Full Audio - The Geometry of Thinking: Logic, Creativity, and Control

Full audio + transcript expanding on the topic of geometry, logic, and human feeling. This is the complete thought process behind the lecture.

Audio:

Transcript:

Back to this idea of geometry and how it’s a great way to develop ideas and to think about things. Not just the shapes themselves, not actual shapes, but sort of an abstraction of geometry can lead to some interesting ideas.

I was just talking about how it can be dangerous teaching geometry because people will only learn geometry, and they’ll lose touch with the human in them. You know, they’ll atrophy as humans – human feeling. Structure and geometry, it doesn’t give life. There’s no life to it.  It doesn’t have meaning. It holds meaning if you know how to do it, and it’s all part of life. You need to know how to access it on a high level. You need to get there, though.

To get to that level where you’re able to control geometry and really master it, it is something that – what’s the best way to put this? You’re going to need both sides of you.  To deeply realize the truths of geometry and the use of geometry, you’re going to need to be human, and you’re going to need to be, you know, a geometer robot. You need to be able to do both equally well.

Here’s an idea, for example, that I’ve been thinking about lately. I was just thinking about the construction of silhouettes. Specifically, I’m working on ancient Egyptian, and I love that their most complicated contours are still very easily constructible with nothing more than simple circles and straight lines. I love that, and that’s a great mindset. I got thinking, what are the combinations of circles and lines that really come into play when you’re defining a silhouette of something?

So I just took three different variables. I thought, well, you could have a line that intersects with another line, and then a third line – line, line, line, right? You could have a line that goes to a circle, glides onto a circle, and then glides onto another circle. So that’d be like line, circle, circle. Then I got thinking, all right, well, lines are like logic, and circles are like creativity, L and C. Then I just figured out all the possibilities of these combinations, the combination of three, and so you get a workflow, if you will...

Oscillated cognition, is what I’m calling it, okay? It’s a way to oscillate between different states in a rhythmic pattern over time in order to achieve whatever results you want with art or life.

So an example is like - some things just straight up require entirely logical thinking. Like you don’t want anything creative at all involved. It’s just a straight logic proof. You’re trying to construct something. You’re trying to understand something mathematically. There’s no room for creativity. That’s an L, L, L. That’s three lines, okay? That’s that model.

And you have most of modern art, which would be C, C, C, - the circle, circle, circle model where it’s all just creativity, creativity, creativity. And there’s no room for logic in there. Then there are all these ones in between, and they are really where you want to be with art.

When you’re creating artwork, you want to be able to look at your process and say, “Okay, I’m going to get technical at some point, but do I start constructing or do I start by just feeling and then stop myself at some point to go in and analyze what I’m doing, what I’ve done in a technical way, you know, in a logical way, and make some decisions halfway through that are purely logical, like geometric - lines -  And then after that, you go back to human feeling to bring it home.” Right? So that’s the C, L, C model.

And there are different variants of this. There are eight models on how to go about things. And it’s the ones in the middle that really make the most sense.

What I’ve been finding is that I will start by constructing something logically, and then I will continue to go with logic. And then in the very end, I will just totally throw all that stuff away and just rely entirely on human feeling and then allow myself to know the structures that I’m destroying, and I’m destroying them with intention. I’m allowing myself to just break away from the structure. And it’s a great feeling, and it’s really a great form of expression - to know the structure that you’re abstracting. And it definitely ends with a resolve that feels human, you know, that feels – it has life to it. But then it also has that undertone of something intellectual that’s going on, and you can’t quite understand it, that there’s something going on under the hood. It’s a nice effect, but it’s a great workflow. 

If you don’t harness this type of workflow, you’re going to be trapped in one or the other camps. And that is not where you want to be. You don’t want to be stuck with a mind that is just great at mathematics and terrible at the other things. The best-case scenario, you are excellent at both. You can easily oscillate between creativity and logic. And you can hold them both in your hands at the same time as you’re creating, or you can ping-pong between them.

You can see things from a more divine perspective this way. If you’re trying to look at anything and analyze, make judgments on anything in life, you are closer to a divine perspective if you are not biased one way or the other. You can just step back and say, logically, “Okay, this is what makes sense.” And I also understand the human factors, you know, and the creative aspects of this and the unknowns, the radicals. You get it on many levels... Well. This is a great, great thing. There’s a reason why this really is all one thing in the end, why all of it is tied back to geometry.

Geometry is really something that - to get it to work well, where you’re making geometry create powerful images, for example, what you’re doing is, let’s just take a different example, let’s say you’re using geometry to structure a point that you’re trying to deliver in an essay or whatever. So you have your topic, and you have your supporting paragraphs that are the different angles that you’re going to take, but they’re all going to have their sub-parts and smaller parts. And then you edit it all down so all these different satellites of ideas are intended to strengthen the core idea that is just the nucleus in the middle, the point of what you’re trying to achieve, right? And the stronger that point, the stronger the point, right?

So you reinforce that with these structures like a hierarchy that’s orbiting this main central point that you’re trying to nail in. That’s geometry.

Now that could say it could have said the same thing about a picture.  Like really trying to bring all kinds of different aspects of a picture together to strengthen the heart of a figure, or to put emphasis on their intellect... you want to bring emphasis to that in some way, so that’s where your focus is, that’s where your "point" is.

Well, when we do this naturally, as humans, in our minds, we’re just  trying to make something that’s exactly the same thing... We were trying to make a picture of some somebody thinking that’s, you know, an intellectual person... we can tap into that. And we can create that - we can create it well, super laser focused, like Michelangelo, right? We can make beauty. Just tune out every other thing in the world and focus on this one aspect of what is the pinnacle of beauty.

If you can focus in on that, if you can tap into that, what you’re doing is you are strengthening the center point of a hierarchy, all your thoughts and all your actions are orbiting around the central point, and they are strengthening this one core objective... And that’s to make this beautiful thing.

So there’s mental geometry that is identical to the actual physical geometry that we’re used to seeing. There is geometry in the mind, and that is the reason why we can just - with the power of our mind, create beautiful images and beautiful art that has meaning and that’s alive, and that’s human - and it will be geometrically perfect.

When you go to analyze that afterward, you will find like perfect pentagonal structures and things that you can’t even possibly imagine. It will be like magic, but that is how it works. That’s just how it works. One follows the other. So, you know, choose your path, but definitely do not choose one over the other.

You want to be able to survive and you want to be able to adapt. And in today’s world, in the art world, you are much better off seeing things from both perspectives.

Tommy Hoppe