As I tell my students if you are looking for a binary event to start modeling, look to individual ions moving across the membrane.
So it’s not infinite and can be digitized. :)
But to be more serious, digitized analog recordings is a bad analogy because audio can be digitized and perfectly reproduced. Nyquist- Shannon theory means the output can be perfectly reproduced. It’s not approximate. It’s perfect.
Analog signals can only be “perfectly” reproduced up to a specific target frequency. Given the actual signal is composed of infinite frequencies, you needs twice infinite sampling frequency to completely reproduce it.
“The mean free path in air is 68nm, and the mean inter-atomic spacing is some tens of nms about 30, while the speed of sound in air is 300 m/s, so that the absolute maximum frequency is about 5 Ghz.”
One cubic centimeter of air contains 90,000,000,000,000 atoms. In that context, mean free path is 68nm up to the limits of your ability to measure. That is flip a coin 90 million million times and average the heads and tails. It’s going to be extremely close to 50%.
Not to mention that at 5ghz, the sound can only propagate 68 nm.
It’s an analogy. There is actually an academic joke about the point you are making.
A mathematician and an engineer are sitting at a table drinking when a very beautiful woman walks in and sits down at the bar.
The mathematician sighs. “I’d like to talk to her, but first I have to cover half the distance between where we are and where she is, then half of the distance that remains, then half of that distance, and so on. The series is infinite. There’ll always be some finite distance between us.”
The engineer gets up and starts walking. “Ah, well, I figure I can get close enough for all practical purposes.”
The point of the analogy is not that one can’t get close enough so that the ear can’t detect a difference, it’s that in theory analog carries infinite information. It’s true that vinyl recordings are not perfect analog systems because of physical limitations in the cutting process. It’s also true for magnetic tape etc. But don’t mistake the metaphor for the idea.
Ionic movement across membranes, especially at the scale we are talking about, and the density of channels in the system is much closer to an ideal system. How much of that fidelity can you lose before it’s not your consciousness?
"I’d like to talk to her, but first I have to cover half the distance between where we are and where she is, then half of the distance that remains, then half of that distance, and so on. The series is infinite. "
I get it’s a joke but that’s a bad joke. That’s a convergent series. It’s not infinite. Any 1st year calculus student would know that.
"it’s that in theory analog carries infinite information. "
But in reality it can’t. The universe isn’t continous, it’s discrete. That’s why we have quantum mechanics. It is the math to handle non contiguous transitions between states.
How much of that fidelity can you lose before it’s not your consciousness?
That can be tested with c elegans. You can measure changes until a difference is propagated.
Measure differences in what? We can’t ask *c. elegans * about it’s state of mind let alone consciousness. There are several issues here; a philosophical issue here about what you are modeling (e.g. mind, consciousness or something else), a biological issue with what physical parameters and states you need to capture to produce that model, and how you would propose to test the fidelity of that model against the original organism. The scope of these issues is well outside a reply chain in Lemmy.
So it’s not infinite and can be digitized. :)
But to be more serious, digitized analog recordings is a bad analogy because audio can be digitized and perfectly reproduced. Nyquist- Shannon theory means the output can be perfectly reproduced. It’s not approximate. It’s perfect.
https://en.m.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem
Analog signals can only be “perfectly” reproduced up to a specific target frequency. Given the actual signal is composed of infinite frequencies, you needs twice infinite sampling frequency to completely reproduce it.
There aren’t infinite frequencies.
“The mean free path in air is 68nm, and the mean inter-atomic spacing is some tens of nms about 30, while the speed of sound in air is 300 m/s, so that the absolute maximum frequency is about 5 Ghz.”
The term “mean free path” sounds a lot like an average to me, implying an distribution which extends beyond that number.
One cubic centimeter of air contains 90,000,000,000,000 atoms. In that context, mean free path is 68nm up to the limits of your ability to measure. That is flip a coin 90 million million times and average the heads and tails. It’s going to be extremely close to 50%.
Not to mention that at 5ghz, the sound can only propagate 68 nm.
It’s an analogy. There is actually an academic joke about the point you are making.
The point of the analogy is not that one can’t get close enough so that the ear can’t detect a difference, it’s that in theory analog carries infinite information. It’s true that vinyl recordings are not perfect analog systems because of physical limitations in the cutting process. It’s also true for magnetic tape etc. But don’t mistake the metaphor for the idea.
Ionic movement across membranes, especially at the scale we are talking about, and the density of channels in the system is much closer to an ideal system. How much of that fidelity can you lose before it’s not your consciousness?
"I’d like to talk to her, but first I have to cover half the distance between where we are and where she is, then half of the distance that remains, then half of that distance, and so on. The series is infinite. "
I get it’s a joke but that’s a bad joke. That’s a convergent series. It’s not infinite. Any 1st year calculus student would know that.
"it’s that in theory analog carries infinite information. "
But in reality it can’t. The universe isn’t continous, it’s discrete. That’s why we have quantum mechanics. It is the math to handle non contiguous transitions between states.
That can be tested with c elegans. You can measure changes until a difference is propagated.
Measure differences in what? We can’t ask *c. elegans * about it’s state of mind let alone consciousness. There are several issues here; a philosophical issue here about what you are modeling (e.g. mind, consciousness or something else), a biological issue with what physical parameters and states you need to capture to produce that model, and how you would propose to test the fidelity of that model against the original organism. The scope of these issues is well outside a reply chain in Lemmy.