/sci/ - Science & Math

https://vocaroo.com/1dTu8dkNFpEy

>>12655044
Thanks. Really.

>>12655023
so you assume zfc to be consistent, set a process defined by it to then explore within itself where the boundary of its knowledge is limited by all possibilities consistent with it preserving itself. where then within this self terminating process where it ends its search does it run into an infinite loop of self termination

>>12655184
sure thing
>>12656435
>infinite loop
This depends entirely on how curiosity is modeled by the system.
For example, you could have a very incurious system that only responds to queries of the form: attempt to search for a derivation of p for the next ___ minutes. This system will always stop consuming resources after its time limit for serving a query has been reached.
Alternatively, one could program a system to be infinitely curious: enumerate the sentences p of the signature of set theory and spend ten minutes trying to find a derivation of each one.
This is the opposite: the only way to interact with this program is by starting it and reading the output, i.e. there is no interaction after turning on the power switch and it runs forever.

>>12655023
there are maybe a handful of people on this board who aren't retarded so you're probably not going to get an interesting response

>>12657012
Can a line of line of logic that would say something like 'if a then b, b is true if c is false, given c (something), therefor a is d given b is true' be given a line of logic where randomly it creates a paradox by shuffling the logic to be inverted and conclude the opposite premise? Could you then take this antilogic and set up a twin for your self actualizing zfc and set up a protocol where truth seeker runs into a p or q derivation string it say hey bro check this out, where lie maker runs a similar protocol. This could map a sort of antilogic space and with both being composed of the same elements yet different interworkings you could see whether their field converges or diverges. in the case that it converges zfc is then proven inconsistent.

>>12659262
how difficult can it be to implement this in Python or JavaScript
you need: Languages Proof Logic (1999) and Shorter Model Theory (1997) or equivalent
you can get both of those at genDOTlibDOTrusDOTec
only problem with using Python is I don't know an easy way to render TeX to an OpenGL context, so without an investment in that facility you'd have to settle for ASCII Fitch derivations
with JavaScript you could use HTML tables and MathJax
if you added about 10 pages of intro and definitions and some example code and derivations, any CS retard in a decent undergrad program could knock this out in a couple of weeks, probably less than 5 days for most
only problem is the design isn't very well specified so you'd have to spend several hours doing a close reading, which is more of a /lit/ skill
all of those details and snags would be fixed and sanded off during curriculum development

>>12660111
If you use html, program is called "html" if you use node.js program is called "javascript"

and never the else.

>>12659988
Since you haven't proven that ZFC is inconsistent, I'm not curious about formal systems that are weaker than it at the moment, although the fact of the matter is that it's quite natural to make such explorations: simply consider the power set of N. Any element is a formal system that is no stronger than ZFC, so those are the natural candidates to look for when weakening ZFC to a consistent formal system.

>>12655023
A is 1 string long
B is however many strings it takes
define A to be a string of logic that includes enough elements to match as many operators and every iteration of those operators in and of itself so that it is a complete and completely circular string. Create from A, B where for every operator or element in A, B creates a string of reordered elements and operators and their subsequent chains, until it goes through all possible iterations. Each of these new strings then has a potential to be a representation in a break for the circular argument A. B will then contain all circular arguments as equivalent permutations of A, but a new category will arise. This category will define all permutations of arguments possible by the system who's operators are analyzed in this context. set within B an operation which recursively collapses strings who's aggregate argument has an equivalence of a lower degree, count these for a set which tells us how many times this happened for the process, this tells us the degree of the upper boundary of iterations. This number derived from base set can be used to approximate a field of potential instances for all arguments of different complexity. Beyond this, you could create your incoherent logic set and then run the convergence test. Inside of your lie maker process set a protocol to permit B to be created within it but not believed for all iterations of B. Lie maker will then map the boundary of impossibility. Lie makers set would define all potential strings for what is and not within ZFC thereby proving the consistency of ZFC.

>>12655044
dumb music + talks like mouth is full of mucus
pathetic

>>12660490
then you do it in < 10 minutes
https://www.youtube.com/watch?v=Drii8bVAX1w

>>12655044
If you slowed down somewhat while reading you might sound smarter since you stutter so much its evident you're reading it aloud faster than your brain can process

>>12660586
https://vocaroo.com/1fvXWvjy0egV

ez

>>12660111
I want to design a cryptocurrency, well I already have to some extent, that uses the space of variations within a uint256 but constantly changes based on inputs for the effect of privacy. My understanding of ZFC set theory and this is cursory with only a few minutes of reading and a basic understanding of math, is to overcome the PN problem and find a solution within a set through a sort of shortest route for a salesman. I would like to defeat this force through a series of random rotating prime numbers that are shifted based on incoming txs or interactions with the blockchain.

What prime number factorizations or base prime numbers should I use?

>>12655023
How is this any different from building an automated theorem prover with Con(ZFC) adjoined to the tautologies as an additional axiom?

Okay OP Im really interested and Ill try to read it in detail later, but I would suggest you try to rewrite this in a bit of a better style. Having a large block of text iss too much schizo. You will reach more people if you manage to give this thing some structure. Make it clear what you want to do. I can see you're describing a computer running a certain program, but the question what this program does and what it's goal is, and what you hypothesize its result is are questions whose answers are buried in the text instead of clearly stated in the introduction.

>>12661806
>to the tautologies as an additional axiom?
surely you aren't suggesting that a tautology is an axiom

>>12661698
ask /biz/

>>12661630
much better. could you... repeat but closer to the mic, a little slower and more gently? please

>>12662280
>Having a large block of text iss too much schizo
millennial detected

>>12660300
you don't know anything

>>12661331
thanks
I'll stick with stupid and fast for now though

>>12662306
Half of what makes a good academic/scientist/thinker is being able to actually convey their ideas to people. A mathematical paper which is just a wall of formulas is useless as no one will bother to read it. A wall of text is even worse when it comes to mathematical content.

Idk man what I understood of this is that after having spent a bunch of time looking for an [math] x [/math] so that [math] A_p(x) [/math], it might make sense to start looking for a [math] y [/math] so that [math] A_{\exists_x A(x)}(y) [/math], and then you can look for a z so that [math] A_{\exists_y A_{\exists_x A(x)}(y)}(z) [/math] etc. etc...
But what is the point of this?

>>12662290
>surely you aren't suggesting that a tautology is an axiom
In the sense than an axiom is a statement that is self-evidently true, yes it is.
The consistency of a theory is unaffected by whether you take all of its statements as axioms, or merely some of them (and deduce the rest).