If we want people to learn... to learn to build, not break down... we're going to have to show ourselves that it means something.

When math is as a woman, it means something.
What we have here is two views -- front and back -- of a 3 dimensional 'function-of-functions'.

To me it resembles, first, a pair of breasts. .Beyond this, it also recalls an 'hour-glass' waist, and a pair of gently curving shoulders as seen from behind.

In all it seems to function, outside Aphrodite's 'first' curves, as a sort of general-feminine-form; expressing many things, but none precisely.

If this is not enough... its smaller, (inset), back view seems to hold a meditating figure ...depending on imagination.

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I'm embarassed to say that I don't have a mathematical understanding of why the shape(s) are as they are.

It's deeper math than the 'Triabolic Roots' series. .For what we're watching here is not many actions of a single exponent, but many actions of many.

I'll explain what I can below, with lots more views to make the shape clearer; and probably learn something in the process, as is often the case.

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But first, more talk.

In an earlier draft, I mentioned "Intelligent Design".

I find myself in the ironic position, for an anti-Christian, of agreeing with fundamentalists -- for my own reasons.

Their thinking is that the complexity of nature, and of life in particular, indicates that something outside the system -- God -- has worked wonders.

My thinking is that the system itself seeks outcomes which will overcome obstacles before it... in recognition of the paths available to it.

Much like water seeks its way past the stones in a stream, or lightning seeks a path to ground -- this is not a singular, 'thinking' intelligence.

To invoke the 'two slit experiment', where photons were used to demonstrate that particulate outcomes can travel on possibility waves, (my interpretation);

a system of individually mindless entities may collectively behave as though they see not only their options, but eachother. .('Design Intelligence')

The fluid through which these 'possibility waves' would pass is the conductive medium of co-incidence; (conductive in that each outcome affects others).

From there my thinking on the whole thing wanders, (further if you will), into the woods... so that it's more a philosophy than a theory.

But then the same has been said of 'Intelligent Design'. .The difference is in the approach: .From without, or from within?

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"No other body-plan is as capable of developing and applying intelligence." .Let's go into that.

Aphrodite's curves recalls a pair of childbearing hips. .Her second curves, above, imagines breasts to feed the child,

a remarkable coincidence... and as previously stated: the narrowing waist, which if the variables are right, fits the hips well.

Even after years, the idea that related mathematical systems could represent and complement, here, is awe inspiring.

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Retorical questions: .What distinguishes humans? .Why have we assumed such mastery of our environments?

Retorical answers: .The brain. .This and hands that work. .(Language and community too, but these aren't covered here).

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We are medium sized creatures, small enough so that we can walk bipedally, which frees our forelimbs to specialize.

Yet we are large enough for an advanced brain to be housed in our skulls. .But to get that a further specialization was required.

Enter the hips. .They allow women to have babies with oversized heads, holding a brain already large at birth.

And of course, breasts with which to feed the newborn; allowing it to grow quickly and passing antibodies to disease in the process.

It may be chauvanistic, but I believe that the humanoid is a, perhaps the, fundamental biological form for technological life.

Here on Earth, people are primates -- we evolved from apes, (although the creationists would have it otherwise);

but this form could almost as easily have developed from raccoons or squirrels. .Their 'detailing' would be different.

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Back to pictures. .Below are some rotations of the form. .They're taken from an earlier, cruder graphing, and this shows. .Sorry.

At the bottom I complain about the "bleaching out" of the colors. .These are intended to run from purple through white to yellow.

However, as can be seen particularly the 45 and 135 degree miniatures; Mathcad can have trouble displaying closely spaced points.