Tag Archives: first law

First law of geography: everything is related to everything else

One of the benefits of supervising research students is that you can read a large number of scientific papers by proxy.  In other words, my research students read more papers than I would ever have time to read and then they write reviews of the scientific literature that allow me to quickly gain an understanding of research in a particular field.  Every now and again, a student refers to a paper that raises my curiosity to read it for myself.  One of these was a paper published by Waldo Tobler in 1970 in which he describes the computational modelling of urban growth in Detroit, Michigan.  Although, I used to live in Michigan, it was not the geographical connection that interested me but his invocation of the first law of geography: ‘everything is related to everything else, but near things are more related than distant things’.  Professor Tobler was writing from the University of Michigan in Ann Arbor which he used in an example by highlighting that the population growth in Ann Arbor from 1930 to 1940 depended not only on the 1930 population of Ann Arbor, but also on the 1930 population of Vancouver, Singapore, Cape Town, Berlin and so on.  Perhaps if he had been writing in 2020 he would have suggested that the rate of infection from coronavirus in Ann Arbor depends not only on the number of cases in Ann Arbor, but also on the number of cases Taipei, Milan, Toulouse, Dublin and so on.

Source:

Tobler WR, A computer movie simulating urban growth in the Detroit Region, Economic Geography, vol. 46, Supplement: Proceedings. Int. Geog. Union. Commission on Quantitative Methods, 234-240, 1970.

Image: Crisco 1492Own work

Do you believe in an afterlife?

‘I believe that energy can’t be destroyed, it can only be changed from one form to another.  There’s more to life than we can conceive of.’ The quote is from the singer and songwriter, Corinne Bailey Rae’s answer to the question: do you believe in an afterlife? [see Inventory in the FT Magazine, October 26/27 2019].  However, the first part of her answer is the first law of thermodynamics while the second part resonates with Erwin Schrödinger’s view on life and consciousness [see ‘Digital hive mind‘ on November 30th, 2016]. The garden writer and broadcaster, Monty Don gave a similar answer to the same question: ‘Absolutely.  I believe that the energy lives on and is connected to place.  I do have this idea of re-joining all of my past dogs and family on a summer’s day, like a Stanley Spencer painting.’ [see Inventory in the FT Magazine, January 18/19 2020].  The boundary between energy and mass is blurry because matter is constructed from atoms and atoms from sub-atomic particles, such as electrons that can behave as particles or waves of energy [see ‘More uncertainty about matter and energy‘ on August 3rd 2016].  Hence, the concept that after death our body reverts to a cloud of energy as the complex molecules of our anatomy are broken down into elemental particles is completely consistent with modern physics.  However, I suspect Rae and Don were going further and suggesting that our consciousness lives on in some form. Perhaps through some kind of unified mind that Schrödinger thought might exist as a consequence of our individual minds networking together to create emergent behaviour.  Schrödinger found it utterly impossible to form an idea about how this might happen and it seems unlikely that an individual mind could ever do so; however, perhaps the more percipient amongst us occasionally gets a hint of the existence of something beyond our individual consciousness.

Reference: Erwin Schrodinger, What is life? with Mind and Matter and Autobiographical Sketches, Cambridge University Press, 1992.

Image: ‘Sunflower and dog worship’ by Stanley Spencer, 1937 @ https://www.bbc.co.uk/news/entertainment-arts-13789029

Ramblings on equality

By David Samuel, User:Hellodavey1902 – Own work, CC BY-SA 3.0,

I had some time to spare in Oxford last week and visited the Treasury in the Weston Library again (see my post entitled ‘The Red Crane‘ on July 26th, 2017).  I was amazed to be confronted by an eight-hundred year-old copy of the Magna Carta.  No fuss, no fanfare, just sitting there behind a glass screen as close as you are to your screen as you read this blog.  But the Bodleian Library has four copies of the Magna Carta; so, maybe it’s nothing special to them!  This one is slightly dogged-eared, or to be more precise, rodent-nibbled – there were a couple of small holes where an animal had gnawed it while it was folded up and stored at Osney Abbey from its issue following King John’s death in 1217 until the Abbey’s dissolution in 1539.  The equivalent documents in the USA, the declaration of independence, the constitution and the bill of rights, are housed in the grandiose building on the National Mall, shown in the picture.

After the Weston Library Treasury, I went to the bookshop next door and could not resist buying a couple of books: ‘Signs Preceding the End of the World‘ by Yuri Herrara and ‘The Wandering Falcon‘ by Jamil Ahmad.  Hopefully, I will not succumb to tsundoku (see my post on ‘Tsundoku‘ on May 24th, 2017) and will eventually read these novels.  BTW – you can read the Magna Carta here.

It’s October and the start of university term, which also means that once again I am teaching thermodynamics to first-year undergraduate students. I have blogged on thermodynamics frequently; so, I am going to provide links to these posts during the next couple of months.  Primarily for those of my undergraduate students who find their way to this blog, but hopefully these links will also be of interest to regular readers. My opening lecture set thermodynamics in the context of the more familiar sciences as described in my post entitled ‘And then we discovered thermodynamics‘ on February 3rd, 2016.  Last week’s lecture started with the Zeroth Law of Thermodynamics, which I have discussed in two posts entitled ‘All things being equal‘ on December 3rd, 2014 and ‘Lincoln on equality‘ on February 6th, 2013 – now I’ve gone in a full circle, if somewhat shakily!

Slowing down time to think [about strain energy]

161-6167_imgLet me take you bungee jumping.  I should declare that I am not qualified to do so, unless you count an instructor’s certificate for rock-climbing and abseiling, obtained about forty years ago.  For our imaginary jump, pick a bridge with a good view and a big drop to the water below and I’ll meet you there with the ropes and safety gear.

It’s a clear early morning and the air is crisp and fresh – ideal for throwing yourself off a bridge attached to a rope.  The rope is the star of this event.  It’s brand new, which is reassuring, and arrived coiled over my shoulder.  A few days ago, I asked you how much you weigh – that’s your real weight fully clothed, at least I hope that’s the number you gave me otherwise my calculations will be wrong and you’ll get wet this morning!  I have calculated how much the rope will stretch when it arrests your free-fall from the bridge parapet; so, now I am measuring out enough rope to give you an exciting fall but to stop you short of the water.  I’m a professor of structural materials and mechanics so I feel confident of getting this bit right; but it’s a long time since I worked as an abseiling instructor so I suggest you check those knots and that harness that we’ve just tightened around you.

You’ve swung yourself over the parapet and you’re standing on the ledge that the civil engineers conveniently left for bridge jumpers.  The rope is loosely coiled ready with its end secured to a solid chunk of parapet.  As you alternate between soaking up the beautiful view and contemplating the chasm at your feet, you wonder why you agreed to come with me.  At this moment, you have a lot of potential energy due to your height above the sparkling water [potential energy is your mass multiplied by your height and gravitational acceleration], but no kinetic energy because you are standing motionless.  The rope is relaxed or undeformed and has zero strain energy.

Finally, you jump and time seems to stand still for you as the fall appears to be happening in slow motion.  The air begins to rush past your ears in a whoosh as you build up speed and gain kinetic energy [equal to one half your mass multiplied by your velocity squared].  The bridge disappeared quickly but the water below seems only to be approaching slowly as you lose height and potential energy.  In reality, your brain is playing tricks on you because you are being accelerated towards the water by gravity [at about 10 metres per second squared] but your total energy is constant [potential plus kinetic energy unchanged].  Suddenly, your speed becomes very apparent.  The water seems very close and you cry out in surprise.  But the rope is beginning to stretch converting your kinetic energy into strain energy stored by stretching its fibres [at a molecular level work is being done to move molecules apart and away from their equilibrium position].  Suddenly, you stop moving downwards and just before you hit the water surface, the rope hurls you upwards – your potential energy reached a minimum and you ran out of kinetic energy to give the rope; so now it’s giving you back that stored strain energy [and the molecules are relaxing to their equilibrium position].  You are gaining height and speed so both your kinetic and potential energy are rising with that squeal that just escaped from you.

Now, you’ve noticed that the rope has gone slack and you’re passing a loop of it as you continue upwards but more slowly.  The rope ran out of strain energy and you’re converting kinetic energy into potential energy.  Just as you work out that’s happening, you run out of kinetic energy and you start to free-fall again.

Time no longer appears to stationary and your brain is working more normally.  You begin to wonder how many times you’ll bounce [quite a lot because the energy losses due to frictional heating in the rope and drag on your body are relatively small] and why you didn’t ask me what happens at the end.  You probably didn’t ask because you were more worried about jumping and were confident that I knew what I was doing, which was foolish because, didn’t I tell you, I’ve never been bungee jumping and I have no idea how to get you back up onto the bridge.  How good were you at rope-climbing in the gym at school?

When eventually you stop oscillating, the rope will still be stretched due to the force on it generated by your weight.  However, we can show mathematically that the strain energy and deformation under this static load will be half the values experienced under the dynamic loading caused by your fall from the bridge parapet.  That means you’ll have a little less distance to climb to the parapet!

Today’s post is a preview for my new MOOC on ‘Understanding Super Structures’, which is scheduled to start on May 22nd, 2017.  This is the script for a step in week 2 of the five-week course, unless the director decides it’s too dangerous.  By the way, don’t try this home or on a bridge anywhere.