Still not as good as "Einstein's Theory of Relativity in Words of Four Letters or Less". Excerpt follows:
A few more of us got it, then. But most of us just said, "What are you two on? Put down the bong and get real! This is way too wild to be true." But they just said, "Just try and see if it isn't true."
So we came up with ways to test old Al's idea, and each time Al hit the gold. His idea had the sun's rays a tiny bit more red than what Izzy said. They were. His idea put Mars a tiny bit off from how Izzy had Mars. It was.
The big one, the one that got told over and over, was the one with the dark-at-day time. You know, when the moon gets in the way of the sun. At that time you can get a real good look at a star when it's up next to the sun. (Next to it in the sky, that is. Not next to it for real. You know what I mean.) They went off and got a good look at a star that was very near the sun, and then they used a book to see just what spot that star was in. You see, the rays from the star pass so near the sun that they get bent, on the way to us. Old Al, his idea said just how much the rays get bent. With Izzy, the rays get bent, too, but only by half as much. So they took a look at the star, and they took at look at the big book, and ... well, I'll bet you can tell me as well as I can tell you just how far off that star was.
A-yup.
And then all of us, we all just sat back and said: "Whoa."
Newtonian gravitational lensing (not sure if that is an actual term). Newton's gravity could be applied to photons to get some lensing, but this predicted was half of that predicted with general relativity
> A naive application of Newtonian gravity can yield exactly half this value, where the light ray is assumed as a massed particle and scattered by the gravitational potential well.
I think you absolutely need mathematics to understand the theory of relativity.
Freeman Dyson writes when he was a child "I had read some of the popular literature about Einstein and relativity, and had found it very unsatisfying. Always when I thought I was getting close to the heart of the matter, the author would say, 'But if you really want to understand Einstein you have to understand differential equations,' or words to that effect." Later on, he goes on to say how he ordered Differential Equations by H. T. Piaggio with over seven hundred problems, most of which he solved over Christmas vacation. Then when he attempted Peter Eddington's Mathematical Theory of Relativity, it came very easily after the differential equations practice.
Peter Collier wrote his beautiful "A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity" out of a similar desire... in the introduction he mentions that as a kid he always thought relativity was easy to understand but later came to realize you really can't fully appreciate it without the necessary math. So he sat down, took a year off (if I remember correctly) and wrote this book. It's beautiful and enlightening.
To be fair, "just" reading Russian isn't that hard. A grammar textbook and a dictionary gets me through polyphonic greek lit and modern german lit. Try it! You might be surprised at how easy your brain will pick it up.
I think this is actually pretty common for graduate students of mathematics.
> students are required to demonstrate the ability to read mathematics in French, German, or Russian by passing a two-hour, written language examination.
I'm considering tackling this book: "Einstein's Theory: A Rigorous Introduction for the Mathematically Untrained" by Øyvind Grøn and Arne Næss which claims to provide "an introduction to the theory of relativity and the mathematics used in its processes".
Stipulating that "understand" can cover a lot of territory, one can perhaps develop a surface and somewhat metaphorical understanding of aspects of modern physics without math. However, you're almost certainly right that any deep understanding of, say, the standard model or relativity is deeply rooted in the math.
But math is just a bunch of ideas expressed in a very efficient notation. All those notational squiggles represent ideas, and ideas can also be represented with words. It would be much less efficient, but anything explained by math should be able to be explained by words.
I had a girlfriend who insisted that "two plus two equals four" was a better expression than "2+2=4", but then she also had trouble with any concepts past algebra (and most of algebra for that matter). The notation is efficient and precise. English, and most other languages, are not. We may be able to express the idea of relativity or Newtonian mechanics or anything else in words, but the base concepts end up requiring us to move into a more expressive and precise language when we want to understand and apply (which today is mathematics expressed with the notations of algebra, trigonometry and calculus).
Math is a great example of how notation is sooo important. Doing math with roman numerals is.... possible, sure. But for pretty much any math that's worth anything, it's just a bad notation. It obscures what's going on and makes it harder to mentally deal with. Notation is a critical tool of thought.
Absolutely. The same is also true of programming, music, and natural languages. Probably nearly every discipline that uses its own notation and significantly divergent (from the primary natural language) nomenclature sees a major boost in understanding and expressivity by using custom notations and language.
Re programming: Some languages are simply better at expressing certain types of programs than others, C may be great, but it gets pretty hairy when you try to use it in certain parallel/concurrent coding contexts (i.e., you're probably using a lot of extra libraries and tooling).
Re music: Could you imagine expressing any piece of significant length or complexity in plain English? Even a mathematical (concise and precise) symbolic language would prove difficult, compared to the visual and multi-dimensional notation customarily used. (At least for reading, a case could possibly be made for more expressive and concise notations for writing musical pieces.)
Re natural languages: This is why we borrow so many words in English (and other languages, I'm sure) from elsewhere. A larger set of words allows us to produce more expressive and nuanced statements and questions.
In principle, yes, but in practice, no. Tools let us think previously unthinkable thoughts. See Bret Victor's Media for Thinking the Unthinkable [1], where he quotes al-Khwarizmi from the ninth century:
What is the square which when taken with ten of its roots will give a sum of thirty nine? Now the roots in the problem before us are ten. Therefore take five, which multiplied by itself gives twenty five, and amount you add to thirty nine to give sixty four. Having taken the square root of this which is eight, subtract from this half the roots, five leaving three. The number three represents one root of this square, which itself, of course, is nine. Nine therefore gives the square.
He's solving x^2+10x = 39 by completing the square.
You don't have to use those words. For instance, for
n >> k >> ln(n) >> 1,
he says "Specifically, we require n much greater than k much greater than log n much greater than one", and says it's unwieldy. Well, if you say it like that, then it is.
"Specifically, we require than the magnitudes of n, k, log n, and one be in decreasing order with significant distance between each."
Not a problem. Just don't try to read notation literally in the order it's written.
The Greeks did that for a while, before the efficient notation was invented. It didn't work out too well, the explanations get very complex very quickly and it's hard to hold all the facts in your head without some convenient shorthand.
Thank you for finding it. I was interested in seeing how difficult the problems were. The first page does seem it requires knowledge of calculus and partial derivatives. The problems he referred to are of the "Examples for Solution" kind like the one on page 3. For motivation, Dyson also said "The difference between a text without problems and a text with problems is like the difference between learning to read a language and learning to speak it. I intended to speak the language of Einstein, and so I worked my way through the problems. I started at six in the morning and stopped at ten in the evening, with short breaks for meals. I averaged fourteen hours a day. Never have a I enjoyed a vacation more."
Don't dismiss it so early. I'm reading it and it's very clear up to now. Just do the exercises. Anything in particular you find challenging on page one?
I guess this comment probably comes up every time Munroe's common-word pieces come up, but I can't help but feeling like you only really understand (or care) about the article if you already know enough about relativity.
> The first idea is called the special idea
No, it's not. Relaxing the rules to use key words (especially proper nouns) would go a long way. You can call it Special Relativity and still "explain relativity using only common words", can't you?
The result is that instead of an article explaining relativity, you end up with an article about relativity translated into a common-word subset of English.
Of course, I do enjoy decoding into normal English in my head as I read!
>> Of course, I do enjoy decoding into normal English in my head as I read!
I enjoy trying to minimize the amount of decoding I need to understand it. Only when I was about 2/3 of the way through did I realize it wasn't just someone using Munroe's style, but that he was actually the author. His ability to do this is probably unique.
I find I really like the labels "the special idea", and "the big idea." I like it because it introduces the nature of the theory quite approachably, where a theory is at it's heart an idea or a concept. Then, by labeling one "special" and on "big", the relationship between the two is immediately obvious; we see that one idea is covering a smaller but more particular area, while the other idea covers a larger but potentially less-special and more general area.
The piece isn't as "strictly accurate" as it could be, but that's the point. By making something approachable you'll hook into many more minds than otherwise, and the knowledge of the reader that "this is not all, there is more to learn" is powerful bait for the curious.
Bill Gates recently reviewed Munroe's "Thing Explainer" (a book consisting entirely of explanations written in this style), and in his closing paragraphs states the following:
"If I have a criticism of Thing Explainer, it’s that the clever concept sometimes gets in the way of clarity. Occasionally I found myself wishing that Munroe had allowed himself a few more terms—“Mars” instead of “red world,” or “helium” instead of “funny voice air.”
Of course, that would defeat the purpose of the book. And Munroe himself is aware of the tension. In “Page Before the Book Starts”—a.k.a. the introduction—he acknowledges that some terminology is inescapable. “To really learn about things, you need help from other people, and if you want to understand those people, you need to know what they mean by the words they use. You also need to know what things are called so you can ask questions about them. But there are lots of other books that explain what things are called. This book explains what they do.”
And it does that beautifully. Thing Explainer is filled with cool basic knowledge about how the world works. If one of Munroe’s drawings inspires you to go learn more about a subject—including a few extra terms—then he will have done his job. He has written a wonderful guide for curious minds."
I completely agree. Things written in this style occasionally start to feel a bit clumsy, but the fact that my curiosity has been piqued to delve deeper into a given topic is more than worth it.
This idea of explaining complicated things using only the most common words is horseshit. I don't know if that is exactly what this article was trying to do, but it's very annoying, and makes it even harder to understand.
A fun exercise in 'constrained' writing about a complex topic.
However making that claim that it 'explained' Relativity is not valid in any reasonable sense.
I found the reliance on keeping to the 1000 most commonly used words to be actually fairly painful to read thru to the end and even harder to understand.
Perhaps "Relativity as explained to a 6 year old" might make it more accessible. A 6 year old has a vocabulary of ~5000 to 10000 words (for reference) and being able to take these "verbal shortcuts" aka words would make for better understanding.
I have never before seen a popularized attempt to explain things like light bending that managed to get things right. He even took time to mention that the popularized image of a sheet of rubber with a ball in it is an incomplete way to think about things.
If it does not match your previous understanding of the topic, I'd suggest reading it again. The only better explanations that I've seen involve tensor calculus.
I read the previous comment not as saying that this explanation was wrong, but that it's just unlikely to be truly enlightening to someone who didn't already know the subject reasonably well. I'm on the fence about whether I agree: the cognitive load of interpreting the odd phrasing certainly does compound the cognitive load of understanding the deeply non-intuitive physics.
This is quite a good presentation of the topic (or, parts of it), but if clarity of understanding were the primary goal you could probably do substantially better by translating it at least partway back into ordinary language. (But then, fewer people might be intrigued or entertained enough to read that version. So I'm not really complaining.)
It is worth pointing out that only about 10% of Mercury's parahelion shift is due to the effects of general relativity. The other 90% are due to gravitational influence of the other planets. It is really quite remarkable that astronomers of the 1800s made precise enough observations to be able to tell that the parahelion shift was not entirely explained by known objects in the solar system (since the effect is on the order of 10%, you have to know the mass and position of every other major object in the solar system to about that accuracy to be able to tell).
I believe this was posted recently, or linked like I'm doing now in a comment. Scientists in the 1800s tried to explain that 10% with a hypothetical 10th planet within Mercury's orbit.
I ran the entire text of this article through XKCD's simple writer tool (http://xkcd.com/simplewriter/) and it pointed out that "movement" is not among the 1000 most common English words. The word "movement" is used exactly once in this article.
So I guess this should be Theory of relativity explained using the 1000 most common English words and one additional word :)
True, though Munroe has been quite liberal about word derivations, and '-ment' is a somewhat salient morpheme in English, despite not being very productive.
But still I'm surprised the article didn't pass the updated validator. Perhaps an editor actually made the change?
I found it very easy to read (as in understand), but very hard to read (as in finish), because I'm a bit sleep deprived at the moment and it was putting me to sleep.
It would be interesting to compare explanations like this[1] to mostly equivalent explanations as they would traditionally be presented for learning on a few topics I'm not familiar with to see if the concepts conveyed came across better.
1: With footnotes for specific terms so the jargon can be linked.
Which shows part of the problem of this approach: The word doctor is in the top 1000 words in its usage for "medical doctors" but it's not in the top 1000 words in its usage as a reference to PhD graduates.
Is this a typo, or just a misunderstanding on my part? These two quotes seem to be diametrically opposed in their explanation of Special Relativity in two parts of the article.
> When you go fast, he said, the world around you changes shape, and time outside starts moving slower.
> Since the boats are going fast, the space doctor’s special idea says that their watches will run a little slower than the ones on Earth.
Shouldn't time outside start moving faster in the first quote?
That's the beauty of relativity, and why it is called relativity: it's all relative.
When you go fast, and look outside, it looks like it is the outside that is moving fast (unless you are experiencing acceleration, at which point General Relativity kicks in). Therefore, to you, it looks like time outside is moving slower.
When the space boats are doing their thing, to us on the outside it looks like they are moving fast. Therefore, to us, it looks like time for them is moving slower.
I think your watch is slow and you think mine is slow in the following sense. For each of many events, I record their time t and position x while you, moving relative to me at constant velocity, observe a different time T and position X. Between two events with the same X-value, such as ticks of your pocket watch, the difference in t-times is larger than the difference in T-times by a factor gamma. Conversely, between two events with the same x-position, such as ticks of my pocket watch, the difference in T-times is larger than the difference in t-times by that same factor gamma.
There is no contradiction because events with identical x-positions do not have identical X-positions.
Was it? Not sure. It's too new-agey and commercialized for me, so I never checked. Blogger and Jekyll-github all the way! Perhaps if someone leveraged those technologies well, you actually would have source control for essays.
He's also done a similar piece explaining how rockets work using only the thousand most common words in English. The one detail that I remember is that apparently "thousand" is not one of the thousand most common words, as it was rendered as "ten hundred".
For a layman's mathematical understanding of relativity I recommend "Why does E=mc^2" by brian cox and jeff forshaw, which explains both the theory and why the equations used to describe the theory, well, describe the theory. It does it all with a nice just-so narrative that builds on physics from galileo all the way through to einstein and ends up at particle physics. It's just a very good book.
"If you’re in a car, you see watches outside the car go slower. They only go a little slower, so you wouldn’t notice it in your normal life; it takes the best watches in the world to even tell that it’s happening. But it really does happen."
The crazy thing about special relativity is that from the perspective of the observer in the car, they're sitting still and everyone else is moving. That means that the observer in the car will see the watches of people on the sidewalk ticking slowly, at the same time that the people on the sidewalk will see the car's clock ticking slowly.
Everyone sees everybody else's watch ticking slowly (unless they appear to be at rest). And yet it all hangs together in a beautifully consistent way. The catch is that moving observers don't just disagree on whose watch is running slow, they also tend to disagree on whether distant clocks are correctly synchronized or not. The disagreements about which clock is ticking too slow always perfectly balance out the disagreements about which clock chimed noon earlier.
In the path from special to general you have to give this point of view up.
More exactly, special relativity starts with the assumption that there are special inertial frames of reference, here is what they look like, and here is what they look like relative to each other.
General relativity starts with arbitrary coordinate systems, and ways of expressing physics such that whatever was measured in one coordinate system can be translated into what should have been measured in another. These coordinate systems can have any mixture of weird effects.
The physics involves something called a metric. General relativity is what falls out if you insist on the following statements:
1. "Locally" things behave like special relativity.
2. Given only low velocity and low mass, things behave like Newtonian gravity.
3. The terms of the metric satisfy a first order differential equation whose definition is independent of the chosen coordinate system.
This gives you general relativity up to an arbitrary constant of integration (the cosmological constant). And in the presence of mass it gives you the prediction that no truly inertial frame of reference exists over any region with matter in it. (The effects of gravity are all due to stuff being non-inertial.)
From that prediction we find that the point of view and understanding from special relativity is only a local approximation. You can't really describe any interesting system that way.
A few more of us got it, then. But most of us just said, "What are you two on? Put down the bong and get real! This is way too wild to be true." But they just said, "Just try and see if it isn't true."
So we came up with ways to test old Al's idea, and each time Al hit the gold. His idea had the sun's rays a tiny bit more red than what Izzy said. They were. His idea put Mars a tiny bit off from how Izzy had Mars. It was.
The big one, the one that got told over and over, was the one with the dark-at-day time. You know, when the moon gets in the way of the sun. At that time you can get a real good look at a star when it's up next to the sun. (Next to it in the sky, that is. Not next to it for real. You know what I mean.) They went off and got a good look at a star that was very near the sun, and then they used a book to see just what spot that star was in. You see, the rays from the star pass so near the sun that they get bent, on the way to us. Old Al, his idea said just how much the rays get bent. With Izzy, the rays get bent, too, but only by half as much. So they took a look at the star, and they took at look at the big book, and ... well, I'll bet you can tell me as well as I can tell you just how far off that star was.
A-yup.
And then all of us, we all just sat back and said: "Whoa."
http://www.muppetlabs.com/~breadbox/txt/al.html