It doesn't actually find a calculation flaw in Einstein's work.
In a letter to Mt. Wilson observatory, he requested that they point their telescope just off the edge of the sun in full daylight - NOT during an eclipse - to determine whether the stars whose light passed through the sun's gravity would be out of place with respect to the positions of those stars when the sun was not nearby.
He was apparently unaware that to point an observatory scope that close to the sun - I don't recall whether it was the 100" or the 60" - would melt the glass photographic plate.
His calculations of where the stars would be, was wildly inaccurate.
Someone - a Mt. Wilson astronomer I expect but don't really know - had to point out to Einstein that he required an eclipse. I expect someone else had to do the arithmetic for the African eclipse expedition.
In my original post I clearly distinguished symbolic mathematics from arithmetic. I've studied some tensor calculus, while straightforward in principle it is conceptually quite difficult to follow.
Einstein had his tensors right what he did not have correct was "2 + 2". I mean like he'd try that computation then come up with "5".
What a terrible theoretical physicist, not knowing mundane details of astronomy.
While Caltech had a physics laboratory requirement - for everyone, not just the physics majors - there was a way that one could be excused from it, typically as a result of the destruction of expensive equipment.
I don't really know but would be unsurprised were Einstein one such, when he was an undergrad.
It's not well known but it is well documented, that Einstein wrote his four historically-important papers in the simple hope of getting a modest raise in pay.
Patent examiners with doctorates were paid more than examiners who didn't have PhD's, you see. He hoped one of the papers would be accepted as his dissertation.
(E=mC^2 was derived from one of the first four.)
What I've been repeatedly pointing out is that Einstein was appallingly poor at arithmetic.
I am also repeatedly pointing out that his theories are flawless, as far as we can tell through experiment.
When Einstein attempted to predict the experimental results of his theory, while the theory was correct, his predictions were wildly inaccurate, because he was really, really bad at arithmetic.
I'm not just making this up - I learned it in physics class at Caltech, from the president of the Institute.
Caltech is in pasadena, Mt. Wilson overlooks pasadena, the Mt. Wilson Observatory office is in pasadena. Mt. Wilson and Caltech are different organizations but work very closely together.
There's no reason to repeatedly point out that Einstein's theories are flawless. The article specifically says "To most physicists, such discussions are largely irrelevant, as these classic experiments were only the first ones in a long series of tests that showed the complete agreement between observations and predictions from special relativity."
See also http://www.phdcomics.com/comics.php?f=1632 .
There is a common misperception that Einstein was lousy at math. Some sources say it's because the Swiss and German systems both use a numerical scale, but in opposite directions, so what looks like an excellent grade in one is lousy in the others. Others conjecture that it was because he didn't originally think that high mathematics was important for physics, so was considered a lazy student. (See http://www.quora.com/Is-it-true-that-Albert-Einstein-failed-... for various comments.)
It seems that MichaelCrawford is unaware of this misperception, as the claim that Einstein was "appallingly poor at arithmetic" is attributed only be reputation of the speaker of said claim. While that may be a good first step, anyone who was aware of the misperception would know it is necessary to have stronger evidence to remove doubt.
Such evidence does not exist.
Instead, we see that MichaelCrawford doubles down by appealing again to authority, instead of doing a search for "Einstein bad at arithmeic". All 10 of the first hits from Google describe how Einstein was not bad at algebra and how such a belief - even when expressed by a tenured CalTech professor - is simply wrong.
In http://io9.com/the-math-problem-that-had-einstein-asking-for... we even see a case where Einstein did get the math wrong - he had miscalculated coefficient of friction. Had he been "appallingly poor at arithmetic" there would be many more, and much more clear, examples of arithmetic errors.
http://huntingtonblogs.org/2015/03/einstein-and-the-astronom...
Also, by the way, the first result on Google when I searched for it.
As you will see (if you care to read the article) his first calculation was made in 1911, only 3 years after his special relativity publication, and before he even knew about differential geometry.
His second calculation was based on general relativity, and the fact that it predicts twice the angle of his previous calculation is hugely important in the history of science.
Goldberger was quite specific that Einstein asked that the telescope be pointed right at the edge of the sun. I've studied german but not in enough depth that I could translate Einstein's letter.
One arc second is not far from the limit of the resolution of an amateur telescope. While in principle the larger telescopes could resolve finer detail, atmospheric turbulence leads them not to resolve much better - they can see dimmer objects, but not more clearly. It is only in recent years that adaptive optics, faster imaging sensors and more-sophisticated image processing algorithms enable better resolution.
I don't know but expect that when the 1919 expedition confirmed GR, it was done by measuring the positions of multiple stars to determine that their positions were, on the average, out of place. The scope they used was not that big, as they had to carry it out into the African countryside.
The tensor calculus used in GR is quite complex. To reduce that to specific predictions of the star locations would require quite a lot of arithmetic. Back then they would have used logarithm tables and adding machines.
I am willing to concede the Einstein could balance his checkbook, but numerical analysis is hard enough to get right on a modern computer, it is quite hard when done the old-fashioned way, with logarithms and the like. It would be easy to write down a single digit incorrectly, or to not carry the computation out to enough significant figures.
Dr. Goldberg was also quite specific about Einstein's computations - not his theory - being "wildly inaccurate".
Finally, that article brought back many memories for me, some good some bad. I love the Huntington, I love Mt. Wilson but I had a rough time at Caltech.
I was, for a very brief time, a solar astronomer, but at Big Bear Lake.
'Es ware deshalb von grosstem Interesse, bis zu wie groszer Sonnennahe helle Fixsterne bei Anwendung der starksten Vergrosserungen _bei Tage_ (ohne Sonnenfinsternis) gezehen werden konnen.'
My translation:
'It would therefore be of the greatest interest [to know], until how near to the sun bright fixed stars could be observed, under the largest magnification and by day (without solar eclipse).'
One can see venus with the naked eye during the day - but not when it is near the sun.
I expect that a red filter would get rid of some of the scattered atmospheric light. A telescope should be able to see some of the brighter stars during the day.
But to get the scope so near the edge of the sun that you can measure that arc-second displacement, you'd have quite a lot of sunlight entering the telescope. The atmospherically scattered light in that region is quite intense.
One can use an "Occulting Disk" but they are of limited effectiveness. When the sun is in the sky, hold your hand out at arm's length, then block the sun with your thumb; you'll see that the skylight is quite bright around your thumb. That's not from the solar corona - not much of it - but from atmospheric scattering.
http://www.todayifoundout.com/index.php/2011/12/albert-einst...
Einstein was, in fact, so good at math that at 15 he passed that portion of a university entrance examination (although he failed every other subject).
A very real example of a super-intelligent human, which normal people regard as "learning disabilities" due to their own inability to comprehend or cope that intelligence - as has been demonstrated in the comments section of this post.
I aced the junior year E&M final without ever having shown up to class nor attempted any of the problem sets. I don't recall sitting for a midterm exam, maybe I spaced it.
I also successfully petitioned for credit for UCSC's optics class. In my written narrative evaluation, Dr. Scherr said that while I got the correct answers, my derivations were quite different from those of the other students.
I know quite a lot about Einstein as a person.
Clearly not. According to Maria, Einstein had immense aptitude for applied arithmetic by age 12.
> My point being that I know quite a lot about relativity.
How is your knowledge of relativity relevant to the discussion? The topic of Einstein's arithmetic aptitude was raised.
The original protest to my comment about Einstein's arithmetic, made the claim that I was in agreement with the eccentrics who claim Einstein's theories are incorrect.
To the extent that they have been verified by experiment, I know that the theories are correct. We haven't found gravitational waves yet, which is a concern but all other experiments have worked out.
Not my emphasis on experiment: even when theoretical derivations, proofs and the like are flawlessly carried out, that doesn't mean that they correspond with physical reality.
That's the whole point of being a physics researcher. That's not well understood by most members of the public; the exciting thing about physics is to prove a theorist wrong through experiment. It's helpful to prove a theorist right, but uninteresting to do so.
My protest with that comment about his arithmetic is that it is incorrect.
> You are being disingenuous.
No I am not. I am pointing out that you bringing up your educational level is completely irrelevant to the argument. Your education about Einstein's work has absolutely no bearing on your potential knowledge about his person or arithmetic ability - you are setting yourself up as an authority in a plea to authority. I'd take his sister, Maria's, word about his arithmetic ability over yours - regardless of your degree.
Your degree, profession, hobby, articles and so forth (that you keep bringing up out of context) hold absolutely no authority in that original assertion that you made. Being a theoretical physicist does not make you right about everything, even on matters about the physicists who pioneered fields that you are an expert on.
It is you who is being disingenuous by attempting to diminish other people's intelligence by explaining how you are more intelligent than them by virtue of your talent in physics - I can't fathom any other reason why you would bring up that irrelevant information.
I never said that you are stupid, I said that you are wrong. If you believe that you are right because you are a physicist then you are most certainly a fool (which is still different from stupid).
He and I blame her for being a control freak. I didn't want to come right out and say so to her face.
I figured it would make peace between my friend and his business partner were I to move out of her house.
I read lots of articles - that's why i hang at hacker news.
I write them too.
While I haven't exactly studied general relativity in a formal way I've attended quite a few talks on it by cosmologists and the like.
I was an astronomy major at Caltech, but switched to Physics when I realized I prefer to build telescopes rather than look through them. Astronomers don't build telescopes; Opticians do that. However Physicists commonly build their own experimental apparatus.
I've spent years trying to diagnose it. I've got some theories but nothing conclusive. It seems to help if I do something like:
$ sudo ping -f -c 1000 www.nytimes.com
Stop making embarrassing excuses and just read the article.
I can see the problem when I do a traceroute.
Tonight's activity leads me to believe my cyberstalking friend from Kuro5hin has finally turned up.
It's hard to say, he's generally anonymous.
Regular users voted you down because you backed controversial claims by appeal to authority or your education.
Also, you wrote comments without reading the article, which is usually considered bad here.
Oddly she is completely cool with using webmail from cybercafes - she travels quite a lot.
Mom isn't stupid, she only acts that way.
The original document is 185512 bytes. The download can be read locally in 'links' with no additional network connections. At 28.8Kpbs that's a bit over a minute. Even with a noisy connection, that's well under the 21 minute gap pointed out elsewhere between your posts.
There is no reason to drag your mother's beliefs into this. Simply stop at "I don't have good internet access." All else is needlessly placing the blame or shifting the focus elsewhere ... that being your willingness to completely ignore the topic and instead name-drop your own history, connections to authority, and personal beliefs - even when they have no basis in fact.
Opthalmologists diagnose and treat disease of the eyes. An optometrist can perform an opthalmological exam but cannot prescribe medicine nor practice eyeball surgery.
optician ɒpˈtɪʃ(ə)n/Submit nounBRITISH a person qualified to prescribe and dispense glasses and contact lenses, and to detect eye diseases ( ophthalmic optician ) or to make and supply glasses and contact lenses ( dispensing optician ). US a dispensing optician.
There are some good reasons one requires a professional prescription from eyeglasses; if you wear the wrong lenses for any length of time, it can screw up your eyesight. Although the effect is commonly temporary it _can_ be debilitating.
So a dispensing optician would be someone who sells eyeglasses, given a prescription from an optometrist or an opthalmologist.
It is quite definitely the case that opticians make telescopes. From time to time I call myself an astronomical optician. I don't grind glass much anymore but I am quite good at making astronomical telescope optics.
There is a great deal of difference between symbolic mathematics - calculus and the like - and arithmetic.
While not as bad as Einstein, I'm very poor at arithmetic as well.