There are various people speculating on the economic significance of this solution, which, to me, is rather missing the point. It's like measuring the significance of the excavation of Tutankhamen's† tomb by the tourist revenues of museums. The point of economics is that it keeps us alive so we can do math and also think in other ways; the point of consciousness is not to make money.I don't think there is any economic significance. They found a closed-form formula, not a manufacturing process. They verified that it produces numerically correct results to 12 significant figures, but typical lens grinding is only accurate to about 100 nm; if your lens is 10 mm thick, that's an error in the 5th significant figure of any coordinate. Calculating a numerical solution to the Wasserman–Wolf problem to 5 significant figures is straightforward, and you could probably do it by hand if you didn't have a computer (although that would involve significant economic cost). In fact, it's not that hard to calculate it to 14 significant figures. The achievement is finding a closed-form solution rather than an iterative numerical approximation.† Or Tutankhaten, as we used to call him.

 > The point of economics is that it keeps us alive so we can do mathThe most hacker news comment I read all year
 It reminded me of a quote from Stephen King [0] "life is not a support system for art; it's the other way around".[0] beautifully rendered as a short comic here https://zenpencils.com/comic/king/
 That's a beautiful comic, thanks for sharing.
 I love it, though. Perhaps the more general statement “the point of economics is that it keeps us alive so we can appreciate beauty” would be more universally agreed to.
 The specificity gives it a funny edge though. If I were a math student I'd print it and put it on my wall.
 That seems like a circular dependency...Can you do economics without math?
 Modern macroeconomists will disagree.
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 It's well known that Soviet Union didn't really have economics
 I notice you don't seem to have dared to say you disagree — would you say that the point of consciousness is to make money?
 There's more to life than either math or money, haha. I think a lot of people might fit something in there about friends, family, or community. Spiritual growth maybe?There's options.
 I venture to say that spiritual growth is part of consciousness — that is, it's "math and thinking in other ways", which is of course what I said above, not "math".As for friends, family, and community, what is it that gives friendship value, if not your conscious experience of the friendship, and your friend's? Could you coherently call something a good friendship if neither friend enjoys it or improves their thinking from it? The same questions generalize to family and community, though in more complex ways.
 Although I agree with your main point (it's closer to the truth that the point of economics is so that we can do mathematics, than the other way around), perhaps it can be refined to incorporate the fact that not all experience is cognitive; not all enjoyment is intellectual. The feeling of joy/bliss/whatever from being with friends and family, of doing a job well, of leaving a legacy, of having good health, dignity, curiosity, material comfort, relationships, spiritual growth, having a good “life story” for oneself / serving some higher purpose etc (everything on “Maslow's hierarchy“), are not always cognitive or even conscious in nature, though some (like curiosity) tend to be.The Greeks used the word eudaimonia for this highest / all-encompassing utility function (the experience that everything is in service of: the “point”); in Indian thought it's called ānanda. But yeah, making money is only a means to it, and not the point. (Even this understanding can get clouded. In Indian thought, “religion” only posits a higher ānanda that can be obtained by experience of the divine, without denying the everyday sorts of joy that resemble it. In Western thought, influenced by the monotheistic religions with their opposition between true and false, the fact that neither money nor comfort is the highest good gets reflected in ideas like “money is the root of all evil” or “Happiness versus Meaning” that tend to vilify them in order to counter our impulses towards them, rather than recognize them as being partial means to some components of happiness. It's fine; whatever works I guess.)PS: Totally offtopic, but thanks for your transcript of Knuth's Web of Stories interview!
 No. But there are things besides money and math. Like photography!
 I thought the point of photography was primarily so that you (people, in general, not necessarily just you individually) could look at the photos, i.e., experience them consciously, and secondarily to consciously experience the process of photography itself. But perhaps you have a different reason for considering photography worthwhile, other than the conscious experience of the photographs and of the photography process? Or do you consider photography to be a good-in-itself, even if nobody ever sees the photos or experiences the process of taking them?
 > i.e., experience them consciously, and secondarily to consciously experience the process of photography itself. > other than the conscious experience of the photographs and of the photography process?Is there a way of unconsciously experiencing these things?
 None that I'm conscious of.
 Hmm, I'm uncomfortable with the conflation of consciousness, awareness, sapience, and cognition.
 Also, most crucially, experience — qualia. How would you formulate the relations among these five possibly different things?
 Sure, various systems can use photographs to automatically do useful stuff like pea sorting even if a person is never aware of individual photos.
 That sounds like a means to making money, not a viable third alternative.
 It’s not just cheaper products, self driving cars are another advantage to machines taking and interpreting their own photos.Extend this to asteroid tracking and it may be the difference between human survival and extinction.
 Again, you are offering ways that photography can be a useful means to an end that we previously accept as good for other reasons, not ways that photography can be a good in itself. Suppose the humans were already extinct; would you then consider it a good in itself for machines to be taking and interpreting photos? Would you set up a video camera with a solar panel in a park, endlessly taking 60 photos per second, then deleting them, because photography is good even if nobody looks at it and it produces nothing else outside of itself?I am fond of the humans and so I would like them to survive, but only because that is a means for them to be conscious, at least in some cases.
 Efficiency can turn something from useless to useful, which means the outcome is not inherently useful.Thus if photography is required and the only thing that makes it possible then it as a means becomes and end to it's self.Consider, in a pure nitrogen environment animals will suffocate under no great distress. The goal has become separated from the result.
 You seem to be unclear on the distinction between means and ends, which is to say, instrumental and terminal values.
 A legacy that lives past humanity seems better than one that does not. If something views or does not view that legacy is effectively irrelevant as humans would never know.PS: As to your final central point, some feel keeping a loved one alive even if they never recover consciousness is a net good.
 Higher quality affordable lenses yield more conscious enjoyment of photographs. Hence the question of economic applicability.
 Your comment seems to be an attempt to answer my questions, but I can't figure out how it relates to them. Do you have a different reason for considering photography worthwhile, other than the conscious experience of the photographs and of the photography process? Or do you consider photography to be a good-in-itself, even if nobody ever sees the photos or experiences the process of taking them?
 Photography can be likened to painting, it's a form of art.
 I just like the smell of the chemicals (yes, I know).
 > It's like measuring the significance of the excavation of Tutankhamen's† tomb> † Or Tutankhaten, as we used to call him.This is a rare case where the name change is original to the foreign subject. Akhenaten, the heretic Pharaoh, threw out the traditional religion of Egypt and replaced it with monotheistic worship of the aten, the sun-disc. This didn't go over well -- after Akhenaten died, the traditional system reestablished itself, various records were "corrected", and Tutankhaten's name was changed, during his own lifetime, to something more traditional. Unlike his father, Tutankhamen didn't have the political power to maintain the heresy.
 Yeah, I meant it's what we called him when he was a kid.
 >The point of economics is that it keeps us alive so we can do mathWell yes, life continuity is not something to subestimate. Thinking derives from perceiving and acting in the world. I agree that the achievement was finding the _closed-form solution_. But it will have a beautiful impact in wealth creation, now and in the future, no doubt. Can't be seen now and who knows when and to what extent this could disrupt optics for the better. Maybe not too much or maybe four decades from now this make possible to start using devices that we can't recognize now. Holodeck, yeah I'm watching you!
 I can't see some of the other comments so maybe someone else has put this out there, but economics Is definitely one of those topics that are interesting and worth thinking about. It's not (just) about money, its about the distribution of resources and the structures that facilitate that distribution. Economic theory certainly can have applications beyond informing world economic policy, not to mention that informing policy is also a good idea.With respect to this solution, I bet it will be great for astronomy, especially superpowered space telescopes that need to squeeze every bit of accuracy out of their projected lifetime. They might also improve optical telescopes but I'm not sure how much there is to improve before running into physical limits. I can't think of any other big impacts off the top of my head, but I bet there are others.Not sure how much of an economic impact this result will ultimately have, and I agree that that's missing the point here, but in general I think asking about the potential economic impact of scientific/technological advances is a prudent line of questioning.
 Couldn't you use the formula to create a correction algorithm?
 A correction algorithm will probably rely more on the shape of the lens than the shape of an 'ideal' lens.A single image also won't technically contain enough information to even allow you to reconstruct the image, but with sparse reconstruction you might be able to get it done.In fact I'm fairly sure people have tried to do exactly that, and phone manufacturers seem pretty willing to throw software at the problem as well, although the latter don't really care much for the method as long as it looks nice.
 The economy is, and always has been, the society.I get that your comments are playful, at least in part, but the thing that makes discoveries worthwhile is usually getting them in the hands of mere mortals.
 Since they put the paper on the arXiv, any mere mortal with internet access can download and read it, and some of them will find that worthwhile.The economy is an important part of society, but only part of it.
 arXiv works because of a combination of abundance and game theory; it's lovely that we all have access to such a tremendous resource, but it's not as though it gets to live "outside" the economy.
 This is phrased as if it were a disagreement with something I have said. Why?
 It might be useful for a massive scale gravitational lens in some post-scarcity future :)It's still incredibly cool that there are solvable problems of this sort still put there.
 Next question: give a formula that describes the best lens taking into account manufacturing tolerance on the lens faces.
 > The point of economics is that it keeps us alive so we can do math and also think in other ways; the point of consciousness is not to make money.The point of consciousness absolutely is to make money - or rather, to improve the organism's efficiency and thereby survivability by making it capable of introspection and self-optimisation.
 It is true that evolution optimizes organisms' efficiency and survivability. Chemical reactions, similarly, optimize the potential energy of assortments of compounds, and gravity optimizes the potential energy of assortments of masses. Would you therefore say that the point of an iron bridge in air is to rust and collapse?An individual human consciousness, its genes, and its memes have different goals which sometimes come into conflict. I suggest you choose sides in these conflicts, and not against yourself.

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