My husband is an electrical engineer (VERY math oriented - as is my son) and sometimes I read through the journals they get. I mostly understand the concepts when they are in words - but when the article then goes on to express the concepts in equations or other math tools - I am lost.<P>

Basheva, from what I recall your facility with mathematics (as opposed to the specific area of arithmetic) is limited. Thus isn't the problem with the equations etc. in your husband's journals analogous to the problem that would arise if it was in Swedish?

Stuart - HUH? LOL !!<P>Those equations are Swedish to me. LOL

You know those tests they give you to determine if you're left-brained or right-brained? Well, my results are usually in-conclusive; not enough to suggest one or the other. I guess that means I'm either an alien or a freak...<P>Mr Sweeney, perhaps your Mensa brain can figure that one out.

<----------DENSA BRAIN

As an engineer *and* a dancer, I don't make a large differentiation between mathematics and dance and/or music -- it's all just patterns to me. If I can find a pattern in it, I can do it. Working with a complex piece of music or a difficult combination, I don't remember the steps, I remember the pattern the sound of my footfalls make - the pattern, or rhythm of the thing. Same for math. Or remembering birthdays, or dates, or what have you...<P>I've taken those tests for right/left brain-edness, and they always say I'm dead down the middle. Go figure.

Hello Klmin - welcome to our board - glad to have you with us.<P>It is interesting that you say you hear the sound pattern of your feet and that is how you remember the dance pattern. It reminded me that I have a friend who remembers phone numbers by the sound tones of the numbers. To her it is a "song pattern" - she doesn't remember the numbers - but that tone pattern.

If you are looking for a relationship between mathematics and the fine arts then I would say look at the connection between maths and music; both involve the handling of abstract concepts. As a music graduate who studied maths to (UK) A level (i.e. till I was 18), I am sure that the fascination of structures in sound appeals in the same way as a neat piece of algebra. But of course there's more to music than that, and we want our emotions to be stirred, though there is also a sort of emotional satisfaction that comes about when considering the sheer exactness of the structure of e.g. a Mozart symphony.<P>Throughout 30+ years of teaching music I have noticed the variety of approach that different students exhibit. Some are highly intellectual, and cannot tear themselves away from the printed page (or do so with difficulty); these can find improvisation difficult. Others are more intuitive, and are not great mathematicians. Some lucky ones are blessed with the right mixture of all faculties.<P>All arts surely require a balance between technique and expression, and the result will tilt either in the direction of Apollo or Dionysus.<P>The area concerning the relationship between music and movement, including dance, is one that fascinates me. At a most basic level, some can look co-ordinated with an instrument and others not; some can recognise the difference between two beats in a bar and three beats; others find it rather harder. Some can move to a beat; others find it a problem (look at opera choruses....! I've seen these problems in embryo while directing school musicals, as I am sure has many another teacher).<P>It's too easy for musicians to 'intellectualise' their performances, especially in this age of exactness in time-keeping through computers and other electronic devices. There's much about performance (and rhythmic pulse/style/flow that musicians can learn from dance (taking part, I mean); for a start you have to work from memory - which is a habit musicians can easily lose. On the other hand, you hope to find a musical dance teacher; not all of them are, and it does my head in when they start indiscriminately in the middle of a phrase! This is where mere counting lets dancers down.<P>Regarding the use of memory in performance, different people prefer to use different types of memory - and that's a big subject. But the performance obviously musn't look too 'studied' or careful; when something becomes second nature, the freedom granted by technical security allows the performer to inhabit the work show it as his or her own.<P>Back to a couple of thoughts on response to basic rhythm. First, it has often been noticed by music examiners in England that, even at 16+, school students sometimes find it hard to identify 3 beats in a bar; we live in a 4/4 culture. (Contrast this with the 19th century when waltz rhythms abounded in any ballet, set in any country, at any period!). Second, that if music teaching is to use clapping/tapping rhythms, the students might as well get off their seats and use the rest of their bodies; only the other day I had a class of 13-year-old boys (at the end of a school music class) using the march from Stravinsky's 'The Soldier's Tale' where the underlying ostinato rhythm is in two-time (though it's not written as such) but the melody does all sorts of mad things - the challenge is not to be put off by the uneven rhythms of the melody. (Many other similar examples are there for the taking - you just have to be resourceful! Sometimes you can find an example where the melody line has a very vivid and varied shape, while fitting into a regular beat - as in the scene with the drunken revellers from Prokofiev's 'The Prodigal Son').<P>What about dance classes using more varied music, e.g. in 5/4? Pliés with 5 beats down and 5 beats up? It would make a change from those dreadful versions of poor old Chopin et al., complete with their total annihilation of his rhythmic genius.<P>Musicians, dancers, and mathematicians can learn a lot from each other - and develop the whole brain in the process!

I have to say as a dancer and a teacher of dance I adored having many different kinds of music in the class.<P>I did find it very difficult at first counting something like a 5/4 - but that was simply because it was so seldom done. But when we had a clever pianist, it was done - and it was very interesting.<P>As a teacher, except for the most basic class, I always used symphonic, operatic, and music from musicals. Mostly because that steady clinking "ballet music piano" just bored me to tears. It was terrific for my students to learn to move (whether it was for barre work or actual center dance) to music with rests, arpeggios, etc. <P>------------------<BR>Approach life as a dancer approaches the barre, with grace and purpose.<BR>

Richard, many thanks for your stimulating contribution to the debate. On the links between music, dance and mathematics, one of the most interesting examples currently is Mark Morris. He places musicality ahead of technique for selecting dancers for his company and encourages his dancers to sing the music as they perform it in rehearsal. <P>On rhythm, Morris spent a critical period in his teen years performing in a semi-professional Bulgarian dance group with the complex time signatures that feature in that style. It's clear that this experience has had a major impact on his dance career.<P>An aspect of mathematics that we haven't discussed yet is the incorporation of random events into our view of the world. The leading exponent of this in dance is Merce Cunningham of course, who introduces chance into his choreography and in the interaction with the rest of the artistic team. His dancers do not dance to the music, which might be changed from one performance to another. In the recent 'Biped' every performance has a different link to the music, in one instance with the music finishing some 20 seconds before the dancers had completed their steps. Similarly, the computer engineers who generated the dancing images for the front projections in 'Biped', obtained some step sequences from Cunningham and filmed them on his dancers wearing light cells. Then they constructed their own film which plays independently from the dance and the music, producing benign coincidences (hopefully).

Stuart, thanks for bringing in mention of Merce. Post-Merce developments can be enjoyed at quite a modest level, I've found. I've worked with a teacher who trained at Dartington in the 1970's (for those who aren't aware of it, the relationship between Dartington and Modern Dance goes back a long way, and includes names such as Laban and Jooss, among others). Work might include, for example, group improvisations based on a few dance phrases (and the slight variations that individuals might make), where each should be aware of (and might react/respond to) the work of others as they happen to meet ('happen to meet' because running or walking the length of, or across, the space might also be part of the exercise). This can bring about very satisfying effects, but for best results you have to think about what you are doing! It keeps the grey cells lubricated. As you suggest, the music must have a sort of independence, as developed in the collaboration between Merce C/John Cage; the music is 'inhabited' rather than replicated -Steve Reich fits the bill.

At Columbia College Chicago, where I was trained, it is the norm to teach composition by instructing students to create movement before picking out and adding music, thereby (hopefully) creating serendipitous situations wherein a dance phrase and musical phrase will meet without any prior planning. It is with this use of chaos that the dance is seemingly allowed to stand on its own with the music playing strictly a supportive role. It is also common to instruct the creation of pieces done solely in silence. When doing a silent piece with more than one person, any unison idea can only come together if each dancer possesses a natural sensed time that will match up with the breath of every other dancer. This sensed time, or inner rhythm can not be taught per se, but must be drawn out through silent exercises.<P>Along the Merce Cunningham idea, Bob Eisen (before moving himself and his dance genius to New York) held a "Chance Dance" festival every summer in Chicago which brought in companies and individual artists from all over who utilized ideas of chaos and serendipity to create dance pieces. Bob used to set up a chart wherein each phrase had a number and each person had a number. He would pull many numbers out of a hat, place them on a chart in such a way that it would show which dancer would do what series of phrases on what side of the stage. The sequence changed every night, and so did the music. His charts could almost take on the look of a mathematical formula: music+stage direction+dancerxphrases=dance piece.<P>tura

A timely article:<P> <BLOCKQUOTE><font size="1" face="Verdana, Arial">quote:</font><HR><B>Dancing numbers</B><P>T. Lalith Singh, The Hindu<P>Peacocks dance. Humming bees flitter. Snake slithers across. No, they are not real, but are the beautiful imageries created by a group of dancers on the stage. And, as the nature unveils itself, it's mathematics that comes alive.<HR></BLOCKQUOTE><P><A HREF="http://www.indiaserver.com/thehindu/2001/02/24/stories/0424403j.htm" TARGET=_blank><B>More</B></A>

I believe it was Salzberg who commented on the location of Broca's area relative to handedness. Alas, it isn't so simple. Only about 10% of left-handed people have Broca's area located in the right brain. It is also only one of the areas associated with speech. Brains are such interesting things!