Earliest memories: Part 1

I wrote the following some while ago and thought I had published it, but either I hadn't or else I had accidentally unpublished it. So here it is, but as I now have more material I want to share it will have to be renamed with "Part 1" in the title.

Possibly my earliest memory is sharing a bath with my older sister and somehow slithering around so that I was face down in the water, at which I made such a commotion that I was quickly rescued. This occurred more than once so that taking a bath became a dangerous mission. For me to remember this at such an early age, it must have been very traumatic and may well be why I still easily panic when out of my depth in water.

I've noted elsewhere how I distinctly remember posing for this photo, feeling the coarse sand-dune grass scratching my body. I like to think the location was our favourite holiday haunt Brea Hill, Daymer Bay but I cannot be sure.

I remember, pre-school, standing, legs apart, on the dining room fireplace hearth and swaying from one foot to the other whilst enquiring of my older sister what was school like, and then years later asking her what senior school was like ("Physics" - 'what's that?', "oh ever so boring, all about light and speed and weight and stuff" - 'sounds very interesting to me!')

Pose for annual official photo at APS

Of course I remember my first day at Alresford Preparatory School ('APS', a dame school), at least I remember being introduced by my older sister. My older sister comes into many of these tales. I can remember not wanting this cheap toy telephone to be in my official photograph but being told to pose like this. Back then the government provided all pupils with a third pint bottle of milk every day and this we consumed via a straw. In the winter it was sometimes frozen and I remember the disgust I felt at the teacher saying it was "just like ice cream". Adults sometimes say ridiculous things to children and expect them not to be taken in. On one occasion I tried blowing instead of sucking through the straw, with disastrous results. But it was only an experiment - how else does one learn? 

My mother and me

That's my mother, just how I remember her: this picture still gives me a lump in my throat. Memory is so frustrating: I feel like I ought to be able to recall, oh, so much more but in fact I remember so little about my parents, good as they were. She loved flowers, that much I can remember - and her signature meal was roast lamb with all the trimmings (which would include Yorkshire pudding even with lamb).

We aggravate the world by first being born then, in order to stay alive, by consuming its bounty until we die and rot in our graves leaving behind no more than an aroma and a feint but gradually vanishing memory in the minds of those we came in contact with.  Such is life and what is achieved?  All is vanity!

I did it! Again!

This time the goal was to "do" the Granite Way, a dedicated cycle route from Okehampton to Lydford on the track bed of the former Dartmoor railway which originally ran all the way to Cornwall and follows the northern border of Dartmoor passing several of its Tors.

My track: 94.2 miles, 2045m elevation gain, average 10.3mph

The outward journey was the same as for the Tarka trail up to Crediton. To ring the changes my return journey started with a segment of A30 which is a major trunk dual carriageway with very fast traffic and then veered northwards at Whiddon Down crossing the mid-Devon aka Tarka branch line several times.

A carefully dosed administration of magnesium ions in the form of supplement tablets and, on returning home, an Epsom salts bath successfully warded off cramp which on former long bike rides has plagued me.

You can view my photos here. Some notes on the photos in order:

• The trail starts at Okehampton station which is currently being resurrected from 50 years of inactivity;
• The trail is initially adjacent to the still existing but disused railway track as far as and which served a quarry; 
• Beyond the quarry the trail goes over the Meldon steel girder viaduct, after which I deviated to view the nearby Meldon reservoir and dam from which the viaduct is visible;
• Later on it crossed a second smaller viaduct made of granite
• The trail terminates rather abruptly in Lydford, a charming village where everyone I met was very friendly;
• I went a bit further to check out Lydford castle and church;
• To return I retraced my steps, stopping to snap a lovely beech avenue, a sample of the short stretch of unpaved surface, and a view of the Sourton Tor on the skyline;
• Some more views of the Meldon viaduct and its inner workings;
• I left the trail just before its end to access the A30 as suggested by Google maps and to do so had to masquerade as an Emergency Vehicles Only;
• I've included a couple of views of where I crossed the mid Devon line.

Whilst 94 miles in one day seems like an achievement for me, it was nothing compared with the guts and stamina and tenacity we have witnessed in the 2020 Paralympics.

Can you know for sure?

Every science pupil knows about drawing a best-fit straight line by eye through a scatter plot of experimental data. But at college level I discovered something so much better in regression analysis. Better, because the resulting best-fit (trend) curve or line (polynomial) is mathematically deterministic and no longer depending on the vagaries of human judgement. Apt and questionable use of regression is well illustrated by...

The black dots represent experimental data, the same in all 12 graphs, and the various red lines are "best fit" attempts to determine the underlying theory that explains these data. In the simplest case the experimenter will massage the theory into an equation of a straight line, plot the data according to this equation and then using linear regression to fit the best straight line as in the first graph. The resulting gradient and y-intercept are the summary data and the correlation coefficient provides a measure of confidence level. 

Measured data is generally discrete as well as being subject to experimental error, whereas the theory is hoped to be exact and generally continuous. For example, with an experiment to verify the well known equation for the period of a simple pendulum:

the period T will be measured for discrete values of length L.  Squaring both sides of the theoretical equation shows that plotting T² against L should result in a straight line through the origin whose gradient will give a value for the acceleration of free fall g.

Whereas the period might have been measured for discrete lengths, regression will give us a value for the period at any length. Getting a value in this way within the experimental range is called "interpolation", or outside that range is called "extrapolation". The latter is often unreliable, as illustrated in the last graph above, especially for higher orders of the regression polynomial.

Valid or spurious?

But even interpolation can be tricky. Consider the experimental data depicted in the above graph. The "outlier" red point might be due to human measurement error or might describe some real but anomalous phenomenon. If in fact no measurement had been taken at this x-axis value any such phenomenon would have been missed. Of course the correct action in either case would be to take more measurements. But this freedom to re-measure is not always feasible, particularly if we are dealing with data measured historically or with apparatus that is no longer available or is too costly to set up.

We are talking about experimental data versus theory. Science is all about coming up with theories to explain observed phenomena. In physics the epitome would be to fulfil the quest for the so far illusive Theory of Everything. 

As you can see from the Curve Fitting Methods image, there might be more than one theory that fits the same experimental data, so which is the correct one? An example is the wave / particle duality of elementary particles. That light was observed to sometimes behave as a wave, and at other times as a stream of particles, birthed the start of what we now call Modern Physics. Back then these two theories seemed to be at odds but we now accept that they are different facets of the same truth. Enter the "greatest mistake" in Arago's spot. And we are similarly happy with the concept that what we call matter is not as tangibly solid as suggested by Thomas' "Unless I see in his hands the mark of the nails, and place my finger into the mark of the nails, and place my hand into his side, I will never believe" but rather is subject to the fuzzy laws of probability - or at least so quantum theory says.  But these are theories often beset with hard or costly to obtain data and of course we can neither directly "see" nor touch some of this stuff. Think Large Hadron Collider, the world's largest and highest-energy particle accelerator.

To the uninitiated the various "modern" theories such as General Relativity, String theory and the Standard Model with its quarks and more recent supposed anyons that can only exist in 2D appear whacky indeed and the only reason there are no large scale public demonstrations to either refute or endorse them is, I suppose, because the average member of the public doesn't have a clue about what they all mean or their relevance to every-day life.

But perhaps none of these currently accepted theories is in fact the best fit to the data, witness that a Theory of Everything has not yet been proposed. And perhaps a similar argument can be applied to other realms, for example climate change aka global warming and the role of CO2 where a lot depends on questionable extrapolation. Add to this the political agendas that seem so often to have the media promoting particular theories to their own end and you have such a mishmash that all the ordinary person is left to choose is whether to go with the flow or go against the flow, neither course being as strongly based on science or truth as we would like. 

Part 2