uncertainty

Less uncertain predictions

Ultrasound time-of-flight C-scan of the delaminations formed by a 12J impact on a crossply laminate (top) and the corresponding surface strain field (bottom).

Here is a challenge for you: overall this blog has a readability index of 8.6 using the Flesch Kincaid Grades, which means it should be easily understood by 14-15 year olds.  However, my editor didn’t understand the first draft of the post below and so I have revised it; but it still scores 15 using Flesch Kincaid!  So, it might require the formation of some larger scale neuronal assemblies in your brain [see my post entitled ‘Digital Hive Mind‘ on November 30th, 2016].

I wrote a couple of weeks ago about guessing the weight of a reader.  I used some national statistics and suggested how they could be updated using real data about readers’ weights with the help of Bayesian statistics [see my post entitled ‘Uncertainty about Bayesian statistics’ on July 5th, 2017].  It was an attempt to shed light on the topic of Bayesian statistics, which tends to be obscure or unknown.  I was stimulated by our own research using Bayesian statistics to predict the likelihood of failure in damaged components manufactured using composite material, such as carbon-fibre laminates used in the aerospace industry.  We are interested in the maximum load that can be carried by a carbon-fibre laminate after it has sustained some impact damage, such as might occur to an aircraft wing-skin that is hit by debris from the runway during take-off, which was the cause of the Concorde crash in Paris on July 25th, 2000.  The maximum safe load of the carbon-fibre laminate varies with the energy of the impact, as well as with the discrepancies introduced during its manufacture.  These multiple variables make our analysis more involved than I described for readers’ weights.  However, we have shown that the remaining strength of a damage laminate can be more reliably predicted from measurements of the change in the strain pattern around the damage than from direct measurements of the damage for instance, using ultrasound.

This might seem to be a counter-intuitive result.  However, it occurs because the failure of the laminate is driven by the energy available to create new surfaces as it fractures [see my blog on Griffith fracture on April 26th, 2017], and the strain pattern provides more information about the energy distribution than does the extent of the existing damage.  Why is this important – well, it offers a potentially more reliable approach to inspecting aircraft that could reduce operating costs and increase safety.

If you have stayed with me to the end, then well done!  If you want to read more, then see: Christian WJR, Patterson EA & DiazDelaO FA, Robust empirical predictions of residual performance of damaged composites with quantified uncertainties, J. Nondestruct. Eval. 36:36, 2017 (doi: 10.1007/s10921-017-0416-6).

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Coping with uncertainty

The first death of driver in a car while using Autopilot has been widely reported with much hyperbole though with a few notable exceptions, for instance Nick Bilton in Vanity Fair on July 7th, 2016 who pointed out that you were safer statistically in a Tesla with its Autopilot functioning than driving normally.  This is based on the fact that worldwide there is a fatality for every 60 million miles driven, or every 94 million miles in the US, whereas Joshua Brown’s tragic death was the first in 130 million miles driven by Teslas with Autopilot activated.  This implies that globally you are twice as likely to survive your next car journey in an autonomously driven Tesla than in a manually driven car.

If you decide to go by plane instead then the probability of arriving safely is extremely good because only one in every 3 million flights last year resulted in fatalities or put another way: 3.3 billion passengers were transported with the loss of 641 lives, which is a one in 5 million.  People worry about these probabilities while at the same time buying lottery tickets with a much lower probability of winning the jackpot, which is about 1 in 14 million in the UK.  In all of these cases, the probability is saying something about the frequency of occurance of these events.  We don’t know whether the plane will crash on the next flight we take so we rationalise this uncertainty by defining the frequency of flights that end in a fatal crash.  The French mathematician, Pierre-Simon Laplace (1749-1827) thought about probability as a measure of our ignorance or uncertainty.  As we have come to realise the extent of our uncertainty about many things in science (see my post: ‘Electron Uncertainty‘ on July 27th, 2016) and life (see my post: ‘Unexpected bad news for turkeys‘ on November 25th, 2015), the more important the concept of probability has become.   Caputo has argued that ‘a post-modern style demands a capacity to sustain uncertainty and instability, to live with the unforeseen and unpredictable as positive conditions of the possibility of an open-ended future’.  Most of us can manage this concept when the open-ended future is a lottery jackpot but struggle with the remaining uncertainties of life, particularly when presented with new ones, such as autonomous cars.

Sources:

Bilton, N., How the media screwed up the fatal Tesla accident, Vanity Fair, July 7th, 2016

IATA Safety Report 2014

Caputo JD, Truth: Philosophy in Transit, London: Penguin 2013.

Ball, J., How safe is air travel really? The Guardian, July 24th, 2014

Boagey, R., Who’s behind the wheel? Professional Engineering, 29(8):22-26, August 2016.

More uncertainty about matter and energy

woodlandvalley

When I wrote about wave-particle duality and an electron possessing the characteristics of both matter and energy [see my post entitled ‘Electron uncertainty’ on July 27th, 2016], I dodged the issue of what are matter and energy.  As an engineer, I think of matter as being the solids, liquids and gases that are both manufactured and occur in nature.  We should probably add plasmas to this list, as they are created in an increasing number of engineering processes, including power generation using nuclear fission.  But maybe plasmas should be classified as energy, since they are clouds of unbounded charged particles, often electrons.   Matter is constructed from atoms and atoms from sub-atomic particles, such as electrons that can behave as particles or waves of energy.  So clearly, the boundary between matter and energy is blurred or fuzzy.  And, Einstein’s famous equation describes how energy and matter can be equated, i.e. energy is equal to mass times the speed of light squared.

Engineers tend to define energy as the capacity to do work, which is fine for manufactured or generated energy, but is inadequate when thinking about the energy of sub-atomic particles, which probably is why Feynman said we don’t really know what energy is.  Most of us think about energy as the stuff that comes down an electricity cable or that we get from eating a banana.  However, Evelyn Pielou points out in her book, The Nature of Energy, that energy in nature surrounds us all of the time, not just in the atmosphere or water flowing in rivers and oceans but locked into the structure of plants and rocks.

Matter and energy are human constructs and nature does not do rigid classifications, so perhaps we should think about a plant as a highly-organised localised zone of high density energy [see my post entitled ‘Fields of flowers‘ on July 8th, 2015].  We will always be uncertain about some things and as our ability to probe the world around us improves we will find that we are no longer certain about things we thought we understood.  For instance, research has shown that Bucky balls, which are spherical fullerene molecules containing sixty carbon atoms with a mass of 720 atomic mass units, and so seem to be quite substantial bits of matter, exhibit wave-particle duality in certain conditions.

We need to learn to accept uncertainty and appreciate the opportunities it presents to us rather than seek unattainable certainty.

Note: an atomic mass unit is also known as a Dalton and is equivalent to 1.66×10-27kg

Sources:

Pielou EC, The Energy of Nature, Chicago: The University of Chicago Press, 2001.

Arndt M, Nairz O, Vos-Andreae J, Keller C, van der Zouw G & Zeilinger A, Wave-particle duality of C60 molecules, Nature 401, 680-682 (14 October 1999).

 

Steadiness and placidity

Picture5Writing a weekly blog must be a little like being a newspaper columnist except that I am not part of team of writers and so there is no one to stand in for me when I go away.  Instead I have to get a few weeks ahead before I go away. So I will be on vacation when you read this post and I hope that I will have achieved a certain level of ‘steadiness and placidity’ to quote Michael Faraday.  Faraday used to escape to Hastings, on the south coast of England, for breaks away from the hustle and bustle of London.  He would take walks [see my post on August 26th, 2015 entitled ‘Take a walk on the wild side‘] and spend time on the seashore [see my post on May 4th, 2016 entitled ‘Horizon Therapy‘] to achieve ‘a kind of mental detachment, an ability to separate himself from things as they are and accept the given – certainties and uncertainties’ [from his biography by James Hamilton], which he described as ‘steadiness and placidity’.

Source:

Hamilton, J., A life of discovery: Michael Faraday, giant of the scientific revolution. New York: Random House, 2002.