Split

I knew a woman once whose talent lay

in splitting apples in a special way.

Inserting thumbs between the stalk and flesh,

she’d twist her hands and, making fun of physics and the mesh of atoms that composed the whole, 

the apple would perform a joke and with a crack, would lose control.

And split. 

From front to back.

Latterly, physics.

A Boy. Mull.

When an object moves sideways, horizontal or parallel to the source of gravity, at a constant velocity, the effect of gravity on the object is independent of the object's lateral movement.

So, whilst engaged in a pre decided battle of maths with my nemesis in the main body of the school, cold winter afternoons were spent in far more enjoyable and understandable ways.

Physics was taught in post war Prefab buildings known as the 'Huts'. Concrete and steel bunkers set in wasted playground space, just low enough to be scaled in rubber soled shoes. Just narrow enough to prevent the concealment of a prone schoolboy hiding on the asbestos roof, from the police.

In retrospect, it is tempting to think that the Art, Physics and Music that were taught in the huts were more liberal and humorous sessions due to their physical distance from the great toad squat bulk of the main school. Less likely than internal classrooms to receive visits from the rector or prefects bearing bad news and/or summonses. More close knit and comfortable due to our sense of isolated camaraderie.

On initial inspection these were cold and forbidding places, The Huts. For years, I assumed that the enthusiasm of the teachers who inhabited them was due to their adventurous spirit. I now realise, it was due to the meanness of spirit demonstrated by senior staff that demanded young, newly qualified and enthusiastic teachers start their careers in isolation. Away from central heating and out of earshot as their classes fell into chaos. They seldom did. 

I like to think that the imposition of discomfort backfired on the seniors. As many of them languished in tedium in over heated, musty oak panelled classrooms, we and our near contemporaries in teaching robes were kept sharp and playing together outside. Altogether healthier learning environments.

My weekly boarding home. Kilbowie Hostel.

Keen eyed readers may have already discerned the foundation of my physics lessons was couched in the fascination afforded by Lily Cowan's bust, its movement and the lack of it. It was the sideways movement that fascinated me.

In primary school, my voracious reading had revealed basic facts about the physical universe. Lily's provision of Victorian and Edwardian reading books gave a fabulously diverse view of the world and our influence on our small lunar system. Distances were expressed in Rods Chains and Perches. Weights in Pecks, Bushels and Grains. Friction was demonstrated by the burning wooden axles of Greek slave driven carts tumbling downhill from battles purposely lost and Gravity by Newton sitting waiting under an apple tree. The significance of mass and attraction interested me. I had read of the Galileo falling weight experiment and was not impressed by Newton really. Galileo had gone to the trouble of climbing the Tower of Pisa and dropping weighted spheres. Newton merely sat and waited for the truth to appear from nature. Or so I was told by the editors of these Readers.

Dropping the balls. Pisa.

A Buoy. Mull

For me, Gravity was already something wonderful and mysterious. (enhanced by the bending of a rubber sheet by cricket balls as shown on Open University programmes by doctor this or that, looking for all the world like a member of ZZ Top). I had a sense of it's purveying all our space and spaces. Bending time and light. I understood the nature of Red Shift and the Doppler effect, absorbing these from stories by Clarke and and Asimov, watching the sky and sea become one peach glow as the sun set over our loch, emptying the world of its horizon and unifying all my simple theories.

The day our teacher showed that gravity exerted more effect on dropped mass than lateral travel I realised the germ of my lifelong affection for the little things that make a difference. In Lily's sweep across the classroom floor, no movement north to south could be discerned but expansive sways to left and right bore simple witness to these forces and their effect on momentum. The appearance and disappearance of her pearl and heather brooch beneath her cardigan, a measure of the speed and moment of her carriage.Lily was a walking accellerometer. A Pilotless coastal freighter. Plying the same course, day in day out and teaching all the time. Whether she knew it or not.

Primarily Ethics

The school comprised the left, older part only. Where the old meets the new, there was an outside toilet. The windows were purposedly high. To limit distraction.  I have always loved clouds.

My primary school teacher, Lily Cowan had the biggest bosom it was possible to have in the 1960's. Her bust would announce her approaching self before she entered a room. The whole magnificent globular cluster was a source of great mystery and wonder to me. She held her twin armfuls in check by employing an intriguing combination of the barely visible and the patently obvious. Her undergirdering, whilst effective and magnificently engineered was a part of the mystery. These great boudin blancs would move only slightly in response to her occasional sneeze or laugh or launched attack with duster or ruler. The effort caused just sufficient strain on her immaculate cream nylon blouse to only just betray the potential for a Hindenburg like disaster. Her decorum never nudged, she plowed through her small world with determination and the certainty of Scottish Presbyterianism. Breasts to the fore. Badged with heather and a pearl and seemingly only ever signaling her tight wound femininity by weight. Lily and lust were long ago estranged I assumed. Who knew?

Her carriage must have caused her some concern. Never less than straight and set fair, the pull on her dorsal muscles and on her lumbar spine would nowadays be offered help by friendly plastic surgeons over coffee. Lily had only herself to pop and twist into support garments both above and below the skirt line. The whole was representative of unwavering authority, tempered by regular and necessary inspection in covertly placed looking glasses hidden behind doors. She was the very essence of decorum in the scary red and black world of threatened communism and Martin Luther King. This altogether concentrated teaching machine held us all safe whilst the fear of Bay of Pigs and reckless rock and rollers roiled about us far away.

And all the time, she taught me physics, maths, classics and ethics without ever knowing it at all.

Our little school held fourteen pupils all the time I attended with my younger brothers. There being two years between us all, it was never likely that we would share a class so, as the new family, arrived from England with our flat vowels and our apparent and assumed confidence, Lily's task was probably just a little daunting. I was aware by the age of six, just how much easier the world became to manage if adults were regarded as dangerous but generally benign beings who enjoyed the lack of effort needed to maintain my interest. Reflecting back words and phrases offered to me was a skill I adopted early. Avoiding precociousness became my life's work. Lily allowed me some respite from this effort. She recognised in me an eagerness to learn and, while short on time she made every attempt to foster this by offering bok after book after book. Eventually, I was given the job of Library monitor, enabling the first choice of the bi monthly delivery. I spent the majority of my school day reading, fingers in ears or lying in the playground staring at the clouds and dreaming. Either way, it suited Lily.

Realising that intonation and correct vocabulary were more important than context more often than not, I must have been at times unbearable. I generally got away with it however. There was a quick understanding sealed between Lily and me. I was a competent reader with no comprehension problems. The level of numeracy I was expected to achieve in comparison to my peers was already in place. There was time to nurture a mutual support system. It was hard to remember not to overdo it sometimes but the system worked. She left me mostly to my own devices whilst I occasionally dropped back into 'helpless' in order that we neither of us forgot just who was holding things in check.

Mornings at Dervaig Primary began with exactly the same ritual each day. We had slim green, hard backed hymn books from which Lily would choose one of four that she could competently play along to on the piano. She favored 'Jesus Loves Me' over others. I imagine this choice was due to the refrain being relatively short and requiring little prompting to keep to rhythm. Following the successful rendition of this assurance of divine adoration, we were required to recite 'The Lord Is My Shepherd' before finally topping this mini service off with The Lords Prayer.
I was impressed by the words of the 23rd psalm. It felt more poetic than the other stuff we intoned. Lily smiled over my careful phrasing. We were as one in the recitation. We understood the cadences as having import and it felt as good as any of the many compulsive rituals that bind a class together. But then, one Tuesday, she caught me out in a tiny moment of deceit. An act seeming so trivial today as to be laughable but on that day, an act of such personal portent as had not been witnessed since Martin Luther's nailing of his theses to the church doors in Wittenberg.

Dervaig Village Church

Our mother had made it her business to ensure that any good that was to be squeezed from the drying fruit of her Catholicism should be regularly reapplied as varnish to her eldest's soul. I accompanied her to mass from very early on. My life thus far and the tall, spicy, draughty caverns of the church were intertwined. Beginnings and ends of the week punctuated by observance of this or that.
Prayers said, penance shared. Magic witnessed and revered. My father did not share this stuff. He proclaimed a mysterious claim what he called agnosticism. A term that was to come to mean more than faith or atheism together later on. A get out of mass free card which I assumed was bought at a cost to his future destiny. Being certain of my fate, I wondered what prizes awaited the agnostic. My assumption was, as far as I could see at that time, that he and other such uncertain men would be granted visiting rights or holidays in paradise where we would keep their beds and houses clean and warm for their return. Young boys and their mothers meanwhile resided in the blessing of full tenure.

What became of the uncertain soul between these celestial holidays remained a hazy conjecture. How long they were expected to remain outside the gates.. who knew? Our future glory as full communicants was assured, if only due to the tedious adherence to a powerful ritual that my father and his ilk were blessedly permitted to ignore. He was a regular at a table where Pascal's was the best wager on offer. My mother and me were not allowed to play.

The Lord's Prayer as recited by our church differed from the Protestant version in a number of ways. Where they had Debts and Debtors we suffered Trespasses and Trespassers. Our verses felt a little longer as a result and we added an extra 'Ever' into the mix, finally emphasising the nature of infinity as understandable only by us catholics and no others. Our Ad Infinitum was a better class of the Unbounded altogether.

I managed the recitation of this difference as covertly as I could. I would mouth the requisite Protestant version whilst thinking the longer one alongside. This gymnastics was frequently too much for my brain to manage and I would come to a grinding halt, allowing only the faintest expressions of fading adoration to expire between my lips. On this Tuesday, I opened my eyes in an unconcious attempt to pull both halves of my cortex into play. And met Lily's own, first astonished, then with a furious light rising behind them as she gathered herself for the recrimination.

'You are a wicked little boy'. she moaned, 'Wicked and sinful for taking the Lord's Prayer and turning it into a NURSERY RHYME'. Her voice rose in a measured cadence like the bellows of pre partum cattle by the loch.

Suddenly I understood two things simultaneously. I understood why some writers liked to use the phrase 'She Thundered' and, in the very real blink of an eye, I understood the true nature of oraganised ritual. All this intonation. All this singing and recitation was for Lily. For the fabric of the school and her position as conduit of all things right. My previous understanding of a forgiving, lenient god flew from my world to be replaced with plain and simple compassion for Lily in her insecurity. I understood that any sense of right and wrong was, from this point on,mine to negotiate with others and it had never been in the gift of an inexplicable myth.

This was the day I turned to the gaming tables and wondered what the wager would benefit me. It was a little while later that my purse was snatched from me as I laid my bets, by an itinerant priest with little good in him at all.

(an audio version, recorded under the stairs with lapel mics is available here)

Overstanding.

Readers of this diary will have perhaps discerned a tentative theme linking all the other posts. My thoughts are never far from my effort to weave maths into my understanding of our physical environment and of our universe. I'm never far away from media and have become an info junkie where TV and Podcasts are concerned. There are good and not so good resources available. The BBC and Channel 4 generally make a good fist of it, with Discovery tending towards the more populist, music video approach.

It was with some trepidation that I watched Morgan Freeman interpret the script, whilst attempting to bring a basic guide to Universe theory to the Discovery audience. 'Through the Wormhole' is (note I say 'is' as all television is now immediately recallable) the latest in Discovery Channel's canon of Whoosh Bang 'docutainment' pieces. It attempts to draw a linear comparison between three basic concepts and does so with clarity and imagination. (In as far as imagination now requires the kind of cinematography that Kubrick pioneered in 2001 and has not changed since).

Amongst the fireworks, the gravitas and the biblical references chucked in at the start, to appease those who don't hold with physics, there lies a gem. Freeman tells of a group of scientists inhabiting roughly the same time and space, who together and separately develop ideas that challenge each others concepts then come to compliment and add to the sum of all our understanding.

My maths, as some will have gathered by now, has always been a sparring partner. I was given to understand that algebra was the key to all. Without an understanding of 'Sets' then understanding of numbers was impossible. Without an understanding of numbers then calculus and trigonometry would be to me as Chinese or Serbian languages are to British Wild Flowers. 

And all the while, I failed to see what was so difficult about the concepts so described. I grasped Sets and got Venn Diagrams. My view of the world allowed the notion of difference between Apples and Oranges without trouble. There was no problem as far as I could see, with the seemingly impossible task of grouping shapes into forms and relating them to each other. The physical world was so described. I was being told what I already knew. But I was also being told that I didn't and wouldn't understand it.

It was arithmetic I didn't understand. Because I could not see why it was important to be able to perform long division in order that my comprehension of the universe be complete, I stopped looking for links.

Branded a difficult innumerate child, the only gratification I recall registering in my teachers face was when I did indeed fail 'O' level Arithmetic. A feat seemingly reserved for those in 'Remedial' classes and one that cut a notch in the stick they used to beat those unfortunates into servitude on leaving school.

Since that time, and in pursuit of knowledge and creativity, I have gradually come to love the maths I once feigned illness to avoid. There is nothing in our world that is not perfused with the essences of information common to ourselves. We are a part of many sets. Our advantage over other's is our way of seeing the resulting diagrams and making bright diversions into tools.

'Through the Wormhole', adds much to this in it's simple descriptions of the passage of understanding. We have The Big Bang as formulated on the back of Einstein and others. Expansion, currently propounded by brilliant minds at MIT, and M Theory bringing in the whole. This last, a mind expanding beauty, neither confirming nor denying previous notions but fitting all into wonderful, ultimately graspable integrity.
It is to the credit of the program makers that the term 'Wormhole' never appears in the script of the first episode.

Having viewed the program and been through a series of physical symptoms known to all thrill seekers, I wondered about how to turn this clarity and excitement into useable form. How to benefit from the story in a lasting way.

I took the puppy for a walk and we talked about up and down and sideways and how long it took to get from here to there and why.

Alfie now 'sits' much quicker. A definite side benefit.

 We decided, Alfie and me, that it was less than helpful to think about our small three dimensional space as having markedly different elements. It is, after all, only our experience of gravity that confines us to Up or Down or Sideways. If all three directions we inhabit are merely termed as 'space' it becomes easier to think about the addition of a further one direction. That thought removes the need for numbers to be involved. For now.
We walked and, in the sudden clarity that seems to enhance access to memories I remembered questioning my teacher once (and only once) about the axis that may be between x and y on a graph.

Further, I wondered was there an 'out of' the point Zero where positive and negative plot points converge. 
It may well be that he had not encountered the idea of 'x', 'y' and 'i' and probably considered the Sqare Root of minus one to be an amusing mathematician's witticism. Either way and in any and all possible events, he sneered at my ambition and turned his back. I remember that black robed back very well indeed. I also remember wishing that I could feel confident in an encouraging respomnse had I discussed my thoughts with him about Topology and the similarities between the wood on five bar gates and gravity.

So, armed with the safety of a general sense of 'surround' it becomes more possible to pull a fourth way into the picture. One that does not yet require Time but remains within our linear perception.

We play with Möbius Strips and Klein Bottles (as seen in previous posts). We enjoy having our perceptions messed about with so long as we return to the safety of comprehension at the end. I remember watching the beautiful simplicity of Carl Sagan's teaching when demonstrating how a square may be 'forced' into another dimension as it is revealed as a cube and casts a shadow on a two dimensional world. His desktop became a Flatland analogy and a little girl watching, was rapt.

I play computer games. We have come a long way from Space Invaders now in many respects. Although the necessary suspension of disbelief remains the key to their success. We are now able to become immersed in stories that require our presence, to spring into being and live with us here. The cinematic metaphor no longer applies to gaming, (beyond those magical intro sequences) and we are now offered character parts in tales without boundaries, tales that require our skills and creativity to develop and defeat or lose. Our actions are limited only to the quantum distance between pixels, as described in photons. We have access to all the dimensions we know and, due to the confines of a screen, our recreation in some more dimensions is made fact. There has not been so great a revolution in narrative entertainment since the invention of the printing press. A radio play and good book will always win out as simplicity is all when great stories are successful but we now approach Gaming in a new way. We are able to exercise our understanding of the world in ways impossible before.

'Portal 2' is, of course, in two dimensions. I literally shudder to imagine the task that faced it's programmers as they sketched out the concept way back when. We play, as the developers know, to their rules. Rules that we have agreed to adhere to as we have bought into their previous works, the Half Life series and Portal 1, which gradually abandoned the need for shooting, ducking and hiding in favour of the manipulation of your environmental dimensions. All this for entertainment. And, just as we walk, and Alfie fetches willingly, unaware of the hidden agenda that has taught him to return and sit on cue, I gratefully immerse myself in others efforts. I am entertained, delighted and informed along the way. The programmers toss me pixels. I part with cash. The payoff though, for me is much, much bigger than my wallet.

Briefly, set in a dystopian, industrial testing station, you are awakened to discover that your success in the prequel has resulted in merely starting your ordeal again...
Negotiating the various topological tests you are offered depends on your ability to manipulate your surroundings using a new physics.
Portal requires the creation of an 'In' and an 'Out' door in selective, flat surfaces. Sometimes to escape the confines of a room and sometimes to advance your understanding of the natural laws.
Using a 'Portal Gun' it is possible for example, to enter a wall and immediately exit the ceiling of the same room. The potential for adventurous problem solving geometry and topological exploration becomes enormous.
Physics remains constant. The further you fall the faster your momentum gathers and the further you may correspondingly leap as a result. There is much hilarity and there are actual 'pit of the stomach' moments as you successfully fire a portal at an approaching floor and rush headlong at twice your entry speed, onto a previously unscalable height.

And all the while, remembering that the gates you make are not merely 'holes in walls' but that they are actually 'bending space', becomes your increasingly mesmerising mantra. Correspondingly, the comprehension of inter dimensional geometry becomes tangibly 'in the world'.

Suddenly, with help from a belligerent, anxious maths teacher (see above), the abandonment of religion as a cheap salve to confusion and a computer doing what it does best, M Theory is put within the reach of the innumerate.

The journey that led to the development of M Theory was intriguingly fraught with difficulty. Having come to separate similar conclusions about their individual efforts to understand expansion as an explanation of the creation. Two scientists not only worked in tandem with their opposition in the field but used the scientific process to it's limits and beyond, in order that all predecessing information was not lost. The humility with which they greeted the condemnation of the scientific community made for a consolatory lakeside walk in the early hours, in Finland where a conference had heard their thoughts and tossed them back. A time to discuss where they may have missed the point, where the goal became the thing rather than the workings. And so Dark Energy was conceived.
And suddenly, the simple construct of a never ending cyclic system comes real. The desperate grip we have maintained on traditional ideas of 'time' is loosened. At once, it is possible to turn and face the world we live in and relinquish gods.

I am so tempted to talk here about my own humility. To make a blushing statement about my inability to grasp the bigger picture and to leave the workings to the boffins there at Cern. Why should we do that though? A understanding stands of value regardless of the numbers. And it was with a burst of pleasure that I found myself writing on the back of a magazine, in mathematical symbols with the names and dates. Reminding myself of key events and elements of the theory, arrows and equals signs and 'more than' crossings out. Here, I was joining in the dialogue. The maths made real. My mind was suddenly engaged and all this possible at last through my fantasy and hope of confluence of science and art. I seem to be a mathematician after all. And so because a common  language binds the themes.

The theory? If we are stuck with linear Time and the minuscule 'A-Tomic' nature of the Big Bang from a Singularity of infinite Density and Heat, then our minds are stuck with "Yes, but what before?". Here is the rod that I have been swiped at with by creationists in doorstep and online debate. They come from a far more powerful position, all they need to do is wait, and point at scripture. They have a strange interpretation of our common philosophy but it allows them to maintain a millenium of belief, backed up by frightened church authority and those without the stomach for a fight. Misunderstanding or ignorance are thrown back as 'Lies' and God is cited as the arbiter of reality.

This arbiter has, however only been available to us for a few thousand years. gods the world over have only flourished as a result of technology and before, it was never made clear why they only showed their faces to a few rural peasants or quite why there has been no encouragement to write the tracts that bind the faith together over and over as we gain more empirical understanding of the world.
There is no need for super nature. We are still recovering from the medieval construct of our world. We need no longer permit this halting force to stay progress.

If my understanding remains simple and I get the basic premise then, there is no need either for a Uni-verse. Any more than there was evidence for flat earth or a single solar system or a solo Milky Way. The probability of more than 4 dimensions makes more sense. Space time and gravity and light are armatures and through the incomprehensible gaps in structure, information is shared across, from small time to infinitesimally small time.

Our universe will once again become too close in time and state to another. There will be more almost instant conversions of matter as Membranes converge or touch. A bigger bang may well result and round and round we go again. Except, there is no 'again' and no 'round'. There just 'is'.

We inhabit time as we inhabit space. Equipped only for the bits that we can sense. If able to abandon those senses, even briefly. It is possible to get a wonderful impression of our suddenly enhanced position in our place. No gods, no fairies and no beginning or end. Just so.

And furthermore, as Alfie has no concept whatsoever of his origins in Spain, and the worms that inhabit his gut are ignorant of their simple place, I relish being wrong about these thoughts. Because I can. I am allowed.

Imagining the unimaginable?

There are many challenges in my exploration of ideas. My attempt to fit a small understanding of String theory into the earthbound topographic universe via lawn strimming is fraught with the potential for misinterpretation and retreat from the unimaginable.
I am reminded of Father Dougal in 'Father Ted', trying to do a jigsaw with a hammer. If at first you don't succeed, hit it until it fits.

In balance, the small understanding that occurs may be a 'good enough' payoff. Hardly Socratic, but close...

It pays to adopt a Lewis Carrol attitude I think. (I know, I know, the quote is 'Wonderland', the image is 'Looking Glass'. More of this later!)


"Alice laughed: "There's no use trying," she said; "one can't believe impossible things."
"I daresay you haven't had much practice," said the Queen. "When I was younger, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast."
Alice in Wonderland.

The concept of multiple dimensions, accommodating particles and 'states of matter' in various ways has been elegantly played with by Greg Egan, Isaac Asimov, Stanislaw Lem and many others. Fiction is the common starting point for so many ideas and mental journeys. It is through these writings that I have formed a curiosity.

There are times when the sheer unlikelihood of a thing shocks you into a more receptive, less logic bound state. It is this shock that keeps me entertained by my scant acquaintance with Physics.
I read in the Guardian today of one such unlikely thing.

I mean, first off, just how unlikely is this thing?



It gets better. Apparently, the Platypus has new secrets recently unlocked.

We humans, not far along the evolutionary scale from these fabulous creatures, have two sex chromosomes X and Y. The Platypus has ten. Five of each kind. In humans, sex is determined by one pair of chromosomes: a woman has two X chromosomes, and a male has an X and a Y.
One of the platypus's sex chromosome pairs contains combinations similar to these, but another resembles the ZZ/ZW sex chromosome system found in birds. This raises an opportunity for an Impossible thing moment. How would you perceive a sex that was neither male nor female? Is it necessary to define gender if exploring this concept? Does sex decide reproductive function? Is it necessary or desirable to have complimentary sexes? Should we ask the gastropods?

Speed and sneezing

Today's run


Set off from home today to try 20 miles. Got to Blyth in good time and decided to press on to Bedlington. Here's a site about a rather grand building just outside the village.

En route, I became aware of a tickle in the nose and a powerful aroma of plasticine. Rounding the corner of the road to Nedderton, (neat topiary sir!) I found myself bounded by two rape fields..

Pollen is interesting stuff. Not only irritating and , at times, debilitating of those suffering hay fever. I remembered that it had a part to play in the Einstein story. I thought for a bit and then remembered Brownian Motion was illustrated by the movement of pollen grains in apparent agitated ways when observed in water.

To my young mind, this was magical in a Clarkeian way (Any sufficiently advanced technology is indistinguishable from magic). When I read about it as it seemed to link our world, with it's clumsy analogy seeking science to the quantum world where small things travelled huge distances but never impacted on us in any observable way.

Inspired, I took the next downhill corner at speed and broke the limit for the first time since I did my penance for infringement of the rules at a local roadworks (34 in a 30 area. I ask you!). My computer showed a 'mx spd' of 35.9 mph. The average for the trip (31.5 miles) was a mere 13.9 mph. This does illustrate the fabulous efficiency of the bicycle however.
Speeds of around 17 mph make very real distances achievable and make for a rival to the car. Whilst Claire can easily run to South Shields and make this a meaningful journey in emergencies, the bike makes such journeys possible in practicable time with plenty left over for life saving, retrieving lost sunglasses or a nice lunch out etc...