sen

Karma: 171

sen Jun 30, 2017, 7:01 AM
0 points
in reply to: cousin_it’s comment on: Kelly and the Beast
It can make sense to say that a utility function is bounded, but that implies certain other restrictions. For example, bounded utility functions cannot be decomposed into independent (additive or multiplicative, these are the only two options) subcomponents if the number of subcomponents is unknown. Any utility function that is summed or multiplied over an unknown number of independent (e.g.) societies must be unbounded*. Does that mean you believe that utility functions can’t be aggregated over independent societies or that no two societies can contribute independently to the utility function? That latter implies that a utility function cannot be determined without knowing about all societies, which would make the concept useless. Do you believe that utility functions can be aggregated at all beyond the individual level?
- Keep in mind that “unbounded” here means “arbitrarily additive”. In the multiplicative case, even if a utility function is always less than 1, if an individual’s utility can be made arbitrarily close to 0, then it’s still unbounded. Such an individual still has enough to gain by betting on a trillion coin tosses.
You mentioned that a utility function should be seen as a proxy to decision making. If decisions can be independent, then their contributions to the definition of a utility function must be independent*. If the utility function is bounded, then the number of independent decisions something can decide between must also be bounded. Maybe that makes sense for individuals since you distinguished a utility function as a summary of “current” decision-making, and any individual is presumably limited in their ability to decide between independent outcomes at any given point in time. Again, though, this causes problems for aggregate utility functions.
- Consider the functor F that takes any set of decisions (with inclusion maps between them) to the least-assuming utility function consistent with them. There exists a functor G that takes any utility function to the maximal set of decisions derivable from it. F,G together form a contravariant adjunction between set of decisions and utility functions. F is then left-adjoint to G. Therefore F preserves finite coproducts as finite products. Therefore for any disjoint union of decisions A,B, the least-assuming utility function defined over them exists and is F(A+B)=F(A)*F(B). The proof is nearly identical for covariant adjunctions.
It seems like nonsense to say that utility functions can’t be aggregated. A model of arbitrary decision making shouldn’t suddenly become impossible just because you’re trying to model, say, three individuals rather than one. The aggregate has preferential decision making just like the individual.

sen Jun 29, 2017, 5:34 PM
0 points
in reply to: MrMind’s comment on: Kelly and the Beast

Also it’s unclear to me what the connection is between this part and the second.

My bad, I did a poor job explaining that. The first part is about the problems of using generic words (evolution) with fuzzy decompositions (mates, predators, etc) to come to conclusions, which can often be incorrect. The second part is about decomposing those generic words into their implied structure, and matching that structure to problems in order to get a more reliable fit.

I don’t believe that “I don’t know” is a good answer, even if it’s often the correct one. People have vague intuitions regarding phenomena, and wouldn’t it be nice if they could apply those intuitions reliably? That requires a mapping from the intuition (evolution is responsible) to the problem, and the mapping can only be made reliable once the intuition has been properly decomposed into its implied structure, and even then, only if the mapping is based on the decomposition.

I started off by trying to explain all of that, but realized that there is far too much when starting from scratch. Maybe someday I’ll be able to write that post...

sen Jun 29, 2017, 5:25 PM
0 points
in reply to: MrMind’s comment on: Kelly and the Beast
The cell example is an example of evolution being used to justify contradictory phenomena. The exact same justification is used for two opposing conclusions. If you thought there was nothing wrong with those two examples being used as they were, then there is something wrong with your model. They literally use the exact same justification to come to opposing conclusions.

The second set of explanations have fewer, more reliably-determinable dependencies, and their reasoning is more generally applicable.

That is correct, they have zero prediction and compression power. I would argue that the same can be said of many cases where people misuse evolution as an explanation.

When people falsely pretend to have knowledge of some underlying structure or correlate, they are (1) lying and (2) increasing noise, which by various definition is negative information. When people use evolution as an explanation in cases where it does not align with the implications of evolution, they are doing so under a false pretense. My suggested approach (1) is honest and (2) conveys information about the lack of known underlying structure or correlate.

I don’t know what you mean by “sensible definition”. I have a model for that phrase, and yours doesn’t seem to align with mine.

sen Jun 29, 2017, 5:17 AM
1 point
in reply to: cousin_it’s comment on: Kelly and the Beast
Would your answer change if I let you flip the coin until you lost? Based on your reasoning, it should not. Despite it being an effectively-guaranteed extinction, the infinitesimal chance is overwhelmed by the gains in the case of infinitely many good coin flips.

I would not call the Kelly strategy risk-averse. I imagine that word to mean “grounded in a fantasy where risk is exaggerated”. I would call the second strategy risk-prone. The difference is that the Kelly strategy ends up being the better choice in realistic cases, whereas the second strategy ends up being the better choice in the extraordinarily rare wishful cases. In that sense, I see this question as one that differentiates people that prefer to make decisions grounded in reality from those that prefer to make decisions grounded in wishful thinking. The utilitarian approach then is prone to wishful thinking.

Still, I get your point. There may exist a low-chance scenario for which I would, with near certainty, trade the Kelly-heaven world for a second-hell world. To me, that means there exists a scenario that could lull me into gambling on wildly-improbable wishful thinking. Though such scenarios may exist, and though I may bet on such scenarios when presented with them, I don’t believe it’s reasonable to bet on them. I can’t tell if you literally believe that it’s reasonable to bet on such scenarios or if you’re imagining something wholly different from me.

sen Jun 28, 2017, 4:37 PM
0 points
in reply to: Dagon’s comment on: Kelly and the Beast
Dagon: You can artificially bound utility to some arbitrarily low “bankruptcy” point. The lack of a natural one isn’t relevant to the question of whether a utility function makes sense here. On treating utility as a resource, if you can make decisions to increase or decrease utility, then you can play the game. Your basic assumption seems to be that people can’t meaningfully make decisions that change utility, at which point there is no point in measuring it, as there’s nothing anyone can do about it.

The point of unintuitive high utilities and upper-bounded utilities I believe deserves another post.

sen Dec 10, 2016, 1:02 PM
3 points
in reply to: btrettel’s comment on: Which areas of rationality are underexplored? - Discussion Thread
Regarding the Buckingham Pi Theorem (BPT), I think I can double my recommendation that you try to understand the Method of Lagrange Multipliers (MLM) visually. I’ll try to explain in the following paragraph knowing that it won’t make much sense on first reading.

For the Method of Lagrange Multipliers, suppose you have some number of equations in n variables. Consider the n-dimensional space containing the set of all solutions to those equations. The set of solutions describes a k-dimensional manifold (meaning the surface of the manifold forms a k-dimensional space), where k depends on the number of independent equations you have. The set of all points perpendicular to this manifold (the null space, or the space of points that, projected onto the manifold, give the zero vector) can be described by an (n-k)-dimensional space. Any (n-k)-dimensional space can be generated (by vector scaling and vector addition) of (n-k) independent vectors. For the Buckingham Pi Theorem, replace each vector with a matrix/group, vector scaling with exponentiation, and vector addition with multiplication. Your Buckingham Pi exponents are Lagrange multipliers, and your Pi groups are Lagrange perpendicular vectors (the gradient/normal vectors of your constraints/dimensions).

I guess in that sense, I can see why people would make the jump to Lie groups. The Pi Groups / basis vectors form the generator of any other vector in that dimensionless space, and they’re obviously invertible. Honestly, I haven’t spent much time with Lie Groups and Lie Algebra, so I can’t tell you why they’re useful. If my earlier explanation of dimensionless quantities holds (which, after seeing the Buckingham Pi Theorem, I’m even more convinced that it does), then it has something to do with symmetry with respect to scale, The reason I say “scale” as opposed to any other x * x → x quantity is that the scale kind of dimensionlessness seems to pop up in a lot of dimensionless quantities specific to fluid dynamics, including Reynold’s Number.

Sorry, I know that didn’t make much sense. I’m pretty sure it will though once you go through the recommendations in my earlier reply.

Regarding Reynold’s Number, I suspect you’re not going to see the difference between the dimensional and the dimensionless quantities until you try solving that differential equation at the bottom of the page. Try it both with and without converting to dimensionless quantities, and make sure to keep track of the semantics of each term as you go through the process. Here’s one that’s worked out for the dimensionless case. If you try solving it for the non-dimensionless case, you should see the problem.

It’s getting really late. I’ll go through your comments on similarity variables in a later reply.

Thanks for the references and your comments. I’ve learned a lot from this discussion.

sen Dec 9, 2016, 10:44 AM
2 points
in reply to: btrettel’s comment on: Which areas of rationality are underexplored? - Discussion Thread
See my response below to WhySpace on getting started with group theory through category theory. For any space-oriented field, I also recommend looking at the topological definition of a space. Also, for any calculus-heavy field, I recommend meditating on the Method of Lagrange Multipliers if you don’t already have a visual grasp of it.

I don’t know of any resource that tackles the problem of developing models via group theory. Developing models is a problem of stating and applying analogies, which is a problem in category theory. If you want to understand that better, you can look through the various classifications of functors since the notion of a functor translates pretty accurately to “analogy”.

I have no background in fluid dynamics, so please filter everything I say here through your own understanding, and please correct me if I’m wrong somewhere.

I don’t think there’s any inherent relationship between dimensionless parameters and group theory. The reason being that dimensionless quantities can refer to too many things (i.e., they’re not really dimensionless, and different dimensionlessnesses have different properties… or rather they may be dimensionless, but they’re not typeless). Consider that the !∘sqrt∘ln of a dimensionless quantity is also technically a dimensionless quantity while also being almost-certainly useless and uninterpretable. I suppose if you can rewrite an equation in terms of dimensionless quantities whose relationships are restricted to have certain properties, then you can treat them like other well-known objects, and you can throw way more math at them.

For example, suppose your “dimensionless” quantity is a scaling parameter such that scale * scale → scale (the product of two scaling operations is equivalent to a single scaling operation). By converting your values to scales, you’ve gained a new operation to work with due to not having to re-translate your quantities on each successive multiplication: element-wise exponentiation. I’d personally see that as a gateway to applying generating series (because who doesn’t love generating series?), but I guess a more mechanics-y application of that would be solving differential equations, which often require exponentiating things.

Any time you have a set of X quantities that can be applied to one another to get another of the X quantities, you have a group of some sort (with some exceptions). That’s what’s going on with the scaling example (x * x → x), and that’s what’s not going on with the !∘sqrt∘ln example. The scaling example just happens to be a particularly simple example of a group. You get less trivial examples when you have multiple “dimensionless” quantities that can interact with one another in standard ways. For example, if vector addition, scaling, and dot products are sensible, your vectors can form a Hilbert space, and you can use wonderful things like angles and vector calculus to meaningful effect.

I can probably give a better answer if I know more precisely what you’re referring to. Do you have examples of fluid dynamicists simplifying equations and citing group theory as the justification?

sen Dec 6, 2016, 9:23 AM
0 points
in reply to: Lumifer’s comment on: Beware of identifying with school of thoughts
Or is it that a true sophisticate would consider where and where not to apply sophistry?

sen Dec 6, 2016, 9:11 AM
0 points
in reply to: ChristianKl’s comment on: Making intentions concrete—Trigger-Action Planning
Information on the discussion board is front-facing for some time, then basically dies. Yes, you can use the search to find it again, but that becomes less reliable as discussion of TAPs increases. It’s also antithetical to the whole idea behind TAP.

The wiki is better suited for acting as a repository of information.

sen Dec 6, 2016, 7:12 AM
0 points
in reply to: NatashaRostova’s comment on: Beware of identifying with school of thoughts
I don’t understand what point you’re making with the computer, as we seem to be in complete agreement there. Nothing about the notion of ideals and definitions suggests that computers can’t have them or their equivalent. It’s obvious enough that computers can represent them, as you demonstrated with your example of natural numbers. It’s obvious enough that neurons and synapses can encode these things, and that they can fire in patterned ways based on them because… well that’s what neurons do, and neurons seem to be doing to bulk of the heavy lifting as far as thinking goes.

Where we disagree is in saying that all concepts that our neurons recognize are equivalent and that they should be reasoned about in the same way. There are clearly some notions that we recognize as being valid only after seeing sufficient evidence. For these notions, I think bayesian reasoning is perfectly well-suited. There are also clearly notions we recognize as being valid for which no evidence is required. For these, I think we need something else. For these notions, only usefulness is required, and sometimes not even that. Bayesian reasoning cannot deal with this second kind because their acceptability has nothing to do with evidence.

You argue that this second kind is irrelevant because these things exist solely in people’s minds. The problem is that the same concepts recur again and again in many people minds. I think I would agree with you if we only ever had to deal with a physical world in which people’s minds did not matter all that much, but that’s not the world we live in. If you want to be able to reliably convey your ideas to others, if you want to understand how people think at a more fundamental level, if you want your models to be useful to someone other than yourself, if you want to develop ideas that people will recognize as valid, if you want to generalize ideas that other people have, if you want your thoughts to be integrated with those of a community for mutual benefit, then you cannot ignore these abstract patterns because these abstract patterns constitute such a vast amount of how people think.

It also, incidentally, has a tremendous impact on how your own brain thinks and the kinds of patterns your brain lets you consciously recognize. If you want to do better generalizing your own ideas in reliable and useful ways, then you need to understand how they work.

For what it’s worth, I do think there are physically-grounded reasons for why this is so.

sen Dec 6, 2016, 6:19 AM
1 point
in reply to: WhySpace_duplicate0.9261692129075527’s comment on: Which areas of rationality are underexplored? - Discussion Thread
“Group” is a generalization of “symmetry” in the common sense.

I can explain group theory pretty simply, but I’m going to suggest something else. Start with category theory. It is doable, and it will give you the magical ability of understanding many math pages on Wikipedia, or at least the hope of being able to understand them. I cannot overstate how large an advantage this gives you when trying to understand mathematical concepts. Also, I don’t believe starting with group theory will give you any advantage when trying to understand category theory, and you’re going to want to understand category theory if you’re interested in reasoning.

When I was getting started with category theory, I went back and forth between several pages (Category Theory, Functor, Universal Property, Universal Object, Limits, Adjoint Functors, Monomorphism, Epimorphism). Here are some of the insights that made things click for me:
- An “object” in category theory corresponds to a set in set theory. If you’re a programmer, it’s easier to think of a single categorical object as a collection (class) of OOP objects. It’s also valid and occasionally useful to think of a single categorical object as a single OOP object (e.g., a collection of fields).
- A “morphism” in category theory corresponds to a function in set theory. If you think of a categorical object as a collection of OOP objects, then a morphism takes as input a single OOP object at a time.
- It’s perfectly valid for a diagram to contain the same categorical object twice. Diagrams only show relations, and it’s perfectly valid for an OOP object to be related to another OOP object of the same class. When looking at commutative diagrams that seem to contain the same categorical object twice, think of them as distinct categorical objects.
- Diagrams don’t only show relationships between OOP objects. They can also show relationships between categorical objects. For example, a diagram might state that there is a bijection between two categorical objects.
- You’re not always going to have a natural transformation between two functors of the same category.
- When trying to understand universal properties, the following mapping is useful (look at the diagrams on Wikipedia): A is the Platonic Form of Y, U is a fire that projects only some subset of the aspects of being like A.
- The duality between categorical objects and OOP objects is critical to understanding the difference between any diagram and its dual (reversed-morphisms). Recognizing this makes it much easier to understand limits and colimits.
Once you understand these things, you’ll have the basic language down to understand group theory without much difficulty.

sen Dec 6, 2016, 5:31 AM
1 point
in reply to: NatashaRostova’s comment on: Beware of identifying with school of thoughts
The distinction between “ideal” and “definition” is fuzzy the way I’m using it, so you can think of them as the same thing for simplicity.

Symmetry is an example of an ideal. It’s not a thing you directly observe. You can observe a symmetry, but there are infinitely many kinds of symmetries, and you have some general notion of symmetry that unifies all of them, including ones you’ve never seen. You can construct a symmetry that you’ve never seen, and you can do it algorithmically based on your idea of what symmetries are given a bit of time to think about the problem. You can even construct symmetries that, at first glance, would not look like a symmetry to someone else, and you can convince that someone else that what you’ve constructed is a symmetry.

The set of natural numbers is an example of something that’s defined, not observed. Each natural number is defined sequentially, starting from 1.

Addition is an example of something that’s defined, not observed. The general notion of a bottle is an ideal.

In terms of philosophy, an ideal is the Platonic Form of a thing. In terms of category theory, an ideal is an initial or terminal object. In terms of category theory, a definition is a commutative diagram.

I didn’t say these things weren’t influenced by past observations and correlations. I said past observations and correlations were irrelevant for distinguishing them. Meaning, for example, you can distinguish between more natural numbers than your past experiences should allow.

sen Dec 5, 2016, 6:56 AM
0 points
in reply to: ChristianKl’s comment on: Making intentions concrete—Trigger-Action Planning
Fair enough, though I disagree with the idea of using the discussion board as a repository of information.

sen Dec 5, 2016, 6:09 AM
0 points
in reply to: NatashaRostova’s comment on: Beware of identifying with school of thoughts
Is there ever a case where priors are irrelevant to a distinction or justification? That’s the difference between pure Bayesian reasoning and alternatives.

OP gave the example of the function of organs for a different purpose, but it works well here. To a pure Bayesian reasoner, there is no difference between saying that the heart has a function and saying that the heart is correlated with certain behaviors, because priors alone are not sufficient to distinguish the two. Priors alone are not sufficient to distinguish the two because the distinction has to do with ideals and definitions, not with correlations and experience.

If a person has issues with erratic blood flow leading to some hospital visit, why should we look at the heart for problems? Suppose there were a problem found with the heart. Why should we address the problem at that level as opposed to fixing the blood flow issue in some more direct way? What if there was no reason for believing that the heart problem would lead to anything but the blood flow problem? What’s the basis for addressing the underlying cause as opposed to addressing solely the issue that more directly led to a hospital visit?

There is no basis unless you recognize that addressing underlying causes tends to resolve issues more cleanly, more reliably, more thoroughly, and more persistently than addressing symptoms, and that the underlying cause only be identified by distinguishing erroneous functioning from other abnormalities. Pure Bayesian reasoners can’t make the distinction because the distinction has to do with ideals and definitions, not with correlations and experience.

It’s really hard for me to see under what model of the world (correct) Bayesian analysis could be misleading.

If you wanted a model that was never misleading, you might as well use first order logic to explain everything. Or go straight for the vacuous case and don’t try to explain anything. That problem is that that doesn’t generalize well, and it’s too restrictive. It’s about broadening your notion of reasoning so that you consider alternative justifications and more applications.

sen Dec 4, 2016, 2:21 PM
1 point
in reply to: Kaj_Sotala’s comment on: Making intentions concrete—Trigger-Action Planning
That’s not what OP says, and it’s also a non-sequitur. Obviousness and intuitiveness does not imply that all goals should be turned to TAPs or that vague triggers shouldn’t be used. It’s obvious and intuitive to anyone that’s flown on an airplane that the Earth is spheroid, but that doesn’t mean I should use geodesics to compute the best way to get the the grocery store.

TAPs are useful for people that have problems following through with intentions. OP mentions three example indicators of such problems. If you don’t have problems following through, then there is no reason to “make all of your goals into TAPs” or “never think anything with a vague trigger”. Putting effort into solving a non-problem is a waste.

To answer your question, hell no. It’s clear why this would help certain people, but it’s certainly not optimal for people that can look ahead a bit into a future, keep things in mind for later, or… you know, stick to things. The general idea behind TAPs is that people are lazy when they have planning left to do, and they can’t remember to do things. Yes, I’ll set up notes sometimes, but for the vast majority of things, my brain just reminds me without any explicit triggers. It’s not like I feel lazy either, and I don’t feel off-put by non-concrete goals, not even a little.

I’m satisfied with my level of productivity, I don’t get discouraged by planning or non-concrete goals, and I don’t have trouble remembering to do things. TAPs has nothing to offer for me other than ideas on how to model certain aspects of people’s brains.

sen Dec 4, 2016, 11:35 AM
0 points
in reply to: ChristianKl’s comment on: Which areas of rationality are underexplored? - Discussion Thread
System 1 and 2 I don’t think are relevant since they’re not areas of rationality. It’s the difference between a design and an implementation. I don’t think this thread is about implementation optimizations, and I do see numerous threads on that topic.

Regarding double crux, I actually don’t see that when I browse through the recent threads, even going back several pages. Through the site search, I was able to find another post that links to a November 29th thread, which I think is the one you’re talking about.

Here’s an excerpt from that double crux thread.

Ideally, B is a statement that is somewhat closer to reality than A—it’s more concrete, grounded, well-defined, discoverable, etc. It’s less about principles and summed-up, induced conclusions, and more of a glimpse into the structure that led to those conclusions.

(It doesn’t have to be concrete and discoverable, though—often after finding B it’s productive to start over in search of a C, and then a D, and then an E, and so forth, until you end up with something you can research or run an experiment on).

That’s not out of context. The entire game description and recommendations are written with the focal point of increasing precision and making beliefs more concrete.

I want you to take the time to seriously consider whether you think I’m crazy for thinking that “increasing precision” and “making beliefs more concrete” could possibly be a bad thing when trying to understand how someone thinks. Think about what your gut reaction was when you read that. Think about what alternative there could be. Please don’t read on until you’re sure I’m just trolling so maybe you can see how screwed up this place this.

How about doing the exact opposite? How about making things less precise? How about throwing away useless structure and making it easier to reason by analogy, thereby letting people expose the full brunt of their intuition and experience that really leads to their beliefs? How about making beliefs less concrete, and therefore more abstract, more general, and easier to see relationships in other domains?

If you convince someone that A really might not lead to B and that there are n experiments you could use to tell, whoopee do, they are literally never going to use that again. If you discover that you believe uniforms lead to bullying because you mentally model social dynamics as particle systems, and bullying as a problem that occurs in high-chaos environments, and that uniforms go a long way in cooling the system thereby reducing the chaos and bullying… That’s probably going to stick with you for a while, despite being a complete ungrounded non-sequitur.

sen Dec 3, 2016, 1:21 PM
2 points
on: Making intentions concrete—Trigger-Action Planning
Reading through this, it seems completely obvious and intuitive, and yet I see a lot of “thumbs up” (or whatever the LW colloquialism is). For the sake of metaoptimization, I have to ask… Has this post actually helped anyone here? Reading through the comments, it seems again like everyone already knew this, and that people are just commenting with their own experiences. If this post didn’t actually help anyone here, the obvious follow-up question would be whether the “thumbs up” signal is actually conveying the intended meaning.

sen Dec 3, 2016, 11:23 AM
4 points
in reply to: DataPacRat’s comment on: Open thread, Nov. 28 - Dec. 04, 2016
You don’t place bets based solely on probabilities. You place bets based on probabilities, odds, timescales, investments, and alternative options. Specifically, you place bets to optimize for growth of principle with respect to time. What you’re doing is not placing a bet. If you were placing a bet and wanted feedback, it would have been appropriate to provide a lot more information, such as what you expect to gain from your bet, what you expect to lose in the negative case, what you’re hoping to optimize, what your expected costs are, and what alternatives you’re considering spending your time or money on. It’s not appropriate for you to provide any of that information because what you’re doing is not placing a bet.

What you’re doing is panicking and looking for an echo to tell you that your beliefs are sensible, that the world really is crashing, and that what you’re doing is justified. Your beliefs are not sensible, and the world isn’t really crashing. I don’t know if what you’re doing is justified, as that would require a lot more information, but honestly I think that’s irrelevant.

sen Dec 3, 2016, 10:18 AM
4 points
in reply to: DataPacRat’s comment on: Open thread, Nov. 28 - Dec. 04, 2016
I said you sound insane because of your paranoia, not because of what you wanted to do as a result of that paranoia. Whether or not you would be creating backups in other circumstances is irrelevant, except as an indicator of how paranoid you are. I don’t think such an indicator is necessary because your first two paragraphs already demonstrate what I see as an extreme level of paranoia, and so to me it’s irrelevant whether you already have backups of various sites. It’s perfectly reasonable for you to create backups given your beliefs. Those beliefs though I consider insane. The solution then is not to stop creating backups, as that would accomplish nothing. The solution is to stop browsing sites that are specifically designed to make you insane.

sen Dec 3, 2016, 9:09 AM
3 points
in reply to: DataPacRat’s comment on: Open thread, Nov. 28 - Dec. 04, 2016
You sound insane desu.

Stop browsing reddit for a while. Any board where attention is explicitly rewarded, whether in the form of (You)s or upboats, will almost by definition tend towards encouraging high volatility of beliefs and emotions. It sounds like you’ve been riding that wave a bit too long.

Also, learn to recognize fear mongering.