Category Archives: Bad Maths

Talking to crackpots, or how can we communicate science better?

It is widely acknowledged – by scientists at least – that today’s science has become so complex that it is no longer possible to be an encyclopaedic autodidact like it still was in the 17- 19 centuries. While there are still (very, very) few research scientists who have always worked outside academia, none of them are more active than scientists who are at least sometimes working within academia. Today almost all fields in 21st century physics and mathematics are very much community efforts. This does not only have to do with the need for laboratories, but with the sheer complexity of the knowledge accumulated to date even in the most theoretical fields. The stereotypical lone thinker is not only not the norm, but pretty much structurally impossible due to the complexity of what today counts as cutting-edge science.
Thanks to a friend, I came across a wonderful article about science communication written by Sabine Hossenfelder (Frankfurt Institute for Advanced Studies, Germany). She offers a sympathetic, sociological view on what many scientists tend to immediately dismiss as “big theory of everything science crackpots”, from the viewpoint of a professional physicist. 

“Sociologists have long tried and failed to draw a line between science and pseudoscience. In physics, though, that ‘demarcation problem’ is a non-problem, solved by the pragmatic observation that we can reliably tell an outsider when we see one. During a decade of education, we physicists learn more than the tools of the trade; we also learn the walk and talk of the community, shared through countless seminars and conferences, meetings, lectures and papers. After exchanging a few sentences, we can tell if you’re one of us. You can’t fake our community slang any more than you can fake a local accent in a foreign country.”

The problem is, she says, that science enthusiasts (both the “crazy” and the “non-crazy” varieties – though Foucault would tell you that the label “madness” reveals at least as much about the rules and structures of the society which surrounds a person, as about that person’s personality)

“know so little about current research in physics, they aren’t even aware they’re in a foreign country”.

So why do some [men] still persist in trying to offer their grand theories to society – from outside the “not-so-ivory towers” of contemporary universities?

 As for why they are (in Hossenfelder’s sample at least) all men: there is undoubtedly a link between what society thinks a scientist is, and does, a sort of warped folk-theoretical image of lone male geniuses in white lab coats. This is something that researchers of scientific masculity would be better able to analyse.

But I’d turn the question on its head and instead ask: why are we surprised that anybody else is interested in science? As scientists [I always use the word scientist to denote all fields of knowlege in English, like I would in Bulgarian or German, including the humanities] we know only too well that science is one of the most interesting things. So then the difference between “us” and then becomes one of access to the “right” kind of knowledge, which sociologically means access to the “right” kind of knowledge spaces and knowledge institutions. It is important to realise that not all crackpots are crackpots. Some, perhaps many, are curious minds who might have become scientists, had they taken another career track.

This has to do with the different possible purposes of the university: is it a Humboldtian institution aimed at creating public good and educating critical thinkers, or a factory producing skilled workers and commodified knowledge for the market? Of course, neither of these ideological forms exists in a pure way, but German universities are still closer to the form, and American ones to the latter. 

And indeed, as my autodidact friend commented, in Germany they don’t have such “crackpots” and his hypothesis as to why, is that Germany has widely available science libraries and a culture of using them. This should be changing with the advent of online science spaces, but hasn’t. Clearly, cultural change is lagging behind technological change, and there are still people interested in (and obsessed by) science who do not use the multiple and very useful online science forums.

 (Just to make it clear: I’m not at all claiming that German universities are intrinsically better, only that they are more public than market-oriented: they have a whole zoo of other interesting and frustrating problems, such as chronic underfunding, badly functioning internal stratification, inefficient bureaucracy, rigid professorial apparatus, no jobs between postdoc and professor, etc.)

Hossenfelder makes a pertinent observation about ways in which science communication can go wrong: 

“… in the absence of equations, they project literal meanings onto words such as ‘grains’ of space-time or particles ‘popping’ in and out of existence. Science writers should be more careful to point out when we are using metaphors. My clients read way too much into pictures, measuring every angle, scrutinising every colour, counting every dash. Illustrators should be more careful to point out what is relevant information and what is artistic freedom.

Her next point is a much less popular one but possible even more important. In my conversations with mathematicians, I’ve heard many frustrated mathematicians say similar things:

“…journalists are so successful at making physics seem not so complicated that many readers come away with the impression that they can easily do it themselves. How can we blame them for not knowing what it takes if we never tell them?”

So how should we communicate science better? 

First of all, we should communicate science much more. The public deserves to know if not the ins and outs of cutting-edge science, then at least be aware about its existence, and its significance. We must know where to get a map for the “countries” which we may one day (or never) want to visit in person.

Second, the public deserves to know that there are many different valuable types of knowledge, including very abstract or inapplicable fields. This cannot happen while even scientists on the same campus don’t know anything (or don’t even respect) the work done in other university departments.

Third, science must appear real, done by real humans of different genders, colours, classes, ages, voices, faces, talents, interests, family situations, bodily capacities, demeanours, etc. – as it really is, and not as it used to be in some imagined 18th century.

Fourth, science must be presented not simply as a ready product, but as the process and a journey that it is. If the public knew more about the blind alleys, difficulties and disputes along the way, people would not only see science as more real, but also would perhaps appreciate its value more. (Thanks to Marion for adding this point in the comments!) 

Fifth, science must appear fascinating,yet not easy: because it isn’t. It is damn difficult. And you need a group to do it with.

Sixth, and this will counterbalance some of the negative effects of number 4 above: we must get away with the pernicious ideas that difficult = undoable, or that failure = stupidity. In school, kids must learn to learn and to fall many times but never to give up; but also to be smart about finding the right sources to learn from. 

Then there will be more appreciation of science – and perhaps fewer “crackpots” who are curious but lost in the wilderness of unattained knowledge and seeking it in all the wrong places.

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The Spectre of Maths Anxiety

What an anger-inducing report for a Monday morning. It is a good report, but the subject made me angry. Reading a full historical account of why there is such a thing as maths anxiety at all, and why it persists into the 21st century, and why it is especially more prevalent among women, is so depressing. Besides, I’m certain that things are better (or at least less bad) in countries other than the UK, especially in ex-state socialist education systems. The gender imbalance exists, but is far less horrible – and this is linked, I believe, with the far less rigid “class” structure of the societies. Also in places like Italy and Portugal. How come nobody bothers to look and steal the good ideas. 
 
The full report (very readable):
The Fear Factor: Maths Anxiety in girls and women, 2015, by Samantha Callan, a report commissioned by Maths Action.
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The Perils of Maths

This would be funny if it weren’t real. When I read this story I first thought it was a remake of the old joke about Al-Gebra (check out the link for a detailed history of this dangerous terrorist movement):

“At New York’s Kennedy airport today, a person later discovered to be a public school teacher, was arrested trying to board a flight while in possession of a ruler, a protractor, a drafting triangle, a compass, and a calculator.

During a press conference the Attorney General said he believed the man was a member of the notorious al-Gebra movement and the FBI intends to charge him with transporting weapons of math instruction. […]”

(from Weapons of Math Instruction, http://daryld.com/weapons-of-math-instruction/)

And there was another joke, about a postdoc from Iran flying to a conference and working last minute on his paper about “blowing up points on a plain”.

But alas. This week, a real mathematician, Guido Menzio of the University of Pennsylvania, recipient of the 2015 Carlo Alberto Medal for best Italian economist under 40, was questioned and removed from a flight because a fellow passenger thought that his differential equations were “in Arabic”, he was concentrating too hard, and suspiciously avoiding questions, and the flight attendants had to investigate the complaint.

Dr Menzio was brought back with an apology and the 40-minute flight did leave, with a 2 hour delay.

The whole story (written up with some good humour): https://www.washingtonpost.com/news/rampage/wp/2016/05/07/ivy-league-economist-interrogated-for-doing-math-on-american-airlines-flight/

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I can’t get my head around the grammar of the opening sentence of this document I found on the EPSRC webpage:

“A clearly thought through and acceptable pathways to impact is an essential component of a research proposal and a condition of funding.”

“Pathways to Impact – guidance for applicants and reviewers”, Engineering and Physical Sciences Research Council, https://www.epsrc.ac.uk/funding/howtoapply/preparing/impactguidance/

On research impact and grammar

Why the world needs more scientific literacy.

Scientific literacy is one of those things which are easiest to spot by their absence. We need more scientific literacy to make sure there are fewer articles like this…”A Michigan Newspaper Claims the Large Hadron Collider is Being Used as a Stargate

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A mathematician’s nightmare: Lockhart’s lament

I might have posted this already, but here it is again for George! One of my favourite texts written by a mathematician about mathematics and the way in which it is (but ought not be) taught.

https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

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My pet hate: I wish people stopped opposing “math” to “creativity”!

What a bad article to read before going to bed at 1am. Now I won’t sleep, grr. No, the article itself isn’t bad, it is even making a valid point: “Creativity just as important as math and science”. What made me angry, you ask? 

The argument is always “science and math are essential, especially in today’s job market”. I agree, they are essential on the job market. Just as literacy, the ability to retell, interpret, improvise, communicate, the knowledge of history, cultures and languages. Many things are important “on today’s job market”. But I do wish people asked themselves more often what is essential for the development of a person, for the wellbeing of society, and for the enjoyment of life. Perhaps then – to come back to our “not enough people do math” problem which is only a symptom of  a bigger problem in the way we treat learning – more people would enjoy playing with maths. But Peter Lockhart said it better. I am going to shamelessly quote the first 1.5 pages from his amazing essay just to make sure that more people read it. Please, read it, whether you have always liked, hated, or been undecided about mathematics. I will check in my stats how many people click on the link.

Amusician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made— all without the advice or participation of a single working musician or composer.

Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.” It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school.

As for the primary and secondary schools, their mission is to train students to use this language— to jiggle symbols around according to a fixed set of rules: “Music class is where wetake out our staff paper, our teacher puts some notes on the board, and we copy them ortranspose them into a different key. We have to make sure to get the clefs and key signatures right, and our teacher is very picky about making sure we fill in our quarter-notes completely. One time we had a chromatic scale problem and I did it right, but the teacher gave me no credit because I had the stems pointing the wrong way.”

In their wisdom, educators soon realize that even very young children can be given this kind of musical instruction. In fact it is considered quite shameful if one’s third-grader hasn’t completely memorized his circle of fifths. “I’ll have to get my son a music tutor. He simply won’t apply himself to his music homework. He says it’s boring. He just sits there staring out the window, humming tunes to himself and making up silly songs.”

In the higher grades the pressure is really on. After all, the students must be prepared for the standardized tests and college admissions exams. Students must take courses in Scales and Modes, Meter, Harmony, and Counterpoint. “It’s a lot for them to learn, but later in college when they finally get to hear all this stuff, they’ll really appreciate all the work they did in high school.” Of course, not many students actually go on to concentrate in music, so only a few will ever get to hear the sounds that the black dots represent. Nevertheless, it is important that every member of society be able to recognize a modulation or a fugal passage, regardless of the fact that they will never hear one. “To tell you the truth, most students just aren’t very good at music. They are bored in class, their skills are terrible, and their homework is barely legible. Most of them couldn’t care less about how important music is in today’s world; they just want to take the minimum number of music courses and be done with it. I guess there are just music people and non-music people. I had this one kid, though, man was she sensational! Her sheets were impeccable— every note in the right place, perfect calligraphy, sharps, flats, just beautiful. She’s going to make one hell of a musician someday.” 

Waking up in a cold sweat, the musician realizes, gratefully, that it was all just a crazy dream. “Of course!” he reassures himself, “No society would ever reduce such a beautiful and meaningful art form to something so mindless and trivial; no culture could be so cruel to its children as to deprive them of such a natural, satisfying means of human expression. How absurd!”

Meanwhile, on the other side of town, a painter has just awakened from a similar nightmare…

I was surprised to find myself in a regular school classroom— no easels, no tubes of paint.”Oh we don’t actually apply paint until high school,” I was told by the students. “In seventh grade we mostly study colors and applicators.” They showed me a worksheet. On one side were swatches of color with blank spaces next to them. They were told to write in the names. “I like painting,” one of them remarked, “they tell me what to do and I do it. It’s easy!”

After class I spoke with the teacher. “So your students don’t actually do any painting?” I asked. “Well, next year they take Pre-Paint-by-Numbers. That prepares them for the main Paint-by-Numbers sequence in high school. So they’ll get to use what they’ve learned here and apply it to real-life painting situations— dipping the brush into paint, wiping it off, stuff like that.
Of course we track our students by ability. The really excellent painters— the ones who know their colors and brushes backwards and forwards— they get to the actual painting a little sooner; and some of them even take the Advanced Placement classes for college credit. But mostly we’re just trying to give these kids a good foundation in what painting is all about, so when they get out there in the real world and paint their kitchen they don’t make a total mess of it.”

“Um, these high school classes you mentioned…”

“You mean Paint-by-Numbers? We’re seeing much higher enrollments lately. I think it’s mostly coming from parents wanting to make sure their kid gets into a good college. Nothing looks better than Advanced Paint-by-Numbers on a high school transcript.”

“Why do colleges care if you can fill in numbered regions with the corresponding color?”

“Oh, well, you know, it shows clear-headed logical thinking. And of course if a student is planning to major in one of the visual sciences, like fashion or interior decorating, then it’s really a good idea to get your painting requirements out of the way in high school.”

“I see. And when do students get to paint freely, on a blank canvas?”

“You sound like one of my professors! They were always going on about expressing yourself and your feelings and things like that—really way-out-there abstract stuff. I’ve got a degree in Painting myself, but I’ve never really worked much with blank canvasses. I just use the Paint-by-Numbers kits supplied by the school board.”

***

Sadly, our present system of mathematics education is precisely this kind of nightmare. In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.

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“I do it to make mathematicians cry”

I love my research topic. Math[ematicians]-related procrastination is fun. This post of the Saturday Morning Breakfast Cereal: “I do it to make mathematicians cry” almost made me spit out my breakfast cereal onto the keyboard earlier today. As my friends over in the maths institute like saying, the physicist in this comic strip needs to have his infinity licence revoked! Nice to see the mathematician prevail in the happy end. Oh, you thought i was unbiased? No, I’ve totally gone native.

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