Thursday 28 November 2013

Lattice Labyrinth Tessellations: Look-out World!


On Wednesday 27th.November 2013, the first sheets of giftwrap arrived from Spoonflower. I'm biased; what do you think?

Well, actually, that ISN'T one I ordered. How about this:

or a design I call, stare hard and see why, Logistical Nightmare.

If you'd like to know more about these tessellations of the infinite Euclidean Plane (sorry) or unbeschränkte Ebene ( entschuldige, but I like the sound of that) and their even more amazing relatives, then:
1. come to my talk at Scarthin Books on Saturday 14th. December, 7.30 for 8.00 ( in the cafe; light refreshments)
2. have a look at or contribute to my infant latticelabyrinths blog 
and/or 3. buy the BOOK and discover how to construct many of the infinite families of Lattice Labyrinth Tessellations. They are out there, waiting to be seen for the first time by human as opposed to Platonic eye. We are taking orders for rare signed first editions at the Bookshop.

Friday 8 March 2013

Some Simple Sums: How we Wrestle with Numbers

Some Simple Sums 

1. Wrestling with Numbers

Maths is notorious for inducing mental panic – and yet it is supposed to SIMPLIFY thinking. Suppose that there are n people in this room, to stop fights breaking out, let’s all shake hands. Let t be the time to shake hands, then if everyone shakes hands with everyone else, then each of n people must shake hands with n-1 others, so the total time, big T,  taken by this orgy of peace-making equals  n(n-1)t – or does it? Let’s run a test for a small value of n. Suppose n=2, then the formula yields 2t, but we know only one handshake is required. Aha, our formula has counted every handshake from the point of view of every person- every shake has been double-counted, so the correct formula is n(n-1)/2. Let’s tabulate this for various n, Café Philosophiques do attract a variable attendance -actually, rather more people than I have included below, with our normal attendance of between 20 and 30, we would be a long time shaking.

A Constant
Number of people:  n/1
No. of shakes  n(n-1)/1x2
No. of three- hugs

You notice I have added some other columns. A New-age three-hug requires at least three people, and to work out the number of different three-hugs we have to divide by 3 times 2, the number of different orders in which the three people can be chosen in order to eliminate double-counting and get the right answer. When counting just the number of people (column 2) I have put in a “divide by 1”, as there is no double counting. I have also added a column of constant unity to the left and finally also a row for zero people. These modifications are there to bring out the beautiful simplicity of this table. You can now see that you don’t need to bother with multiplying figures together. As you go to the right, the figure in each cell of the table can be found by simply adding the figure in the cell above to the figure in the cell above and to the left. This means that the figure in each cell is also the sum of the series of ALL the numbers in the column to the left up to and including the cell above and to the left. If you know some algebra, you recognise that the first column tabulates value of a constant, the second of a linear function, the second of a function including a square of n ( a quadratic function), the third a cubic function, and that we could go on adding as many columns to the right as we liked in order to tabulate values of the function  n(n-1)(n-2)……..(n-r+1)/ 1x2x3…xr, which is the number of r-hugs and is a polynomial involving n to the power r, where r can be as large as we like. We call 1x2x3x4…..xr, r factorial, or r! for short, as factorials crop up all over the place in combinatorial mathematics (which is what we have been talking about), probability theory and statistics. For me, this has been a classical and beautiful mathematical exercise, embarking on a potentially endless journey into more and more general results, with wider and wider implications, starting from just one simple idea – that of shaking hands.

Does this sort of thing worry you? Well, you are in good company. We can trace mathematical thinking back to, for instance, Babylonian student excercises still preserved on 4000-year-old inscribed and baked tablets. Already in those days, the master was setting examples that can still terrify us today, such as the brain-twister below.
I found a stone but did not weigh it. I weighed out six times its weight and added 2 gin, then added one third of one seventh of this weight multiplied by 24. The total weight was finally 1 man-na. What was the original weight of the stone?
Answer, 4 and1/3 man-na .This works out correctly if 1 man-na equals 60 gin.

Incidentally, we see just how long ago and far away the basis of our conventional division of hours into 60 minutes and minutes into 60 seconds, both of time and of angle, was established.

An Egyptian problem, found on a Papyrus about 3600 years old, seems simpler:

If 10 hekat of fat is given out for a year, what is the amount used in a day?   (c.f. if 104 black bin-bags are given out for a year, how many are used in a week?)
The answer however is not so simple, being expressed as:
1/64 hekat and 3+2/3+1/10+1/2190 ro. (I hekat = 320 ro)

Here we see that, with the exception of 2/3, and maybe also 3/4, the Egyptian notation and probably the Egyptian mind could not deal with fractions other than “One share of however many”. A fraction like 56/73 (to which the above addition of shares is equal) was beyond writing down and probably beyond thinking about.

Problems with notation have taken much of the following three and a half thousand years to deal with. Modern fractions like 56 73rdsonly gradually permeated Europe from Arabia and Italy during the Middle Ages. Present-day algebraic notation, x‘s and y’s and all that, came into use gradually between the fifteenth and seventeenth centuries; British calculus is said to have been held up for more than a century by Newton’s now largely abandoned notation – patriotism inhibited the adoption of Leibniz’s more adaptable dy/dx expressions.  Maybe there are improvements still to be made. Our own personal struggles with algebra and mathematics in general can perhaps be excused when you consider how many centuries even those cleverest-of-the-clever leading mathematicians took to get their notation, and their corresponding thought processes,  straightened out.

Note that the above-mentioned three and a half thousand years, say 3511 years, to be precise, could have been expressed as: three millennia plus five centuries plus one decade plus one year. It is revealing to quote a Derbyshire sale catalogue dating from 1920 for lands belonging to His Grace the Duke of Rutland: Here is a typical lot description (shortened):
Yeld Wood Farm, Woodlands & Cottage situate close to the Village of  Baslow…, containing an area of about 82 Acres 3 Roods and 22 Perches.
As you will know (?) there are forty perches to a rood and four roods to an acre which was the area that could be ploughed in a day, 4840 square yards. A rood can be well visualised as the typical area of a mediaeval strip (or perhaps half a strip), one furlong long by one pole wide, or 220 yards by 5 ½ yards. A perch is simply a square rod (or pole), 5 ½  yards by 5 ½  yards.
So, you see how the prospective buyer can actually visualise the land area involved, whereas giving it as 82.87265, say 82.88, acres, or 82 and 71/80 acres, requires the farmer to visualise 0.88 of an acre; probably he’d rather have it in roods and perches. An ancient Egyptian might render the area for sale as 82 ½  ¼ 1/8 1/80 acres.

All this takes me back to primary school, I used to be able to add, subtract and even multiply in acres, roods and perches, and in miles, furlongs, chains, rods, yards, feet and inches. Measurement systems like this are meant to avoid the need to think in terms of fractions or decimals. Almost any quantity can be expressed as integral (whole number) multiples of units you have a habitual feel for. Same with old money: one pounds, seven shillings and six pence ha’penny. Nowadays, since decimalisation, we still have the various sized coins reflecting our  physical need to hand over change in “roods and perches”, to speak metaphorically, namely the 50p, the20p, the10p, 5p, 2p and 1p coins, but we no longer (or, I hope, do not YET) have common names for these coins and may get quite confused trying to convert, say, 83p into a practical palmful of change.

We are not confused, say the mathematicians! They, or maybe We, have surrendered the primitive need to visualise the sizes of the quantities we deal with in exchange for the extreme simplicity of manipulating numbers in the decimal system. Everything is in multiples or divisors by ten. 82.87265 acres may be hard to imagine, but it can be multiplied by a hundred by a simple double shift of the decimal point. Other multiplications, additions and subtractions take a bit longer than this but are completely straightforward. In contrast, imagine trying to work out how many 4 ounce bags of sweets can be made up from a day’s production of 2 tons, 7 hundredweights, 3 stones, 5 pounds and 12 ounces, which latter is expressed entirely in units I still have a real feel for. 2.372 tonnes = 2372 Kilograms =  23,720 100gramme bags is so much easier!

This handy decimal system goes back at least to the India of a couple of thousand years ago. For the next stage of the discussion, we need to simplify it a bit more.
10, 100, 1000, 10000, 100000, 1000000,….
is getting hard to write, let alone distinguish just how many 0’s there are. So generalising on 100 being 10 squared, written 10², we can write the sequence as:
10,10,²10³,104,105,106, … and so on, these being the sort of numbers that appear in successive columns of our handshake and hug table.
Similarly, the sequence of numbers less than 1:
0.1, 0.01, 0.001, 0.0001, 0.00001,…. 
Can be written 10‾1 (that is one over ten), 10-2 (one over ten squared), 10-3, and so on.
(For mathematicians to deal with numbers less than 1 in these elegant decimal and power expressions took a lot longer in the adoption than dealing with the larger-than -one numbers. Finally, to join these sequences of powers together we are forced to adopt the convention that the number 1, unity itself, = 10° , even though multiplying a number by itself zero times seems meaningless)
 Now, at last we are in a position to start measuring the Universe. 

2. Getting the Measure of the Universe

In reaching out to see and grasp the great and the little, we start with a handy measure of our own size, one metre – a stride, an arm’s length, a child’s height. – this is our unity, our 10°.
Lets start going up in scale in powers of ten, or, as practical scientists say “orders of magnitude”
Order 1 10metres;  the width of the bookshop
Order2 100 metres;  a sprint, how far a shout will carry, or a missile be thrown
Order 3 1 kilometre;  a walk to the station, a waving friend visible
Order 4 10 Km;  the distance to the nearest town, a long run
Order 5 100 Km; a journey to the regional capital, to court, to prison, to the seaside. Now we are beginning to reach the edge of the pre-industrial ordinary person’s experience
Order 6 1000 Km; travelling to the national capita city, to another country, or on a pilgrimage
An experience of only a few courtiers, merchants, churchmen, armies
Order 7 10,000 Km; The voyage of Christopher Columbus, Marco Polo’s travels
We are now getting to the edge of the ordinary person’s experience, but not beyond the ingenious measurements of the Classical Greek geometers, who obtained very good estimates for the size of the Earth.
Order 8 100,000 Km; A girdle around the Earth.
Order 9 1 million Km; The distance to the Moon; beyond the ordinary mortal, but again not beyond the ingenious Greeks, whose curiosity and method is humbling. They visualised the distance in “stades”, a foot-race distance of about 200 yards.
Order 11 100 million Km; Of the order of the distance to the sun. Even this the Greeks tried to measure, and their estimate was “correct” to within an order of magnitude; it was more accurately known by the 17th.Century. A digression, a triumph in science may long remain useless in practice!
Order 12 1 billion Km; The distance to Jupiter. Only the invention of the “Gallilean” telescope made this possible to conceive .Galileo first observed Jupiter’s 4 largest moons in 1610. They are easily seen with binoculars and, as early as 1676, small delays in their eclipsing by the planet were used to obtain a good stab at the speed of light, unimaginably high at 186,000 miles ( Anglo-Saxon motorway units) per second.
Order 16 1 Light Year, or a third of a Parsec. The nearest star is about 4 light-years away. Note the introduction of new units to try to help us visualise the immensities.  The distance to a star (not a planet) was first measured in 1838, using parallax, the slight change in direction from opposite sides of the Earth’s orbit. A parsec is the distance at which the parallax of a star, subtended by the RADIUS of the Earth’s orbit, is one second of arc
Order 21  Diameter of the Milky Way, our galaxy (100,000 light years) Advances in the measurement and understanding of starlight spectrums and in so-called Cepheid variable stars made measurements like this possible by about 1915.

A digression. To quote from the internet, how to bring the Universe down to size:
 There are an estimated 150 globular clusters that swarm around our galaxy.  Each of them contains 100,000 to 1,000,000 stars in a spherical region ONLY a few hundred light-years in diameter.
Order 22 1 million light years, is the approximate distance to the nearest other galaxy, The Great Nebula in Andromeda, M 31. Controversy about whether “galaxies”, those fuzzy objects, were gas clouds, perhaps forming stars, in the Milky Way, or other collections of stars at a great distance, was finally settled only in 1923 (the approximate birth-date of physicist Freeman Dyson)  with the aid of the 100 inch Mount Wilson telescope– Hubble identified individual variable stars in nebula M 31.
Order 25 1 billion light years.  In 1929, Edwin Hubble proposed his celebrated “expanding universe” theory. The dimmer the supernovae, the further away the galaxy and the bigger the red shift, explained by its receding from us. A billion light years was uintil recently about the limit for observations of this type on galaxies.
Order 26  Ten billion light years. The distance to the edge of the observable universe is currently estimated as about 16 billion light years, giving a visible diameter of twice this.
So, the largest number we can come up with, relating the size of the observable Universe to a stretchy human pace-length is some 3 X 1026.
Though the Greeks’ imagination reached out to their estimate for the Sun’s distance, of order 10, it was not until the 17th.Century that planetary distances became accepted, order 11 to 12, not until the 19th.Century that the true remoteness of the fixed stars was revealed, order 16 and not until the lifetime of the parents of many at this meeting that the true scale of the observable Universe, orders 22 to 26, was understood and accepted.
Surely we must  question whether any existential philosophy more than 200 years old can have more than inspirational or allegorical significance?

3. Smaller and ever-smaller
 Time now to turn from telescopy to microscopy and go down in scale to the smaller and smaller, starting again from our “zeroth” order of I metre.
Order Minus 1 10cms.  A “handy” size, the scale of a handspan, a fist, a stone, a sheet of writing paper, a jug of milk.
Order Minus 2 1 cm.  A finger’s-breadth, a flower, handwriting, an easily snapped  twig, a pebble
Order Minus 3  1 mm. Getting hard to see. Grit, a seed, a pin-head, your nails needing cutting
Order Minus 4  0.1 mm. About as small as can be seen or imagined to be visible to the naked eye. Small seeds, sand-grains, eye of a needle. From mediaeval times, magnifiable to a more comfortable scale by single-lens “reading glasses” (as in Umberto Eco’s monastically set Name of the Rose)
Order Minus 5  0.01mm., 10 micro-metres. Silt or “soil” particles; they don’t float but do smear. Pollen grains – may blow about but can and need to settle. The cells of animal and plant tissues are often in this range; first described by Robert Hooke, c. 1670, from his microscopic observations
Order Minus 6  1 micrometre. Dust. As we know, you can’t see it till it settles. In the 17th. Century, the double-lens microscope allowing X20 to X200 magnification brought this scale into view.
Order Minus 7  0.1 micrometres or 100 nanometres. The wavelength of visible light is in the range 400-700 Nm. and this limits what could be distinguished using the best optical microscopes by late Victorian times.
Order Minus 9   1 nanometre, a billionth of a metre; about the diameter of a sugar molecule. The actual existence of “molecules” became accepted during the 19th. Century, but the direct investigation of their structure only began c. 1920 with X-ray crystallography, X-rays having a wavelength comparable to molecular sizes.
Order Minus 10 1 Angstrom, a tenth of a nanometre, 100 picometres; typical effective size and separation of atoms.
Order Minus 12 1 picometre , a billionth of a millimetre. The wavelength of the electrons used in microscopy is about 5 picometres. This limits the electron microscope, developed in the 1930’s.
ORDER minus 13 100 Femtometres This is where “High Energy Physics” takes over; larger and larger linear and circular accelerators:-, particularly since about 1960, CERN and the infant Large Hadron Collider
Order Minus 15 1 femtometre  roughly the radius (whatever that means) of a proton or electron. The existence of the electron was deduced about 1900, but protons and neutrons not until their tracks could be followed in cloud or bubble chambers from about 1930
Order Minus 18  1 attometre or nano-nanometre. About the feasible limit of High Energy Physics and correspondingly the scale of elementary forces and particles studied.
Order Minus 45 The Planck Length. An entirely hypothetical and especially hard to understand concept. May perhaps be thought of as the ultimate limit of the precision with which a particle’s position could be ascertained in the quantum theory. The energy of the probing particle/wave would be such that a black hole would be formed, so no measurement would result (!?!)
I have gone down to the very (to the 27th. Power) silly Planck Length just because I want to give the Universe a chance to resist the power of the human mind!
So, the extension of man’s ability to look at very small things has gone from order 7  to order 18 in little more than 100 years. As with the very large, surely our outlook should have changed radically with such an expansion in our ability to observe the sub-sub-microscopic entities of which everyday objects and ourselves are made up. Certainly, we are filled with wonder by television programmes, articles and books, but most of even us “educated classes” experience little outside the everyday scale in our everyday lives. We are mostly scientifically ill-informed and even more inexperienced ; we probably do not own or rarely use a microscope or a telescope, let alone an x-ray diffractometer or a linear accelerator! It is very easy, still, for us to live in an unquestioning mental world akin to that of the “ancients” in which only a few visionaries posed fundamental questions. How many of us have ever thought of estimating the moon’s distance by timing the length of a lunar eclipse, as did the Greek natural philosophers.
4. But how BIG is the Universe, actually?
"Space is big. Really big. You just won't believe how vastly hugely mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space.”
Douglas Adams: The Hitch-hiker’s Guide to the Galaxy

 That is, how many conceivable points does it contain? EASY!
  4πR³, where R is the radius in Planck Lengths, 1.6πX10 to power71x3, let’s approximate a bit, after all my calculations may not be that precise, 10 to the power 324 is near enough.
5. God’s Numbering System
But the very hairs of your head are all numbered.  Matthew Ch. 10 Verse 30

God is supposed to have no problem numbering, that is describing and knowing, every point in the World, now known to be so much bigger than the Evangelist could have thought, and implied in the quotation.
The readers of the Bible are supposed to be awe-struck by this degree of omniscience. Not so Archimedes, who explains, in the 3rd. century B.C, in a paper addressed to a King Gelon, that his numbering system is capable of dealing easily with the number of grains of sand that might be needed to fill the Universe. Our numbering system is also perfectly capable of dealing with the scale of things, as we have already seen.
Another way to look at this is to perform a card trick. Imagine I am holding three  perfectly normal  packs of 52 cards, excluding troublesome jokers, 156 cards which to simplify things can be considered all to be different, each pack having a different design on the back. I assure you that this pack has not be prepared or tampered with in any unfair way, but the cards are of course in one particular order, with one letter per card, I’ve written out a short passage from Shakespeare. Now, watch carefully.
Dave fans, shuffles, fumbles and drops the whole pack on the floor. What a mess!
Oh *******!!  How am I ever to sort them out again? Well, if I work through all the possible orders to find the right one – the 152-letter message from Shakespeare, I will need not merely all the time in the world, but much more than that!
There are just two ways of ordering two cards, six of ordering three, twenty-four of ordering four, in short 1x2x3x4x……x156 of ordering them all – its that FACTORIAL again, 156! This number is rather large. I haven’t had time to calculate it, but I’m told that 70! Is approximately 10 100, so 100! is going to be at least 10150 and somewhere around the three-pack mark the number of ways of ordering the cards is going to exceed 10324 , the number of “Planck points” in the visible universe. So there on the floor is all that God needs to set up a one-to-one correlation with number all the hairs on the head of all of space.
Now there is a very theoretical minimum conceivable time interval called the Planck Time, about 10 -43 seconds.( this is about one ten thousandth. of the time it takes light to cross the diameter of an atom) The present age of the Universe is a mere 1018 seconds (and counting, slowly) which comes to 1061 Planck Times. So, there is no way those playing cards could be got into the right order to rediscover Shakespeare’s message in a time equal to the lifetime of the Universe so far.
We can also see that God would not need many more playing cards to number not merely each point in the Universe, but each point at each instant in the life of the Universe, each point in space time, with plenty of room left over to describe what is going on at each point, whether empty, or associated with a particle, or with the scale and direction of each possible force field, and finish by giving this point in space-time a fanciful name, perhaps inspired by Peak Rock-climb or Lead-mine nomenclature! Don’t Sneeze Now Arete or Second-Cousin’s Fortune. There are even more names available that orderings of playing cards, which leads us to:

6. Monkeys Typing Shakespeare
Shall I compare thee to a Summer’s Day,
Thou art more beautiful and more temperate.
Rough winds do shake the darling buds of May
And summer’s lease hath all too short a date.
At this point I had intended to embark on some intricate calculations of the time it would take the proverbial “monkeys” to type even this and the other eight lines of one supreme sonnet of Shakespeare, but I think you have got my drift by now. It's going to be an absurdly long time, though we could calculate a decent estimate! Even were the monkeys able to employ, not typewriters, but the still proverbial “Quantum Computer”, they would have no chance of discovering even an early draft by the Bard within the lifetime of the Universe. This is, I suppose, a commonplace observation, but it is less commonplace to ask;
 “How then DID the sonnets of Shakespeare ever GET written – starting from the blankish, even if anthropophilic slate of the early Universe”
particularly as the Universe got off to such a laggardly start in the race against the monkeys to see who could write Shakespeare’s works first. Nearly ten billion years were given over just to forming giant stars, letting them manufacture heavy elements and then blow themselves up, so that the scattered materials could condense into a second generation solar system, our sun and planets, some solid and iron- and silicon-rich. Another half-billion years at least were required for things to solidify a bit on planet Earth and for Jupiter to vacuum up most of the dangerous impacting meteors. Another mere hundred million years or two sufficed for life to appear, but more than three billion years were used up before it crept out of the sea. Another 300 million years were needed to evolve mammals and 298 million years to evolve the first self-consciously intelligent species. And during all this time, the monkeys can be imagined typing randomly away, by now they are well in the lead – they’ve got as far as several very beautiful lines of a risqué sonnet. Even the last two million years before the present, about a ten-thousandth of the lifetime of the Universe, have largely been employed in developing language from scratch, honing all our subtle passions, emotions and abstract intelligence and in developing the art of story-telling and aural tradition. Only in the last 50,000 or less years have written alphabets allowed remembered culture to develop and be passed on. Urban living, with all its special crafts, including those of playwright and poet, seems to extend back no further than 10,000 years before the present, and this period is essentially that which has allowed literature, philosophy and science to be recorded so that the likes of Shakespeare and Newton could rejoice in “standing upon the shoulders of giants” to achieve there own dazzling in- and out-sights.
So we allowed the typing Monkeys a very long start indeed, but we still got there first! This shows the true scale of the wonder of human thought. Douglas Adams once again got here first – his super-computer Deep Thought, faced with discovering the QUESTION to which 46 is the ANSWER to The Riddle of Life, the Universe and Everything announces that it needs to design:
“A computer which can calculate the Question to the Ultimate Answer, a computer of such infinite and subtle complexity that organic life itself shall form part of its operational matrix…. And it shall be called..the Earth

7. The Interstellar Pen is mightier than the  Sword
So much for the scale of the Universe, we can hack it! But can we affect it, or even explore it - hardly at all. You might think of scientists and engineers working on Earth to be analogous to a gathering of pub philosophers gathered in an English inn scheduled for closure! But that is another story - SETI, the Search for Extraterrestrial Intelligence - and this article has gone on too long already!

Energy & Oysters; Sizing up the Quest for Renewable Energy

Energy and Oysters

Sizing up the Quest for
 Renewable Energy

A Light-hearted Look at
 Heavy-handed Projects

Dave Mitchell

Leaning heavily on:
SUSTAINABLE ENERGY – without the hot air
By David J.C.MacKay
paying homage to
The Hitch-hiker’s Guide to the Galaxy
By Douglas Adams

Scarthin Books 2012

Oysters and Energy

Numbers are famously feared to “phase” folk. Even in the so-called serious press and Radio-4 culture they are used just to impress rather than to inform. Few journalists and commentators appear to understand let alone have the ability to employ numbers to inform the public. Among the innumerate is numbered at least one Chancellor of the Exchequer. 

A typical misuse of numbers, from a 2010 issue of the Independent newspaper’s magazine supplement:

“In 1860, the three oyster companies in Whitstable alone, employing more than 100 boats and over 500 people, sent 50 million tons of oysters to London.”

Let me illustrate ways I customarily make sense of, and check the plausibility of numbers. This is a million tons of oysters a week, 125,000 tons a day or 5000 tons an hour – 6 times the rate at which coal is fed up the conveyor into a typical German 2GW power station, such as Ratcliffe on Soar. Allowing for the weight of inert shell, maybe the oysters could be burned to produce 8MW of electricity – about a fifth of our generating capacity (from about a quarter of our one-time coal-mining production). – Out with wind-turbines, in with Oysters! It’s also 10 tons of Oysters per year per inhabitant of London, or a trainload from Devon every 5 minutes. I think it is the tons that crept or was slipped in there, 10 oysters a year per Londoner sounds about right.

I’m going to quote lots of figures, and most of them I’ve subjected to what we might call the Oyster Absurdity Check: looked at in other ways, do they seem ABOUT RIGHT? The whole talk has been produced without using a calculator; we’re dealing in round figures and in estimates that should be right to an error of maybe plus or minus about 20%. So far are we from coming to terms with the long-term implications of our way of life, that such accuracy is an adequate guide to figures that are subject to variation or cannot be precisely known. I’m going to stick to metric units, much easier to manipulate, besides we do have a feel for a kilogramme (about 2 lbs, 1000 make a tonne) and for a kilowatt-hour – the famous one-bar electric fire or fan heater.
Human Energy and Power

Running a fit, skinny 65kg body like I used to have up the Bookshop stairs in 2 seconds, at rather more than 1 metre per second = 700 watts or 0.7 kW,  a quick burst of adolescent human power,  about the steady output of a horse, 1 horsepower.
Running up a mountain at 1200 meters per hour = 200 watts,
0.2 kW
A fit day-long ascension at 600 metres per hour = 100 watts, ) 0.1 kW. Actual useful steady output of a manual labourer, or a serene old Monroe-bagger, maybe 75 watts on average.

I’ll concur with David MacKay’s (Sustainable Energy – without the hot air) approximation of 1kwH per day per person as a ballpark figure for adult human output, we can buy that much electric power for about 10 to 20 pence. So that’s what we’re worth as manual labourers – hence our replacement by JCB’s.  Think of that when virtuously winding up your torch, radio or watch to save energy. We need to eat the equivalent of several times this output of course, as us small chemical engines, are, at about 25%, somewhat less efficient than car engines and coal-fired power stations. A quick check on the reasonableness of this calculation.  At 25%, we need to input about 4kWh of food, or about 3500 kcalories (often referred to as 3500 Calories with a capital C) in heat energy units. Yup, that’s about the sort of daily intake we’re supposed to need if working normally hard.

Historical Energy Use by not so ancient Brits

Fortunately, we get a bit of help from nature – already complex mediaeval and renaissance European societies were very energetic, founding and naming ALL our villages and towns – Wirksworth, Bonsall, Matlock, Cromford, Snitterton, Tansley -  routing nearly all our town-centre and village roads, establishing esssentially ALL of our hedges and walls, building ALL our village churches and ALL our cathedrals, without having heard of as yet unborn Watt. In the Derbyshire Peak especially, we are renting unfurnished a world built by our pre-industrial foreparents. Interestingly, hardly enyone wants to actually LIVE in the modern world built by machines – even in Dubai, those who can live in detached villas.

These foreparents did have some help in boosting their 1 kWh per day. Taking just Renaissance England England, around 5 million people had the power of more than a million oxen and horses to draw on, so this added perhaps as much as 2kWh per day per person to their power They had 125,000 square kilometres to divide up between no more than one tenth of today’s population, so they had lots of woodland – maybe 50,000 sq. kilometres, growing wood at the rate of 0.2 Watts per sq metre. Work it out: 50,000 x 106 x 0.2 = 1010 watts = 10 million Kilowatts, 2 kWh per person, or 48kWh per day per person – maybe they utilised a quarter of this, say 12 kWh per day per person. No wonder we are so fond of open fires and campfires! Indirectly, the power of the sun  turned their wind and waterwheels, perhaps 20, 000 of them in England, generating 12kW each, or 50W per person for maybe 10 hours a day, a handy 0.5 kWh per person per day. Also courtesy of the sun, they grew food to feed themselves and their beasts, used for meat and milk and wool as well as for power, maybe producing another 10 kWh per person per day so you can see that they had already, by Shakespeare’s time managed to multiply their personal power output by a factor of 20 or 30 by what we would call sustainable methods, producing or at least utilising some 25 KwH per person per day. Nature provided everyone with 24 slaves. This estimate is supported by similar levels for today’s Algeria, Egypt, Indonesia and other “developing” economies.

So - Back to the Land?

Sorry, there’s a catch. Were the ten times more of us to attempt to go back to Olde Englande’s way of working and living, that 25kWh per person per day  would be reduced to 2.5 kWh per person per day. That’s what a back to the land, self-sufficiency, backyard-windmill-and-chickens life would mean. Maybe we should indeed envy France, which supported a mediaeval population of some 20 millions, a full third of today’s number, on 4 times England’s land area.

Back to Today’s Feasting on Energy

How much power in total do we ACTUALLY use per head per day in early 21st. Century Europe – well, it’s hard to be exact, with all the global trade and moving around, but the figure seems to be about 125 kWh per day. 125 kWh per day!? I’ve seen an estimate as high as 140kWh per day.  5kW roaring away every hour of the day for every one of us – 12kW per household!!??

Yes, give or take a bit, it is so, and, at 15p per kWh, we in Europe can (just about) afford it – £19  per day per head, maybe £50 per day per household, 8 hours work at the minimum wage – it is already becoming a strain, may we have some working tax-credit please?

Where does it come from – well, mostly from coal, oil and gas of course – hence the global warming we’re warned about. And, on that front let me say that I fear that we ain’t seen nothing yet – you can’t multiply the concentration of a gas in the atmosphere by 50% without having effects. It’s lucky for us that the concentration of  carbon-dioxide in the used air in our lungs is already two orders of magnitude (about a hundred-fold) greater than the ambient levels, or we would all find ourselves panting continuously even when resting. Fortunately, our evolving forbears had plenty of time to accustom themselves to ancient carbon dioxide concentrations which are scientifically controversial but probably 2-3 times the present level.

An Everyday Tale of Cromford Folk

How do we manage to use all this energy? I nip into Matlock to pick up our Clare from the community minibus, six stop-and-start miles in the van, about a litre of fuel used, 10 kW-hours used at 30% efficiency, or about 3 x my daily output of power, or, roughly, input of food! Maybe with the right equipment I could hand-haul the van to and from Matlock in three days. I could have walked it easily and gently in two hours, expending 200 watt-hours and Clare 100 watt-hours, needing about a kWh of food intake, or about a tenth of the energy actually used, but at the cost of (say)  £20-worth of my time. The actual money cost, doubling the fuel cost, was about £2,30 Afterwards, a cup of tea! – boil up a litre of water through 80 degrees, 80, 000 calories, 80kcals, about 100 watt-hours. Well, that’s better, I could produce that much in an hour -but how, in practice – cuddling the kettle would only get the water to about 350C. Later, a bath for Clare – 70 litres through 25 degrees, say 1.5kWh, or one and a half times my daily power output, but costing me only about 25 pence. A week of baths for Clare for less than the price of a pint. No wonder pubs are struggling – daily baths for all the family for the price of a round this Friday night.

These apparently trivial examples indicate how without thinking we use prodigious amounts of energy in our daily lives. Us Mitchells have had a very long generation time averaging about 35 years for three generations now, so my Granddad remembered life in the late 19th.century – he an iron-ore miner, Grandma a milkmaid in  a Cumberland village. Sounds mediaeval, but it wasn’t. Their society, with its profligate and inefficient use of coal – 5 tons or more per head per year – got through over 100kWh per head per day. The blink in time of 250 years since the Industrial revolution seems like for ever to us, the profligate use of energy goes back not just to our own upbringing, or to that of our parents, but far beyond the tales even of our great-grandparents.

Can this go on – of course not! – the reservoirs of fossil fuels are finite, only, typically about100 years of them are left at current usage rates. Global warming is just a little sibling of the family problem of use of finite and irreplaceable fossil fuels to provide energy – we’d better find other sources damn quick.

Finite Resources Last for Ever – the Chocolate bar Effect

 Actually, this isn’t quite true. Logically, we CAN make a finite resource last for ever. Consider this bar of basic best-value chocolate (I recommend repeating this demonstration). Total Dave-reserves one bar. Consideration-time’s up! Current comfortable rate of consumption, half a bar a day. Dave’s reserves will only last for two bites, two days, then the end of life as I gnaw it. But wait, remedial action, I’ll reduce my consumption by 50% per day. Next bite is a quarter, next an eighth, next a sixteenth. It’s the old frog-in-the-well commonplace that I’ll never quite eat all of that chocolate. Even though there were only two bites of proven reserves, and half were consumed on the first day, the bar will last for ever. Coincidentally, we are thought to have used around a half of everything there is in the way of finite resources in a “day” of about 100 years (200, actually, but the equivalent of a much shorter period at late-20th. Century rates), so to make a rough stab, to eke out what remains for ever we need to use up only half of what remains in the next hundred or so years.

Generally, the maths is beautifully simple – for 2 years of natural resources to last forever, we have to halve consumption each year, for reserves of 50 years to last for ever we have only to reduce consumption by a fiftieth or 2% per year, for a 100 year reserve to last forever we need to reduce consumption by a hundredth or 1% a year to make the resource last FOR EVER. Eventually, of course, our consumption will reach very low levels, and will be significantly lower after as little as ten or twenty years, but surely such a rate of retrenchment should be possible.

Not so easy, however. If we continue at present energy-use levels then even such an apparently small, say 1%, annual reduction in fossil use implies an enormous rate of increase in the provision of renewable energy, from a baseline near zero. Fossil fuel use would go down in the series 100,99,98,97,96,95, roughly, but renewables must therefore go up in the series 0,1,2,3,4,5. The final 5 in that series is about where we are at in the UK with regard to electricity generation now, so to achieve just a 1% further reduction in fossil fuel use, we have to increase pour renewable energy output from 5% to 6% - a 20% annual increase in capacity;  a tall order. You can see why it is that people quote 10 to 20 years as the minimum period it takes to get from the pioneering stages to a substantial use of replacement technologies.

Sources of Renewable Energy

How might we replace fossil fuels? By renewable energy we tend to think of wind, water, tide or sun. However, to quote an article in the latest Scientific American:

Nathan Lewis of Caltec says that by the year 2050, civilisation must be able to generate more than 10 trillion watts of clean energy (what he means is 10 terawatts, or 10,000 Gigawatts, which he says is 3 times the average US energy demand of 3.2 Terawatts) (c.f. UK  400GWatts). Damning up every lake, stream and river on the planet, Lewis notes, would provide only five trillion watts, about half his target.

We can do that sort of calculation for the UK. Area of UK is 245,000 square kms, or 245 x 109 sq metres, so if we could generate 2 W per sq metre of our land area from renewable sources of energy,, we could generate at a power of 500GW, approximately our current level. But is anything approaching 2 W per sq metre practicable?

Hydro: David MacKay estimates the maximum theoretical hydro-power in lowland Britain as only 0.02 W per sq metre, (one hundredth of the target) and in Highland Britain as 0.24 W per sq metreaverage about 0.15 W per sq metre and what proportion of this could we utilise in practice? – 20%?  That gets us down to 0.03 Watts per sq. metre. Really, the contribution this can make is almost trivial, and just think of the expense,  fun though it might be to mess about with Archimedean screws in Cromford Dam.

Wind.  Coincidentially (or is it?), the practically extractable wind energy per sq metre in the UK seems to average about 2 Watts per square metre ,so we could get to the target by covering the entire country with wind turbines at the optimum spacing. Actually, probably only about two-thirds of the country has wind-speeds high enough to justify installing turbines – but we can probably make up for that by employing off-shore area. If we wanted only to replace current electrical power generation as end-use then about an eighth of the country would do. If a quarter of current electricicity generation is the target, then about a thirtieth of our land area would suffice. This begins to sound more feasible, and is indeed about what the UK is currently aiming for, I think, and not far beyond what has already been installed in Denmark, Germany and Spain. That amounts to an average output of 4 GW, which assuming a 20% load factor requires 20Gw of rated capacity, only about 10,000 two-megawatt turbines, an investment of only around 20 billion pounds in today’s money. A wind-turbines-on-all-hills policy seems to be going ahead in Spain, where I suspect wild country is still viewed as wasteland, pending romantic poetical publications by their equivalents of Wordsworth, Coleridge and Ruskin. More of Wordsworth’s view of the Lake District later.  Averages, however, conceal fluctuations from zero to more-than-we-need. Wind-generated power needs to be stored for when required, a knotty problem considered below.

The sun, the sun!  Even in this country, it’s often burning down at the rate of a full kilowatt per square metre – from 10 sq metres, the footprint area of your house maybe, we can replace a 1 litre of petrol (10Kw) in an hour! Alas, however, there are clouds, low sun angle and winter - cutting into the potential is the knife of the long nights! (not quite original – a rockband got there first). So the average power available in the UK is only 100 Watts per square metre. Still, the human body, lazing in the sun all year would absorb about 2.4kWh per day;  2 kiloCalories if it could ALL be converted into food. So what about:

Sun via Biofuel?  Europe’s best plants in bright sunlight and warmth can achieve about 2% efficiency in converting our 100 W per square metre average sunlight into carbohydrate fuel; but the effect of cold and their tendency to have evolved to switch off in low-light conditions reduces this in practice to  somewhere in the region 0.2 to 0.5 W per sq metre. What proportion of our agricultural land could we spare? Well, as much as two thirds of our land area is classified as “agricultural”, but only about a quarter as “arable”. We still need to eat, and upland pastures would be very inefficient at producing biofuel, so I think 10% of our land area is the absolute maximum that could be utilised, so for the whole country that brings the Watts per metre down to  0.05 to 0.02 watts per metre – like hydro, symbolic rather than significant.

Was it Fred Hoyle who remarked that the sensitivity of photosynthesis to different light wavelengths suggested that life had evolved on a planet with a different solar spectrum to our sun and had arrived here from space via meteorites. Certainly, if we want to propagate our form of life in the Universe, something like sending out exploding warheads of poppy-seeds might well be the best way (but doing the maths is depressing). Plants utilise the red and blue ends of the visible spectrum, but with a big hole in the middle – hence the green colour of leaves, reflecting or transmitting the unexploited wavelengths.

Are scientists even now working on  genetically modified plants that would utilise the whole visible spectrum? Their all-sunlight-absorbing leaves would of course look BLACK. The era of black grass will then be upon us. Scientists would assure us that they’d built in safeguards such as susceptibility to a modified Roundup, in case the gene spread – but black plants being so much quicker-growing, they’d inexorably oust those old outmoded green species – England’s Black and Pleasant Land would soon be upon us. A fantasy? “Imagine my surprise” to open an issue of the Scientific American at an article entitled “Reinventing the Leaf “  “Researchers are devising artificial leaves that could…..convert sunlight and water into hydrogen fuel, which could be burned to power cars, create heat or generate electricity, ending dependence on fossil fuels.” These particular leaves would, however, be entirely artificial and non-propagating. Phew! The present aim is to get 10% efficiency in convertion of sunlight to fuel energy.

Sun via photovoltaics Currently, photovoltaics are very expensive financially and dangerously greedy for rare metals or expensive silicon products. Nevertheless, they are encouragingly efficient – about 16% conversion of light energy to electricity is the current standard, 20% the current commercially available limit, 30% to 40% achievable but so far only in the lab. So that’s 16 W per sq metre. If we put 20 sq. metres of photovoltaics on the roofs of 25 million buildings, that is 500 million sq metres, we’d be covering only a five-hundredth of the UK land area, so our watts per sq metre on average is down to (surprise, surprise.. about 0.03 W per sq. metre – pretty trivial once more – and the capital cost of that, even at £100 per square metre (well below current costs) would be £50 billion.

Sun via Ground or Air-source Heatpumps  There is an example in the building where this diatribe was originally presented (the Derbyshire Eco-centre), a plant said to be able to produce some 20kW of underfloor heating for an input of about 8 kW – an efficiency of 250% - about 4 x that obtainable from the most efficient gas-burning boiler or from combined-heat-and-power fossil-fuel generating stations. MacKay estimates an energy flow into the ground, derived from solar-heating as 3 to 5 W per sq metre, averaged over the whole day and year,  much lower than the 100 watt average flux because of reflection and the low conductivity of soils and rocks. But at least we do have a figure in the right ball-park again! The trouble is, our dwellings, offices and factories are packed into rather less than 10% of our land-area, so the heat energy extractable in or adjacent to urban areas is going to be only 0.3 to 0.5 W per sq metre averaged over the whole country. Nevertheless, such a reservoir could supply enough heat for a high proportion of dwellings. Air-source doesn’t apparently suffer from the limits of ground-source, but could surely have the effect of significantly cooling the local air on winter’s days. One might not want to live downwind of a major conurbation. With airflow halted by evening temperature inversion would the bowls in which Cromford and Wirksworth lie become intolerably frozen? Would the cold air of Wirksworth, perfumed by the tobacco of outside-the-pub smokers, pour over the lip of Cromford Hill, right by the Eco-centre, to immerse the Cromfordites? I haven’t done the maths on this yet…..
Tide and Wave Power.  The potential around the UK is considerable, our islands are breakwaters upon which the Atlantic presses and around which the tides are divided and accelerated. The energy extractable turns out, once again, to be in the 2 W per sq metre area – to match our demand, we have to find ways of harnessing wave and tide over areas of sea comparable to the area of the UK – again a daunting task.

We could do some maths for Wirksworth

25 sq kilometres sounds about right for the area of the parish, 3 miles by 3. 200 people per sq. km, not far from the English average. There’s no hydro, wave or tidal power (are there small tides on Carsington Reservoir, though – a project for Anthony Gell school?). Wind it must be.

25 x 1,000,000 sq metres x 2 Watts per sq. metre – 50,000 kW, 50 megawatts, which amounts to 10kW, or 240kWh per day, for each of the town’s 5000 persons – sounds very useful; just the sort of level we need. – more than enough on average if a bit short of peak demand. But to generate that, with turbines that on average deliver no more than about 20% of their rated power, we would need to install wind turbines rated at 5 times the desired average power output: 250 Megawatts – 100 very large state-of-the-art 100 metre-tall turbines. 10 x10 at 500 metre intervals. Puts the Carsington or Matlock Moor projects rather in the wind-shadow. Cost say £250 million or £50, 000 per person, about £125,000 per household. A lifetime’s mortgage for everyone – that’s the sort of cost we’re looking at.

Tidal power is predictable, but predictably variable over the year’s lunar cycles. Solar power is fairly predictable, but VERY variable over the day, Wave and wind are very unpredictable. We’d need to store lots of energy from the good times to see us over those windless, and perhaps waveless frosty winter nights and cold-snap weeks.

Storage by Slartibartfast

You may recall Douglas Adams’ revelation in The Hitch-hiker’s Guide to the Galaxy that the Norwegian Fjords were designed on the planet Magrathea by planetary-architect Slartibartfast, who won an award for the design. I asked him to redesign a fjord to store enough energy to keep the UK’s lights on during a period when the wind doesn’t blow. Let’s assume we’ve installed enough wind energy to provide in ideal conditions a quarter of our electricity generation capacity: 10 gigawatts (ten thousand megawatts, ten million kilowatts)  To replace this during a windless hard-as-iron week in the deep midwinter we need to store 10 x 24 x 7 gWh– about  2000 gWh  = 2 x 109 kWh, which equals 6 x 109 megajoules, 6 x 1015 Joules of energy.

Alas for Slartibartfast – his greatest work, the celebrated Sognefjord would have to be sacrificed to progress. The Sognefjord is a deep trough about 100Km long and typically 5 Km wide. We just need to dam up its mouth and a few side arms at Balestrand, Hoyanger and Ardal and pump-store energy therein as raised seawater – like the Dinorwic or Ben Cruachan schemes in the UK but on a rather larger scale. Dinorwic can store about 1.5 GWh – so we need about 1300 Dinorwics (this ties in nicely with MacKay’s estimate of 400 Dinorwics to store two days wind energy) Slartibartfast pointed out that as the fjord empties back down to sea level when generating, the dam will need to be twice the average water height. I won’t bore you further with the details, but, remembering that we need 1 joule of energy to raise 1 kg through 1 metre, Slartibartfast’s design requires a dam height of 2000 metres, or about 6500 ft. A less obtrusive policy might have been to use the wind-generated power to empty out the Fjord to that depth (refilling it to reclaim the electricity) – but it’s average depth is less than 1000 metres. The high plateau above the Fjord’s mountain walls lies at about 1500 metres above sea-level, so Slartibartfast reports that he can’t meet the full spec, but can guarantee only about 4 or 5 days emergency supply. We haven’t put this proposal to the Norwegian Government yet, though there are already plans to lay a high-tension cable under the North Sea on the pretext of adding to the flexibility of the European Grid. If the Norwegians charged a 5p per kWh premium to give the energy back, they’d earn £75million every  time the Fjord was emptied from 1500 metres.  Not to be sniffed at, it might be a return on the capital cost??
Energy density

Mechanical energy, such as hydro-power is, indeed, a very volume-consuming way of storing energy. The so-called energy density,( measured in kWh per cubic metre, say) is very low – imagine trying to run a car on the energy from a descending pendulum weight.  We could alternatively manage the job of storing the week’s UK windpower energy using an oil tank of volume 2 x 108 litres, i.e. 2 x 105  cu metres, or 200 metres by 100 metres by 10 metres tall – about the size of the Argos distribution centre you pass on the A38 the other side of Burton on Trent. An oil-tanker-full in fact. Liquified natural gas would do just as well. But has only about two thirds the energy density of diesel oil.  I suspect that some such project may well be in hand, so the Sognefjord may be safe, at least until the oil and gas run out.

Saving Energy

I know what any Transition Wirksworth, Transition Matlock or Sustainable Youlgreave persons are going to say. Hold on, we all know that SAVING energy is a far better and cheaper way to go than trying to generate our present demand from renewable sources. Indeed the whole message of what I’ve said so far is to point out the appalling scale of any meaningful renewable energy project - disruption of great swathes of land and sea, tens of billions of pounds of investment. Can’t we reduce our demand instead?  But saving energy isn’t easy either.
The RULE OF HALF seems to me to apply almost universally. We could all use cars that are twice as efficient (i.e smaller and less overpowered); we could all insulate our houses and change to more efficient condensing-boiler or heat-pump warming – and halve our household energy needs ; we could all recycle metals, paper, plastics, glass, which reduces the energy needed to make new finished materials, typically by – guess what – a half. Maybe we could fly half as often ( I can’t help much here as I don’t fly at all – What never? Well….hardly ever.). But that only halves our energy consumption – and how are we going to force people to do that? Only about 10% of us at the outside take any practical interest in these matters, and most of what we do is talk. Tony Blair for Instance:“Unless we act now, not some time distant but now, these consequences, disastrous as they are, will be irreversible. So there is nothing more serious, more urgent or more demanding of leadership.” (October 2006).Two months later, responding to the suggestion that he should SHOW leadership by not flying to Barbados for holidays: a bit impractical actually….”. The Lord of the Manor declines to halt another Tragedy of the Commons …. You can interpret “Commons” either way.

Embedded Energy

A big almost logically inevitable problem is that if we spend less on driving or heating or flying, we’ll have more to spend on something else, and absolutely everything we eat or buy has oodles of energy embedded (to use the customary term) in it. In the table below are some examples.
Energy cost
kWh per kg
100 ( 0.6 kWh per drink can)
2 - 3
20 - 40
20 – 40 (0.7 kWh per drink can)
6 - 10
7 - 8


45 (non vegan)
7-8  (6 kWh per kg back by burning)
13  kWh per Kg
15 kWh for average diet
I slipped petrol and food into the bottom of that table just to point out that nearly everything we use is similarly energy intensive- but of course we don’t burn or throw away the THINGS we use – or do we?? Well, as I’ve said above, we can recycle materials other than food and fossil fuels, and that reduces the figures in the above table by a factor of two or three (MUCH more in the case of Aluminium) – but every time our possessions go through the recyle cycle, they are still absorbing typically 5 to 10 kWh per kilogramme. A car, incidentally, even if kept permanently in the garage has an embedded energy equal to about 100,000 km of driving. The only solution in my opinion is:
Becoming Poorer

So, how can we reduce our energy consumption down towards a level that might be sustainable? We have simply to consume less of EVERYTHING; substitution just won’t do. (Prodnose: what about playing golf instead of flying?) A free-market economist would jump in here and say – “no need to worry, the MARKET will take care of all that, as fossil fuels get scarcer and mining them more expensive, energy prices will rocket and, hey presto, we’ll all get poorer automatically”. The market, however, has a way of getting hysterical, of booming and busting, and it only works efficiently if EXTERNAL COSTS are charged to the producer – which they blatantly are not. Sainsbury’s pay me nothing for the time I waste stuck at their bloody traffic lights! And, given the contemporary very long-tailed income distribution, the details of “leaving it to the market”, in terms of social injustice and conflict, might be very unpleasant.

Prudently Looking Ahead

The Market is not allowed to be very good at sorting out international problems, either. Unexpected political and military conflicts get in the way. Our position in the UK and in Europe generally is one of fragility, our supply routes by air, sea, rail and pipeline stretch far across the globe. Twice last century, U-boats came close to winning wars by a successful blockade of Britain. We only grew our own pit-props AFTER the first war (too late). After the post-second-war unification of Western Europe the potential aggressor became the Soviet Union, and - surprise, surprise! - they built up a very large submarine fleet – over 100 nuclear and many more diesel-powered, based initially on WW2 German designs – I wonder why?  Pit-props should have been on the pre-first war defence budget and, likewise, the excess cost of generating  energy locally, and that means from renewable and nuclear sources, should be considered as part of today’s defence budget; an alternative to maintaining a “global military reach”. We can become more secure AND poorer at one stroke.  To quote the Economist of September 4-10th. “Renewables in Germany are growing more quickly than in almost any other EU state…but that is only because consumers pay a large subsidy, some Euros 10 Billion last year.” Great! They’re making themselves poorer! Such a better use of  high-tech expenditure  than our out-of-date white-elephant Trident system.

Political Stance

So, can Transition Wirksworth, Matlock, Middleton and Youlgreave have any significant effect? Directly, the answer is a resounding NO. Indirectly, the result might be to help educate a public opinion that will make very big central government action possible . And that’s a remarkable statement, coming from Dave Scarthin, a classic anti-government, pro-small-business suspected closet Thatcherite.

Oh, and I briefly mentioned the baleful effect of Wordsworth on our attitude to wilderness, re-branding the useless wastes of the Lake District as a Shrine to Natural Beauty. A contemporary bard has taken up arms. Whether he’s for or against the Lakeland Poets and for or against Wind Turbines is of course a matter of literary interpretation.

Reflections in Windermere  by William Wirksworth

I wandered lonely as a cloud
That floats on high o’er vales and hills
When all at once I saw a crowd,
A host, of silver windermills.
Lake and trees were hid by sails,
Motionless despite the gales.

Occasionally one turned, like star
That shines but rarely, hid by cloud.
They margined each high fell and scar;
Round every bay another crowd.
Ten thousand saw I at a glance,
Each one in need of maintenance.

The waves beside them danced but they
With gearbox jammed could scarcely turn.
A poet could no more be gay
At sight of so much money burned.
I gazed - and gazed – took one more gander,
How all that cash could help Ruanda!

For oft when on my couch I lie,
Nought else to do in power cuts,
They flash upon the inward eye
Those warm, remembered, fossil nuts.
The light’s come on! – Where’s Dorothee?
Boil the kettle!  Cup of Tea!

Dave Mitchell, Scarthin Books.

Written as a talk to “oppose” Evan Rutherford at a Wirksworth Festival Special Café Philosophique, at Derbyshire Eco-Centre, September 2010;  tidied up September 2012