Goodbye Aberration: Physicist Solves 2,000-Year-Old Optical Problem
petapixel.com
petapixel.com
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 most hacker news comment I read all year
Is there a way of unconsciously experiencing these things?
Extend this to asteroid tracking and it may be the difference between human survival and extinction.
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.
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.
PS: As to your final central point, some feel keeping a loved one alive even if they never recover consciousness is a net good.
There's options.
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.
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!
[0] beautifully rendered as a short comic here https://zenpencils.com/comic/king/
Can you do economics without math?
> † 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.
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.
Well 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 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.
The economy is an important part of society, but only part of it.
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.
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.
It's still incredibly cool that there are solvable problems of this sort still put there.
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.
> He then ran to his computer and started programming the idea. When he executed the solution and saw that it worked, he says he jumped all over the place. It is unclear whether he finished eating the Nutella bread.
This is my favorite quote from the article. Soon to be the most famous slice of Nutella bread?
Poof! And the solution materialized. Of course, all the groundwork had been laid. All the neurons primed. Just incredible.
And that formula. Damn.
Why would I think that?
Work hard on it for a while, then leave it for one-two days. More often then not this give a way better end result.
amazing what people think of
...snapped into focus
After placing an ice-cube in my delicious glass of refreshing coca-cola brand carbonated beverage, I yelled Eureka! and jumped out of the bath.
Is that really how it happened? Is it not inconsistent with the pursuit of truth?
Brands exploit this mechanic in language so that any time a, thereto unknown, good has to be addressed, that identification become advertising. It shifts from being a unique identification of an object/item/thing to a conjuring of the ethos/identity that contextualizes that good as being different from all the others (un)like it.
I'm sure the dude was just having some hazelnut spread and that's how they recalls it but us, like them, are getting hacked. Now if you'll excuse me, the rey--, I mean tinfoil, is starting to get itchy, I need to switch it out.
Huh? ‘degenerate set’ being what, the brand placement? I likes me some Semiotics, though not sure what this passage refers to.
In the context of a photography site, brand mentions must be a hazard. The author has no problem name dropping an Ancient Greek, Newton, Leibniz, Huygens. Why not Nutella? Rather than increasing the cognitive gap between the auditor (us) and the subject (2000 year old problem), Nutella seems to take the shining brilliance of those luminaries down a notch and in line with the form of writing—a neutral density filter? Haha. Or maybe it’s just a laugh and some color.
I'm working with this informal idea that there is always a relationship between the audience and the speaker. That relationship define a shared knowledge space.
If I am speaking to a group of my friends and need to refer to my brother the set of identifiers that uniquely conveys his identify to my friends might be {brother, Joe, Joe Blow, brother-man, etc}. Any of those identifiers coming from to me specify exactly one person, my brother. The degeneracy is that they equally identify him to the audience.
If you were not that close to me, and I say "brother", you might wonder if I have more than one brother. If you did not know me at all I might say Dr. Joe Blow to identify him and why he might be relavent in some area of expertise. As the relationship between speaker and and audience grows more distant the set size decreases. Inversely, the context-free uniqueness of the identification provided by the remaining identifiers has to be greater, with proper names maintaining greater uniqueness (sorry to the John Smiths of the world!) than nicknames and so forth.
To return to my point, the scientist in question called it Nutella because he does not have a deep relationship with his audience and that is the most unique way of identifying it. I don't believe he was doing anything atypical or nefarious. If he knew the audience well, he could have just said "breakfast", and they would know exactly what he meant because he has the same thing for breakfast most mornings.
The problem is that brands, unlike most proper names(obviously famous people are an exception), have a greater ethos associated with them. If my brother was named Joe Blow or Jim Deal, my unique referencing of him doesn't do much to color the statement around it. This is contrast to how much extra you get when you call a car a Ferrari vs a grand tourer. My point is that advertisers recognize this linguistic norm and exploit it, this is what brand identity is. As such, just the natural mention of a good becomes advertising.
From your original comment: “...contextualizes that good as being different from all the others (un)like it.”
This is textbook Semiotics. Meaning is not derived from the designation (‘apple’ is the red fruit with the thin skin and firm ...eh flesh. Rather, Apple is not a banana; not a kiwi; not a tomato; not beef; ad infinitum.
All that said I just order an intro book on Semiotics. Interest definitely peeked.
No one says "hazelnut spread", they say Nutella.
No one says "resealable sandwich bags", they say ziploc bags.
TIL what ziploc bags are. Just called "sandwich bags" here. Cling film isn't "sarran wrap" here either. :)
Even then, it may not be. There are plenty of places where Coke has become the generic name for pop, and doesn't necessarily refer to the brand.
Because a spoonful of palm oil and sugar with hazelnut flavoring is tasty?
[0]Just went into the kitchen to check
Everyone says resealable bags. I've never even heard the word ziploc. In New Zealand.
Perhaps no one in New Zealand, but New Zealand has the population of a small US state.
For one thing, Nutella is chocolate flavored. No one would ever even consider calling it "hazelnut spread".
(Compare the consistency of nutella to the consistency of peanut butter.)
Why would your definition be more valid than the manufacturers?
In other words, Brands by definition must be distinct from regular language.
Not really, no. There's no scientific funding riding on your reading this article in a photography magazine.
Specificity is almost always recommended in any creative writing from song lyrics to infotainment like this. It enhances humor and mental imagery, which enhance general enjoyment. That's all that's happening here. Hanlon's razor is your friend.
For anyone unfamiliar: supposedly, while bathing; he suddenly realized the principals of buoyancy. He then jumped out of the bath and ran down the street -- without clothes -- yelling "Eureka!" (I have found it). Not sure if this is true or just a legend, but I doubt we'll ever find out what happened to that Nutella bread either...
The King had order a gold crown, and after receiving it suspected that the goldsmith may have replaced some of the gold with cheaper silver. The King asked Archimedes to figure out if the crown was pure gold.
Archimedes could do that by figuring out its density, but to do that he needed to get the weight of the crown and the volume of the crown. Weight was easy, but he had no idea how to get the volume, other than melting it down and reshaping it into a shape whose volume he could calculate. Naturally, the King wanted Archimedes to answer the question without destroying the crown.
His realization that the volume of water displaced by an object that is more dense than water is equal to the volume of the object gave him a way to get the volume of the crown without harming it.
Shouldn't be too hard to figure out appropriate contact details. :)
Maybe it should have convinced him to procrastinate instead. Now, I know where all my inefficiency is coming from.
In math terms, f:X->X where X is compact and convex, and f is continuous, has a fixed point (exists x_0 in X, f(x_0)=x_0)
Since no one has clearly pointed it out, "¡Madres!" is a multipurpose Mexican expression that rarely has to do with actual motherhood. "Holy crap!" is a good analogy in this case.
https://www.urbandictionary.com/define.php?term=madre https://www.spanishdict.com/translate/madre
The author’s have a paper from March 2019 (in arXiv) that uses the result to build some novel telescope geometries.
[1] https://arxiv.org/abs/1903.11129 "Single lens telescope"
Any reasonable chance of of implications for projective geometry?
I have a strong suspicion that the numerical solution is as precise as needed and the limiting factor is the manufacturing, but I would be interested to hear how this results in something new.
The real boon of this discovery is in designing lenses. For example, the authors have already used it to design a single-lens telescope for the first time [1]. I don't know much about the forefront of optics, but at least in my field having analytical models that you quickly iterate on and use to prime intuition are extremely useful.
Of course it depends on the field. It's a requirement here in the UK to publish a paper to get your PhD (at least I've been led to believe that), and many particle physics students really struggle to manage to fulfill this. On the other hand gravitational wave detectors have a huge amount of unexplored science as there are so many things that we still do not fully understand about the detectors themselves.
Categorically false. I did my physics PhD in the UK and while I did publish a paper, it was not a requirement and I have plenty of friends who did not publish a paper and still got their physics PhD.
That's of course nevermind the effort involved in grokking the book. Especially, if particles are more subdivided than we think/know they are.
Think of it as knowing the rules of the game vs developing strategies for it.
We can build things that deal with unimaginable precision, create new elements, compute with quantum effects, but we don't know why flat things stick together?
The solution is to use combination of a few lens of different glasses, to compensate the differences. It's not easy to design these kind of system, because they must compensante also for other types of aberrations.
More details:
The implication here is that you can build lenses that have a consistent focal plane across their entire surface. A pair of glasses made this way would have crystal clear vision regardless of your 'look' direction (as an example). It also suggests that you could build lenses for lasers that were much more consistent, so a laser projector could project an in focus image from edge to edge rather than "fuzzing out" at the corners.
If there is a top prize in optics these guys clearly deserve it.
"Real world" simulation optics I'm meaning (eg for material design/prototyping), more than gamer oriented. ;)
I wouldn’t be terribly surprised if this result helps indirectly with off-axis aberration, though — a closed-form solution to the spherical aberration problem may make it easier to optimize for lens shapes that minimize other aberrations.
Spherical aberration causes the single point in the center of the object to focus to a different place depending on where the ray hits the lens. This means that the image of that single point is not fully sharp. If you restrict what parts of the lens can be hit by rays from that point (by closing the iris, for example), you reduce the area in the focal plane that the rays hit.
I didn't check out the paper in detail, sounds like the shape of the correction surface depends on the distance to what you're imaging? Does it do so in a non-trivial way? If so, this sounds a bit more like an academic victory, no?
If it's just a mild deformation and offset, then yeah I guess technology similar to adaptive mirrors could work well.
Or maybe they'll find a way to apply it to make better lenses that need less software-based corrections. They struggle a lot not just with clarity at the edges but god rays and glare too.
Like the description of Einstein sitting watching a clock and imagining what it would be like to move towards it as a ray of light
"The author’s have a paper from March 2019 (in arXiv) that uses the result to build some novel telescope geometries."
There are some serious problems when building large telescope lenses; if they get too heavy, they start to deform under their own weight, and non-spherical shapes are hard and expensive to produce.
It would be awesome if this analytical solution inspired improvement in real applications, but I'm cautions about that.
There's a few notable exceptions, like the Lick Observatory, but in terms of impacting the state or progress of astronomy, the research from this article is unlikely to have an impact outside of small scale labs and amateur astronomy.
That's not to say the benefits there won't be appreciable for those who rely on optical telescopes, but you won't see this research make a difference for ground based arrays like NRAO, VLA, or in space telescopes.
Two thoughts:
1) The size of the equation is rather large. Nature tends to like simple equations, I wonder if this equation could be restated in a simpler format and not lose its efficacy. I also wonder if there are still simpler versions that trade off efficacy for degrees of error.
2) If the equation cannot be reduced, then this equation bears looking at from an information preservation perspective, that is, to people who study how the universe preserves information under various conditions, this is one of the equations they should add to their list of equations to study...
But, overall a brilliant, laudable, commendable work with great applications and benefit to society!
Well done!
I fully believe this will be the death of all but professional cameras in 5 years or less. (Yes, I know cameras are already in sharp decline, but I’m talking true death - bankruptcies and firms leaving the market).
Why? What makes you think this will be easier to implement than existing methods?
What am i missing?
I assume that if numerically solving for a correcting shape was burdensome you would model an element using a first surface and a 'dummy' second surface that your software just treats as magically correcting. ... then when you are happy with your design, you go ahead and compute the actual shape for that second surface... or similar.
I would expect a closed form solution to more useful for meta analysis of the problem-- looking at its behaviors (and especially derivatives) in various external cases may suggest interesting and novel optical system designs. Like, "oh, foo changes cubically with with an infinite focal length that means if we could make lenses with cherry flavored unobtanium we could bounce a gravitation particle beam off the main deflector dish!".
This article is alright.
I hope you mean alright alright, and not just _alright_ because I loved that line!
/joke
definitely generated by mathematica
That's some serious precision. I wonder if this would have been possible to calculate on a Pentium?[0] After last week, cloud service providers would be happy for 3 nines.
> Moreover, the solution involved aspherical elements, which are harder to manufacture in a precise way and are thus more costly.
> Their findings were published in the article General Formula for Bi-Aspheric Singlet Lens Design Free of Spherical Aberration, in the journal Applied Optics.
I’m no expert in optics, but that does not sound like the kind of advancement that cheapens lenses, even if the math work is mathematically relevant
- Current solution is expensive because it uses aspherical elements.
- New solution promises cost reduction.
- New solution uses aspherical elements as well.
Either there's some hidden detail that the article fails to mention, or it's claims are overstated. If you actually know about optics, I'd be glad to know which is the true or if I'm missing anything here, otherwise I would appreciate to keep your snarkiness to yourself.
These people solved optical abberation. Even if their work leads to lenses that are twice as expensive as they are today, people whose research, or jobs, rely on perfect optics will be more than happy to pay what it costs to work with those.
Anyone else can wait until one or more companies figures out how to make the manufacturing process cost effective at scale.
But yes, only for applications that care about abberation.
How is it not? The article actually makes that claim:
It would help make better and cheaper to manufacture optical systems in all areas, be it telescopes, microscopes, and everything in between.Madre is used more often in phrases, such as "Madre de dios!", Or "La madre putria," or "Pinche tu madre", or it's used as a formal to refer to one's mother. It's similar in English, such as "On my mother's side", "Mother fucker", "Mother of God!", etc.
In Mexico, "tu madre" can be a general insult, probably shortened from "pinche tu madre", though in English we have a similar vulgar retort of "your mother". As a weird turn on the phrase, "de puta madre" is slang for a good thing.
I'm not aware of an association with brothels in Mexico, but certainly in some Latin American country it could have.