Let’s say we create an idealized real computer, a computer that has uncountably infinite computing power and uncountably infinite memory via reducing the Planck constant to 0.
This is a hypercomputer, a computer that is more powerful than a Turing machine.
Then we ask it to simulate exactly a civilization that can make this computer, and it simulates another ad infinitum.
The important thing is that while there’s an infinite regress here, there’s no contradiction logically/mathematically speaking, unlike the finite case, since multiplying or adding infinities together, even infinitely many times, gets you an infinity from the same cardinality, but in the finite case, we have a computer with finite memory being multiplied by an infinite amount of simulations, meaning the computer is infinite, which contradicts our description of the finite computer we had earlier.
This is another way in which infinity doesn’t add up to normality or common sense, and messes with our intuitions.
Let’s say we create an idealized real computer, a computer that has uncountably infinite computing power and uncountably infinite memory via reducing the Planck constant to 0.
This is impossible, in this universe at least. There’s a maximum limit to information density per Planck volume. The Bekenstein bound.
It isn’t logically impossible, which is my point here. It’s likely physically impossible to do, but physically impossible is not equivalent to mathematically/logically impossible.
A better example of a logically/mathematically impossible thing to do is doubling the cube using only a straight-edge.
The definition of the Planck constant entails it must be non-zero. A zero constant isn’t anything at all. Hence a logical impossibility for any constant to be zero.
Alright, I’ll concede somewhat. Yes, the constants aren’t manipulatable, but nowhere does it show that a constant that just happens to be 0 isn’t logically possible, and thus I can reformulate the argument to not need manipulation of the constants.
And this is for a reason: Physics uses real numbers, and since 0 is a real number, it’s logically possible for a constant to be at 0.
Also, see vacuum decay for how a constant may change to a new number.
And this is for a reason: Physics uses real numbers, and since 0 is a real number, it’s logically possible for a constant to be at 0.
What? This doesn’t make any sense.
Physicists definitely use more than just Real numbers. And all well known physics journals have papers that contains them. You can verify it for yourself.
And even if for some reason that was not the case, what can be considered a constant has more than one requirement.
Logical possibility can also entail multiple prerequisites.
In retrospect, I still believe you can get a 0 constant to be logically possible under real, rational, integer and 1 definition of the natural numbers, I was just being too quick here to state, and that’s just the number systems I know, and physics almost certainly uses rational and integer numbers constantly, as well as natural numbers.
Can you elaborate on this?
Let’s say we create an idealized real computer, a computer that has uncountably infinite computing power and uncountably infinite memory via reducing the Planck constant to 0.
This is a hypercomputer, a computer that is more powerful than a Turing machine.
Then we ask it to simulate exactly a civilization that can make this computer, and it simulates another ad infinitum.
The important thing is that while there’s an infinite regress here, there’s no contradiction logically/mathematically speaking, unlike the finite case, since multiplying or adding infinities together, even infinitely many times, gets you an infinity from the same cardinality, but in the finite case, we have a computer with finite memory being multiplied by an infinite amount of simulations, meaning the computer is infinite, which contradicts our description of the finite computer we had earlier.
This is another way in which infinity doesn’t add up to normality or common sense, and messes with our intuitions.
This is impossible, in this universe at least. There’s a maximum limit to information density per Planck volume. The Bekenstein bound.
Yep, I know that, and indeed the only reason that we can’t make hypercomputers is because of the fact that the Planck constant is not 0.
So your proposed scenario is logically impossible. Why then does it matter for any case?
It isn’t logically impossible, which is my point here. It’s likely physically impossible to do, but physically impossible is not equivalent to mathematically/logically impossible.
A better example of a logically/mathematically impossible thing to do is doubling the cube using only a straight-edge.
The definition of the Planck constant entails it must be non-zero. A zero constant isn’t anything at all. Hence a logical impossibility for any constant to be zero.
Hm, can you show me where the definition of the physical constants entails it being non-zero?
https://en.wikipedia.org/wiki/Physical_constant#:~:text=A%20physical%20constant%2C%20sometimes%20fundamental,have%20constant%20value%20in%20time.
This a pretty common formulation. There are many more reference sources that are publicly accessible.
Alright, I’ll concede somewhat. Yes, the constants aren’t manipulatable, but nowhere does it show that a constant that just happens to be 0 isn’t logically possible, and thus I can reformulate the argument to not need manipulation of the constants.
And this is for a reason: Physics uses real numbers, and since 0 is a real number, it’s logically possible for a constant to be at 0.
Also, see vacuum decay for how a constant may change to a new number.
What? This doesn’t make any sense.
Physicists definitely use more than just Real numbers. And all well known physics journals have papers that contains them. You can verify it for yourself.
And even if for some reason that was not the case, what can be considered a constant has more than one requirement.
Logical possibility can also entail multiple prerequisites.
In retrospect, I still believe you can get a 0 constant to be logically possible under real, rational, integer and 1 definition of the natural numbers, I was just being too quick here to state, and that’s just the number systems I know, and physics almost certainly uses rational and integer numbers constantly, as well as natural numbers.