Math 1.0 can be considered to be a special case of Math 2.0, where certain aspects of reality are ignored for the purpose of making things black and white and therefore easier to manipulate and compute.

Math 1.0 is helpful in specific circumstances like simple counting and manipulation of number, adding, subtracting, multiplying, dividing of pure number, and for making approximations, and is also useful in statistical manipulations where it is valid to manipulate data away from its context. Math 1.0 thinking successfully delivered a rocket to the moon but has failed to deliver insight into most chronic problems affecting humanity today. Math 1.0 thinking is part of the problem!

Math 1.0 is not valid in the domain of measurement nor when ‘counting’ is actually for the purpose of measuring ‘things’. And yet we use Math 1.0 with measurement all the time!

Using Math 1.0 as the ‘logic vehicle’ for interpreting changes in measurement data is a major reason why we have witnessed so many decisions by leaders and politicians in the last few decades that have turned out to be wasteful and that have exacerbated rather than solved ‘problems’. This happens when the Math we learn at school (Math 1.0) is applied into the world of measurements. And a science based around this maths re-inforces it as a science of reduction and ‘ism’ (“ism” happens when a discipline comes to believe its working model of the ‘world’ as true rather than ‘useful in defined situations’). So the belief (as true) in the mechanistic universe and the use of Math 1.0 as a sturdy, reliable and incontrovertible companion has led the traditional Newtonian scientist up the proverbial garden path and is still being led there daily. Multi-billion pound projects based on the assumptions of a reductionist science leading absolutely nowhere, whereas situations that could be drastically improved based on a science thinking in terms of systems and Math 2.0 are not being allocated the same research money.

To fully appreciate the meaning and consequences of data measurements, a good understanding of Math 2.0 and its application is required. If we care to look, we will find that the scientific, political and business literature is littered with examples where statisticians (who we would think would know better) have fallen into the trap of applying the thinking of Math 1.0  to the situations described best by Math 2.0, thereby giving us misleading ‘expert’ information and advice

This venn diagram shows the relationship between Math 1.0 and Math 2.0:

It was Walter Shewhart (the man who has been called the father of quality) who said “Data is meaningless outside of its context”. Using my language here, he could have rephrased this as “Data is meaningless unless processed using Math 2.0″ (Math 2.0 is a way of working with numbers that keeps the important context ‘in view’)

Math 1.0 is the Math of the Counters. Math 1.0 works for the abstract Math-World. Math 2.0 however is needed for Real-World Problems. Many of our “number experts” (mathematicians and statisticians for example) base their life-long working knowledge on this Math 1.0, so they are then part of the problem. Math 1.0 is entrenched in academia and science. It is now one of those implicit unquestioned assumptions (like water is to fish and air to birds) that Math 1.0 is numeracy and that Math 1.0 describes the sole reality of numbers. There will certainly be a few people in very high powerful places who know about Math 2.0 but are happy for the rest of us to just learn Math 1.0. When it comes to comparing things, Math 1.0 does not clarify issues, instead it clouds them. All this means so few people know or understand the limitations of numbers, and therefore that numbers can be used to keep us all in the dark (ages?) about most things. We will never really know whether our Health Service or Schools are getting better or worse using Math 1.0. What is certain is that using Math 1.0 we get into endless debate about the trivia from the data (we can call this “noise”) and we will nearly always be missing the important understandings (we can call this the “signal”). Without Math 2.0 the useless information (noise) is drowning out the important information (signal).So although it seems ludicrous that some, if not most, of our main ‘experts’ in Maths and Statistics use a Math that was devised for the special case of pure numbers and counting and that is strictly NOT applicable to numbers as MEASUREMENT. But it is such experts that write a numeracy curriculum for our schools, universities and accountants that is based on a special case with numbers (the Math of simple counting – Math 1.0). In the real world most of the important numbers we deal with on a day to day basis are to do with measurement, or involve counts that are being used as measures, and so we need to apply “Math 2.0″ in order to interpret these situations. When we use simple Math 1.0 for interpreting data measurements we create problems and misunderstanding. Because we have come to rely on numbers in every facet of life and business (we found we could no longer trust the word of leaders, doctors, scientists etc so we needed their numbers) numbers now heavily impinge on our emotions. We can get very angry when we see numbers we don’t like. The problem is often there is no valid reason to get angry with the numbers, it is Math 1.0 we should be getting angry with. We should be getting angry that we are not taught the ‘numeracy of measures’ at all. Everyday we are all making decisions with sometimes life-threatening or very severe unintended consequences because of a lack of real-world numeracy because we don’t have the skills of Math 2.0No-one is excluded. Politicians, scientists  and business leaders all continually make poor decisions when they apply Math 1.0 thinking to real-world Math 2.0 situations, making us depend on numbers in a way that is totally irrelevant, abstract, misleading, artificial, and distorting. Our lack of real-world numeracy Math 2.0 skills is I believe a big part of the problem why so much today seems to be going wrong. We follow the numbers but we don’t understand the numbers and as a consequence we jump to the wrong conclusions and we take actions misguidedly on the numbers and actually then make matters worse rather than better. (Deming called action based on misguided interpretation of data – tampering and he devised the funnel experiment to help us understand how tampering makes matters worse)So at this point you may be asking what is this Math 2.0, why isn’t it taught in school and what difference would it make? I will some outline the key differences between Math 1.0 and Math 2.0 next time but here is a taster.Math 1.0 is an artificial world where lines have no thickness, parallel lines can’t meet and numbers are absolute. When we use Math 1.0 there is only one correct answer and it is not possible to have variation in the answer. (in the real world however variation is always present)Math 2.0 on the other hand is a real-world Math where lines have thickness, parallel lines can meet and most importantly measured numbers are never absolute. As variation exists in all things Math 2.0 does not ignore its effects (whereas Math 1.0 assumes random variation does not exist)So here is a little teaser to see if you are working from Math 1.0 or Math 2.0MATH 1.0Math 1.0   2 + 2 = 4   YES this is absolute, there is only one answer and that is 4Math 1.0 implies that this answer is the same whether we are using simple counts or measures. So 2 inches plus 2 inches will always equal 4 inchesMATH 2.0Math 2.0 – when simply counting, the results are the same as for Math 1.0So 2 + 2 = 4   this is absolute, there is only one answer and that is 4However when adding together measures or comparing measures: 2 + 2  =  4  but only on the average (so each time we take measurements and add them together the answer can vary either side of the number 4 by an amount which Math 2.0 can reliably approximate )this scenario would be more precisely written as:2 (v1) + 2 (v2) = 4 (v3) where v1,v2,v3 is the variation (plus minus 3-standard deviations) that is inherent in each measurementThis brings me on to a further significant difference between Math 1.0 and Math 2.0. In Math 1.0 there is ALWAYS significance in any change of number and therefore there is value in comparing just two data points. So if something measured 20 last month and 23 this month Math 1.0 says there is a change (an improvement if good stuff, a worsening if the measure is bad stuff. So as Math 1.0 is the math of pure counting if we have 20 apples in one basket and 23 apples in another it is clear that the second basket has (three) more apples in it. Math 2.0 would come to the same conclusion. However if the tree in your garden produced 23 apples this year and 20 last year we actually need Math 2.0 when seeking to make a decision about whether this difference means the tree yield is improving? For we are now not looking at the pure count of the apples we are seeking to use the numbers to give us knowledge about the tree. Now instead of apples and tree performance think of pupil exam success and school performance. And then by way of extrapolation think school success and league tables.In Math 2.0 we CANNOT KNOW IF THERE IS A DIFFERENCE between 20 and 23 unless we have more data (and then a lot of the time Math 2.0 will show there will be no likely significant change). Math 2.0 tells us that comparing just two data points is ALWAYS meaningless (and of course it can provide the evidence for this). Each time we just compare two data points we are viewing the data outside of its context.If only journalists were schooled in Math 2.0 we would not have so many meaningless, stupid headlines in our papers. But there again, they probably wouldn’t sell so many newspapers, so you could see that their bosses would be quite happy that their journalists are only numerate to Math 1.0 level. Using Math 2.0 many headlines in the newspapers would read “Probably no change in the trade figures this month” rather than something that appears very dramatic like “4% fall in trade figures throws UK back into recession”. Which of these two headlines would make you buy the newspaper – the first one (‘probably no change” so nothing much is happening  -  a quite likely scenario using Math 2.0) or the second headline derived using the inappropriate use of Math 1.0 ?Have I grabbed your attention? If you already know what I mean by Math 2.0 great, please post your own examples here about how Math 1.0 misleads, If you think I am a raving lunatic and it simply can’t be possible that we are being taught the wrong numeracy at school for making sense of the real-world, then please follow, watch and learn. And if you still think I’m being stupid tell me so.In the next two articles in this series I will be comparing in much more detail some of the differences between Math 1.0 and Math 2.0 and seeking to impress upon the sceptics out there that this is really important stuff.Next Time: Maths and Science leading us up the (wrong) garden path

• Surveillance – generally in favour of more surveillance, more cameras
• Nanny State – generally in favour of new laws and telling people how they should behave (whilst they carry on as usual) including:

Roads – in favour of more and more ‘restrictions’ particularly with regard to speed limits

Food and Drugs – Tell us what to do based on the limited ‘science’ of the day

• Statistics and numbers – all Parties misuse data thereby confusing issues and preventing true debate (not always deliberately but this reflects general numerical literacy of people in high places)
• Health – All Parties promote a National “Illness” service rather than a National “Wellness” service, where the priorities are not on helping to promote wellness but to prioritise illness.

However we must not forget that ‘Parties’ follow some (not all) of these policies because they believe that is what the ‘voter’ wants (and thus will keep them in power).  Indeed we ourselves have created a Society that makes most of its decisions from a culture of blame and fear rather than one of community and love.  So many of the “sameness’ policies are doing what ‘fearful’ people really feel they want. However what sort of a life is it when all of us are being led by fear rather than by Joy .If we are to educate and change society’s unhelpful behaviours (these behaviours are unhelpful if we want to improve the real quality of life) – then politicians should be leading the people and not simply following them. So are all Political Parties the same (except in the detail)?

“Eliminate Targets and work standards that prescribe arbitrary numerical 
quotas and goals” W.Edwards Deming (the father of quality improvement)

“Targets are capricious. While they are assumed to provide a spur to improvement, they actually make performance worse. The next time we hear about the Government’s use of targets, we should be asking why they have not been abandoned.” John Seddon (Vanguard Consulting)

Without knowledge of what a better way of working might look like, all that anyone can do, given a ‘target’ is ‘more of the same faster’; whereas quality improvement requires finding, researching, planning, trialing, studying and implementing ‘a different method’, so much easier to distort the system or fiddle the data.I will leave you with some additional quotes taken from a John Seddon article “On Target To Achieve Nothing” in the Guardian Newspaper in 2000 (full article here http://www.systemsthinking.co.uk/6-targets.asp) And this article demonstrates to me that NOT ONE of our main Political Parties has learnt anything about improvement in the nine years since this was written! (It is my underlining in the text)

On a recent Radio 4 Today programme a Liberal Democrat spokesman was invited to criticise the Government’s use of targets for managing the public sector At last, I thought, someone is going to point out that targets don’t get us what we want.

Alas, the spokesman could only suggest that they should be used better. The fact is that targets don’t help us get to where we want to be. Worse, they actually obviate the possibility by making people focus on the wrong things. In the police, schools, health service and local authorities targets are hindering performance rather than fostering improvement.

What I had hoped the spokesman would say was that the whole idea of targets is flawed – that their use in a hierarchical system engages peoples’ ingenuity in managing the numbers instead of improving their methods. Peoples’ attention turns to being seen to meet the targets – fulfilling the bureaucratic requirements of reporting that which they have become ‘accountable’ for – at the expense of achieving the organisation’s purpose. In simple terms, all this effort constitutes and causes waste – inefficiency, poor service and, worst of all, low morale.

The notion of a target is plausible. In principle, there is nothing wrong with individuals having targets that they may set themselves – lose weight, run further, get another job, earn more money. But targets in a hierarchical system is that it is imposed with authority, by people who are generally detached from the work being carried out. Targets are therefore arbitrary. They may suit a plan, but they do not start from a knowledge of capability – what the system predictably achieves and why.

What the spokesman should have said was that instead of targets people need measures that lead to questions of method – ‘How can we do this better?’

So currently no main political party has in their manifesto “we will abolish targets so we can get on with improving not distorting services”Coming Next:   More on areas where Political Parties are the same