non physical mathematical entities. — EnPassant
Within the experiment many things are arguably determined including the choice to follow the digits but the choice itself is determined by the digit, not by a brain state or physical state: the digits determine what happens next and in this sense the choice itself is not physically deterministic. The digits are not determined to be what they are by any physical state. They are eternal truths.The choice to follow the digits is determined, so the paradigm is still in effect. Its pretty inescapable. — DingoJones
Now our choice is not determined by any physical or neurological state. — EnPassant
At each step of your process there is determinism. When you’re choosing the square root of 11, what to put on your list etc etc — DingoJones
As I think others implied, we would still have to address the decision to 'run' your algorithm in the first place. — macrosoft
I think the number has to be transcendental, not algebraic and hence not just irrational. Then it Works, I assume. You see algebraic numbers are countable. The square root of two is irrational, yet it is a solution of the polynomial equation x2 − 2 = 0.Comments? — EnPassant
I think the number has to be transcendental, — ssu
Any physical determinism that would have made the choice is terminated at the point when the digit intervenes and makes the choice. — EnPassant
Now our choice is not determined by any physical or neurological state. It is determined by purely non physical mathematical entities.
it's determined by the marks on the paper/whatever medium (or mental representation) and what you "chose" to assign as the course of action for that particular digit. — MindForged
Extreme determinsts maintain that the physical universe is just an outworking of the laws of nature and everything is predetermined by these laws. — EnPassant
We determine what symbols mean. They have no intrinsic meaning.
So why then irrational numbers in the first place? Unknown in advance is quite a loose definition the way you say it.No. All that is required is that the digits are unknown in advance (to counter the argument for brain states making the choice.) I can say 'I will choose the 75th digit in the expansion of the square root of 7'. I then go and see what it is and act accordingly. In this way physical determinism has not made the choice, it has been replaced by mathematical determinism. Any physical determinism that would have made the choice is terminated at the point when the digit intervenes and makes the choice. — EnPassant
here's no such thing as a nonphysical anything. — Terrapin Station
In what way is the “choice” the numbers make not moored to the equation itself and thus determined in precisely the same way as other deterministic processes? — DingoJones
So why then irrational numbers in the first place? — ssu
So basically irrationality or what the number would be used here wasn't important. "Known in advance" is quite vague definition here. By whom? Someone who isn't good at math (then even a rational number makes it) or the a math-enthusiast who can use his brain as a calculator?I chose irrational expansions simply because they are more in the spirit of the experiment, as opposed to predictable, repeating, rational expansions that could be known in advance. But there are all kinds of mathematical entities that would suffice. — EnPassant
This is a bit confusing. How do you define these two to being "physical", yet then something being "mathematical" as opposition to the first?But if physical determinism is to obtain all the way through it must be shown how the value of the digit is determined by physical laws. But it is not. It is mathematically determined. — EnPassant
Just for the record, math is a game that we play, with definitions and rules.
Math does not really exist outside of the human mind. It is simply an analytical tool that humans use to do things in an organized manner, such as count buffalo by prehistoric hunters. — hks
Reality follows patters which we can infer through scientific observation and measurement.
However the math that we humans have invented to approximate it is not reality. — hks
Restricting Determinism to direct physical objects is a straw man. — DingoJones
So basically irrationality or what the number would be used here wasn't important. "Known in advance" is quite vague definition here. By whom? — ssu
This is a bit confusing. How do you define these two to being "physical", yet then something being "mathematical" as opposition to the first? — ssu
Those are still determinate events since you could say it was your neurological (clasical) state which chose the irrational number. — JupiterJess
No, because as I said reality does have a mathematical structure to it. To call that "not reality" is just incoherent, the structure of reality is obviously part of reality. — MindForged
Laplace's original formulation concerned physical law and matter and that is what I am addressing. Mathematical truth is not physically determined by any physical state in the universe. I am not talking here about applied mathematics, I am talking about pure number theory. It is what it is, eternally. That is what is important. Eternal mathematical truth determines what happens, not any physical state. — EnPassant
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