As you may know, I’ve been erring in uncharted territory of the mathematical mind in seeking to understand fractals and the fractal nature of our world. In doing so, I tripped over a fallen tree marked “creativity”. If fractals have led me astray then creativity has me beamed into another universe and before you cross the bridge to the next paragraph, please be warned that in that other world, logic has its own rules and received wisdom was refused entry.
One of the features of trees that has stumped me, are branches. Huh? Branches? Yep, branches. We are very comfortable with things splitting into two. Couples separate, atoms split and T-junctions send you in two directions. So what.
As a mathematician I have no fundamental tools for splitting things other than by applying an external axes. Numbers don’t magically clone themselves. Plus signs don’t break up into other operators. Other than artificial constructs, a fundamental thing is a fundamental thing and if you manage to break it up, it means that it wasn’t fundamental but made up out of two things to start with.
But trees do branch. Fractals are trees with the peculiar property that branches resemble the very branches they grow from and are part of. But for my crawling through the mud of dark thought, this is not important. I’m talking trees. Simple trees, just a few lines on paper. Lines that branch away.
Lines that branch but shouldn’t, on my planet. One moment there is one line and the next moment there are two. This is the mystery of creation: a new line pops up out of nowhere.
And I don’t buy that.
I looked at convincing examples of such phenomena in nature, science and mathematics and didn’t find an example that actually works like that. When you really zoom in, there is never a point where one thing becomes two. There were always two somethings to start with in every example I looked at.
At times like that, I feel that I am a complete idiot. I see problems where there are none. I ask questions that most people abandon at the age of 6 and if anyone seriously asked them again, they will give a crystal clear explanation that can only end with: duh!
But on my planet, in my dark woods, I will happily trudge on. My boots are soaked and my cheeks are scratched by sharp branches that whip my face. What can I do? Fundamental things don’t split and simple lines don’t branch. These are the laws of my physics.
But if trees don’t branch and ones don’t become two’s then … the path that takes to left is a different path from the one that takes us to the right. There isn’t one path that splits: there are two that happen to overlap for a bit.
Clearing. Sunshine. Pond. Bench.
Fast forward, enjoy the break by all means but you got the picture. Trees are a collection of many twigs that go all the way back to a tiny root and that are bundled together in things we call trunks and branches. No wonder they are fatter at the bottom!
In my world, you can generalise from a tree to the universe faster than the speed of light: there is no instance in the universe where anything ever branches or duplicates. Everything is a collection of individual strands that bunch together and give the illusion of unity.Nothing is created out of nowhere. Not even a branch.
(Almost) every atom in my body, that is most definitely one, unique and slightly overweight, is a single strand that goes all the way back to the big bang. Check. What other proof do I need in my own special world that all objects, meaningful or not, are a bunch of space-time strands of particles?
Could the same model hold for thoughts? This ever expanding tree of knowledge, expression, content and so on? If a tree is not a tree but a bunch of twigs, than the tree of knowledge is a bunch of pico-ideas that go all the way back to the beginning of thought – and before. The fact that we clump them together into concepts like “digital watch” (remember those!) or “skippy ball”(OK, I’m old), doesn’t mean that there is anything new in there. Just a trunk of ancient pico-ideas that have been clumped into smarter and smarter concepts until we could finally hop around the lawn and know that the time was 88:88.
I’m not alone on my planet. There is this other dude who will walk up to me and say: ‘Bullshit. ‘
Don’t worry, I am used to that and tend to read between the lines. I think the point he is trying to make is that the idea of pico-idea trees is just a model. And besides, why would pico-ideas clump together? Why would anything clump together into meaningful trunks and branches?
Back to the forest.
On one side I have a swirling mess of particles and pico-ideas and on the other I have un-stainable shoes, Euler’s identity (remember e^i pi +1 = 0) and other great innovations. What happens in between? Think, think, think, said Tigger before he bounced away.
Let’s keep it simple. Let’s say that things clump together that fit together. That would suggest that things that clump together have certain complementary shapes or patterns. Puzzle pieces if you will. Imagine this swirling mess of puzzle pieces and occasionally two pieces that fit together just find themselves in the right place. Bingo. A new piece is created.
If you are from my planet, then this little mind experiment is enough to imagine an entire universe with planets and ape-like life forms being created from random clumping of meaningless bits and pieces. Meaningless?
[if you are running for the exit by now, please note the bridge to sanity at the end of this blog post]
Aren’t we intelligent? Aside from what I say, isn’t there real creativity? What about consciousness or God? I can here the other dude laughing. Whilst I am slaving away among the trees, he has put a lounger by the beach and is sipping Margaritas. I’ll be back, dude!
At the pico-scopic scale that my mind currently operates, there are only tiny puzzle pieces that are heaving and mixing. Triangles, squares, spheres, sticks and any other blob we can imagine. It occurs to me that it is quite clever that two of those might fit together. If you insist on the Anthropomorphism, I will allow that the fact that pieces fit together is intelligent. I realise that that is a pretty unsophisticated dumbed down form of intelligence, but it has to start somewhere. I will also allow that when they physically clump together, it is an act of creation. Stupid construction for sure, but creation all the same.
It has gone quiet by the beach. That does happen. The dude does shut up when he hears a good thing.
Intelligence is form.
Creation is intelligent forms, matching strands, sticking together.
I can hear the breeze rustle the leaves in the canopy. The silence passes as a Cockatoo screeches. My world begins to turn again and clocks resume their ticking.
I am left with observing the swirling mess of particles and pico-ideas that have clumped into this beautiful world around us. Even meaning and reality are clumped trunks and as a result all the things we hold dear are real and meaningful.
Ever since my mind started functioning after adolescence got out of the way, I have wondered about creation. Where do good ideas and things come from? Long ago I learned that good ideas come from giving the mind a break. Stop paying attention to the things that concern you. Meditate if you can; there is a cornucopia of good ideas ready to spring its bounty on you. I have now understood that all of those creative ideas originate from an unending universe of pico-idea strands that may just get close enough inside your brain for them to stick together and to form your next good thought; assuming you can still the mind enough for the swirling to slow down and let ideas form.
The dude has joined me; I am one again. He asks me if I told you about consciousness being self-observation and how duality dies when you understand that things are either one or two and that we often confuse these. I sigh. No, I haven’t. I’d like to but, even on my planet you need to demonstrate things from time to time. Philosophy and mathematics have one thing in common: you can prove anything you like, no matter how false it is. Fortunately, our brains are wired to be convinced by what it sees. So right now, I’m scouring the forest floor for evidence of any of this. I know its there.
So let me get back to you on duality.