Yes, it is really readable. I've got an illustrated edition as a teenager, and it is still one of my cherished bookds. BTW, in "non math" knowledge areas it is impressive how readable are the seminal papers.
Math's Syntax and 'universal' language is a great barrier that unlocks the world's knowledge. Applied scientific fields take almost 10-20 years until they sieve/diffuse the knowledge, due to this barrier. (In my perception at least)
I wish math used a pythonesque and popular alternative language, so that very low- or high-level 'assumptions' weren't blocking a greater audience from participating in the field. Although I'm familiar with it, I find it sometimes a little too elitist, because almost every symbol requires an explanation, before it can be used. Javascript and Python have this great balance, I feel is urgently needed in Maths.
I dont get it. Are you saying new scientific fields take decades to become "known", and that this supposed delay is due to... notation? None of these theses make any sense to me.
Also, a notation that is suited to one field (programming), may not be necessarily best suited to another (mathematics). Personally I feel much the opposite of you: mathematical notation is often clean and expressive, while programming language and its string-of-chars constraint makes for much more difficult to understand notation.
>> mathematical notation is often clean and expressive, while programming language and its string-of-chars constraint makes for much more difficult to understand notation.
Yes, it's clean, if you know all symbols. But it's an unnatural mental burden. We think in patterns and structures. Our language should be similar, because what we express with language is unavoidably self-similar.
I'm gratefull for all the replies, as it seems to underline that this thought resonates strongly. Notation hinders understanding and the farther away symbols deviate from structures we use everyday, the stronger. Even though I personally prefer Unicode/Pictograms, it can't be that we have to reinvent Notation evertime that subsums recurring structures in programming, mathematics, physics, chemistry and every other conciously disconnet field in the same way. Because of universal properties I don't know about.
Yes, field specific notation has it's local and inherent beauty, but the price is too high! We can't fix education globally, at least not at this stage of our development. Thus we should drop efforts put into keeping Notations diconnect. It will widen the knowledge gap between the systemically uneducated majority stronger and stronger.
A solution? Biomimicry has always been our strongest weapon! I think nature is also far ahead in adopting a universal and often times visual language, we only acknowledge when we become isolated experts in a narrow sub-field, such that the language reveals itself.
It's acceptable to have rich symbols, if we can't get an universal notation based on a better generalizing (structural?) representation instead. I guess some of you may think about a more readable form of set-theory, others of geometric computing or mathematical manifold theory. Whatever it is that makes nature so efficient in reusing sub- and system-languages via controlling structures is what we should also define, understand, formalize and adopt throughout all fields via government backed efforts. I believe this is more important than I can currently imagine for our long-term future. An universal language, able to describe not only other languages, but also defining properties of complex systems, that's so alien it might work.
I think I've unknowingly stated a probably open mathematical problem. But can't put my finger on it. Can someone help?
PS: Sorry for coming late, deadlines coupled with a awfully slow laptop...
I am very sorry, I wish english was my mother language or I had better writing skills. But you can catch me up off HN, I'd be glad to talk and listen to a fellow mind :)
As the joke goes
Programmer : chooses her variables always different, with a name as explicit as possible
Mathematician : chooses her variables from a handful of greek letters
... from a handful of greek letters that usually already have agreed upon meaning or connotation within her subspecialty. So everyone reading it understands what is going on.
Unfortunately, it doesn't generalize across specialties.
By comparison, the programmer chooses names explicitly based her own understanding and modeling of the problem, which may confuse others.
both approaches have their strengths and weaknesses.
> ... from a handful of greek letters that usually already have agreed upon meaning or connotation within her subspecialty
I think you mean sub-sub-sub-subspecialty. I don't often read mathematics papers but when I do, it's infuriating how people think that [squiggle] has a universally understood meaning when in actual fact there are only a handful of people in the world (most of whom probably work in the same building as the author) who use [squiggle] to mean that.
No, I mean sub-speciality. At least, my experience is nothing like you describe. For the most part, the people who are likely to attend each others conference talks agree on notation. They may, however, disagree with the people down the hall.
Bear in mind, though, the papers are written for that same group. For good or for ill.
Well I guess you could write sum() instead of Σ, and dot() instead of ·, but I’m not sure it would really help people understand it. Do people find Mathematica expressions easier to understand than traditionally formatted equations?
The reason I personally prefer sum() to Σ is I can google "what is a sum". If I Google "what is Σ" I get answers about the greek letter Sigma. If I Google "what is Σ math" it incorrectly says "Standard Deviation". Also if I don't know what Sigma is, it's very hard to ask someone else what the weird uppercase E means.
Putting in "what does the symbol sigma mean" into google (incognito mode) gives the google blurb of:
"In addition to being the 18th letter of the Greek alphabet, sigma also means 'sum' and 'deviation' in the mathematics world. Learn what each symbol looks like and how each formula works."
It first hit is titled,"Sigma Notation - Math is Fun", with the text 'Sigma Notation. Σ This symbol (called Sigma) means "sum up"'
I think learning the names of the Greek letters is not too high a bar to get started on learning physics and math. Fun too. You really need to know the names of things to start to understand them and ask people about them.
I think the reason people like compact formulas is that it is much easier to understand and check a formula if one can have the whole thing in eyes view.
That's part of my point though. You had to know Σ means sigma to search that in the first place. If you search "what does Σ mean" or "what does symbol Σ mean" you get answers for lowercase sigma saying standard deviation.
At the very least it means it takes 2 searches, one to find the name of a symbol, and a second to search using that, sometimes I can't do that if the notation is an image of TeX output. Then it becomes "what does box symbol with line through it mean" or something.
Thankfully StackExchange now renders math notation in a way that can be copy pasted, but still, here's an example I was reading recently that started as an ascii email chain and moved to stackexchange, I feel like it was more easily readable before.
It's still tough to Google that Π(u) is the same as the rect() function
> I think learning the names of the Greek letters is not too high a bar to get started on learning physics and math.
But the original point was that for someone who doesn't know math, writing it in a more english-like notation wouldn't be helpful. But because of search engines it is.
You do get different (and better) results if you search "What is Σ" rather than "why is Σ" or just "Σ". Like the other commenter said, it's better when you'd rather find a forum or SO post matching that title, rather than getting back Google's own answer.
I dont think you and the other response understand.
Google used to conduct a relatively straightforward string matching search. That means if you used words like "what" you could end up with unrelated matches, or lower quality matches, because they would match with the word "what".
Now, bear with me, these days google seems to use some kind if machine learning to suggest results to you based on what others have searched and chosen.
What does this mean, practically? At least two things:
1.Laymen have to think less critically, less technically when searching. Considering google is, for the average person, basically the window to knowledge, I think this is ultimately a disservice to society.
2. Search quality for technical information seems to be declining, now that laymen and non-laymen alike are searching using the same " extra" words and, I may just be projecting a poor understanding of neural nets here, but our technical results end up getting sort of clustered with everything else.
Am I the only one who has this problem with the decline of google search's technical relevance? Maybe I'm doing something wrong...I still think what google has done to make the internet more accessible may be a net harm to society.
Nah, I understand. I had to attend a 1 day class in my university on how to properly use Google and Google Scholar. I also miss some of those operators and tricks.
But nowadays, it's not as simple as just machine learning to understand your query, but the way the information is stored is less and less like a text storage. If I search for something involving "car' it's very likely I'm okay with results containing "sedan", "vehicle", or various brand/model names of cars. I'm also probably fine with "vehcile" or "vehiclle" or "carr" but not "cat". And Google is well aware of this and considers this when building their model.
Furthermore, the way you ask SHOULD change answers, especially because it attempts to automatically answer you at the top of the page. A search for Sigma and What generally means I want to know what it means, how to use it. But a search for "why" should bring up the historical reasoning Sigma was chosen over another letter, or another culture's alphabet entirely. That's too much information to fit into any result for simply "Sigma", and the query is too vague to help pare it down.
I do agree with you though that it is declining for technical information. But I think overall it has gotten much better at becoming a general "window to knowledge" and I think it's worth the tradeoffs.
But this is not common. If you don't know what uppercase sigma refers to, sum is a much better guess than standard deviation of multivatiate normal distribution.
In this case google is probably simply case insensitive.
not to mention that sum() or forall() might mean nothing to people who don't speak English, so for them those would just be another set of things to memorize anyway
