mlionson

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David Deutsch: A new way to explain explanation

I don't think he is saying, "good explanations are hard to vary while preserving their predictions".

As described above the statement "Everyone just acts in his own interest" very easily preserves its predictive power in a multitude of situations. Indeed, the problem with it is that the statement preserves its predictive power in too many situations! The explanation is consistent with just about whatever happens, so one cannot design a test that makes one believe that the statement is certainly false. So it is too easy to vary and hence a bad explanation.

Against Modal Logics

Evolution does not increase a species' implicit knowledge of the niche by replicating genes. Mutation (evolution's conjectures) creates potential new knowledge of the niche. Selection decreases the "false" implicit conjectures of mutations and previous genetic models of the niche.

So induction does not increase the implicit knowledge of gene sequences.
Trial (mutation) and error (falsification) of implicit theories does. This is the process that the critical rationalist says happens but more efficiently with humans.

Many Worlds, One Best Guess

I think I see where we are disagreeing.

Consider a quantum computer. If the laws of physics say that only our lack of knowledge limits the amount of complexity in a superposition, and the logic of quantum computation suggests that greater complexity of superposition leads to exponentially increased computational capacity for certain types of computation, then it will be quite possible to have a quantum computer sit on a desktop and make more calculations per second than there are atoms in the universe. My quote above from David Deutsch makes that point. Only the limitations of our current knowledge prevent that.

When we have larger quantum computers, children will be programming universes with all the richness and diversity of our own, and no one will be arguing about the reality of the multiverse. If the capacity for superposition is virtually limitless, the exponential possibilities are virtually limitless. But so will be the capacity to measure “counterfactual” states that are more and more evolved, like dead cats with lower body temperatures. Why will the body temperature be lower? Why will the cat in that universe not (usually) be coming back to life?

As you state, because of the laws of thermodynamics. With greater knowledge on our part, the exponential increase in computational capacity of the quantum computer will parallel the exponential increase in our ability to measure states that are decohering from our own and are further evolved, using what you call the “Everett camera”. I say “decohering from” rather than “decoherent from” because there is never a time when these states are completely thermodynamically separated. And the state vector has unitary evolution. We would not expect it to go backwards any more than you would expect to see your own cat at home go from a dead to an alive state.

I am afraid that whether we use an Everett camera or one supplied to us by evolution (our neuropsychological apparatus) we are always interpreting reality through the lens of our theories. Often these theories are useful from an evolutionary perspective but nonetheless misleading. For example, we are likely to perceive that the world is flat, absent logic and experiment. It is equally easy to miss the existence of the multiverse because of the ruse of positivism. “I didn’t see the needle penetrate the skin in your quantum experiment. It didn’t or (even worse!) can't happen.” But of course when we do this experiment with standard needles, we never truly see the needle go in, either.

I have enjoyed this discussion.

Many Worlds, One Best Guess

“To really make progress here, what we need is a thought-experiment in which a macroscopic superposition is made to yield information about more than one branch, as the counterfactualist rhetoric claims. Unfortunately, your needle-in-the-arm experiment is not there yet, because we haven't gone into the exact details of how it's supposed to work. You can't just say, 'If we did a quantum experiment where we could produce data about glucose levels in someone's bloodstream, without the needle having gone into their arm, why, that would prove that the multiverse is real!' Even just as a hypothetical, that's not enough. You need to explain how the decoherence shielding works and what the quantum readout system is”

I think you are mistaken here, Mitchell. But let me first thank you for engaging. Most people, when confronted with different outcomes than they expected from the fully logical implications of their own thinking, run screaming from the room.

Perhaps someone could write on these very pages a detailed quantum mechanical and excellent description of a hypothetical experiment in which a “counterfactual” blood sugar measurement is made. But if so, would that then make you believe in the reality of the multiverse? It shouldn’t, from a logical point of view. Because my (or anyone else’s) ability to do that is completely irrelevant to the argument about the reality of the multiverse...

We are interested in the implications of our understanding of the current laws of physics. When we now talk about which “interpretation” of quantum mechanics is the correct one, and that is what I thought we were talking about, we are talking about interpreting the current laws of physics. (Right?) What do the currently understood laws of physics allow us to do, using whichever interpretation one wants, since each interpretation is supposed to give the same predictions. If all the interpretations say that we can make measurements on counterfactual realities, then do all of the interpretations still make logical sense?

I think I have not yet heard an answer to the question, “Is there a current law of physics that prohibits a blood sugar measuring device from measuring counterfactual blood sugars?

Since I doubt (but could be mistaken) that you are able to point to a current law of physics that says that such a device can’t be created, I will assume that you can’t. That’s OK. I can’t either.

To my knowledge there is no law of physics that says there is an in principle limit on the amount of complexity in a superposition. If there is, show me which one.

Since there is no limit in the current laws of physics about this (and I assume we are agreeing on this point), those who believe in any interpretation of quantum mechanics (that makes these same predictions) should also agree on this point.

So adherents to any of the legitimate quantum mechanical interpretations (e.g Copenhagen, Transactional, Bohm, Everettian) should also agree that our current laws of physics do not limit the amount of complexity in a superposition.

And if a law of physics does not prevent something, then it can be done given enough knowledge. This is the most important point. Do you (Mitchell) dispute this or can anyone point out why I am mistaken about it? I would really like to know.

So if enough knowledge allows us to create any amount of complex superposition, then the laws of physics are telling us that any measurement that we can currently perform using standard techniques (for example measurements of blood sugars, lengths of tables, colors of walls, etc.) can also be performed using counterfactual measurement.

But if we can make the same measurements in one reality as another, given enough knowledge, why do we have the right to say that one reality is real and the other is not?

Update Yourself Incrementally

"What makes this theory a good one is that people have eaten turkeys for Thanksgiving in the past and induction tells us they are likely to do so in the future (absent other data that suggests otherwise like a rise in Veganism or something)."

I do appreciate your honesty in making this assumption. Usually inductivists are less candid (but believe exactly as you do, secretly. We call them crypto-inductivists!)

But there is no law of physics, psychology, economics, or philosophy that says that the future must resemble the past. There also is no law of mathematics or logic that says that when a sequence of 100 zeroes in a row are observed, the next one is more likely to be another zero. Indeed there are a literal INFINITE number of hypotheses that are consistent with 100 zero's coming first and then anything else coming next.

With respect, the reason you believe that Thanksgiving will keep coming has everything to do with your a-priori theory about culture and nothing to do with inductivism. You and I probably have rich theories that cultures can be slow to change, that brains may be hard-wired and difficult to change, that memes reinforce each other, etc. That is why we think Thanksgiving will come again. It is your understanding of our culture that allows you to make predictions about Thanksgiving, not the fact that it has happened for! For example, you didn't keep writing the year 19XX, just because most of your life you did so and did so repeatedly. You were not fooled by an imaginary principle of induction when the calendar turned from 1999 to 2000. You did not keep writing 19...something, just because you had written it before. You understood the calendar, just as you understand our culture and have deep theories about it. That is why you make certain predictions (Thankgiving will keep coming but you won't continue to write 19XX, no matter how many times you wrote it in the past.

I think you can see that your rationality,( not a principle of induction, not that everything stays the same) is actually what caused you to have rational expectations to begin with.

Many Worlds, One Best Guess

And if no law of physics precludes something from being done, then only our lack of knowledge prevents it from being done.

So if there are no laws of physics that preclude developing bomb testing and sugar measuring devices, our arguments against this have nothing to do with the laws of physics, but instead have to do with other parameters, like lack of knowledge or cost. So if the laws of physics do not preclude things form happening, we might as well assume that they can happen, in order to learn from the physics of these possible situations.

So for the purposes of understanding what our physics says can happen, it becomes reasonable to posit that devices have been constructed that can test the activity of Elitzur-Vaidman bombs without (usual) detonation or measure blood sugars without needles (usually) penetrating the skin. It is reasonable to posit this because the known laws of physics do not forbid this.

So those who do not believe in the multiverse but still believe in their own rationality do need to answer the question, "Where is the arm from which the blood was drawn?"

Or, individuals denying the possibility of such a measuring device being constructed need to posit a new law of physics that prevents Elitzur-Vaidman bomb testing devices from being constructed and blood sugar measuring devices (that do not penetrate the skin) from being constructed.

If they posit this new law, what is it?

Many Worlds, One Best Guess

The Elitzur-Vaidman bomb testing device is an example of a similar phenomenon. What law of physics precludes the construction of a device that measures blood sugar but with the needle (virtually never) penetrating the skin?

Update Yourself Incrementally

"And if the event happens even more when you expect it to then

it is even more evidence for the theory, "

I am not sure you agreed with this based on your response but I will assume that you did. But correct me if I am wrong!

If you did agree, then consider the Bayesian turkey. Every time he gets fed in November, he concludes that his owner really wants what's best for him and likes him, because he enjoys eating and keeps getting food. Every day more food is provided, exactly as he expects given his theory, so he uses Bayesian statistical inference to increase the confidence he has in his theory about the beneficence of his master. As more food is provided, exactly according to his expectations, he concludes that his theory is becoming more and more likely to be true. Towards the end of November, he considers his theory very true indeed.

You can guess the rest of the story. Turkeys are eaten at Thanksgiving. The turkey was killed.

I think you can see that probabilistic evidence, or any evidence, does not (can not) logically support a theory. It merely corroborates it. One can not infer from an example of something, a general rule. Exactly the opposite is the case. One cannot infer that because food is provided each day, that it will continue to be provided each day. Examples of food being provided do not increase the likelihood that the theory is true. But good theories about the world (people like to eat turkeys on Thanksgiving) helps one develop expected probabilities of events. If the turkey had a good theory, he would rationally expect certain probabilities. For example he would predict that he would be given food up until Nov. 25th, but not after.

I can summarize like this. Outcomes of probabilistic experiments do not tell us what it is rational to believe, any more than the turkey was justified in believing in the beneficence of his owner because he kept getting food in November. Probability does not help us develop rational expectations. Rational expectations, on the other hand, do help us to determine what is probable. When the turkey has a rational theory, he can determine the likelihood that he will or will not be given food on a given day.

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