An illustrative example is that, when explaining lightning, Maxwell’s equations are simpler in this sense than the hypothesis that Thor is angry because the shortest computer program that implements Maxwell’s equations is much simpler than an emulation of a humanlike brain and its associated emotions.
I just realized that this argument, long accepted on LW, seems to be wrong. Once you’ve observed a chunk of binary tape that has at least one humanlike brain (you), it shouldn’t take that many bits to describe another (Thor). The problem with Thor isn’t that he’s humanlike—it’s that he has supernatural powers, something you’ve never seen. These supernatural powers, not the humanlike brain, are the cause of the complexity penalty. If something non-supernatural happens, e.g. you find your flower vase knocked over, it’s fine to compare hypotheses “the wind did it” vs “a human did it” without penalizing the latter for humanlike brain complexity.
(I see Peter de Blanc and Abram Demski already raised this objection in the comments to Eliezer’s original post, and then everyone including me cheerfully missed it. Ouch.)
I originally agreed with this comment, but after thinking about it for two more days I disagree. Just because you see a high-level phenomenon, doesn’t mean you have to have that high-level phenomenon as a low-level atom in your model of the world.
Humans might not be a low-level atom, but obviously we have to privilege the hypothesis ‘something human-like did this’ if we’ve already observed a lot of human-like things in our environment.
Suppose I’m a member of a prehistoric tribe, and I see a fire in the distance. It’s fine for me to say ‘I have a low-ish prior on a human starting the fire, because (AFAIK) there are only a few dozen humans in the area’. And it’s fine for me to say ‘I’ve never seen a human start a fire, so I don’t think a human started this fire’. But it’s not fine for me to say ‘It’s very unlikely a human started that fire, because human brains are more complicated than other phenomena that might start fires’, even if I correctly intuit how and why humans are more complicated than other phenomena.
The case of Thor is a bit more complicated, because gods are different from humans. If Eliezer and cousin_it disagree on this point, maybe Eliezer would say ‘The complexity of the human brain is the biggest reason why you shouldn’t infer that there are other, as-yet-unobserved species of human-brain-ish things that are very different from humans’, and maybe cousin_it would say ‘No, it’s pretty much just the differentness-from-observed-humans (on the “has direct control over elemental forces” dimension) that matters, not the fact that it has a complicated brain.’
If that’s a good characterization of the disagreement, then it seems like Eliezer might say ‘In ancient societies, it was much more reasonable to posit mindless “supernatural” phenomena (i.e., mindless physical mechanisms wildly different from anything we’ve observed) than to posit intelligent supernatural phenomena.’ Whereas the hypothetical cousin-it might say that ancient people didn’t have enough evidence to conclude that gods were any more unlikely than mindless mechanisms that were similarly different from experience. Example question: what probability should ancient people have assigned to
The regular motion of the planets is due to a random process plus a mindless invisible force, like the mindless invisible force that causes recently-cooked food to cool down all on its own.
vs.
The regular motion of the planets is due to deliberate design / intelligent intervention, like the intelligent intervention that arranges and cooks food.
This seems right, though something about this still feels confusing to me in a way I can’t yet put into words. Might write a comment at a later point in time.
Once you’ve observed a chunk of binary tape that has at least one humanlike brain (you), it shouldn’t take that many bits to describe another (Thor).
Maxwell’s Equations don’t contain any such chunk of tape. In current physical theories (the Standard Model and General Relativity), the brains are not described in the math, rather brains are a consequence of the theories carried out under specific conditions.
Theories are based on postulates which are equivalent to axioms in mathematics. They are the statements from which everything else is derived but which can’t be derived themselves. Statements like “the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer.”
At the turn of the 20th century, scientists were confused by the apparent contradiction between Galilean Relativity and the implication from Maxwell’s Equations and empirical observation that the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer. Einstein formulate Special Relativity by simply asserting that both were true. That is: the postulates of SR are:
the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer.
The only way to reconcile those two statements is if time and space become variables. The rest of SR is derived from those two postulates.
Quantum Field Theory is similarly derived from only a few postulates. None of them postulate that some intelligent being just exists. Any program that would describe such a postulate would be relatively enormous.
In current physical theories (the Standard Model and General Relativity), the brains are not described in the math, rather brains are a consequence of the theories carried out under specific conditions.
Yeah. But not sure you got the point of my argument. If your brain is a consequence of theory+conditions, why should the hypothesis of another humanlike brain (Thor) be penalized for excessive complexity under the same theory+conditions?
You’re trying to conflate theory, conditions, and what they entail in a not so subtle way. Occam’s razor is about the complexity of a theory, not conditions, not what the theory and conditions entail. Just the theory. The Thor hypothesis puts Thor directly in the theory. It’s not derived from the theory under certain conditions. In the case of the Thor theory, you have to assume more to arrive at the same conclusion.
Thor isn’t quite as directly in the theory :-) In Norse mythology he’s a creature born to a father and mother, a consequence of initial conditions just like you.
Sure, you’d have to believe that initial conditions were such that would lead to Thor. But if I told you I had a neighbor named Bob, you’d have no problem believing that initial conditions were such that would lead to Bob the neighbor. You wouldn’t penalize the Bob hypothesis by saying “Bob’s brain is too complicated”, so neither should you penalize the Thor hypothesis for that reason.
The true reason you penalize the Thor hypothesis is because he has supernatural powers, unlike Bob. Which is what I’ve been saying since the first comment.
Thor isn’t quite as directly in the theory :-) In Norse mythology...
Tetraspace Grouping’s original post clearly invokes Thor as an alternate hypothesis to Maxwell’s equations to explain the phenomenon of electromagnetism. They’re using Thor as a generic stand-in for the God hypothesis.
Norse mythology he’s a creature born to a father and mother, a consequence of initial conditions just like you.
Now you’re calling them “initial conditions”. This is very different from “conditions” which are directly observable. We can observe the current conditions of the universe, come up with theories that explain the various phenomena we see and use those theories to make testable predictions about the future and somewhat harder to test predictions about the past. I would love to see a simple theory that predicts that the universe not only had a definite beginning (hint: your High School science teacher was wrong about modern cosmology) but started with sentient beings given the currently observable conditions.
Sure, you’d have to believe that initial conditions were such that would lead to Thor.
Which would be a lineage of Gods that begins with some God that created everything and is either directly or indirectly responsible for all the phenomena we observe according to the mythology.
I think you’re the one missing Tetraspace Grouping’s point. They weren’t trying to invoke all of Norse mythology, they were trying to compare the complexity of explaining the phenomenon of electromagnetism by a few short equations vs. saying some intelligent being does it.
You wouldn’t penalize the Bob hypothesis by saying “Bob’s brain is too complicated”, so neither should you penalize the Thor hypothesis for that reason.
The existence of Bob isn’t a hypothesis it’s not used to explain any phenomenon. Thor is invoked as the cause of, not consequence of, a fundamental phenomenon. If I noticed some loud noise on my roof every full moon, and you told me that your friend bob likes to do parkour on rooftops in my neighborhood in the light of the full moon, that would be a hypothesis for a phenomenon that I observed and I could test that hypothesis and verify that the noise is caused by Bob. If you posited that Bob was responsible for some fundamental forces of the universe, that would be much harder for me to swallow.
The true reason you penalize the Thor hypothesis is because he has supernatural powers, unlike Bob. Which is what I’ve been saying since the first comment.
No. The supernatural doesn’t just violate Occam’s Razor: it is flat-out incompatible with science. The one assumption in science is naturalism. Science is the best system we know for accumulating information without relying on trust. You have to state how you performed an experiment and what you observed so that others can recreate your result. If you say, “my neighbor picked up sticks on the sabbath and was struck by lightning” others can try to repeat that experiment.
It is, indeed, possible that life on Earth was created by an intelligent being or a group of intelligent beings. They need not be supernatural. That theory, however; is necessarily more complex than any a-biogenesis theory because you have to then explain how the intelligent designer(s) came about which would eventually involve some form of a-biogenesis.
Yeah, I agree it’s unlikely that the equations of nature include a humanlike mind bossing things around. I was arguing against a different idea—that lightning (a bunch of light and noise) shouldn’t be explained by Thor (a humanlike creature) because humanlike creatures are too complex.
Well, the original comment was about explaining lightning
You’re right. I think I see your point more clearly now. I may have to think about this a little deeper. It’s very hard to apply Occam’s razor to theories about emergent phenomena. Especially those several steps removed from basic particle interactions. There are, of course, other ways to weigh on theory against another. One of which is falsifiability.
If the Thor theory must be constantly modified so to explain why nobody can directly observe Thor, then it gets pushed towards un-falsifiability. It gets ejected from science because there’s no way to even test the theory which in-turn means it has no predictive power.
As I explained in one of my replies to Jimdrix_Hendri, thought there is a formalization for Occam’s razor, Solomonoff induction isn’t really used. It’s usually more like: individual phenomena are studied and characterized mathematically, then; links between them are found that explain more with fewer and less complex assumptions.
In the case of Many Worlds vs. Copenhagen, it’s pretty clear cut. Copenhagen has the same explanatory power as Many Worlds and shares all the postulates of Many Worlds, but adds some extra assumptions, so it’s a clear violation of Occam’s razor. I don’t know of a *practical* way to handle situations that are less clear cut.
I just realized that this argument, long accepted on LW, seems to be wrong. Once you’ve observed a chunk of binary tape that has at least one humanlike brain (you), it shouldn’t take that many bits to describe another (Thor). The problem with Thor isn’t that he’s humanlike—it’s that he has supernatural powers, something you’ve never seen. These supernatural powers, not the humanlike brain, are the cause of the complexity penalty. If something non-supernatural happens, e.g. you find your flower vase knocked over, it’s fine to compare hypotheses “the wind did it” vs “a human did it” without penalizing the latter for humanlike brain complexity.
(I see Peter de Blanc and Abram Demski already raised this objection in the comments to Eliezer’s original post, and then everyone including me cheerfully missed it. Ouch.)
I originally agreed with this comment, but after thinking about it for two more days I disagree. Just because you see a high-level phenomenon, doesn’t mean you have to have that high-level phenomenon as a low-level atom in your model of the world.
Humans might not be a low-level atom, but obviously we have to privilege the hypothesis ‘something human-like did this’ if we’ve already observed a lot of human-like things in our environment.
Suppose I’m a member of a prehistoric tribe, and I see a fire in the distance. It’s fine for me to say ‘I have a low-ish prior on a human starting the fire, because (AFAIK) there are only a few dozen humans in the area’. And it’s fine for me to say ‘I’ve never seen a human start a fire, so I don’t think a human started this fire’. But it’s not fine for me to say ‘It’s very unlikely a human started that fire, because human brains are more complicated than other phenomena that might start fires’, even if I correctly intuit how and why humans are more complicated than other phenomena.
The case of Thor is a bit more complicated, because gods are different from humans. If Eliezer and cousin_it disagree on this point, maybe Eliezer would say ‘The complexity of the human brain is the biggest reason why you shouldn’t infer that there are other, as-yet-unobserved species of human-brain-ish things that are very different from humans’, and maybe cousin_it would say ‘No, it’s pretty much just the differentness-from-observed-humans (on the “has direct control over elemental forces” dimension) that matters, not the fact that it has a complicated brain.’
If that’s a good characterization of the disagreement, then it seems like Eliezer might say ‘In ancient societies, it was much more reasonable to posit mindless “supernatural” phenomena (i.e., mindless physical mechanisms wildly different from anything we’ve observed) than to posit intelligent supernatural phenomena.’ Whereas the hypothetical cousin-it might say that ancient people didn’t have enough evidence to conclude that gods were any more unlikely than mindless mechanisms that were similarly different from experience. Example question: what probability should ancient people have assigned to
vs.
Yeah, that’s a good summary of my view (except maybe I wouldn’t even persist into the fourth paragraph). Thanks!
This seems right, though something about this still feels confusing to me in a way I can’t yet put into words. Might write a comment at a later point in time.
Maxwell’s Equations don’t contain any such chunk of tape. In current physical theories (the Standard Model and General Relativity), the brains are not described in the math, rather brains are a consequence of the theories carried out under specific conditions.
Theories are based on postulates which are equivalent to axioms in mathematics. They are the statements from which everything else is derived but which can’t be derived themselves. Statements like “the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer.”
At the turn of the 20th century, scientists were confused by the apparent contradiction between Galilean Relativity and the implication from Maxwell’s Equations and empirical observation that the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer. Einstein formulate Special Relativity by simply asserting that both were true. That is: the postulates of SR are:
the laws of physics are invariant (i.e. identical) in all inertial frames of reference (i.e. non-accelerating frames of reference); and
the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer.
The only way to reconcile those two statements is if time and space become variables. The rest of SR is derived from those two postulates.
Quantum Field Theory is similarly derived from only a few postulates. None of them postulate that some intelligent being just exists. Any program that would describe such a postulate would be relatively enormous.
Yeah. But not sure you got the point of my argument. If your brain is a consequence of theory+conditions, why should the hypothesis of another humanlike brain (Thor) be penalized for excessive complexity under the same theory+conditions?
You’re trying to conflate theory, conditions, and what they entail in a not so subtle way. Occam’s razor is about the complexity of a theory, not conditions, not what the theory and conditions entail. Just the theory. The Thor hypothesis puts Thor directly in the theory. It’s not derived from the theory under certain conditions. In the case of the Thor theory, you have to assume more to arrive at the same conclusion.
It’s really not that complicated.
Thor isn’t quite as directly in the theory :-) In Norse mythology he’s a creature born to a father and mother, a consequence of initial conditions just like you.
Sure, you’d have to believe that initial conditions were such that would lead to Thor. But if I told you I had a neighbor named Bob, you’d have no problem believing that initial conditions were such that would lead to Bob the neighbor. You wouldn’t penalize the Bob hypothesis by saying “Bob’s brain is too complicated”, so neither should you penalize the Thor hypothesis for that reason.
The true reason you penalize the Thor hypothesis is because he has supernatural powers, unlike Bob. Which is what I’ve been saying since the first comment.
Tetraspace Grouping’s original post clearly invokes Thor as an alternate hypothesis to Maxwell’s equations to explain the phenomenon of electromagnetism. They’re using Thor as a generic stand-in for the God hypothesis.
Now you’re calling them “initial conditions”. This is very different from “conditions” which are directly observable. We can observe the current conditions of the universe, come up with theories that explain the various phenomena we see and use those theories to make testable predictions about the future and somewhat harder to test predictions about the past. I would love to see a simple theory that predicts that the universe not only had a definite beginning (hint: your High School science teacher was wrong about modern cosmology) but started with sentient beings given the currently observable conditions.
Which would be a lineage of Gods that begins with some God that created everything and is either directly or indirectly responsible for all the phenomena we observe according to the mythology.
I think you’re the one missing Tetraspace Grouping’s point. They weren’t trying to invoke all of Norse mythology, they were trying to compare the complexity of explaining the phenomenon of electromagnetism by a few short equations vs. saying some intelligent being does it.
The existence of Bob isn’t a hypothesis it’s not used to explain any phenomenon. Thor is invoked as the cause of, not consequence of, a fundamental phenomenon. If I noticed some loud noise on my roof every full moon, and you told me that your friend bob likes to do parkour on rooftops in my neighborhood in the light of the full moon, that would be a hypothesis for a phenomenon that I observed and I could test that hypothesis and verify that the noise is caused by Bob. If you posited that Bob was responsible for some fundamental forces of the universe, that would be much harder for me to swallow.
No. The supernatural doesn’t just violate Occam’s Razor: it is flat-out incompatible with science. The one assumption in science is naturalism. Science is the best system we know for accumulating information without relying on trust. You have to state how you performed an experiment and what you observed so that others can recreate your result. If you say, “my neighbor picked up sticks on the sabbath and was struck by lightning” others can try to repeat that experiment.
It is, indeed, possible that life on Earth was created by an intelligent being or a group of intelligent beings. They need not be supernatural. That theory, however; is necessarily more complex than any a-biogenesis theory because you have to then explain how the intelligent designer(s) came about which would eventually involve some form of a-biogenesis.
Yeah, I agree it’s unlikely that the equations of nature include a humanlike mind bossing things around. I was arguing against a different idea—that lightning (a bunch of light and noise) shouldn’t be explained by Thor (a humanlike creature) because humanlike creatures are too complex.
You’re right. I think I see your point more clearly now. I may have to think about this a little deeper. It’s very hard to apply Occam’s razor to theories about emergent phenomena. Especially those several steps removed from basic particle interactions. There are, of course, other ways to weigh on theory against another. One of which is falsifiability.
If the Thor theory must be constantly modified so to explain why nobody can directly observe Thor, then it gets pushed towards un-falsifiability. It gets ejected from science because there’s no way to even test the theory which in-turn means it has no predictive power.
As I explained in one of my replies to Jimdrix_Hendri, thought there is a formalization for Occam’s razor, Solomonoff induction isn’t really used. It’s usually more like: individual phenomena are studied and characterized mathematically, then; links between them are found that explain more with fewer and less complex assumptions.
In the case of Many Worlds vs. Copenhagen, it’s pretty clear cut. Copenhagen has the same explanatory power as Many Worlds and shares all the postulates of Many Worlds, but adds some extra assumptions, so it’s a clear violation of Occam’s razor. I don’t know of a *practical* way to handle situations that are less clear cut.
I made a kind of related point in: https://www.lesswrong.com/posts/3xnkw6JkQdwc8Cfcf/is-the-human-brain-a-valid-choice-for-the-universal-turing