How can labour productivity growth be an indicator of automation? 2020-11-16T21:16:03.576Z
Mathematical Intuitionism and the Flow of Time 2020-04-14T00:25:10.524Z
Why hasn't the technology of Knowledge Representation (i.e., semantic networks, concept graphs, ontology engineering) been applied to create tools to help human thinkers? 2020-03-09T06:11:13.632Z


Comment by polytopos on [Linkpost] AlphaFold: a solution to a 50-year-old grand challenge in biology · 2020-12-02T19:19:01.567Z · LW · GW

I find it hard to believe your prediction that this breakthrough will be insignificant given what I've read in other reputable sources. I give a pretty high initial credence to the scientific claims of publications like Nature which had this to say in their article on Alphafold2:

The ability to accurately predict protein structures from their amino-acid sequence would be a huge boon to life sciences and medicine. It would vastly accelerate efforts to understand the building blocks of cells and enable quicker and more advanced drug discovery.


Comment by polytopos on The next AI winter will be due to energy costs · 2020-11-30T06:22:38.340Z · LW · GW

Agreed. Open AI did a study on the trends of algorithm efficiency. They found a 44x improvement in training efficiency on ImageNet over 7 years.

Comment by polytopos on Less Wrong Rationality and Mainstream Philosophy · 2020-11-17T16:41:36.456Z · LW · GW

I find reading this post and the ensuing discussion quite interesting because I studied academic philosophy (both analytic and continental) for about 12 years at university. Then I changed course and moved into programming and math, and developed a strong interest thinking about AI safety.

I find this debate a bit strange. Academic philosophy has its problems, but it's also a massive treasure trove of interesting ideas and rigorous arguments. I can understand the feeling of not wanting to get bogged down in the endless minutia of academic philosophizing in order to be able to say anything interesting about AI. On the other hand, I don't quite agree that we should just re-invent the wheel completely and then look to the literature to find "philosophical nearest neighbor". Imagine suggesting we do that with math. "Who cares about what all these mathematicians have written, just invent your own mathematical concepts from scratch and then look to find the nearest neighbor in the mathematical literature." You could do that, but you'd be wasting a huge amount of time and energy re-discovering things that are already well understood in the appropriate field of study. I routinely find myself reading pseudo-philosophical debates among science/engineering types and thinking to myself, I wish they had read philosopher X on that topic so that their thinking would be clearer. 

It seems that here on LW many people have a definition of "rationalist" that amounts to endorsing a specific set of philosophical positions or meta-theories (e.g., naturalism, Bayesianism, logical empiricism, reductionism, etc). In contrast, I think that the study of philosophy shows another way of understanding what it is to be a rational inquirer. It involves a sensitivity to reason and argument, a willingness to question one's cherished assumptions, a willingness to be generous with one's intellectual interlocutors. In other words, being rational means following a set of tacit norms for inquiry and dialogue rather than holding a specific set of beliefs or theories. 

In this sense of reason does not involve a commitment to any specific meta-theory. Plato's theory of the forms, however implausible it seems to us today, is just as much an expression of rationalism in the philosophical sense. It was a good-faith effort to try to make sense of reality according to best arguments and evidence of his day. For me, the greatest value of studying philosophy is that it teaches rational inquiry as a way of life. It shows us that all these different weird theories can be compatible with a shared commitment to reason as the path to truth.

Unfortunately, this shared commitment does break down in some places in the 19th and 20th centuries. With certain continental "philosophers" like Nietzsche, Derrida and Foucault their writing undermines the commitment to rational inquiry itself, and ends up being a lot of posturing and rhetoric. However, even on the continental side there are some philosophers who are committed to rational inquiry (my favourite being Merleau-Ponty who pioneered ideas of grounded intelligence that inspired certain approaches in RL research today).  

I think it's also worth noting that Nick Bostrum who helped found the field of AI safety is a straight-up Oxford trained analytic philosopher. In my Master's program, I attended a talk he gave on Utilitarianism at Oxford back in 2007 before he was well known for AI related stuff. 

Another philosopher who I think should get more attention in the AI-alignment discussion is Harry Frankfurt. He wrote brilliantly on value-alignment problem for humans (i.e., how do we ourselves align conflicting desires, values, interests, etc.).

Comment by polytopos on How can labour productivity growth be an indicator of automation? · 2020-11-17T06:15:47.788Z · LW · GW

Ah, thanks for clarifying. So the key issue is really the adjusted for inflation/deflation part. You are saying even if previously expensive goods become very cheap due to automation, they will still be valued in "real dollars" the same for the productivity calculation. 

Does this mean that a lot rides on how economists determine comparable baskets of goods at different times and also on how far back they look for a historical reference frame?

Comment by polytopos on How can labour productivity growth be an indicator of automation? · 2020-11-17T02:26:27.230Z · LW · GW

Thanks for your comment Phil. That's helpful, I hadn't considered the question of where labour shifts after less of it is needed to produce an existing good. 

I understand you as saying that as productivity increases in a field and market demand becomes saturated then the workers move elsewhere. This shift of labour to new sectors could (and historically did) lead to more overall productivity, but I think this trend may not continue with the current waves of automation. It seems possible that now areas of the economy where workers move to are those less affected by the productivity enhancing effects of technology. I think this is what actually happened with the economic shift from manufacturing to service industries. Manufacturing can benefit a lot from automation technology, whereas service jobs (especially in fields where the human element of the service is what makes the service valued) are not as capable of becoming more productive. e.g., A massage therapist is not going to get much more productive no matter how much technology we have. So what I imagine is that as automation makes it take less and less labour to produce physical and digital stuff, then most of the jobs that remain will be in human-centered fields which are inherently harder to make more productive through technology. 

Thus, it still seems possible that automation could cause worker productivity to go down (which is the opposite of what Krugman was assuming). This is counter-intuitive because clearly there is a common sense way in which the automated economy is much much more productive. More and more goods become plentiful and virtually free. But these cheap plentiful goods do not have much market value, despite their value to us as human beings, so they don't contribute to labour productivity as measured by economists.

Comment by polytopos on The tech left behind · 2020-11-16T08:21:15.468Z · LW · GW

Digital knowledge management tools envisioned in the 1950s and 60s such as Douglas Engelbart's hyperdocument system has not been fully implemented (to my knowledge) and certainly not widely embraced. The World Wide Web failed to implement key features from Engelbart's proposal such as the ability to directly address arbitrary sub-documents, or the ability to live embed a sub-document inside another document. 

Similarly both Engelbart and Ted Nelson emphasized the importance of hyperlinks being two-directional so that the link is browsable from both the source and the target document. In other words, you could look at any webpage and immediately see all the pages that link to that page.  However, Tim Berners-Lee chose to make web hyperlinks one directional from source to target, and we are still stuck with that limitation today.  Google's PageRank algorithm gets around this by doing massive crawling the web and then tracing the back-links through the network, but back-links could have been built into the web as a basic feature available to everybody.

Comment by polytopos on Are Humans Fundamentally Good? · 2020-07-30T23:15:39.678Z · LW · GW

I second this book recommendation. I just finished reading it and it is well written and well argued. Bregman explicitly contrasts Hobbes' pessimistic view of human nature with Rousseau's positive view. According to the most recent evidence Rousseau was correct.

His evolutionary argument is that social learning was the overwhelming fitness inducing ability that drove human evolution. As a result we evolved for friendliness and cooperation as a byproduct of selection for social learning.

Comment by polytopos on Introduction to Introduction to Category Theory · 2020-06-12T03:44:57.517Z · LW · GW

I don't know enough math to understand your response. However, from the bits I can understand, it seems leave open the epistemic issue of needing an account of demostrative knowledge that is not dependent on Bayesian probability.

Comment by polytopos on Introduction to Introduction to Category Theory · 2020-06-10T16:30:01.906Z · LW · GW

Interesting. This might be somewhat off topic, but I'm curious how would such an Bayesian analysis of mathematical knowledge explain the fact that it is provable that any number of randomly selected real numbers are non-computable with a probability 1, yet this is not equivalent to a proof that all real numbers are non-computable. The real numbers 1, 1.4, square root 2, pi, etc are all computable numbers, although the probability of such numbers occurring in an empirical sample of the domain is zero.

Comment by polytopos on A new kind of Hermeneutics · 2020-06-09T14:28:22.080Z · LW · GW

I was excited by the initial direction of the article, but somewhat disappointed with how it unfolded.

In terms of Leibniz's hope for a universal formal language we may be closer to that. The new book Modal Homotopy Type Theory (2020 by David Corfield) argues that much of the disappointment with formal languages among philosophers and linguists stems from the fact that through the 20th century most attempts to formalize natural language did so with first-order predicate logic or other logics that lacked dependent types. Yet, dependent types are natural in both mathematical discourse and ordinary language.

Martin-Lof developed the theory of dependent types in the 1970s and now Homotopy Type Theory has been developed on top of that to serve as a computation-friendly foundation for mathematics. Corfield argues that such type theories offer new hope for the possibility of formalizing the semantic structure of natural language.

Of course, this hasn't been accomplished yet, but it's exciting to think that Leibniz's dream may be realized in our century.

Comment by polytopos on Introduction to Introduction to Category Theory · 2020-06-09T14:07:31.271Z · LW · GW

I disagree with the idea that one doesn't have intuitions about generalization if one hasn't studied mathematics. One things that I find so interesting about CT is that it is so general it applies as much to everyday common sense concepts as it does to mathematical ones. David Spivak's ontology logs are a great illustration of this.

I do agree that there isn't a really good beginners book that covers category theory in a general way. But there are some amazing YouTube lectures. I got started on CT with this series, Category Theory for Beginners. The videos are quite long, but the lecturer does an amazing job explaining all the difficult concepts with lots of great visual diagrams. What is great about this series is that despite the "beginners" in the title he actually covers many more advanced topics such as adjunction, Yoneda's lemma, and topos theory in a way that doesn't presuppose prior mathematical knowledge.

In terms of books, Conceptual Mathematics really helped me with the basics of sets and functions, although it doesn't get into the more abstract stuff very much. Finally, Category Theory for Programmers is quite accessible if you have any background in computer programming.

Comment by polytopos on Introduction to Introduction to Category Theory · 2020-06-09T13:56:53.926Z · LW · GW

It seems odd to equate rationality with probabilistic reasoning. Philosophers have always distinguished between demonstrative (i.e., mathematical) reasoning and probabilistic (i.e., empirical) reasoning. To say that rationality is constituted only by the latter form reasoning is very odd, especially considering that it is only though demonstrative knowledge that we can even formulate such things as Bayesian mathematics.

Category theory is a meta-theory of demonstrative knowledge. It helps us understand how concepts relate to each other in a rigorous way. This helps with the theory side of science rather than the observation side of science (although applied category theories are working to build unified formalisms for experiments-as-events and theories).

I think it is accurate to say that, outside of computer science, applied category theory is a very young field (maybe 10-20 years old). It is not surprising that there haven't been major breakthroughs yet. Historically fruitful applications of discoveries in pure math often take decades or even centuries to develop. The wave equation was discovered in the 1750s in a pure math context, but it wasn't until the 1860s that Maxwell used it to develop a theory of electromagnetism. Of course, this is not in itself an argument that CT will produce applied breakthroughs. However, we can draw a kind of meta-historical generalization that mathematical theories which are central/profound to pure mathematicians often turn out to be useful in describing the world (Ian Stewart sketches this argument in his Concepts of Modern Mathematics pp 6-7).

CT is one of the key ideas in 20th century algebra/topology/logic which has allowed huge innovation in modern mathematics. What I find interesting in particular about CT is how it allows problems to be translated between universes of discourse. I think a lot of its promise in science may be in a similar vein. Imagine if scientists across different scientific disciplines had a way to use the theoretical insights of other disciplines to attack their problems. We already see this when say economists borrow equations from physics, but CT could enable a more systematic sharing of theoretical apparatus across scientific domains.

Comment by polytopos on Why does category theory exist? · 2020-06-07T23:16:04.386Z · LW · GW

I am not a mathematician but I've been studying category theory for about a year now. From what I've learned so far it seems that it's main benefit within pure mathematics is that it gives a way of translating between different domains of mathematical discourse. On the face of it, even if you've provided a common set-theoretic foundation for all areas of math, it isn't obvious how higher level constructions in say, geometry, can be translated into the language of algebra or topology, or vice versa. So category theory was invented to facilitate this process of sharing mathematical insights across mathematical sub-disciplines. (I think specifically the context in which it originated was algebraic topology, which as the name implies uses techniques from abstract algebra to study topology.)

Later, computer scientists realized that category theory was useful for thinking about the structure of programs (e.g., data types and functions). For example, the concept of a Monad in functional programming which allows the simulation of side effects in a pure functional programming language comes directly from category theory. Bartosz Milewski is the person to look to if you are interested in learning about this aspect of things.

Even more recently (the last 10 years or so) people have started applying category theory to science more generally. Two books by David Spivak explore this here and here. I think much of this work in applied category is too recent to expect to see much in the way of big practical discoveries or breakthroughs. It remains to be seen if it will produce major innovations, but I think it is very promising. The hope is that category theory will provide scientists a way to model model more of the structure of both their research domain and the research process itself in a unified formalism. It also shows promise for modelling natural language concepts and argumentation, which could lead to better methods of computer knowledge representation.

On a more philosophical level, some have argued that category theory provides support for structuralism in the philosophy of mathematics. This view argues that mathematical entities are essentially structures, which is to say patterns of relationship. In category theory, what an object is is entirely determined by the pattern of relationships (morphisms) with other objects, within a given context (category). This contrasts with set theory, where sets are described in terms of their internal structure of elements and subsets. In practice, this means that set theory starts from the bottom (the empty set) and builds up to the whole mathematical universe, while category theory starts from the top (the category of categories) and then defines everything else in terms of universal properties.

Essentially, category theory validates the intuition that the number 5 isn't some specific object floating out in Platonic heaven, nor is it just a made up meaningless symbol. It is a structure that is defined by it's properties, and those properties are all determined by its relations to everything else. Without actually studying category theory it is difficult to see how this idea could be cashed out in a rigorous non-hand wavy way.

Comment by polytopos on Category Theory Without The Baggage · 2020-06-07T22:31:51.306Z · LW · GW

David Spivak offers an account of Categories as database schemas with path equivalencies that is similar to the account you've given here in his book Category Theory for the Sciences. He still presents the traditional definitions, giving examples mainly from the category of sets and functions. I also didn't find his presentation of database schema definition especially easy to understand, but it is very useful when you realize that a functor is a systematic migration of data between schemas.

Comment by polytopos on Mathematical Intuitionism and the Flow of Time · 2020-04-14T15:11:05.411Z · LW · GW

Thanks for your comment. My replies are below.

"so Gisin's musings... are guaranteed to be not a step in any progress of the understanding of physics."

What is your epistemic justification for asserting such a guarantee of failure? Of course, any new speculative idea in theoretical physics is far from likely to be adopted as part of the core theory, but you are making a much stronger claim by saying that it will not even be "a step in any progress of the understanding of physics". Even ideas that are eventually rejected as false, are often useful for developing understanding. Gisin's papers ask physicists to consider their unexamined assumptions about the nature of math itself, which seems at least like a fruitful path of inquiry, even if it won't necessarily lead to any major breakthroughs.

"mathematical proofs are as much observations as anything else. Just because they happen in one's head or with a pencil on paper, they are still observations."

This reminds me of John Locke's view that mathematical truths come from observation of internal states. That is an interesting perspective, but I'm not sure it an hold up to scrutiny. The biggest issue with it seems to be that in order to evaluate the evidence provided by empirical observations we must have a rational framework which includes logic and math. If logic and math themselves were simply observational, then we have no framework for evaluating the evidence provided by those observations. Perhaps you can give an alternative account of how we evaluate evidence without pre-supposing a rational framework.

"The difficulty of calculating a far-away digit in the decimal expansion of pi has nothing to do with pi itself: you can perfectly well define it as the ratio of circumference to diameter, or as a limit of some series"

I agree with this statement. I think though it misses the point I was elaborating about Brouwer's concept of choice sequences. The issue isn't that we can't define a sequence that is equivalent to the infinite expansion of pi, I think it is rather that for any real quantity we an never be certain that it will continue to obey the lawlike expansion into the future. So the issue isn't the "difficulty of calculating a far-away digit" the issue is that no matter how many digits we observe following the law like pattern, the future digits may still deviate from that pattern. No matter how many digits of pi a real number contains, the next digit might suddenly be something other than pi (in which case we would say retrospectively that the real number was never equal to pi in the first place). This is actually what we observe, if we are to say measure the ratio of a jar lid's diameter to it's circumference. The first few digits will match pi, but then as we to smaller scales it will deviate.

"...the idea that Einstein's equations are somehow unique in terms of being timeless is utterly false"

I made no claim that they are unique in this regard.

Comment by polytopos on How effective are tulpas? · 2020-03-12T13:24:11.031Z · LW · GW

I agree that the term mindfulness can be vauge and that it is a recent construction of Western culture. However, that doesn't mean it lacks any content or that we can't make accurate generalizations about it.

To be precise, when I say "mindfulness meditation" I have in mind a family of meditation techniques adapted from Theravada and Zen Buddism for secular Western audiences originally by Jon Kabat-Zinn. These techniques attempt to train the mind in adopt a focused, non-judgemental, observational stance. Such a stance is very useful for many purposes, but taken to an extreme it can result in de-personalization / de-realization and other mental health problems.

For research to support this claim I recomment checking out Willoughby Britton's research. Here are two PDF journal articles on this topic: one, and another one.

Comment by polytopos on How effective are tulpas? · 2020-03-11T17:59:30.332Z · LW · GW

I agree about mindfulness meditation. It is presented as a one-size-fits-all solution, but actually mindfulness meditation is just a knob that emphasizes certain neural pathways at the expense of others. In general, as you say, I've found that mindfulness de-emphasizes agential and narrative modes of understanding. Tulpa work, spirit summoning, shammanism, etc. all move the brain in the opposite direction, activating strongly the narrative/agential/relational faculties. I experienced a traumatic dissociative state after too much vipassana meditation on retreat, and I found that working with imaginal entities really helped bring my system back into balance.

Comment by polytopos on How effective are tulpas? · 2020-03-10T21:38:46.884Z · LW · GW

I have often thought that the greatest problem with the tulpa discourse is the tendency there to insist on the tulpa's sharp boundaries and literal agenthood. I find it's much more helpful to think of such things in terms of a broader class of imaginal entities which are semi agential and which often have fuzzy boundaries. The concept of a "spirit" in Western magick is a lot more flexible and in many ways more helpful. Of course, this can be taken in an overly literal or implausibly supernateralistic direction, but if we guard against such interpretations, the idea of spirits as agentized meanings is very helpful.

How is this practically useful? For me it comes down to leveraging the huge part of the brain which works in terms of agency and narrative. Learning how to work with imaginal entities opens up a vast amount of general processing power that would otherwise be domain specific.

Of course, all the warnings that people have said about mental health and possible psychosis and dissociation are genuinely worrisome. So embarking on these sort of practices should be undertaken with quite a lot of care.

Comment by polytopos on Why hasn't the technology of Knowledge Representation (i.e., semantic networks, concept graphs, ontology engineering) been applied to create tools to help human thinkers? · 2020-03-10T18:37:58.957Z · LW · GW

Thanks to the comments and discussion, I was motivated to do more research into my own question. What I've found is that there have been some attempts to use semantic technologies for personal knowledge management (PKM).

I have not found evidence one way or the other as to whether these tools have been helpful for knowledge discovery, but they seem promising.

The main tool that would be accessible to the average user is Semantic MediaWiki, this is an extension to Wikipedia's popular MediaWiki software that adds KR functionality based on semantic web technologies.

Here is an article about how to set this up for PKM.

PDF Journal article Semantic Wikis for Personal Knowledge Management

-This article does a good job outlining a general theory of how to build a semantic knowledge application for PKM. The arguments are not tied to a specific software implementation.

PDF Journal article Learning with Semantic Wikis

-I haven't read this article yet, but from the abstract it sounds generally useful

Comment by polytopos on Why hasn't the technology of Knowledge Representation (i.e., semantic networks, concept graphs, ontology engineering) been applied to create tools to help human thinkers? · 2020-03-09T19:38:38.148Z · LW · GW

Interesting, can you give some examples to illustrate how causal/Bayes nets are used to aid reasoning / discovery?

I see merit in the idea that semantic networks may focus too much on the structure of language, and not enough on the structure of the underlying domain being modelled. As active thinkers, we are looking to build an understanding of the domain, not an understanding of how we talked about that domain.

Issues of language use, such as avoiding ambiguity, could sometimes be useful especially in more abstract argumentation, but more important is being able to track all of the relationships among the domain specific entities and organizing lines of evidence.

Comment by polytopos on Why hasn't the technology of Knowledge Representation (i.e., semantic networks, concept graphs, ontology engineering) been applied to create tools to help human thinkers? · 2020-03-09T15:39:48.328Z · LW · GW

Got it:

Comment by polytopos on Why hasn't the technology of Knowledge Representation (i.e., semantic networks, concept graphs, ontology engineering) been applied to create tools to help human thinkers? · 2020-03-09T12:54:38.910Z · LW · GW

Good hypothesis, here is why I don't think it's likely to be true.

It seems to me that when humans make explicit arguments with written language, we are doing a natural language form of knowledge representation. In science and philosophy the process of making conceptual models explicit is very useful for theory formulation and evaluation. i.e., In conceptual domains, human thinkers don't learn like today's neural nets, we don't just immerse ourselves in a sea of raw numbers and absorb the correlations. We might do something like that on the perceptual level, but with scientific and philosophical thought, we are able to abstract over experience and explicitly formulate hypotheses, theories, and arguments. We name patterns to form concepts, and then we reason about these concepts. We make arguments to contextualize and interpret the significance of observations.

All of these operations of human thinking involve a natural language version of knowledge representation. But natural language is imprecise and it doesn't scale well. It is transmitted through books and articles that pile up as information silos. I'm not saying we can or should eliminate natural language from intellectual inquiry, it will always have a role, but my question is why haven't we supplemented it with a formal knowledge representation system designed for human thinkers.

Comment by polytopos on Why hasn't the technology of Knowledge Representation (i.e., semantic networks, concept graphs, ontology engineering) been applied to create tools to help human thinkers? · 2020-03-09T12:41:14.560Z · LW · GW

Hi Said. I'm new here, would you mind explaining what a sidebar is, maybe providing a link or instructions to find said sidebar? Thanks.

Comment by polytopos on What is your Personal Knowledge Management system? · 2020-03-09T06:11:13.644Z · LW · GW

I use I mostly use it like a wiki, but I find the rich formatting and easy move-ability of the blocks to be helpful. I also use the database features to collect notes for ongoing projects, using it more like a journal. Notion is slow on mobile, but I find that taking the time to transfer bookmarks and insights to Notion helps consolidate them.

For organizing ideas that have a temporal component, I use timeline. This is great for keeping track of books I've read and for medium and long term planning.

For longer thoughts and writing I use Google docs. I use Google Drawings for mindmaps and conceptual diagrams. I then link to the docs and drawings from Notion.

For PDF articles I use Notability on my iPad. This has excellent highlighting and note-taking features.

For ebook reading and organization on the iPad, I use Kybook.

For video lectures Youtube playlists, with youtube-dl gui for offline viewing.

I have been wishing for a long time for a fully integrated solution, but each tool has it's strengths and weaknesses.