We have to ask why smallpox was a unique event, and we never used this method for any other virus. Did we even ever consider it?
There are two strains of smallpox, one of which is much less deadly than the other. People practicing variolation tended to use variolous material from a mild cases, including those successfully variolated. Some of the success of smallpox variolation was probably due to this practice and the resulting tendency for the inoculations to contain variola minor.
How about:
Specialization of Labor vs. Transaction/Communication costs: a trade off between having a task split between multiple people/organizations vs. done by a single person. Generalism vs.Specialization might be a more succinct way to put it.
Also, another pair that has a close connection is 3 and 7. Exploration is flexible strategy, since it leaves open resources to exploit better opportunities that turn up, while exploitation gains in commitment.
As someone with a Ph.D. in math, I tend to think verbally in as much as I have words attached to the concepts I’m thinking about, but I never go so far as to internally vocalize the steps of the logic I’m following until I’m at the point of actually writing something down.
I think there is another much stronger distinction in mathematical thinking, which is formal vs. informal. This isn’t the same distinction as verbal vs. nonverbal, for instance, formal thinking can involve manipulation of symbols and equations in addition to definitions and theorems, and I often do informal thinking by coming up with pretty explicitly verbal stories for what a theorem or definition means (though pictures are helpful too).
I personally lean heavily towards informal thinking, and I’d say that trying to come up with a story or picture for what each theorem or definition means as you are reading will help you a lot. This can be very hard sometimes. If you open a book or paper and aren’t able to get anywhere when you try do this to the first chapter, it’s a good sign that you are reading something too difficult for your current understanding of that particular field. At a high level of mastery of a particular subject, you can turn informal thinking into proofs and theorems, but the first step is to be able to create stories and pictures out of the theorems, proofs, and definitions you are reading.
Interestingly, advertiser, lawyers, and financial traders all have in common that they are agents who play zero-sum or almost zero-sum games on behalf of someone. People who represent big interests in these games are compensated well, because of the logic of the game: so much is at stake that you want to have the best person representing you, so these people’s services are bid up. But there is still the feeling that the game is wasteful, though perhaps unavoidably so.
Also, problematically for first sentence, I don’t think many people would necessarily come up with the four professions named, especially “advertiser” and “salesperson”, if asked to name the most important professions in the modern world, and some important professions, like “scientist”, are widely valorized, while others, like “engineer”, are at the least not reviled.
The theme of this book, then, must be the coming to consciousness of uncertain inference. The topic may be compared to, say, the history of visual perspective. Everyone can see in perspective, but it has been a difficult and long-drawn-out effort of humankind to become aware of the principles of perspective in order to take advantage of them and imitate nature. So it is with probability. Everyone can act so as to take a rough account of risk, but understanding the principles of probability and using them to improve performance is an immense task.
James Franklin, The Science of Conjecture: Evidence and Probability before Pascal
Well, just because the rule doesn’t by itself prevent all possible cases of inappropriate cross-rank fraternization doesn’t mean it has no value. There are other norms and practices that discourage generals from hanging out with lieutenants, e.g. generals usually get fancy lodging separate from the lieutenants. I suspect that cutting off lower-ranking officers from fraternizing with enlisted men prevents what would otherwise be one of the more common problematic cases.
If the military were even more concerned with this problem, it could have three or more groups instead of two, say, enlisted, officers and super-officers. But there are also tradeoffs to having more groupings, so the military sticks with two (part of this might be historically contingent, maybe three groups would work just as well but everyone is just copying the consensus choice of two).
I think that in the military, the “no fraternizing with enlisted personnel” rule might be one reason why a hard separation is useful. This kind of rule requires a cutoff and can’t easily be replaced with a rule like “no fraternizing with people of a rank three or more below your own.” For instance, how would you set up the housing arrangements? Also, promotions would be awkward under this system, since you would always have a group of people you previously could fraternize with but no longer can.
I think the containment of the SARS epidemic in 2003 is a under-appreciated success story. SARS spread fairly easily and had a 9% mortality rate, so it could well have killed millions, but it was contained thanks to the WHO and to the quarantine efforts of various governments. Their wasn’t much coverage in the vein of “hooray! one of the worst catastrophes in human history has been averted!” afterwards.
“But the sacrifice is too great” is a relevant argument, you think that “Yeah doing Y is right” is potentially mistaken.
I think I disagree with this. On a social and political level, the tendency to rationalize is so pervasive it would sound completely absurd to say “I agree that it would be morally correct to implement your policy but I advocate not doing it, because it will only help future generations, screw those guys.” In practice, when people attempt to motivate each other in the political sphere to do something, it is always accompanied by the claim that doing that thing is morally right. But it is in principle possible to try to get people not to do something by arguing “hey this is really bad for us!” without arguing against it’s moral rightness. This thought experiment is a case where this exact “lets grab the banana” position is supposed to be tempting.
Thanks for this response. One comment about one of your main points: I agree that the tradeoff of number of humans vs. length of life is ambiguous. But to the extent our utility function favors numbers of people over total life span, that makes the second scenario more plausible, whereas if total life span is more important, the first is more plausible.
I agree with you that both the scenarios would be totally unacceptable to me personally, because of my limited altruism. I would badly want to stop it from happening, and I would oppose creating any AI that did it. But I disagree in that I can’t say that any such AI is unfriendly or “evil”. Maybe if I was less egoistic, and had a better capacity to understand the consequences, I really would feel the sacrifice was worth it.
I don’t think that’s what I’m asking. Here’s an analogy. A person X comes to the conclusion fairly late in life that the morally best thing they can think of to do is to kill themselves in a way that looks like an accident and will their sizable life insurance policy to charity. This conclusion isn’t a reducto ad absurdum of X’s moral philosophy, even if X doesn’t like it. Regardless of this particular example, it could presumably be correct for a person to sacrifice themselves in a way that doesn’t feel heroic, isn’t socially accepted, and doesn’t save the whole world but maybe only a few far-away people. I think most people in such a situation (who managed not to rationalize the dilemma away) would probably not do it.
So I’m trying to envision the same situation for humanity as a whole. Is there any situation that humanity could face that would make us collectively say “Yeah doing Y is right, even though it seems bad for us. But the sacrifice is too great, we aren’t going to do it”. That is, if there’s room for space between “considered morality” and “desires” for an individual, is there room for space between them for a species?
Hmm, you are right. Thanks for the correction!
I think this example brings out how Pearlian causality differs from other causal theories. For instance, in a counterfactual theory of causation, since the negation of a mathematical truth is impossible, we can’t meaningfully think of them as causes.
But in the Pearlian causality it seems that mathematical statements can have causal relations, since we can factor our uncertainty about them, just as we can other statements. I think endoself’s comment argues this well. I would add that this is a good example of how causation can be subjective. Before 1984, the Taniyama-Shimura-Weil conjecture and Fermat’s last theorem existed as conjectures, and some mathematicians presumably knew about both, but as far as I know they had no clue that they were related. Then Frey conjectured and Ribet proved that the TSW conjecture implies FLT. Then mathematician’s uncertainty was such that they would have causal graphs with TSW causing FLT. Now we have a proof of TSW (mostly by Wiles) but any residual uncertainty is still correlated. In the future, maybe there will be many independent proofs of each, and whatever uncertainty is left about them will be (nearly) uncorrelated.
I also think there can be causal relations between mathematical statements and statements about the world. For instance, maybe there is some conjecture of fluid dynamics, which if true would cause us to believe a certain type of wave can occur in certain circumstances. We can make inferences both ways, for instance, if we observe the wave we might increase our credence in the conjecture, and if we prove the conjecture, we might believe the wave can be observed somehow. But it seems that the causal graph would have the conjecture causing the wave. Part of the graph would be:
[Proof of conjecture -> conjecture -> wave <- (fluid dynamics applies to water) ]
[Proof of conjecture ← conjecture → wave ← (fluid dynamics applies to water) ]
“Actually” isn’t intended in any sense except emphasis and to express that Eliezer’s view is contrary to my expectations (for instance, “I thought it was a worm, but it was actually a small snake”).
Eliezer does seem to be endorsing the statement that “everything is made of causes and effects”, but I am unsure of his exact position. The maximalist interpretation of this would be, “in the correct complete theory of everything, I expect that causation will be basic, one of the things to which other laws are reduced. It will not be the case that causation is explained in terms of laws that make no mention of causation”. This view I strongly disagree with, not least because I generally think something has gone wrong with one’s philosophy if it predicts something about fundamental physics (like Kant’s a priori deduction that the universe is Euclidean).
I suspect this is not Eliezer’s position, though I am unsure because of his “Timeless Physics” post, which I disagree with (as I lean towards four-dimensionalism) but which seems consonant with the above position in that both are consistent with time being non-fundamental. If he means something weaker, though, I don’t know what it is.
Imagine a universe that is made only of ideal billiard balls eternally bouncing around on a frictionless, pocketless billiard table. Essentially the same thing as selylindi’s idea of a gas in thermodynamic equilibrium. Imagine yourself observing this universe as a timeless observer, or to aid the imagination, that it’s “time” dimension is correlated to our space dimension, so we see the system as an infinite frozen solid, 11 by 6 by infinity, with the balls represented by solid streaks inside that go in straight lines except where they bounce off each other or the boundary of the solid.
Now, this system internally has a timelike dimension, except without increasing or decreasing entropy. And the physics of the system are completely reversible, so we have no basis of saying which way is the “future” and which way is the “past” in this system. We can equally well say a collision at one time is “caused” by the positions of the balls one second in the “past” or one second in the “future”. There is no basis for choosing a direction of causality between two events.
In our universe, our time is microscopically reversible but macroscopically irreversible, because of the fact that the universe is proceeding from a low entropy state (we call that direction the “past”) to a high entropy state (the “future”). I am curious, can anyone coherently describe a universe with nothing similar to irreversible time, but with a useful notion of causation? Or with something like irreversible time, but no causation whatsoever? I have tried (for much more than five minutes!) and not succeeded , but I am still far from sure that it’s impossible to do. It might be too much to ask to imagine actually being in a universe without causation or time, but perhaps we can think of how such a universe could look from the outside.
I am confused by these posts. On one hand, Eliezer argues for an account of causality in terms of probability, which as we know are subjective degrees of belief. So we should be able to read off whether X thinks A causes B from looking at conditional probabilities in X’s map.
But on the other hand, he suggests (not completely sure this is his view from the article) that the universe is actually made of cause and effect. I would think that the former argument instead suggests causality is “subjectively objective”. Just as with probability, causality is fundamentally an epistemic relation between me and the universe, despite the fact that there can be widespread agreement on whether A causes B. Of course, I can’t avoid cancer by deciding “smoking doesn’t cause cancer”, just as I can’t win the lottery by deciding that my probability of winning it is .9.
For instance, how would an omniscient agent decide if A causes B according Eliezer’s account of Pearl? I don’t think they would be able to, except maybe in cases where they could count frequencies as a substitute for using probabilities.
Consider “Elaine is a post-utopian and the Earth is round” This statement is meaningless, at least in the case where the Earth is round, where it is equivalent to “Elaine is a post-utopian.” Yet it does constrain my experience, because observing that the Earth is flat falsifies it. If something like this came to seem like a natural proposition to consider, I think it would be hard to notice it was (partly) meaningless, since I could still notice it being updated.
This seems to defeat many suggestions people have made so far. I guess we could say it’s not a real counterexample, because the statement is still “partly meaningful”. But in that case it would be still be nice if we could say what “partly meaningful” means. I think that the situation often arises that a concept or belief people throw around has a lot of useless conceptual baggage that doesn’t track anything in the real world, yet doesn’t completely fail to constrain reality (I’d put phlogiston and possibly some literary criticism concepts in this category).
My first attempt is to say that a belief A of X is meaningful to the extent that it (is contained in / has an analog in / is resolved by) the most parsimonious model of the universe which makes all predictions about direct observations that X would make.
Your view reminds me of Quine’s “web of belief” view as expressed in “Two Dogmas of Empiricism” section 6:
The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience. A conflict with experience at the periphery occasions readjustments in the interior of the field. Truth values have to be redistributed over some of our statements. Reevaluation of some statements entails reevaluation of others, because of their logical interconnections—the logical laws being in turn simply certain further statements of the system, certain further elements of the field.
Quine doesn’t use Bayesian epistemology, unfortunately because I think it would have helped him clarify and refine his view.
One way to try to flesh this intuition out is to say that some beliefs are meaningful by virtue of being subject to revision by experience (i.e. they directly pay rent), while others are meaningful by virtue of being epistemically entangled with beliefs that pay rent (in the sense of not being independent beliefs in the probabilistic sense). But that seems to fail because any belief connected to a belief that directly pays rent must itself be subject to revision by experience, at least to some extent, since if A is entangled with B, an observation which revises P(A) typically revises P(B), however slightly.
No 2^alpeh0=aleph1 is the continuum hypothesis, which is independent of the standard axioms of math, and can’t be proven. I think maybe you mean he was close to showing 2^aleph0 is the cardinality of the reals, but I think he knew this already and was trying to use it as the basis of the proof.
Making mistakes like Eliezer’s is a big part of learning math though, if we are looking for a silver lining. When you prove something you know is wrong, usually it’s because of some misunderstanding or incomplete understanding, and not because of some trivial error. I think the diagonal argument seems like some stupid syntactical trick the first time you hear it, but the concept is far-reaching. Surely Eliezer came away with a bit better understanding of its implications after he straightened himself out.
The model seems not far off estimating peak hospitalization date, at least for states that are currently peaking like CA and NY. The peaks in places that are close to peaking can be pretty accurately estimated just with curve fitting though, I assume that being fit to past data is why the model works OK for this.
It’s clearly overly optimistic about the rate of drop-off after the peak in deaths, at least in some cases. Look at Spain and Italy. Right now here’s how they look:
Italy: graph shows 610 deaths on April 9. Predicts 335 on April 10, 281 on April 11. Actual is 570 on April 10, 619 on April 11.
Spain: graph shows 683 on April 8, Predicts 372, 304, 262 on next three days. Actual 655, 634, 525.
The model for New York says deaths will be down to 48, 6% of the peak, in 15 days. Italy is 15 days from it’s peak of 919 and is only down to 619, 67% of the peak.
The model for the US as a whole is a little less obviously over-optimistic, assuming the peak really was April 10. it’s only predicting 40% decline in the next 15 days. California model predicts an even slower decline. It seems to think fast growth in cases in the outbreak phase leads to fast recovery, which has not been borne out thus far in Italy and Spain.