Hi. So, you have used True Randomness™ to build an instance of 3SAT. Okay. What I don't understand (and what you haven't proven as far as I can tell) is: how do you know that this instance of 3SAT cannot be solved in polynomial time?

@Stef I assumed if a deterministic algorithm couldn't be created to solve it then by default it couldn't be solved in polynomial time and only nondeterministically. as then the nondeterministic turing machine would be the most efficient method.

But how do you know that a deterministic algorithm couldn't be created to solve it?

BTW, if a nondeterministic algorithm can solve a given problem, then it's possible (and easy) to build a deterministic algorithm that can solve the same problem. What we don't know is whether we can keep things polynomial-time during this conversion.

@Stef well this may be a flaw in my knowledge, I was under the impression that if it is unpredictable by definition, then you would not be able to predict a solution deterministically with an algorithm. I might be wrong though.

What do you mean by "unpredictable"?

@Stef my understanding was that true randomness is unpredictable, as in you cannot predict the result without seeing it actually happen, meaning unless you check the right value for everything you won't be able to get the right value

Note that just because you use randomness doesn't necessarily mean that everything you build will be "unpredictable". For instance, imagine the following scenario: I flip a (truly-random) coin. If it's heads, I go have a haircut then I go have a beer. If it's tails, I go buy new shoes then I go have a beer. Before flipping the coin, I ask you the question: Am I going to have a beer today? Even if the coin is truly unpredictable, you can easily predict that I am going to have a beer.

@stef I see what you are saying, the idea is that since each variable was selected truly randomly, they have no relationship to each other in the actual problem.

Or this magic trick: Use true randomness to generate an integer between 1 and 9. Multiply this number by 3. Add 3 to the result. Multiply the result by 3. Now I will predict that the sum of the digits of the result is equal to 9.

@Stef you would be wrong most of the time and essentially guessing, and it wouldn't be deterministic.

No, I would never be wrong. Try it. I predict that the sum of the digits is going to be 9. I guarantee that my prediction was made using a deterministic algorithm.

@stef ahh I get what you're saying it is always 9, but you are creating something that is not completely random, as you have constants in it.

Indeed. And yet it was created using true randomness to generate a number. But I was able to give an entirely deterministic prediction about the result.

only because you have constants, with no constants that would not be possible, in the 3SAT there are no constants.

Okay, new version without constants. Generate a number X using true randomness. Add X to it. Add X to the result. Add X to the result. Add X to the result. Add X to the result. Add X to the result. Add X to the result. Add X to the result. I predict that the sum of digits of the result is equal to 9 now.

@Stef you would be wrong almost every time. because you haven't defined a constraint, anytime x is not equal to 1 you would be wrong which is almost 100% of the time.

No, I would always be correct. Try it if you don't believe me. I guarantee the sum of digits is going to be equal to 9.

@Stef 3+3+3+3+3+3+3+3+3=27

Yes. And the sum of digits of 27 is............ Roll drums....

@Stef ahh I misunderstood 10098764+1+1+1+1+1+1+1+1

@stef does not equal 9

What does "10098764+1+1+1+1+1+1+1+1 " mean and how does it relate to anything we've said before?

Anyway. I pointed out two of the flaws in your reasoning and tried to explain with concrete examples. Just because you use true randomness inside your work does not mean that nothing can be predicted about this work. Weather is most definitely random and yet we have weather forecast. Movement of individual particles is most definitely random and yet the behaviour of a gas is predictable. And you can generate a random number X and then predict the sum of digits of X+X+X+X+X+X+X+X+X.

@Stef I get what your saying, I just think those are false equivalences, because the concepts are different. For example weather is not truly random, and you cannot generate the number and predict the sum of the digits without specific limitations.

So none of the things that I talk about are "truly random", but the 3SAT instance that you've constructed is "truly random"? That's convenient. What does "truly random" mean, and do you have a proof that your 3SAT instance is "truly random"?

@Stef truly random is only found in quantum mechanics at the foundations of the universe physics.stackexchange.com/questions/560067/….

But you said your 3SAT instance was truly random. Surely your 3SAT instance is not the foundation of the universe.

@Stef no but I use an experiment en.wikipedia.org/wiki/Quantum_eraser_experiment that shows true randomness to decide the values within the 3SAT

Yes, but that doesn't prove anything. You can use true randomness to generate a number X and then add it to itself like we did earlier and then the sum of the digits of the result can be easily predicted. So, just the fact that you've used something truly random to build your 3SAT instance doesn't imply that your 3SAT instance is unpredictable. You'd need to define what the property of "truly random" or "unpredictable" means, and prove that your 3SAT instance has that property.

@Stef unpredictable means impossible to predict, we know the problem is truly random, because all factors are based off of something truly random.

So let me reformulate. I gave you this example where X was random and the sum of digits of 9X was not random. You identified that in my example, there was something that "killed the randomness" (you claimed that it was the constant 9). Now my question is: how do you know that in your 3SAT construction, there isn't also something that "kills the randomness"? It's not an easy question and you can't just claim "I know that my 3SAT problem is truly random" without justification. You need to define what "truly random" means, and prove that your 3SAT instance has that property.

@Stef that is something I can get behind I will attempt to do that

@Stef If all factors are created by true randomness they maintain the properties that come with it, and I have used true randomness for every factor in the equation, for example if you have a dice role and you transfer the number to a paper the number is still just as random as it was a minute ago, and if you plug the numbers in the equation that equation would follow the same rules for randomness as the dice.

@Stef which would be it is equally hard to predict the numbers in the equation as it would be if you just lined them up.

And yet all the terms in X+X+X+X+X+X+X+X+X were created by true randomness, but the sum of their digit was always equal to 9. So apparently that's not a sufficient condition.

@Stef the difference is 1 your not working in boolean algebra, 2 you created a limit on the length meaning not all variables are truly random meaning the problem is not truly random.

you can put a limit on the numbers sure, you have a range but the second something turns into a constant the equation is no longer truly random.

@ChadTheVlad the mistake is that you use structure to limit your true randomness. That structure you used is the structure of 3SAT problem. You can very well generate any problem with true randomness as a source to generate an instance of that problem. For example, you can use true randomness to generate a 2SAT problem. But we know that 2SAT can be solved in polynomial time.

@justhalf I will look into it.

@justhalf my conclusion is I have limited certain types of algorithmic approaches but not all of them, so I will continue to take my unorthodox approach of limiting algorithms until they have no option but to brute force.

@justhalf I have idea