, blue) in various proportions, so the most intuitive co-ordinate system for building a color space would be a cube.  Black at the origin, white at the other end of the diagonal, and pure red, blue, green at the vertices nearest to the origin. Feels good, but try representing it on a non-interactive 2d computer screen without loss of information. In general, my test is: if it can be painted on a piece of paper without loss of information, its good.

Even when we have two separate widgets for hue and brightness, the hue widget allows for a lot of flexibility in design. This widget needs to show only the proportion of the 3 component colors in a 2d plane, not the actual values of each. Even with this additional degree of freedom, I have noticed that many applications do not deliver the right solution. A lot of them allow for all possible combinations of either of any of two colors from the three, but not various combinations of all the three colors simultaneously.

Here is one of my initial attempts at creating a complete hue selection image:

Now on to an attempt to solve the initial problem. We need to show all the hues in the above triangle, AND show them with various intensities from dark to bright, in the SAME image, with minimum discontinuity from color to color, brightness to brightness. This is what I got on the first attempt:

Useless, isn’t it? The discontinuity is extreme. Here’s my next attempt:

Much better, but the aspect ratio is pretty wierd. Here’s the next attempt:

This is the best I’ve come up with so far, although I acknowledge it is not even close to being end-user acceptable. The locality of similar colors is still too low. It even looks as if there are lots of duplicate regions or that the entire spectrum is not accounted for, but both of these are optical illusions. Nothing is duplicated, and everything is included.

If anyone has ever seen a better solution, please let me know, I’m all eyes. Meanwhile I’ll continue trying myself. The one direction I am thinking of going next is a non standard shape for the image. Maybe a spiral? A mobius strip? A fractal pattern? Sometimes I think a sierpinski gasket might be the key to the solution, but I can’t quite place how.

Uptil yesterday, I used to think that thinking in 4 spatial dimensions is a purely analytical play (and “Time” as the 4th dimension never seemed intriguing enough anyway). But I just finished reading “The Möbius Strip” by Clifford Pickover, and now I believe I am actually able to mentally and somewhat visually integrate at least some key concepts. Now I not only accept, but also understand why two infinite planes which intersect each other in our 3-D world, could actually be non-intersecting planes in a 4-D world. The book has many other such amazing concepts explained with remarkable ease, and is highly recommended for the spatially inclined. If you are an origami aficionado, it is a definite must read.

There are theories out there that electricity, magnetism, gravity, and all the invisible forces are manifestations of the unseen 4th dimension. Sounds plausible enough. But String Theory is said to include 10, 11 or even 26 dimensions. Just like our 2 intersecting planes in 3-D can be made non-intersecting by adding a 4th dimension, it appears physicists keep adding an extra dimension to their theories to “get around” every new spatial incongruency they encounter in their thought experiments.

The inevitable questions..does “intelligence” have anything to do with all of this? Does it “emerge” by way of some unseen interaction in the 4th dimension. Is this why despite the hundreds of thousands of hu-man-hours spent pondering this problem, we have not been able to truly emulate a high form of intelligence? Does it mean that because of this extra-dimensional dependency, we will never be able to grasp the real mechanism?

I’m certainly not convinced that the brain’s functioning is somehow dependent on a 4th spatial dimension with a separate manifestation over and above the basic forces of nature (electricity, magnetism etc). I think “massive parallelism” is basis of the the complexity (quite a traditional view) that we are unable to overcome in our thought experiments. In fact, massive parallelism is the cause of the complexity in everything science is not able to do well today. The weather, fluids, the stock market, are all examples of systems where a huge number of entities comprise the system, and most of them are in turn dependent on even more other types of variables.

The problem in understanding our own brain’s function, I believe, also stems from some kind of innate capacity limit upon an intelligence trying to fathom its own composition.  For example, by my definition, to be called an “intelligence”, it must be “aware” of itself, or rather, of “something” that it perceives to be itself. What form that “itself” takes is the crux of the matter. If someone built a computer simulation of an intelligence which solves some problems given some reward/pain stimuli, imagine what it would look like if this intelligence suddenly understood its own construction! This would mean that it has become “aware” that it is a piece of software code which runs inside a computer. But get this, this would mean that it also understands what “software is”, and even what a “computer” is. This would imply that at the instant of its birth, it is pretty much as intelligent as the average hu-man!

For those that have pet dogs, I’m sure they appreciate the levels of emotionally complex and intelligent behavior these animals are capable of. They are all “intelligent” beings, and also self-aware. But does this mean that every dog out there primally understands that the seat of its intelligence lies in a glob of soft matter just behind its eyes? Certainly not. Even in hu-mans, most likely this knowledge is usually gained by virtue of the education system. To be a successful self-aware intelligence, it need not imply being aware of the low level physics of the awareness.

Imagine if a particular hu-man suddenly becomes fully self-aware. He can close his eyes, and look at his brain solve a mathematical problem, while solving it. Neurons are firing left and right for solving the problem, chemicals are rising and ebbing in tiny but significant portions, but at the same time this same brain is also looking at itself doing all of this activity. This act of “looking” would also cause various other neurons to fire, which would then need to be looked at as well. Sounds recursive, doesn’t it? I guess this is why I always get a headache whenever I contemplate this stuff too much.

A simple way to get out of this recursion would be to get a hu-man A to look at the brain activity of another hu-man B. As soon as A’s brain truly understands what is going on in B’s brain, it means A’s brain is able to simulate B’s brain to completeness, all the while still retaining the identity of A. This happening can only mean that A has a vastly more architecturally complex brain than B (not just higher IQ, but structurally more advanced). This means that the above scenario is not possible where A and B are both hu-mans.  To grasp why this must be generally true, think what would happen if while A is looking at the activity of B’s brain, B turns around and starts trying to follow A’s brain. Have you ever pointed a live video camera at the TV it is connected to? In summary, I theorize that:

a) To observe and understand an intelligence of complexity X, we would need another intelligence of at least complexity X^2. 

From which follows the corollary:

b) If an intelligence A is able to comprehend another intelligence B’s construction, it automatically means that B can never hope to comprehend A, no matter how hard it tries.

Where does all of this take us? I think it means that we will never be able to simulate human intelligence at the drop of a hat, or by turning on a computer and running a program, because only an intelligence vastly more complex than humans can do that.  A complete human like intelligence, if it has to run on different hardware than hu-mans themselves, will HAVE TO BE EVOLVED. And since we cannot replicate the hu-man hardware, the intelligence MUST EVOLVE DIFFERENTLY. As controllers of the hardware we will initially retain god-like status in controlling the direction of the evolution, but we will never know what lies next. Inevitably, one fine morning, a surprise will await us all.