Physicist Solves 2,000-Year-Old Optical Problem (petapixel.com) 153
Mexican physicist Rafael Gonzalez has found the solution to spherical aberration in optical lenses, solving the 2,000-year-old Wasserman-Wolf problem that Isaac Newton himself could not solve. Newton invented a telescope that solved the chromatic aberration, but not the spherical aberration. PetaPixel reports: Fast forward to 2018 when Hector A. Chaparro-Romo, a doctoral student at the National Autonomous University of Mexico (UNAM), who had been trying to solve this problem for 3 years, invited Rafael G. Gonzalez-Acuna, a doctoral student from Tec de Monterrey, to help him solve the problem. At first, Gonzalez did not want to devote resources to what he knew to be a millenary, impossible to solve problem. But upon the insistence of Hector Chaparro, he decided to accept the challenge. After months of working on solving the problem, Rafael Gonzalez recalls, "I remember one morning I was making myself a slice of bread with Nutella, when suddenly, I said out loud: Mothers! It is there!" 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. Afterwards, the duo ran a simulation and calculated the efficacy with 500 rays, and the resulting average satisfaction for all examples was 99.9999999999%. Which, of course, is great news for gear reviewers on YouTube, as they will still be able to argue about the 0.0000000001% of sharpness difference among lens brands. Their findings were published in the journal Applied Optics. They also published an article in Applied Optics that gives an analytical solution to the Levi-Civita problem formulated in 1900. "The Levi-Civita problem, which has existed without a solution for over a century, was also considered a mythical problem by the specialized community," reports PetaPixel.
"In this [algebraic] equation we describe how the shape of the second aspherical surface of the given lens should be given a first surface, which is provided by the user, as well as the object-image distance," explains Gonzalez. "The second surface is such that it corrects all the aberration generated by the first surface, and the spherical aberration is eliminated."
"In this [algebraic] equation we describe how the shape of the second aspherical surface of the given lens should be given a first surface, which is provided by the user, as well as the object-image distance," explains Gonzalez. "The second surface is such that it corrects all the aberration generated by the first surface, and the spherical aberration is eliminated."
![this [algebraic] equation](https://petapixel.com/assets/uploads/2019/07/formula.gif){kind=link}
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Well, I think the idea is now they can do it in realtime with passive optics instead of having to pass a recording through a ffmpeg filter.
But (Score:1)
What the Hell happened to the NUTELLA BREAD???!!!???
Damn it I MUST Know!
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Re: Yeah, so? (Score:5, Funny)
Yeah, instead of aimlessly scribbling for a couple of years and stacking up Nutella they cold have simply asked âoeWhat is the General formula for bi-aspheric singlet lens design free of spherical aberration, pleaseâ from Wolfram Alpha. Besides, even most toddlers know light so itâ(TM)s really a childâ(TM)s play to come up with equations about it. My niece scribbled Maxwell equations on a cereal box just like that, while trying to separate magnets from each other.
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stacking up Nutella
I found those Nutella references strange. It's almost like the physicist is bucking for and advertisement or product advocate deal with Nutella:
"Eat Nutella for breakfast, and you will solve 2,000 year old physics problems!"
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Unfortunately, the article writer completely glossed over how exactly that nutella bread brought the scientist on the path to the solution, which would indeed have been interesting. Now, as it is, the article is a pretty meatless fluff piece, whose contents can be summed up a
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to avoid spherical aberration, use a lens which is not spherical
... and yes, aspheric lenses [wikipedia.org] are a thing, and are commercially available since a while already in prescription glasses and high-end camera lenses. So what exactly did this scientist solve that was not already solved before?
Re: Yeah, so? (Score:5, Informative)
Differently than previous results which knew only specific shapes (and were thus problematic for instance for achromatic aberration), now you can solve the problem for any lense shape.
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Re: Yeah, so? (Score:4, Interesting)
Maybe there was something in the way Nutella spreads on the bread that gave him an idea how to solve the problem? A little bit like Archimedes had his idea about buoyancy in the bathtub, where he could feel it. Or Newton's apple story.
The tacit allusion to the bathtub and apple incidents is deliberate. The writer wants you to place him on a pedestal next to those of Archimedes and Newton.
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The tacit allusion to the bathtub and apple incidents is deliberate. The writer wants you to place him on a pedestal next to those of Archimedes and Newton.
But, with the bathtub and the apple, you get to know the relationship between the event and the discovery. With the nutella, you don't.
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Unfortunately, the article writer completely glossed over how exactly that nutella bread brought the scientist on the path to the solution, which would indeed have been interesting.
It could have nothing whatsoever to do with the Nutella. It was most likely just a moment of clarity, this happens to me on occasion as well. Perform a mundane task (like making a sandwich, take a shower) and your subconscious is able to work out a solution.
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It could have nothing whatsoever to do with the Nutella. It was most likely just a moment of clarity, this happens to me on occasion as well. Perform a mundane task (like making a sandwich, take a shower) and your subconscious is able to work out a solution.
But then, why stress that the was spreading Nutella? Why not just say "while having breakfast"? By being so specific, the article's writer sets up expectations which are then left unanswered. So either he gets sponsorship money from Nutella, or there is indeed a deeper link which the article writer didn't understand when the scientist explained it to him. Neither of the 2 hypothesis are flattering for the article writer :-(
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I doubt it's 13% cocao. Probably more like 10%. Pretty much milk hazelnut, with chocolate added.
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There's a whole subset of computing that deals with this class of problems. Literally child's play.
ORLY? Name it, name a relevant tool, and show us a childishly simple application of it that yields this formula.
And even if you DO manage that ...
One of the strongest observations on invention and science is that breakthroughs often seem obvious, but only AFTER somebody makes them, while people struggle with the issue for years, (or centuries, or millennia) before the insight occurs.
It's even a legal principl
Translation (Score:2, Informative)
The article does not explain it, but that "Mothers!" is equivalent in spanish to a "Holy shit", if anyone was wondering
Thank you (Score:2)
I didn't realize it needed a translation but it did seem pretty odd. Thanks for the clarification!
Re:Translation (Score:4, Informative)
Directly from the article:
(Note: “Madres” is a Spanish word that means, of course, many moms. But in this context it is equivalent to the expression “Holy sh*t!” in English, or, to a lesser extent, “Eureka!” in Greek.)
2000 years old? (Score:3)
Re:2000 years old? (Score:5, Informative)
Re:2000 years old? (Score:5, Funny)
> Who knew?
Diocles
Comment removed (Score:5, Funny)
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He gives Marvin a pain down his left side.
Re: 2000 years old? (Score:4, Funny)
He's someone with a font kerning issue.
Not 2,000 years old (Score:4, Interesting)
Was there a Snellocles? (Score:2)
Did Diocles discover snell's law?
Not really Snell's law (Score:3)
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For lenses, we did not even have an accurate law of refraction
Interesting fact about this: Light always follows the fastest path. The speed of light through glass is slightly lower than speed through air, so the fastest path goes through thinner piece of the glass.
https://en.wikipedia.org/wiki/... [wikipedia.org]
Light does not always take the fastest path (Score:2)
Interesting fact about this: Light always follows the fastest path.
No it does not. If I have a long thin rod with a high refractive index if I shine a light ray down the length of the rod it will go down the length of the rod while the faster path would be to bend through 90 degrees, leave the rod, bend 90 degrees again to travel the length of the rod outside in the air where light travels a lot faster due to the lower refractive index, and then jump back into the rod at the end.
You need to read down in the article you linked. The more correct, modern way to state Ferm
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You need to read down in the article you linked.
I did, but I purposely chose to quote the simpler version for easier understanding, and then added the link for the correct and more detailed explanation.
Re:2000 years old? (Score:5, Informative)
Before the invention of optically clear glass?
Euclid (325 BC–265 BC) wrote about geometrical optics and so did Hero of Alexandria (AD 10–70), Ptolemy actually wrote a book called 'Optics' and by he 980s Ibn Sahl was writing about lenses and focal points. Alhazen (965–1040 AD) who was known in the west under the name 'Alhacen' actually described a 'camera obscura' among other things in his work 'Book of Optics'. That work is credited with having extensively influenced the development of optics in Europe from the 13th century onwards (so if Ben Shapiro ever asks you what Islamic cultures ever contributed to science now you can name at least one very important thing). There is archeological evidence of rock crystal lens production on Gotland during the 10th century. At first these lenses seem to have been mainly for jewellery but the later examples of Viking age lenses evolved into a form that is actually useful for magnification and examination of small objects although I doubt the guys making them were aware of classical writing about Optics, they seem to have been clever enough to notice that these things had some very useful properties. Lenses were being used to create eyeglasses in Germany and Italy as early as the turn of the 12th/13th century.
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Slashdot is meant for opinions and pseudo-reasoning presented as iron clad truth known by super-intellects who need not stoop to logical reasoning or mere facts. The certainty of egomania is the only standard here and by that criteria your post is a failure.
You are in the wrong place and will be modded down to -1,000,000,000. Sorry about that, better luck next time.
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And he didn't even use a car analogy.
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On a side note, it's sadly humorous that, during the dark ages, Islamic scholars sometimes gave refuge to European scholars being hounded due to western religious oppression of scientific ideas - and now, in the present day, it's often Islamic scholars who are forced to flee their home countries for America and Europe in order to escape religious oppression of scientific ideas.
Re: 2000 years old? (Score:2)
"if Ben Shapiro ever asks you what Islamic cultures ever contributed to science now you can name at least one very important thing"
Like most political asides, this is idiotic.
*Nobody* questions the massive contributions the Muslim world has made to science like astronomy, math, biology, medicine.
The point is that they really haven't done anything meaningful since the 15th century.
Which you (again) just sort of proved.
I'm sure Ben would be proud of you.
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Rampant recentism strikes again.
Just imagine how—after not accomplishing much for the last six million years—Mother Nature must be positively itching to introduce Homo chagrinus any day now.
Nuclear facilities in Iran [wikipedia.org]
Homo sapiens epitaph: two legs good, but far too much regression into cat and mouse.
Final grade on project: B+
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According to whom?
Looks like as recently as just a couple of months ago he publicly admitted he was entirely wrong and apologized.
https://www.cnn.com/2019/05/11... [cnn.com]
Why the strawman about Ben Shapiro?
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All he is sorry about is walking out of an interview and not knowing who is interviewer was before accepting the interview.
He didn't apologize for throwing a hissy-fit over being asked a seemingly left-leaning question.
And, he still has not actually answered the question. Even if he is proven wrong on whatever his answer would be, there is exactly no chance he would back down. His alt-right followers have no tolerance for anyone that changes their position on a subject given new information; and Ben knows i
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Triggered much? Show me on the doll where Ben Shapiro touched you. Boy, that must be burning in your brain to bring it up like that. Yikes!
Me? ... triggered? ... Not in the slightest. You on the other hand seem to be outraged at me taking a shot at the central theorem in Shapiro’s case for the innate intellectual superiority of Judeo-Christians and their culture. It only takes one counter example to take down a theorem.
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Shapiro: European cultures did things better, which is why they dominate the world.
You: But once there was an Arab that made minor incremental advances on Greek and Indian science! That proves Europe isn't better!
Please, take a logic class. There are MANY flaws in Shapiro's arguments, but beating up a strawman isn't going to help the discussion.
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Shapiro: European cultures did things better, which is why they dominate the world. You: But once there was an Arab that made minor incremental advances on Greek and Indian science! That proves Europe isn't better!
Please, take a logic class. There are MANY flaws in Shapiro's arguments, but beating up a strawman isn't going to help the discussion.
Firstly I pointed out two Arabs that made major advances to the work of Greek thinkers in the field of mathematics and optics (You wingnuts should really learn how to count) Secondly, Shapiro's theorem is that Arabs never contributed a thing to modern science therefore Judeo-Christian culture is superior to theirs and so are its adherents. Arabs contributed many things to modern science, not only in the field of optics to the point where a lot of what Europeans later did in that field was based on the work
Re: 2000 years old? (Score:5, Informative)
I thought it would be nice to see the awesome contributions of the arab golden age of science being duly celebrated for once.
I was very very wrong.
That museum was a hogwash of propaganda. Every little advance was basically attributed to arab scholars, much in the way you described - some interesting small addition to science was used to justify a mentality of "we did this! we are better!"
The most ridiculous thing was that they seriously claimed that arabs 'discovered' the Americas, because some blurry piece of paper basically had a line on it that might resemble some american coastline, if you look at it in a certain way and have a good imagination.
It was really quite maddening, that the great parts of Arab scientific legacy were abused in that way.
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Those Turks. Everyone knows that the Russians discovered America first!
- Pavel Chekov
Re: 2000 years old? (Score:5, Informative)
Yeah, but the Ottomans got lazy on all the riches they skimmed off of trade between Europe, India and China. Then Europeans decided to build big boats, and the Ottomans suddenly had no money. All their technology (which included firearms superior to European ones) didn't matter in the end.
The Muslim world has a lot of complex problems. Major military defeats are part of it. American imperialism is a BIG part of it. But at the moment, too many Muslim countries are in chaos to the point they can't devote sufficient resources to scientific research. And some of that chaos is local. Not one top tier science university in Dubai? Corruption of Muslim leadership also has its place.
Ottoman firearms were more or less on par with the best in Europe from the 15th century onward. Ottoman Arsenals didn't ever really lose the ability to produce 1st rate firearms until the late 19th century when they became reliant upon imported industrial equipment. In fact their artillery was organisationally superior to much (though not all) of what could be found in Europe into the 17th century. What killed the Ottoman empire was corruption, the rigid conservatism of the feudal society from which the Sultans drew much of their military strength, the Sultan's political weakness vis a vis the nobility, economic stagnation partially due to their societal structure and partly due to shifting trade routes. Their religion had precious little to do with it. I just have issues with the clam that the Islamic cultures contributed nothing to modern science and engineering. The water hammer and the air pump powered steel furnaces copied from the Arabs in Spain took European from beating out a breastplate in a week or two by hand to each water hammer begin able to churn out one breastplate per day. The furnaces made possible the extensive use of high grade metal in wooden ships, which in turn enabled the construction of very large ocean going wooden ships to begin with. In fact, some early Spanish and Portuguese, ship designs with which they made their great discoveries were based on the Arab Dhow and when the Europeans made their discoveries in places like Africa and Asia, they very often found that there were already Arabs and Turks in the places they were 'discovering'. That does not detract from the Europeans' achievements as explorers but it kind of destroys the idea of the superiority of Judeo-Christian culture as an engine for superior levels of scientific discovery, business acumen, boldness, courage and moral superiority in it's adherents.
Re: 2000 years old? (Score:5, Interesting)
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Well it just seemed quite odd to inject that in there out of nowhere. If our culture isn't innately superior, I'd like to see what is. Certainly not Islamic countries that throw people off buildings for being gay. I still do not understand why the Western Left allies with them. They hate your guts and will happily ruin you, just like they did after the 1979 revolution in Iran. You know the history of the leftists there, eh? I bet you don't. Look into it.
Come now - you and I both know why. We have reached peak opposition.
It's how far left feminists can ally with a culture that allows women to be buried in the sand and the neighborhood worthies throw rocks at her until she dies, for the crime of bumping uglies with a guy she shouldn't. And he gets to throw rocks too.
These same feminists will call a press conference in their CEO office to tell us that western women have never been so oppressed.
Make sense? Nope. Until you factor in that the religious
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"It's how far left feminists can ally with a culture that allows women to be buried in the sand and the neighborhood worthies throw rocks at her until she dies, for the crime of bumping uglies with a guy she shouldn't. And he gets to throw rocks too. "
Yeah this lie has been repeated for decades and it doesn't get any closer to the truth.
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"It's how far left feminists can ally with a culture that allows women to be buried in the sand and the neighborhood worthies throw rocks at her until she dies, for the crime of bumping uglies with a guy she shouldn't. And he gets to throw rocks too. "
Yeah this lie has been repeated for decades and it doesn't get any closer to the truth.
Which part is the lie there?
The Western Left doesn't ally with them (Score:3)
The Left is generally all inclusive as long as violence is off the table, and for many Muslims it is. Pretty much all the Abrahamic religions allow and encourage for widespread violence against infidels. The difference between Islam, Judaism and Christianity is how far along they are in rejecting the violent parts of their holy passages.
Islam was pretty well on i
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Black Panthers. Antifa.
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If our culture isn't innately superior, I'd like to see what is. Certainly not Islamic countries that throw people off buildings for being gay.
75 years ago, Europe was executing gay people in gas chambers. Even today, there are places in the United States that encourage the use of electroshock therapy to "cure" them.
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I think you mean hypothesis.
... or conjecture. To most people that's what it is. Shapiro, however, presents his assertion that Islamic cultures never contributed anything to science as a basic fact, an axiom, not a hypothesis or a conjecture.
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https://en.wikipedia.org/wiki/... [wikipedia.org]
The Greeks figured out the Earth was a sphere by looking at shadows....
Still making round lenses? (Score:4, Interesting)
Shouldn't we have something better by now [bbc.com]?
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spherical aberration (you're trying to take light coming from a spherical scene and project it onto a flat image sensor)
Spherical aberration is the distortion you get from using lenses ground with spherical surfaces. https://en.wikipedia.org/wiki/... [wikipedia.org]
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Wait, could we use 6 flat lenses to make 1 Time Cube? Genius!
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Conventional lenses are either done by molding or grinding/polishing. Molding (usually plastic) allows somewhat arbitrary shapes, but the technology and materials to do it very well are only ten or 20 years old and still not universally accepted by premier lens makers. Grinding/polishing (usually glass) produces spherical surfaces unless the process is modified in a carefully controlled manner to produce other shapes -- usually paraboloids or hyperboloids, if I understand correctly.
The lenses proposed by yo
Carl Zeiss Biogon lens (Score:5, Interesting)
Re:Carl Zeiss Biogon lens (Score:5, Interesting)
According to the paper's abstract, the design is an aspheric *singlet* lens -- just one piece of glass ground on two surfaces.
The Zeiss lenses you mention have eight or nine pieces of precisely ground glass. Given that complexity, I doubt very much they were just hacked together by trial-and-error.
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Surprisingly enough, the summary even has the relevant quote:
“In this equation we describe how the shape of the second aspherical surface of the given lens should be given a first surface, which is provided by the user, as well as the object-image distance,” explains González. “The second surface is such that it corrects all the aberration generated by the first surface, and the spherical aberration is eliminated.”
This is a fully general mathematical solution; not a one off numerical approximation. This should be a great help for lens design, and may allow bypassing of IP nonsense.
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Indeed, and the formula is actually shown in the article linked first in the summary - and it is a doozy!!!
I counted thirty odd large pairs of parenthesis and over sixty square-rooted quantities. Hell, I'd give a masters degree in programming to anyone who could write a computer program to compute it, and succeed on the first attempt.
Hardly as elegant as E=mc^2, but impressive in a completely opposite way. Kudos to Rafael Gonzalez for having a brain big enough to contain this formula before breakfast.
I ha
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Nah, give me the LaTeX/TeX source that was used to typeset that and I can turn it into correctly functioning C first time :-)
What I want to know is... (Score:1)
...why isn't an autonomous university solving these problems for itself without human interventionâ½
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Boo Slashdot! No Interrobang support!!!!
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"It is unclear whether he finished eating the Nutella bread."
Have we examined the kitchen? Do we have fingerprint samples for everyone in the house at the time? Is it too late to get a warrant for a sewage DNA test? Answers must be had!
What he really said (Score:5, Funny)
Rafael Gonzalez recalls, "I remember one morning I was making myself a slice of bread with Nutella, when suddenly, I said out loud: Mothers! It is there!"
Yeah right, you know he really said, "Puta madre, ahi está la chingada!"
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I realize you are probably angling for a funny mod, but it kinda dishonors a fellow who has made a great achievement.
It is much more likely he said something like, "Madre mia! Alli esta."
Which sound in Spanish a lot like the English phrase "Whoop! There it is."
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Madre mia!
That sounds like Italian, not Spanish.
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It's the accent. Read it again.
Re: What he really said (Score:2)
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"Mexican physicist Rafael Gonzalez..." (emphasis added)
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English is the same. French as well. All languages.
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Amazing! (Score:1)
Jesus lost his glasses? (Score:2)
Sorry, that was the first optical 'problem' coming to my mind.
The most important question now is: (Score:2)
Would another chocolate hazelnut spread have worked as well or is it just Nutella?
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Yeah, it appears we're getting product placement in scientific discovery announcements now. I wonder how much it costs to have your product name-dropped in a once-in-century scientific discovery?
Nutella is not a "hazelnut spread" (Score:1)
Nutella is a sugar/fat spread. It consists of 56.3% sugar, palm oil, 13% hazel nuts, 8.7% skimmed milk powder.
If you want something that can rightfully be called a hazelnut spread, you'll probably have to make your own. (Some other brands contain like 33% percent hazel nuts, which still isn't gread.)
let there be no cultural impurities (Score:2)
Dirac: I have an equation.
Feynman: Well, I have an equation, too.
Gonzalez: Hey guys, I have one, too!
Feynman: Who are you and where did you come from?
Dirac [dispensing with pleasantries]: So what's yours?
Gonzalez whips a Tensegrity easel out of his pocket, unfurls it with a single snap, and winds the first "paper"-thin sheet of Euro A2 Buckyskin off a very thin spool onto the business end.
* formula.gif [petapixel.com]
Feynman [uneasily]: Nice easel.
Dirac: My, that's a stiff membrane you have there.
Gonzalez [absent mindedly]
Re:Impressive but won't change much (Score:5, Insightful)
I expect them to get much smaller, thinner, and less complex, personally.
Although "discovery by brute force" is a thing that helps in practical terms, an algebraic solution brings the answer into the realm of pure mathematics, where it can result in all kinds of solutions to related problems and - thus - other solutions helping it work even better.
It'll be a while but, if proven, this could easily make tiny lens manufacture cheaper and easier... and could improve everything from observatories to smartphones.
Not because "it gives you the answer we already had anyway", but because "it tells you why that's the answer". That kind of understanding is invaluable, and often leads to all kinds of things that nobody could have conceived by just poking numbers around.
You've only got to be able to, for example, incorporate those equations into a physical model of... say... some material expansion (under heat, pressure, inflation, whatever) and you might well find a correlation that leads to perfect material that can modify the lens shape in use in a controllable fashion while maintaining focus and reducing distortion. Something that "we solved one particular case involving multiple lenses" couldn't without billions of trials and trying to fit it to known materials.
In a world swamped in fibre optical communications and on the cusp of optical processing... this could quite well be a game-changer.
You won't see it specifically. Nobody's going to make a fuss that they use this particular equation to generate a perfect miniature optical processor, but it'll add to a base of knowledge to be combed for such things.
Mathematics is often subtle and powerful, but unlike an awful lot of other areas, literally everything in mathematics is linked to everything else. Solve one problem here, you discover an alternative solution there, which leads to a different interpretation, which helps you solve that previously insoluble equation there. Where other sciences do the same, it's almost invariably because of the mathematics linking them.
Finding a true equation is like finding the actual, original puzzle piece in a jigsaw... with an approximation, you may have been able to sketch from the edges of the surrounding pieces and guess what was in the middle piece, and where those disconnected pieces may be located in order to line up... but finding a true equation is the stuff that makes a dozen already-useful pieces click into place perfectly, provides a huge boost to the overall picture, reveals where you hadn't quite aligned the other pieces, and lets you pull out the pieces that didn't actually fit where you had put them.
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