Answer by bogdanbiv for Intuitive crutches for higher dimensional thinking

2010-05-28T09:57:35Z

The first thing you'd want to do is to take away the continuum of space, because humans understand better discreet space. Its easier to think of space in discrete chunks, that is I divide space in units of known conventional size. Let's take the example of LCD screens in computers: the LCD is made of many pixels put on a 2-dimensional matrix. You can tell if a line on the screen is longer than another an for all purposes here it behaves like normal space, respects the same math laws and so on.

But then, each pixel that makes the screen has 3 tiny devices that make it emit light in different spectrum ranges, that is RED, GREEN, BLUE (RGB for short). Each device for a given pixel and color takes one input in the range of 0..255 to know the intensity of the light it lets out, 0 stands for no light emitted and 255 for the brightest. One pixel can be bright red and have all the other columns shut - that is it's RGB are (RED: 255, GREEN: 0, BLUE: 0). It is unessential that a pixel with RED 255, GREEN 0, BLUE 255 is actually purple.

And now the essential: you could consider each of those color values as a new dimension. Your LCD screen has now 3 new dimensions, making up for a total of 5 dimensions. But now, another contraption: what if you could stack several LCD displays on top each other (and see through any depth you wish for)? You could then "see" 6 dimensions, right?

Now, if you could imagine that such an "LCD cube" takes part of a space with pixels infinite small, infinite range for all dimensions width, height, depth and color and there you have a continuum 6-dimensional space. Again not considering that two colors make another color (red and blue make purple as stated above), you could add more color coded dimensions. I don't think you could represent these in real life or in software, but hey, this is imagination! So, given an "N" number of colors, there you have it: N-dimensional space with color coded dimensions!

If you want to know more about colors and displays the best place to start is the browser using HTML and CSS. You can make a txt file with <div style="background: rgb(255, 0, 255)"></div> as content and start experimenting with colors. Search the web for: [http://www.google.com/search?client=ubuntu&channel=fs&q=html+colors&ie=utf-8&oe=utf-8]HTML color[1] and you'll find plenty.

Another example is thermal gradient which measures "How hot it is at a given distance from a hot object?". Measuring that in many points around a hot object makes a 3D heat map. In this case temperature gradient is a fourth dimension, representing it however still uses color codes (usually dark/green, red, yellow, white for cold, hot, hotter and respectively the hottest). Thermal gradient

Comment by bogdanbiv

2010-05-28T14:48:36Z

B) How do you feel N-dimensional space? In 1D, 2D and even 3D humans compute distance natively - that is if one gives you 2 segments anywhere in sight you can see which segment is longer. It doesent take a scientist to find out the answer. With N-dimensional space that's much harder to compute even with a pencil and a paper! Without computing distance automatically in the brain, our perception of the (X, Y, Z, Red) space is crippled. There is no empiric feeling about it and we rely on Rational Process, instead of Vision, in order to see through it. Never mention XYZRGB space or higher dims.

Comment by bogdanbiv

2010-05-28T14:31:37Z

A) Let's try it just to see how difficult it is to repesent: we add the fourth color coded dimension PURPLE. So now we have X, Y, Z, RED, GREEN, BLUE and PURPLE. We take three points in this space as an example, keeping X, Y, Z, as 0 because everyone knows about them. First we need to know that (0, 0, 0, 1, 0, 1, 0) and (0, 0, 0, 0, 0, 0, 1) although are different points they will show as just one point because in real LCD's colors don't change independently as in our "algebraic LCD screen".

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Answer by bogdanbiv for Intuitive crutches for higher dimensional thinking

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