Lateralus: When Pilates meets Fibonacci

For some reason, the issue of numbers has been swirling around in my head recently.  How many repetitions? How many exercises? How many springs? How quick or how slow can something be done? What loads have we used and what is the progression week-on-week looking like? Numbers are absolutely everywhere in a Pilates studio. So it’s kind of hilarious that the cliché of a Pilates teacher is they can’t count to 10.

‘How many times should I do this Dan?’  Usually 10 is my response. But why 10? Why not four? Or 13? Or seven (my favourite number)? Why the number 10? I find it’s the easiest one for me to count to, so that everyone keeps moving so that everyone can feel a movement, and so everyone has a set goal from Beginner to Advanced Practitioner. So to be honest the reason for 10 is one of general convenience, a sort of shorthand for my practice. 

But is it the best option? Sometimes 10 isn’t the right option – fatigue, injury and stress might actually dictate that less is better. Or maybe it’s Ok to do that extra couple of repetitions because a student is having a moment discovering the movement. Wouldn’t it be more important to discover the movement rather than stopping at 10? Of course, you said yes — but how many more would you do? Three more repetitions? 10 more? If the purpose of your time in the studio is to move your whole body in as many ways as it can as much as you can, (and that should be your purpose), what would you then remove from your session for those extra repetitions? It’s a fine balancing act of creating movement options and managing time.

There is something wonderful about getting lost in how a session in the studio is feeling and exploring the movement for a time. Not worrying about numbers and just moving. I find the best sessions are those where time seems to fly past. How clever of a little German dude born in the late 19th Century to come up with it and all the equipment he built and designed himself. Surely he was a genius. Well, I’m not sure about the genius tag but one thing we know about Joseph is that he worked incredibly hard refining and designing his methods over decades. As he did so, he examined how people moved and what would and wouldn’t work, and he settled on a few things that are now considered ‘standard’. The first standardised Pilates order most people encounter is the standard or Classical Mat-work which consists of 34 exercises done in a certain order.  It’s the first one most people encounter because it was written down and published in ‘Return to Life Through Contrology’ – one of the few things actually written by Joseph that survives to this day. It is a great routine that takes control, effort and practice, and involves moving in lots of different ways and forming lots of shapes that repeat and get harder and harder. 

But that number 34 is interesting…..

Why is 34 so interesting? Well, it’s an odd sort of number to land on. I mean couldn’t it just as easily be 35 or 40? Most Pilates teachers could easily rattle off 100 Pilates Mat-work exercises so why was it 34? I have an interesting theory – are you ready to go down the rabbit hole?

Things start to get weird

The number 34 just so happens to be the ninth number in the famed Fibonacci sequence. What. Is. That? 

Well, let’s take a quick trip to geometry land. The Fibonacci sequence, named after an Italian mathematician, is an interesting sequence of numbers who’s pattern tend to show up again and again in nature.  Everything from wave formation, plant growth, embryonic development, cellular replication, the shape of our galaxy all seem to fit into this sequence.

For the math nerds the sequence looks like this:

(0), 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…

And when represented graphically it looks a little bit this:

And in nature it can look a little bit like this:

Once you start looking at it you recognise the pattern all around you. Now how does this relate to our old mate Joe Pilates?  So glad you asked! It’s probably just a cute coincidence that the Classical Mat-work sequence is 34 exercises in length… right?

If we take the exercises from the original Matwork and number them one to 34, and then just take out all of the exercises that don’t correspond to the Fibonacci Sequence we end up with:

1. The Hundred
1. The Hundred
2. Roll-up
3. Rollover
5. Rolling Back (Rolling Like A Ball)
8. Spine Stretch
13. One Leg Kick
21. The Side Kick
34. Push Up

Look over that list; you will notice that every single muscle is moved and catered for, (and that double Hundred start is pretty brutal!).  I’ve often remarked in classes, especially when teaching this traditional sequence, that there are many repeating shapes maybe there is a reason for this repetition. I like to think that these nine movements are some kind of marker or simply ‘end points’ for all of the previous exercises, with the whole 34-exercise sequence leading to a perfect spiral.  Each sequence of exercises up to a new ‘end point’ can help achieve the next ‘end point’. So The Hundred can help with The Hundred, which can help achieve Roll-up; and then The Hundred and Roll-up can help achieve the Roll Over; The Hundred, Roll-up, Rollover and Leg Circle (movement number 4) help achieve Rolling Back and so on and so forth.  As you keep spiralling out, more and more movements help achieve the next endpoint. It also sets up a beautiful Golden Ratio where the sum of the parts fit together very neatly – each ‘end point’ requiring more and more input.

The Golden Ratio in mathematics is said to be existance for two quantities if the ratio of those two quantities is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0. Its usefulness is disputed but it certainly seems to have inspired many creative types over the years but the Golden Ratio and the Fibonacci sequence are linked together.

Curiouser and curiouser

The other thing that is very, very striking about Joseph’s instructions about attempting his exercises in ‘Return to Life Through Contrology’ is that his extremely firm in telling students to do exactly the number of repetitions described – no more no less. Every exercise describes an exact number to do except for one – Single Leg Stretch. In this he asks you to start at 5 and work up to no more than 12 repetitions. So for that one I’ll use the mean of 8 repetitions. So…..if you count up all the repetitions that he asks you to do you get to 144….another Fibonacci number.

I think my brain just broke

What does that actually mean?  I have no idea. It’s probably just a weird coincidence. We have heard that Joseph took inspiration from the Greeks for many of his thoughts and ideas on health and movement so maybe he also delved into philosophy and maths. There is a story that sometime between the World Wars in Germany Joseph Pilates met, befriended and possibly worked with Rudolf von Laban, one of the pioneers of modern dance. Why is that important? Laban was known as a radical thinker and developed a system of dance notation based on geometry which is possibly based on his previous university education as an architect. 

During that time he would have been exposed to the idea of The Golden Ratio as it is an important concept for engineers and architects to understand. It was believed to be things that follow this ratio are more pleasing to the eye, more perfect. Old-style anatomy books and posters, such as the Vitruvian Man by Leonardo da Vinci, also quite often made reference to the Golden Ratio.

Vitruvian Man by Leonardo da Vinci

So…. if Joseph’s friend, Laban, was curious and interested in how geometry shaped movement in dance, and Greek mathematicians and philosophers proposed that there was an almost divine influence of these ratios and equations, and Renaissance artists and anatomists referred to them, isn’t it possible that somehow these numbers influenced his work too? Could it be that in the quest to refine his Mat-work exercises to one complete perfect sequence Joseph decided to try to fit into the mathematics of nature?  Probably not…. but what if it did? Wouldn’t it then lead to the other apparatus such as the Reformer, Wunda-chair and Cadillac? Maybe it did…

Most of the Classical orders tend to be somewhere between 50 and 60 exercises long depending on how you count the movements. Each teacher has brought their own influences to it, so it can be tough to figure out Joseph’s original order. Oh, to be a fly on the wall in the original studio!  From what I can tell, one of the Pilates Elders Jay Grimes’ order is smack bang on 55 exercises, so if we apply the Fibonacci Sequence to his Reformer order you end up with something like this:

1. Footwork
1. Footwork
2. The Hundred
3. Overhead
5. Rowing Series
8. Long Box – Back Stroke
13. Long Stretch
21. Stomach Massage -– Twist
34. Snake/Twist
55. Russian Squats

It’s another example of the Fibonacci Sequence fitting nicely into a set order and giving you a full body workout. It’s also an example where maybe those 10 exercises are ‘end points’ and that all the exercises in between help you get to those ‘end points’.

But what does it all mean?!?

It may all just be crazy conjecture but isn’t there a possibility that Joseph Pilates, in the effort to present to the world a perfect set of exercises, used the idea of a perfect ratio to make it sensible and rational in his mind. Or could it simply be an act of serendipity where a practice was refined until perfection and it just so happened to contain 34 movements? Almost like the universe is saying that the Pilates Method might just be the simplest and yet most complete exercise practices ever devised. Whether or not my weird thoughts about numbers and sequences actually holds any truth, I will probably never know – it is kind of fun to ponder though as you head from The Hundred to a Rollup.

In the end, just move

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