Steve’s first lesson in music

As someone once said concerning art: “genius is 1% inspiration and 99% perspiration.” The same certainly applies to playing the piano. Great pianists have practised for a lifetime before sprinkling their efforts with a shake of genius.

I tend to apply the opposite ratio: a smidgen of practice resting beneath a bucketload of winging it. Of course, the end result is not really being able to play anything: I can sort of play a lot of things, I can sort of improvise, I sort of know about keys and I can sort of read music.

This is sort of fine when playing alone, but when playing in a group or playing solo in public you have to think on your feet to hold everything together. So, for the record, here are some musical explanations for the piano player who spends most of the time trying to work out what on earth is happening whilst the music relentlessly continues to its climax.

Accelerando Hurrying up because it is all going badly wrong and I want it to finish as soon as possible
Adagio Note to self: resist temptation to improvise
Atonal A term used to describe improvisations which accidentally fall out of key
Beat Something lacking from some hymns
Breve Possibly a  minim
Bridge Possibly the chorus
Canon A chance for the men to sing worse than the women
Cantabile Times I wish I had learned the cello
Chord progression A set of chords played until I find the one I wanted
Chorus Possibly the bridge
Coda A section of music designed to make me lose my place
Conductor Someone you avoid looking at
Crochet Possibly a quaver
Da Capo Something joined to a coda to make the chance of losing my place into a certainty
Dissonance Playing wrong notes with confidence
Divertimento Any showy gesture or flurry of notes made to draw attention away from a mistake
Doppio movimento A speed adjustment made following a failure to read the time signature
Encore A reason to leave the stage quickly
Espressivo Pretend to be Liberace
Etude Any piece that I can’t play
Finale Often the penultimate chorus
Grace note(s) Any short note mistakenly played before you hit the right one
Impromptu The feeling you get when you have forgotten how things went in rehearsal
Key Signature A seemingly superfluous piece of information which sometimes suddenly becomes important mid verse
Mezzo I always think of hummous
Minim Possibly a breve
Mysterioso The realisation that I have no idea what is going on
Obbligato Having to sing because nobody else wants to
Ornaments The basic decoration which should be applied to all notes
Osinato Play with exceptionally self-indulgent head movements and facial gestures
Perdendosi The trick of fading away when it has all gone wrong
Precipitato Trying to play whilst stopping the music falling off the stand
Progression A sequence of chords played before finding the one I was looking for
Quaver Possibly a crochet; More often the feeling of dread before that tricky hymn
Recapitulation The realisation that you don’t know what key you are playing in
Refrain The feeling of sadness upon realising that you have over-improvised
Relative pitch The realisation that you are playing in the wrong key
Repeat A point in the music where there is a good chance of things going wrong
Reprise A fortunate moment of quiet when I can find my place again
rit A brief period in which you can find your place
Round See canon
Rubato A musical device to allow you to play the difficult bits
Run A sequence of notes played until you hit the right one
Syncopation Something to confuse the singers
Theme A bit of tune you play quietly when you are lost
Time signature That which is so often overlooked
Tremolo The hands upon playing the bridal entry or a tricky hymn
Variations A set of attempts at playing a theme correctly
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Quick ways to make the world a happier and simpler place

I don’t know if anyone else finds the problems of the world depressingly intractable? Well, this made me wonder  if there were any quick, easy to implement ways to make the world a better place. And there are, because I have thought of some. I’m sure that a better list might be constructed, but this is at least a start:


Whilst tidying up in preparation for Christmas I discovered our iron and, a little later, the ironing board. As I moved them out of the way, I wondered how much time this year I have wasted moving them out of whatever way they happen to be in at the time. I have possibly also used them, in conjunction, a couple of times this year. Even more of a waste of time. Some people, I am told, iron regularly. It seems that the social convention which suggests that piecewise differentiable clothes are a good thing is responsible for millions of hours of wasted time. And this isn’t fun wasted time, like watching football. It causes misery. All that needs be done is for everyone to agree that creased clothes are Cool and ironing can immediately become a thing of the past, making millions of people happier.


This one, clearly, would improve the lives of all. Although many people might not quite understand why at the moment.


Confusibles: How many people have had the conversation ‘This curry is hot’ ‘Do you mean temperature hot or chilli-hot’ ‘Well, both, but at the moment there is too much temperature for me to eat it comfortably, so mind that you don’t burn your tongue’. All a waste of time. Come on: in the 21st century we could presumably remove ambiguity from the language?

Conversation snippets: How many times does the phase ‘how are you doing’ have a rather complicated answer? A simple ‘hiya’ is often better, but sometimes leads to a complex decision regarding choice of answer. It would doubtless be easier if the ‘hiya’ greeting were extended with ‘hiyb, hiyd, hide’ etc. The unknown greeting ‘hiyx’ would be met with another unknown greeting ‘hiyz’. A matrix of standard responses could be created to determine how to proceed from a greeting combination.

For example,

‘hiya’ might mean ‘hello, I am open for conversation and am in the market for smalltalk’

‘hiyb’ might mean ‘hello, I am open for conversation but not smalltalk’

‘hiyc’ might mean ‘hello, would you like to walk and talk?’

‘hiyd’ might mean ‘hello, I intend to talk AT you, so you’d better make any excuse for an exit’

through to

‘hiyq’, which might mean ‘hello. Shall we converse entirely in poetic verse?’


Bank holidays, it seems to me, cause, on average, misery. Many families plan extended trips and visits and events around bank holidays which are, on the face of it, one additional day of weekend. So, they get stressed out planning a trip whilst at work. Squeeze the family into the car, drive for miles and miles, sit in traffic jams for hours and hours and then get together with other pre-stressed families for tense times and argument.

Banks no longer need holidays. So, bank holidays could be grouped into a more significant block of mid-year holiday time when a proper holiday could be had. Perhaps coupled with a driving ban and some great TV everyone might have a nice time.


Traditional education is, essentially, a transaction between two parties: a learner and another party (who may be the TV, a teacher, the internet or a book, or even the learner themselves, for example). It seems to me that the mode of this transaction is something that nearly everyone seems to have a strong opinion on. If people said to themselves: I understand that this transaction is complex, requires empathy and skill to manage then that would be good. If people want to solve a complex mathematical problem they often ask a mathematician. If people want to solve a complex mathematics-education problem then they should ask an expert in mathematics education.

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Comfortable clothing

People often ask me ‘Is there a relationship between the genus of an item of clothing and its comfort?’. This is a good question, and one I often think about whilst getting dressed.

I believe that the answer is simple: the lower the genus the more comfortable the item of clothing.

I suppose that we ought to get some matters straight: this is a practical issue of topology so will look at the large-scale topology of clothing, by which I mean clothing is locally 2D Euclidean space rather than a complicated network of pieces of cloth, thread or molecules. A hole in the clothing refers to a designed hole which is intended to serve some functional or embeautification purpose [I can think of no other legal reason for inserting a hole into an item of clothing(an example illegal scenario is, for example, ‘you wish to shoot someone to death’ and their clothing forms a barrier between you and their internal organs; you might imagine other illegal topology changing processes)]

Two other points of detail: Firstly, although biologists will smirk at this, I will consider people as modelled as closed surfaces of genus 0 onto which the clothes are to be put; Secondly, the problem is not entirely topological in that most people have a head which is wider than their neck and some appendages which have an important geometrical arrangement which must be taken into account when designing comfortable clothing.

Anyway, to prove my case let us consider different clothing categories in turn. I’ll only consider unisex clothes as people of male, female and mixed gender are all likely to have experience of unisex clothing.

After some thought, it seems that the universe of clothes is as follows:

Genus 0: All in one hooded romper suit; Socks; Untied tie; Entry-level hat; Gloves; Untied scarf; 1 Slip on shoe/slipper; No clothes at all

Genus 1: Poncho; Most caps

Genus 2: Open cardigan/zip up top without buttons, basic pants, basic tracksuit trousers, leggings

Genus 3: Closed zip-up top, Basic T-shirt; Vest; Trousers with a zip fly and single button.

Genus 4: Diving suit; all-in-one work overalls,

Large genus (5 or more): Buttoned up shirt; Most  items of clothing which has been  enhanced with buttons or modified for beauty purposes; balaclava or complex hat; many advanced shoes; mittens

Looking at the list we see clearly that there are distinct clothing types: Trousers, Tops, Underwear, All-in-ones, Accessories. If you peruse this list then for any item of clothing-type you will see that you will be more comfortable wearing a similar item of clothing with lower genus: it’s a fact.

To conclude, here are some examples:

Comfy combo: (daytime) Tracksuit (top unzipped), vest, gloves, entry-level hat, socks, slippers, basic pants: Combo genus total 6

Evening/partywear: Poncho, leggings, slip on shoes, no socks, T-shirt: Combo total 6:

Uncomfy combo: (daytime) Shirt, tied-up tie, button up jacket, lace up shoes (10 eyelets each), socks with sock suspenders, waistcoat, mittens (genus: really big)

Uncomfy combo: As for daytime, but without the mittens and put on a  button-up vest and corset on under the shirt and wear a complex hat along with advanced shoes (genus: really, really big).

So, there we have it: when getting dressed choose the lowest genus possible and enjoy a more comfortable day.

p.s. I never was any good at counting, so professional advice should be sought before determining genus of clothing for professional purposes.

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Is making a decision the same thing as making a choice? I don’t really know for sure. However, I DO know that if you were to rank my skills in order, relative to the manifestation of those skills in the general population, decisions and choice making would be pretty low down the list. Probably even lower than, say, keepy-uppy. I mean, I can usually manage  two or, possibly three, keepy-uppys. And some people can’t manage more than one. What I am trying to say, perhaps with more verbosity this is strictly necessary, is that I am rubbish at making decisions.

For example, yesterday I was in Tesco’s attempting to choose between an aerial booster and an aerial extension lead. These seemed to be the natural options when it came to linking my TV to a too-distant aerial socket. I dithered so much that in the end the security guard, when convinced that I wasn’t loitering with intent to shoplift, said ‘Buy the cable; that’s what I’d choose’. I accepted his decision with gratitude, to his obvious amusement, and the purchase was made. The amazing thing to me was that his decision was made instantly; whereas mine was plagued with what-ifs, withertos, wherefores and other slightly obscure English terms.

I have a couple of things in common with one of my intellectual heroes: the great Ed Witten. First, we both were theoretical physicists between 1994 and 1999; second, I am told, that we are both unskilled in the art of mundane decision making. I remember with pleasure reading the story, according to his wife, that the great Witten was unable to choose between models of exercise bike, whereas he was able to be the most brilliant mathematical physicist ever to have lived. (For point of clarity I wouldn’t even consider comparing myself mathematically against people such as Witten, although I do wonder if I might hold my own against any of the greats in an indecision contest).

The problem with mundane decisions is that they are so complicated. Taking my recent trial in hand, the factors coming into a cable/aerial purchase are almost overwhelmingly complex – there are so many ramifications of any particular choice. If you try to track any of the decisions to its causal conclusion then either: checkmate occurs, and one of the decisions is ruled out (this one rarely occurs,it seems to me) OR: stalemate occurs and the problem becomes similar to a dog trying to pick up a large ball with his jaw: there is no obvious way in.

Anyway: decision-making, a problem many mathematicians have trouble with.

Some are extraordinarily good at making decisions because they have algorithms for making them: For example “Which socks?” “I never wear socks.” or “Which route will you take” “The shortest route according to road distance” or “Are you coming for tea?” “No – I will go for tea at 3:45, as usual”

Some, like me, are extraordinarily bad at decision-making.  Such people usually attempt to analyse any decision carefully before choosing. For example: “Tea or coffee” [hmm, not sure. What time is it? How many coffees have I had? Is the tea better than the coffee? Who is making it? Are they likely to make it well? Which cups are available? What sort of milk is there? Do I fancy some sugar? Who is having what?  Is there anything to accompany the drink, such as chocolate or a biscuit? Do I, in fact, fancy either a tea or a coffee?] ” Erm. Yes.”

Both of these decision making systems have their strengths and flaws. The first is good for Rapid Decision Making, the second is good for Very Important Decision Making. However, the first system fails when a situation arises for which the decision-maker’s collection of algorithms do not apply. Something novel has arisen, such as: “Do you think that the sunburnt-orange or the burnished-mocha brings out the colour in my eyes better?”. The second system, unfortunately for me, fails almost all the time: “What do you want for tea” “Erm”; “What time do you want to leave” “Erm”; “Which shoes do you like” “Erm”; “What film shall we choose” “Erm”. “What shall we call our child” “Erm”.

Actually, thinking about it, mathematical activity as a whole is a bit like this. Some problems are algorithmic, clearly defined, and linear; others are broad, ill-defined and non-linear. I like the second. I love taking a really hard, ill-formed problem and hacking away at it until the essence of it remains. I don’t like anything systematic; for others the converse is true.

It seems to me that it is possible to take a philosophical stance on decisions: Is a non-random, rational decision always possible? Mathematically we can model a decision as making a choice in a particular situation: for any given situation we could craft a set of possible choices; the decision is to pick one of these choices. More generally we could consider a humongous set S of all possible situations, along with all possible choices for each member of S. If it is possible to make a decision then we must be able to determine some method of assigning a choice to each member of S. The size of S and the sets of associated choices is somewhat mind-boggling. Could we always choose in principle? This is not a trivial matter, even if the sets are cleanly and mathematically defined.

Fortunately, mathematicians have thought about this in great detail and, it turns out, there are in fact two versions of mathematics: the first in which choice is always possible and the second in which choice is not always possible. As a mathematician you need to choose between ‘Maths with the axiom of choice‘ and ‘Maths without the axiom of choice

I prefer the second. It makes me feel better when failing to decide between tea and coffee. Oh, go on. Will you choose for me?

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Colours. We all sort of know what they are: things are yellow, red, blue, yellowish, reddish, blueish; yellowish-red and so on. As the rapid proliferation in the previous list indicates, I would imagine that it is uncontroversial to suggest that we all agree that there are simply too many colours around. And with good reason: the list simply continues ad infinitum, with colours such as (yellowish-red)ish-blue or (reddish-blueish)-yellowish-(blueish-black) or suchlike.

To combat this problem, humans have invented various systems to cope with these descriptive issues. People who are interested in clothes or interior design might use words such as avocado-mocha or tarnished-raspberry to describe colours such as blackish-blue-red-yellow or blueish-black-red. Web designers have quantified colours according to the amount of ish-ness of each colour: either the ishness of (red, blue, yellow) or the ishness of (cyan, magenta, yellow). Of course, since cyan and magenta can hardly be deemed acceptable colours (cyan is used to describe any number of ishnesses of blue and magenta any number of ishnesses of redish-whiteish) this systems is flawed in terms of applicability to the task in hand, namely that of describing the hue of a visible object.

How can we have reached such a state of confusion? Mathematicians dislike vague confusibles, so it seems clear that we need to search for a better system of colorologisation.

When I start to solve any (well, not any, but certainly many) problem(s), I first survey the landscape to see which parts of the structure under analysis are likely to lead to insights of further structure and which parts are merely window dressing, as window dressers might say.

I would suggest that the best way to begin would be to determine which colours are structural and which are distracting window dressing.

According to Wikipedia’s List_of_colours there are clearly only a few different colours. However, if you look carefully at their names you will see that a great many of these are window dressed:

Valid Colours — White, Black, Grey, Red, Orange, Yellow, Green, Blue

Semi-Valid Colours — Purple, Pink, Brown etc.

Barely-Valid Colour — Fuchsia, Puce, Violet, Indigo etc.

Invalid Colours — Thistle, Papaya Whip, Fandango, Gamboge, Pale Cerulean, Chamoisee

Do I need to go on? I mean, Papaya Whip? Surely that is a joke? Did someone really sit down and decide that the best way to describe (red, green, blue) =  (255, 239, 213) would be the ‘representation of the color that would result if mashed papayas were blended with vanilla ice cream or yogurt.’ This is the least mathematical thing I can recall encountering in a long time. From my fridge, if I scrabbled for papayas and (presumably) the old carton of natural yogurt the colour resulting would be more of a speckled-brownish-papaya whip, as opposed to the pure papaya whip that, presumably, one might purchase in a well-regulated franchise-like operation such as Starbucks (whom, for the record, I admire greatly due to the simplicity of their excellent filter coffee which is served full or not full, using the code ‘NOT(room for milk)’).

As with all situations where nonsense proliferates, it is because there is no sense to the underlying structure – the continuum of hue is too complex for the human brain to understand properly, at least without a physics degree.

I would therefore propose a practical simplification of the colour system in which valid colours are simply the four primaries (Black, Red, Green, Blue) along with straight 50-50 mixes of a pair of colours or 33-33-33 mixes of three of the colours or 25-25-25-25 mixes of four of the colours of Black, Red, Green, Blue.

This leaves a very pleasing, unambiguous mix of colours: Black, Red, Green, Blue, BlackRed, BlackGreen, BlackBlue, RedGreen, RedBlue, GreenBlue, NOT(Black), Not(Red), Not(Green), Not(Blue), Not()=BlackRedGreenBlue.

Mmm, now I’ve decided what colours we should have I wonder what they actually look like? Excel came to the rescue, and this is the palette obtained:

I wonder what names for these are given by Probably some ridiculous things, such as telephone green or sunset chocolate. Anyway, that’s irrelevant. These should be the permissible colours, and that’s that.

Once these are in place we have certain simplifications. For example, the colours of the rainbow become:

Red, Red, Yellow, Green, Blue, Blue, Blue (Richard, Real Yorkshireman, Gave Battle Bloody Badly)

Actually, I was tempted to look up the official names of these colours: I have (in order of dubiousness) Black, White, Blue, Yellow, Red (OK so far),  Purple (probably identifiable), Maroon, Olive, Teal (I’ve heard of them. Probably red-ish, green-ish, blue-ish or something) , Trolley Gray, Office Green (my office is green, but my trolley is made of wood) and, finally Ao (English) and Electric Cyan. What sort of a descriptor is Ao??? Any decent colour ought to be identifiable by your average person. So, my system fails: we need to kill off the last 3 and probably maroon and teal aswell (Olive survives on account of the fact that it describes, in fact, the colour of an olive; I’ve never seen a maroon or a teal, although I have seen someone steal a macaroon, if that helps).

At this point, I suppose that I ought to point out that I am red-green colour blind. Although I can distinguish red and green in large blocks, small amounts are tricky. Perhaps my eyes are telling me something obvious: we need to identify red with green or kill off green or kill off red. I’d go with the latter, but that it just a personal preference.

Colours of the rainbow then become:

Black, Green, Blue, BlackGreen, BlackBlue, GreenBlue and NOT()

Ah, much better. Looking for the closest match the rainbow becomes -,Green, Green, Green, Blue, Blue, Blue which is a lot simpler to remember. (a suitable version of ‘Richard of York’ eludes me at the moment)

Shame that some ridiculous names still survive. Still, at least I now know the Teal is BlackGreenBlue.

Maybe I’ll see what various images look like in this new, nicely discrete colour system. But maybe not. I think that I am happy that a sensible solution exists.

As with all my blog posts, please read my disclaimer.


Papaya Whip, The Internet.

list_of_colours, The Internet.

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I planned some time ago to start sharing my thoughts on a blog but procrastinated with excellence. Why was this? I realised that I was struggling with the mental challenge of finding a starting point to an essentially random set of future posts. But without a starting point, future posts can never arrive in the present. Fortunately I have resolved this impasse: where better to begin than a disclaimer whence all subsequent posts can be disclaimed? Here are my thoughts on this matter.

BLOG DISCLAIMER – To be applied to this and all subsequent posts

Any comments or implied opinions on this blog may or may not actually be my opinion. It might be the case that they were my opinion and are no longer so. It might be the case that they were not my opinion but have become so since the appearance of the entry. Or, it might be some other possibility: perhaps they have fluctuated in and out of opinion, or will do so in the future. It’s really quite hard to say. Opinion is such a volatile thing. I suppose the most important thing to do as a reader is to determine whether comments are something you choose to form opinions about: in the case of a binary agree/disagree opinion, either way is fine by me; in the case of a more complex opinion spectrum, any point on the spectrum is also fine by me. Of course, this doesn’t mean that I won’t vigorously disagree with you, subject to the disclaimer about which I now write. (Note, as a point of interest, that this disclaimer is now defined in a recursive fashion. I’ll assume that the disclaimer is somehow well-defined, subject to the  vague and ad-hoc construction of the English language)

I might also refer to mathematicians and/or their actions from time to time. I think that it is wise to assume that I refer to mathematicians like me. Moreover, I will assume that such a set is not empty by adopting the convention that if two things are identical then they are also like each other: as I am identical to myself, I am like myself; thus, the set of mathematicians like me does, in fact, contain at least one mathematician (the wise reader may also choose to make the default assumption that there is exactly one member in that set, due to the diversity of characteristics of mathematicians). Getting back on track. in order to determine some notion of like-ness, there seem to be two obvious ways forward: I could choose to define likeness in terms of matching characteristics; alternatively, I could proceed along the route of similarity.

Matching Characteristics Approach: Here we choose some well-defined characteristics, such as located in the Northern Hemisphere, or Male which an entity either possesses or does not. Two entities are ‘like’ according to a particular characteristic if they each possess that characteristic. Sometimes we might well be able to infer ‘likeness’ according to another characteristic if neither of two entities possess a given characteristic, but sometimes not. However, I digress somewhat. We might say that two entities are similar if they share enough characteristics. However, since there are so many possible characteristics out there, and there is always a sense of grey-ness in any physically-based characteristics (e.g. hermaphrodites; someone with one foot in the Northern Hemisphere and one foot in the Southern Hemisphere and the connecting parts of the body variously split between equator and the hemispheres) this is all just too confusing. Also, for any set of similar characteristics, I would likely be able to find an entity with whom I match on each characteristic in the set with whom I feel that I am less similar than another entity with whom I do not match on all of the characteristics in the same set. An obvious point being that I feel that I am more similar to some females that I know than to many males that I know (Is it really necessary to warn you to take care against any unfounded inference based on this point? Is it really necessary to warn you to take care against any unfounded inference based on the purpose of including the previous sentence? The few people who make any inference, founded or otherwise, beyond the previous sentence will doubtless understand the point of the sentence before that, so I’ll say no more here). Since a decent definition must suitably represent the underlying point, I am going to abandon the Matching Characteristics Approach to ‘similarity’. (Which, presumably, is also abandoned in the standard disclaimer ‘Any similarity to any persons living or dead is entirely coincidental’: it is not a coincidence that Jack Bauer is similar to many people on the characteristic of Male. In fact, that is expected and not coincidental. Perhaps on the matching characteristics definition I would be able to accept this version of the standard disclaimer: ‘It is coincidental that we can choose a large set of characteristics of a character in this piece of fiction such that were there is a single factual person on the planet who matches the fictitious character on all of those characteristics’. Mmm, despite the obvious flaws at present, this certainly has some merit, but I won’t pursue it here.)

Similarity Approach: We have abandoned, with good reason, the TRUE/FALSE approach to similarity. We (why have I now become ‘we’ instead of ‘I’? Force of habit, I suppose. Since it is intended to refer to My blog, We will revert to I) I think that a scale of similarity will work better (N.B.: logically, the crossing out of the word ‘We’ should happen here. I’d never considered the limitations associated with the linearity of meaning permitted by the written word). For this there is a scale of matching from ‘totally identical’ to ‘no possible match’ on such and such a characteristic. Perhaps we need a metric of sorts, although this would require the quantification of a given characteristics. Could be done, of course. But hopefully this won’t be required, and the quantification would need to be done on a characteristic-by-characteristic basis. Interesting stuff to think about. However, I can’t think of an example where this scale of similarity fails to make sense, incorporating naturally, as it happens, binary characteristics.

So, where were we? I’ve forgotten what I was actually talking about. Ah, scanning back up this entry reminds me that the purpose of this was to define a notion of similarity which arose as I attempted to disclaim anything and everything that might arise in my blog, and to indicate that all contained might or might not be my opinion.

And we recurse again.

Confused? Welcome to the world of mathematicians like me.


[NEXT TIME: Due to the number of asides which seemed to occur in this post, I ought next time to talk about the value of parentheses (which are brackets ((no offense to anyone who knew that!)(which can also be nested (fewer people know that (but maybe not, on reflection))))).]


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