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Consistency in Arithmetic

Double the debt: 2 -1 = -2 *Ok

But: -2 -1 = 2 *Ok?

Who will allow you to multiple your debt with another's debt to get rid of it?

2 -1 + -2 - 1 = (2 - 2) -1 = 0 -1 = 0

But...

2 -1 + -2 -1 = -2 + -2 * -1 = 0

Therefore...

-2 * -1 = 2

Ian Stewart, Professor Stewart’s Cabinet of Mathematical Curiosities, Profile Books, 2008, pages 37-38;

So mathematics is mentally-created, it looks objective because of primordial choices we have made? As a form of a subconscious of the Species and we've created computers because we think that way and choose to think that way? Our truths may be grounded on habit and rationality may be a self-imposed restriction, nature being more non-bivalent than we would like it to be. Under the same logic, the furniture in our room might have been subject to similar primordial choices. Oh, and especially I, Ourselves, Identity.

The degrees of what's available in nature might be infinitely greater than we think and a self-imposed boundary might be inherently limiting.

A Musico-Logical Offering

Hofstadter opens with the story of J.S. Bach's Musical Offering for King Frederick, which contains a particular canon that sneakily shifts from one key to another before its apparent conclusion, and when this modulation is repeated 6 times, the piece ends up at the original key but one octave higher. This is our first example of a "Strange Loop":

The "Strange Loop" phenomenon occurs whenever, by moving upwards (or downwards) through the levels of some heirarchical system, we unexpectedly find ourselves right back where we started. (Here, the system is that of musical keys.)

Other examples occur in the drawings of M.C. Escher, for example this famous one.

Is the water going up or down?

Dagon9y90

Units would help a lot in your debt example. 2 $-1 = $2, two instances of $1 debt is $2 of debt. The multiplier and multiplicands are DIFFERENT - the multiplicand is dollars of debt and the multiplier is a count of debts. And -2 $-1 = $2, yes. If you have negative two debts of $1 (that is, you remove two of them), you have a net of positive $2.

Never do you multiply a debt by another debt - that would give you square dollars, which makes no sense.

edit: fix typo

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9 Open thread, Feb. 06 - Feb. 12, 2017

by MrMind

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[-]Viliam9y140

From "A Bitter Ending":

At a conference back in the early 1970s, Danny [Kahneman] was introduced to a prominent philosopher named Max Black and tried to explain to the great man his work with Amos [Tversky]. "I’m not interested in the psychology of stupid people," said Black, and walked away.
Danny and Amos didn’t think of their work as the psychology of stupid people. Their very first experiments, dramatizing the weakness of people’s statistical intuitions, had been conducted on professional statisticians. For every simple problem that fooled undergraduates, Danny and Amos could come up with a more complicated version to fool professors. At least a few professors didn’t like the idea of that. "Give people a visual illusion and they say, ‘It’s only my eyes,’ " said the Princeton psychologist Eldar Shafir. "Give them a linguistic illusion. They’re fooled, but they say, ‘No big deal.’ Then you give them one of Amos and Danny’s examples and they say, ‘Now you’re insulting me.’ "
In late 1970, after reading early drafts of Amos and Danny’s papers on human judgment, Edwards [former teacher of Amos] wrote to complain. In what would be the first of m

... (read more)

2MrMind9y

Oh my. Wondering how many computation cycles humanity has wasted since the beginning of time debating words will give me nightmares. Have we in four thousands years of history accumulated a month of creative, uninterrupted thoughts about truth that wasn't about definitions?

0Viliam9y

Heh. Humanity did a lot of useful work by observing things, and in recent centuries by applying math. Also, humans are traditionally good at making tools, because they require near-mode thinking. So we do have a few strengths. It's just that understanding the difference between a map and the territory, in absense of constant experimental feedback, is not one of them. I have met a few smart people who had a similar reaction to the whole "heuristics and biases" topic. They react as if the idea that human brain could be somehow imperfect is a personal offense aimed at to them, and immediately start composing verbal arguments about how biases are not "really" mistakes. For example, people who are otherwise skeptical about evolution when it interferes with their religious beliefs, suddenly say things like "but, an irrational brain would be an evolutionary disadvantage, so it could never evolve!" (On a second thought, I guess the true reason of discomfort of these specific people could be that the idea of cognitive biases is not really compatible with an idea of an omniscient and omnibenevolent intelligent designer. I mean, intentionally designing an intelligent mind that systematically thinks incorrectly and cannot help itself, that sounds quite evil.)

[-]WalterL9y110

We don't have an open quotes thread on the main page, but this made me chuckle:

"mathematician thinks in numbers, a lawyer in laws, and an idiot thinks in words." from Nassim Taleb in

http://www.thehindu.com/books/%E2%80%98Trump-makes-sense-to-a-grocery-store-owner%E2%80%99/article17109351.ece

4PhilGoetz9y

I came here looking for a Rationality Quotes thread to quote that in. :) I'm especially sensitive to it because I spent a lot of time last year reading postmodernist literary theory, which rejects logic in favor of rhetoric. They support theories that have impressive-sounding words because postmodernist theory says the point of theory is to have fun rather than to understand things.

3Viliam9y

Do they really admit they are just trolling? :O

0Lumifer9y

In literary theory that might well be true :-/

[-]James_Miller9y80

I think this paper implies that rare harmful genetic mutations explains lots of the variation in human intelligence. Since it will soon be easy for CRISPR to eliminate such mutations in embryos, I think this paper's results if true means that genetic engineering for super-intelligence will be relatively easy.

2Douglas_Knight9y

I don't think that this shows anything different from earlier studies, which it shouldn't because it doesn't use different methods.* I guess it simultaneously measures that 25% of the variance is due to common variants and another 25% is due to rare variants in LD with common variants, while previously those results came from separate studies. I have only skimmed the paper, but I reject the claim in the abstract that these "rare" variants are due to mutation-selection balance (aka mutational load). That is the claim you are talking about, right? They are rarer than the SNPs on the chip, but I think they are too common to be purely deleterious. I don't see how they could measure such rare variants without sequencing at least some of the subjects. * One method that is different is that it doesn't throw out close relatives. This is how it distinguishes common variants from those merely in LD with them. Potentially this could detect the effect of variants rarer than in the earlier article, but it did not. ---------------------------------------- Having a choice between targeting common variants and rare variants can only make things easier than not having a choice, but why do you think rare variants are easier? There are tradeoffs between several difficulties. I see three axes. (1) Knowing what variants to target; (2) Cost of edit: (2a) cost of CRISPR and (2b) deleterious effects of the edit; (3) Benefit per gene. Mutational load likely eliminates (2b). Proofreading the genome allows us to skip (1), but at the cost of doing a tremendous number of edits (2a). Do you really expect that to be easy soon? Alternately, we could try to identify which super-rare variants affect intelligence, paying cost (1), but I think this will be extremely difficult. I expect the effect size (3) to be smaller for rarer variants, although I'm not sure I have a good reason for this.

2James_Miller9y

Yes Eliminating rare variants almost certainly won't have negative side effects. If X and Y reduce my intelligence and X is a rare variant and Y a common one, then there is a much bigger chance that Y does something good for me than that X does. If we have solid evidence that CRISPR editing could result in super-geniuses I expect lots of resources (perhaps in China) to be devoted to the relevant practical problems.

0Douglas_Knight9y

Yes, super-rare variants have some advantages, but as I said, common variants have other advantages. It sounds to me that you have fixated on one approach, rather than considering tradeoffs. For that matter, consider the option of cloning, a mere engineering problem. It won't get you "super-geniuses," but that is an arbitrary threshold. It seems to me that you have imposed multiple arbitrary thresholds to isolate this one path.

[-]tetronian29y70

Is it currently legal to run a for-money prediction market in Canada? I assume the answer is "no," but I was surprisingly unable to find a clear ruling anywhere on the Internet. All I can find is this article which suggests that binary options (which probably includes prediction markets) exist in a legally nebulous state right now.

5Douglas_Knight9y

I think you are misreading the article. I think that it is saying that betting on financial markets is heavily regulated. The whole reason those sites exist is avoid claiming to give access to financial markets. At one point the SEC(?) negotiated a deal with Intrade that it could have American customers in return for not offering financial bets. Sports betting websites are much less lightly regulated and I'm pretty sure political prediction markets are legal. Why do you ask? What does it matter where a market is located? As that article shows, the Canadian government, unlike USG, doesn't try hard to block Canadians from using off-shore services that would not be legal in Canada. Prediction markets are definitely legal in Ireland. What more do you need? It might be dangerous to live in Canada and run a sketchy betting site nominally located in the Caribbean, but Ireland? If you follow Irish law, no problem. Again, I put odds at 90% that it is legal in Canada. The problem with prediction markets is lack of demand and lack of access to Americans. Added: this says that sports betting is a gray area and even these sites are not based in Canada. Also, I checked the example I had in mind and it was not registered in Canada. So probably I was wrong about Canada, but, again, Ireland is all you need.

[-]Daniel_Burfoot9y70

Request for programmers: I have developed a new programming trick that I want to package up and release as open-source. The trick gives you two nice benefits: it auto-generates a flow-chart diagram description of the algorithm, and it gives you steppable debugging from the command line without an IDE.

The main use case I can see is when you have some code that is used infrequently (maybe once every 3 months), and by default you need to spend an hour reviewing how the code works every time you run it. Or maybe you want to make it easier for coworkers to get... (read more)

8Lumifer9y

Converting local time to UTC and back. Time zones, daylight savings times, etc. are very messy.

2Daniel_Burfoot9y

Good idea, thanks!

[-]maxjmartin9y70

(some previous discussion of predictionbook.com here)

[disclaimer: I have only been using the site seriously for around 5 months]

I was looking at the growth of predictionbook.com recently, and there has been a pretty stable addition of about 5 new public predictions per day since 2012 (that is counting only new predictions, not including additional wagers on existing predictions). I was curious why the site did not seem to be growing, and how little it is mentioned or linked to on lesswrong and related blogs.

(sidebar: Total predictions (based on the IDs of ... (read more)

4WhySpace_duplicate0.92616921290755279y

I use Metaculus a lot, and have made predictions on the /r/SpaceX subreddit which I need to go back and make a calibration graph for. (They regularly bet donations of reddit gold, and have occasional prediction threads, like just before large SpaceX announcements. They would make an excellent target audience for better prediction tools.) I've toyed with the idea of making a bot which searched for keywords on Reddit/LW, and tracked people's predictions for them. However, since LW is moving away from the reddit code base, I'm not sure if building such a bot would make sense right now.

2ChristianKl9y

I don't think that the dev's touched predictionbook in quite a while. In general discovery of interesting public predictions doesn't work well because it's not easy to search and there are no tags. There's https://www.metaculus.com and https://www.gjopen.com/ for curated public predictions. For private prediction there's a new Android App (still very much in Beta and in development): https://play.google.com/store/apps/details?id=squirrelinhell.lwpredictions I also did a bunch of prediction tracking in less structured ways. Our LW dojo had a while a shared Workflowy for predictions.

0maxjmartin9y

Yes, this is true. I believe they accept pull requests but there has not been much development for a long time and the site is quite basic. I didn't know about this one, thank you!

0ChristianKl9y

That's might be true, but from my perspective, a few pull requests won't change the fate of predictionbook significantly. It's likely that another service will sooner or later overtake it. I like the Android App at it's current state but don't know how much time it's creator plans to invest in it in total. For personal prediction tracking the Android App is already more handy for me than predictionbook as I caryy my mobile phone around and it's relatively straightforward to add new predictions when I have nothing else to do at the moment while traveling from place A to B. Arbital might sooner or later build it's own prediction tracking. It's also possible that someone starts a completely new project.

0VincentYu9y

Just adding to the other responses: I also use Metaculus and like it a lot. In another thread, I posted a rough note about its community's calibration. Compared to PredictionBook, the major limitation of Metaculus is that users cannot create and predict on arbitrary questions, because questions are curated. This is an inherent limitation/feature for a website like Metaculus because they want the community to focus on a set of questions of general interest. In Metaculus's case, 'general interest' translates mostly to 'science and technology'; for questions on politics, I suggest taking a look at GJ Open instead.

[-]J Thomas Moros9y40

Has there been any discussion or thought of modifying the posting of links to support a couple paragraphs of description? I often think that the title alone is not enough to motivate or describe a link. There are also situations where the connection of the link content to rationality may not be immediately obvious and a description here could help clarify the motivation in posting. Additionally, it could be used to point readers to the most valuable portions of sometimes long and meandering content.

[-]Brillyant9y40

Looks like the 'RECENT ON RATIONALITY BLOGS' section on the sidebar is still broken.

Is this a difficult fix?

[-]Viliam9y40

What advice would you give to a 12-years old boy who wants to become great at drawing and painting?

(Let's assume that "becoming great at drawing and painting" is a given, so please no advice like "do X instead".)

My thoughts: There is the general advice about spending "10 000 hours", for example by allocating a fixed space in your schedule (e.g. each day between 4AM and 5AM, whether I feel like doing it or not). And the time should be best spent learning and practicing new-ish stuff, as opposed to repeating what you are already... (read more)

6ChristianKl9y

Make a habit of including a lot of pictures for any notes for school. Dan Roam's "The Back of the Napkin". The ability to translate ideas into good pictures is commercially valuable. I don't see the paint of exploring many different kinds of 2D painting. I would expect that a digital pen beats most other tools. Especially in the future as technology advances. It might be worth looking into 3D virtual reality painting. It's a new medium and thus valuable.

2Han9y

There are a lot of people who say that piano is the most versatile instrument, and they're right about that on a superficial level. You can do polyphonic things with a piano that you can't do with a clarinet or a trumpet. And like a digital pen, a digital piano can simulate a lot of other instruments, especially if you hook it up to flashy synthesis software that knows all the different articulations for those instruments. But using a digital piano doesn't feel very much like using those instruments, and you won't express the same way you would if you had one. A calligraphy brush is really fun and you can't replicate the feeling of using it without the physical tools. Many of them have nice texture and you can feel their shape when you rotate them in your hands -- they're also lightweight, so if you're not holding one to the page it feels more like a pencil than like a paintbrush. A lot of my friends do art, and I do art too when they ask me to try it with them. Different art tools feel different, and for some people, some tools are more fun than others. I think it's really important to try these things out before you make a decision about them.

2Erfeyah9y

Actually the piano is one the least versatile instruments. You get control of which key you press, a chosen velocity and the sustain pedal. A piano performance can be midi recorded using these three values and reproduced in an extremely high level of detail. If you try to do the same with a truly versatile instrument like for example the violin you will find that it is impossible. Not difficult, impossible.

0Han9y

I'm confused. Isn't it evident from the rest of my comment that I agree with you? (On an unrelated note: I think my upvote button has vanished. Otherwise I would have clicked it for your post!)

2Erfeyah9y

Ah, sorry to confuse you. Yes it is obvious that you agree. I was just expanding on the point :) (You need 20 karma to be able to upvote)

0Han9y

Thank you for the information! My brain does something weird when I see the word "actually," so I don't think I was charitable when I read your post.

0Erfeyah9y

No problem :)

0ChristianKl9y

Yes, the point isn't to express yourself the same way. I don't think "what tool feels most fun" should be the guiding principle for a person who wants to build up drawing skills that he can use as a career.

4Han9y

You're probably right! (At least some of the time.) In music, I know a lot of people who think about things the same way you do, and they sensibly learn to use versatile tools like FM synthesis because FM synthesis covers a wide range of sounds really broadly. A lot of them even know how to make human voice-like sounds using these tools. On average if you stick to those tools you'll do pretty well. They still fall back on using physical instruments for a lot of techniques, because you can do elaborate expressive things with physical instruments a lot more easily than with the machine. In music, machines have been getting better, but they aren't perfect yet. A lot of input devices, even well-regarded ones, don't have the build quality of instruments made for professionals. It's really hard to simulate the physical feel of an acoustic instrument without actually building an acoustic instrument -- don't ask me why, but I've shopped around a lot and I've only found a couple input devices that really feel great for me after long-term use. In art, there are a lot of hardware limitations. It's hard to make a tablet that looks great and feels great, and talking to an art program means you're subject to a lot of latency, and -- if your tablet doesn't have a display -- you're going to see your drawing appear on a different plane than you made it on. A lot of digital artists struggle with line quality and width variation because those things can be awkward on tablet input devices -- and depending on medium, those are often super fundamental (1) to how you pick out parts and subparts of an image and (2) to how you read its form. You will notice there are a lot of really good digital painters and a lot of really bad digital line artists. That's a part of why! Don't get me wrong, though. I think your point totally holds for parts of art that can be rehearsed and repeated an indefinite number of times until they look right. I also think that for planning and prototyping, you

0ChristianKl9y

Currently, it's true that line quality on a device like the Surface isn't perfect. I personally expect both Microsoft and Apple to solve the issue on their pens in the next five years. I don't object to doing planning and prototyping on paper with a pencil. While the 12 year old sits in school it's likely that taking graphical notes on paper is better appreciated by the teacher than taking those notes with a tablet.

0Viliam9y

I like the creation of idea-related sketches. I would imagine that various constraints imposed by their various disadvantages can take you out of your comfort zone, for example when you use a tool that is unable to create small details, you will give up the small details and instead focus on the overall composition... and learning this may somehow become useful even when you return to using a tool that allows you to do details. Like, using an insanely wide brush could make you reinvent impressionism. Probably yes, but the non-digital tools might give you an idea about what settings you want to try with the digital ones. For example, do you want the new color to completely overwrite the underlying one, or rather to blend with it. Or maybe -- although this is mostly a fake purpose -- setting the digital tool to resemble high-status non-digital tools (something that Leonardo da Vinci would use, as opposed to what a teenage manga fan uses) could add a high-status feeling to your pictures. On the other hand, going digital and becoming familiar with the digital tools has some added value. For example, having a nice picture is cool, but turning it into a WordPress template could be more profitable.

0ChristianKl9y

I would rather try different digital tools than different analog ones. Getting a 3D printer also imposes some constraints.

4ChristianKl9y

It has the added benefit that a lot of time sitting in school can be used for that purpose.

4Elo9y

http://bearlamp.com.au/how-to-learn-a-new-area-x-that-you-have-no-idea-about/ http://lesswrong.com/r/discussion/lw/mmu/how_to_learn_a_new_area_x_that_you_have_no_idea/ I wrote a guide.

2Viliam9y

Thank you!

2Erfeyah9y

In my opinion, the most important advice: * Find a teacher that can demonstrably draw/paint to a high level. * Observe the first few lessons to make sure that he is also good at transmitting the information and is passionate about the art. Art has a rational component which we can call the 'technique' or 'craft' of the field. In drawing this would be light/shade, perspective, texture, drawing material etc. but it also has an intuitive component that results from developing an aesthetic sense. It is important to realise that art is not learned just from painting but by seeing the world through a painters eyes. Observing the world and understanding the way the eye perceives it and the mind reproduces it.

2Strangeattractor9y

I once went to a workshop on Sumi-e painting at the local Japanese cultural centre, and it changed how I look at paintings. So I'd recommend taking a Sumi-e class, or these days, I suppose watching Sumi-e tutorials on Youtube might do. In general, getting an idea of how different cultures look at visual arts can be eye-opening. In addition to learning by doing, going to different museums and galleries can be a way to learn about art from many different time periods and cultures in different mediums. Another thing that changed my perspective is a book called An Eye For Fractals by Michael McGuire. It taught me to break down things into different types of shapes when looking at them, and to appreciate a different kind of beauty than is usually taught to children. It is an exploration of Benoit Mandelbrot's famous quote

2[anonymous]9y

I am "not terrible" at various forms of art / media so I might be able to give some adviceL In my case, I spent a bunch of time drawing human figures in only a few specific angles, and this hindered me a lot. So definitely focus on getting the kids drawing lots of different things. As a general note, focus more on the general shape of things than specific details (EX: have the whole body anatomy roughly done is better than just a nice-looking face). Other than that, in my education I'm unsure there are generally accepted "core books", comared to other subjects. I think this may also be because art/painting is a large subject. So I'd recommend doing these obvious things (happpy to chat more via PM if you want to get into more detail): * Focus on letting the kid do the stuff he enjoys. When forced to attend drawing class, that took a lot of the fun out of it. * The first point being said, if you can find a class/teacher that specifically teaches the sorts of things the kid is interested in (i.e. they enjoy going to the class), this is a pretty good idea. * Practice. Obviously the more you draw the better you'll get. * Google "best books / resources for X" where X is whatever things / medium the kid is interested in. * Nice materials. It's surprising how helpful a good sketchbook / high-quality pens can make the whole process feel more excellent. I'm not suggesting you shell out several hundred for some huge Copic set, but some nice Canson paper and Prismacolor pens can go a long way.

2Gunnar_Zarncke9y

Is he aware of the consequences? Maybe ask him the most important question: https://markmanson.net/question

2moridinamael9y

I am not "great" at drawing and have never put any time into painting. That said, the workbook Drawing on the Right Side of the Brain caused a quantum leap in my sketching ability. (There is a separate, much longer long-form book with the same title, but the workbook consolidates all the exercises and I found it more practically useful.)

2Viliam9y

Thanks, I was thinking about this, but I didn't know there was a separate workbook. Now I have... ahem... purchased both.

[-]Commander Zander9y20

Does anyone have a backup of that one scifi short story from Raikoth about future AGI and acausal trade with simulated hypothetical alien AGI? The link is broken. http://www.raikoth.net/Stuff/story1.html

5Douglas_Knight9y

9-tsiak awoke over endless crawling milliseconds... archive.is and archive.org are tools for answering questions like this.

0Commander Zander9y

Thank you very much!

[-]turchin9y20

"Why Boltzmann Brains Are Bad" by Sean M. Carroll https://arxiv.org/pdf/1702.00850.pdf

Two excepts: " The data that an observer just like us has access to includes not only our physical environment, but all of the (purported) memories and knowledge in our brains. In a randomly-fluctuating scenario, there’s no reason for this “knowledge” to have any correlation whatsoever with the world outside our immediate sensory reach. In particular, it’s overwhelmingly likely that everything we think we know about the laws of physics, and the cosmological... (read more)

[-]ingive9y00

Consistency in Arithmetic

Double the debt: 2 -1 = -2 *Ok

But: -2 -1 = 2 *Ok?

Who will allow you to multiple your debt with another's debt to get rid of it?

2 -1 + -2 - 1 = (2 - 2) -1 = 0 -1 = 0
But...
2 -1 + -2 -1 = -2 + -2 * -1 = 0
Therefore...
-2 * -1 = 2

Ian Stewart, Professor Stewart’s Cabinet of Mathematical Curiosities, Profile Books, 2008, pages 37-38;

9Dagon9y

Units would help a lot in your debt example. 2 $-1 = $2, two instances of $1 debt is $2 of debt. The multiplier and multiplicands are DIFFERENT - the multiplicand is dollars of debt and the multiplier is a count of debts. And -2 $-1 = $2, yes. If you have negative two debts of $1 (that is, you remove two of them), you have a net of positive $2. Never do you multiply a debt by another debt - that would give you square dollars, which makes no sense. edit: fix typo

0Lumifer9y

Actually, I would argue that multiplying by -1 is just the notation picked to express this particular operation which is flipping the sign.

0ingive9y

I think you meant (-2 * -1 = $2) I meant, multiply by a negative count of debt and not itself. So a debt multiplied by a negative count of debts leads to no debt at all, a positive. I'm not sure how you can have a negative count of debts. $2 debt squared does make sense, though, it is $4 and no debt. So by our mathematics, I could call the bank and ask them to multiply my debt with yours, I would return a positive. The point I am making is that we've made it this way because have chosen to. It says to me that mathematics is more of a mental creation, albeit a very useful one and that nature might be infinitely greater than our own self-imposed boundaries. Take a look at this picture does the water goes up or down? Is bivalent thinking necessarily nature or simply a mental creation? When it comes to truths (true or false) or computers (by primordial decisions) (1 or 0)

3roystgnr9y

No, it is $$4. If that's what you meant to write, and it's also obvious to you that you could have written 40000¢¢ instead and still been completely accurate, then I'd love to know if you have any ideas of how this computation could map to anything in the real world. I would have thought that "kilogram meters squared per second cubed" was utter nonsense if anyone had just tried to show me the arithmetic without explaining what it really meant. If that's not what you meant to write, or if it takes a second to figure out why $$4 isn't 400¢¢ instead of 40000¢¢, then you've just got the illusion of sense going on. And yes, I just noticed that pun and it wasn't intentional.

0Dagon9y

thanks, corrected. A negative count maps well into my understanding of physical reality. Positive count is adding multiple similar things, negative count is removing those things. Removing 2 debts is the same as adding 2 of the values of the debts. Thus -2 * $-2 = $4. Removing two $2 debts is equal to adding $4. There are elements of math and symbolic reasoning that don't map to reality, fine. But those parts which DO map well, are pretty strong, and are empirically correct in addition to being symbolically/conventionally well-formed. Mathematics is a mental creation, but that doesn't make it unrelated to reality - it's a pretty good and well-tested model of our universe. As to that picture, the water goes neither up nor down - it's a still drawing.

0ingive9y

I'm sorry if I don't understand, but multiplying my debt with a greater debt leads to no debt. It is true as the mathematics show. If we say to the bank, check account A debt and multiply with account B debt, account A will have no debt. It is independent on how you want to phrase it. What does each operation in your equation represent? "Removing two $2 debts is equal to adding $4" It is true because the mathematics has to stay consistent, it is based on primordial choices. That's my point, we choose it this way. So, if I understand right, you think that mathematics is a mental creation and does map well to reality, but it doesn't make it unrelated to reality. Reality seems to be independent of our maps, and a relation between a map and it would be a mental one. Yet reality is beyond any maps or limits. Well, the drawing is non-bivalent yet we choose our thinking to be such, as evident towards a lot.

3Viliam9y

You keep ignoring the issue of units. Multiplying dollars by dollars would lead to square dollars, which is a mistake (and not just because dollars are actually rectangular in shape). It is "-2 × $-2", not "$-2 × $-2". Money are not multiplied by money. Money are mutliplied by... number of accounts, or number of repetitions, or other dimensionless numbers.

[-]siIver9y00

Reposting this from last week's open thread because it seemed to get buried

Is Newcomb's Paradox solved? I don't mean from a decision standpoint, but the logical knot of "it is clearly, obviously better two one-box, and it is clearly, logically proven better to two-box". I think I have a satisfying solution, but it might be old news.

[-]Dagon9y100

It's solved for anyone who doesn't believe in magical "free will". If it's possible for Omega to correctly predict your action, then it's only sane to one-box. Only decision systems that deny this ability to predict will two-box.

Causal Decision Theory, because it assumes single-direction-causality (a later event can't cause an earlier one), can be said to deny this prediction. But even that's easily solved by assuming an earlier common cause (the state of the universe that causes Omega's prediction also causes your choice), as long as you don't demand actual free will.

2siIver9y

I agree that it's clear that you should one box – I'm more talking about justifying why one-boxing is in fact correct when it can't logically influence whether there is money in the box. Initially I found this to be unnerving initially, but maybe I was the only one.

2username29y

The correct solution is not to one-box. It is to decide based on the flip of a coin. Take that, Omega. Seriously, the problem is over-constrained to the point of being meaningless, not representing reality at all. Part of the problem that leads to intuition breakdown is that the setup deals with omniscient knowledge and infinite computation, which surprise surprise has weird results. "Infinities in math problems leads to paradox: News at 11." The setup of the problem assumes that Omega has full knowledge about your decision making process and that you have no reciprocal insight into its own, other than assumption that its simulation of you is correct. Well, of course the correct answer then is to one-box, if you insist on deterministic processes, because by definition two-boxing results in empty boxes. This only feels weird because it seems acausal. But the solution is equivalent as Dagon said to eliminating free will -- without the intuitive assumption of free will the outcome is predictable and boring. Imagine the "you" in the setup was replaced with a very boring robotic arm with no intelligence that followed a very strict program to pick up either one or both of the boxes, but was explicitly programmed to do one or the other. Omega walks up, checks the source code to see whether it is configured to one-box or two-box, and fills the boxes accordingly. The weirdness comes when we replace the robot with "you", except a version of you that is artificially constrained to be deterministic and for which the physically implausible assumption is made that Omega can accurately simulate you. It's a problem of bad definitions, the sort of thing the Human's Guide to Words warns us against. Taboo the "you" in the setup of the problem and you find something more resembling the robotic arm than an actual person, for the purposes of the problem setup. However if you change the setup to be two Omegas of finite capability -- "you" have full access to the decision-making facili

4Viliam9y

...which makes a part of your brain scream: "As far as I know, this is not possible. Someone is trying to scam you. You should grab both boxes and run!"

2username29y

I call that the pragmatic intuition. It is the heuristic to disagree/distrust anything not grounded in physical reality. Some people, particularly mathematicians, lack this intuition. Others, particularly seasoned engineers, have it in spades. I think it is a useful heuristic to have, particularly if you want your beliefs to reflect the real world.

0Dagon9y

That's pretty much the heart of the issue, isn't it? Clearly, by the omniscience of Omega's prediction, your choice is extremely correlated with what's in the box. So whether your choice determines the box contents, the box contents determines your choice, or some other thing determines both your choice and the box contents, there is a "logical influence" between your choice and the money in the box. The assumption that your choice is independent of the state of the universe is flawed.

1Lumifer9y

If you assume away free will, the problem loses meaning. What is that "choice" between one and two boxes that you are supposed to make? You don't make any choices.

0Dagon9y

Indeed. You experience results of the progression of states of the universe. It feels like you're making a choice, but that's illusory. Not so much "assume away" free will, but "dissolve the concept" and recognize that it's meaningless. Or, at least that's the case in a universe where Omega can perfectly (or even near-perfecty) predict your "choices" - choice is meaningless if it's that predictable. It's not actually proven that this is possible, or that our universe (including consciousness) works that way.

0WalterL9y

How else would it work? Where is the decision going to come from that Omega can't see?

0Dagon9y

I don't know how else it would work. But I also don't know how it could work in the first place, so that doesn't tell us much. Omega doesn't (as far as I know) actually exist, so "it doesn't work at all" is a justifiable answer as well. There's only so much you can learn about the actual universe from thought experiments.

0Dagon9y

Thanks for starting the discussion, but please ALSO post your solution. Pretty much everything on the topic is old news, so no harm even if yours is already known to some.

0ChristianKl9y

I don't see an issue besides the decision standpoint that matters (and that could be solved). Depending on where you see the issue it's likely dependent on the assumptions you make about the problem.

0Oscar_Cunningham9y

What we have is a list of proposed decision theories (Evidential Decision Theory, Causal Decision Theory, Timeless Decision Theory, Updateless Decision Theory), each of which acts the same on standard decisions, but which deal with Newcomb-like problems differently. Some of these decision theories satisfy nice general properties which we would want a decision theory to satisfy. There's argument about which decision theory is correct, but also about what the various decision theories actually do in various situations. For example CDT is normally thought of as being the two-boxing theory that people intuitively use, but some people argue that it should take into account the possibility that it is in Omega's simulation and hence it even people following CDT should actually one-box. So the discussion is more nuanced than "What is the correct thing to do in Newcomb's problem?", it's more "By what general criteria should we judge a decision theory?". Of course any particular insight you have about Newcomb's problem might generalise to this way of looking at things.

[-]Thomas9y00

Another problem to solve:

https://protokol2020.wordpress.com/2017/02/05/physics-problem/

2Lumifer9y

Actually, I think I've come up with a more elegant idea than altitude-triggered airbraking. There is no requirement that when released they go down into the gravity well :-D Your two objects are leaky zeppelins.

0Thomas9y

Helium Zeppelins aren't exactly rigid bodies. But vacuum Zeppelins are. Those could be arranged to do the job.

2Lumifer9y

What does "equal" mean?

0Thomas9y

The same shape, mass and of the same material.

0Lumifer9y

Are the two objects interchangeable -- that is, can we swap A and B and get the same result? A simple answer to your question is that atmosphere is not homogeneous. Dropping one object, say, over a hurricane downdraft and another over an updraft would result in different velocities relative to ground and so the one dropped from a higher altitude can reach the surface earlier.

1Thomas9y

Yes. We can swap A and B and get the same result. No, we drop them both over the Central Atlantic and then both will have about the same weather. It's the same, unexceptional weather for both.

0Lumifer9y

So it seems we can swap both the objects and the locations? In your setup, if we take object A and lower it to the altitude of B, then take B and lift it up to the (former) altitude of A, will the object B reach ground first?

0Thomas9y

Yes. Yes, the object B will reach ground first.

0Lumifer9y

Can the objects do anything during their descent, such as opening a parachute at a predetermined altitude? changing their aerodynamics?

0Gurkenglas9y

Also, can they include sensors and electronics?

2Oscar_Cunningham9y

This seems like it could have many possible answers. The most obvious is that A has a different shape or weight to B, and so is less affected by air resistance. Reading the problem literally it could just also be that A was dropped substantially before B.

0Thomas9y

No, they are equal. No. At the same time.

1Richard Korzekwa9y

Air density drops with increasing altitude. The object dropped from a higher altitude reaches a higher speed before reaching the denser air where object B is dropped. I'm not sure if a realistic density profile will allow object A to arrive first, but it is easy to show that there is some air density profile which will cause this to happen. I suspect that a necessary condition is that object A is already above the terminal velocity at object B's initial height when it reaches that height. Or, if you interpret "free fall without any initial relative velocity against the planet" to say that it is stationary with respect to both the Earth's center of mass and the Earth's surface, then drop B from a geostationary orbit, and A from a higher position, where it will have insufficient angular velocity to be in orbit. It will fall to Earth, while B's orbit will decay. Edit: It is permitted to assume that they are dropped over the equator, since the problem says "Central Atlantic". Edit 2: Wait, I did this wrong. If object A has a rotational velocity of 1/day, and it is at an altitude higher than a geostationary orbit, it will be in some larger more eccentric orbit, so it won't fall to Earth any sooner than object B.

0Thomas9y

Your first idea should be elaborated. But it is quite sound. Your second idea is wrong. Above geostationary orbit and not moving relative to the Earth surface, means an escape orbit. Still, I would prefer a non - atmosphere solution. But yes, your first idea is also good albeit a little undeveloped.

0Richard Korzekwa9y

It's not an escape orbit, it's just a more eccentric orbit (unless it is much higher). Still, you are correct that my second solution will not work (see my second edit). I started solving the trajectory for an exponentially decaying air density and a drag force that scales linearly with density and quadratically with velocity, but I did not immediately see the solution to the resulting differential equation, nor did I see a clever trick for avoiding the calculation. I'll look at it again later.

0Thomas9y

You are absolutely right. It CAN be an escape orbit, if it is high enough. But it may also not be an escape orbit. You are right. Still, not a good solution.

0skeltoac9y

Given only that both objects will splash into the Central Atlantic, there is wiggle room in choosing latitudes and longitudes such that lateral distance between the objects is vastly larger than the difference in altitude. Suppose the lower-altitude object is placed safely inside the eastern boundary of this region and the higher-altitude object is placed inside the western boundary, such that each will splash into the Central Atlantic according to the rules. The objects can be several 1000km apart but only 1cm different in altitude. Now we just need a natural force to slow the descent of the lower-altitude object more than it slows the higher-altitude object. Let's use the gravity of the Moon. Drop the objects when the moon passes directly above the lower-altitude object. The Moon exerts a greater upward pull on the lower-altitude object, slowing its descent slightly more than it slows the descent of the higher-altitude object.

0Thomas9y

I don't know. This Moon is a terrible idea, but it is real. The Moon is there. A solution, I don't exactly love, but what can I do. Can you make it without the Moon?

0skeltoac9y

You don't seem to prefer aerodynamic solutions but they are abundant so here's another one. Orientation is unspecified so we can drop one object right-side-up and drop the other upside-down. A shape can be designed such that both orientations are stable (neither will switch orientations during free-fall) and such that one orientation has a different ballistic coefficient, creating a different terminal velocity. This could be accomplished with fan blades or pitot tubes of different sizes or protruding at different angles, converting different amounts of kinetic energy to heat depending on the direction of airflow.

0indexador29y

The thing that brings my attention is the phrase "without any initial relative velocity against the planet". They might not move relative to the planet, but Earth is not an inertial reference frame and is rotating, so bodies in different latitudes would have different speeds in relation to an inertial referential.

0Thomas9y

This might give some ideas to someone. But not very directly, I think.

0garabik9y

My first thought was that B reaches terminal velocity and that's it, but the object A is dropped from substantially higher altitude, picks up speed much higher than the terminal velocity and the atmosphere won't slow it down enough, I do not feel like oing the math, but there is a simpler solution: jnvg sbe n jnir naq gvzr gur qebc va fhpu n jnl gung bowrpg N, orvat uvture ol yrff guna gur jnir urvtug, uvgf gur perfg bs gur jnir.

0Thomas9y

There are no such special conditions for A and another special conditions for B. The sea and the air are roughly equal for both.

0garabik9y

Well, if you said "the sea is rough equally for both of them" it would be obvious:-) Another idea: A ebgngrf. Gur Zntahf rssrpg cebivqrf yvsg naq fybjf qbja gur snyy.

0Thomas9y

No, they both rotate or neither one rotates. They are equal, so the same rotation must be assumed. Their initial places are different and any difference only comes from that fact. Still, an interesting suggestion.

0garabik9y

If both rotate (I assume the same angular velocity) , what can be said about the direction of their axes of rotation? Another idea: Gurl ner zntargvp, pybfr rabhtu gung gurl nggenpg gurzfryirf, fgvpx gbtrgure naq gur ubevmbagny nflzrgel pnhfrf gur bowrpgf gb ghzoyr naq gur uvture bar pbzrf qbja svefg.

0Thomas9y

This one does not need air-breaking. I like it! But instead of magnetism, the gravity may work even better. Two massive objects with non-negligible gravity between themselves. That's my favorite idea.

0garabik9y

If their gravity is significant enough, then it is incorrect to describe that they splash into the Atlantic - it's the Atlantic that splashes into them. I'd prefer solutions that do not destroy the Earth :-)

0Thomas9y

Two giant golden balls, dropped somewhere bellow the geosynchronous orbit might do the trick of a little orbiting around each other and then splashing into the ocean, one after another. That might cause some damage, but the Earth would survive as a planet. Rather costly and not environment friendly solution.

0Lumifer9y

What do you mean "costly", we end up with two giant golden balls :-D

0garabik9y

Or two ordinary small balls, one dropped from just above the geosynchronous orbit, the second one from far above the orbit. While the first one slowly drifts away to the space, the second shoots away, makes a complete (retrograde) orbit around Sun and splashes into the Atlantic while the first ball is still drifting... Requires some careful timing, though.

0Thomas9y

This is true, but those Moon or Sun solutions aren't my favorite. Moon, Sun, Jupiter and so on are external agents I've forgotten to explicitly forbid. Next time, I'll be even more careful when posting a problem. :-)

0Manfred9y

Airplanes dropped in different orientations, or in a way that's sensitive to initial conditions and leads to B gliding while A stalls. B is dropped from right above a passing eagle and gets carried off to Mordor. They're "dropped" far out past geostationary orbit so that "stationary relative to the planet" in fact means that they're flung off into space, and only reach Earth by getting slingshotted around other planets. Both are dropped over Brazil with notes to please throw them into the Atlantic, and A is dropped so that its coriolis motion as it falls will push it to a more visible area. They're microscopic black holes dropped from the other side of the earth.

0Thomas9y

There is some wit here, but no proper solution.

0Manfred9y

Since you clearly have something in mind, once you reveal it, are we going to go "Oh, yeah, that's much more sensible than the gliders that are dropped near the boundary of glide vs. stall air pressure," or are we going to go "well, that's arbitrary." Rigid hot-air-balloon shapes that start out at 1500 Celsius and fall to earth once they are no longer keeping the air under them hot. Seed crystals in a hailstorm. Any object that falls faster if broken and will break if dropped from the higher altitude. Solid-state electrostatic thrusters pointed downward, that arc and fail if the pressure is too high. Spinning propeller craft thrusting downward that undergo a laminar to turbulent transition if the pressure is too high.

0Thomas9y

As Lumifer said, "freefall" and as the initial conditions say - rigid bodies.

0Lumifer9y

The problem specified "freefall", so thrusters are out. But I agree that it's underspecified -- there are way too many things which fit so we are reduced to guessing what Thomas had in mind.

0Thomas9y

It is not what I have in mind. Anything goes, which does not break the initial conditions.

0Lumifer9y

The initial conditions did not forbid dropping object A into a downdraft and object B into an updraft :-) But here is another attempt: objects A and B open parachutes 3 seconds after passing altitude X. Object B starts at altitude X, accelerates from zero for three seconds, and then radically slows down. Object A starts higher, so when it passes altitude X it is already going fast and so in three seconds is capable of passing B which is already braked by a parachute.

0Thomas9y

Yes, well. There is some wit here again. The best solution I have in mind don't require an atmosphere at all. Well, maybe just for the sake of the liquid ocean water. Which is only for the sake of "a mountain and a valley soulution" prevention.

0gjm9y

If this scenario is actually possible then it seems like the reason should be that the thing dropped from higher up gets to accelerate faster at first due to the thinner atmosphere. However, I've tried quite a lot of toy examples with different dependencies of air resistance on height and on speed, and none of them showed the trailing object ever quite catching up; unless I've screwed up or there's some other thing going on (relating perhaps to the earth's magnetic field or solar wind or something, but these seem like desperate longshots), either this doesn't actually happen or it happens only when the circumstances are just right.

0Thomas9y

It should always happen, when there are no extreme conditions which would prevent it.

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Open thread, Feb. 06 - Feb. 12, 2017 — LessWrong