Stravinsky and the problem of mathematics

It has been a horrible week. A post on Pieria was the cause of a series of really rather nasty personal attacks both in the comments on the post and on Twitter. It seems that some people didn't like me criticising one piece of sloppy work by an academic econometrician whose other work they admire.

I find this bizarre. One piece of poor work does not invalidate someone's entire output. When I was at the Royal College of Music, I attended a Stravinsky Festival at the South Bank. It went on for weeks and covered Stravinsky's entire instrumental output. By the end of it I never wanted to hear another piece of Stravinsky ever again. But one of the things I learned in the course of this was that great composers are fallible. Igor Stravinsky is a great composer. The Rite of Spring is one of the greatest orchestral pieces ever written. But that doesn't mean that every piece he wrote is great. Far from it. Some of his output is frankly rubbish and should be consigned to the dust of history. And quite a bit of the rest is mediocre. There are a few wonderful pieces, and it is these that make him great - not his extensive output of potboilers, experimental sketches and dead ends.

Now suppose that, rather than sitting through every piece of instrumental music Stravinsky ever wrote, I attended a single performance that happened to be an experimental twelve-tone piece that really needs to be quietly buried. I might write an entire essay about the piece that I heard, explaining in detail exactly what is wrong with it. I might even conclude at the end of the essay that Stravinsky is a rubbish composer. I would be correct within the limits of my knowledge of Stravinsky, but incorrect in relation to Stravinsky's entire output. Would Stravinsky fans tell me that I am ignorant of music (even though I was a music student)? Would they attack my musical understanding? Perhaps - but not if they are responsible critics. Stravinsky is a great composer, but not all of his music is great. A responsible Stravinsky fan would surely say to me, "Frances, this is a poor piece by Stravinsky, but he's written some really wonderful pieces - listen to these" and send me recordings of The Rite of Spring and The Firebird.

So it is with the critics of my post. They could simply have said to me "Frances, this was not one of Milas's better efforts, but some of his other work is excellent" and sent me some links. But that's not what they did. Instead of accepting that my criticisms of his piece might be valid, they attacked my mathematical ability. Instead of informing me about Milas's better work, they accused me of saying things I did not say. They even said that since I had not done a similar piece of work myself, I was in no position to criticise. That's like saying that because I had not written a piece of twelve-tone music myself I was not in a position to criticise Stravinsky's piece. Is the educated listener unable to judge the quality of a piece of music? Clearly not. Nor is the educated reader unable to judge the quality of a piece of mathematical analysis.

Of course, to my critics I am not an "educated" reader. I did not use the right terminology, and therefore - to them - I lack understanding. Not using econometric terminology is no more an indicator of lack of understanding than not using twelve-tone terminology necessarily indicates lack of understanding of the twelve-tone system. But all too easily we mistake linguistic fluency for comprehension.

 But worse, my failure to use the right language marked me as an "outsider". My principal critic was perfectly reasonable to the person who translated my post into econometric-speak, even though that person was really only repeating what I had said. Use of the right jargon is a tribal identity, a badge of "belonging": if you use our jargon you demonstrate that you are "one of us" - but if you don't use our jargon you aren't one of us, you are potentially an enemy and if you criticise one of us we will attack. Academics and econometricians are as guilty of tribal behaviour as anyone else, and my critics today demonstrated this in spades. I am neither an academic nor an econometrician, and I criticised one of their number. They went for the jugular.

My criticism of Milas's work was severe, because it was in my view a very poor piece of work: bad statistical analysis by econometricians has led to some very bad policy decisions, with serious consequences for welfare. It may be that I went too far in my criticism, since I was not familiar with his other work. And I accept that the way I presented my criticism could be interpreted as an ad hominem attack, though it was not intended in that way. But the personal attacks on me in the comments were every bit as bad, and in some cases far worse, than my comments about Milas. This was no credit to anybody. Fighting fire with fire achieves nothing. However loyal people are to the person whose work I am criticising, and  however much they may disagree with me, vindictive personal attacks are always unjustified.

I made the mistake of admitting in the post that I am not confident about maths - a point that one critic explicitly used as a reason to criticise my mathematical competence. But it has dawned on me that this is ridiculous. I am no less competent in maths than I am in music. I have an MBA with a specialism in financial risk management, for heaven's sake. You don't get that without being a competent mathematician. So never, ever again will I suggest in a post that I am not confident about my mathematical ability. And never, ever again will I accept criticism of my mathematical competence from people with axes to grind.

What I will do, though, is think about how I "do" maths. In this post I have mentioned twelve-tone music, which is the most mathematical form of music. It has had an enduring fascination for composers as diverse as Schoenberg, Webern, Berio, Dallapiccola and even Benjamin Britten. Many composers, including Stravinsky, experimented with twelve-tone music but moved on beyond it, finding their own unique musical voices. And I have in the past written twelve-tone pieces myself, though I don't find it easy - it feels like a foreign language. I understand the system and the terminology, but it isn't how I "do" music. I too have had to find my own musical voice. So it is with maths. I think logically and mathematically, but standard mathematical terminology feels foreign to me. I need to find my own mathematical voice.

UPDATE. The Pieria post has now been taken down at my request, as dealing with a continual stream of adverse comments was becoming a major distraction from other work. This post will remain up though.

Related reading:

The problem of mathematics

A selection of Stravinsky's music: 
The Firebird
The Rite of Spring
Epithaphium (serial)
Threni (serial)


  1. Going experimental in music/voicings is the same as tinkering with possibilities, like when playing Jazz. All the music theories are just models derived from the pattern recognition. I'm sure it's possible to come up with your own unique voice in maths without complicating matters. Hmm, like Mozart's "twinkle twinkle little star"? You don't need complicated chord progression to make it good and understood.

    Presenting math and econs in layman terms and accepting more peer review from the general public would make it more robust, wouldn't it? I wonder why they are keeping such subjects within a confined group of academics with difficult terminologies rather than keeping it simple enough that earthlings can absorb the ideas. I remembered watching Lawrence Krauss presenting elegant laws of the universe in simple layman terms. Imagine a topic about the whole universe being presented as simple as possible without derailing from truth, now that's a feat and a well accepted, robust subject. Here's a link to one of the lectures :

  2. I'm saddened to hear that you will no longer be humble about your ability for maths. Such restraint and introspection is all too rare in the world of finance and economics.

    Not that I believe you have reason to be humble, of course.

  3. music is mathematical too, the scale is the simple and harmonious ratios from the route note , 1 9/8 5/4 4/3 3/2 5/3 15/8 2

  4. I too had not heard of VARS before and am happy to have learned of their existence. However I read the article again an can see no direction of causality identified in it.

    This is the crucial phrase -

    "In the low growth regime (Figure 3), however, shocks to public finances have a negative impact on UK growth within a 4-year horizon which are statistically significant."

    note the use of the word "have" rather than "correlates" , no reason why that causality has been concluded upon is given in the sentence or the figure.

  5. I would be very disappointed Frances if you thought my comments on your blog and on Twitter were nasty and personal. They were certainly not intended as such and I apologise if they came across that way. I don't agree entirely with your characterisation of the debate, surprisingly enough, but let's not start that again! Given your feelings about this, I will consider how I might modify my online behaviour too.

    1. Thanks Ken. I think all of us have said things that were interpreted in ways we did not intend.

  6. Cheer up Frances, I am a stats man by trade and I agreed with everything you said in the article, it was an agenda driven piece of propaganda in my opinion. No economist ever starved from writing "research" purporting to prove that debts have to be paid, the quicker, the better. Your deconstruction of the article was 100% spot on mathematically and empirically.


  7. Sorry to had to take some flak. it is my view that criticism is better measured and balanced, just as revenge is better taken cold. Also, I believe that mathematical economics is a contradiction in terms. The math may have uses and be of advantage and supportive in some respects, but can never be the whole because it depends on previous data and assumptions. I was into Stravinsky when he was a dangerously modern composer, an interesting choice for comparison. Some works are marvels, for my money Firebird, others can be hard work. Rather like economics.

  8. I regularly use this quick lookup chart to identify which Rhetorical Fallacy my critics are hurling at me:

    I hope you find it useful, it sounds like you might need it.

  9. Frances

    You probably regret your comments on Milas' teaching ability but some of the comments on Pieria struck me as simple bullying. Don't let it get to you - many of us enjoy your writing greatly.

    1. Yes, I do regret what I said. Deeply. I don't see any point in changing those remarks now - they have been widely read. But I did put an explanation in the post. Trouble is, someone completely misunderstood it - took it as a further insult. The same person also misunderstood this post and a remark I made on twitter, made baseless assumptions about my motives and has accused me of all sorts of things that are completely untrue. I don't know what else to do now.

      Thanks. I really do appreciate your support.

  10. The analogy with composers is interesting, but I'm not sure that it's the most apt. Perhaps surgeons would be better. How many times does a surgeon have to make a mistake without cancelling out the reputation for competence gained through more numerous successful operations?
    As to the Pieria spat, I hope you stick to your guns. Precisely because, as you say, poor academic analysis can lead to bad real-world policy decisions. It's thoroughly arrogant for academic experts inthefield to presume that only other initiates can properly criticise their work, especially as a) their field of study
    hardly has a triumphant track record of yielding well-founded theories; and b) the problems that you pointed out do not turn on esoteric technical details.
    By the way, IMHO Stravinsky was a great composer but poor critic, showing the lack of connexion between the two skills

    1. Thanks Elliot. And I appreciate your comments on Pieria, too.

      The whole episode is really strange. If Milas's research had been adequately peer-reviewed, the weaknesses that I and others identified probably would have been eliminated before publication of the research findings. But there doesn't seem to be a peer-reviewed paper supporting Milas's post. Indeed, Milas seems to have made significant changes to his model in the last few days in the light of my criticisms (and those of others, too) and published a new set of findings, again in a blog post (though this time not on Pieria). He has provided details of his workings this time. But I wonder what his motives are. If he had provided details of his workings in the first place, he could have used Pieria (and LSE blog) as an informal means of obtaining feedback from peers. But he didn't provide anything like enough detail for peer review to be possible. I have to conclude therefore that he was grandstanding research that had not been peer reviewed and therefore wasn't actually ready for publication - as Tony Yates said, it was "premature". But it's really not appropriate to put research that isn't ready for publication on a public blog site. The whole thing looks very odd. I wonder why he did it.

  11. Frances - I do plenty of econometrics, and your points were all spot on. Given how well you think and write about the set of macro-finance issues, please don't let this get you down.

    But I think whether or not your econometrics was or wasn't correct misses the point slightly. When a highly technical piece of work gets put out into the econoblogosphere, it's fair game for people without economics degrees. Indeed I think everyone agrees that the chief virtue about this sort of blogging is that it's a great leveller of ideas, and helps push arguments beyond the clique of academics who already understand them. Professor Milas put a polemical and yet very statistical piece out into mainstream circulation, so isn't that exactly what he was asking for? He put it on Pieria, which has this sort of mingling between expert and non-expert opinion as its raison d'etre. So whether or not you were right, I can't see any way how your comments weren't fair game.

  12. Jonathon, thanks. I will survive!

    On your wider point - of course my comments were fair game. I would never, ever, refuse to accept legitimate criticism of points I have made. Indeed when this was first posted I engaged with comments questioning my maths. At that point it was a lively and interesting discussion. It only became nasty later on, when some people resorted to ad hominem attacks and simple misrepresentation of what I had said.

  13. I am novice reader, but I can see from where you are coming.I have read your other work and I can only say that it's been a pleasure doing it.As far as criticism goes, I think it is important that people should know when there is a sloppy piece of work out there that can possibly lead novice people like me to wrong conclusion.Keeping that in mind I can only say thank you for pointing out such mistakes.If it did turn out that the econometrics was indeed correct,It is still helpful because if anything it would teach some person out there , how to do econometric research and what are the pitfalls to be avoided.Anyways, I hope you keep posting because rest assured, there are people out there like me who are willing to learn.

  14. I certainly hope this does not put you off blogging. Your incisive and clearly written comments are invaluable and a joy to read. There is nothing wrong with robust criticism as long as it is honest.

  15. Nevertheless I think whether your econometrics had been or even weren't proper misses the point a little. Every time a highly specialized good article gets put out in the econoblogosphere, it's fair activity for people with out economics degrees. Certainly I think all people agrees which the fundamental advantage concerning this type of blogging can be it is an excellent leveller connected with concepts, along with facilitates press reasons beyond your clique connected with academics whom by now realize these people. Teacher of Math Practice Test Milas place the polemical yet extremely statistical item out and about in mainstream blood flow, thus isn't really that will exactly what this individual had been asking for? He or she don it Pieria, which has this type of mingling between specialist along with non-expert view as it is raison d'etre. Consequently whether you had been suitable, I can not discover in whatever way just how your comments wasn't fair activity.


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