7. A second Conversation between the dog and his mad master
MM: See this chewing stick?
MM: Now it represents a line – one dimensional object.
D: Ok, I got it – now can I have it?
MM: Wait, see here are two more sticks? We can put them together and form a triangle – two dimensional object. Now after you ate them – where is the triangle?
MM: No! It still exists. Even more – it existed before, and it will exist forever when all the objects representing it will be gone.
D: Can I have more?
MM: What can we do with four sticks?
D: Four?! Where are they?
MM: Well, – now we will operate with pencils. We can form a square using four pencils.
D: triangles are better.
MM: Forget sticks. And actually forget pencils. They were just representations. The objects themselves existed anyway and will do so indefinitely. They are primordial. I would even call them extraordial if there is such a term. They exist independently of anything material.
MM: Triangle and Square are the most basic polygons. We can make more – pentagons, hexagons and so on, the list is infinite. Now let’s think in 3D – if we put four triangles together we get the first prime 3D solid – tetrahedron. Again one can build representations of it – pyramids out of anything. The next one is hexahedron or Cube – the only one with a common name – made out of six squares. The next is Octahedron, followed by a Dodecahedron build out of twelve pentagons.
MM: So it looks like we can continue indefinitely like with polygons, what do you think?
D: Of course!
MM: NO! There is just one more – Icosahedron. And that’s it – no more.
D: It’s a disappointment – what do you mean – no more?
MM: That’s the Law – only five prime solids exist. They are called platonic solids because they were first described by an ingenious man Plato many centuries ago.
D: That’s just plain boring. What can they do?
MM: Not much
D: So are we supposed to just stare at them?
MM: Well some people could. But you made a very good point – we need them to function. And that’s what I found for myself the most meaningful – making working Geometry.
Everything around us is dual, first – it exists and second – it functions. The being and the acting go together.
Plato’s solids represent the most primal entities in our Universe. There must be the most primal action as well. What else can perform it better than a mechanism based on one of the prime solids?
Apparently they can only function if they have parts. But how, you might ask, one can get parts of something as primal?
MM: By using the discoveries of two other geniuses – Johannes Kepler and Louis Poinsot. They found that faces of the solids can be extended until they intersect itself creating stellations. That’s where my quest should be directed – the star forms can be dissected using their own faces only – in a way that they will move in harmony. The proof of such mechanisms already exits – The Diagonal Star.
I already attempted to make the Plato’s solids to function. That’s why I made my Star of Red Pyramids. Unfortunately it moves along dissections which are not its faces.
D: So what?
MM: So it loses its relation to the solids. When the dissections are artificial the purpose is defeated. When you loosen up the requirements you get a different playing field. Say if you allow the solids to be made out of different polygons, you end up with fifteen more – Archimede’s solids (another great man BTW).
D: So use those, what’s the big deal.
MM: I have to concentrate on the forth Plato’s polyhedron – Dodecahedron.
MM: Because last summer I was sent an image of its second stellation incarnated in rusty metal. This summer I was sent an image of its third stellation incarnated in black onyx.
D: Do you know how crazy this sounds even for a dog?
MM: It very well might be. But I believe it’s the second human instinct comes into play.
D: What are you saying – there is one more?
MM: I believe so. It’s a drive to find your own purpose in this world.
D: I don’t feel that ever.
MM: And you don’t have to. It’s human’s burden.
D: Ok, I’ve heard enough, now let me speak. I got a feeling that you resent animal instincts in humans. That is affirmatively condescending towards both animals and humans following them.
MM: Not at all. 99 percent of high human emotions come from deeply unconscious urges, like love and hate, compassion and disgust. In fact all cultures in some ways are build on these basic instincts.
D: So why are you so against them?
MM: I am not. It’s just that humans are better of understanding what really drives them.
D: Why is that?
MM: Because Nature is beyond any moral, but humans are moral creatures. They can understand what’s bad, what’s not, and act on that understanding. Let’s say, a carnivore in Nature must be aggressive, fearless and totally senseless to the suffering of its prey. That’s the law of survival. People are carnivores too, and as such we possess a very gruesome instinct –
D: Are you saying – we, animals don’t have a choice but you, humans do?
MM: Yes, we do if we choose to. The problem is that most humans don’t even bother to analyze what’s driving them… This quotation gives a graphic description of major driving forces behind human behavioral patterns:
MM: So I’ve been looking at the GSHD for about a month and slowly realized that the ‘Four Spikes’ solution I found is also flawed. It will not function at all. Unlike the green-orange model, which wouldn’t hold together, this one is not going to assemble at all. Luckily I only made one part, not all five.
D: And what are you going to do now?
MM: I need to upgrade my skills. I am now dealing with such a complex geometry, that I need to learn a 3D software. I used to be able to handle these images in my head and make just paper models, like people did for centuries. That approach has been very genuine and authentic, but it’s just not powerful enough any more. I am learning Google SketchUp. It’s quite interesting, I already made some simple models. And I can print them! I am now printing my version of the Penrose puzzle…
D: You don’t sound too excited. You look lost again. Is it because you are not sure if any of this makes sense?
D: Let me ask you a question then. A tale you told your wife and cousin last winter – do you really believe it yourself? I mean the story about the computation machine. I heard it well then. Do you really think that the world can end due to something as negligible as a piece of paper folded and glued?
MM: It was more a figure of speech. I believe when you start something, regardless of its nature, you have to believe that it will be something absolutely incredible, the bestest of all, the best of anything done to date. Then it might have some value.
If you don’t believe it yourself, you better off not starting it at all.