nshepperd
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You don’t need to estimate this.
A McGill University study found that more than 60 percent of college-level soccer players reported symptoms of concussion during a single season. Although the percentage at other levels of play may be different, these data indicate that head injuries in soccer are more frequent than most presume.
A 60% chance of concussion is more than enough for me to stay far away.
Prevention over removal. Old LW required a certain amount of karma in order to create posts, and we correspondingly didn’t have a post spam problem that I remember. I strongly believe that this requirement should be re-introduced (with or without a moderator approval option for users without sufficient karma).
Proof of #4, but with unnecessary calculus:
Not only is there an odd number of tricolor triangles, but they come in pairs according to their orientation (RGB clockwise/anticlockwise). Proof: define a continuously differentiable vector field on the plane, by letting the field at each vertex be 0, and the field in the center of each edge be a vector of magnitude 1 pointing in the direction R->G->B->R (or 0 if the two adjacent vertices are the same color). Extend the field to the complete edges, then the interiors of the triangles by some interpolation method with continuous derivative (eg. cosine interpolation).
Assume the line integral along one unit edge in the direction R->G or G->B or B->R to be 1⁄3. (Without loss of generality since we can rescale the graph/vectors to make this true). Then a similar parity argument to Sperner’s 1d lemma (or the FTC) shows that the clockwise line integral along each large edge is 1⁄3, hence the line integral around the large triangle is 1/3+1/3+1/3=1.
By green’s theorem, this is equal to the integrated curl of the field in the interior of the large triangle, and hence equal (by another invocation of green’s theorem) to the summed clockwise line integrals around each small triangle. The integrals around a unicolor or bicolor triangle are 0 and −1/3 + 1⁄3 + 0 = 0 respectively, leaving only tricolor triangles, whose integral is again 1 depending on orientation. Thus: (tricolor clockwise) - (tricolor anticlockwise) = 1. QED.
Your interpretation of the bolded part is correct.
We got to discussing this on #lesswrong recently. I don’t see anyone here pointing this out yet directly, so:
Can you technically Strong Upvote everything? Well, we can’t stop you. But we’re hoping a combination of mostly-good-faith + trivial inconveniences will result in people using Strong Upvotes when they feel it’s actually important.
This approach, hoping that good faith will prevent people from using Strong votes “too much”, is a good example of an Asshole Filter (linkposted on LW last year). You’ve set some (unclear) boundaries, then due to not enforcing them, reward those who violate them with increased control over the site conversation. Chris_Leong gestures towards this without directly naming it in a sibling comment.
In my opinion “maybe put limits on strong upvotes if this seems to be a problem” is not the correct response to this problem, nor would be banning or otherwise ‘disciplining’ users who use strong votes “too much”. The correct response is to remove the asshole filter by altering the incentives to match what you want to happen. Options include:
Making votes normal by default but encouraging users to use strong votes freely, up to 100% of the time, so that good faith users are not disadvantaged. (Note: still disenfranchises users who don’t notice that this feature exists, but maybe that’s ok.)
Making votes strong by default so that it’s making a “weak” vote that takes extra effort. (Note: this gives users who carefully make weak votes when they have weak opinions less weight, but at least they do this with eyes open and in the absence of perverse incentives.)
#2 but with some algorithmic adjustment to give careful users more weight instead of less. This seems extremely difficult to get right (cf. slashdot metamoderation). Probably the correct answer there is some form of collaborative filtering.
Personally I favour solution #1.
I’ll add that this is not just a hypothetical troll-control issue. This is also a UX issue. Forcing users to navigate an unclear ethical question and prisoner’s dilemma—how much strong voting is “too much”—in order to use the site is unpleasant and a bad user experience. There should not be a “wrong” action available in the user interface.
PS. I’ll concede that making strong votes an actually limited resource that is enforced by the site economically (eg. with Token Bucket quota) would in a way also work, due to eliminating the perceived need for strong votes to be limited by “good faith”. But IMO the need is only perceived, and not real. Voting is for expressing preferences, and preferences are unlimited.
Good post!
Is it common to use Kalman filters for things that have nonlinear transformations, by approximating the posterior with a Gaussian (eg. calculating the closest Gaussian distribution to the true posterior by JS-divergence or the like)? How well would that work?
Grammar comment—you seem to have accidentally a few words at
Measuring multiple quantities: what if we want to measure two or more quantities, such as temperature and humidity? Furthermore, we might know that these are [missing words?] Then we now have multivariate normal distributions.
How big was your mirror, and how much of your face did you see in it?
C is basically a statement that, if included in a valid argument about the truth of P, causes the argument to tell us either P or ~P. That’s definitionally what it means to be able to know the criterion of truth.
That’s not how algorithms work and seems… incoherent.
That you want to deny C is great,
I did not say that either.
because I think (as I’m finding with Said), that we already agree, and any disagreement is the consequence of misunderstanding, probably because it comes too close to sounding to you like a position that I would also reject, and the rest of the fundamental disagreement is one of sentiment, perspective, having worked out the details, and emphasis.
No, I don’t think we do agree. It seems to me you’re deeply confused about all of this stuff.
Here’s an exercise: Say that we replace “C” by a specific concrete algorithm. For instance the elementary long multiplication algorithm used by primary school children to multiply numbers.
Does anything whatsoever about your argument change with this substitution? Have we proved that we can explain multiplication to a rock? Or perhaps we’ve proved that this algorithm doesn’t exist, and neither do schools?
Another exercise: suppose, as a counterfactual, that Laplace’s demon exists, and furthermore likes answering questions. Now we can take a specific algorithm C: “ask the demon your question, and await the answer, which will be received within the minute”. By construction this algorithm always returns the correct answer. Now, your task is to give the algorithm, given only these premises, that I can follow to convince a rock that Euclid’s theorem is true.
It seems that you don’t get it. Said just demonstrated that even if C exists it wouldn’t imply a universally compelling argument.
In other words, this:
Suppose we know the criterion of truth, C; that is, there exists (not counterfactually but actually as in anyone can observe this thing) a procedure/algorithm to assess if any given statement is true. Let P be a statement. Then there exists some argument, A, contingent on C such that A implies P or ~P. Thus for all P we can know if P or ~P. This would make A universally compelling, i.e. A is a mind-independent argument for the truth value of all statements that would convince even rocks.
appears to be a total non sequitur. How does the existence of an algorithm enable you to convince a rock of anything? At a minimum, an algorithm needs to be implemented on a computer… Your statement, and therefore your conclusion that C doesn’t exist, doesn’t follow at all.
(Note: In this comment, I am not claiming that C (as you’ve defined it) exists, or agreeing that it needs to exist for any of my criticisms to hold.)
It doesn’t seem to be a strawman of what eg. gworley and TAG have been saying, judging by the repeated demands for me to supply some universally compelling “criterion of truth” before any of the standard criticisms can be applied. Maybe you actually disagree with them on this point?
It doesn’t seem like applying full force in criticism is a priority for the ‘postrationality’ envisioned by the OP, either, or else they would not have given examples (compellingness-of-story, willingness-to-life) so trivial to show as bad ideas using standard arguments.
As for my story about how the brain works: yes, it is obviously a vast simplification. That does not make it false, especially given that “the brain learns to use what has worked before and what it thinks is likely to make it win in the future” is exactly what Eliezer is advocating in the above post.
Even if true, this is different from “epistemic rationality is just instrumental rationality”; as different as adaptation executors are from fitness maximisers.
Separately, it’s interesting that you quote this part:
The important thing is to hold nothing back in your criticisms of how to criticize; nor should you regard the unavoidability of loopy justifications as a warrant of immunity from questioning.
Because it seems to me that this is exactly what advocates of “postrationality” here are not doing, when they take the absence of universally compelling arguments as license to dismiss rationality and truth-based arguments against their positions.¹
Eliezer also says this:
Always apply full force, whether it loops or not—do the best you can possibly do, whether it loops or not—and play, ultimately, to win.
It seems to me that applying full force in criticism of postrationality amounts to something like the below:
“Indeed, compellingness-of-story, willingness-to-life, mythic mode, and many other non-evidence-based criteria are alternative criteria which could be used to select beliefs. However we have huge amounts of evidence (catalogued in the Sequences, and in the heuristics and biases literature) that these criteria are not strongly correlated to truth, and therefore will lead you to holding wrong beliefs, and furthermore that holding wrong beliefs is instrumentally harmful, and, and [the rest of the sequences, Ethical Injunctions, etc]...”
“Meanwhile, we also have vast tracts of evidence that science works, that results derived with valid statistical methods replicate far more often than any others, that beliefs approaching truth requires accumulating evidence by observation. I would put the probability that rational methods are the best criteria I have for selecting beliefs at . Hence, it seems decisively not worth it to adopt some almost certainly harmful ‘postrational’ anti-epistomology just because of that probability. In any case, per Ethical Injunctions, even if my probabilities were otherwise, it would be far more likely that I’ve made a mistake in reasoning than that adopting non-rational beliefs by such methods would be a good idea.”
Indeed, much of the Sequences could be seen as Eliezer considering alternative ways of selecting beliefs or “viewing the world”, analyzing these alternative ways, and showing that they are contrary to and inferior to rationality. Once this has been demonstrated, we call them “biases”. We don’t cling to them on the basis that “we can’t know the criterion of truth”.
Advocates of postrationality seem to be hoping that the fact that P(Occam’s razor) < makes these arguments go away. It doesn’t work like that. P(Occam’s razor) = at most makes of these arguments go away. And we have a lot of evidence for Occam’s razor.
¹ As gworley seems to do here and here seemingly expecting me to provide a universally compelling argument in response.
I’ll have more to say later but:
The way that I’d phrase it is that there’s a difference between considering a claim to be true, and considering its justification universally compelling.
Both of these are different from the claim actually being true. The fact that Occam’s razor is true is what causes the physical process of (occamian) observation and experiment to yield correct results. So you see, you’ve already managed to rephrase what I’ve been saying into something different by conflating map and territory.
This stuff about rain dancing seems like just the most banal epistemological trivialities, which have already been dealt with thoroughly in the Sequences. The reasons why such “tests” of rain dancing don’t work are well known and don’t need to be recapitulated here.
But to do that, you need to use a meta-model. When I say that we don’t have direct access to the truth, this is what I mean;
This has nothing to do with causal pathways, magic or otherwise, direct or otherwise. Magic would not turn a rock into a philosopher even if it should exist.
Yes, carrying out experiments to determine reality relies on Occam’s razor. It relies on Occam’s razor being true. It does not in any way rely on me possessing some magical universally compelling argument for Occam’s razor. Because Occam’s razor is in fact true in our universe, experiment does in fact work, and thus the causal pathway for evaluating our models does in fact exist: experiment and observation (and bayesian statistics).
I’m going to stress this point because I noticed others in this thread make this seemingly elementary map-territory confusion before (though I didn’t comment on it there). In fact it seems to me now that conflating these things is maybe actually the entire source of this debate: “Occam’s razor is true” is an entirely different thing from “I have access to universally compelling arguments for Occam’s razor”, as different as a raven and the abstract concept of corporate debt. The former is true and useful and relevant to epistemology. The latter is false, impossible and useless.
Because the former is true, when I say “in fact, there is a causal pathway to evaluate our models: looking at reality and doing experiments”, what I say is, in fact, true. The process in fact works. It can even be carried out by a suitably programmed robot with no awareness of what Occam’s razor or “truth” even is. No appeals or arguments about whether universally compelling arguments for Occam’s razor exist can change that fact.
(Why am I so lucky as to be a mind whose thinking relies on Occam’s razor in a world where Occam’s razor is true? Well, animals evolved via natural selection in an Occamian world, and those whose minds were more fit for that world survived...)
But honestly, I’m just regurgitating Where Recursive Justification Hits Bottom at this point.
This is a reinforcement learning system which responds to rewards: if particular thoughts or assumptions (...) have led to actions which brought the organism (internally or externally generated rewards), then those kinds of thoughts and assumptions will be reinforced.
This seems like a gross oversimplification to me. The mind is a complex dynamical system made of locally reinforcement-learning components, which doesn’t do any one thing all the time.
In other words, we end up having the kinds of beliefs that seem useful, as evaluated by whether they succeed in giving us rewards. Epistemic and instrumental rationality were the same all along.
And this seems simply wrong. You might as well say “epistemic rationality and chemical action-potentials were the same all along”. Or “jumbo jets and sheets of aluminium were the same all along”. A jumbo jet might even be made out of sheets of aluminium, but a randomly chosen pile of the latter sure isn’t going to fly.
As for your examples, I don’t have anything to add to Said’s observations.
Indeed, the scientific history of how observation and experiment led to a correct understanding of the phenomenon of rainbows is long and fascinating.
I’m sorry, what? In this discussion? That seems like an egregious conflict of interest. You don’t get to unilaterally decide that my comments are made in bad faith based on your own interpretation of them. I saw which comment of mine you deleted and honestly I’m baffled by that decision.
If I may summarize what I think the key disagreement is, you think we can know truth well enough to avoid the problem of the criterion and gain nothing from addressing it.
and to be pointed about it I think believing you can identify the criterion of truth is a “comforting” belief that is either contradictory or demands adopting non-transcendental idealism
Actually… I was going to edit my comment to add that I’m not sure that I would agree that I “think we can know truth well enough to avoid the problem of the criterion” either, since your conception of this notion seems to intrinsically require some kind of magic, leading me to believe that you somehow mean something different by this than I would. But I didn’t get around to it in time! No matter.
If I may summarize what I think the key disagreement is, you think we can know truth well enough to avoid the problem of the criterion and gain nothing from addressing it.
That’s not my only disagreement. I also think that your specific proposed solution does nothing to “address” the problem (in particular because it just seems like a bad idea, in general because “addressing” it to your satisfaction is impossible), and only serves as an excuse to rationalize holding comforting but wrong beliefs under the guise of doing “advanced philosophy”. This is why the “powerful but dangerous tool” rhetoric is wrongheaded. It’s not a powerful tool. It doesn’t grant any ability to step outside your own head that you didn’t have before. It’s just a trap.
I don’t have to solve the problem of induction to look out my window and see whether it is raining. I don’t need 100% certainty, a four-nines probability estimate is just fine for me.
Where’s the “just go to the window and look” in judging beliefs according to “compellingness-of-story”?
Of course not, and that’s the point.
The point… is that judging beliefs according to whether they achieve some goal or anything—is no more reliable than judging beliefs according to whether they are true, is in no way a solution to the problem of induction or even a sensible response to it, and most likely only makes your epistemology worse?
Indeed, which is why metarationality must not forget to also include all of rationality within it!
Can you explain this in a way that doesn’t make it sound like an empty applause light? How can I take compellingness-of-story into account in my probability estimates without violating the Kolmogorov axioms?
To say a little more on danger, I mean dangerous to the purpose of fulfilling your own desires.
Yes, that’s exactly the danger.
Unlike politics, which is an object-level danger you are pointing to, postrationality is a metalevel danger, but specifically because it’s a more powerful set of tools rather than a shiny thing people like to fight over. This is like the difference between being weary of generally unsafe conditions that cannot be used and dangerous tools that are only dangerous if used by the unskilled.
Thinking you’re skilled enough to use some “powerful but dangerous” tool is exactly the problem. You will never be skilled enough to deliberately adopt false beliefs without suffering the consequences.
But surely… if one is aware of these reasons… then one can simply redo the calculation, taking them into account. So we can rob banks if it seems like the right thing to do after taking into account the problem of corrupted hardware and black swan blowups. That’s the rational course, right?
There’s a number of replies I could give to that.
I’ll start by saying that this is a prime example of the sort of thinking I have in mind, when I warn aspiring rationalists to beware of cleverness.
“Above the map”? “Outside the territory”? This is utter nonsense. Rationality insists no such thing. Explicitly the opposite, in fact.
Given things like this too:
At this point I have to wonder if you’re just rounding off rationality to the nearest thing to which you can apply new-age platitudes. Frankly, this is insulting.