The Space Doctor’s Big Idea
newyorker.com
newyorker.com
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."
What does this refer to?
> 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.
https://en.wikipedia.org/wiki/Gravitational_lensing_formalis...
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.
Natural languages are not precise, and they lead to misunderstandings.
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.
It's still math.
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.
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.
https://archive.org/stream/DifferentialEquations_91/Piaggio-...
> students are required to demonstrate the ability to read mathematics in French, German, or Russian by passing a two-hour, written language examination.
This preview on Google Books [ https://books.google.com.sg/books?id=7zFalCF_LiEC&printsec=f... ] appears to show it starts from basic mathematical principles and builds on from that.
> 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!
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.
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.
"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."
http://www.gatesnotes.com/Books/Thing-Explainer
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.
The first example I saw of this was this video: https://www.youtube.com/watch?v=2p_8gx-XHJo -- and I found it very frustrating to listen to.
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.
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.)
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.
So I guess this should be Theory of relativity explained using the 1000 most common English words and one additional word :)
But still I'm surprised the article didn't pass the updated validator. Perhaps an editor actually made the change?
It was reviewed by Bill Gates recently: http://www.gatesnotes.com/Books/Thing-Explainer
This article is likely an excerpt from that book.
[0] May also apply to other languages.
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.
FTFY ;-)
Bill Gates' review is here: http://www.gatesnotes.com/Books/Thing-Explainer
> 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?
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.
If I'm moving very fast with respect to you, I see your watch running slow, and you see my watch running slow.
So the first paragraph is true, if it's talking about your view - the world around you changes shape, and time outside moves slower, as seen by you.
The second paragraph is true, as seen from Earth, not from the boats.
There is no contradiction because events with identical x-positions do not have identical X-positions.
If you already know what a partial derivative is, see the first paragraph of this: http://mathpages.com/rr/s4-07/4-07.htm
* * *
He said it backwards...
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.
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.