For the full notes see here
https://streamofrandompodcast.wordpress.com/2021/01/02/stres1e203-the-goedel-fractal/
goedelfractal
This episode has extensive notes, if the links are not clickable in your podcast player visit the anchor.fm/str website for detailed show notes.
Nassim Haramein
The Nassim Haramein podcast can be found here.
Goedel number as a fractal.
Given the right encoding system, a number or a text can come to life as an executable program with the key to interpret it.
You can of course take a fractal program and encode it into a number using the Goedel numbering scheme, you can also compile it to a binary and convert the binary to assembly language as well.
brainfuck
Brainfuck is a programming langauge that is very close to a turning machine or goedelnumber.
It has the following operations,
0 > Move Right
1 < Move left
2 + Increment
3 – Decrement
6 [ While true
7 ] End while
4 , Input
5 . Output
8 Skip
Here is a mandelbrot fractal implement in brainfuck.
Here is a video of it rendering
PI
PI is a language that implements code in a number, so this is what hello world looks like
3.14159265358979323842264332327250288412716939927513582397492459230721640628220899867803480534311206298214838653322233664709084463955358323172235940832848311725028410370193853110525964460294895293032196422880097562591344612147514823378178346528120090214562856642346134861345532264821332360736034914137372428700663631558417448152392396222925459170536432789259026051133013014882046252138214295194153160243205227036275959395309212613732192261379310211855807440237946274952735182575273489122743848301134912983467436444065634308652133494633522473749030217386093370277033921317659317670238267581846066440
ternary
ternary is anthor language based on number.
Fractals in number
So you can see that we can encode a fractal generating program inside a number.
We can imagine that ever more complex things can be created using code not just fractals. Machine learning algorithms are again things that can be represented as just numbers as well as search engines.
We can use code to create ever more complex numbers or things that inspire imagination. The celluar automatons of wolfram he claims are a new kind of Science.
Fractals in imagination
The fractals create quite the emotional and imaginative reaction in people. The Holofractal group on reddit is quite interesting. We can see that presented with some fractals people imagination is trigged. We can see that a creative response is forthcoming. We covered this topic on the introspector model episodes where we define meaning as instructions that direct the mind to imagine things. Items that create a sensory response
Enscheidungsproblem
Given enough memory and space it can continue forever, this is however the large problem. We want to limit and be careful about what programs are allowed to execute.
Once activated a program can also never terminate or act in a way that is malicious. It is not generally possible to determine what the true nature of a given program is. The forms that life can express themselves in are varied.
The essential Turing: seminal writings in computing, logic, philosophy, artificial intelligence, and artificial life, plus the secrets of Enigma
The turing halting problem
The Halting Problem Link2 and termination problem The website Goedel Universe has some great information.
Unknowable Information
This is like the question of what is at the eye of providence? Who is behind the curtain. We dont know some things and we may never know them. This is the essence of the goedel incompletness theory.
We can also take the entire system of systems and turn that into a new goedel number, and array of them.
If we imagine that each point in the system is another number that references a different system, this can stretch out for a long time. It is possible to embed all the system into one number, all the numbers into one larger number. We can keep on folding them up.
The human mind itself may be an like a computational device in the Computational Theory of Mind, but we wont be able to express it as a number so easily, yet we can express the entire universe as a number or math.
I always thought of the name of god theorectially as an endless number of letters that encoded the entire universe.
If we were to clone or teleport or copy ourselves, even split into parallel universes does not mean we can describe everything as a number or symbol. Yet Terrance Mckenna claims that Phillip K Dick said in Valis that there existed a life in pure information, in logos.
Dr. Stone said. "The Logos would be living information, capable of replicating." Source1 Source2
There is the difference between a gene and a meme system.
The genes are physically expressed as life (unless we consider genetic computation etc)
and memes are expressed as physically encoded and represented yet copyable. They live h
