I have been involved in the creation of a European pre-standard for the validation of computational models used to predict the structural performance of engineering systems [see ‘Setting Standards‘ on January 24th, 2014]; so, an example of a two thousand year old standard in the National Palace Museum in Taipei particularly attracted my interest during a recent visit to Taiwan. A Jia-liang is a standard measure from the Xin Dynasty dated to between 9 and 24 CE. It is an early form of standard weights and measure issued by the Chinese emperor. The main cylinder contains a volume known as a ‘hu’; however, if you flip it over there is a small cylinder that contains a ‘dou’ which is one tenth of a ‘hu’. The object that looks like a handle on the right in the photograph is third cylinder that holds a ‘sheng’ which is one tenth of a ‘dou’ or one hundredth of a ‘hu’; and the handle on the left contains a ‘ge’ when it is as shown in the photograph and a ‘yue’ when the other way up. A ‘ge’ is tenth of ‘sheng’ and a ‘yeu’ is a twentieth. The Jia-liang was made of bronze with all of the information engraved on it and was used to measure grain across the Xin empire.
I stayed in Sheffield city centre a few weeks ago and walked past the standard measures in the photograph on my way to speak at a workshop. In the past, when the cutlery and tool-making industry in Sheffield was focussed around small workshops, or little mesters, as they were known, these standards would have been used to check the tools being manufactured. A few hundred years later, the range of standards in existence has extended far beyond the weights and measures where it started, and now includes standards for processes and artefacts as well as for measurements. The process of validating computational models of engineering infrastructure is moving slowly towards establishing an internationally recognised standard [see two of my earliest posts: ‘Model validation‘ on September 18th, 2012 and ‘Setting standards‘ on January 29th, 2014]. We have guidelines that recommend approaches for different parts of the validation process [see ‘Setting standards‘ on January 29th, 2014]; however, many types of computational model present significant challenges when establishing their reliability [see ‘Spatial-temporal models of protein structures‘ on March 27th, 2019]. Under the auspices of the MOTIVATE project, we are gathering experts in Zurich on November 5th, 2019 to discuss the challenges of validating multi-physics models, establishing credibility and the future use of data from experiments. It is the fourth in a series of workshops held previously in Shanghai, London and Munich. For more information and to register follow this link. Come and join our discussions in one of my favourite cities where we will be following ‘In Einstein’s footprints‘ [posted on February 27th, 2019].
The opinions expressed in this blog post reflect only the author’s view and the Clean Sky 2 Joint Undertaking is not responsible for any use that may be made of the information it contains.
An axiom is a statement so evident or well-established that it is accepted without controversy or question. However, in his review of Sokal’s Hoax, Steven Weinberg has suggested that ‘none of the laws of physics known today (with the possible exception of the general principles of quantum mechanics) are exactly and universally valid’. This propels physics to the same status as biology (see my post entitled ‘Laws of biology?‘ on January 13th 2016) – in lack exactly and universally valid laws and it suggests that there are no scientific axioms.
‘Things that are equal to the same things are equal to each other’ is Euclid’s first axiom and in thermodynamics leads to the Zeroth Law: ‘Two things each in thermal equilibrium with a third are also in thermal equilibrium with each other’ (see my posts entitled ‘All things being equal‘ on December 3rd, 2014 on ‘Lincoln on equality‘ on February 6th, 2013). Thermal equilibrium means that there is no transfer of thermal energy or heat between the two things, this leads to the concept of temperature because when two things are in thermal equilibrium we say that they are at the same temperature. Last week I explained these ideas in both my first year undergraduate class on thermodynamics and my on-going MOOC. This week, I have challenged MOOC participants to try to identify other measurement systems, besides temperature, that are based on Euclid’s first axiom.
For instance, its application to mechanical equilibrium leads to Newton’s laws and from there to mass as a measure of a body’s inertia. We use Euclid’s axiom to evaluate the mass of things through a chain of comparisons that leads ultimately to the international kilogram at the Bureau International des Poids et Mesures in France. Similarly, we measure time by comparing our time-pieces to an international standard for a second, which is the duration of 9,192,631,770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
However, given Weinberg’s statement perhaps I can give you a harder challenge than MOOC participants: can you identify exceptions to Euclid’s first axiom?
I think I can identify one: if you calibrated two very accurate timepieces against a cesium 133 clock and then took one on a journey through space travelling at the speed of light while the other remained on Earth, when you brought the two together again on Earth they would not agree, based on Einstein’s theory of relativity, or what he called relativity of simultaneity. Now see what you can come up with!
Joseph Schwartz & Michael McGuinness, Einstein for Beginners, London: Writers and Readeres Publishing Cooperative, 1979 & Penguin Random House, 2013.
Albert Einstein, Relativity: The Special and the General Theory, (translated by Robert W. Lawson), London: Methuen & Co Ltd., 1979 & on-line at www.bartleby.com/173/