Are our brains Bayesian? (2016)(rss.onlinelibrary.wiley.com)
rss.onlinelibrary.wiley.com
Are our brains Bayesian? (2016)
https://rss.onlinelibrary.wiley.com/doi/full/10.1111/j.1740-9713.2016.00935.x
69 comments
I don't think it will be, unfortunately. I think it's important to distinguish between explaining "how the brain works" and "understanding the brain, the mind, and their relationship". There are hundreds of studies every year elucidating correlations between certain kinds of brain activity and certain states of conscious experience. There are also many valiant attempts at modeling various aspects of human cognition and brain function. Unfortunately, none of this research says anything at all about the nature of the actual feelings and experiences we have.
People are taught in school that a sufficient response to the question "how do we hear things?" is to talk about sound waves, the shape of the outer ear, the tympanic membrane, malleus, incus, stapes, cochlea, etc. At some point you arrive at: "and then the brain processes the signal in the auditory cortex and stuff." We have become accustomed to this sort of answer, but it really doesn't even begin to answer the real (and interesting) question: why does all that processing result in the felt experience of hearing, rather than the nervous system just bubbling up and causing a behavior with no feelings? Why does it "feel" that way and not some other way? Is there a different kind of hearing that "feels" fundamentally different from our experience?
My point is that, we are closer to explaining some functional aspects of the brain, but when it comes to explaining the nature and character of our qualitative experience, we are at the same place as the ancient Eastern philosophers - we've really gotten nowhere.
People are taught in school that a sufficient response to the question "how do we hear things?" is to talk about sound waves, the shape of the outer ear, the tympanic membrane, malleus, incus, stapes, cochlea, etc. At some point you arrive at: "and then the brain processes the signal in the auditory cortex and stuff." We have become accustomed to this sort of answer, but it really doesn't even begin to answer the real (and interesting) question: why does all that processing result in the felt experience of hearing, rather than the nervous system just bubbling up and causing a behavior with no feelings? Why does it "feel" that way and not some other way? Is there a different kind of hearing that "feels" fundamentally different from our experience?
My point is that, we are closer to explaining some functional aspects of the brain, but when it comes to explaining the nature and character of our qualitative experience, we are at the same place as the ancient Eastern philosophers - we've really gotten nowhere.
> why does all that processing result in the felt experience of hearing
Fortunately, it is a question, which can stay unanswered with no practical consequences. It is a subjective counterpart of "Why is there something rather than nothing?", and we aren't answering either anytime soon.
> Is there a different kind of hearing that "feels" fundamentally different from our experience?
Even if there is, we will need different brain hardware to experience it first-hand, otherwise we'd have to do with analogies or, for more precision, with functional descriptions of perceptual processing.
Fortunately, it is a question, which can stay unanswered with no practical consequences. It is a subjective counterpart of "Why is there something rather than nothing?", and we aren't answering either anytime soon.
> Is there a different kind of hearing that "feels" fundamentally different from our experience?
Even if there is, we will need different brain hardware to experience it first-hand, otherwise we'd have to do with analogies or, for more precision, with functional descriptions of perceptual processing.
Fortunately, it is a question, which can stay unanswered with no practical consequences. It is a subjective counterpart of "Why is there something rather than nothing?", and we aren't answering either anytime soon.
Utterly absurd and completely false. An explanation for the question of why pain feels the why it does, for example, has enormous practical implications and consequences. The current neurological and medical approaches to pain management are poorly understood and often dangerous in extreme cases. We literally don't know why or how Tylenol works. That is a huge problem. The current best-case scenario, absent an explanation of the nature of the character of pain experiences, is that we find some neural activities that we can alter with advanced medical techniques which reliably suppress pain experiences. But it's not clear that 1) we will ever find such techniques, 2) that such techniques would exhaustively alter all the kinds of physical pain a human might experience, 3) that such techniques wouldn't negatively alter other aspects of a person's mind. If we had a fuller explanation of the nature of the character of the experience itself (rather than just treating consciousness like a black box), we might be able to alter the experiences more precisely and appropriately.
Utterly absurd and completely false. An explanation for the question of why pain feels the why it does, for example, has enormous practical implications and consequences. The current neurological and medical approaches to pain management are poorly understood and often dangerous in extreme cases. We literally don't know why or how Tylenol works. That is a huge problem. The current best-case scenario, absent an explanation of the nature of the character of pain experiences, is that we find some neural activities that we can alter with advanced medical techniques which reliably suppress pain experiences. But it's not clear that 1) we will ever find such techniques, 2) that such techniques would exhaustively alter all the kinds of physical pain a human might experience, 3) that such techniques wouldn't negatively alter other aspects of a person's mind. If we had a fuller explanation of the nature of the character of the experience itself (rather than just treating consciousness like a black box), we might be able to alter the experiences more precisely and appropriately.
For all those ends you'll need observables: patient reports, behaviors associated with pain and so on. You probably have in mind the question "why this pain processing results in the observed effects?"
I was talking about the question "why does all that processing result in the felt experience [...]?"
I was talking about the question "why does all that processing result in the felt experience [...]?"
No, I have in mind the exact question I outlined at the beginning of my response.
Then I don't understand you. What is important to address the problems you outlined is the question of "How brain activity corresponds to the felt experiences (as reported by subjects)?", not "Why there are felt experiences corresponding to brain activity?"
Even if we had the answer for the second question (say, "There is immaterial soul which is responsible for our felt experiences and that's why we feel"), it will not help with pain treatment.
Even if we had the answer for the second question (say, "There is immaterial soul which is responsible for our felt experiences and that's why we feel"), it will not help with pain treatment.
Musicologists have been asking this question from a phenomenological angle for some time. It's quite interesting how listening and perception in the English language have almost no distinction from each other. Our ears listen always, but our brain perceives is about as far as we get. In French musicology and music psychology, there is much more desperation between modes of listening and they all have their own definitions.
Neeral-based computing paradigms go as far back as the 1950s.
https://en.wikipedia.org/wiki/Perceptron
Leslie Valiant proposed a mathematical model for human learning (and mostly applied to machine learning theory) in the 1980s, and it's been been refined to more explicftly Bayesian models recently:
https://en.wikipedia.org/wiki/Probably_approximately_correct...
http://web.mit.edu/6.435/www/Valiant84.pdf
Anyway, these aren't intended to be faithful models of hmuan brains, but more loosely inspired by functions observed in human brains. There's on good reasoning that an naturally evolved human brain would operate under one simple, sound, fundamental computing principle. It's far more likely to be a mishmash of unsound models, like all evolved physical characteristics of animals.
https://en.wikipedia.org/wiki/Perceptron
Leslie Valiant proposed a mathematical model for human learning (and mostly applied to machine learning theory) in the 1980s, and it's been been refined to more explicftly Bayesian models recently:
https://en.wikipedia.org/wiki/Probably_approximately_correct...
http://web.mit.edu/6.435/www/Valiant84.pdf
Anyway, these aren't intended to be faithful models of hmuan brains, but more loosely inspired by functions observed in human brains. There's on good reasoning that an naturally evolved human brain would operate under one simple, sound, fundamental computing principle. It's far more likely to be a mishmash of unsound models, like all evolved physical characteristics of animals.
>There's no good reasoning that an naturally evolved human brain would operate under one simple, sound, fundamental computing principle. It's far more likely to be a mishmash of unsound models, like all evolved physical characteristics of animals.
Quite the opposite, actually. Anything essential to survival and reproduction is optimized for its design constraints quite heavily, resulting in many attributes of observed organisms being physiologically optimal.
You should look into the "rational analysis" paradigm in cognitive science.
Quite the opposite, actually. Anything essential to survival and reproduction is optimized for its design constraints quite heavily, resulting in many attributes of observed organisms being physiologically optimal.
You should look into the "rational analysis" paradigm in cognitive science.
I'm not sure I agree with that professor's claim - who was this, what kind of professor? Look at the claim itself. For instance, who is this "we" that is "always assuming"? Is it biologists at large? Because they do not tend towards unified, reductionist explanations of neuroscience based on computer science.
Theories of mind have been going back thousands of years from before the time computers were dreamed of. This idea of a technological paradigm of neuroscience falls apart quite easily when you consider the far longer exploration into human consciousness and neurophysiological function, both fields of inquiry are far older than computer science.
Never mind the fact, those that study neuroscience, they speak of neurochemical signaling pathways, of pre- and post-synapatic chemical reaction, or of the functional imaging of the brain's different regions. There is a great deal of genetic analysis, of pharmaceutical interest, and of genuine biological mysteries. I'm sorry but I just don't agree that neuroscientists are couching their field in terms of computers.
Theories of mind have been going back thousands of years from before the time computers were dreamed of. This idea of a technological paradigm of neuroscience falls apart quite easily when you consider the far longer exploration into human consciousness and neurophysiological function, both fields of inquiry are far older than computer science.
Never mind the fact, those that study neuroscience, they speak of neurochemical signaling pathways, of pre- and post-synapatic chemical reaction, or of the functional imaging of the brain's different regions. There is a great deal of genetic analysis, of pharmaceutical interest, and of genuine biological mysteries. I'm sorry but I just don't agree that neuroscientists are couching their field in terms of computers.
Computer science: https://www2.eecs.berkeley.edu/Faculty/Homepages/feldman.htm...
The we refers to computer scientists.
And even before computers, we still had technology. But we didn't really have an understanding of brain physiology thousands of years ago, so the statement really only applies to theories on how we get from brain physiology to computing, not theory of mind.
The we refers to computer scientists.
And even before computers, we still had technology. But we didn't really have an understanding of brain physiology thousands of years ago, so the statement really only applies to theories on how we get from brain physiology to computing, not theory of mind.
>The we refers to computer scientists.
Well of course computer scientists compare the brain to whatever the most advanced AI is. That's how they pitch grant applications!
Hell, I'm doing it right now in this application I've got on Overleaf in another tab, though I guess in reverse: I describe what we know functionally about the brain, then propose to build computational models to study it.
Well of course computer scientists compare the brain to whatever the most advanced AI is. That's how they pitch grant applications!
Hell, I'm doing it right now in this application I've got on Overleaf in another tab, though I guess in reverse: I describe what we know functionally about the brain, then propose to build computational models to study it.
>But we still have no idea how we get from brain biology to rational (and irrational) thought. I'd be excited if we solved this within my lifetime.
The problem there is that "rational" has dual meanings:
* The a priori kind of "rational", as in "optimal according to some equation", where that equation is often Bayesian or RL-related
* The a posteriori kind of "rational", where we decide that science and math are better than intuition and so on.
I pretty much support the Bayesian brain assumption, and the labs I work with follow it in a few different forms, but I suspect that the cognitive science of rationality will some day be a pretty fruitful field. That is, I suspect that a posteriori rationality can't be neatly reduced to a priori optimality[1].
[1] -- http://www.saet.illinois.edu/papers_and_talks/event-07/nolea...
The problem there is that "rational" has dual meanings:
* The a priori kind of "rational", as in "optimal according to some equation", where that equation is often Bayesian or RL-related
* The a posteriori kind of "rational", where we decide that science and math are better than intuition and so on.
I pretty much support the Bayesian brain assumption, and the labs I work with follow it in a few different forms, but I suspect that the cognitive science of rationality will some day be a pretty fruitful field. That is, I suspect that a posteriori rationality can't be neatly reduced to a priori optimality[1].
[1] -- http://www.saet.illinois.edu/papers_and_talks/event-07/nolea...
Your point about irrational thought brought to mind this Turing quote I really like: "If we want a machine to be intelligent, it can't also be infallible."
source: Lecture to the London Mathematical Society on 20 February 1947, pdf: http://www.vordenker.de/downloads/turing-vorlesung.pdf, also see this Quora answer for details: https://www.quora.com/What-did-Alan-Turing-mean-by-his-state...). Actually his exact phrasing is the reverse (on pg 13): "... if a machine is expected to be infallible, it cannot also be intelligent. "
source: Lecture to the London Mathematical Society on 20 February 1947, pdf: http://www.vordenker.de/downloads/turing-vorlesung.pdf, also see this Quora answer for details: https://www.quora.com/What-did-Alan-Turing-mean-by-his-state...). Actually his exact phrasing is the reverse (on pg 13): "... if a machine is expected to be infallible, it cannot also be intelligent. "
By Goedel's incompleteness theorem.
Whenever this comes up, I think about the conjunction fallacy https://en.m.wikipedia.org/wiki/Conjunction_fallacy. The observation that human subjects seem to assign higher probability to joint events than a single event. Which is weird because the probability of two events at the same time (conjunction) is always less than or equal to the probability of a single event on its own.
How does the Bayesian brain hypothesis deal with this fallacy? It seems to me that nothing based on classical probability can explain this fallacy. So either the observation that humans can assign higher probability to joint events is wrong or human decision making isn't exactly probabilistic (in the classical sense, can't rule out exotic probabilistic approaches).
EDIT: As several folks have commented that the conjunction fallacy can be explained away by different arguments based on interpretation and semantic issues. Indeed, the original Linda problem was susceptible to these issues. However, since then several researchers have tried to study this effect more carefully and it seems to still persist. An example that I'm aware of is the following https://link.springer.com/article/10.3758/BF03195280 where the authors used unambiguous language and a betting paradigm, but still found the effect. Again, this is most likely not fool proof. Regardless, I do not think the fallacy can be trivially explained away as an effect of ambiguous language.
How does the Bayesian brain hypothesis deal with this fallacy? It seems to me that nothing based on classical probability can explain this fallacy. So either the observation that humans can assign higher probability to joint events is wrong or human decision making isn't exactly probabilistic (in the classical sense, can't rule out exotic probabilistic approaches).
EDIT: As several folks have commented that the conjunction fallacy can be explained away by different arguments based on interpretation and semantic issues. Indeed, the original Linda problem was susceptible to these issues. However, since then several researchers have tried to study this effect more carefully and it seems to still persist. An example that I'm aware of is the following https://link.springer.com/article/10.3758/BF03195280 where the authors used unambiguous language and a betting paradigm, but still found the effect. Again, this is most likely not fool proof. Regardless, I do not think the fallacy can be trivially explained away as an effect of ambiguous language.
Regarding the Conjunction fallacy my theory is that many people who are not used to math problems implicitly modify the question based on the context.
Instead of choosing from options:
1) Linda is A
2) Linda is A and B
they might actually understand the first statement in the context of the second statement as:
1) Linda is A and not B
Instead of choosing from options:
1) Linda is A
2) Linda is A and B
they might actually understand the first statement in the context of the second statement as:
1) Linda is A and not B
FWIW, there was a similar experiment in the form of a dice game [1], and the phenomenon was still present.
[1] https://www.lesswrong.com/posts/QAK43nNCTQQycAcYe/conjunctio...
[1] https://www.lesswrong.com/posts/QAK43nNCTQQycAcYe/conjunctio...
No, that's not what's going on. The reason for the fallacy is that we tend to find more detailed stories more convincing than less detailed stories.
However, not everybody, you can be trained against that. I've heard that police interrogators are less prone to this fallacy because they know that liars who had time to prepare often add dozens of details to their story that no ordinary person would remember.
However, not everybody, you can be trained against that. I've heard that police interrogators are less prone to this fallacy because they know that liars who had time to prepare often add dozens of details to their story that no ordinary person would remember.
> 'fallacy is that we tend to find more detailed stories more convincing'
Anecdotic: Somebody asked: "Why do I feel often that angry, when I get a 'Typ5-Answer'?" (With the background an TYp5-Answer is located in the field of the manipulation of (someones) reality.
HINT: Typ1-Answer: labeling of 'Objects' / Type2-Answer: naming of coherencies / Ty ....(-;
Anecdotic: Somebody asked: "Why do I feel often that angry, when I get a 'Typ5-Answer'?" (With the background an TYp5-Answer is located in the field of the manipulation of (someones) reality.
HINT: Typ1-Answer: labeling of 'Objects' / Type2-Answer: naming of coherencies / Ty ....(-;
> How does the Bayesian brain hypothesis deal with this fallacy?
Maybe brain operates here on a syntactical level: which sentence is more likely to be present in a narrative about a subject and system 2 ([0]) fails to preempt the answer.
[0]: https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow Two systems
Maybe brain operates here on a syntactical level: which sentence is more likely to be present in a narrative about a subject and system 2 ([0]) fails to preempt the answer.
[0]: https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow Two systems
These are structured as: Do you choose (A) alone, or do you choose (A) and (B)? (A) is often benign and (B) is often something the subject thinks is a good fit. So, in some ways these seem like "trick questions" - I wonder what happens if both options are benign. As the Wikipedia article mentions, in the typical case the subject may end up choosing to use an easy heuristic rather than thinking hard about the actual definition of probability and such.
There are other ways the brain could be Bayesian though. For example, at the lowest level our neurons could use Bayesian inference. How this manifests itself at much higher levels such as with language and planning might be difficult to predict.
There are other ways the brain could be Bayesian though. For example, at the lowest level our neurons could use Bayesian inference. How this manifests itself at much higher levels such as with language and planning might be difficult to predict.
I would describe that heuristic as Bayesian, since the subject evaluates the prior evidence for each option, and then chooses the one with the most supporting information, instead of considering the options' logical or mathematical properties.
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This is a fallacy of interpretation (translating verbal representations of events into mental representations of events), not of probabilistic reasoning.
The crux I think is that when
A. bank teller
is juxtaposed with
B. bank teller and feminist,
we vaguely and falsely interpret A as "bank teller and not feminist", while the correct explicit interpretation is "bank teller and possibly feminist, but possibly not".
The crux I think is that when
A. bank teller
is juxtaposed with
B. bank teller and feminist,
we vaguely and falsely interpret A as "bank teller and not feminist", while the correct explicit interpretation is "bank teller and possibly feminist, but possibly not".
Just to add something that I found interesting when my logic professor said it at the time: while that “bank teller and not feminist” interpretation is strictly incorrect in a theoretical world, IRL it’s useful for humans to just assume pieces of information. Most people are not particularly feminist, so it’s probably safe to assume someone - especially a bank teller, maybe - isn’t feminist if it’s not mentioned.
Rather than a fallacy of some kind, people may actually be so good at correct inferences that they are bad at leaving that intuition out of their reasoning process when thinking about a weird, outlying theoretical world.
Rather than a fallacy of some kind, people may actually be so good at correct inferences that they are bad at leaving that intuition out of their reasoning process when thinking about a weird, outlying theoretical world.
It doesn't seem surprising at all that we fail to understand abstract questions like this. The experts only learned to answer them correctly after millennia worth of mathematical development!
To study how accurately Bayesian some animals are, I think you need to find ways to pose them questions which are relevant to them, and read off their inferences from their behaviour. This is obviously harder to do, and you have to worry a great deal about the animal optimising for something that differs from your first guess (e.g. it doesn't want maximum food on a good day, it wants not to starve on a bad day). I don't have references to hand but I think that when we can do this, the results are quite good.
To study how accurately Bayesian some animals are, I think you need to find ways to pose them questions which are relevant to them, and read off their inferences from their behaviour. This is obviously harder to do, and you have to worry a great deal about the animal optimising for something that differs from your first guess (e.g. it doesn't want maximum food on a good day, it wants not to starve on a bad day). I don't have references to hand but I think that when we can do this, the results are quite good.
That's still a fallacy, even if the mechanism behind is successful on average. Assuming a bank teller is non-feminist is rational only if the feminism matters, which it does not. Even if 0 bank tellers are feminist, it's still unhelpful (and harmful is even 1 bank teller is feminist) to assume that an unknown teller is feminist for the purpose of the question. Prejudices are often statistically more correct than incorrect (though socially problematic), but in some cases are still flat-out inorrect, as they are in this example. Too to much of a "good" thing is toxic.
The Wikipedia article on the effect mentions that the experiment has been done to correct that by explicitly wording it better and it reduces the magnitude of the effect but it still exists.
Good point. But... this particular objection has a flaw (which may be copied by the BBH).
The Bayesian machinery tells you how to update your beliefs given evidence. It doesn't tell you what shape those beliefs should be in the first place.
My theory is that we carry around a deck of personas or sterotypes. We hear of a new person, and some behaviour of theirs. We then predict which persona was likely to generate that behaviour. Conditional on the distribution over personas we answer the questions about that person's predicted behaviour.
In the `Linda` example the theory above suggests we take the background information about all their political commitments at college, which from the description would seem to give strong evidence about their persona.
The common and wrong answer to the question stems from predicting, based on the persona, that the person would continue with their political commitments.
The 'shape being wrong' issue here is that maybe personas are not the right way to structure the problem. But Bayes's theorem doesn't tell you that. That's a whole load of extra machinery that people have additionally developed and should deploy when using Bayes's theorem.
Back to the word problem. An issue is that the options:
- A
- A&B
Both include A. In a world where A always happens the only non-trivial way to read the question is that the first option must implicitly mean (A&!B).
If A is assumed to be true, the question then becomes is B more likely to be true or not true. The background information given is a reasonable explanation for the common answer of people selecting (A&B).
The Bayesian machinery tells you how to update your beliefs given evidence. It doesn't tell you what shape those beliefs should be in the first place.
My theory is that we carry around a deck of personas or sterotypes. We hear of a new person, and some behaviour of theirs. We then predict which persona was likely to generate that behaviour. Conditional on the distribution over personas we answer the questions about that person's predicted behaviour.
In the `Linda` example the theory above suggests we take the background information about all their political commitments at college, which from the description would seem to give strong evidence about their persona.
The common and wrong answer to the question stems from predicting, based on the persona, that the person would continue with their political commitments.
The 'shape being wrong' issue here is that maybe personas are not the right way to structure the problem. But Bayes's theorem doesn't tell you that. That's a whole load of extra machinery that people have additionally developed and should deploy when using Bayes's theorem.
Back to the word problem. An issue is that the options:
- A
- A&B
Both include A. In a world where A always happens the only non-trivial way to read the question is that the first option must implicitly mean (A&!B).
If A is assumed to be true, the question then becomes is B more likely to be true or not true. The background information given is a reasonable explanation for the common answer of people selecting (A&B).
Solving epistemology doesn't solve ontology. Bingo.
In more strictly mathematical terms, having a "normative" update rule (Bayes' rule) doesn't tell you what topology of latent variables the generative model "ought" to have, only how to link new information into a preexisting generative model.
Using the KL divergence of the posterior predictive distribution as a target to optimize does a bit better, but still isn't a "solution".
Using the KL divergence of the posterior predictive distribution as a target to optimize does a bit better, but still isn't a "solution".
Seriously, what doeos "topology of latent variables" even mean?
A topology on U is a system of subsets of U that's closed under union and finite intersections and containing the empty set and U itself. Go!
A topology on U is a system of subsets of U that's closed under union and finite intersections and containing the empty set and U itself. Go!
>Seriously, what doeos "topology of latent variables" even mean?
The simple answer is: the graph topology of the resulting program traces, equivalent to the topology of a graphical model sampled from a distribution over graphical models. The complicated answer is: the Scott topology of the program-trace space.
The simple answer is: the graph topology of the resulting program traces, equivalent to the topology of a graphical model sampled from a distribution over graphical models. The complicated answer is: the Scott topology of the program-trace space.
Most of the decision making while shooting for a hoop in basketball (the example from the article) is subconscious and reflexive, while decisions made related to the conjunction fallacy are conscious. So it's quite possible different mechanisms are used in subconscious motor -control reflexes and conscious 'logical' decision making.
I realise both are implemented using neural networks, but as an analogy digital computers can implement bayesian algorithms, boolean algorithms, predicate logic, etc. It's quite possible our neural systems have optimised to different behaviours to solve different problems, and in _some_ cases these implement or approximate to Bayesian methods.
I realise both are implemented using neural networks, but as an analogy digital computers can implement bayesian algorithms, boolean algorithms, predicate logic, etc. It's quite possible our neural systems have optimised to different behaviours to solve different problems, and in _some_ cases these implement or approximate to Bayesian methods.
I don't think that's right, or at least not so binary. The average person (and even highly rational people, when they are being informal) uses "logical" reasononing that is intuitive, not calculated, not so different fro "muscle memory" of shooting hoops. Even professional mathematicians, (in published papers!) sometimes make statements that "feel" correct even though they are disproven under scrutiny (and not due to small (but important) mistakes like getting a sign wrong in a calculation)
With assumptions of noise in the inputs human judgements are probabilistically rational: https://onlinelibrary.wiley.com/doi/pdf/10.1002/bdm.618
I'm currently reading The Book of Why by Judea Pearl and I think that he makes that claim that our brains are Bayesian and then some.
Haven't finished yet, he gets into artificial intelligence in the next few chapters, but he seems to make the claim that our brains work by doing a number of computations involved in causal inference beyond just Bayesian inference, such as subconsciously constructing causal diagrams and using them for causal inference including asking questions about counterfactual scenarios.
Would be interested to hear if anyone else who has read this book can help elaborate on this some.
Haven't finished yet, he gets into artificial intelligence in the next few chapters, but he seems to make the claim that our brains work by doing a number of computations involved in causal inference beyond just Bayesian inference, such as subconsciously constructing causal diagrams and using them for causal inference including asking questions about counterfactual scenarios.
Would be interested to hear if anyone else who has read this book can help elaborate on this some.
Judea Pearl continues to insist on causal diagrams, but the rest of us have moved on to probabilistic programs ;-).
My understanding of Bayesian thinking is that we form new beliefs that are a function of our prior beliefs plus new evidence. That's my interpretation of the article.
Another way of thinking is to form new beliefs that are a function of prior evidence plus new evidence, e.g., by setting all old beliefs aside and starting afresh with the complete body of available evidence.
It's not clear to me that these two methods produce the same results, though I can't think of a counterexample. But to the extent that our brains probably remember both beliefs and evidence, we are not probably not fully Bayesian.
Another way of thinking is to form new beliefs that are a function of prior evidence plus new evidence, e.g., by setting all old beliefs aside and starting afresh with the complete body of available evidence.
It's not clear to me that these two methods produce the same results, though I can't think of a counterexample. But to the extent that our brains probably remember both beliefs and evidence, we are not probably not fully Bayesian.
See also the book _Surfing Uncertainty_ (https://www.amazon.com/Surfing-Uncertainty-Prediction-Action...) which convincingly details many brain subsystems as approximating Bayesian updates.
Yes of course it is. Experience allows you to make decisions without having a statistically valid sample all the time.
Are our brains Bayesian?
1990s Internet debater #1: "The plural of anecdote is not data"
2010s Internet debater #2: "True, but it does make a good bayesian prior"
1990s Internet debater #1: "The plural of anecdote is not data"
2010s Internet debater #2: "True, but it does make a good bayesian prior"
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Do our brains use a reasoning process invented by our brains?
Could our brains have come up with a way of describing a process that was already there before?
Well, when (and if, I guess) we do finally properly understand how our brains work, then we'll know (somewhat tautologically) that they do use a reasoning process discovered by our brains.
Discovered not invented.
Does it exist somewhere in a platonic realm of forms?
If our brains are Bayesian, evolution is what invented it.
When I studied biology it was drilled into us that evolution doesn't have agency. Has that changed?
You don't need to have "agency" to invent.
LSD and sticky notes were invented by accident -- as were tons of other things.
Sure, one could add several pedantic reservations here, if they wanted to be thick on purpose, but the meaning of the parent's statement is clear. This series of passive aggressive counter-questions seems to violate the principle of charity.
LSD and sticky notes were invented by accident -- as were tons of other things.
Sure, one could add several pedantic reservations here, if they wanted to be thick on purpose, but the meaning of the parent's statement is clear. This series of passive aggressive counter-questions seems to violate the principle of charity.
It's good that you are concerned with the principle of charity, perhaps you should apply it here?
It's pretty obvious that evolution didn't "invent" anything because accident or not, to invent requires an originator or discoverer which is to say an entity with agency. It's as absurd as saying relativity invented black holes.
It's pretty obvious that evolution didn't "invent" anything because accident or not, to invent requires an originator or discoverer which is to say an entity with agency. It's as absurd as saying relativity invented black holes.
>It's pretty obvious that evolution didn't "invent" anything because accident or not, to invent requires an originator or discoverer which is to say an entity with agency.
And yet everybody understood what the parent means, which is that it was created by an evolutionary process.
And also everybody understands that the pedantic minutiae of whether "invent" can be used here is beside the actual point the parent makes.
And yet everybody understood what the parent means, which is that it was created by an evolutionary process.
And also everybody understands that the pedantic minutiae of whether "invent" can be used here is beside the actual point the parent makes.
Not as such, no, but if a heritable trait increases the likelihood of survival to reproduction, there is little other than unnecessary pedantry in the way of saying in a lay forum that evolution "invented" it.
I don't mean "invented" in the sense of conscious design process with foresight or intentions. I just mean the way the blind evolutionary process creates any "design".
Something doesn't have to exist in a "platonic realm of forms" to be discovered.
It's enough that it exists in the real world.
It's enough that it exists in the real world.
Is god in the image of a man? Probably not.
You're downvoted, but I think you were just pointing out the reverse causality in the parent post, right? I.e. even if our brains are Bayesian, it's not that "they use a process discovered by them", it's just that they managed to decode what is the process that they were already using. Which doesn't seem ridiculous at all.
It's not even a matter of causality, it's just a category error. Are there cranial phenomena that are analogous to Bayesian statistics? I don't see why not. But that doesn't mean that is how the brain operates. It's a matter of membership not isomorphism.
Invented? How do you know it didn’t exist before?
Who’s asking?
This is actually an idiotic question. The molecular biology does not employ a concept of a number (or any concepts whatsoever in principle), since this requires an intelligent observer (to form the abstract notion of a number) which is not available at that level.
The "concrete", real-world biological systems, including our brains, however employs frequencies and "weights", which corresponds to wideness of a pathway, which does not require any numbers or counting.
Mother Nature Does Not Count (and it does not compute any probabilities, of course). Higher level intellect does.
Math and logic are superimposed on the Universe and Nature. It is naive to assume that the Universe and Nature is based on math and logic, as ancient Greek views suppose.
Yes, there is basis behind Modus Ponens - in a certain conditions having Hs and Os inevitably leads to H2Os because universe has its laws, and because it has its laws it produces certain regularities and certain patterns which could be matched and even generalized by an intelligent observer, but it is not the other way around.
The "concrete", real-world biological systems, including our brains, however employs frequencies and "weights", which corresponds to wideness of a pathway, which does not require any numbers or counting.
Mother Nature Does Not Count (and it does not compute any probabilities, of course). Higher level intellect does.
Math and logic are superimposed on the Universe and Nature. It is naive to assume that the Universe and Nature is based on math and logic, as ancient Greek views suppose.
Yes, there is basis behind Modus Ponens - in a certain conditions having Hs and Os inevitably leads to H2Os because universe has its laws, and because it has its laws it produces certain regularities and certain patterns which could be matched and even generalized by an intelligent observer, but it is not the other way around.
You don't have to use numbers to implement a Bayesian system. It's quite possible to build one using analog methods.
In the same way Voltage = Current x Resistance describes the behaviour of an electrical circuit and we can evaluate it numerically, but electrical circuits are analog and don't encapsulate or express those values numerically at all.
The brain might exhibit Bayesian behaviour without encoding or evaluating anything numerically. After all the values in Bayesian formulae are probabilities on a continuous scale, so there's nothing inherently discrete about their values.
In the same way Voltage = Current x Resistance describes the behaviour of an electrical circuit and we can evaluate it numerically, but electrical circuits are analog and don't encapsulate or express those values numerically at all.
The brain might exhibit Bayesian behaviour without encoding or evaluating anything numerically. After all the values in Bayesian formulae are probabilities on a continuous scale, so there's nothing inherently discrete about their values.
The silicon atoms in my CPU also don't employ any numbers either, but "it's a thing that can calculate" is a decent high level description of what it does.
>Math and logic are superimposed on the Universe and Nature. It is naive to assume that the Universe and Nature is based on math and logic, as ancient Greek views suppose.
I think it’s more naive to think that the question has been settled..
https://en.m.wikipedia.org/wiki/Mathematical_universe_hypoth...
I think it’s more naive to think that the question has been settled..
https://en.m.wikipedia.org/wiki/Mathematical_universe_hypoth...
It depends on who is asking. If it is a "good" philosopher, who is in on the quest to unveil the nature and laws of what is, then it is settled.
If, however, you are fond of joggling with abstractions and of studying of philosophers themselves and various philosophical systems (instead of what is) then, of course, you could put together yet another pile of abstractions and even systematically compare it with another pile of abstractions, and so on. Lots of people do.
Universe is one (at least we and everything else is bound by this one single unfolding process we call Universe) while abstractions are infinite, and most of them are disconnected from what is - they generalize nothing but other disconnected abstractions.
If, however, you are fond of joggling with abstractions and of studying of philosophers themselves and various philosophical systems (instead of what is) then, of course, you could put together yet another pile of abstractions and even systematically compare it with another pile of abstractions, and so on. Lots of people do.
Universe is one (at least we and everything else is bound by this one single unfolding process we call Universe) while abstractions are infinite, and most of them are disconnected from what is - they generalize nothing but other disconnected abstractions.
In the 90s we finally switched it up, and developed computing paradigms based on human biology, and came up with applying neural nets to brain science. Then someone had the idea to create a Bayesian NN.
Each iteration we get closer to explaining how the brain works, but showing that each iteration is closer to workable based on our knowledge of the biology of the brain.
But we still have no idea how we get from brain biology to rational (and irrational) thought. I'd be excited if we solved this within my lifetime.