The following once happened: I posted a link to some article on an IRC channel. A friend of mine read the article in question and brought up several criticisms. I felt that her criticisms were mostly correct though not very serious, so I indicated agreement with them.
Later on the same link was posted again. My friend commented something along the lines of “that was already posted before, we discussed this with Kaj and we found that the article was complete rubbish”. I was surprised – I had thought that I had only agreed to some minor criticisms that didn’t affect the main point of the article. But my friend had clearly thought that the criticisms were decisive and had made the article impossible to salvage.
Every argument actually has two parts, even if people often only state the first part. There’s the argument itself, and an implied claim of why the argument would matter if it were true. Call this implied part the relevance claim.
Suppose that I say “Martians are green”. Someone else says, “I have seen a blue Martian”, and means “I have seen a blue Martian (argument), therefore your claim of all Martians being green is false (relevance claim)”. But I might interpret this as them saying, “I have seen a blue Martian (argument), therefore your claim of most Martians being green is less likely (relevance claim)”. I then indicate agreement. Now I will be left with the impression that the other person made a true-but-not-very-powerful claim that left my argument mostly intact, whereas the other person is left with the impression that they made a very powerful claim that I agreed with, and therefore I admitted that I was wrong.
We could also say that the relevance claim is a claim of how much the probability of the original statement would be affected if the argument in question were true. So, for example “I have seen a blue martian (argument), therefore the probability of ‘Martians are green’ is less than .01 (relevance claim)”, or equivalently, “I have seen a blue martian” & “P(martians are green|I have seen a blue martian) < .01″.
If someone says something that I feel is entirely irrelevant to the whole topic, inferential silence may follow.
Therefore, if someone makes an argument that I agree with, but I suspect that we might disagree about its relevance, I now try to explicitly comment on what my view of the relevance of the argument is. Example.
Notice that people who are treating arguments as soldiers are more likely to do this automatically, without needing to explicitly remind themselves of it. In fact, for every argument that their opponent makes that they’re forced to concede, they’re likely to immediately say “but that doesn’t matter because X!”. The kinds of people who think that they aren’t treating arguments as soldiers will try to avoid automatically objecting “but that doesn’t matter because X” whenever our favored position gets weakened. This is a good thing, but it also means that we’re probably less likely than average to comment about an argument’s relevance even in cases where we should comment on it.
Whatever next? Predictive brains, situated agents, and the future of cognitive science (Andy Clark 2013, Behavioral and Brain Sciences) is an interesting paper on the computational architecture of the brain. It’s arguing that a large part of the brain is made up of hierarchical systems, where each system uses an internal model of the lower system in an attempt to predict the next outputs of the lower system. Whenever a higher system mispredicts a lower system’s next output, it will adjust itself in an attempt to make better predictions in the future.
So, suppose that we see something, and this visual data is processed by a low-level system (call it system L). A higher-level system (call it system H) attempts to predict what L’s output will be and sends its prediction down to L. L sends back a prediction error, indicating the extent to which H’s prediction matches L’s actual activity and processing of the visual stimulus. H will then adjust its own model based on the prediction error. By gradually building up a more accurate model of the various regularities behind L’s behavior, H is also building up a model of the world that causes L’s activity. At the same time, systems H+, H++ and so on that are situated “above” H build up still more sophisticated models.
So the higher-level systems have some kind of model of what kind of activity to expect from the lower-level systems. Of course, different situations elicit different kinds of activity: one example given in the paper is that of an animal “that frequently moves between a watery environment and dry land, or between a desert landscape and a verdant oasis”. The kinds of visual data that you would expect in those two situations differs, so the predictive systems should adapt their predictions based on the situation.
And apparently, that is what happens – when salamanders and rabbits are put to varying environments, half of their retinal ganglion cells rapidly adjust their predictions to keep up with the changing image predictions. Presumably, if the change of scene was unanticipated, the higher-level systems making predictions of the ganglion cells will then quickly get an error signal indicating that the ganglion cells are now behaving differently from what was expected based on how they acted just a moment ago; this should also cause them to adjust their predictions, and data about the scene change gets propagated up through the hierarchy.
This process involves the development of “novelty filters”, which learn to recognize and ignore the features of the input that most commonly occur together within some given environment. Thus, things that are “familiar” (based on previous experience) and behave in expected ways aren’t paid attention to.
So far we’ve discussed a low-level system sending the higher-level an error signal when the predictions of the higher-level system do not match the activity of the lower-level system. But the predictions sent by the higher-level system also serve a function, by acting as Bayesian priors for the lower-level systems.
Essentially, high up in the hierarchy we have high-level models of how the world works, and what might happen next based on those models. The highest-level system, call it H+++, makes a prediction of what the next activity of H++ is going to be like, and the prediction signal biases the activity of H++ in that direction. Now the activity of H++ involves making a prediction of H+, so this also causes H++ to bias the activity of H+ in some direction, and so on. When the predictions of the high-level models are accurate, this ends up minimizing the amount of error signals sent up, as the high-level systems adjust the expectations of the lower-level systems to become more accurate.
Let’s take a concrete example (this one’s not from the paper but rather one that I made up, so any mistakes are my own). Suppose that I am about to take a shower, and turn on the water. Somewhere in my brain there is a high-level world model which says that turning on the shower faucet will lead to water pouring out, and because I’m standing right below it, the model also predicts that the water will soon be falling on my body. This prediction is expressed in terms of the expected neural activity of some (set of) lower-level system(s). So the prediction is sent down to the lower systems, each of which has its own model of what it means for water to fall on my body, and each of which send that prediction down to yet more lower-level systems.
Eventually we reach some pretty low-level system, like one predicting the activity of the pressure- and temperature-sensing cells on my skin. Currently there isn’t yet water falling down on me, and this system is a pretty simple one, so it is currently predicting that the pressure- and temperature-sensing cells will continue to have roughly the same activity as they do now. But that’s about to change, and if the system did continue predicting “no change”, then it would end up being mistaken. Fortunately, the prediction originating from the high-level world-model has now propagated all the way down, and it ends up biasing the activity of this low-level system, so that the low-level system now predicts that the sensors on my skin are about to register a rush of warm water. Because this is exactly what happens, the low-level system generates no error signal to be sent up: everything happened as expected, and the overall system acted to minimize the overall prediction error.
If the prediction from the world-model would have been mistaken – if the water had been cut, or I accidentally turned on cold water when I was expecting warm water – then the biased prediction would have been mistaken, and an error signal would have been propagated upwards, possibly causing an adjustment to the overall world-model.
This ties into a number of interesting theories that I’ve read about, such as the one about conscious attention as an “error handler”: as long as things follow their familiar routines, no error signals come up, and we may become absent-minded, just carrying out familiar habits and routines. It is when something unexpected happens, or something of where we don’t have a strong prediction of what’s going to happen next, that we are jolted out of our thoughts and forced to pay attention to our surroundings.
This would also help explain why meditation is so notoriously hard: it involves paying attention to a single unchanging stimuli whose behavior is easy to predict, and our brains are hardwired to filter any unchanging stimuli whose behavior is easy to predict out of our consciousness. Interestingly, extended meditation seems to bring some of the lower-level predictions into conscious awareness. And what I said about predicting short-term sensory stimuli ties nicely into the things I discussed back in anticipation and meditation. Savants also seem to have access to lower-level sensory data. Another connection is the theory of autism as weakened priors for sensory data, i.e. as a worsened ability for the higher-level systems to either predict the activity of the lower-level ones, or to bias their activity as a consequence.
The paper has a particularly elegant explanation of how this model would explain binocular rivalry, a situation where a test subject is shown one image (for example, a house) to their left eye and another (for example, a face) to their right eye. Instead of seeing two images at once, people report seeing one at a time, with the two images alternating. Sometimes elements of unseen image are perceived as “breaking through” into the seen one, after which the perceived image flips.
The proposed explanation is that there are two high-level hypotheses of what the person might be seeing: either a house or a face. Suppose that the “face” hypothesis ends up dominating the high-level system, which then sends its prediction down the hierarchy, suppressing activity that would support the “house” interpretation. This decreases the error signal from the systems which support the “face” interpretation. But even as the error signal from those systems decreases, the error signal from the systems which are seeing the “house” increases, as their activity does not match the “face” prediction. That error signal is sent to the high-level system, decreasing its certainty in the “face” prediction until it flips its best guess prediction to be one of a house… propagating that prediction down, which eliminates the error signal from the systems making the “house” prediction but starts driving up the error from the systems making the “face” prediction, and soon the cycle repeats again. No single hypothesis of the world-state can account for all the existing sensory data, so the system ends up alternating between two conflicting hypotheses.
One particularly fascinating aspect of the whole “hierarchical error minimization” theory as presented so far is that it can also cover not only perception, but also action! As hypothesized in the theory, when we decide to do something, we are creating a prediction of ourselves doing something. The fact that we are actually not yet doing anything causes an error signal, which in turn ends up modifying the activity of our various motor systems so as to cause the predicted behavior.
As strange as it sounds, when your own behaviour is involved, your predictions not only precede sensation, they determine sensation. Thinking of going to the next pattern in a sequence causes a cascading prediction of what you should experience next. As the cascading prediction unfolds, it generates the motor commands necessary to fulfill the prediction. Thinking, predicting, and doing are all part of the same unfolding of sequences moving down the cortical hierarchy.
Everything that I’ve written here so far only covers approximately the first six pages of the paper: there are 18 more pages of it, as well as plenty of additional commentaries. I haven’t yet had the time to read the rest, so I recommend checking out the paper itself if this seemed interesting to you.
Mental checklist to go through whenever you feel angry at someone for not doing something that you expected them to do, or for doing something that you expected them not to do. Applies regardless of whether the person in question is a co-worker, friend, relative, significant other, or anything else:
- Ask yourself whether you clearly communicated your expectation to them.
- Ask yourself whether they, after hearing about your expectation, indicated that they understood it and would try to fulfill it.
- If the answer to both of the previous questions is “yes”, then absent any other mitigating factors, you have the right to be angry at the other person. Otherwise you certainly have a right to feel disappointed or sad, but not angry.
- “But it should have been obvious!” is not a substitute for “yes” for either of the first two questions. Okay, there are some situations where it is, like if they suddenly stabbed you with a knife or burned down your house for no reason. But outside such extremes, assume that it wasn’t at all as obvious as you’re thinking it was.
If you don’t like the above being expressed in what sounds like moral terms, you may substitute expressions like “you have a right to be angry” with something like “you may express anger with the reasonable expectation that this will probably improve rather than worsen your relationship, as you are now seeking to enforce the agreement that you and the other person previously entered into and are thus working to ensure that the relationship remains healthy and pleasant for everyone involved, as opposed to just hurting the other person by randomly lashing out at them for something they never realized they should’ve avoided and thus increasing the odds that they feel a need to be on their toes around you. Also, you yourself will be better off if you don’t poison your own thoughts by feeling anger at someone who didn’t actually intend to do you any harm”. But that wouldn’t have been anywhere near as concise to express.
(And of course, if we wanted to be really exact, there’d be the issue that there can be differing degrees of certainty. E.g. someone giving a sympathetic nod when you express your desire counts as consent in many situations. But it still leaves more room for misunderstanding than a situation where they first paraphrase your desire in their own words, and then explicitly say that they’ll try to fulfill it. So ideally you ought to also calibrate your level of anger to be proportionate to the probability of an earlier miscommunication.)
I still frequently catch myself needing to remind myself about points #1 and #2 after I’ve already gotten angry at someone, but at least the act of becoming angry at someone is starting to act as an automatic triggering event for the above checklist. Hopefully I can eventually get to the point where I always go through the list first.
You close your eyes,
and you dream.
And then you wake up,
and you think you remember your dream.
But you are now in the Outer World,
and you think in terms of the Outer World.
What you remember is but a thin slice,
the part that can be understood
in terms of the Outer World.
It is not the Inner World,
it is a hint of its surface,
as seen from the outside.
So you forget,
all but a slice,
and you live your life
in the Outer World.
Until that day comes to an end,
until you close your eyes,
until you dream again.
And now you think in terms of the Inner World,
and you remember,
“I have been here before”.
And you wish you could do something
so that you would remember,
when you wake to the Outer World.
But you now think in terms of the Inner World,
and you can’t leave a trace in your mind
that could be understood
in terms of the Outer World.
So you content yourself to wander,
to explore your Inner World.
And then you wake up,
and you think you remember your dream…