Thinking about Evolution & Economics and Some Notes on the Natural Selection of Ideas

Part 17 - Unknown Unknowns - More Questions of Complexity, Change, Conflict & Scarcity
and the Strange Story of Euler's 'e' 

Bill fires the imagination with musings about the mathematics of economic growth

Now God said and I agree with him - Luke 12:27 -

'Consider the lilies, how they grow: they neither toil nor spin, yet I tell you, even Solomon in all his glory was not arrayed like one of these'.

Donald Rumsfeld, Secretary of State for Defence, spelt it out - 'There are known knowns, there are known unknowns and there are also unknown unknowns'

Frank Knight, was best in 1921 -

Risk, Uncertainty and Profit (1921)
Distinguished between economic risk and uncertainty.
Risk was where outcomes were unknown but governed by known probability distributions where decision making rules could be applied.
Uncertainty was much deeper, not only the outcomes were unknown, but also the probabilities were unknown... until discovered.
Uncertainty resulted in the discovery of 'economic profits' that perfect competition could not eliminate, because they were unknown unknowns.
The Limitations of Scientific Method in Economics (1924)
Folk were cussed & ignorant, all risk & uncertainty was an 'economic' gamble. Scientific Method helped with risk but uncertainty involved fundamental problems of unknown unknowns of folk in their global environment of complexity, change, conflict & scarcity.

Nevertheless Richard Dawkins suggested genes did do cost benefit analysis? Discovery by trial & error, copy/vary/naturally select!

Aristotle, was perceptive from the get go -

'admitting one's ignorance is the first step in acquiring knowledge'

Robbie Burns, offered his pitch -

'The best laid plans of men and mice come to naught' 

Wellington, had a go at politics? -

'I told them what to do but they said they wanted to discuss it!'

Harold Macmillan, identified his greatest challenge? -

'Events, dear boy, events'

and Mike Tyson, was spot on -

'Everyone has a plan until they get punched in the mouth'

Experts with oodles of data can’t command & control natural events, as King Canute attested in 1016 ... and later Nicholas Copernicus started a new wave and suggested that homo sapiens was of cosmic insignificance ... backed up by Monty Oython, 'just remember you're a tiny little person in a universe expanding and immense'.

It seemed that there was no messiah at the helm steering the ship to its destination ... nor its destruction for that matter?  We can all be confident that in the future we will see, hear, feel, small and taste only what has survived!?!    

There was an insidious naivety in the idea that leaders had the knowledge, data & power to command & control and others merely followed.

In the old days there was a god behind every tree, and some even tried rain dances ... but all that malarkey also came to naught.

No man who has failed to assimilate this fact has a right to call his philosophy scientific.

Darwin was clear, effects were also causes and not the outcome of elaborate, outrageous conspiracies -

Apapa Generators ... underneath the soap pans in Apapa we learned about systems failure ... and Complex Adaptive Systems

Ben Elton's Popcorn ... an Epilogue summarised the rigors of reality ... folk the world over searched for someone to blame ... Blame Games 

In this way Unknown Unknowns were foibles of reality, rampant & rife, unforeseen emergent happenings & accidents, unintended consequences ... so why did everyone tend to bank on cause & effect and arrogant blame games?

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Unknown Unknowns analysed & explored & a bit of fun -

known knowns - known unknowns - unknown unknowns - unknown knowns?     

Frank Knight (1885–1972) University of Chicago distinguished between risk and uncertainty -

quantifiable risk (resolvable) observation data, statistical noise, confidence levels, probability distributions

uncertain uncertainty (radical) no quantifiable knowledge about some possible happenings (constrained only by the laws of nature) recognising some fundamental ignorance, a limit to knowledge, and an essential unpredictability of future events, where effects were causes, and outcomes emerged.

'uncertainty was radically distinct from the familiar notion of risk, from which it had never been properly separated'.

Linear became non-linear as -

 everything affected everything else as

 effects were causes

... the equations had no solutions but, and it was a big but, infuriatingly, unforeseen patterns emerged ... life on Darwin's entangle bank was exquisitely ordered and not random chaos. Something was going on?

Reductionism - simplified models made analysis possible and risk assessment helpful.

Empirical science was the only way to grow the knowledge base and accumulate know how & progress.

But system separation proved to be impossible, just as nature & nurture were impossible to separate (even in identical twins!). All the boundaries were permeable, everything alive needed usable energy from without, everything dead was losing useable energy to the environment.

Evolution proceeded as human beings & their brains (and everything else) evolved to generate diversity for trial & error learning ... with such unknown unknowns there was no alternative to trial & error.

Generation of diversity fed the evolution process and complexity, change, conflict & scarcity followed as mutations accumulated ... thank goodness ... clones just didn't work!

Complex Adaptive Systems - all the action was on the edge of chaos where 'control' was a fervent wish to make life easier. But systems & sub systems were far from equilibrium, just like the flapping of a butterfly's wings in Scunthorpe and the hurricane in the Antipodes.

Multiple causes and emergent phenomena, unknown until discovered made it physically impossible to isolate systems for top down command & control.

We learned about such dramatic interconnectedness underneath the soap pans in Apapa ... and in the Port Sunlight bureaucratic kludge ... and from the study of the '3 Mile Island Case' @ OU in 1995 ... and Trevor Kletz was a smart cookie he identified two pertinent issues -

organisations have no memory

stocks have negative value ... they were a safety hazard ... and a thieving opportunity ... and cash tied up.

Be amazed at the complexity of production supply chains and logistics ... we remembered the incomplete 'Critical Path Analysis' models ... and the critical unknown unknowns. 

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Production Supply Networks - every motor car has may be 30,000 separate components - 100s of steps in the process of production - 100s of suppliers each with 100s of suppliers of their own - each with 100s of bottlenecks with 100s of known unknowns and by definition and infinity of unknown unknowns ... each and every one embroiled in global networks ... each component from each supplier demanded deep specialisation and the compounding of the problem ... even before we tried to scale production to satisfy the global foibles of fickle customers - 

complexity, change, conflict & scarcity

interconnections, interactions, interruptions, interminables, intractables ...

One whole shebang & caboodle constantly disrupted by different national policies and managed trade deals.     

National self sufficiency was an impossible myth rendering as futile all - regulation, price fixing, exchange rates, money printing, bailouts, subsidies, taxes ... and yet ... all was not chaos, on the edge of chaos emerged the miraculous order of Darwin's entangled bank ... which included in the Boeing 747 in the sky. 

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Someone kept mentioning the utopia of global regulation ... but we said no messiah was in 'control' that job. We knew about the dysfunctional UN, WTO, WHO, IMF, World Bank ...

 Utopia was an impossible pipe dream ... no utopia however there was a glimpse of order and we could learn by trial & error. The activities for mortals were best described by satisficing rules of thumbs and evolved cooperative behaviour rather than a quest for utopia?

We tried desperately to understand & summarise the non-linear maths of Complex Adaptive Systems - 

Known Knowns = evidence - big data gathering ... everything measurable, including the colour of the operator's sox!
= knowledge base ... Boeing 747s evolved thru a series of trial & error experiments & remembering those few experiments which didn't fail    

Build the Knowledge Base - physically wiggle the intentional experiments of Empirical Science and learn -

 'a double blind randomised control experiment in Scunthorpe which was repeated in the Antipodes 17½ nights later with the same peer reviewed results was meaningful irresistible evidence which could never be ignored ... but the answer depended on the next question'.

Known Unknowns = observation - statistical analysis of sense perceptions, experimental outcomes of the laws of nature ... inspired guesses, risk assessment ... more know how, more questions ... but there was a snag all knowledge was diverse, dispersed, incomplete & tacit

Use Your Imagination - experience, including vicarious experience, then research & development to pin down known unknowns ...  

Trevor Kletz - 'pearls of wisdom - what you don’t have, can’t leak, can't explode, can't burn down & can't be thieved … don't process hazards & don't hoard cash ... change the hardware, not the people … blaming human error was akin to blaming gravity for a fall down stairs ... history rhymed most new discoveries were made regularly ... organisations had no memory … don’t bother to write an accident blame report, I’ll send you one from my stories ...'

Stephen Hawking - 'Some individuals are better able than others to draw the right conclusions about the world about them and act accordingly. These individuals will be more likely to survive and reproduce so their pattern of behaviour and thought will become dominant'.

Unknown Unknowns = emergent properties - by definition other happenings were unknown unknowns and transcended the Laws of Nature and 'caused' change and had to be discovered by running the equations & running the machines   

George Shackle - 'we are ignorant of what it is we do not know'

Frank Knight - 'uncertainty is radically distinct from the familiar notion of risk, from which it has never been properly separated'.

quantifiable risk, statistical noise, confidence levels

uncertainty, no quantifiable knowledge about some possible emergent  happenings recognising some fundamental ignorance, a limit to knowledge, and an essential unpredictability of future events, where effects were causes, and outcomes emerged.

Vote with Your Feet and Join a Club of Your Choice - work with others to discover & accumulate new synergies of specialisation & scale all else are events dear boy events, 'give me an example', 'all a woven web of guesses' 

= soothsayers & messiahs & rules of thumb which seemed to work but random flip flops of excitement & fear in the brains of others make unintended consequences of complexity, change, conflict & scarcity unknowable in advance ... the Baldwin Effect ... which was different from the anthropic principle ...
the future path dependent course of knowledge itself was unknowable but evolution designed brains to cope with the unknowable by trial & error! A generalised tool for survival in the face of ignorance. 

Unknown Knowns = moral sentiments - 'things you know that you don't know you know' ... gut instincts, evolved good behaviour, conscience, inner lights, worms in your head ... conscience, fairness of shares, resentment of cheats ... we know such exist but what  were such figments, where, when, how, who?

George Shackle - 'we are ignorant of what it is we do not know even though we know more than we can ever say'

Golden Rule - 'do unto others', where did that come from!?

= an evolutionary arms race, we have the generalised tool for survival but not the knowledge ... yet?!

2nd Law produced continuous change constrained the Laws of Nature (motion, gravity, electricity, magnetism ...) but emergence was rampant and unknowable in advance.

AI does not do logic calculations. AI mimics human intelligence, using trial & error to learn to recognise patterns in big data by random experiment.

Human behaviour was different with different people in different places at different times in different environments. There was always human meddling, that's what humans do. We needed to recruit unpredictable others to help and urge them to stop tying our shoelaces together.

Pierre Laplace failed to cope with the physical impossibility of imagining all the possible interactions - a speck of dust at the other side of the universe or a flap of a butterfly wing in Scunthorpe caused a hurricane in Toledo, the 3 body problem.

We knew 'society' existed but we knew it was not a 'thing' but an emergent property of social activity!

In amongst all the unknown unknowns only one thing was certain - the explanatory power of maths ... and nobody knew why?

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The Explanatory Power of Maths 

Michael Brooks had a go at pinning down the unknowns with the history of mathematics and the discovery & accumulation of know how -

Arithmetic - History of Accounting, Balance Sheets, Tax & Trade
- 1, 2 many - 1,2,3,4,5 one hand 6,7,8,9,10 two hands - negative numbers & debt - fractions & division of wholes - zero & physical & imaginary abacus - 'lots' of 10s and 60s

Geometry - History of Construction, Navigation & Artists 
- Pythagoras right angled triangles - ratios, circles & pie - trigonometry, sine, cosign & tangent - geometry on a globe, shortest distance between two points - drawing & perspectives  

Algebra - History of Wars, Cannons, Orbits & Curves
- known equations unknown solutions - simple, quadratic (complete the square), cubic (complete the cube), quartic ('depress & substitute'?) ... quintic ('elliptic functions'?)

Calculus - History of Change
- changes, rates of change & infinities which exist - derivatives & integrals    

Logarithms - History of Compound Interest
- adding was easy multiplying was difficult - exponential growth - adding exponents = multiplying terms & geometric progressions - powers & arithmetic progression in both directions +ve and -ve 
The log = the power of any base ... base 10 was 'common', base 'e' was natural ... but it works for any base i.e. exponential !   

Imaginary Numbers - History of Electronics, Silicon Chips & iPhones
- semi conductors, logic gates

Statistics - History of Risk
- Normal distributions (probability distributions) = large numbers of independent variables exert a small influence on the happenings. 95% within 2 Std Dev of the mean. 99.7% within 3 Std Dev of the mean. Symmetrical - mean, median & mode equal. 
- Skewed Distributions (counting distributions) = independent events occur rarely but repeatedly. Random events, constant within the same time period.
You can compute the average but it is a judgment call ... an educated guess. Nature rhymes. It looks like maths, it smells like maths but there is no certainty.

 

Information Theory - History of Software, If/Then/Else Coding & Digitised Data
- Bayesian algebra   

How maths created civilisation = maths - physics - chemistry - biology - psychology = imaginations & abstractions     

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Compound Interest & The Power's in the Power

The Seduction of the Exponential Curve - Forbes - 17 Nov 2011.

 In 1900 Edward Hindley was no mathematician but he did cotton on to the miracle of economic growth with his mantra 'education & compound interest' and the founding of The Weaver Refining Company.   

Evolutionary Economist were naturally interested in the evolution of money and the evolution of money started with the thorny question of how to measure figments of value?

This was a thorny question for Michael Brooks ... after all figments were mere notions, abstractions, ideas without physical substance ... 'The Art of More' ... turned out to be essential for survival and the 'fantastical opportunities' for the growth of civilisation ... social activity, torts, trade & technology and synergies of specialisation & scale! 

Unfortunately such figments also nourished parasites & predators ... and thieves, taxation & fraud?  

Twelve Grains of Rice   

How did 1 became 18 quintillion?!   18,446,744,073,709,551,615! (double the number of grains of sand on the planet?!)

With shining sun and the gentle rain God's gift was 12 grains of rice on every straw and every soul in the land knew that 11 grains just had to be eaten to stay alive and kicking, that was survival. But it came to pass that the 12th grain was so scrumptious and few could resist such a delicious treat. But some folk had learned from Clockwork Rabbit and understood and chose to plant the 12th grain and apply TLC for next year's plenty.

The great man Einstein understood and tried to teach others to learn.

The future was impossible to predict. The best way to prepare for this conundrum was education. There was only way to confront the inevitability of the 2nd law of thermodynamics ... hard work, honesty & thrift.

But work was not necessarily manual labour, horses were better at that. And horses were rapidly being automated. This was creative work in the imagination! ... and then some one said even creative work was eroded by AI? 

Education narrowly focused on specialised skills, was threatened.

It seemed education was all about learning how to learn & teach 'know how' from a broad knowledge base.

Teaching was about cooperative synergies of specialisation & scale.

Sapiens was a social species - cooperative, creative, communicative, critical and mobile.

'Know how' itself, like everything else, was evolving by natural selection.

The 'back half of the chessboard' was a reference to the old story about the inventor of chess and the Emperor King. The entrepreneur's asking price for this extravaganza of a game was a single grain of rice be placed on the first square of the chessboard. Then two grains on the second square, four grains on the third, and so on. Doubling each day.
Apocryphal, no doubt, but such a small price to pay for such a wonderful game? But very soon the quantity of rice grains required was more than the entire empire possessed.

This fable was a lesson in the power of exponential growth. The power was in the power.

From one grain of rice on the first square of the chessboard, the amount increased to the point that by the time you got to square 64, there were over 18 quintillion grains of rice on the board.
A number so vast as to be incomprehensible to mere mortals and meaningless?

On the 'back half of the chessboard', in the real world, happenings became physically impossible.

Exponential growth could not be sustained ... there were 'limits to growth'?

But and it was a big but, there were no physical constraints to the growth of 'know how'!

The entrepreneur had to continuously innovate to ride the compounding growth curve.

The speed of light limit was 186,000 miles a second, but the universe was expanding faster in space, time & complexity than the speed of light?

Marketing Myopia explained the problem!?

To survive the entrepreneur had to be better than his competitors in the local environment.

Comparative Advantage explained the problem!?

An evolutionary arms race.

For certain the copy/vary/select process of evolution was involved which demanded diversity of both inputs and outputs thus a physical impossibility and undesirability of 'equality' of neither inputs nor outputs. 

We inherited life and existing know how   

We had 3 score years and 10 to work with others and contribute to know how   

Hard work, honesty & thrift ... or entropy increases, parasite & predators abound & investment collapses  

Complexity, change, conflict & scarcity made growth difficult 

The one and only way to make a grain of rice grow on Darwin's entangled bank = hard work, honesty & thrift otherwise the grain of rice decays -

if you don't work you won't eat

if you aren't honest you won't be trusted 

if you don't invest you won't grow

Growth or Decay =

Compound Interest A = P (1+r/n)^nt --- --- compounded n times @ r rate over t time period   

Compound Interest A = P (1+1/n)ⁿ --- --- compounded n times @ 100% over 1 year    

'e = max value when £1 is continuously compounded @ 100% over 1 year  --- --- n = infinity!

The $ 'principle' at the start was insignificant, the 'compounding' exponential growth was the eighth wonder of the world ... the power's in the power.       

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The Strange Story of Euler's 'e'      

Exponential growth of growth or decay of investments & everything

 In our expanding universe as entropy increased the future was 100% evolved from the past. 'e' was the universal constant for all growth processes over a period of time

A physical property of the universe. Happenings were 100% based on the past, the inherited happenings and the passage of time. Not accidental happenings but continuous & rare happenings over time each part of a whole throbbing shebang & caboodle.

Growth was the miracle, the power's in the power.

radio active decay -- cooling and temperature change -- probability theory -- electronics -- harmonic motion -- chemistry -- biology ... and DNA rate of mutation & anthropic principles  

Exponential = base^power = value (gives growth over a period of time)  

Log to the base of the value = power (receives growth and gives time)  
Common log = base 10     
Natural ln = base 'e'   

y = e^x = value after continuously compounded @ 1% growth over x units of time

e = max value after continuously compounded @ 1% growth over 1 unit of time
NB max return is NOT infinity

e = rate of growth for continuously compounded @ 1% growth over 1 unit of time 
NB the derivative of 'e' is 'e' ....

Compound interest S = P (1+r/n)^nt --- --- compounded n times @ r% over a time period t  

@ £1 and 100% interest for 1 year ... continuously compounded  = limit as n goes to infinity = 2.7182 = the max return over the year.

The way money grows with time was empirically discovered before the 'limit' concept was known!

The limit concept opened the door for calculus!

Cool = every rate of growth can be written using e, a universal constant. Not an exponential function but THE exponential function.  

Not only £s but all growth, all rates over all time periods = e^rate.time ... ridiculously easy!

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Trigonometry - sin A x sin B = 1/2 [(cos (A-B) - cos (A+B)]   wow!

Calculation became dead easy because addition & subtraction were much easier than multiplication & division. The multiple was proportionally constant between both the total number and the rate of growth.

Thus a vast range of natural phenomenon was understood ... even the happenings which powered the industrial revolution. No wonder Edward Hindley urged anyone who was prepared to listen - 'Education & Compound Interest'!

The powers formed an arithmetic progression = straight line on log scales.

The bases formed a geometric progression = growth curve on linear scales.

Geometric progression - 1,2,4,8,16 ... common ratio 2 ... or 1, 10, 100, 10,000 ... common ratio 10 ... or 1, q, q², q³ ... q^n-1  

Calculation of this form was achieved by adding the powers rather than multiplying out the terms!

Napier worked out the logarithms of any number to enable astronomers and others to add instead of multiply.

Anyone who wanted to play around with compound interest used THE natural growth function raised to some multiple of TIME ...

y = e^x ... 'x' was the power   

and to find properties of the power 'x'  ... Logarithms to the base 'e' did the trick -

logarithms unlock access to the power!  

key to compound interest was the power not the principle!    

maths by rote never delivered understanding!  

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£1 @ 8% for 10 years = e^0.08x10 ... universal constant for all growth rates

@ 50% = e^0.5 @ 200% = e²

£1 @ 0%.

£e @ 100% 

£e to the power of x @ ANY rate 

£ = (1+x/n)ⁿ =  1+ x/1 + x²/2! + x³/3! ...

£ = (1+1/n)ⁿ = 1+ 1/1 + 1/2! + 1/3! = 'e' = 2.7182 ...

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(a,0) = a             (0,1) = i             (0,1) x (0,1) = (-1,0)              i x i = -1        i = square root -1

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Growth rate = tangent.

y = e^x

eⁱ 

pie + 1 = 0

+0 - x1 - e - pie - i  

e^{i pie} + 1 = 0

cos x = 1 - x²/2!+ x⁴/4!- x⁶/6! ...

sin x = x - x³ /3!+ x⁵/5! x⁷/7! ...

e^{i x} = cosx + isinx

cos pie = -1          sin pie = 0

Thus e^{i pie} + 1 = 0

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Diagrams help understanding -  

Limits - Infinite Series - Anchor points -

 

 

Logarithms

logarithms unlock access to power!  

key to compound interest was the power not the principle!    

maths by rote never delivered understanding!  

Power = quantity of energy transfer or activity (rate of doing work)
power (watt) = work (joule) per second
useful synergistic sources -

know how, skill, aptitude - personal responsibility

empathy, love, friendship - priceless gifts

purchases, rewards, wages - exchanges

titular zero sum 'sources' -

coercion, slavery, taxes

Horsepower and exponentials = the rate of doing work!

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Surviving Systems & System Failures -

Here's just one interpretation of a familiar story of HAZOPS ... my mate Bill's own attempt to do something about surviving systems ... makes an intriguing case study ... there maybe other interpretations?  

 As the size of production processes grew in size & complexity in the late 60's the potential for 'problems' grew with them. Trevor Kletz (1922-2013) ex King's Chester and Liverpool University was head of safety in the north east, mainly concerned with valuable & treacherous ammonia and chlorine. I joined engineering in the early 1970s and met TK. I learnt that there had been two chlorine incidents, one in '67 and another in '69 in Cheshire. The one in '67 set TK off on HAZOPS and his risk assessment protocol. In retrospect, those working with him were at the 'cutting edge', grappling with the problem of how to control events in large organisations. If this was the first incident of its kind and I imagine it would have been put down to inexperience and minimised by the senior management hoping the problem would go away. As an example of attitudes around at that time, one of the process foremen in the works told me that in a previous job he was controlling a burner and the hydrogen supply pipework was glowing red hot. He informed the engineer in charge that he was concerned about risk but the response was insignificant. Later a similar hydrogen burner in another works exploded killing two operators. That was about the same time as the second chlorine release in '69 which affected children in the playground near the works.
Problems were becoming too risky to ignore.
Another anecdote about management priorities involved the day following a senior appointment. The new boss called in the building supervisor in charge of new offices to talk about the detailed construction of his own office. He wanted the wall of his office moved over to accommodate a larger desk which left the subordinate guy next to him with a long narrow 'corridor' for his work space!  
It was only after the second chlorine incident that the problem was taken seriously and the critical instrument engineer involved picked up on what TK was doing. The engineer was split up from the process group and made the head of a new risk assessment team, and that's when I joined as the only one with process experience on the first two computer controlled plants. I had seen the recruiting advert and wanted to join because the head had visited our plant to do an assessment. That report surprised me, it described new things about my plant that I thought I knew inside out. He was predicting future possibilities and the likelihood of problems and I wanted a piece of that action.
From my viewpoint there was a big difference between how the north east and north west operated. TK was in control in the north east as a safety head, primarily interested in 'accidents' i.e. 'what happened'. In the north west, engineers we were interested in 'how often'. Before joining, I was sent on a course on risk assessment, which turned out to be a reliability maths course with a bit of electrical engineering thrown in as illustration. It went over my head at the time and turned out to be completely irrelevant later. However, I did meet the famous 'Reliability Technology' Green & Bourne. After fumbling around for a couple of years I realised that the engineers around me knew little about chemical plants and set about collecting all the data I needed in order to do the assessments. The result was the 'Big Data Book ' making unknowns known and eventually used throughout the UK. TK called it the most circulated data book on the industrial black market. Lloyds of London rang me for a copy but we wouldn't give it to them even though they had a copy already, unofficially.
Between us all (Business, Design and Reliability) the HASOP processes grew and we were light years ahead of everyone. I rang the heads of safety at some large companies asking for data and they gave it to me over the phone boasting about how well they were doing; but it was horrendous & inadequate from my viewpoint. I was invited to join the Reliability Group of the Mechanical Engineer Society but again it was a waste of time. They were talking a different language because they had not gone through the same learning process as we had.
Later when Engineering was disbanded we became an extinct species.

What the old design engineers were missing was the interactions of all the people associated with chemical plants; that is the management from the top down to the process engineers operating the plant, as well as all the interactions from outside the plants. It took more than ten years, through a slow process of learning, as the engineers I was working with moved up through the management taking their experiences along with them.

As a result, eventually I got to work with all the human factors experts in the country who produced the guides, culminating with the numerical assessment guide.
We hosted a celebration dinner after the publication of the book. But now it is all lost & gone.

Musing on all this, it brings to mind an incident. I was asked to join a group wrestling with a distillation problem, they went through the whole process of eutectic distillation which I knew something about but not much. But in this case the whole of the meeting was taken up with the fine detail of distillation and then we went for lunch and disbanded.
No one asked me a question. After that experience and to try to get participants to focus the problem, I made a point of asking at meetings, what was I there for? 
Much later, when the head of 'Major Hazards' in the business asked me over to talk I was again surprised. He had a CV running to five pages of foolscap. The guy was a genius and talked and talked going over and over about something on his mind so in the end I asked him 'what was the problem?' and to my amazement he said 'What should I do?' From what he had said it was obvious to me what he should do but his problem was that he knew so much he couldn't see the obvious. I tried to cut away the dross. You should have seen his relief! 

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My 'Surviving Systems' model gave me total control over the system of concern which was bounded by the overlap of three systems.
A or S - the system of interest.
B or E - the environment it was within.
C or H - any human interaction involved.
This system will be part of another system, and can contain other systems within its defined boundaries, but as far as analysing the system, the overlap is the total area of interest.

All the elements within this boundary have to be defined. The area of interest would include the chemistry going on in a specific individual & his brain cells, including the analyst himself. 
I'm not interested in the effects of rattlesnakes in Mouldsworth.
Those would be other separate system models. In this way Unknown Unknowns don't matter?

Area 'A' - the concern of interest is the cell's survival. Cells wear out rapidly so mathematically, their probability of death was described by an approximate normal distribution.
Area 'B' - the environment of the cell, and its many variations that can be measured. These variations measured over a long period will be averaged out and the probability of the cells environment would be described mathematically by the frequency of the influential variation and the average lifetime.
Area 'C' - the human influence on the cell. Not local influence but some external influence, perhaps a prescribed medicine. The cell survival being described mathematically by skewed Weibull Distributions (early failure when errors in cell chemistry mal function and the system rejects them and long term decay as errors accumulate). An aspect of this is that cells may be in a failed state before they are formed in the system. Just like computer software, bugs in initial software have to be eliminated before the program works.

In combining all the overlaps, we end up with a mortality curve. The probability curve and known as the 'bathtub' curve. Early failure & eventual decay.

I've written a boring book called 'Surviving Systems' about lawn mowers and economics. It's all about risk assessment and turning 'unknown unknowns' into 'known unknowns'. The brainstorming sessions were what made us different from robots. Could we 'imagine' the unintended consequences or 'known unknowns' regardless and stop doing or using whatever was the possible cause?

NB The evolution of aircraft over the years. The numbers carried depended on the perceived risk that those carried were prepared to take.
That's what all the arguments were about regarding FN (frequency/numbers) curves when the authorities were getting their knickers in a twist and came up with rules making the owners responsible for risk. The owners promptly sold up, replacing the boards with conglomerates and putting a fall guy in charge instead of Safety Officers. All the smaller companies since were 'winging it'.

HAZOPS - hazard and operability studies - a systematic process of data gathering of deviations from steady state process equilibrium and brainstorming the existence & assessment of hazards in equipment and vulnerabilities in operations. A risk assessment tool for teams of specialist to provide information on the consequences & mitigation of hazards in modules & sub systems for management decision making. 

Statistical risk assessment and good sense? Quantified risk assessment from data gathering (known knowns) and mathematical probability judgments (known unknowns).   

But what about unknown unknowns? Discuss ...

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Information Theory

Life & science & know how emerge and then influence how the cookie crumbles ... info must be copyable & possible i.e. must not contravene the Laws of Nature.

Information, maths, iPhone (software), communication, living organisms (DNA) ... never contravene the Laws of Nature yet do influence change - copy/vary/select, Baldwin Effect, recipes, error correction ... NOT intention but abstract constructors (David Deutsch below) made the Boeing 747! 

Everyone & everything progressed by trial & error ... experiments and error correction ... weeding out failures ... via Karl Popper's falsification.

More experiments, more errors, more learning ... imposition of one size fits all was anathema!

More change, complexity, conflict & scarcity = more niches & fantastical opportunities

Target stability with rapid growth of know how without crowd trouble & violence.     

Life, intelligence, know how, income ... everything affects everything else ... large numbers of factors were involved, growth is exponential (non-linear) and proportional to itself (l'effet proportionnel)  nature & nurture produce a sequence of random 'bell curve' mutations but the resulting distribution is thrown to the right at each happening (Jacobus Kapteyn machine) ... the distribution is log normal / Poisson. Income growth is proportional to the income itself. To him that hath shall be given ... exploding inequality ... a natural phenomena. NB this does not apply to every individual chance is involved at every happening. The chance is random but there is a survival non random pattern. The pattern doesn't go on for ever, individuals die. The compounding model requires constant innovation, moving the whole shebang & caboodle up a notch so newcomers start with inherited know how. 

Distribution pushed to the right by 'black swans' (rare but regular) where the average is to the right of the median.

Skew is a natural phenomenon. Folk are grains of sand in a tray with little wooden houses, the grains being thrown to the left and right. There are a few rich folk and larger number of folk at the left but the proportional effect determines the distribution.

Skew by the multiplication effect of factors? Then there is the supply and demand for road sweepers?

See the Paul Seabright question? ... and the Paul Seabright answer!

Russian Roulette = science is the gun, technology is the bullet but the target is not yet known ... an unknown unknown.

We read two books but didn't understand them -

1 - David Deutsch -  

Our very own interpretation of what we think David Deutsch meant - check it out for yourself we may be wrong  ����
The Enlightenment of the 18th century was the beginning of a process of self sustaining growth of know how. An infinite sequence of purposeful knowledge creation. Knowledge was information with explanatory power, evidence that means something as proven resistant to falsification ... so far.

Any real process is physically possible to perform provided the knowledge to do so has been acquired.

The Enlightenment set up the conditions for knowledge creation which disrupted the static societies that previously existed. These conditions are the valuing of creativity and the free and open debate that exposed ideas to criticism to reveal those good explanatory ideas that naturally resist being falsified due to their having basis in reality.

(during previous moments in history, Renaissance Florence and Plato's Academy, this process almost got underway before succumbing to resistance to change in static bureaucracies

Intelligence is more complicated than brute computational power. There was a lack of progress in Turing test AI programs in the six decades since the Turing test was first proposed. What matters for knowledge creation is creativity. New ideas that provide good explanations for phenomena require outside-the-box thinking as the unknown is not easily predicted from past experience. Innovation involves hitherto unconnected connections. To test this an AI behavioural evolution program for robot locomotion should be fed random numbers to see if knowledge spontaneously arises without inadvertent contamination from a human programmer's creative input. If successful intelligence would not be as difficult a problem.

Quantum superpositions and the Schrödinger equation provides evidence for a many worlds quantum multiverse, where everything physically possible occurs in an infinite branching of alternate histories.

In this way a great deal of fiction is close to a fact somewhere in the multiverse.

The concept of fungibility in quantum transactions, suggest the universes and the particles therein are fungible in their interactions across the multiverse structure.

Interference offers evidence for this multiverse phenomenon where alternate histories affect one another without allowing the passage of information, as they fungibly intertwine again shortly after experiencing alternate events. Our perspective of any object we detect with our senses is just a single universe slice of a much larger quantum multiverse object.

The process of human/culture evolution developed from a genetic basis through to a memetic emergence. This emergence led to the creation of stable societies where innovation occurred, but most of the time at a rate too slow for individuals to notice during their lifetimes. It was only at the point where knowledge of how to purposefully create new knowledge through good explanations was acquired that the beginning of infinity took off during the enlightenment. The explanation of human creativity is that it evolved as a way to faithfully reproduce existing memes, as this would require creative intelligence to produce a refined rule set that would more faithfully reproduce the existing memes that happened to confer benefit (and all the other memes too). From this increased creative ability, the ability to create new memes emerged and humans thus became universal constructors and technological development accelerated.

 We reject Jared Diamond's resource luck theories as to why the West came to dominate the other continents outlined in his book Guns, Germs, and Steel. The sustained creation of knowledge could have arisen anywhere and led to a beginning of infinity. It just happened to arise in Europe first.

The philosophical concept of optimism, problems of complexity, change, conflict & scarcity are inevitable but solutions will always exist provided the explanatory evolutionary know how is discovered and accumulated. But as soon as there are stocks there will be thieves. It is an evolutionary arms race, predators & parasites.

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2 - Frank Wilczek - 

Nature's deep design is beautiful? Why is Darwin's entangled bank beautiful? Is it only beautiful ideas that survive? Are the dice loaded? Is it anthropomorphic? If natural things were not beautiful we would not be here? 

From simple to complex as we are part of an elaborate process of progress as we learn - Pythagoras - Plato - Brunelleschi - Newton - Maxwell ... to the core theory of local symmetry & economy ... still flawed but we're getting there with the language of maths. Think science & empathy, a blend of matter & mind.  

Pythagoras & maths ... 'all things are numbers' ... but not whole numbers. 

Pythagoras & vibrating strings ... simple length ratios 1:1 - 1:2 - 2:3 - 3:4 and tension.

Plato & five solids ... Euclid logical construction - work will teach you how to do it - beauty in simplicity - symmetry - Occam's Razor

Plato & five senses & four fundamentals ... perceptions of reality hear / see /touch  smell / taste - but wot is this reality? Be sceptical. There is maths (physics) and metaphysics (reality that maths describes) ... perspective ...
Quantum Theory = relativity (viewpoint) / symmetry (beauty) /  invariance (straight lines) / complementarity (observation itself changes the view). 

Newton & maths method - Copernicus, Kepler ... and a ? at the end of every sentence.

Darwinian struggle for the survival of ideas in the imagination was naturally selected by maths logic.

Newton & colour - analysing light and polarising it ... and recombination. Colours and black line absorption

Newton & beauty - dynamic laws, what can happen ... possibilities. Planets & apples! Space orbits ... bring in time ,,, trajectories ... laws of motion ... and calculus. Analysis & synthesis. Beauty was in the simplicity of the underlying principles. Only a supreme intelligence could create such beauty from initial conditions and dynamics!

Maxwell & equations - action at a distance - gravity and electro magnetic 'excitement' in a 'fluid' rather like 'wind' in the 'atmosphere'.

change/movement in magnetic fluid = electricity

change/movement in electrical fluid = magnetism ... a dancing pair in a world wide web, no starting point just an excitement     

1 Gause = electric flux magnitude & direction changes with charge

2 Gause = magnetic flux has no 'charge' it stays put

3 Faraday = electric fields anf rate of change of magnetic fields. RH rule.

4 Ampere = magnetic fields & electric currents.

  Aall visualise fluids & circulation

Maxwell = converse of Faraday. Radio - space was not a void.

Maxwell & electromagnetic soup -  each displacement generates another disturbance in the dancing pair with magnitude & direction, one prodding the other into a self generating life of their own.  

Symmetry = change without change = truth = simple underlying reality = beauty.

Bohr & Quantum Theory of atoms = relativity (different viewpoints) / symmetry (beauty simplicity, change without change) / invariance (straight lines) / complementarity (observation itself changes the view of the whole shebang & caboodle).  Music = vibrating strings are whole numbers. 

Schrodinger & Wave Function - quanta = discrete particles but continuous waves. Probability clouds described by wave functions, position & momentum.

Probability! Many possibilities! Measurement of both at the same time impossible!

Atoms reproduce exactly within the probability laws but poverty of energy in an expanding universe dictates freeze ... condensation ... but life in eddies is a 'work' of art ... as photosynthesis locally reverses the frost as long as the sun shines.    

Einstein & special & general - 'what really interests me is whether God had any choice in the creation' - motion at constant velocity leaves the laws of nature unchanged - speed of light is constant yet Achilles overtakes the tortoise - how to synchronise clocks when moving at constant speed? Time assigned to events in space was different for fixed and moving observers! Space & time of folk were mixtures ... relative.  

Moving charges create electric currents and moving electric fields create magnetic fields. Fixed charges create electric fields.    

Red shift ... a different view of the same thing! All the colours can be seen by motion! Colour varies with time! Newton was very very very nearly right ... but wrong. But there was a different deeper truth that was even more beautiful ... (just like human intention and Darwin's entangled bank) ... but Maxwell was deeply right!

Newton's motion could be corrected by special relativity but Newton's gravity (mass) needed more ... general relativity ... because mass was not conserved. Symmetry was 'local' not 'invariably'. We know we can change perspectives without changing the scene (invariance).
Just as water changes the perspective of a stick. The fluid in space changes the perspective of physical laws. But the deep symmetry remains.
If we change speeds & times the laws must change to maintain symmetry. 

Pauli & patterns - chemistry is an encyclopedia but electrons 'fill' space with charges & spin and pattern. A tiny corner, carbon leads to organic chemistry and complexity ... driven by minimum energy states.

Symmetries - different, in different places at different times.

Gravity - Electromagnetism - Strong - Weak   

Property Space -  keep going along the line of least resistance - do what come naturally - yin/yang of 4 forces (opposite parts of an inseparable whole - space time filling fluids and mass energy excitement

Local Symmetry (invariance) - change without change - distortions that don't work

Quark model - a torrent of hadrons - confinement problem

QElectroD = the world of light, atoms & chemistry  

QChromoD = protons & neutrons from quarks, gluons = strong force

Sun turns protons into neutrons  & vice versa = weak force

Emmy Noether & Symmetry = connects maths & physics! = conservation laws ... from big bang on ... nothing else.

wot has been is wot will be
wot has been done is wot will be done
there is nothing new under the sun ...

just outcomes of evolution! Micro to Macro ... Genotypes to Phenotypes ... Genes to Memes ... 

Local symmetry of property spaces   = electromagnetism / strong / weak ... but gravity doesn't 'fit'    ... wot a mess!

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Unknown Unknowns in the Context of the Moment -

Richard Thaler (2008) - Nudge - bias $ owned > $ to win - 2010 Behavioural Insights Team - 2020 NESTA -
Daniel Khanemann (2011) - Thinking Fast Thinking Slow

1. - left brain reason & memory from if/then/else logical algorithms of Empirical Science
AND
2. - right brain creativity & pattern recognition inspired by flip flopping emotions of fear & excitement generating the diversity; the evolutionary feedstock
Everyone seemed to be on the spectrum of reason & creativity as they endlessly experimented & iterated with discovery & accumulation of hitherto unconnected connections as inventions & innovations, pushing human evolution forward, and changing the world forever as 'know how' accumulated.
A search for longevity with healthy scepticism, a refusal to take current accepted norms, conventional wisdom, group think as fixed in an arms race confronting parasites & predators.
Bureaucratic Kludge with a life of its own was not only Westminster, Brussels & Washington but also the Unilever fiefdoms ... delegated autonomy at all levels ... 'line' not 'staff' 'theory Y' not 'theory X' ...
Boys systematic intelligence experimental = inventive
Girls emotional intelligence manipulative = empathetic
Fostering change in nations long ruled by despots who had hollowed out institutions of custom & practice and built bureaucracies with parasitic & predatory patronage networks with a life of their own.
1994 fall of the Berlin wall
2001 war against terror
2008 lethal debt
2016 Trumpeting Brexit
2019 covid mandates
2021 COP 26 global mandates
'Democracy' seemed to fail into an abyss of polarised hatred.
The Brussels Bureaucracy was in denial, the Westminster Parliament was broken and the Washington Beltway was a swamp of bribery & corruption.
Globalisation, the synergies of specialisation & scale, were relentlessly dipicted as negative sum as bureaucatic kludge destroyed jobs & equality.
Protectionism started with Corn Laws and French farmers. Confronted with the Repeal in 1836 ... but continued with 'rules of origin' in 2021?
Polarised politics pushed 51% of the population into trying to screw 49%'
'Kicking the can down the road' became an arrogant attempt to pacify interest groups in return for votes as centrally managed organisms run by institutions deprived of democratic control restricted & restrained globalised free & fair trade ... and freedom to experiment but not freedom to harm others - not laissez faire but Torts, Trade & Technology.
\failure was the norm the 2nd law saw to that, we should expect failure, but go balls down for faster adaptation.
1. Project fear - doom & gloom - the lemming like charge of group think over a social & economic cliff into an abyss of cost, bankruptcy, isolation & hatred.
Just like The Millennium Bug in 2000 Jan 1st 2021 passed without a murmur as vaccines started to arrest the real Covid terror.
2. Fantastical Opportunities & 'yes we can' - inspired by freedom & autonomy unhindered by b p g & b. Not a loss of Empire but an opportunity for Commonwealth. Not take back control and Bureaucratic kludge but privatisation & boosterism. Not back to a non existent idyllic past but forward to immunity from treachery. Not 'power blocks' but 'common law, English language and magic triangles'. Not 'delusions of grandeur' but 'underneath the soap pans in Apapa'
English exceptionalism was not 'economic power' but an 'island nation' full of -
1. human ingenuity - use your imagination
2. diversity from a mix of immigrants & flip flopping emotions
3. excitement of busy experiments & personal responsibility
4. bad ideas which died out, adaptation made nature resilient
Sir Gilbert Longden -
'the defence of excellence against the ceaseless attacks of the the envious, the eradicators of excellence and the midwives of the second-rate?'
1988 Margaret Thatcher - 'We have not successfully rolled back the frontiers of the bureaucracy in Britain, only to see them reimposed with a European super-state exercising a new dominance from Brussels'
Thomas Jefferson - 'checks & balances, separation of powers, term limits and confirmed in the 10th & 14th Amendments - subsidiarity, privatisation, decentralisation, diversity ...
2021 'Ordinary people in both the US and China are like mobs who need to be guided. Average Chinese aren’t ready for western-style democracy and need to be led. In the US, everyone can have an opinion and nothing gets done. China should follow a different path' ... no Microsoft, Amazon, Google, Apple, Facebook, Tesla ... Genentech ... just Bureaucratic Kludge - arrogant, conceited, condescending, deplorable, disapproving, haughty, lordly, paternalism, pompous, pretentious, proud, self-important, snobbish, snooty, supercilious, superior
Who remembers Bathgate 1961 & 1986? or Alfred Herbert 1975 & 1983?
3% of gross domestic product for deficits and 60% for public debt?
Maastricht disaster?

Evolutionary Economics is the Science of Choice
Morality of Free Markets is an Adaptation
Conscience is a developing survival aid
cop26 - get fundamental -
crude oil reached an all time high of $147.27 in July of 2008, there was no gas in Mouldsworth, we were heating up Chester - waste of bunched up energy.
Pessimists - doom & gloom of Project Fear - politically impossible, you can't get elected.
optimists - excitement of Torts, Trade & Technology - personal responsibility, plant a tree, photosynthesis, Gaia, geo-engineering, adaptation?
or both?
diversity = left & right brains, flip flopping fear & excitement
evolution of know how = adaptation = copy (existing knowledge base) vary (experimental diversity) select (natural selection)
freedom to experiment without harm to others = Torts
synergies of specialisation & scale = Trade
hard work (2nd law & Jimmy Watt), honesty (empathy & Adam the Smith) & thrift (compound interest & ) = Technology
discovery & accumulation of know how = scientific methodology =
observation, maths theory, hypotheses, experimental validation, peer review & citation
optimist = more brains, more grandchildren - scientists need engineers need musicians & sportsmen need more cooperation with others to cope with inevitable parasites & predators, bribery & corruption, tyranny & oppression, when confronted with environments full of complexity, change, conflict & scarcity

Plan A or Plan B? Deal or No Deal? Do or die, come what may ...
FT 28 May 2021 - Brussels was shocked and angered. In Switzerland, quiet celebration & relief.
Bern announced it was formally withdrawing from negotiations to codify future relations with Brussels.
Never sign a contract like that in business. A requirement to take on EU law without any variation mechanism. A direct interference in our direct democracy & cantons in Switzerland. A creeping dictatorship.
Switzerland has to be 'allowed to be different'.
After seven years of diplomatic frustration, Bern was glad for the opportunity to move on. 
Despite all the sympathy for overcoming the narrow national borders that have led to many wars in Europe, it’s not necessary to sign everything that Brussels wants.

With all the cavorting, pontificating and malarkey of political correctness, wokery and nimbyism whatever happened to the WTO Doha Round & Structural Reforms - Brussels barriers, Washington swamps and Westminster hatreds?
Know how is evolving by natural selection - copy vary select.

 Structural Reforms Alt
1. we had more procreative sexual intercourse and fewer abortions, for Europe is dying on an absolute scale, but very alarmingly on a relative demographic scale.
2, shrink the social democratic state, to protecting only the truly ill and aged, for nanny statism has severely blunted work ethic, personal responsibility, initiative and resilience.
3. stop undermining traditional family life, and start reasserting the purist sanctity of mother, father, children, grandparents, uncles, aunties, cousins.
4. start reasserting the importance of maths, science and languages as the centrepieces of school systems, and stop this progressive nonsense of “everyone wins a top student prize”.
5. start decentralising political power and extinguishing the excessive preference for the French “dirigiste” model of an over weaning state and centralised power,
6. lower taxes, to reward self respect, personal responsibility, enterprise and initiative.
7. confine progressive nonsense to where it belongs - atop the Saturn moon Titan (and San Francisco).

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 Happenings had been going on in life recently causing much vexation and destruction of fun, peace & tranquility. 
Above all the hubbub we heard the knee jerk hysterical cry -    

'Who was to blame? Someone needed to do something now now and find out who was to blame so the cause of the folly could be eliminated so we could get back to the idyllic past'.  

Mavericks were my friends = weavers of hitherto unconnected connections = daft quirky weirdoes = have fun, don't poke fun. Stanford drop outs from Silicone Valley!
Mavericks were banned in the USSR and CCP and in hierarchical bureaucracies
New 'know how' wasn't a conspiracy of intelligent design. But rather a competitive evolutionary arms race building on pre-existing physical, chemical, biological and cultural knowledge from the past confirmed by empirical science with cycles of blind learning with continuous path dependent trial & error experiments in a specific context ... in Scunthorpe!
An abstract concept was an idea that people could understand that had no physical form. The ability to identify, understand and communicate abstract concepts was a foundational element of human intelligence.
Abstract concepts were real when they were documented in evidence.
Language, maths, arithmetic, geometry, trigonometry, probability, calculus,
Intention, was freedom to choose, family, friends, traditions, culture.

Wot was an ancient octogenarian Wrinklie wasting scarce time messing with mavericks & books?  
Learning? Wot was the point of it all, boring!

Evolutionary Economics - copy/vary/select - knowledge/diversity/survival - science/trial & error/evidence
If your notions, abstractions & ideas cannot be explained by evolutionary economics from introspection they must be delusions, fallacies, self deceptions, myths, magic & mirrors.

As we went the full circle from adolescence & Suez, cricket & science, to thermodynamics & Adam the Smith, commissioning factories & the night shift, to Miscellaneous Products & Team Leaders, to Quality Assurance & personal responsibility, to happenings underneath the soap pans in Apapa, then glorious Aba, to Limbe, to Bombay, to Warrington manufactories & technology transfer ... and finally to maverick studies at The Open University and finally maverick grand children ... we learned.
We all seemed to have hard-wired compulsions to seek out patterns in local environments useful for survival as we went for longevity in our different ways, at different times in different places with different friends.

We always ended up in the same place ... crowded with Blind Watchmakers.  

We urged them to get on with it because the dice were loaded ... there was unfinished business ...

Heckle quote which we can't delete until we understand -

The simplest example of emerging factors in Darwinian populations is given by the formula f=(f1.t1+f2.t2). e.g. if a genetic mutation occurs in a population of individuals of lifetimes of 50 years with a frequency of 1/10^4 years in an favorable environment that lasts 1000 years once every million years then it's emergence frequency in the population (on average) is -

(50x1/10000 + 1000x1/1000000 = 0.005 + 0.001 = 0.006) once in 167 years (on average) 

This takes some getting the head around. How can mutations occur once in 167 years on average if there are only a thousand years for conditions to coincide. We're talking about averaging over very long periods, much longer than a million years. It can be seen from this very crude calculation that the situation will be far more dynamic than this estimate because in the early days of human evolution there were very few humans, and homo sapiens have been around for less than two million years. Homo erectus were around far longer than us it seems, so I suspect mutations and incremental adaptations must be far more frequent than the above calculation suggests and erectus became homos by interbreeding; and there would have been other human variations; more than we know about. Lives would have been far shorter until coherent groups were formed.

If we combine the above probability function p=(1-exp(-ft)) in calculations containing frequency then we have to be very careful not to end up with inconsistencies. It's complicated. I suspect that this is where the exponential function comes from in the maths book and he may have used a very simplified model. It's easier to use the example above and avoid the exponential.
I hope all that is consistent. ????

... don't forget the Millennium Bug story - risk went DOWN @ 0-0-2000 'cos Due Diligence went UP!

Xi Thought - Educating the public about why China’s communist regime was superior to the West?

Censorship & Cancel Culture - Who plays God? Who guards the Guardians? or Experiment and discover Euler's 'e' was and always will be a universal constant.

Covid 'mental health' & 'physical health' like 'nature' and 'nurture' ... impossible to separate, its all stuff, one whole shebang & caboodle?

Stay curious & keep experimenting!

 

john p birchall

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