That seems non-obvious to me. It’s highly problematic, sure—but not “key”. “Key” is “adequate range of data”.
I can see where you’re coming from. I may have mistaken “adequate range of data” for simply “range of data.” Thus it read more like, “I have this set of data. Which hypothesis is most closely like the ‘ideal explanation’ of this data.” Thus, the key piece of information will be in how you define “ideal explanation.”
Re-reading, I think both are critical. How you define the ideal still matters a great deal, but you’re absolutely right… the definition of an “adequate range” is also huge. I also don’t recall them talking about this, so that may be another reason why it didn’t strike me as strongly.
...and can’t say I entirely agree with the notion that our universe in no ways truly behaves probabilistically
Could you explain this? I thought that the fact that our universe did behave probabilistically was the whole point of Bayes’ theorem. If you have no rules of probability, why would you have need for a formula that says if you have 5 balls in a bucket and one of them is green, you will pull out a green one 20% of the time? If the universe weren’t probabilistic, shouldn’t that number be entirely unpredictable?
In other words; a Bayesian believes that each trial will have a set outcome that isn’t ‘fuzzy’ even at the time the trial is initiated. The frequentist on the other hand believes that probability makes reality itself fuzzy until the trial concludes. If you had a sufficiently accurate predicting robot, to the Bayesian, it would be ‘right’ in one million out of one million coin flips by a robotic arm. To the frequentist, on the other hand, that sort of accuracy is impossible.
Now, I believe Bayesian statistical modeling to be vastly more effective at modeling our reality. However, I don’t think that belief is incompatible with a foundational belief that our universe is probabilistic rather than deterministic.
Critical I can agree to. “Key” is a more foundational term than “critical” in my ‘gut response’.
I can dig.
If you had a sufficiently accurate predicting robot, to the Bayesian, it would be ‘right’ in one million out of one million coin flips by a robotic arm. To the frequentist, on the other hand, that sort of accuracy is impossible.
My initial response was, “No way Bayesians really believe that.” My secondary response was, “Well, if ‘sufficiently accurate’ means knowing the arrangement of things down to quarks, the initial position, initial angle, force applied, etc… then, sure, you’d know what the flip was going to be.”
If you meant the second thing, then I guess we disagree. If you meant something else, you’ll probably have to clarify things. Either way, what you mean by “sufficiently accurate” might need some explaining.
My initial response was, “No way Bayesians really believe that.”
When I was first introduced to the concept of Bayesian statistics, I had rather lengthy conversations on just this very example.
Either way, what you mean by “sufficiently accurate” might need some explaining.
“Sufficiently accurate” means “sufficiently accurate”, in this case. sufficient: being as much as needed; accurate. Synthesize the two and you have “being as without error and precise as needed”. Can’t get more clear than that, I fear.
Now, if I can read into the question you’re tending to with the request—well… let’s put it this way; there is a phenomenon called stochastic resonance. We know that quantum-scale spacetime events do not have precise locations despite being discrete phenonema (wave-particle duality): this is why we don’t talk about ‘location’ but rather ‘configuration space’.
Now, which portion of the configuration space will interact with which other portion in which way is an entirely probabilistic process. To the Bayesians I’ve discussed the topic with at any length, this is where we go ‘sideways’; they believe as you espoused: know enough points of fact and you can make inerrant predictions; what’s really going to happen is set in stone before the trial is even conducted. Replay it a trillion, trillion times with the same exact original conditions and you will get the same results every single time. You just have to get the parameters EXACTLY the same.
I don’t believe that’s a true statement. I believe that there is and does exist material randomness and pseudorandomness; and I believe further that while we as humans cannot ever truly exactly measure the world’s probabilities but instead only take measurements and make estimates, those probabilities are real.
Your “read into where I was tending with the request” was more like it. Sorry if I was unclear. I was more interested in what phenomenon such a machine would have at its disposal—anything we can currently know/detect (sensors on the thumb, muscle contraction detection of some sort, etc.), only a prior history of coin flips, or all-phenomenon-that-can-ever-be-known-even-if-we-don’t-currently-know-how-to-know-it? By “accurate”
I was more meaning, “accurate given what input information?” Then again, perhaps your addition of “sufficiently” should have clued me in on the fact that you meant a machine that could know absolutely everything.
I’ll probably have to table this one as I really don’t know enough about all of this to discuss further, but I do appreciate the food for thought. Very interesting stuff. I’m intuitively drawn to say that there is nothing actually random… but I am certainly not locked into that position, nor (again) do I know what I’m talking about were I to try and defend that with substantial evidence/argument.
Then again, perhaps your addition of “sufficiently” should have clued me in on the fact that you meant a machine that could know absolutely everything.
Funny thing. Just a few hours ago today, I was having a conversation with someone who said, “I need to remember, {Logos01}, that you use words in their literal meaning.”
I’m intuitively drawn to say that there is nothing actually random...
It’s a common intuition. I have the opposite intuition. As a layman, however, I don’t know enough to get our postulates in line with one another. So I’ll leave you to explore the topic yourself.
Indeed. Whether I should have caught on, didn’t think about what you wrote or not, or perhaps am trained not to think of things precisely literally… something went awry :)
To my credit (if I might), we were talking fairly hypothetical, so I don’t know that it was apparent that the prediction machine mentioned would have access to all hypothetical knowledge we can conceive of. To be explicitly literal, it might have helped to just bypass to your previous comment:
know enough points of fact and you can make inerrant predictions; what’s really going to happen is set in stone before the trial is even conducted...I believe that there is and does exist material randomness and pseudorandomness; and I believe further that while we as humans cannot ever truly exactly measure the world’s probabilities.
That would have done it easier than reference to a prediction machine, for me at least. But again, I’m more of a noob, so mentioning this to a more advanced LWer might have automatically lit up the right association.
So I’ll leave you to explore the topic yourself.
Sounds good. Thanks again for taking the time to walk through that with me!
I can see where you’re coming from. I may have mistaken “adequate range of data” for simply “range of data.” Thus it read more like, “I have this set of data. Which hypothesis is most closely like the ‘ideal explanation’ of this data.” Thus, the key piece of information will be in how you define “ideal explanation.”
Re-reading, I think both are critical. How you define the ideal still matters a great deal, but you’re absolutely right… the definition of an “adequate range” is also huge. I also don’t recall them talking about this, so that may be another reason why it didn’t strike me as strongly.
Could you explain this? I thought that the fact that our universe did behave probabilistically was the whole point of Bayes’ theorem. If you have no rules of probability, why would you have need for a formula that says if you have 5 balls in a bucket and one of them is green, you will pull out a green one 20% of the time? If the universe weren’t probabilistic, shouldn’t that number be entirely unpredictable?
Critical I can agree to. “Key” is a more foundational term than “critical” in my ‘gut response’.
The below might help:
In other words; a Bayesian believes that each trial will have a set outcome that isn’t ‘fuzzy’ even at the time the trial is initiated. The frequentist on the other hand believes that probability makes reality itself fuzzy until the trial concludes. If you had a sufficiently accurate predicting robot, to the Bayesian, it would be ‘right’ in one million out of one million coin flips by a robotic arm. To the frequentist, on the other hand, that sort of accuracy is impossible.
Now, I believe Bayesian statistical modeling to be vastly more effective at modeling our reality. However, I don’t think that belief is incompatible with a foundational belief that our universe is probabilistic rather than deterministic.
I can dig.
My initial response was, “No way Bayesians really believe that.” My secondary response was, “Well, if ‘sufficiently accurate’ means knowing the arrangement of things down to quarks, the initial position, initial angle, force applied, etc… then, sure, you’d know what the flip was going to be.”
If you meant the second thing, then I guess we disagree. If you meant something else, you’ll probably have to clarify things. Either way, what you mean by “sufficiently accurate” might need some explaining.
Thanks for the dialog.
When I was first introduced to the concept of Bayesian statistics, I had rather lengthy conversations on just this very example.
“Sufficiently accurate” means “sufficiently accurate”, in this case. sufficient: being as much as needed; accurate. Synthesize the two and you have “being as without error and precise as needed”. Can’t get more clear than that, I fear.
Now, if I can read into the question you’re tending to with the request—well… let’s put it this way; there is a phenomenon called stochastic resonance. We know that quantum-scale spacetime events do not have precise locations despite being discrete phenonema (wave-particle duality): this is why we don’t talk about ‘location’ but rather ‘configuration space’.
Now, which portion of the configuration space will interact with which other portion in which way is an entirely probabilistic process. To the Bayesians I’ve discussed the topic with at any length, this is where we go ‘sideways’; they believe as you espoused: know enough points of fact and you can make inerrant predictions; what’s really going to happen is set in stone before the trial is even conducted. Replay it a trillion, trillion times with the same exact original conditions and you will get the same results every single time. You just have to get the parameters EXACTLY the same.
I don’t believe that’s a true statement. I believe that there is and does exist material randomness and pseudorandomness; and I believe further that while we as humans cannot ever truly exactly measure the world’s probabilities but instead only take measurements and make estimates, those probabilities are real.
Your “read into where I was tending with the request” was more like it. Sorry if I was unclear. I was more interested in what phenomenon such a machine would have at its disposal—anything we can currently know/detect (sensors on the thumb, muscle contraction detection of some sort, etc.), only a prior history of coin flips, or all-phenomenon-that-can-ever-be-known-even-if-we-don’t-currently-know-how-to-know-it? By “accurate”
I was more meaning, “accurate given what input information?” Then again, perhaps your addition of “sufficiently” should have clued me in on the fact that you meant a machine that could know absolutely everything.
I’ll probably have to table this one as I really don’t know enough about all of this to discuss further, but I do appreciate the food for thought. Very interesting stuff. I’m intuitively drawn to say that there is nothing actually random… but I am certainly not locked into that position, nor (again) do I know what I’m talking about were I to try and defend that with substantial evidence/argument.
Funny thing. Just a few hours ago today, I was having a conversation with someone who said, “I need to remember, {Logos01}, that you use words in their literal meaning.”
It’s a common intuition. I have the opposite intuition. As a layman, however, I don’t know enough to get our postulates in line with one another. So I’ll leave you to explore the topic yourself.
Indeed. Whether I should have caught on, didn’t think about what you wrote or not, or perhaps am trained not to think of things precisely literally… something went awry :)
To my credit (if I might), we were talking fairly hypothetical, so I don’t know that it was apparent that the prediction machine mentioned would have access to all hypothetical knowledge we can conceive of. To be explicitly literal, it might have helped to just bypass to your previous comment:
That would have done it easier than reference to a prediction machine, for me at least. But again, I’m more of a noob, so mentioning this to a more advanced LWer might have automatically lit up the right association.
Sounds good. Thanks again for taking the time to walk through that with me!