LESSWRONG
LW

Comment Permalink

Thanks for your enticing comment!

I understand your first point, but my math knowledge is not up to par to really understand point #2, and point #3 just makes me want to learn category theory. BTW, I also posted this question on the philosophy stackexchange: http://philosophy.stackexchange.com/questions/14689/how-does-abstraction-generalization-in-mathematics-fit-into-inductive-reasoning.

Do you have any recommendations of what to study to understand category theory and more about the foundations of math? (Logic, type theory, computability & logic, model theory seem like contenders here)

MrMind11y10

You're welcome!
Foundation(s) of math is a huge and fascinating topic by itself, but if you're more interested in the intricacy of abstraction hierarchies you should look no further than category theory, the Yoneda lemma, up up to doctrine theory. I love as a good introduction Category Theory by Awodey. As for the foundation of math, very good for dipping your toes are the first chapters of Marker's introduction to model theory and the recently reprinted Set theory by Kunen (set theory models are a vast subject by themselves...)

See in context

8 Open thread, 14-20 July 2014

by David_Gerard

14th Jul 2014

1 min read

146

8

Previous thread

If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one.

3. Open Threads should be posted in Discussion, and not Main.

4. Open Threads should start on Monday, and end on Sunday.

Open Threads

Personal Blog

8

Open thread, 14-20 July 2014

New Comment

146 comments, sorted by

top scoring

Click to highlight new comments since: Today at 11:45 PM

Some comments are truncated due to high volume. (⌘F to expand all)Change truncation settings

[-]sediment11y240

Request for advice:

Like many people on lesswrong, I probably lie towards the smart end of the bell curve in terms of intelligence, but I'm starting to suspect that I lie somewhere below the mean in terms of ability to focus, concentrate, and direct my attention.

I only recently became concerned about this because it wasn't much of a problem when I was in school. There, I was able to do acceptably well overall by doing well in the subjects that came easily to me without working hard (science, maths... you know the score) and mediocrely in those that didn't. Ditto my undergrad/bachelor's degree.

But I'm currently struggling rather with the thesis project for my master's degree in computer science. The specifics of the thesis itself don't matter, other than that it's a piece of empirical/numerical research involving a lot of coding and a prose write-up. None of the technical aspects of it are beyond me, and yet I feel like in some way it's the first very difficult thing I've ever tried, really tried, at. The hard part is sustaining interest over the whole length of the thing, planning and organizing the overarching, erm, arc of the project as a whole, and forming a 'narrative' out of al... (read more)

[-]Toggle11y130

I just want to say that this is extremely similar to my struggles with a Master's degree. Mine is in geology, so your username continues the parallels amusingly. I'm a bit further along, with some marginal successes in efficiency. Here are some of the tactics that I have tried:

*Excercise. My diet is pretty terrible, but regular exercise to offset that has been invaluable. I used weight lifting (if I have a high-calorie diet, then I might as well put the energy to use)- the 5x5 schedule is a good way to gamify things a bit without introducing more complexity than its mindshare allows. This is probably the most useful habit that I have been able to maintain.

*Nootropics. Cautiously. 500mg Choline and about 1600mg Piracetam per day. These are cheap and extremely safe, with moderate-to-questionable benefits. Under this regimen, I have seen quantifiable improvements, including competitive game performance and concentration length. The placebo effect is a strong contender, but rationality means winning, so why not? Previously, I relied on caffeine as my performance enhancer, but the addictive downsides became distracting at the volumes I was using. I don't know much about Mod... (read more)

4sediment11y

Thanks for the thoughtful response. Exercise: I recently started a regime of 2 x 1 hour bodyweight sessions / week with a friend of mine, but we haven't had a session in a while because he recently took an injury boxing. I think I'll start running on my own so I'm not so tied to that one activity (and in accordance with the advice in Optimal Exercise). Pens: I actually like this advice. On the other hand, I use vim, a programmer's editor, to write everything (including my prose), and I love love love it. (I'm even writing this reply in it.) The 'feel' (not only tactile) of being able to shunt text around so effortlessly (at the paragraph, sentence, clause, word level) is so pleasant that it's hard to give up. On the other hand, there is some sense to what you say about working without a computer. Natural light patterns: Good thinking. I work in a room with great sunlight during the day; so far so good. But a while ago my monitor broke, and I was able to fix it only by jettisoning its buttons. (Long story.) End result: my monitor is stuck on full brightness all the time. I just checked, though, and I found a linux program (Redshift) capable of adjusting the monitor brightness and colour temperature based on the time of day. I installed it and it seems to work; perhaps it will help. The lamp I use for reading at night also has a slightly harsh, blue-ish hue to it, though it isn't excessively bright. I'll see if I can do something about that, too. Accountability: Hmmm. I'll think about this. It's certainly the case that periods of poor work correlate with seeing my tutor less. The causation isn't just one-way, though: I'm also less likely to want to see him when things are going slowly. (Perhaps there's something of a nasty positive feedback loop going on here.) Thanks. This actually did help.

1cameroncowan11y

You also might wish to consider the ways in which you learn or like to take on large projects. Personally, I am a list maker. I like to have a map a plan if you will. When I'm working on a novel I do the same thing and it may get revised several times before the work is completed. When I was in my Master's program I had my system down so that I could wrote a 25 page paper on International Relations and associated topics in 3 days starting from research to final completion. To do that required caffeine, medication, and no sleep but it was what I had to do at the time to get the job done. You have to create a system, a habit, to do this. If you can find a reliable way of working rather than working ad hoc then you will be able to do more easily and tackle large projects in the future.

6James_Miller11y

Then get a job where you will have a boss who keeps you on track by monitoring your short-term progress. For many people college is the only time when they have neither a parent nor boss who pushes them to succeed.

4solipsist11y

Warning: such high-overhead jobs are often less well paid. And a lucrative and low stress path for you, programming, often has hard-to-measure short-term progress and are usually not closely monitored.

0eeuuah11y

If you work somewhere they do pair programming that can help with a lot of the issues though.

0sediment11y

This makes sense.

6Gunnar_Zarncke11y

Did you try lukepros Algorithm for Beating Procrastination? From your description I take it that the expectancy of the task is moderate (you reliably gain a degree), but its value is partly low: Personally you gain a degree but the thesis itself provides little value on which you could build and which might be intrinsically important for you. The main problems seem to be delay as is often the case with thesis work. I'd think that your experience with pomodoros should help here: You could break down the thesis into parts, espl. the prose parts. I'm not clear about your impulsiveness. It appears that you never had to work hard and were able to follow your interests. I can relate to that as it was the same for me. It is kind of a flaw of our society to make some things too easy (not that I'd cry about it). It can hurt us in the long run though. I got out easy: I found a motivation to work hard: Family, esp. my children. You have to make your mind up on this. I'm not even entirely clear whther procrastination is a bad thing: It's our sobconscious way of telling us that the work has no or may not have long-term potential.

6Viliam_Bur11y

Some things I tried: Compassion meditation. It doesn't seem as cool as attention-focusing meditation, but it associates pleasant feelings with meditating. Such associations can be useful when you later need to calm yourself down while doing the attention-focusing meditation. My problem with work is often that I try to avoid even thinking about the work. When I should be doing the work, it is difficult to focus, but when I don't have to work, I completely avoid it in my mind. The problem is, with the things I am successful at, this doesn't happen. It's the other way round: even when I'm not doing them, I keep thinking about them. And I suspect that this thinking is a critical component. So now I sometimes try to think about the work when not working. It's emotionally easier, because it is without the pressure of having to do it right now. And sometimes I have a good idea, which I can use later. Maybe a good strategy would be to go away from the work physically, for a few minutes, but stay with the work mentally. Not typing on the keyboard isn't the problem; not thinking about the project is. Also, organizing my thoughts is easier when I keep notes on paper. It is easier to split a big problem to smaller parts, when I write them down. Especially when my mind tries to not think about the topic. I mean, if in my mind I realize this problem has a subproblem, and the subproblem has a subsubproblem... that feels like the right moment to run away from everything. However, if I write the subproblem and the subsubproblem on the paper, then I can decide to just focus on the subsubproblem, and temporarily ignore the rest. The algorithm is: "Either it's easy, and I solve it immediately, or it is difficult, and then I write down why specifically it is difficult, what needs to be solved first... and then I resursively focus on the subproblems. At some moment the subproblem is so easy there is just no excuse not to do it. (And if you have an excuse not to do the task, you don't

4ephion11y

Huh -- I've found that pomodoros help me stay on task tremendously. I generally keep a timer tab open, and my brain seems to think "Oh, I can avoid facebook for another five minutes... let's keep working!"

4Metus11y

Not a medical professional and so on. Difficulty focusing and difficulty to sleep can be symptoms of underlying emotional issues like depression. In countries with universal health care a consultation with a psychologist is usually free for a number of sessions to rule out something like this. Though the symptoms are quite similar to "being tired and having a headache" w.r.t. somatical issues as they appear with nearly every syndrome. First of course check if you do the bare minimum: Eating healthy and exercising at least two times a week. Then you should worry about underlying issues.

2sediment11y

Thanks. I had actually already wondered about whether I was depressed. I don't think I am, though this was not at all obvious to me, and I had to consider the possibility for some time before rejecting it. I perhaps have a slightly flat affect compared to some, but I think I enjoy life and have a basically happy disposition. I recently starting a bodyweight exercise regime with a friend (2 x 1 hour sessions / week), but we haven't had a session in a while because he recently took an injury boxing. I think I'll start running on my own so I'm not so tied to that one activity (and in accordance with the advice in Optimal Exercise). I think my diet is decent.

3EvelynM11y

The life hygiene issues of exercise, sunshine, good sleep, social support are all helpful in getting stuff done. Beyond that, don't rely exclusively on your working memory for keeping track of all of the things you need to do. You are already taxing that with learning, and offloading everything you can to external aids is helpful (todo lists, experimental journals, daily 3 page mind-dump journaling). A regular review cycle of what you have written can give you a sense of accomplishment, which can be lacking in multi-year projects with few intermediate wins. Count volume of output as a goal, and use beeminder or something similar to remind you to track it, and show you what you have accomplished (pages written, commits made, hours worked...).

1Will_BC11y

Regarding the mediation, I had a professor of Eastern Philosophy speak at one of my clubs, and he led us in a meditation. When I asked him how long it took before he saw results from his meditation practice, he said about six months, so it's not maximally effective immediately. Anecdotally, I can say that I I have noticed my ability to focus during the meditation to have improved, though I haven't maintained it for six months yet.

0sediment11y

Thanks. Do you feel like it's had much impact on your mental state when not meditating?

1Will_BC11y

It's hard to say, since there are confounds to changes in my mental state, but it does seem like I'm calmer and more self-aware, and if I make the connection to meditation I can quickly focus on my breath and change my focus.

[-]Metus11y210

Be careful what you argue for.

For the longest time I was opposing nationalism and the concept of citizenship. I researched the issue, read and crafted arguments in favour of my position and convinced myself that this is a rational opinion to have. Then some things happened that made me feel more connected to the soil I was born on. Still I feel that my identity is not determined by my passport but my previous arguments seem a whole lot less convincing and the arguments I dismissed as unreasonable seem more convincing.

The quest to be more rational is one of the more humbling things I ever did with the hardest lesson to learn being that I am wrong very often and my beliefs are largely not rational.

8Viliam_Bur11y

Maybe the risk is in trying to argue for our positions more strongly than we actually feel them. More extreme positions feel higher-status... but then comes the moment when one realizes "oops, I actually don't feel this", and the pendulum swings to the opposite direction. Sometimes we are pushed to an extreme position by people who argue for the opposite extreme position. They keep giving arguments for one side... and to argue with them, we focus on the arguments for the other side. Of course we shouldn't underestimate the impact of peer pressure. But that's a bad reason to change opinions. On the other hand, realizing that one's position isn't truly as extreme as it seemed originally, and updating towards the true position, that is a good reason.

8polymathwannabe11y

As a fervent anti-nationalist, I'm very curious as to what arguments and/or evidence made you change your mind.

9Prismattic11y

The term "nationalism" is used in at least two very different ways. The particularist use is more accurately termed "national chauvinism", usually but not always ethnically-based, is the idea that one's own nation is in some way better than all the others, and the interests of its people should be accorded disproportionate weight. Note that this kind of nationalist doesn't necessarily care about political organization outside of his own country; he has an ideology about his nation, not necessarily about nations in general. I would agree that used in this sense, "nationalism" is basically indefensible. There is a different, generalist use of the term "nationalism," however, which traces academically to people like Ernest Gellner, and philosophically, arguably back to people like Friedrich List. Nationalism in this sense, is merely the proposition, "National boundaries should coincide with state boundaries." Importantly, it doesn't require ethnically-defined nations, merely people who self-identify as being part of a common national community, whether that be based on blood, culture, or something else. A natural corollary of this view of nations and nationalism is that, at least in the world as it actually exists now, everyone is either a nationalist or an imperialist (one could carve out a small exception for anarchists). In this generalist sense of "nationalism," which makes claims not about "my nation" but about "all nations," I think there are tradeoffs on both sides. I identify as an somewhat ambivalent nationalist. But unlike the the first sense, I don't think you can argue that the nationalist position is prima facie inferior from a consequentialist standpoint.

[-]Emile11y150

The particularist use is more accurately termed "national chauvinism", usually but not always ethnically-based, is the idea that one's own nation is in some way better than all the others, and the interests of its people should be accorded disproportionate weight.

The "in some way better than all others" bit isn't a very charitable reading of that position; if a Frenchman wants the french government to further the interests of France and Frenchmen (even at the expense of other countries), then it's a form of nationalism but doesn't include a belief that "France is better than the rest"; it's only that he cares more about France than about the rest.

Having diminishing "circles of empathy" for others depending on whether they're in your family, your city, your country, your religion or race etc. is pretty normal, but there's variance about what levels are considered as more important; (pretty much) everybody cares more about their family, but some may see religion or political affiliation or their city as a "more important" identity than one's country (this is assuming country = nation, which as you say is usually the case in the West now); "national chauvinists" would be the ones who put their country above other identities.

0A1987dM11y

This BTW is my beef with Mencius Moldbug when he points out that German nationalism is considered bad and Czech nationalism is considered good.

8Metus11y

Neither arguments nor evidence. That is the exact point of my post. But to answer a more lenient reading of your request: After making an effort to be less hostile to group celebrations, people in general and local cultures and traditions I could relax enough to take part in those and/or enjoy them. As a result I both feel more belonging to the country I live in and also I appreciate other cultures and cultural traditions more. Does that answer your question?

4polymathwannabe11y

From your description it appears you have gained a stronger connection with your local culture and empathy for those of other cultures who strive to preserve theirs, but I don't see the line linking that with political support for nation-states.

[-]Metus11y110

There is none, that is the whole point.

-1Bruno_Coelho11y

Apparently you don´t need a argument to be a nationalist. Guess this is just system 1 working.

6Viliam_Bur11y

Now you made me want to make a rational argument for nationalism. Uhm... let's try this: Imagine that some cultures do things that you consider horrible (e.g. genital mutilation, "honor" killing, killing people for blasphemy or sexual orientation, etc.). Your culture doesn't do that. However, for some reasons, the populations in the other cultures are growing, the population in your culture is not, people immigrate to your country and bring their horrible behavior with them. You are afraid that unless something is done against this, the repulsive behavior will become a norm in your country, too. Maybe not the majority norm, but still something that is more or less tolerated, because no mainstream politician would risk making too many voters angry. How to stop this? Appealing to national feelings may be a realistic strategy. (The point is not to invent something that intellectuals would agree with, but something that has a realistic chance to get a popular support.) You can try to make people more proud of your local culture, and emphasise that not doing X is an important part of what makes this country great. Thus you get a strong political force against X. Related: "Use Your Identity Carefully". -- My analogy is that nationalism is identity on the mass level (identity for NPCs?). It is a tool to preserve a group of memes, both good and bad. Instead of throwing away the tool, you can try to increase the proportion of the good memes in the mix.

7Emile11y

Having a strong national identity, and norms around self-sacrifice in favor of "The Fatherland" seems like pretty good instrumental rationality, in terms of coordination, enforcing cooperation, economies of scale, etc. "Identity for NPCs" sounds a bit dismissive for a mechanism that works pretty well (to me it sounds close to "cooperating is for suckers, rationalists should defect"). I don't think "rejecting weird foreign norms" has much to do with the historical causes of nationalist sentiment; I'd say it had more to do with enforcing strong norms over weak norms (for example, speaking the same language, not engaging in nepotism, obeying the law, sending your children to school, taking up arms to defend the country), and putting the primary focus of loyalty on the country (and not the king, the church, your family or your village). Foreigners from far away with different norms is a more recent phenomenon.

7Viliam_Bur11y

Oh. Uhm, if we put it to the Prisonner's Dilemma language, I'd rather say -- rational people can analyze the situation and choose with whom to cooperate even if the other person is different, but stupid people need some simple and safe algorithm, such as: "cooperate with identical copies of myself, defect against everyone else". Which works decently, if you have many identical copies at the same place, interacting mostly with each other. You cannot be exploited by someone using a smart algorithm. That's a relatively impressive outcome for such a simple algorithm. The disadvantage is that you can't cooperate even with people using functionally identical algorithms with different group markers (e.g. using a different language, or dressing differently). And you have to suppress your deviations from the official norm (e.g. a minority sexual orientation). And you have a barrier to self-improvement, because the improved version is by definition different than the original one. -- On the other hand, if you manage to somehow artificially impose some positive change on everyone at the same time (or very slowly during a long time period), then the positive change will be preserved. Unfortunately, it works the same way with negative changes.

1Emile11y

It's not clear that someone analyzing the situation will choose to cooperate - plenty of smart people have argued that the rational behavior in prisoner's dilemma is to defect. And I would argue that even for smart people, a simple algorithm is more likely to get everyone on board; a complicated but "better" solution which no one else follows (and that would only count as "better" if everybody was following it) is not worth following.

0Alsadius11y

That's certainly one, but there's an even easier argument to make - Burkean conservatism. Your nation's identity is built around stuff that's probably worked pretty well for it in past(or else it probably wouldn't be a nation today). As such, it's got a higher prior probability of working out in your local circumstances. It's not a large effect, of course, but it's a real one, particularly for successful nations.

0A1987dM11y

But my culture also does things that I consider horrible that other cultures don't do! (SCNR.)

0Viliam_Bur11y

Also, the bad things my culture does are "near" (both metaphorically and geographically), and the bad things other cultures do are "far". Which I guess is why I am not a nationalist. But I can imagine a situation that could change it, such as seeing a foreign minority doing their horrible stuff in my neigborhood.

0[anonymous]11y

Does your definition of nationality include language and cultural identity? Do you think it's possible to separate the two?

4cameroncowan11y

I think your thought process is indicative of our modern age. It is hard to concept of nations in the online environment that, at least for the time being, remains borderless. Nationalism has produced 2 world wars and several smaller conflicts and given its impetus in 1648 as a way of allowing kingdoms and countries to decide their religion without outside influence I think the 21st century will see fewer borders rather than more borders. That being said a quick read of any news site would make that statement hard to believe as nations get more nationalistic. However, advances in communication, transportation, and the movement of good, services, capital, and people will make borders less and less meaningless. What is a nation? What is geographical area? What is a political border? Our economy and our way of working is reducing that meaning. 30 years ago your country was the sum total of your upbringing, language, culture, shared values, and chances in life. Movement was long and hard and fraught with difficulty. That is becoming far less in our modern age. I think we all will feel tied to where we were born and grew up because its comfortable, its homey, we know the back routes, we know the cultural rules and being tribal as humans are we generally fit into that tribe. Those are all important things. Your personal identity is never, nor has it ever been tied to a passport. It is just a little book that tells other countries where you are coming from and some information about you. It is not you, it a part of you that is on paper for movement purposes. The lesson in life that you are more often than not wrong is nothing to be afraid of or anything to cause you distress but rather you are finding the juicy part of the human existence.

4Emile11y

News sites don't provide much evidence of increase of nationalist sentiment, unless you take into account the usual spin anytime something bad is reported: "This bad thing happened! Things are getting worse!"

4cameroncowan11y

Yes, however the desire for Colorado to split into two states for California to split into 6 and for the ukraine to split into 2 I think shows that there is a identity/policy crisis going on that is compelling political entities to split. Although one does have to dig past the hype these news sites have their use.

2Azathoth12311y

Part of it is that different parts of the states have different ideas about how the state should be governed.

4cameroncowan11y

Right! Therefore I think its helpful to think about the institution of the nation state and how to govern ourselves as a political entity rather than forfeiting that right to others. Does the nation state concept still have meaning or is it time for a change?

0Jayson_Virissimo11y

Haidt calls this pushing your "hive-switch" (humans are "90% chimp, 10% bee").You can reliably increase your groupishness by simulating your in-group being under attack or by taking certain kinds of drugs.

0cousin_it11y

Note that Haidt's theory relies on group selection, which many people on LW disagree with. From reading this essay by Pinker and the replies by Haidt and others, the whole thing seems complicated.

[-]JoshuaZ11y210

Scott Aaronson has a post on the computational power of digicomps. While the post itself is interesting, it is also worth noting here because it is part of a new experiment he is doing. He writes:

Right now, I have a painfully-large stack of unwritten research papers. Many of these are “paperlets”: cool things I noticed that I want to tell people about, but that would require a lot more development before they became competitive for any major theoretical computer science conference. And what with the baby, I simply don’t have time anymore for the kind of obsessive, single-minded, all-nighter-filled effort needed to bulk my paperlets up. So starting today, I’m going to try turning some of my paperlets into blog posts. I don’t mean advertisements or sneak previews for papers, but replacements for papers: blog posts that constitute the entirety of what I have to say for now about some research topic. “Peer reviewing” (whether signed or anonymous) can take place in the comments section, and “citation” can be done by URL. The hope is that, much like with 17th-century scientists who communicated results by letter, this will make it easier to get my paperlets done: after all, I’m not writing Official Papers, just blogging for colleagues and friends.

[-]David_Gerard11y120

Bob Nelson, of the failed Cryonics Society of California, has written a book. Anyone read the book yet?

[-]arundelo11y100

Richard Bornat, one of the authors of The camel has two humps (about a supposed bimodal distribution of programming ability) recently wrote:

I did a number of very silly things whilst on the SSRI and some more in the immediate aftermath, amongst them writing "The camel has two humps". I'm fairly sure that I believed, at the time, that there were people who couldn't learn to program and that Dehnadi had proved it. Perhaps I wanted to believe it because it would explain why I'd so often failed to teach them.

Read the rest: Camels and humps: a retraction.

5ShardPhoenix11y

Title and excerpt aside, this isn't really a retraction of the actual test, just of the author's overly-aggressive interpretation thereof. Basically he says that the test does have some predictive power but not enough to prove anything about who can or can't pass a programming class.

3Viliam_Bur11y

Did someone actually use an ad-hominem argument against themselves to destroy the credibility of their own paper? Fascinating. Will this start a new wave of "sorry, I was high when writing the paper, please don't take it seriously" retractions? :D

[-][anonymous]11y70

LessWrong meetup question:

Are there any meetups that allow for Skyped in guests? It seems to me setting up a way for guests to Skype or otherwise pop in from long distance would be very useful, especially those who cannot find or start up a meetup otherwise.

5Viliam_Bur11y

There were some purely virtual meetups, but there are technical problems when connecting too many people. Like, ten or more. You could just go ahead and announce your own virtual meetup. Create a public google document where participants can write their names, and set a limit to, say, maximum seven participants per meetup. (If someone realizes they will not be able to come, they should remove their name from the list, to allow other people to join.) If you want, you could make it a recurring event, e.g. once in a week.

2[anonymous]11y

I am weighing my options on trying to start a meetup myself. I've considered the possiblity of starting an Alabama LW meet up. But when the nearest city with a population over 50,000 is 55 miles away, I feel the density of LWers in the area would be too small to sustain it. Or start it at all. I certainly know of no one personally who would be interested, though I could still use it as an excuse to sit in a coffee shop and read. Who are some of the groups that do virtual meetups? If nothing else, I'd like to see how others have tried this. Could give me some ideas for a set up of my own.

2Viliam_Bur11y

Participants of the European meetup in Berlin. They coordinate on Facebook.

0ShardPhoenix11y

We've done this a couple of times in Melbourne. It works as a way to say hi, but not so much as a way to participate more generally.

[-]Pablo11y60

Three weeks ago I came up with a simple productivity technique that I've been using with great results, and thought I should share it here in case it is of help to others. I could write a couple of paragraphs describing how it works, but I think that by taking a look at this spreadsheet you can very quickly understand the idea. In short, I list everything I want to do each day (using a rather fine-grained criterion of act individuation) and motivate myself to do those things by a combination of points and streaks. (Many of my dailies relate to nutritio... (read more)

2Peter Wildeford11y

A couple of questions about your individual situation -- just curious: 1.) What are your morning and night routines like? 2.) Do you think it's valuable to break your don't eat up by food, or just have one junk food category? 3.) Why not sleep during the day? I had previously been in a habit of napping and found it useful, and it's generally regarded as healthy. The only reason I don't nap now is because I have a standard 9-to-5 (well, more like 10-to-7) job. 4.) Why so much caffeine in the coffee and tea? It seems like this would just promote tolerance, which seems bad. 5.) What are the benefits of eating dark chocolate? Olive oil?

5Pablo11y

Hi Peter, 1. Here are my morning and night routines. I try to be quite detailed; don't underestimate the value of checklists. 2. I originally had a single generic junk food category, but the problem was that when I ate one type of junk food on a given day, I had no extra incentive to abstain from eating other types of junk food for the rest of the day. Individuating dailies with a more fine-grained criterion provides an effective way of dealing with this problem. 3. I have sleep problems and wanted to see whether sleeping only at night would help. In addition, I read studies suggesting that people who sleep during the day, esp. those who take long naps, tend to die earlier, though these are correlational studies and it's unclear what causal inferences we can draw from them. 4. I once estimated that my total caffeine intake from drinking two cups of coffee and six cups of green tea was about 300 mg, which I believe is within safe and normal levels. I drink green tea primarily for its health benefits, though, so perhaps I should switch to decaf. As for coffee, there are studies suggesting that low to medium doses have neuroprotective properties, though I'm not sure this is due to the caffeine itself or other properties of coffee. 5. Olive oil is a very good source of monounsaturated fatty acids. The benefits of dark chocolate are, I think, modest and not that well documented; see here. I eat it primarily because I find it delicious.

0Peter Wildeford11y

I solved that problem by tracking how many pieces of junk food I ate rather than a binary of whether or not I ate junk food on that particular day.

0Pablo11y

Yes, I considered that approach. But the vagueness involved in the notion of a "piece of junk food" was such that I found I had considerable latitude in determining how many pieces of junk food I ate on a particular day. By contrast, deciding whether I ate a certain type of junk food at all is usually quite straightforward, and not subject to rationalization. As Jon Elster wrote: (Of course, you may not have a problem if you are sufficiently self-disciplined, as you seem to be.)

0Peter Wildeford11y

Yeah, that seems right. I tend to define it roughly as "250 calories of something that is devoid of nutritional value and consumed primarily for taste".

3kalium11y

I actually find a slight caffeine dependency useful in reminding me to put the kettle on and make a proper breakfast in the morning.

1Gurkenglas11y

Looks like in a month or so, your easy-to-keep items will outstrip all others. Maybe the value should grow logarithmically over time, not linearly?

0Pablo11y

The streak count is not incorporated into the value associated to a task; it is an independent metric. But I'm not sure if this is what you were referring to. If not, can you elaborate? Thanks.

2Gurkenglas11y

Yes, that was what I was refering to and I really should have thought of seeing whether the realized values match up with what I was thinking. I thought it was a neat idea to give yourself some incentive to keep a habit running once you've kept the streak up for a while.

0Emily11y

Looks like a cool system. Curious what you count as being a slip-up in your "sugar" category, since you have a day that's red for cake but green for sugar. Presumably the cake contains sugar (and probably your 10g of dark chocolate does too?) - do you just mean sugar by itself?

1Pablo11y

By sugar I mean "added sugar", as used to sweeten drinks. I have control over whether I put sugar on my coffee, but not on the sugar present in most other foods, including cakes, so it makes sense for me to deal with the two separately. If on a give day I eat cake but don't add sugar to drinks, I would mark the 'cake' daily as a failure and the 'sugar' daily as a success. Incidentally, I eat 100% dark chocolate, which doesn't contain any sugar.

64hodmt11y

As a cheaper alternative to 100% dark chocolate, I drink unsweetened* cocoa made as follows: 1. Fill kettle, start boiling water 2. Add 2 teaspoons cocoa powder to mug, stir in a small trickle of cold water to make a paste 3. Stir in boiling water, filling mug about 2/3rd full 4. Top up with cold milk (*milk contains sugars so this isn't technically zero sugar. You could skip the milk if you think it matters, at the cost of worse taste). Best tasting cocoa powder I've found in the UK is Cadbury Bournville. Some supposedly premium brands (eg. Green & Blacks) taste much worse, bland with a slight burnt taste. Color seems to be a good indication of taste - lighter color generally tastes better.

2palladias11y

I like drinking cocoa made as follows: 1. 1 mug milk (heated in microwave 2. ~1.75 spoons of unsweetened cocoa powder 3. 1-2 dashes of cinnamon 4. (sometimes) cayenne powder

0Emily11y

Isn't this exactly how cocoa is normally made? Either like that or with hot milk instead of boiling water. What would anyone do differently with that sort of cocoa?

2kalium11y

Have you always enjoyed 100% dark chocolate, or did you have to train yourself to do so, and if so how? I'm not particularly interested in eating less sugar, but somewhere around 95% it goes from tasting rich and bitter and fragrant and wonderful to tasting bitter in a way that just doesn't register as food, and I want to know if there's a way to overcome this. I have a similar situation with unsugared black tea, with a single exception that involved LSD.

4Lumifer11y

You should brew tea properly. The bitterness in black tea comes from tannins and you can easily control their extraction during brewing. For black tea: * Use good quality loose-leaf tea, preferably the orange pekoe cut. The tea dust in teabags oversteeps (and becomes bitter) very quickly. * Time the steeping of the tea leaves in boiling water. The usually recommended five minutes is often too long (if you'll be drinking your tea without milk). Try three and a half minutes to start, then adjust as desired. The less time you steep, the less bitter will the tea be (while caffeine generally extracts in the first 30 seconds or so). * Once the tea has steeped for the proper time, pour the tea off the leaves into another teapot (or a cup, etc.). Do not let tea sit on the leaves. * Experiment with different teas as well. Tea from Assam (often sold as Irish Breakfast) is the most tannic. Tea from Darjeeling, for example, is much less so.

0kalium11y

Good advice that I'm already following. I do enjoy Darjeeling with hardly any sugar, but it just doesn't satisfy my "wake you up in the morning" desires the way Assam does. Even with Darjeeling, though, unless I add at least a small amount of sugar (maybe 1/4 of what I'd put in Assam) it's just fragrant water and I don't perceive it as having flavor.

2Pablo11y

No, I haven't always enjoyed 100% dark chocolate. For a long time I ate chocolate with 85% concentration of cocoa, and then gradually moved upwards. I haven't met many people who like pure chocolate, though, and there doesn't seem to be a big market for it, judging from the difficulty of finding it. So my experience may be atypical.

0palladias11y

I like it! But when I eat it, I want much less of it than I would eat of 80-90% in a sitting. (not necessarily a drawback)

0Douglas_Knight11y

More people, by several orders of magnitude, like unsweetened black tea than unsweetened chocolate. And probably another order of magnitude for coffee. Does this mean that you should ask people about tea rather than chocolate? There are a lot more of them. And maybe it's easier with tea. If it's easier with tea, maybe you should do tea first. But if it's easier, maybe the masses of people who do it did it without planning or introspection, while the hard task may be a better source of information.

0kalium11y

I've asked more people about tea than about chocolate. But I haven't asked anyone about coffee, because I don't drink it, and I think that's worth trying.

0Douglas_Knight11y

What is the outcome of asking people about tea? Do they say useful things? specific to tea, or things that might generalize to chocolate?

0kalium11y

With tea, a few people like unsweetened black tea and have always experienced it as having flavor (though there's still the usual acquired-taste aspect of bitter/tannic things). Others, like me, find that without sugar it's just fragrant water that doesn't get experienced as having taste, but they like it that way. I haven't found anyone who's actively learned to enjoy sugarless black tea in the way I would like to.

0eeuuah11y

I enjoy sugarless black tea. I didn't use to. I got into through green tea (which I admittedly still prefer in the general). I think drinking a lot of green tea and getting pretty into it (trying lots of different loose leaf types, learning about ideal steeping temperatures and times) got me used to the basic form of tea, after which it's a lot easier to get into black tea.

0Emily11y

Ah, makes sense! The chocolate sounds cool.

0FiftyTwo11y

Seems a similar concept to HabitRPG

2Pablo11y

Yes, it is similar, and it grew out from my experience with that website. However, I found HabitRPG problematic for a number of reasons. First, the rules are such that I "died" even if I failed to complete a small proportion of dailies. Second, I had little freedom to assign different value points to different tasks. Finally, my system allows me to manipulate the data in all sorts of ways, and create progress graphs that are more informative and motivating than those in HabitRPG.

0polymathwannabe11y

Are you on a gluten-free and/or starch-free diet?

0Pablo11y

No, I just try to avoid foods that are carb-dense or nutrient-light. I'm a vegetarian.

0polymathwannabe11y

Now I'm more curious. Potatoes are vitamin and mineral cornucopias, and peanuts are protein powerhouses. Why avoid those two?

2deskglass11y

Peanuts are not 'protein powerhouses' unless you are trying to measure protein/volume instead of protein/calorie. They give 7g protein per 164 calories. Compare that to tofu which provides 20g protein per 176 calories or salmon which provides about 20g for 183 calories.

1Pablo11y

Potatoes are not nutrient-dense relative to the food I eat. 100 Calories of e.g. spinach contain many times the minerals and vitamins contained in 100 grams of potatoes. Peanuts are not very bad per se, but the opportunity costs of eating them are too high for me, since they substitute other, better nuts from my "nuts" budget (e.g. walnuts, almonds and hazelnuts).

[-][anonymous]11y50

Idea: The Great Filter as a self-imposed measure by sentient life to mitigate inevitable early thought experiment blunders in their histories.

4DanielLC11y

I don't understand. Can you explain that more?

3[anonymous]11y

There exist certain ideas that are very dangerous to think. They make you vulnerable to harm at the hands of future super-intelligences. Such ideas aren't hard to come by, most civilizations stumble upon them. One of the ways to render them inner is to end your existence.

1DanielLC11y

You mean like the basilisk? Getting rid of your species seems like going overboard. If you saved the children and raised them by robots, you'd be able to remove whatever dangerous memes you made. Also, if that is a common reaction to the basilisk, then a fundamental assumption in it is the opposite of true. If your response is ignoring it or less, you have nothing to worry about.

1[anonymous]11y

Like a basilisk yes.

2ZankerH11y

Idea: The concept of a great filter is a collective failure of imagination on the part of humanity, amplified by a severe lack of data.

1Shmi11y

Yeah, I (and others) have been saying this here and elsewhere.

[-]curiousepic11y50

I'm an EA and interested in signing up for cryonics. After cryocrastinating for a few years (ok I guess I don't get to say "after" until I actually sign up), I've realized that I should definitely sign up for life insurance, because of the ability to change the beneficiary. I place a low probability on cryonics working right now, but I can claim a charity or a Donor Advised Fund as the beneficiary until I place a sufficient probability on suspension technology working. In the future, I can change it back if I change my mind, etc.

Any issues tha... (read more)

4kevin_p11y

The main flaw I can think of is that insurance is a money-loser on average - otherwise the people selling it wouldn't make any money, so they wouldn't offer it at that price. I can't immediately find average ratios for life insurance, but typical payouts for medical insurance are 80% of premiums while the figure for property insurance is more like 50%. In other words, the expected net cost of taking out the insurance policy, if you never decide to redirect it to cryonics or loved ones, is going to be somewhere between 20% and 50% of the premiums. Is that worth it for the extra flexibility it gives you? That's something only you can decide.

0Alsadius11y

Remember that life insurance, in most jurisdictions, is tax-exempt. As such, the amount of cash your heirs get to put into their pocket may well be higher than with traditional low-risk investments, even if the top-line return is lower.

0Alsadius11y

I sell life insurance as a big part of my day job, and you should be aware that buying a big life insurance policy for charity is the sort of thing life insurance underwriters tend to be a touch suspicious of. It can be done, but they'll ask for things like your donation history to that charity and why you suddenly feel the need to shower hundreds of thousands of dollars upon them. Insurance applications can be turned down for financial reasons too, not just medical.

0Nisan11y

It might be worth looking into which life insurance companies are friendly to cryonics.

0philh11y

Presumably, it would be more efficient to donate the cost of life insurance directly to the beneficiary. People often fund cryonics with insurance because they can't afford it otherwise, but if you could pay upfront without significantly damaging your quality of life, I'd expect that to be a good idea too.

0Username11y

Well it still costs money, so it will be a constant drain on resources as long as you have life insurance. Which I suppose is fine if the payoff to the charity is worth it as a terminal goal, but I personally feel very weird betting on my own death. (At least in the absence of children or other dependents).

[-]gwern11y40

Politics is not about policy: "Differences in negativity bias underlie variations in political ideology", Hibbing et al 2014 (excerpts; media coverage); abstract:

Disputes between those holding differing political views are ubiquitous and deep-seated, and they often follow common, recognizable lines. The supporters of tradition and stability, sometimes referred to as conservatives, do battle with the supporters of innovation and reform, sometimes referred to as liberals. Understanding the correlates of those distinct political orientations is p

... (read more)

4cameroncowan11y

This is juicy and oh-so-obvious. The people arguing for stability and for things generally staying the same (in the US mostly for their collective benefit) are going to perceive any change as bad unless it directly benefits them. This is rational acting at work: does it or does it not benefit me? Lets remember humans care at a fundamental level three things: reproduction, eating, and life-survival (Can I make with it? Can I eat it? Will it kill me?). Therefore, if something in the environment changes that threatens those fundamental things then it can be perceived as negative. Those on the reform side have a different send of answers to those survival questions and look at those stimuli differently while also having stimuli they view as negative. Ultimately, within this dichotomy the good of "the people" is at debate. Sadly, political systems only work when all parties have at least a partial agreed upon premise. Here in the US the agreed upon premise has gone away and gridlock is the new rule. In Europe things are different post austerity and a new set of shared presumptions is being formed (How involved should countries be in the EU?) It is not often in these charged days that people are willing to stand up and make the hard and often unpopular decisions to do what is expedient for the greatest number of people rather than being beholden to interest groups. Such is politics and you are right, politics has little to do with policy and more to do with reptile mind survival of systems that benefit the people involved rather than what moves society forward or backward to a certain agreed upon ideal.

[-]iarwain111y40

My sense is that the LW wiki has the potential to be a good alternative for someone who wants to learn the ideas of rationality but does not have the time / patience to read through the Sequences. However, the Sequences have the major advantage that they have an order to them (actually several alternative orders - my favorite being Benito's) where someone can start at the beginning and work their way through in an organized way. To my knowledge there is nothing comparable for the wiki.

Anyone out there willing to put together an organized guide to the wiki aimed at a newcomer who wants to quickly learn through the material?

0[anonymous]11y

[sorry; posted on wrong comment]

[-]DanielDeRossi11y30

Request for advice: I'm looking to improve my social ability. specifically my ability to 'read' people and social situations. In addition I would like to be able to apply these insights to be more persuasive and socially effective. I feel like I am below average in these areas. In addition I would like to improve the quality of my relationships. Someone mentioned a social psychology course online. I probably won't take the course , but I'd like a textbook recommendation if possible. What would be ideal and really helpful would be something like Lukeprog's... (read more)

8ChristianKl11y

The Charisma Myth by Olivia Fox Cabane is a evidence-based book that summarizes advice about dealing with social situations. I'm not sure whether it helps in the reading department but it provides practical tips that improve social ability and multiple people on LW recommended the book in the past. When it comes to reading people in my own experience reading other people has a lot to do with being able to read yourself. Developing my own bodily awareness helped me a lot with reading other people. It gave me awareness of things like when a partner of a conversation tenses up when I say something. Paul Ekman sells an online course for detecting microexpression to detect emotional states of other people. Paul Ekman is a serious academic psychologist but it's not 100% clear whether all his claims are true in the strong form in which he makes them. If you have money to spend doing his course seem like a good investment. Creating an Anki deck for Ekman style detection of emotions also seems like a good project from my own perspective. I think a lot of people on LW and in general would appreciate such a deck. All that said, don't think that you will improve social skills by sitting in front of a book. Improvement comes from actually practicing and doing exercises.

0DanielDeRossi11y

Thanks for the recommendations! Definitely looking into it. Some of the 'theory' stuff is interesting too. Things like the posts on lesswrong that conceptualize offense as a grab for status. Any recommendatons on that front? On 'theory' of social interaction.

0ChristianKl11y

If you have to much theory in your head but bad social skills you are likely to analyse the situation in which you are intellectually. As a result your body language might give off signs that you aren't present. Reactions in your face are slightly delayed. As far as I'm aware ideas like "conceptualize offense as a grab for status" are not strongly evidence based. Of course that doesn't mean that it has to be wrong. There probably some writing in the pickup field that slashes out ideas like that in more detail.

0DanielDeRossi11y

Yeah. I've always found (in other areas) , having a good handle on the theory and concepts involved allows me to grasp it intuitively and apply my knowledge better. I guess in soft science , the theory might be a bit more conjectural. Any writings in particular you think of? Thanks in advance.

0ChristianKl11y

When it comes to social situations, normal people have certain emotional reactions to specific stimuli and react based on those stimula. Having theories in your head can reduce you from having natural reactions and acting them out. I generally think that Friedemann Schulz von Thun model of communication is underappreciated in the Anglo-American discourse. We covered the model in school in Germany and later when I went to Toastmasters two separate people hold speeches on it. At my university I had a course about personal development by a computer science professor that also covered the model of Schulz von Thun. Apart from that there isn't specific writing that I would recommend, but other might have recommendations.

[-]Anders_H11y30

Anyone in Oslo interested in being part of a Less Wrong meetup group? I have started a Doodle poll at http://doodle.com/9mg6f3qcya34wciu4kf6kuze/admin#table

[-]DanielDeRossi11y20

Heads up to fellow autodidiacts. Amazon's kindle Unlimited allows you to get a number of select titles for a monthly fee. They have a free 30 day trial on now.

3Shmi11y

US-only so far.

[-]ChristianKl11y10

Did anyone here learned to do lipreading? If so, how did you learn it? Can you recommend resources on the topic?

6gwern11y

SDr is involved with http://lipreading.org/ which may be of interest.

[-]MrMind11y10

As a little side project, I entertain myself with the idea of writing fiction that blends fantasy and mega-structures engineering.
The first step will be to ideate a consistent magic system, but of course, to make the story interesting, I'll have to come up with interesting characters and their conflicts. Do you know about any good story, long or short, that revolves around or has as background mega-structures, that I can be inspired from? Fantasy or extreme science-fiction would be the best.

3kevin_p11y

"Tower of Babylon" by Ted Chiang. It's a novelette that's part of his compilation "Stories of Your Life and Others". To quote Wikipedia, "the story follows a young miner from the town of Elam who ascends the tower of Babylon to help break through the vault of heaven. Along the way he sees many wonderous sights, uncovers mysteries of heaven and earth, and in the end finds them as inscrutable as ever."

0MrMind11y

I read it and really liked it.

2curiousepic10y

Also the books of Karl Schroeder (Sun of Suns series, other standalones)

2Emile11y

Rendez-vous with Rama?

1Illano11y

The Culture series by Iain M. Banks has a lot of different examples of mega-structures, and they tend to feature somewhat prominently in his stories. The books themselves are on the hard-SF side of things, but a few of them delve closer to fantasy when they pull a Star Trek, and have an encounter with a less-developed race.

0MrMind11y

Ah, I love the culture series. Too bad Iain Banks has left the building :( Anyway I read almost all of them, but I'm reluctant to crack open the Hydrogen Sonata, knowing too well that's going to be my last Culture novel...

1drethelin11y

http://en.wikipedia.org/wiki/Titan_(John_Varley) seems perfect

1polymathwannabe11y

The Fountains of Paradise, by Arthur C. Clarke. (space elevator) Entoverse, by James P. Hogan. (planet-sized computer) The Ringworld saga, by Larry Niven. (über-massive artificial planet) Singularity Sky, by Charles Stross. (god-like AI controlling us from the future)

1gjm11y

Ra by Sam Hughes (http://qntm.org), kinda, though the mega-structures involved are very much in the background for much of the story: Warning: work in progress, completion date unknown; posting roughly one chapter per month.

0MrMind11y

I really like it so far (about halfway through it).

0curiousepic10y

A bit late here, but Golden Age by John C. Wright.

0IlyaShpitser11y

"This one speaks as the Power That Helps. [...] Look upon my Helping."

[-]Joshua_Blaine11y10

Where did the brain diagram on the front page go? Is it just an error on my end, or has that actually been removed from the site?

8Nornagest11y

It's gone for me too, but I don't think it'll last. This has happened before, and I think we're looking at either an intermittent glitch on the server side or some kind of resource issue. Personally, though, I'd be just as happy to see it stay gone. It's ugly; it takes up real estate it doesn't need to; and most importantly it's not all that useful for its apparent niche as a guide to newcomers, adding little that the header bar doesn't already have. The article lists aren't too hot either; the stuff they link to is usually years old and the aggregation function seems to be doing some kind of dumb association that usually clusters around some uninteresting keyword. I liked it better when the front page just mirrored Main, although aggregating Main and Discussion might be a better move these days.

2blacktrance11y

I liked the brain, I'm a bit disappointed to see it go.

6Vladimir_Nesov11y

The change is intentional. See the wiki edit (by Jackk from Trike).

[-]Plasmon11y10

I wonder if there's any significance to the fact that there is only one (known?) material out of which a space elevator could be constructed on Earth. Most planets, I would expect, will be such that either no material is strong enough, or several materials are strong enough. Earth lies just on the boundary.

4Manfred11y

We probably won't build a space elevator anyhow - though check out some other options.

3wadavis11y

It is just the current state of technology that only one usable material exists (no fact checking has been done), Given time a wide variety of eligible materials will be developed with appropriate properties. This is nothing special, just the endless advance of science in materials engineering.

1Luke_A_Somers11y

Boron Nitride nanotubes are strong enough, and enough stickier that they'd probably be better than carbon nanotubes.

1Metus11y

Maybe this is part of the great filter? No planets that have lower gravitational force are hospitable to intelligent life and all planets that are hospitable to intelligent life have higher gravitational force. We are just incredibly lucky to lie just one the boundary. I am not suggesting that gravity causes intelligent life to evolve but that the overall characteristic of such planets is such that etc.

0Luke_A_Somers11y

Doubtful. You can lift a seed colony up to where launch is easy.

[-]protest_boy11y00

So there's a MIRIxMountain View, but is it redundant to have a MIRIxEastBay/SF? It seems like the label MIRIx is content to be bestowed upon even low key research efforts, and considering the hacker culture/rationality communities there may be interest in this.

[-]sdr11y00

Here's an evolutionary psychology question:

#1: Lemma: Replicator-selection works only through genes; that is, there is no such thing as group selection; from a reproduction perspective, the only which matters, is delta-reproduction-fitness increase.

#2: Lemma: Technologies, and techniques doesn't require gene-transfer. Once someone comes up with a new idea, that idea can freely spread across the entire population. Therefore, technologies, and techniques doesn't offer delta-reproduction-fitness increase.

#3: Observation: Some people appear to be interested... (read more)

0[anonymous]11y

Warning: worthless evidence-free armchair evopsych speculation coming up: The benefits of technology and techniques don't spread right across the whole population immediately - the primary benefit goes to the inventor and those near to them. So, in the ancestral environment, if inventing a new kind of pointy rock to better kill dinosaurs gives you +1 fitness points, and lying around watching stone-age TV until your neighbour makes a pointy rock then stealing it gives you +2, then genes for inventing will spread until everyone has a 1/2 chance of having an inventor for a neighbour, at which point equilibrium is reached and both gene types will do equally well.

[-]ChristianKl11y00

The label bio is always a quite interesting one. On the one hand the label supports bigger cages for animals and thus serves utilitarian purposes. On the other hand it leads to some farming choices for which there no real reason.

The EU commission just discovered that chicken eggs by nature are neither red nor blue and therefore painting them red or blue might violate the bio idea. Therefore the Eu commission is planning to rule that there no such thing as a red bio-egg.

http://deutsche-wirtschafts-nachrichten.de/2014/07/20/eu-kommission-will-faerben-von-ostereiern-verbieten/ (German source)

3hydkyll11y

(I think what we call Bio in German is called "organic" in English.)

[-]protest_boy11y00

I have a question about the nature of generalization and abstraction. Human reasoning is commonly split up into two categories: deductive and inductive reasoning. Are all instances of generalization examples of inductive reasoning? If so, does this mean that if you have a deep enough understanding of inductive reasoning, you broadly create "better" abstractions?

For example, generalizing the integers to the rationals satisfies a couple of things: the theoretical need to remove previous restrictions on the operations of subtraction and division, a... (read more)

1MrMind11y

A couple of starting points to improve your investigation. First, rigorous inductive reasoning, i.e. bayesian probability, includes as a special case deductive reasoning, at least in the case where deductive reasoning is conflated with "classical logic". AFAIK there have been only sparse and timid research into widening probability to fit other kinds of logic. Second, the example you use to illustrate generalization is a case of what in logic is known as elementary embedding, and it's a pure application of deductive reasoning. Although the process that led the first mathematician to the invention of rational numbers might have very well been one of inductive reasoning. Third, do not be tempted to think that abstraction is generally linear. It may very well be the case that the model C is generalized by model B, which is generalized by model A which is found to be a special example of C. This kind of "strange loops" (I credit Hofstadter for the invention of this term) happens all the time in category theory. The very same four different foundations for mathematics (set theory, type theory, category theory, univalence theory) are all instances of one another (see for example the paper "From Sets to Types to Categories to Sets" by Awodey, which however was compiled before univalence was formalized).

0protest_boy11y

Thanks for your enticing comment! I understand your first point, but my math knowledge is not up to par to really understand point #2, and point #3 just makes me want to learn category theory. BTW, I also posted this question on the philosophy stackexchange: http://philosophy.stackexchange.com/questions/14689/how-does-abstraction-generalization-in-mathematics-fit-into-inductive-reasoning. Do you have any recommendations of what to study to understand category theory and more about the foundations of math? (Logic, type theory, computability & logic, model theory seem like contenders here)

1MrMind11y

You're welcome! Foundation(s) of math is a huge and fascinating topic by itself, but if you're more interested in the intricacy of abstraction hierarchies you should look no further than category theory, the Yoneda lemma, up up to doctrine theory. I love as a good introduction Category Theory by Awodey. As for the foundation of math, very good for dipping your toes are the first chapters of Marker's introduction to model theory and the recently reprinted Set theory by Kunen (set theory models are a vast subject by themselves...)

Moderation Log