Swimming about in mathematics 13th February 2014

Swimming about in mathematics

Looking around the BBC website today I came across a piece by James Gallagher on the beauty that mathematicians routinely see in some of the more famous mathematical equations. Euler’s identity equation has been voted by many of them to be the most beautiful because it is simple to look at yet incredibly profound. It comprises the five most important mathematical constants (meaning they do not change) and it also comprises the three most basic arithmetic operations: addition, multiplication and exponentiation.

                                                                   iπ

               e + 1 = 0

e             (a transcendental number)

i              (fundamental imaginary number)

π             (another transcendental number)

1             (multiplicative identity)

0             (additive identity)

Here is a fun version of what the symbols denote when someone is learning to swim

e              (the aquatic learning potential we are born with)               

i               (the focus of our imagination)                                              

π              (the focus of our aquatic learning circle)                              

1              (the nature and focus of our aquatic guardianship)             

0              (Our openness to aquatic experiences)                                

This is a  little bit of fun and is not a formula of mathematical proof. The five constants (things that remain the same) have been exchanged for complex learn to swim variables (things that can change)

I enjoyed Prof David Percy waxing lyrical about Euler’s equation when he said “Given that e and i are incredibly complicated and seemingly unrelated numbers it is amazing that they are linked by this concise formula. At first you don’t realise the implications. It’s a gradual impact, perhaps as you would feel with a piece of music and then suddenly it becomes amazing as you realise its full potential”

He said beauty was a source of “inspiration and gives you the enthusiasm to find out about things”

Although I cannot pretend to understand complex mathematical formulae I do like to try and I like finding out about things, drinking in any beauty and taxing my brain with difficult ideas because they may bring me new understanding.

What else does the hidden beauty in mathematics have to say about learning to swim?

Marcus Du Sautoy mathematician and Prof for the public understanding of science sees beauty where Fermat proved a relationship exists between prime numbers and square numbers.

Any prime number that can be divided by 4 with a remainder of 1 is also the sum of two square numbers. eg 41 divided by 4 is 10 remainder 1 and is also the sum of 25 and 16 which are both square numbers.

“So if it has remainder 1 it can always be written as two square numbers and there is something beautiful about that.”

“It’s unexpected! Why should the two things (primes and squares) have anything to do with each other, but as the proof develops you start to see the two ideas become interwoven like two threads in a piece of music and you start to see them come together”

He said it was the journey not the final proof that was exciting “Like in a piece of music it is not enough to play the final chord”

Parallel thoughts ripple across the surface of my mind as I ponder how to explain to people that it is the journey that matters and it is not enough to mirror the stroke patterns of accomplished swimmers. Also beautiful truths hide in unexpected places and in the pool I glimpse this as a child takes itself aside to follow its own learning thread between group activities. This little piece of stolen time annoys many teachers but not me because it is often where that child finds some gold they need.

             

e   “we can learn to swim now because water shaped us in our ancestral past”


i    ”it matters where our focus of attention is when we are learning to swim”


π     “it matters what our kith and kin feel about being in water as it influences us”


1    ”we need to feel safe and be safe in water to say we can swim”


0   “Our perceptions about water can change”

Swimmer.......Who do you think you are? 17th January 2014

Swimmer......Who do you think you are?

                              What part has life on the land and life in the water played in our past?

Whenever I am near an inviting piece of open water I always contemplate what conditions were like for that first human ancestor when they chose to enter a local aquatic domain in their landscape. It must have happened at some point in our past when there was no one to teach free style or butterfly?
As earth provides two main elemental environments; terrestrial and aquatic, logic states that being able to use both of them confers a great advantage to a complex mobile creature. This simple piece of logic suggests to me that some of our ancestors became relatively more aquatic than we are today. To suggest otherwise removes ready and bountiful resources to our ancestors from the story of our past.
If we did evolve from tree dwelling apes it makes great sense that watery margins were a useful step.

If the logic of the statement above does not strike you then I need to try and explain why it makes such profound sense to me and also ask you to consider the possibility that the strength of your own personal relationship with water will have a strong bearing on how valid it feels.

The advantages that water could have provided for our semi-aquatic ancestor are:

1. Providing physical support, lessening the negative effects of gravity on the body to help us walk.
2. Access to new, varied, extensive, reliable and nutritious sources of food.
3. An extensive space that could provide a safe haven to rest, learn and play.
4. Disease reduction from dilution or removal of pathogens.
5. Aid to recuperation from physical injury and development of swim gait aids strength building.
6. Increased level of experience in individuals with a life span beyond reproductive years.
7. Grandparents helping to raise young, leading to experience transmission and cultural expansion.
8. An increased amount of shared survival skills lead to greater adaptability to overcome the challenges in numerous new environments and territories. Increased mobility and success worldwide.

The disadvantages that water could have presented to our ancestor are:

1. Predators and physical hazards were present in the water.
2. Local conditions changed suddenly through currents, tides, floods, squalls causing death.
3. Waterborne pathogens, disease and parasites caused disability, infections or death.
4. Drowning occurred due to a lack of positive experience or the example of an experienced other.

This leads me to make logical assumptions about what the first aquatic environment was like initially:

1. The water was clear enough for the floor and a lack of predators to be visible.
2. The water was warm enough to maintain a normal body core temperature relatively easily.
3. The environment was stable for long enough to provide local safe conditions on a reliable basis.
4. The water contained attractive resources which were relatively easy to collect.
5. The underwater substrate and water depth changes provided opportunities for gradual exploratory physical support in the form of banks, bars, spits, slopes, shelves, submerged trees, rocks and plants.
6. There was no initial pressure to enter the water other than to fulfil natural curiosity or retrieve food
7. The water could be entered and exited again relatively easily.

The reasoning I have used is based in part on observational experience over years of teaching swimming to people of all ages. I have also watched footage of how other animals engage with water and recognise patterns common to all. What matters most are the initial conditions which allow an animal capable of learning through play to be free of concern for their survival as they enter the water and move in it. If they are free of concern at this point their mobility is not hampered by an inescapable negative visceral response (panic) and they can feel how to travel freely. This state is crucial for animals to dive and swim successfully. Without it they hesitate, stiffly fearing the future. If their families are engaged in aquatic activities to make their living they learn fast no matter how cold the water is. When animals don't use it they lose connection with it. This is a natural process.

In my opinion the advantages provided by water exceed the disadvantages and every environment has its hazards which lead to positive behavioural changes (adaptation). Humans are arguably the most adaptable ape on the planet able to exist in almost every environment it has to offer and I feel that we became this way through an ancestor entering the water in a state of calm, living in the moment, deeply engaged with their environment and able to freely enjoy all of the benefits it had to offer. This phase did not have to last long as once trans generational experience was retained cultural learning had arrived and we became a supremely resourceful species. The rest was history.

Now we view our ancestral past through the hazy lens of a population largely disengaged from the natural environment. No wonder we cannot see the vital part that watery margins played in our past.

Temperature Matters - 29th September 2013

What an incredible summer we had! I cannot recall having to don a warm top during the day for the best part of two months! I caught myself once or twice in the summer checking to see if I had begun to take it for granted and yes there were signs. However being British I chastised myself for this and made an effort to appreciate the genuine lack of any heat seeking tension in my body each day.

Now as autumn arrives I begin to notice the first signs of the ambient temperature having an impact on some of the swimming pools I teach in. Colder changing rooms, poolside air and pool water all have a bearing on attendance and the outcome of swimming lessons in the winter and even more so for those who are afraid. I am lucky enough to teach at a small school pool where the water and air temperature are well above average and lessons there consistently produce faster progress than other cooler places.

As winter comes upon us I understand that the starting temperature of water entering the pool system is cooler and outside cold increases heat loss making running costs rise for pool operators and any heating breakdowns can take a while to notice and also to fix. There are ways of reducing heating costs over the winter months however such as blanketing the water surface with a bespoke rolleable cover when the pool is unoccupied. That said I would also love operators to understand that there is a substantial cost to its clients being cold and there is certainly no benefit to allow delay of repairs to heating plant or lowering the thermostat to save on heating costs at anytime of year as the warmer the water the greater the progress made by the learners and swimmers. The reason: feeling cold is a major distraction and something that learners can ill afford when they already feel tense and reluctant to open out.

In the past everyone expected cold water unless they were at thermal springs like those in Bath Spa

and had to put up with it no matter the stage of their learning. It must have had a negative impact on learn to swim success rates although there are some suspected health benefits to habitual cold water immersion which intuitively led to the sea dipping habits of historical times. Today a steady warm temperature (water over 30 deg C and air 1 degree warmer than the water) is one of the greatest tools a swimming teacher can employ to reduce tension in the afraid and accelerate learning. If only swimming teachers had access to their pool centre's heating system and were equipped to deal with the vagaries of its maintenance!

                       "Fetch more slaves to stoke the furnaces.....I can't take my coat of in this"


Of course once someone has learnt to swim cold water swimming can be a refreshing delight, be necessary for a nicer workout or be a well managed challenge. It is also vital for all 'swimmers' to understand what it is like to be in cold open water so that they respect their own physiological limitations in natural environments but a comfortable temperature matters a great deal when you are learning.


        

"There's so much down there" 11th August 2013

While clearing my old paperwork in "The ineptitude pile" before it actually crushed someone I found a wonderful article in the Wildlife Trusts News (BBOWT) April 2013 about an artist going sea diving for the first time. I love sculpture and in particular the work of artists like Martin Hayward-Harris so was eager to read how Harriet Mead (harrietmead.co.uk) drew out beautiful underwater wildlife pieces from old tools and iron ware. The way she spoke about her diving experiences was thirst quenching.

"The sea is a whole world I had no knowledge of. We experience wildlife on land in so many ways that it's in our consciousness as children. But when you're an adult and you go underwater for the first time it's extraordinary."

There are communities in the world where such formative views are forged in childhood as their society makes it's living from the sea directly but Harriet's experience is rare in the UK. She goes on to describe the growing array of wildlife before her eyes as it is pointed out to her by an experienced guide and I cannot help but draw parallels with the revealing power of conquer fear instruction for those who thought they knew all there was to know about teaching / learning to swim. To record images of the wildlife she sketched underwater with a graphite stick on super thick water colour paper, bulldog-clipped to a chopping board. It was not easy for her with thick gloves on and the current moved her around but she "cracked on anyway" She then produced some stunning work from her sketches, welding sculptures herself into superb likenesses of a crab, a goby and a lobster from metal objects such as locks, molegrips and saw blades. I already treasure a chunky diver made of metal nuts and bolts purchased while on holiday in Egypt and would love to be able to look at one of her fabulous master pieces everyday.

The enthusiasm for the three dives she did sprang off the page too.

"You're used to seeing a lobster out of water where its legs aren't strong enough to support its weight. But seeing the creature in its environment, where its perfectly adapted, puts it all into context.... little cuttlefish hunting over the sand..... absolutely miniscule..... they are so charming..... a little puff of ink if they are scared" Then she concluded "Sea diving is one of those things where until you have done it you've no idea. From the shore you're just looking at the waves and shingle greyness. But there's so much down there." 

Now she wants to dive again and again and has purchased her own gear. I share her passion for what's down there and for letting people know what they are missing when they make assumptions about things from the surface. If only more swimming teachers were prepared to take a look underneath at what really goes on and not assume that they already know everything that their students will ever need. Also if only more people could appreciate and want to protect what lies under our coastal waters which are some of the best in the world for diving experiences. Infact, research work is constantly being done to record what we have around us in this regard and there is someone who wants to conquer their fear of water in order to be able to dive and fulfill their dream job when the tide comes in too so if you know of anyone who can sponsor them to do this please get in touch.

What goes on inside a learn to swimmer....?

http://youtu.be/ewG2fsutya8  What a fabulous inspiring clip about learning to swim! These people are really keen to speak out about their learn to swim process because they want many others to follow in their footsteps and know what it is like to succeed in the water. When you watch them speak and swim around, do you believe that they are giving an honest reflection of what is going on inside themselves?

This also leads me to ask. "Why is it important to know what does go on inside a learn to swimmer?"

As human beings we are all used to making working assumptions about what someone else is thinking and feeling. We do this by using our brain's mirror neurons and complex social experience to rapidly evaluate subconscious signs and signals to make a judgement about the nature of another's internal state. Sometimes we are right and other times we are completely wrong. Making these decisions without primary facts; based on assumptions is called using judgement heuristics.When people are learning to swim what they are thinking and how they are feeling is very important because it dictates WHAT they learn and HOW reliable they are in the water. In the past this internal consideration was widely neglected by teachers because it was assumed that to learn you always needed to push yourself beyond your own comfort zone. Some people will still dispute the need for any psychological comfort when learning to swim but as testimony from so many non-swimmers shows pushing can lead to failure far more often and insidiously than it makes a permanent gain. This may be perculiar to swimming infact because of the nature of our physiological controls; as we have a deeply primordial instinct for survival in water that overrides our intellect. The features of these primordial mechanisms need to be studied scientifically but I suspect a combination of trigger ratio for blood oxygen:carbon dioxide and the way we store heightened sensorial memories in our body and brain when we are in dangerous situations.

I spend alot of my time spotting discomfort in the water through body language and telltale tension can be viewed below the water far more easily than it can above. This helps me offer the most appropriate next step to people alot of the time. When someone needs close supervision to feel comfortable any physical contact with that person, for example holding their arm or touching their back as they float will tell you if they are holding any tension inside and gives you an idea of how they are feeling. I have however also come to realise that if you are not in direct physical contact with someone the only way to know with any certainty what someone else is thinking/feeling is to ask them. This is not because I am poor at reading some people's body language or because some signals are not being sent. It is because people are sometimes very well practiced at disguising their own emotions, denying they are uneasy and tactically managing fear. The extent to which some people can do this is really quite remarkable.

Fear management is a false economy in the process of learning to swim as the person is vulnerable to set backs which can lead to a disastrous collapse in confidence and control. Therefore bravery in learning to swim is absolutely as hazardous as niaivity.

Making Lemonade - 15th July 2013

Making Lemonade

Swimming with my family at Hinksey pool (heated outdoor lido) in Oxford is always a sheer joy. On one occasion a few years ago my husband decided to play a trick on me. Under the beaming sunshine he asked me to look down in the crystal clear water and then used his forearms to push some air down so that it all rushed upwards past my face as an explosion of bubbles. The experience was invigorating and exhilarating watching the jumbled streams of wobbly glass beads speed and spin past me. The finer bubbles stuck all over my face and neck and then slowly fizzed away. “Well how was that?” he grinned. “Lovely!” I said, “Like being in a glass of lemonade or champagne” we all played with the trick for ages, delighting in its simplicity and great beauty.

There is nothing like finding pleasure in the smallest of things, particularly when they are free and of course the trick has been used a lot in my lessons ever since. Recently I asked a group of children in deep water if they felt like trying to make lemonade there. They did so with gusto! This was stage 3 children using the wall for safety instead of the floor and they were content to laugh underwater as they hung there making their own soda streams jiggle past their faces.  Adults also enjoy making lemonade and it gives them a sensorial feast, a taste of what it would be like to jump in.

Talking of jumping in I was priviledged to visit Farleigh Swimming Club and revel in the sights and sounds of the Great British public enjoying a stunning stretch of the River Frome. Adults had transformed into children wherever you looked, swinging in off ropes, sneaking off on silent forays upstream at eye level with dancing blue may flies, struggling out of steep over hanging banks and water lily margins. I heard one lady say ”Well, I am going to come and do this every day for the rest of my life” and another said “We are so lucky to be here, it’s beautiful”  Everyone chatted as open strangers and picnicked, and adored the weather. One man commented to his companions that they looked calm and easy in the deep water while he could not stop moving, trying mentally and physically to stay afloat. One of his friends laughed like a disembodied head “Well my feet are on the bottom!”

Being afraid to speak

Just how many people are afraid to speak up about any unpleasant experiences in their watery past? Zoe and I have our suspicions it is of epidemic proportions as unresolved fears, even if small at first can grow out of all proportion when they are left or managed. Frank Skinner trying to overcome his fear of water in a very public challenge last year has opened the door a crack for many more people to want to have a look at what may lie on the other side. However, doors can be walked through in two directions. In other words this is mostly seen as an opportunity for many people to want to try again to learn to swim when it is also an opportunity for those who teach to take a look at what lies on the other side of the door at where the learner is coming from. I would like to know the reasons why this is not happening widely.

Recently Zoe and I heard a tale of how great trauma was inflicted upon someone by a swimming teacher and wondered just how that teacher would feel if they knew. Sadly the story the person told us is not uncommon and the truth is that some people would come out the otherside relatively unscathed. To that person however it was devastating and removed life long chances of enjoying the water until they came to us for help. The dilemma is therefore how to build a common thread of communication between the teacher and all pupils so that this unsconscious accidental damage routinely does not happen. If teachers do not look through the door at where their pupils are coming from and want to just override or manage fears then communication stops and fears get the chance to grow much bigger under the radar.

Let's also consider what learning to swim entails. A person is visiting a new and all encompassing environment that almost all of us are born to be able to take advantage of safely but as we are not adapted to be permanently submerged could lose their life in just a few minutes. Where else do we ask people to take on such a challenge? Dolphins, whales, otters, seals, duck-billed platypus and many others are at one with the water and yet they too cannot exist permanently below its surface. They learn how to take advantage of its qualities and minimise it's disadvantages and risks and they are also not born knowing every piece of information they will need to survive in it's challenges. This is why learning to swim is so different from any other activity. It is also why the pyschological side of it is so important and yet is so bizarrely neglected on a regular basis. It also means learning to swim need not be hard at all.

Why the psychological side is ignored is historical and allied to a lack of comfortable exposure time to what is an advantageous and natural environment for human beings. A strong case of use it or lose it. Aquatic knowledge is held in the social fabric and what it says has a huge impact on how comfortable people are in water and how successful they are at achieving their goals. The way to regain lost wider aquatic knowledge is clear. Encourage slow re-engagement with aquatic environments starting with splash parks (wonderful places to start) and the use of our own sense of personal safety to guide us while someone more experienced than ourselves guards our lives too. Feeling safe is as important as being in a safe environment. If you do not feel safe then you are not yet but if you stay comfortable you will have access to your superior human potential to learn. Being afraid of speaking about fear openly through a sense of shame or, blame or expectation of the unknown holds everyone back because the ANSWERS are out there waiting to be used as they have been for millenia. Let's sponge them up?!

Quite new to science a Malaysian fungi called Spongiforma squarepantsii.
 "Sponge bob comes to dry land and is found sitting under a tree?"