Logic in philosophy is limited to physics, and the application of it to all moral forms is useless... We still need to think clearly and speak clearly, so we should be logical in our thoughts and use of words, but the subject is not one given to logical method, no psychology, nor history, nor sociology, and it is not because people do not try; but because we are infinite, both complex, and individually irrational...People only bear as much reason in their lives as they need to achieve their irrational goals... And philosophers starve to death trying to define the logical man while advertizers celebrate with every dollar the many myriads of irrationals...

Here's the thing, though. Your above paragraph (arguably) violates its own notion. To speak of something only to say that one cannot speak of it is still to speak of it. But I respect what your are driving at.

I view logic as the study of the structure of thought. So logic would apply to our thoughts about such things, and also to logic itself. Logic studies what it itself is subject to, the (invariable?) structure of human thinking.

As to ethics transcending logic, I can agree. But this might be saying no more than life is as emotional as it is rational. And that emotion cannot be perfectly calculated, will not fit into a mathematically precise thinking.

You have used the word "infinites," and I think this is a great metaphor. As the infinite cannot truly be thought.

Of infinites, many of which are not objects in fact, but social forms, we cannot say we Know anything no matter how much we presume....We can only have finite knowledge..

Does knowledge that an object is infinite count as finite or infinite knowledge?

Certain modern painters, the ones who abandoned representation, offer us what I like to call "absolute form."

It's just form, brothers and sisters (I'm preaching the gospel here). Form for the sake of form. Aesthetic means sensual. Form for the senses. I can't help but relate Ellsworth Kelly to Webern, for instance, and also to Euler's identity. Absolute form is form reduced to its lowest terms. Absolute form is a cube root. That sort of thing. Does anyone relate to this?

I would not call it an object, which is a judgement were it not finite, and I knew it to be finite; but in any event, all moral forms, as knowledge is, are infinites... They are not objects, and they are not finite... Knowledge is a meaning without a being, as all infinites are...Think of all the spiritual/moral forms we deal with...Are they forms at all when compared to physical forms??? Not....Yet day in and day out we give voice to our desire for liberty, of justice, or love, or happiness... Can you produce a fraction of any of these meanings as objects??? They are not real except for the fact that we make them real...We give them meaning out of the storhouse of meaning that is our own lives...

the absolute form is that which is macro physical

not mathematical

When you say macro, is that not itself a mathematical concept? It all depends on one's conception of math. For me, math deals with any sort of precise structure. You might say that precise structure as intelligible to human beings is math. Not only quantity, but shape. And beyond either of these, any rigorous and precise system of relationships.

what came first the object or the mathematics of the object ?

That's an excellent question. In my opinion, "math" and "logic" are not primal enough to make the same. But their common root is, and that for me is what Kant addressed in his transcendental analytic. What gives an object its objecthood? We must perceive qualia as unified. We must frame experience in order to sort it into objects. Objects are mind-made, but this includes the "mind." Which is why it's so hard to talk about and why Hegel has a questionable reputation.

What is the source of objects? I think this touches upon the Form of Forms.

for objects to be mind made , means that the mind understands that which makes up the object , do you understand the object galaxy without any pre-knowledge of it ?

If a man says he can picture the fourth dimension, why not 4 dimensional color-space?

I don't understand your claim, Recon. How is color space anything but both visual and mathematical?

Flatland is fun, but I think the metaphor is essentially one for transcendentals-- hierarchical reality.

I see what you are driving at, and I agree that we cannot explain the source of it all. But it's important, for me, to understand that both the galaxy and the mind are themselves just objects, albeit mental objects. But then all objects are mental objects, in my book.

This is not to deny the usual view that stuff exists outside us, but rather to stress that sensation (qualia) is organized by concept.

I think it's deceptive to say "objects are mind-made" and leave it at that, for the "mind" is one of these "mind"-made objects.

We need a negative ontology. All finite beings are contingent, which is to say that they are just one way of interpreting qualia. We should rather infer the "form of forms" or conceive of ourselves as conception itself. This is how I understand Hegel. The mind-matter duality is a confusion, no matter how useful it has been. (Confusion is relative to purpose.)

Well, I cannot construct a heptagon, so a seven dimensional system seems a little elusive at the moment.

Supposedly it is impossible. But then, there are many impossible things I would like to see overturned. Why not imagine 4 dimensional color-space?

Buckminster Fuller beautifully anticipated one of my own revelations in dealing with geometry- namely, that the tetrahedron is elementary and not the cube. He was able to construct all the platonic solids from the tetrahedron alone-- and that destroys two thousand years of platonic notions.

But the shape is not what is key: the axis are. In a Cartesian system 3 axis are at 90* and a Tetra system 4 axis are at 60*. More fascinating is the similitude a tetrahedron has with both the cube and the circle. So, although one cannot square a circle, tetrahedrons leave this search as unimportant.

Buckminster Fuller beautifully anticipated one of my own revelations in dealing with geometry- namely, that the tetrahedron is elementary and not the cube. He was able to construct all the platonic solids from the tetrahedron alone-- and that destroys two thousand years of platonic notions.

I'm down with the attempt. And it is conceivable for me even if I can't picture it. And one could call a moving hologram 4-d colorspace if we count movement as a time dimension.

I like this. This is where math gets creative, and that's the best part, one might argue. I just bumped into the polar plane not long ago. I like being introduced to yet another.

I was recently designing games, extensions of chess-shogi concepts, and it became clear to me that designing games was more fun than playing them. And the game systems themselves were art objects more fun to contemplate (at least for me) than to play. And yet their beauty is related to the idea of their playability. I posted these ideas in the creative writing forum.

I just looked at the tetra, and it does indeed seem like a more basic, primal shape than a cube. After all, the tetra seems like the minimum number of sides for a three dimensional shape. I was just exposed to that famous Euler equation about edges, sides, and vertices. It does sound like an exciting thought. I know about the geodesic dome. Obviously I'm a fan of equilateral triangles. So, did Plato build his solids from the cube then? Perhaps the cube appealed because of its math analogy, its simpler area/volume equations? Good stuff. I'm going to do some more research on this.

I found this to be a fascinating read. I hope it aides your love of mathematics. It is many pages long and covers numerous subjects. I think it ends on a rather sour note (nanomachines) compared to what it begins with, but there are still some interesting bits even in regards to nanomachines.

In a geodesic dome, no one "wall" bears the brunt of a strong wind, or carries the weight of a large load. Instead, the inter-angling of its many structural components spreads out the internal forces and balances them with external forces to maintain flexibility and strength even when using the lightest building materials. He called this principle of the equal distribution of forces "tensegrity," a word combining "tensile strength" and "structural integrity." Through applying this principle in architecture, Fuller planned to develop a new series of strong, durable structures whose strength increases with size and lightness rather than the heaviness of its components.23

Yes, I saw a little bit of that on your blog as well. I too have always been a fan of mods and tried making my own games. Friends and I have played board games that in which we designed the pieces; the problem is, however, is that their seems to be 2 popular methods- I prefer the one you present, which is more elementary. The other dives into the lore and fantasy of the pieces a bit too much for my tastes. (starcraft vs warcraft; strategy vs zealotry; gameplay vs roleplay)

There's a good reason why tetrahedra must be packed differently from other Platonic solids, according to the authors. Tetrahedra lack a quality known as central symmetry. To possess this quality, an object must have a center that will bisect any line drawn to connect any two points on separate planes on its surface. The researchers also found this trait absent in 12 out of 13 of an even more complex family of shapes known as the Archimedean solids.