Decline in participation in Mathematics

http://theconversation.com/why-it-matters-that-student-participation-in-maths-and-science-is-declining-47559

Mathematics and Science are the basic tools along with Philosophy that enable us to ask question such as, why is that happening, are there connections, what is…….

Of course we can ask these questions without using a scientific approach but probably such an approach would value certain factors more than they should be. For example, a belief that God will provide, and it is the will of God what happens are, to say the least, problematic.

One wonders the role of doubt in these non-scientific thought processes. Science values doubt, it seems non-science does not.

This non-valuing of doubt results in reactionary thinking, or conservationism in the face of change.

Open positive letter to Clive Palmer – Climate Change

Dear Clive,

Keith is a dear friend from Uni days, he is a paid up PUP member and he is concerned you get this right, too.
Please don’t discount Tim Flanery – he is an excellent communicator and I feel a positive conversation would help developing understanding and awareness…..Tim if I have made any inaccurate statements in what follows please correct me (us).
I am writing to you directly as I was both impressed and dismayed at certain things said to the ABC Insiders and in an interview with Tony Jones.
I am not involved in any political party or movement – I am however a concerned Australian, currently living in Vietnam and soon Istanbul.
And, before we start I am trying to help.
Your statement about 97% carbon in nature and 3% created by man, and the idea that carbon in nature can be reduced is simply impossible.
There is a fixed amount of carbon.
It is stored in various forms e.g. gas, fossils, underground coal gas and plenty more.
The carbon cycle is fundamental to why earth is livable.
Photosynthesis is main process by which the volume of carbon, CO2 is kept in balance not too much and not too little – plants (plankton in the sea being a significant part) recycle Co2 and output Oxygen that we breath – any threat to the oceans will be catastrophic.Along with the layes of atmosphere that filter light and heat rays, with the specific natural balance here we would all fry or freeze.
(a) The science is clear, irrefutable, CO2 lets in sun light but not the reflected heat rays coming from earth’s surface that in normal circumstance simple go back into space, if trapped we get increased heat.
(b) Increased heat is likely to cause increased cloud and water vapor, water vapor acts exactly in reverse, it reflects sunlight back into space but lets through (out)reflected heat from the surface of the earth -hence cooling can occur.
It is very complex in how things will play out, I can assure you the computer simulations are very, very complex pieces of mathematics, each model consistently shows dangerous patterns that we simply do not understand the likely outcomes off.
The 3% you refer to is the increase due to mankind burning fossil fuels.Man is not creating anything, we are simply converting carbon from one for to another, and upsetting the natural cycle, so there is build up, year on year.
Small amounts of CO2 over time are being added that the current natural carbon cycle can’t remove and store. NOTE: it is impossible simple DELETE or destroy carbon, it is simply converted into a different form and stored, and on very long time cycles.
This small amount is hence adding to and gradually increasing the level of CO2 in the atmosphere – and hence the risk of points (a) and (b) occurring is heightened, and also why the issue is referred to as climate change – we could get heating and/or cooling, it is likely however that (a) and (b) will not simple cancel each other out, but this could happen.
To the KEY issue – you cannot remove carbon, the amount is fixed. You can’t simply look at a forest, for example, and somehow remove and throw away carbon, this would be alchemy.
What one can do is to try and restrict the increase of CO2 into the atmosphere – there are many schemes – storing the gas underground, or finding alternative energy sources eg Solar power, and looking eating habits to reduce methane from cows!
And, what is missed in the debate is that CO2 is only one of many gases that we should be worried about.
Australia is a very highly skilled scientific country, what I suggest is getting behind the issue and prompting our science and turning this into industries that employees. The CSIRO is a fantastic institution, a world leader, and acts independent of but is dependent on  Govt funding. As are our fantastic Universities whose only way of thinking at the moment is to increase fees and further reduce the spread of the students able to go to University – intellect is equally distributed, women, men, rich, poor, ethnicity, none matter. The inequity of access to Australian higher education is appalling, notice nobody ever talks about the outputs i.e. the socio economic background distribution of graduates. Public education is and SHOULD be seen as an investment, a right and not one restricted to the rich.
Australia has not been good at turning our knowledge into high added value industries -it is far simpler to dig ore/coal/gas out of the ground and export it, and we have an ethical issue here in that we are directly fueling carbon release in other large population countries.
I strongly urge you to do what you suggest, get briefed, listen and above all understand. I am very worried if indeed you are treated with distain and not listen too or approached, maybe if I am proffer some advice – “ask, shut up, listen, think, then ask questions….you owe it to your party members to get it right and LEAD”
We are talking about a fundamental fact or set of facts, which if not understood invalidates comment, in that if the argument presented cannot be traced back to showing understanding, then it has to be discounted.
I urge you to understand and get behind Australian Science, help with the step of monetizing our knowledge to create industries of high value and employment. Many small companies, in a vibrant intelligent competitive yet cooperative environment is the way forward – none of this silly “you are a dick, not your are, ya f’wit” , lets move on, the current two party system and that ridiculous parlementray question time is anti intellectual, anti business and just a bloody national and international disgrace.
Also, your comment on the NBN is misguided too – at least in my view – Australia must have a highly efficient and fast data transmission infrastructure on which new industries can be built. I have run a very small business in the past educating teachers around the world how to teach computer science – the Internet and access to it via the world wide web has been simply breath taking in the speed of its development, think since around 1995 when the first browsers that were easy to use came about. Get behind Australian education and research and the creation of a backbone NBN.
What is then needed is competition from providers of services – this is were Telstra should not be allowed to operate, Telstra should simple deliver the access to the backbone, across ever part, no inequality.
Your comments about Aboriginal children was appreciated, it is an Australian disgrace!
Good luck and please get to grips with the issue and no more ill informed comment – I am equally amazed that the Insiders said nothing, it exposes their lack of expertise, and credibility rather they are simply interested in the gossipy side of politics and really have no qualifications to comment further.
Kind regards
Dr Andrew Meyenn

Humid visit downtown and what was in the paper

I find idiocy in most things, probably because I am one, an idiot at heart that is. During the past few weeks I have been hiding in doors following an exfoliating treatment on my face and arms, but mercifully this is now on the repair. Cathie is doing an inservice – on a weekend – hence I am dispatched to purchase trinkets for Cathie to give to Drew when she goes home in a few days, and also to drop off some stuff that needs polishing at her favorite Jeweler, and I thought great I can have a spot of brekkie and read of the Age rather than the online version.

At the minute Saigon is about 100% humidity – I just don’t travel well and  sprout like a tap. With instructions ringing in my ears, I took the boat and head to Bahasa – i am sure the toys are on floor two -, NO, the place is being renovated, so I traipse off to the other one, a mere kilometer away! Nothing there either, but at least it was open. I remember the alternative…try the Russian store….so I do and there are many trinkets (I can’t but think about Cook and Hawaii and how well trinkets went there on his last visit), anyway, I purchase some….result. I emerge and start walking off towards the Jeweler, and on route the massage girls take pity, normally they say….you want massage….., but this time some hilarious young lady says ….. you look like you need massage, we have shower too!….in reference to my sodden appearance.

I make it to the brekkie place and find a seat, next to a table with a Vietnamese lady typing at speed on a nice little computer, and answering rings on the ubiquitous iphone, her son then arrives, there is no verbal greeting, in fact no sounds at all due to headphone usage by both, he plonks down and within 5 minutes has slaughtered the inhabitants of planet Zork…on his iPad. In walks Dad, and American – but not the Silent type made famous by Grahame, possibly an ironic title! I think he is greeting what I image is his wife and son, but no, he is using voice recognition on his iPhone to chat (type version) to someone, this continues for some time – as far as I could tell, there was no communication to the wife or son. My small serving of an English arrives and I am distracted, but then out comes the huge MacBook Pro that fully displays his business spreadsheet – and he continues to chat verbally over chat with someone back in the States. As far as I could make out he was involved in selling packs of something that contained 2.5 gallons of an unspecified substance, but obviously a defoliant! By the time I left there had still been no communications!

I travel to the UK a bit and need to replace a light weight Rivers shirt and pants that I have worn….out! There is an advertisement that catches my eye in the paper….Slim fitting (clearly this is for me) with a wrinkle resistant (looking good) and stain repellent finish….must get some. And then there is an advertisement for foot wear…walking shoe only $109.99 each, seems odd, normally a pair is sold. And, then I notice Thermals – high performance, moisture management and breathability (no hyphen, I wonder if the Oxford has caught up with that) are trumpeted as the selling points, what on earth is the ad talking about, is it a computer, would it solve my sweat (oops perspiration) issue? I ask you.

Again there is an odd mix up over plural & singular…..each thermal is advertised as costing $49.99 each or on Sale as 3 for $69.98 EACH! At least you are close to a 69, Andrew don’t be indelicate.

Moving on, and on a serious note, I read an article about the refugee boat arrival issue and a reference to Gareth Evans (affectionately known as Biggles or Gareth, Gareth as he coveted the UN job) by Ken Berry from his book about the Cambodian peace process of the late 1980’s. Which is apt because many people forget it was the Vietnamese who got rid of Pol Pot. Ken posits that in general, and now I quote “pre-conditions for a successful operation [Peace keeping..and anything] include that the plan be conceptually sound and appropriately detailed, with clear and achievable goals, adequately resourced and the support of all the key players“, now how could you argue with that, the article mentioned this in reference to our Foreign Minister’s recent suggestion to Cambodia that they might like to take a few refugees off our hands – inference is obvious.

Funny world!

India

We visit India recently with friends Helen and John Harrison.

You can see some pictures at here

The flight from China was delayed, only a day, so a one night unplanned stop over in Guangzhou during the start of  Chinese new year.

Plenty to see and do, and I will add to this blog at some stage.

 

Postmodern Job Application

Dear Sir/Madam/HR AI Robot – some explanation, I am assuming that you are using an Artificial Intelligence web robot to filter applications, it is not meant to imply that you do not possess real intelligence, although I will reserve judgement if you don’t mind) .

I would like to apply for the appealing position at the Savoy – I am assuming the campus is at a nice hotel by the same name as the London equivalent, very classy and I am sure I would add to that.

JOB TITLE: Dean of the Savoy Campus

-Masters degree minimum – Yes, I have two and a superior one as well, alas it is not in catering or bar service, trust I have not misinterpreted the use of the term Savoy, I guess it could also refer to a popular biscuit severed with cracker barrel cheese

-A minimum 5 years previous experience as an educational administrator – well yes, but why does it need to be restricted to education, my life has been rich and varied (well not rich in the money sense, which I am hoping you will put right) and I have a fabulous sense of the humour.

-In depth understanding of US High School academic programs, International Baccalaureate Diploma Programme preferred – now this makes no sense, it is not possible to have an in depth understand as the US curriculum is far too shallow, think low tide and diving in, there is nothing in depth about it. The use of the e on the end of programme is reassuring for an American school.

-Boarding school experience or equivalent preferred – alas being rogered in the middle of the night by some well meaning farm boy eluded me (in a great many respects I am thankful), but I do a great plough man’s lunch! In private we could discuss if I qualify under the “equivalent”, but I doubt it.

-Overseas teaching or working experience preferred – yes, I have that, but isn’t the Savoy a grand pub, why do you want teaching qualifications, is it food training school as well.

-Familiarity with accreditation systems – yes the Michelin Star system is wonderful, and no doubt there are other less reliable rating services I could easily falsify on the Web, if this is of interest.

-Prior experience as a classroom teacher – well yes, do you have difficult guests, my Gravesend (austere name for a town I grant and Pocohontas caught a fever there an went to the spirit world – little know fact team, file away for the next quiz night) experience will put me in good sted here, handling the delightful Craig (aren’t they all) means I can handle any uppity notable. –

-Coaching or experience in extracurricular activities preferred – yes coached Hockey, footy, and have a range of other experiences and qualities that probably fit into the term extracurricular, which I take it to mean not related to what job one may have – like writing job applications, when at work, perhaps? I have experience herding goats and cats and in fact all manner of idiotic creatures that have not the slightest scintilla of an attention span or resemblance to anything intelligent.

-Computer proficiency, highly organized, task oriented, committed – what do I need to be committed to, you don’t say, but yes unfortunately I do know about computers (but I am assuming this is not important), provided you are clear about the task I will commit (funny how that only has one t, why) to at least consider doing it – you would have to ask others about the odd combination “highly organised”, I am not sure I follow. Being used in the same sentence as “computer” is an oxymoron of sorts – sorry, I don’t mean to imply you are a moron, although you could easily be with some of the dash points (well there not dots are they?)

-Strong interpersonal and communication skills, excellent team-player – I am often referred to as “strong willed and don’t tolerate fools easily”, but it is true that people are very clear what I think or deaf, my writing is, for example, a wonderful exhibit of clear and lucid prose, don’t you think? Well I did play footy, so yes I have played in a team, not sure about the term excellent, some days I missed from a few feet – the goals that is, which is a metaphor for organisational goals when you think about it, is that why you ask?

-Excellent role model Well probably, but to whom, a herd of well meaning strip tease artists perhaps, you really need to be more specific, I am beginning to wonder if I should apply or not, it is a bit like a postmodern-post-modernity exercise in the absurd writing this (let alone anyone that reads it, including the aforementioned HR Robot)

-Strong public speaking skills – after a few I can rant with the best, I can also call “time you lot of arseholes” as well as anyone to clear a bar after hours, odd use of the term Strong, possible “keenly refined, or focused, but strong? What is wrong with just GOOD?

REPORTS TO: – lot of cooks in the pot here mate – see my comments.

Head of School, Managing Director – is this one or two people, anyway I am happy to report, but what do I report, I wish you were more specific.

Interfaces with – what does Belle Epoque mean, Belle means beautiful in Italy, does it mean the same thing in Switzerland? I am probably happy to interface (you have some funny terms) with that Dean, the rest all sound like a bunch of tossers!!

Primarily: Head of School, Dean of Students, Dean of Belle Epoque Campus, Head of Operations, Registrar, Director of Studies for Savoy Campus, and Director of Learning Support Other: Administrators, teaching staff, academic and support service staff, students, and parents.

Appraisal Yearly according to the 360 approach – why 360, aren’t there 365 days in a year, oh I get it, it is circular reference i.e. 360 degrees, bit steep mate, take forever to get that many degrees. Love St Anselm

New Music Express top 25 (500 really) albums

The New Music Express – top 500 I thought it would be fun to have links to the music and a wikipedia link as well – remind us these albums were about!
Indie Rock – explained

1. The Smiths – The Queen is Dead || Info

2. Beatles – Revolver || Info

3. David Bowe – Hunky Dory || Info

4. The Strokes – Is This It? || Info

5. The Velvet Underground and Nico || Info

6. Pulp – Different Class || Info

7. The Stone Roses || Info

8. The Pixies – Doolittle || Info

More Latter.

Blechley Park & Midsomer

In late September I visited the UK on route to Cardiff to work for the International Baccalaureate, which I have done nearly ever year for the past 12. This time I decided to visit Blechley Park and for a bit of fun, look for some of the locations used in long running TV series Midsomer murders.

I booked into the Highwayman a country pub near Kidlington, it is a working persons pup, right by a canal and served a variety of real Ales – the ones that pour by pumping. They also served wonderful ‘Full English’ and India food.

On Saturday I went to Bletchley park, the home of the WWII code breakers and Alan Turing, and the National Museum of computing. Alan Turing is simply one of the most brilliant of mathematicians and conceptual thinker about the notion of computational thinking that lead to the development of not only Enigma code breaking machines but also the modern general computer and the stored program concept. In WWII he was one of the lead scientists who worked to crack the German codes created using a mechanical machine called the Enigma code.

His work went unheralded after the war and he eventually committed suicide when charged with homosexual behaviour in around 1950, illegal in Britain at the time. Not until the late 1950’s did his mother know what he did in the war and that he was a hero, his treatment remains a scandal despite Brown’s letter of apology. A movement is underway to grant a full pardon.

Turing’s writings are wonderful in their clarity of not only the technical mathematical content but for his use of every day language to outline the problems he foresaw that would need a technological solution – one being the idea of data storage being like a book with a direct page reference in preference to storing a series of 1’s and 0’s in a mercury filled tube using waves, this latter technology actually worked, but it was his insight of the need for very large storage beyond that of the immediate primary memory that is impressive. He worked with the American von Nuemann to design and discuss developments in computing during WWII, sub-sequentially the von Nuemann design was adopted and basically all computer still use his fundamental design. It uses the philosophy of doing as many instructions as possible using hardware, a complex instruction set. Turing had proposed an alternative to do only the very basic instructions in hardware and to provide the rest using software, this is what is known today as reduced instruction set architecture and is used commonly in mobile devices.

The role of women at Bletchly park was not known during the war and received scant attention after it. The main British code breaking machine, designed by Turing, was called the Bombe, which is a derivation of a Polish word bomba, meaning cytology or code breaking. The machine was used to determine the Enigma machines daily settings and was operated and managed entirely by WREN’s, many of their stories are now available and apparently the shifts were long, stressful as mistakes were costly, very hot, very smelly (oil as it was a machine with moving parts) and very loud. The fundamental inputs were a series of cables connecting single input points two at a time, these connections had to be made very quickly and without mistake: I can attest that this is difficult as you can visit the hut and try for yourself.

I also visited the National Computing Museum and was reacquainted with similar input devices I used as a student in the early 1970 – enter programs a line at a time, the symbols displaying in electrical displays which were small glass cylinders – one per character, about 10 at a time! There were also the old 300MB, 19 platter disk units which I used to sell for $50,000….bit of a trip down memory lane.

The rest of the trip saw me hunting for Midsomer Murder sites – I visited pubs, took pictures of villages, walked in the woods, made a short movie and saw the windmill, alas the camera obscura on the village green of the village of The Lee is fictional, image my disappointment!

Some pics at

Bletchley Park & Midsomer

I also made a quick visit to Kings College Cambridge – just to say I had been there!

Kings College

and you can listen to the choir of Kings College here.

Climate Change Science

To act, or not to act, and if one acts what should one do, and if no action is desired on what basis is such a decision reached.

Science is a gradual process and not one that claims 100% knowledge at any point in time and more importantly not about likely consequences – political or otherwise. It is also a cautious disciplined approach, a skeptical approach, one where consensus can be upset at any time by a new discovery. Importantly, it is a process which is long term, statistical based decisions made in haste, on poor samples are eschewed, but it is true that Scientists champion causes to promote their tenure and get funding, and once the scientific discoveries enter the political domain the idea of a dispassionate assessment is lost.

When scientist looks at the carbon atom – to pick one of the so called green-house gases – it is found to absorb earths radiation coming back off the earth’s surface otherwise destined for space, hence trapping heat which leads to warming, but good aspects of light rays are not reflected back into the atmosphere rather these pass through to hit earth’s surface, some is absorbed hence increasing temperature.  Remember that light from the Sun is not a single ray, it is made up a wide spectrum, in effect some are good and some are bad, the earth’s atmosphere filters the good and reflects the bad.

Interestingly when scientist look at water vapor H2O it is found that this leads to clouds which reflect sunlight, as do the oceans, but humidity absorbs radiation reflected from earth’s surface, and there is the heat transfer caused during evaporation.

If warming happens it is likely to increase humidity, which will lead to more clouds and more rain brought about in part by ice caps melting releasing stored water from ice – the amount of water is fixed, it is just stored in different ways –the overall heating will increase rainfall in some areas but not others. The result will be increased sea water levels, rain patterns will change. Water vapor is the cause of thunder storms as it changes form via evaporation and hence releases energy, which also warms. This is why it is thought there will be an increase in violent forms of weather.

The amount of carbon is fixed or balanced as well, it is just stored in different forms, the amount in the atmosphere is increasing, past the magic number of 350ppm , the historic maximum reached before (at least what can be worked out)– less than 1% of the total volume of the atmosphere – has now been exceeded. The atmosphere is made up of Nitrogen (78%) and Oxygen (20%) , so green house gases represent less than 2%.. The atmospheric layers play the vital role of reflecting dangerous rays of the spectrum in sunlight – the ozone layer being one form of reflective protection, which science showed was diminishing as gases in spray cans started to accumulate and began to disperse the ozone level to create holes, like the one over Southern Australia, interestingly this science was not disputed, action taken work wide and the trend mitigated.

There is a delicate balance in this over all climate system (and sub-systems of the water cycle and carbon storage) where small changes, when modeled, seem to have the potential for much larger disproportionate effects e.g. warming and changes to climate. But it is unclear the exact nature of what will happen with real mother earth, for instance the increase in clouds may help to temper warming by reflecting sunlight, in fact if there was some catastrophe e.g. a very big Krakatoa or anything that lead to vast increases in clouds that lasted for say two years covering the entire world, then we would have cooling, vegetation would die – including plankton in the oceans hence CO2 would be less absorbed to cycle to give O2 and so on to …….

We have got a complex feedback system here and it would seem foolish to me to ignore this complexity. In another blog article I talked a bit about exponential growth (and decay). The rate of growth of C02 seems to fit an exponential model (equation) which implies that as the steepness of the curve increases then small changes on the X-axis (time) will result in larger disproportionate changes on the Y-axis (levels of CO2 etc). Which implies that if these levels have the potential to alter the behavior of the earth’s climate then whatever impact there will be is likely to be much quicker than we expect – and by implication difficult to reverse or nullify.

Coal provides around 30% of world energy needs (oil and gas 66%)), of which China’s usage represents 50% and of the rest the largest user is the USA. The volume of coal use is increasing, driven mostly by China and India’s consumption patterns. The patterns of consumption (assuming accurate) show increases in China (50%) and India (20%) and decrease in USA(-5%), but that China is doing a considerable amount on the issue of decreasing emissions, whereas India is not.

Longer term the reliance of Australia on the resources sector will continue but at some point demand will slow. To me there is an ethical issue here. Assume for a minute that the climate science is reasonably accurate then Australia is, because of its exports, contributing far more to warming than just the 1% attributed as our contribution to total green-house gas emission. We have a small population so viewed on a per capita basis we are seen by the rest of the world as excessive contributors, but not in an overall sense. China and India are the single largest contributors and our exports are partly fueling that.

On the other hand China and India’s increased development is likely to have positive impacts and hence our exports are helping with this.

Complex issue and not one that is easy to answer. Australia has signed up to international agreements to reduce emissions by 5%, I think by 2020. The now government made much about the claim that the previous government’s carbon tax would raise and continue to do so, electricity prices by some $550 pa., these figures were not disputed expect when one considered a floating price for carbon, the net effect was likely to be then around $150 pa per household. The current government’s policy of direct intervention is one I have some agreement with as I am not a big fan of these trading schemes. And at around $4b over 4 years represents a cost of $43per person, or about $131 per household, using average occupancy of 3 persons, as opposed to $150 increase in yearly electricity prices using floating price of carbon i.e. roughly the same for ONE year, but vastly less expensive on a yearly basis. It is unclear if this type of expenditure is sufficient to meet our target. I am not aware that the current government disputes the need to meet our international agreement, which implies direct acceptance of climate change science, there is just a different approach, which on a basic analysis shows household cost increases would be the same..

Australia is reliant on coal for our electricity, over 50%, so coal use is not going anywhere other than upwards, unless LPG or other sources quickly begin to take some of the increased demand. Domestic demand for coal is pitted against the commercial reality of demand from overseas, if that price is more attractive, domestic electricity suppliers will need to meet or better the price, in so far as that is an increase in input costs then the consumer will pay, hence electricity prices will increase as our domestic demand increases irrespective of what is done with a price on carbon, directly or indirectly. Unless of course providers reduce other costs e.g. labour costs, lower hourly rates, less permanent more casual etc.

All very interesting and complex, is it best handled as a political process? What other process is there?

Something about maths

This problem was posed on FB by an old school friend.

For those with an over stimulated interest in mathematics, riddle me this ….. if I but $10 worth of petrol at $1 per litre I get 10 litres ….. if I buy $10 worth of petrol at $2 per litre I get 5 litres ….. if I buy $10 worth of petrol at $1.50 per litre (as $1.50 is half way between $1 and $2) I should get 7.5 litres ….. but I get 6.66 litres ….. why is it so!?

Mathematics gives us away of looking at the world and abstract problems, often by creating a model with an equation and some assumptions. The equations simply relates what is on the right hand side, normally a computation, to a single value on the left hand side. The LHS is made up of things we call variables, and arithmetic operations are performed to produce a single value.

The above problem looks like a paradox at first until it dawns on you that this is a class of problems described by the equation as y = c/x, where c is the amount of fuel in litres and x is the cost in dollars and y represents the amount per unit by cost. e.g. c=$10 and x=$2 then y = 5 litres per dollar.

The assumption made in the statement of the problem assumes a linear relationship, but the graph of y = 1/x with x>0 shows a curve with the behaviour that as x gets small then y gets big and as x gets big then y gets small, and changes in y happen quickly and not uniformly as x changes uniformly and x=1 gives y=1.

Many will know the frog in boiling water parable. The above is a demonstration of exponential growth for x>1 and unfortunately this does not have nice even spacing for the y values for evenly spaced x values and hence we can’t claim that $10 worth of petrol at $1.50 gives a result evenly divided between petrol costing $1 and $2.

We could make an Integer relationship and force the result e.g. A(x) = {(1, 10), (1.5, 7.5), (2, 5)} and so on, and if we plot these ordered pairs we would see they lie on an imaginary straight line.

Exponential relationships exist everywhere in nature – weather, smoke, economy etc. and commonly we often don’t understand that things may well be speeding up or indeed slowing down, it is probably fair to say our brains tend to shape what we see into something that fits what we know and this is mostly linear. It is why we need to be very careful with claims that appear linear when in fact they are better modeled as exponential.

You will find a very interesting discussion on how it is vital that we understand exponential growth – see Economics and Exponential Growth the point of this article is what has happened in the past may happen 50 times quicker in the future, and the 100 times, then 1000 times i.e. every accelerating or the opposite. Think population growth, carbon entering atmosphere, fish numbers etc.

And a word of caution on models and simulations of these using computers – models are abstractions of reality and exist under assumptions, which may or may not be accurate.

The stock market is an interesting system to consider – by system I mean something that has inputs and outputs, at a simple level we have money to purchase stock as the input and the twin outputs of dividends and capital growth or decay. Today the markets is monitored down to mico-seconds and buy and sell decisions are made as much by decision making software as are made by humans. Caught in the middle of all this it seems to me that it is impossible to draw trends, or those that are drawn are done so on a very much smaller time scale that say a day. Does the market behave in a linear (don’t think so) or exponential manner, probably the latter if you look at the long term chart, but at another level it could be completely random. The only reason we are interested in equations is because they allow use to try and predict things but getting linear and exponential mixed up leads to very poor predictions.

Lets turn to another idea, that of randomness and models. Ants have been studied as they come out of the nest and go to either of two food sources to the left or to the right meeting other ants that are coming back to the nest. It seems that ants to one of three things: go to the food source they have always gone to and never change, randomly choose as they emerge or are influenced to change their mind by a returning ant. I find that fascinating! Consider the most recent election and assume 70% of people vote as they always done, 20% make a random choice and 10% are influenced to change their mind at some point in the time they started thinking about voting and when they tick the box. You can easily model this with what is terms a simple stochastic process and you can run different models making different assumptions about the size of each group – clearly the larger the last group the more you maybe able to influence the result via advertising or some other intervention. The larger the random group the more difficult it becomes to predict, you only need one more vote than your opponent to win.

What I have done here is made a leave of faith that the Ant model is a good one to apply to voters, but when you reflect maybe I am not so mad for doing so – decision processes are open to study, here the voting process does seem to be able to be categorised. For instance we could add those that donkey vote, or those that will vote informal etc. Imagine also if a particular form of advertising was seen to act in an exponential manner i.e. each single day the shift of voters accelerated from one group to another due to FB advertising in a direct sense – this phenomena does in fact seem to exist i.e. phases such as campaign momentum and landside seem to suggest voters can move quickly in time.

My final ramble is about binary arithmetic, and again I find this amazing that something so simple is so, well wonderful. Computers represent stuff as on or off, two states, hence we can use a 1 or 0. How do computers subtract numbers – well by adding complements, this simplifies things in terms of circuits, reduces heat and speeds things up.

1 + complement = 0 this is the result we want. Adding 1 + 1 in binary gives 10 (thing adding 5+7 gives 12), I will not go into bases and place values.

Lets consider we have groups of three 1s and 0s to represent 0 to 8 i.e. (000), (001), (010), (011), (100), (101), (110) and (111) note there are eight groups hence (000) is 0 and (111) is 8.

(000), (001), (010), (011), (100), (101), (110) and (111)

Complement (111), (110), (101), (100), (011), (010), (001) and (000)
add 1 to each (000), (111), (110), (101), (110), (011), (010) and (001)

Now add each pair from the first row to the third row —what do you get, ignore any carry at the end? You get all zeros!

We have our result – value + complement gives ZERO—beautiful.