Sorry, are we talking about effects that are continuous, or effects that are discontinuous but which have probability distributions which are continuous?
I was rather assuming you meant the former considering you said ‘effects that are truly discontinuous.’.
Both of your responses are the latter, not the former, assuming I am understanding correctly.
*****
You can’t get around the continuity of unitary time evolution in QM with these kinds of arguments.
And now we’re into the measurement problem, which far better minds than mine have spent astounding amounts of effort on and not yet resolved. Again, assuming I am understanding correctly.
Sorry, are we talking about effects that are continuous, or effects that are discontinuous but which have probability distributions which are continuous?
We’re talking about the continuity of the function g. I define it in the post, so you can check the post to see exactly what I’m talking about.
And now we’re into the measurement problem, which far better minds than mine have spent astounding amounts of effort on and not yet resolved. Again, assuming I am understanding correctly.
This has nothing to do with how you settle the measurement problem. As I say in the post, a quantum Turing machine would have the property that this g I’ve defined is continuous, even if it’s a version that can make measurements on itself mid-computation. That doesn’t change the fact that g is continuous, roughly because the evolution before the measurement is unitary, and so perturbing the initial state by a small amount in L2-norm perturbs the probabilities of collapsing to different eigenstates by small amounts as well.
The result is that the function g:M→M is continuous, even though the wave-function collapse is a discontinuous operation on the Hilbert space of states. The conclusion generalizes to any real-world quantum system, essentially by the same argument.
[if no-one calls them out on it, declare victory. Otherwise wait a bit.]
No wait, the example shows A (but actually shows A″)
[if no-one calls them out on it, declare victory. Otherwise wait a bit.]
No wait, the example shows A (but actually shows A‴)
[if no-one calls them out on it, declare victory. Otherwise wait a bit.]
No wait, the example shows A (but actually shows A‴’)
etc.
Whereas your argument was:
A->B
Example purportedly showing A’
Therefore B.
[time passes]
No wait, the example shows A.
These, at first glance, are the same.
By ignoring terminology as uninteresting and constructing arguments that initially are consistent with these false proof techniques, you’re downgrading yourself in the eyes of anyone who uses Bayesian reasoning (consciously or unconsciously) and assigns a non-zero prior to you (deliberately or unwittingly) using a false proof technique.
In this case you’ve recovered by repairing the proof; this does not help for initial impressions (anyone encountering your reasoning for the first time, in particular before the proof has been repaired).
If you’ve already considered this and decided it wasn’t worth it, fair I suppose. I don’t think that’s a good idea, but I can see how someone with different priors could plausibly come to a different conclusion. If you haven’t considered this… hopefully this helps.
As far as I can see my argument was clear from the start and nobody seems to have been confused by this point of it other than you. I’ll admit I’m wrong if some people respond to my comment by saying that they too were confused by this point of my argument and your comment & my response to it helped clear things up for them.
It seems to me that you’re (intentionally or not) trying to find mistakes in the post. I’ve seen you do this in other posts as well and have messaged you privately about it, but since you said you’d rather discuss this issue in public I’m bringing it up here.
Any post relies on some amount of charity on the part of the reader to interpret it correctly. It’s fine if you’re genuinely confused about what I’m saying or think I’ve made a mistake, but your behavior seems more consistent with a fishing expedition in which you’re hunting for technically wrong statements to pick on. This might be unintentional on your part or a reflection of my impatience with this kind of response, but I find it exhausting to have to address these kinds of comments that appear to me as if they are being made in bad faith.
It seems to me that you’re (intentionally or not) trying to find mistakes in the post.
It is obvious we have a fundamental disagreement here, and unfortunately I doubt we’ll make progress without resolving this.
Euclid’s Parallel Postulate was subtly wrong. ‘Assuming charity’ and ignoring that would not actually help. Finding it, and refining the axioms into Euclidean and non-Euclidean geometry, on the other hand...
Sorry, are we talking about effects that are continuous, or effects that are discontinuous but which have probability distributions which are continuous?
I was rather assuming you meant the former considering you said ‘effects that are truly discontinuous.’.
Both of your responses are the latter, not the former, assuming I am understanding correctly.
*****
And now we’re into the measurement problem, which far better minds than mine have spent astounding amounts of effort on and not yet resolved. Again, assuming I am understanding correctly.
We’re talking about the continuity of the function g. I define it in the post, so you can check the post to see exactly what I’m talking about.
This has nothing to do with how you settle the measurement problem. As I say in the post, a quantum Turing machine would have the property that this g I’ve defined is continuous, even if it’s a version that can make measurements on itself mid-computation. That doesn’t change the fact that g is continuous, roughly because the evolution before the measurement is unitary, and so perturbing the initial state by a small amount in L2-norm perturbs the probabilities of collapsing to different eigenstates by small amounts as well.
The result is that the function g:M→M is continuous, even though the wave-function collapse is a discontinuous operation on the Hilbert space of states. The conclusion generalizes to any real-world quantum system, essentially by the same argument.
Absolutely. I continue to agree with you on this.
The part I was noting was incorrect was “our understanding of physics seems to exclude effects that are truly discontinuous.” (emphasis added).
g is continuous.f is not[1].
Or rather, may not be.
I think this is a terminological dispute and is therefore uninteresting. My argument only requires g to be continuous and nothing else.
Fair.
Terminology is uninteresting, but important.
There is a false proof technique of the form:
A->B
Example purportedly showing A’
Therefore B
[if no-one calls them out on it, declare victory. Otherwise wait a bit.]
No wait, the example shows A (but actually shows A″)
[if no-one calls them out on it, declare victory. Otherwise wait a bit.]
No wait, the example shows A (but actually shows A‴)
[if no-one calls them out on it, declare victory. Otherwise wait a bit.]
No wait, the example shows A (but actually shows A‴’)
etc.
Whereas your argument was:
A->B
Example purportedly showing A’
Therefore B.
[time passes]
No wait, the example shows A.
These, at first glance, are the same.
By ignoring terminology as uninteresting and constructing arguments that initially are consistent with these false proof techniques, you’re downgrading yourself in the eyes of anyone who uses Bayesian reasoning (consciously or unconsciously) and assigns a non-zero prior to you (deliberately or unwittingly) using a false proof technique.
In this case you’ve recovered by repairing the proof; this does not help for initial impressions (anyone encountering your reasoning for the first time, in particular before the proof has been repaired).
If you’ve already considered this and decided it wasn’t worth it, fair I suppose. I don’t think that’s a good idea, but I can see how someone with different priors could plausibly come to a different conclusion. If you haven’t considered this… hopefully this helps.
As far as I can see my argument was clear from the start and nobody seems to have been confused by this point of it other than you. I’ll admit I’m wrong if some people respond to my comment by saying that they too were confused by this point of my argument and your comment & my response to it helped clear things up for them.
It seems to me that you’re (intentionally or not) trying to find mistakes in the post. I’ve seen you do this in other posts as well and have messaged you privately about it, but since you said you’d rather discuss this issue in public I’m bringing it up here.
Any post relies on some amount of charity on the part of the reader to interpret it correctly. It’s fine if you’re genuinely confused about what I’m saying or think I’ve made a mistake, but your behavior seems more consistent with a fishing expedition in which you’re hunting for technically wrong statements to pick on. This might be unintentional on your part or a reflection of my impatience with this kind of response, but I find it exhausting to have to address these kinds of comments that appear to me as if they are being made in bad faith.
It is obvious we have a fundamental disagreement here, and unfortunately I doubt we’ll make progress without resolving this.
Euclid’s Parallel Postulate was subtly wrong. ‘Assuming charity’ and ignoring that would not actually help. Finding it, and refining the axioms into Euclidean and non-Euclidean geometry, on the other hand...