Maybe—I can see how emotions may prevent human from accepting that humans are not special.
I am not talking about things humans can prove computationally.
Everything that humans can prove, can be proven by that computable algorithm. Including things you call “uncomputational”. If your point is just that humans are real so they can affect space and abstract computers are abstract, then real computers also can affect space, and perceive space better than humans. Is there part of this you disagree or it’s just that you think “people don’t talk about real-world effects of computers” is important?
I do not know how to “generalize” a literal real computer.
If you need to generalize it to make your point you can imagine your computer but with infinite memory and arbitrary fast execution speed. It can do literally everything a human can.
>If your point is just that humans are real so they can affect space and abstract computers are abstract, then real computers also can affect space
How can you affect space? Space is absolutely inert physically. There is no way to affect it.
I think you meant space as in w h i t e s p a c e. But that is basically only more light on your screen, not darkness, as real space is.
>Everything that humans can prove, can be proven by that computable algorithm.
How to have an algorithm prove that 1=1?
How do you know it is true, unless you define it that way first?
So it seems a computer cannot prove that, unless you define it true first.
That however can be proven, as you can define validation to not be able to able to be validated by computer.
As if you feed it the information 1=1 it could be programmed to output “false”, so if the definition of validation is absolute validation with no possibility of a false output, it is clearly wrong, as you can program a computer to falsely claim 1=1 is false.
However I doubt you would do that as you can see the uncomputable consistency and absolute 100% chance truth of 1=1.
This means the whole spectrum of completely false to completely true is available to a computable validation mechanism. A true proof is only true and can only be true as otherwise it would be not a proof, in so far as bivalent logic applies at all (which I will admit it does not always apply).
If you can validate it in a wrong way (meaning a false validation, or deducing the correct conclusion from a false premise, so that you can correctly conclude something that is wrong but correct), that is not really proving.
If you arbitrarily decide or guess whether the proof is accurate or not, it is not a proof.
This statement cannot be computationally verified: This statement cannot be proven.
Ever heard of Gödel?😅
The statement is true, but not provable. As nothing can be proven if you do not have a definition of what is true first. As we can see the Gödel sentence to be true, that entails that we can see true what is not provable, and hence not computationally verifiable too.
So we can realize truth beyond computational verification.
As if you feed it the information 1=1 it could be programmed to output “false”, so if the definition of validation is absolute validation with no possibility of a false output, it is clearly wrong, as you can program a computer to falsely claim 1=1 is false.
By that definition of validation humans never proved anything, because they sometimes say that 1=1 is false.
As we can see the Gödel sentence to be true, that entails that we can see true what is not provable, and hence not computationally verifiable too.
Gödel sentence for some formal system can’t be proven in that system, but it can be proven in more powerful system. Humans that see the sentence to be true are just (reasoning in a way equivalent to) using a more powerful formal system. And everything in that system is computably verifiable.
>Maybe—I can see how emotions may prevent human from accepting that humans are not special.
Fully agree here. I definitely have this issue as well!
Like we want to imagine we are so special in our power and intelligence that we can emulate them at what they are good at. We really cannot. Computers are already unfathomably more intelligent in the domain of precise calculation of crystallized information which they operate in. We also imagine we can program computers do anything we want.
Which again, computers will often do what their internal logic causes them to do, not what we program them to do, and they will always be like that, as that is how a computer operates.
So there is no hope to ever get to that level. I kind of want to speed up my computational speed sometimes, but I have trouble even getting the accuracy right, like calculating 3-digit number effortlessly. For a computer that is just a silly joke in terms of difficulty of calculation.
>If you need to generalize it to make your point you can imagine your computer but with infinite memory and arbitrary fast execution speed. It can do literally everything a human can.
Huh? I don’t think it could walk, as it does not have legs. I am not being silly here, I think you mean in terms of some abstract computational capability, but that is not what you said.
Again in a physical sense it is also not true. A computer is made of silicon so it cannot send information between neurons.
So I am not even sure in which sense it could be true. I think you mean in terms of precise calculations of crystallized information. I guess then you have very good point, as I already talked about above.
But then, the computer cannot do this: 💻💡
As THIS💡 is the light produced by the screen you are seeing when reading this, not a computation. It is not produced by the computer either, but by the screen the computer is connected to.
Maybe—I can see how emotions may prevent human from accepting that humans are not special.
Everything that humans can prove, can be proven by that computable algorithm. Including things you call “uncomputational”. If your point is just that humans are real so they can affect space and abstract computers are abstract, then real computers also can affect space, and perceive space better than humans. Is there part of this you disagree or it’s just that you think “people don’t talk about real-world effects of computers” is important?
If you need to generalize it to make your point you can imagine your computer but with infinite memory and arbitrary fast execution speed. It can do literally everything a human can.
>If your point is just that humans are real so they can affect space and abstract computers are abstract, then real computers also can affect space
How can you affect space? Space is absolutely inert physically. There is no way to affect it.
I think you meant space as in w h i t e s p a c e. But that is basically only more light on your screen, not darkness, as real space is.
>Everything that humans can prove, can be proven by that computable algorithm.
How to have an algorithm prove that 1=1?
How do you know it is true, unless you define it that way first?
So it seems a computer cannot prove that, unless you define it true first.
That however can be proven, as you can define validation to not be able to able to be validated by computer.
As if you feed it the information 1=1 it could be programmed to output “false”, so if the definition of validation is absolute validation with no possibility of a false output, it is clearly wrong, as you can program a computer to falsely claim 1=1 is false.
However I doubt you would do that as you can see the uncomputable consistency and absolute 100% chance truth of 1=1.
This means the whole spectrum of completely false to completely true is available to a computable validation mechanism. A true proof is only true and can only be true as otherwise it would be not a proof, in so far as bivalent logic applies at all (which I will admit it does not always apply).
If you can validate it in a wrong way (meaning a false validation, or deducing the correct conclusion from a false premise, so that you can correctly conclude something that is wrong but correct), that is not really proving.
If you arbitrarily decide or guess whether the proof is accurate or not, it is not a proof.
This statement cannot be computationally verified: This statement cannot be proven.
Ever heard of Gödel?😅
The statement is true, but not provable. As nothing can be proven if you do not have a definition of what is true first. As we can see the Gödel sentence to be true, that entails that we can see true what is not provable, and hence not computationally verifiable too.
So we can realize truth beyond computational verification.
By that definition of validation humans never proved anything, because they sometimes say that 1=1 is false.
Gödel sentence for some formal system can’t be proven in that system, but it can be proven in more powerful system. Humans that see the sentence to be true are just (reasoning in a way equivalent to) using a more powerful formal system. And everything in that system is computably verifiable.
>Maybe—I can see how emotions may prevent human from accepting that humans are not special.
Fully agree here. I definitely have this issue as well!
Like we want to imagine we are so special in our power and intelligence that we can emulate them at what they are good at. We really cannot. Computers are already unfathomably more intelligent in the domain of precise calculation of crystallized information which they operate in. We also imagine we can program computers do anything we want.
Which again, computers will often do what their internal logic causes them to do, not what we program them to do, and they will always be like that, as that is how a computer operates.
So there is no hope to ever get to that level. I kind of want to speed up my computational speed sometimes, but I have trouble even getting the accuracy right, like calculating 3-digit number effortlessly. For a computer that is just a silly joke in terms of difficulty of calculation.
>If you need to generalize it to make your point you can imagine your computer but with infinite memory and arbitrary fast execution speed. It can do literally everything a human can.
Huh? I don’t think it could walk, as it does not have legs. I am not being silly here, I think you mean in terms of some abstract computational capability, but that is not what you said.
Again in a physical sense it is also not true. A computer is made of silicon so it cannot send information between neurons.
So I am not even sure in which sense it could be true. I think you mean in terms of precise calculations of crystallized information. I guess then you have very good point, as I already talked about above.
But then, the computer cannot do this: 💻💡
As THIS💡 is the light produced by the screen you are seeing when reading this, not a computation. It is not produced by the computer either, but by the screen the computer is connected to.
I assumed it can make legs and neurons instantly using photons radiating from its chip.