Writing popular mathematics

[ajb]

I am in the middle of writing a short popular review of the theory of supermanifolds. The account is non-technical but does assume some prior knowledge: functions in many variables, plane geometry and coordinates, and a little elementary algebra. I await to see just how accessible the account really is.

 

 

The ideals I have tried to follow are:

 

1. Limit technical language: explain as best as possible any terms that are not "general knowledge".
   
2. No proofs of theorems or even calculations of anything. Just overall ideas.
   
3. Give simple examples (if possible!).
   
4. Use analogy rather than details.
   
5. Suggest applications, but again present no details at all.
   

 

 

Has anyone here tried to write popular mathematics accounts before? How did it go?

 

Any other ideals one should follow? Are their pitfalls to be avoided?

 

Who are the good mathematics communicators and why?

[imatfaal]

I would definitely fall into the category of 'reader of popular mathematics' not 'writer of popular mathematics' but I do have one major bugbear that I think differentiates good popular science writing from bad. I think it is vital to pick a level of sophistication and stick to it - too many books I read start off holding my hand to an annoyingly patronising extent yet later the author seems to forget the non-academic nature of the work and leave me stranded - it's like the cycle lanes that are well marked and separated from the carriage-way on the nice wide open road but disappear as soon as you get to the junction where you might need some help!

 

Who are the good mathematics communicators and why?

 

At a mathematical curiosity and recreational level Martin Gardner was a league apart - and his writing is still fresh and engaging. At a less sophisticated and more historical level to yours (I presume) Simon Singh gets fairly complicated ideas across very well, and does manage to be a steady guide for the whole trip. The best short piece I have read recently was the brief introduction to Tensors by Joseph C Kolecki on NASAs website suggested by Ydoaps. I will search out the link.

[michel123456]

My advice: use graphs, images, pictures to improve communicabilty.

[ajb]

Thank you for the replies.

 

...too many books I read start off holding my hand to an annoyingly patronising extent yet later the author seems to forget the non-academic nature of the work and leave me stranded ...

 

I have found it difficult to get this just right. Any account will get harder as it goes along, hopefully not too hard.

 

My advice: use graphs, images, pictures to improve communicabilty.

 

The use of diagrams and pictures to illustrate an idea or an analogy is a good idea.

 

I may place a version of the overview I have been writing on the arXiv under math.HO (mathematics, history and overview).

 

When or if I do I will announce it.

 

Anyone else care to comment on writing popular mathematics or indeed popular science more generally?

Edited March 16, 2011 by ajb

[michel123456]

(...)Anyone else care to comment on writing popular mathematics or indeed popular science more generally?

 

Oh yes.

1._I remember visiting with our school a museum where some young scientist explaining the way holograms are made with the help of monochromatic lasers (that was in the late 70's), repeating all along the discourse about monochromatic laser. At the end of the presentation he said "however it is now possible to produce coloured holograms". By this way crumbling down the entire understanding.

 

My advice: don't use the word "however".

Keep your discourse coherent.

For example don't begin with "the concept of speed is relative" and within a second "however the speed of light is constant". because the one is the contrary of the other. Hundred years after, scientists still try to explain.

You see what I mean.

 

2. Never take as granted that people agree with you. Your paper must flow like fresh water. If there are rocks (complications), avoid them.

 

3.Some popular science writers use the repeat-it-thirty-times technique on the principle that people will start believing something not on basis of evidence but on basis of repetition. Don't do that. Please.

 

4.The image of the crazy-genius-scientist is associated with distilled humor. Inversely, using humor may induce people to believe you are a (crazy) genius scientist, and swallow anything you write without further questions.

[Xittenn]

I've seen instances of Michels point 1 where it worked in favour of learning. In my example atoms were dismissed in the discourse of the discussion on sets and so too were people being that they were representative of such structures. Now often when the author would cite an example of a given proposition he would then incorporate people and make note of his doing so. He did it in a rather comical fashion and it served to contrast the achieved solidification of thought by incorporating the atoms with the generalization that is set theory. I'm really not sure why this was so important to the author other than to serve as a means of engrossing the reader in the material by making it feel more real. This was kind of weird because it always felt like it served a more fundamental purpose in the pursuit of knowledge.

 

Imagery is everything but as seen in the thread spin this can break down pretty quickly if there is no imagery to be had. I haven't a clue what is normal in terms of popular anything, at best I have read a couple of Scientific American issues and have watched some episodes of Discoveries Daily Planet. I do find it easier to follow a pretty picture, but more often than not I find that in doing so I miss the much more complex reality, and if it is this reality that is what is important it may not always serve the purpose.

 

I suck at developing images of a concepts for others and this frustrates me. I don't envy you! Funny gets you points ....

[ydoaPs]

I am in the middle of writing a short popular review of the theory of supermanifolds. The account is non-technical but does assume some prior knowledge: functions in many variables, plane geometry and coordinates, and a little elementary algebra. I await to see just how accessible the account really is.

 

 

The ideals I have tried to follow are:

 

1. Limit technical language: explain as best as possible any terms that are not "general knowledge".
   
2. No proofs of theorems or even calculations of anything. Just overall ideas.
   
3. Give simple examples (if possible!).
   
4. Use analogy rather than details.
   
5. Suggest applications, but again present no details at all.
   

 

 

Has anyone here tried to write popular mathematics accounts before? How did it go?

 

Any other ideals one should follow? Are their pitfalls to be avoided?

 

Who are the good mathematics communicators and why?

The only popular mathematics I've read recently is the site advocating Tau vice Pi, and I think it was done fairly well and made the subject matter rather accessible.

[ajb]

I would not say that my article is completely "popular". I am aiming it at A-level maths students and "interested amateurs". So they will know a little maths and not be scared off by the few expressions I give. Though quite a lot of it is analogy and pictorial.

 

Doing this right has proved harder than I first thought!

[the tree]

Writing at the knows-some-math level is particularly difficult, you don't want to get bogged down in technicalities but your readers may get irritated if you aren't concise and try to use analogies in place of precision.

 

I'd say any amount of new terms and new notation (new to the reader, obviously) is completely fine on the conditions that:

1. You explain each new thing.
2. You introduce them one at a time. No-one likes reading more than a couple of definitions in a row and then trying to comprehend them all for the first time in the next example.

[ajb]

Just noticed that all my suggestions for further reading are postgraduate level textbooks! May not be very helpful for most people

Edited March 17, 2011 by ajb

[ewmon]

Answer: Examples, especially visual ones.

 

Mathematics easily tends toward the abstract, which disconnects with reality and loses people. So I strongly recommend not expounding on, or explaining, abstracts for too long without real-life examples, preferably visual ones. Lots of people, including scientists, learn visually much more than they care to admit (or even realize).

[khaled]

1. 1 figure = 1000 words

 

2. Simplify .. simplify .. simplify

 

3. To introduce a new idea, try the projection of your idea on their fields

 

4. Divide the problem into independent parts, Explain each part individually

 

5. Makes examples, related to real-life if possible ...

Edited March 19, 2011 by khaled

[DrRocket]

Just noticed that all my suggestions for further reading are postgraduate level textbooks! May not be very helpful for most people

 

 

Good luck.

 

I have yet to see a good popularization of meanungful mathematics. Physics popularizations generally rely on dumbing down the math. That pretty clearly won't work for your task.

 

Talks that I have heard either lacked content or were understandable only by a small minority -- mathematicians and a few physicsts.

[ajb]

Good luck.

 

Thank you.

 

Talks that I have heard either lacked content or were understandable only by a small minority -- mathematicians and a few physicsts.

 

This exercise has been quite an eye opener. It is hard not to just use language so familiar to yourself, forgetting that only people in your field will have a clue.

 

I will say that biologists are very bad at this also. I struggle with my brothers writings and his speech, quite often the ideas are not too hard to grasp, but the technical language can be horrendous. I am in little he thinks the same of mathematicians!

Edited March 21, 2011 by ajb

[Xittenn]

You will link the material for us to read?

[ajb]

You will link the material for us to read?

 

When I am happy I will let everyone on this form have first look. It may be a while yet as I am going to take my time with this.

[amanda more]

Hi,

For the third book I want to write - letting the "other half" (the politicians and journalists especially )get a clue about basic arithmetic so they can then be able to talk some rudimentary science or to some scientists/techs/mathematicians

 

As an example, I thought I'd use the lottery. Alas, those who are clueless seem especially unable to understand this. Is it too emotional? This isn't even death statistics. I need to do some headshrinking on them to try to find what the deep intense block is.

 

Any guess?

 

Thanks

[DJBruce]

ajb, this may be too late to be of help, and it may not provide any help, but I find that I tend to fall into that category right now of knowing enough math to be bored and frustrated by main stream popularizations, but then not advanced enough to jump into the full details of a subject. My advice to you would be to try and give ample motivation behind things you do. Also to some extent I think theorems, proofs, or at least basic sketches of proofs are nice when they are communicated effectively. The only other tip I would recommend is be sure to explain any notation you are using. Its unbelievable frustrating to not understand what a certain thing is because there is very little way to look up symbols effectively, but if you tell your audience what you are doing they can then do some reading on what that operator, variable, or other thing is.

 

As for writers I think do a good job with semi-technical writing I think of Spivak -although writing a textbook is different from writing an article, but he does a lovely job building upon things, giving counter-examples, and being fairly funny. I also think Keith Ball does a very job in his "An Introduction to Modern Convex Geometry".

[ajb]

I should just follow this up with letting you all know the article has been accepted pending some editing. The article needs to be put into a format they like and there needs to be some technical details removed. The Editors will do all this for me and send me a copy to approve. The Editors have a lot of experience in rewriting articles to the level they want, so I think they can only improve the overall accessibility.

 

I should hear back from them very soon. Once the article is online I will let everyone here know.

 

Thank you for all your advice. Writing for a popular audience is difficult and I now have more respect for those that can do it well.

[imatfaal]

Hi,

For the third book I want to write - letting the "other half" (the politicians and journalists especially )get a clue about basic arithmetic so they can then be able to talk some rudimentary science or to some scientists/techs/mathematicians

 

As an example, I thought I'd use the lottery. Alas, those who are clueless seem especially unable to understand this. Is it too emotional? This isn't even death statistics. I need to do some headshrinking on them to try to find what the deep intense block is.

 

Any guess?

 

Thanks

 

Amanda - what is it about the lottery that you believe people fail to understand? You posted something else on these lines and that didnt really make it clear what your frustration was. Additionally - on a forum like this you need to be clear which state/nation you are referring to. FYG the pan-European Lottery "euro-millions" must be getting close to an expected payout return with four or five rollovers and the prize funds swelling at (I believe) every level of winning ticket.

 

As an aside - with inflation running at 4.5 pct here in the UK, interest rates at well below inflation; the lottery must be getting closer to being a wise investment of a pound a week!

[Marat]

Probably the most famous and successful book ever to present mathematics in a popular way was Lancelot Hogben's 'Mathematics for the Million,' published many years ago. It might be useful to have a look at its approach to get some ideas.

[amanda more]

Amanda - what is it about the lottery that you believe people fail to understand? You posted something else on these lines and that didnt really make it clear what your frustration was. Additionally - on a forum like this you need to be clear which state/nation you are referring to. FYG the pan-European Lottery "euro-millions" must be getting close to an expected payout return with four or five rollovers and the prize funds swelling at (I believe) every level of winning ticket.

 

As an aside - with inflation running at 4.5 pct here in the UK, interest rates at well below inflation; the lottery must be getting closer to being a wise investment of a pound a week!

 

So here it is- the language of science is math. If one wants "the other half"(nonscientists) to have a clue about the modern world then they need some basic understanding of the language of science. But they don't , won't, can't. Why? The simple problem I mentioned was that say - a lottery where the state (or country or whatever) takes in 100 million dollars and keeps 50 million dollars. So, without chi or any upper level stuff, it is basic that then for every $1 spent 50 cents goes to the state (or country or whatever.) Perhaps if this isn't clear then you can help me to understand what is not to understand with this. A higher level term for this than the term- odds is --probability.

[Marat]

I think that the humanistic half of the world has trouble with math because they forget or fail to notice that math is really just a form of disciplined, logical reasoning. Instead they understand math as a system of algorithms which have to be memorized because they make no logical sense, but just solve problems by some sort of occult magic. Thus when you see non-math types trying to solve simple arithmetic problems they should be able to do in their head, they rely entirely on some remembered algorithm from grade school which they perform as a mindless ritual, with no notion that its results can be checked by rational reflection or could have been guessed by simplification and approximation. If a popular math book could just convince them to accept that math was really just a form of thinking and not cabbalistic manipulation of mystical signs, they could do much better with it.

 

I read a psychological study of the mental processes of humanists which sought to explain their trouble with math in terms of their demand for absolute certainty and completeness of understanding at every step of an explanation. In contrast, math types were willing to hold their minds open in a passive way while someone explained some new and unfamiliar math concept to them, and their thinking did not panic and convulse into irrationality or forgetting while being loaded up with defined terms whose ultimate purpose and interrelation was not yet evident at the moment. I suspect that the difference may have to do with the fact that humanists know they are not good at math so they are constantly insisting on getting their bearings as the explanation unfolds, while math types know they will eventually get it so they are more calm. If that's the case, then the brain difference between humanists and math types is just a symptom, not a cause, of their differing aptitudes.

 

I think that people don't play lotteries on the mistaken reasoning that lotteries are a sensible investment overall. Instead, they are just hoping to be lucky, since their dead-end lives leave no other chance for dramatic improvement. There is a certain logic to playing the lottery if you know you are stupid or untalented, since then you take a chance on your luck, which is identical with that of everyone else playing the game, rather than on your intelligence or talent, which put you at a competitive disadvantage.

 

An MIT professor who is a friend of mine always plays the Massachusetts Lottery on the theory that it is a negative insurance. With regular insurance, you pay an insurance company a fee to protect you against improbable catastrophes, and since the company charges you more than their service is worth to make a profit, your buying insurance is to that extent irrational. With a lottery, you are inversely buying, for more than it is worth, a chance that something extraordinarily good will happen to you, and for this you are also paying the company organizing the system enough for its profit. So buying insurance and lottery tickets are both equally rational, though in opposite senses.

[amanda more]

from Marat

 

"I think that people don't play lotteries on the mistaken reasoning that lotteries are a sensible investment overall. Instead, they are just hoping to be lucky, since their dead-end lives leave no other chance for dramatic improvement. There is a certain logic to playing the lottery if you know you are stupid or untalented, since then you take a chance on your luck, which is identical with that of everyone else playing the game, rather than on your intelligence or talent, which put you at a competitive disadvantage."

end Marat

 

 

 

 

Thank you. A lot here. I was wondering if the "other half" might understand it in their language. Some way to engage emotion I suppose with a bully standing around taking lunch money perhaps. But that still aggravates. They have to use math all the time. Why dislike it so strongly here?

 

To consider a type of formal apology for the lottery- My first stab at it is that the poor spend a lot in aggregate and a higher percent of income on lotteries but perhaps since all paycheck is spent (after all poverty and savings don't correlate often) then they are deflecting from other economic choice. Instead of two six packs with the predictive call to the cops later and losing my current squeeze, I play the lottery instead. It could be argued the second six pack has a negative return as it causes more pain than pleasure.

 

It does take some kind of power of authority to let humans know when they are taking a misstep. We are mammals and are exquisitely tuned for the momentary pleasures. Suddenly what everyone knew as evil gambling has been rebranded as fun gaming. So we believe television instead of the words of oldtime pastors as expressed by some in the older generation.

 

I was considering this: If there are measurable costs for attempting say to go to college. The loans. Need not to work at 7-11 during high school losing that cash. Navigating away from the beating from the neighborhood bully. If only 6% of the poor ever get into the middle class or above in this country and the risks could be measured (like in freakonomics) maybe in general there is statistical evidence not to stride for more.

 

If it is a sure loss- most will fail who try then guess what? Only half your money is lost in the lottery.

 

And no student loans.

 

 

 

 

 

[amanda more]

I think that the humanistic half of the world has trouble with math because they forget or fail to notice that math is really just a form of disciplined, logical reasoning. Instead they understand math as a system of algorithms which have to be memorized because they make no logical sense, but just solve problems by some sort of occult magic. Thus when you see non-math types trying to solve simple arithmetic problems they should be able to do in their head, they rely entirely on some remembered algorithm from grade school which they perform as a mindless ritual, with no notion that its results can be checked by rational reflection or could have been guessed by simplification and approximation. If a popular math book could just convince them to accept that math was really just a form of thinking and not cabbalistic manipulation of mystical signs, they could do much better with it.

 

 

 

Wow. This is so relevant to the iPhone app I just programmed (not yet in the store.) I had no idea if some people tried to add $1.23 + 2.95 they may start on the digits to the right - never even occurred to me. This thing may be more beneficial than I had thought. It is also a very,very dose of behavioral change. When this country failed to go metric the school books faltered then left out meaningful measurement. No cups, pints and quarts. They took what any cook has understood for thousands of years and relegated it to silly numerals above and below a line.

Edited July 14, 2011 by amanda more