by Jeevanjyoti Chakraborty
The annual Newport Folk Festival held at Newport, Rhode Island (the smallest state of the United States situated near its north-east coast) between July 26 and 28, 1963 has a special place in the history of music. It was during those three days that a raw, twenty-two year old Bob Dylan first really caught widespread attention after being propped into the limelight by his friend, Joan Baez. His breakthrough song was “Blowin’ in the wind”.
Looking back, that breakthrough had to happen! For, when Dylan asked in his song “… how many years can some people exist before they are allowed to be free”, it reverberated immediately with the zeitgeist – after all, those were the days of the civil rights movement in America. It also was a throwback to the ancient hymns of the oppressed blacks. Indeed, Dylan had adapted the music of the nineteenth-century Negro song, “No more auction block” for his song.
But the issue of origins and inspirations is best left to music historians. The issue that needs explaining, however, is why should we be discussing Dylan’s song in a section devoted to “Science” in this special anniversary issue of Spark? To borrow from the lyrics itself, “the answer, my friend is” in the second stanza of that very song:
Yes, ‘n’ how many years can a mountain exist
Before it is washed to the sea?
So what really is so special about this line from a scientific viewpoint? To answer this question, let us move north from Newport – a mere 37 kilometres – to the capital city of Rhode Island, Providence. For it was here at the Brown University, almost a month after the Newport Folk Festival, from Aug. 26-30, 1963, that the Fourth International Congress on Rheology was held in which Prof. Markus Reiner said the following in a rather interesting lecture:
The way out of this difficulty had been shown by Prophetess Deborah… In her famous song after the victory over the Philistines, she sang “The mountains flowed before the Lord.”
While this quote shows that a line – actually quoted from the Bible – that sounds similar to that line of Dylan’s song had been mentioned in a scientific congress, it hardly signifies any scientific merit in itself. Apparently. To really understand what is going on, we need to look a little deeper. In particular, we need to answer the set of obvious questions thrown forth by the above quote and the context itself:
What is this thing called “rheology”?
Who is Prof. Reiner?
And, most importantly for the key answer, why in a scientific setting was he referring to a Biblical character?
To answer these and appreciate the scientific relevance of Dylan’s line, let us talk a little science and try to get to the roots.
First off, “rheology”. Hmm… looks like a typo (theology?) at first glance but it is very much a field of study in its own right. Let us try to understand what it is all about.
We are all familiar with the flow of water through pipes. We see it all around us. But then what other examples of flow can you find around yourself… inside yourself? Flow of oil; flow of blood. What else? Think of something thicker, something that’s a bit harder to get to flow… Ketchup! Remember how every time you have to get ketchup out of the bottle, you have to shake it hard or hit the bottle at the bottom? Clearly, this behaviour is different from what is exhibited by something like water or refined wall.
Now, consider something different: take your pen cap for example, or a measuring ruler – if you can get a thin metallic one, even better. Our everyday experience says that both the pen cap and the ruler are nice, compact, solid objects. Of course, that’s not quite wrong. After all we can’t “pour” the pen cap or the ruler from, say, one box to another such that a part of the pen cap or the ruler “flowed” into the second box while the remaining part stayed back in the first box! Of course, if you applied a hard enough pressure, you would be able to bend them a bit but the moment you release that pressure they would spring back to their original shape. But what happens if you press really hard? They bend again, a little more this time. And what if you press really, really hard? Well, they bend even more but something interesting happens. This time, after you have pressed really, really hard, if you release the pressure, the pen cap or the ruler doesn’t spring back to its original shape! We might say that the solid material has yielded to our force. And, after it has “yielded”, you would not need to press that hard to deform it further!
In every day parlance, ketchup is a liquid while the pen cap or the ruler is a solid. If we try to define a liquid by saying that it is something which flows, then that is not quite strictly true because, remember, the ketchup didn’t flow until we forced it to. Similarly, if we try to define a solid by saying that it is something which doesn’t flow or deform easily, then that again is not strictly true because the pen cap or even the metallic ruler did begin to deform easily once a threshold had been crossed. In this situation, therefore, the line between liquids and solids begins to get blurred. The field in which a systematic study of this kind of behaviour – solids which might flow or liquids which do not quite flow – is carried out, is called rheology.
The designation of this field of study was coined by Prof. Eugene Cook Bingham back in the 1920s (after consultation with a colleague of classical languages) inspired by the Greek philosopher, Heraclitus’ general thoughts on flow/change encompassed in the aphorism “panta rhei” meaning “everything flows”; rhei in Greek means “to stream”. And guess who Prof. Bingham consulted with regarding the scientific implications of this nascent field of study when the foundations were being laid? That’s right – Prof. Markus Reiner.
So, we now come to the final question: why was Prof. Reiner referring to the Biblical character, Prophetess Deborah in that lecture during the Fourth International Congress on Rheology in 1963?
As he himself pointed out during that lecture, even though the designation of “rheology” was inspired by the “everything flows” concept, it was a bit misleading because that would strictly imply that rheology was a branch of study which had nothing to do with solids which didn’t flow. But the reality is that it does. Indeed, the mathematical framework in rheology is very general and it is well-equipped to capture a wide spectrum of behaviour of “liquids” and “solids” – more appropriately, of a wide variety of soft materials which needn’t necessarily be solids or liquids! It was to correct this situation that Prof. Reiner suggested a more general technique to characterize material behaviour.
We all know that different units are used to measure different things. For example, length is measured in metres, time in seconds, weight in grams, and so on. Some times for some other measurements, the units are named after scientists who contributed to the fundamental understanding of that what is being measured; examples of this kind are Newton for force, Ampere for electric current, and so on. In certain special situations, however, it is easier and more informative if the measurements are expressed not in terms of any unit but as a ratio of some measurements such that the resulting ratio does not have any unit. This method is very useful to understand the intrinsic behaviour of materials. Since they do not have any units, they are referred to as different kinds of “non-dimensional numbers”.
It was this method of using a special non-dimensional number which Prof. Markus Reiner suggested to characterize the behaviour of the materials that are generally studied in rheology. Again in his own words:
We may therefore well define as a non-dimensional number the Deborah number
D = time of relaxation/time of observation.
The difference between solids and fluids is then defined by the magnitude of D. If your time of observation is very large, or, conversely, if the time of relaxation of the material under observation is very small, you see the material flowing. On the other hand, if the time of relaxation of the material is larger than your time of observation, the material, for all practical purposes, is a solid.
…
The greater the Deborah number, the more solid the material; the smaller the Deborah number, the more fluid it is.
If you are wondering what this “time of relaxation” is, just think of it as the time that is required by a system to go to a relaxed or equilibrium state after it has been disturbed – and yes, it is the general property of materials to try to always go to a relaxed state (the one with the minimum energy). Liquids like water have a very low relaxation time in response to disturbances like that due to gravity – which is why they are so easy to pour; on the contrary, ketchup has a larger relaxation time which is why you have to introduce external disturbances (like shaking or hitting the bottle) to effectively reduce the time of relaxation.
So there you have it: one general method of characterizing material behaviour using a simple ratio! In the long list of non-dimensional numbers that are used in the scientific literature, the Deborah number is quite special. Because unlike most other non-dimensional numbers which are named after scientists or the physical phenomenon under consideration, the Deborah number is named after a Biblical character (personally I am not aware of any other non-dimensional number which is named similarly!).
In the King James Version of the Bible published in 1611 (Judges 5:5) we have the following:
The mountaines melted from before the Lord
In the New International Version of the Bible, “melted” is changed to “quaked”. These changes may be attributed to losses in translation from the original Greek, Hebrew, and Aramaic texts from which the books of the Bible were originally collated. Be that as it may, as Prof. Reiner pointed out
But Deborah knew two things. First, that the mountains flow, as everything flows. But, secondly, that they flowed before the Lord, and not before man, for the simple reason that man in his short lifetime cannot see them flowing while the time of observation of God is infinite.
So, to tie it all in, when Dylan sang “… how many years can a mountain exist before it is washed to the sea”, was he aware of this concept that Prof. Reiner explained? Possibly not. After all he had released his song back in 1962, and his performance at Newport in July, 1963 was one whole month prior to that Congress on Rheology at Providence where Prof. Reiner spoke about the Deborah number. Even if Prof. Reiner had spoken about it earlier, it is still highly unlikely that Dylan was keeping track of developments in rheology! It is much more likely that he actually might have been inspired by the song of Deborah directly from the Bible.
Perhaps it would be a far more uplifting experience if we could just ask ourselves how two individuals – two geniuses, Prof. Reiner and Dylan – could speak about completely different things using almost the very same words? Was it sheer chance? Or was their thinking channeled into a common conduit by the spirit of the times they lived in? Perhaps we can only wonder at this beautiful mystery. For we may never know. But perhaps, just perhaps … as Dylan said time and again in that strange, beautiful song of his, that “the answer, my friend, is blowin’ in the wind.”
Thanks a lot!
Beautiful. Simple, no-nonsense style and delightfully quaint !