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Comment by sytelus | Hacker News Reader

The issue is that even a little bit of non-technical language can cause loss of precision. A regular person would love if the technical language was watered down and sprinkled with colorful analogies but this is not often helpful to actually attack the problem. The problems in OP link builds on large pyramid of concepts and abstractions all the way starting from numbers. There is no way out than to walk through this hierarchy of concepts one at a time for many years to finally gain understanding of the problem. Sugar coated explanations might make you feel good but don't actually help work on it.

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I understand that and agree 100%. However, what I was trying to say is that for a non-technical person who is trying to understand a concept rather than solving a problem, accuracy is not the main concern. Sometimes you just need to understand the line of reasoning "roughly speaking". and as I said at the end, I understand that this is a set of M.SC. exam question and my issue is not with this pdf specifically.

Take the problem of Integer Factorization, something that I have personally been fascinated by for years. The problem is so ridiculously simple that a 5 year old could understand it. With that said, google for a few wikipedia articles and see the notation and the way it is presented. The non-mathematician does not care about difference of squares or triangular numbers or what.have.you.

It seems to be the case that mathematicians are unable to talk about math without requiring the person they are talking to to have extensive knowledge of the topic. That's IMO why Carl Sagan and Feynman were so great. They could take complex problems and reduce them (read communicate) in a good way that most could understand and reason about without needing to traverse the entirety of the knowledge pyramid. Similarly, that is what Numberphile does so well.

My suggestion would be to slow down when reading math or about math. Let's take Wikipedia's integer factorization for example: https://en.wikipedia.org/wiki/Integer_factorization

First paragraph is:

"In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these integers are further restricted to prime numbers, the process is called prime factorization."

This is a clear and precise statement of the problem. There are some key words that one might need to look up which takes time, but that's what I mean by slowing down.

Be kind and do this for me: Think of yourself as Sara, an average person in society. Put yourself in her shoes. Now click on the following link and scroll down for a bit.

https://en.wikipedia.org/wiki/Factorization

Scroll as slowly as you want/can. Tell me, do you think that this is a good way to communicate to Sara why this problem is of importance? or even better, do you think Sara will ever give a shit if all she can see is that?

If you want to promote a more scientifically literate society, you should not try to render every single person into a scientists. Rather, try introducing scientific thinking into people's every day lives. The only way that will happen is if those who know the sciences learn to communicate better with the rest of us and help us get it into our daily lives.

can you see where I am coming from? I am not annoyed by math or my ignorance toward the topic. I am trying my best to combat it. But the problem I often encounter is that those who know/can rarely speak the same language as those who cannot. Khan Academy grew big because he knew how to communicate, more people should be like him imo.

All your examples of the problem you are talking about are from Wikipedia, but you give multiple examples in your posts of explanations of maths done the right way. Feynman, Khan Academy, Project Euler. So I guess some maths related text is written one way and some is written another way?

Sure. But I hope that you can see how little access the average person have to mathematical concepts unless he/she have had years of formal training. Khan academy, Numberphiles and the likes have done wonders for lots of us out here. But it is still not enough and more needs to be done. Especially when talking about concepts that are new or truths that we constantly "take for granted".

But is Khan Academy really so different to formal training? I mean, who is going to understand a Khan Academy video on solutions to 2nd order linear homogeneous differential equations if they have never learned any algebra? There is language in there that is necessary to explain it that they will have had to learn before.

It would be great for there to be more resources for learning maths outside being officially enrolled in formal education, but I don't think this has anything to do with the language used in mathematics being too terse or obtuse. Lots of good undergrad textbooks are no less understandable than a Khan Academy video, try those instead of Wikipedia.

I think an aspect of the problem is that wikipedia has become a highly technical reference rather than a traditional encyclopedia for a layperson to educate themselves. e.g. Articles often swamp the basic idea with myriad qualifications and connections to other topics.

There's demand for both levels.

I'd also like a wikitorial or wikixtbook... taking a layperson through to solid understanding but I suppose something like Khan is what's needed for that role.

BTW I've found wolfram often better than wikipedia for maths topics.

I agree that there is a demand for both levels. That's why there is also a "Simple English" version of this page. [1]

I agree that discoverability of this feature can be hard, though.

I also miss the fact that this feature is only available to the English language. There could be a "simple article" feature built into the website, I think.

[1] https://simple.wikipedia.org/wiki/Factorization

what the f... is this sorcery?! this thing exists? O_o

If anything, this should be promoted and slapped on every page as a big green button!

Ah! Right on all counts. I have come across this feature before... but (eg) looking at the ordinary wiki page for factorization, I'm not seeing a link to it...

So, to access the user-friendly, non-technical, layperson version is simple, all you need is to know how to edit the url... that's wot you call ironic, that is.

EDIT It's not even linked under "see also"... ok, your remark on it being only english was a tip-off... it's counted as the language "simple english", and is available under the language icon (a funny looking "A" on the left... which I would never have guessed was for languages). I can see that'a a very easy hack to add an alternate version of a page, since that's what languages are already... but IMHO, layperson versions of a page (or even for experts, wanting to just get the gist) are an essential part of wikipedia's mission and purpose.

Re: simple versions in other languages: they could use the same hack, and have (eg) "simple french", "simple japanese" etc, but because it's so important, I'd suggest another explicit level, something like "https://simple.en.m.wikipedia.org/wiki/Factorization" (BTW that's also a mobile url, since I'm on a phone... I'd say, "simple" is just as important).

I understand wikipedia reached a level of completion a few years back, and the organization consequentally changed in character. A push for simple versions of everything coukd revitalize it.

I feel weird posting this link, because I was relatively old when Wikipedia became a thing and still remember what "real" encyclopedias were like.

https://www.britannica.com/topic/algebra/Applications-of-gro...

> Some other fundamental concepts of modern algebra also had their origin in 19th-century work on number theory, particularly in connection with attempts to generalize the theorem of (unique) prime factorization beyond the natural numbers. This theorem asserted that every natural number could be written as a product of its prime factors in a unique way, except perhaps for order (e.g., 24 = 2∙2∙2∙3).

That seems like a pretty good first step to me.

The first sentence is perfectly comprehensible (factorization is decomposing an object into factors which, when multipled together, gives back the original). As for the most of the rest of the article... there's really no reason for the average Sara to care about polynomial factorization at all (unless it's just algebraic manipulation for doing homework).

To promote a scientifically literate society, improve the secondary school curriculum to teach statistics: How does conditional probability work? What do sensitivity and specificity mean? When a poll comes out, what does the margin of error mean? What are some common probability fallacies and how to recognize and avoid them? Etc.

In addition to Khan Academy, also check out the OpenStax textbooks (https://openstax.org/subjects) over the likes of Wikipedia (which is more often a mix of technicalese or a bunch of trivia depending on the subject of the article).

I was with you until you said "there's no reason for the average sarah...unless...homework"

I was the average Sarah, a lot of the people I went to public school with were the below than average sarah and it's the elitist math attitude that's being talked about here that turns kids off from that.

It wasn't until years later, after a career in concept art, then vfx and now programming that I realize..."hey the Fibonacci sequence isn't just some parlor trick for 'math types', it's a thing we can look at to study recursion and integrate in our code to make actual products".

Products that the average sarah uses and maybe even loves and would be supremely interested in learning about but doesn't because she's not a "math person".

I also lament the fact I didn't get into maths and see the beauty of it until years later when it was really too late to get into it at any professional level just because I was always implicitly told I was never meant to be a "math person".

Maybe I'm not, but if we could get more kids into maths, even if they're not geniuses, I think society as a whole and they themselves would greatly benefit from that.

a-fucking-men!

Same thing happened to me. I picked up math at 25 after not having done a single math related thing in almost 10 years. I picked it up after realizing that a lot of the things that I do on daily basis are heavily related to concepts such as triangular numbers and other sequences. My life would have been completely different had my teachers communicated math in better ways than simply saying here is an equation, solve!

It's not elitist to dismiss polynomial factoring, though, just dismissive. I really can't think of any reason to care about the deeper points of polynomial factorization (anything other than repeated trial division), so maybe it's just ignorance on my part.

Stats? Now there's math you can use and is useful in understanding our world! And yet schools prefer to teach calculus in high school over however much stats you can teach without calculus. No one uses the integration bag of tricks in daily life, but everyone gets lied to with numbers.

> Scroll as slowly as you want/can. Tell me, do you think that this is a good way to communicate to Sara why this problem is of importance? or even better, do you think Sara will ever give a shit if all she can see is that?

"In all cases, a product of simpler objects is obtained."

That right there seems like a fairly well-stated explanation of the importance of factorization. As long as you're able to understand that a formula can be composed of objects, which I honestly don't think is that much of an abstraction, the very first paragraph (and in fact the very third sentence, the one that immediately follows two easy-to-understand examples of things that can be factored) tell you that factorization lets you express something in simpler terms.

Wikipedia isn't really meant for introductory articles

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