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Are we really Numerate? How numbers lead us up the garden path!

On 10.06.09, In Non Political Party, numeracy, by Barry Mapp

Are we really Numerate? How numbers lead us up the garden path!
Our Politicians and Business Leaders talk about the need for us all to be both literate and numerate when we leave school and as such literacy and numeracy are key subject components of the National Curriculum and beyond.
But are we infact teaching the literacy [...]

Are we really Numerate? How numbers lead us up the garden path!

Our Politicians and Business Leaders talk about the need for us all to be both literate and numerate when we leave school and as such literacy and numeracy are key subject components of the National Curriculum and beyond.

But are we infact teaching the literacy and numeracy required for success in the real world?

I think not and I will be posting my thoughts on this over the next few weeks on this blog

Here I make a start, looking at Numeracy.

I call the numeracy that we learn at school and in our universities “Math 1.0″ (And in general this is the only form of numeracy we are taught, so most if not all of our leaders are only numerate to the level of Math 1.0)

This is a Math that is useful, but only in the very simple domain of counting and manipulating pure numbers. This domain is what Donald Wheeler (one of the few statisticians in the world who seems to understand this stuff) calls “Math World” a strange world that has very little bearing on everyday reality. It is very misleading in fact when, in the Real World, we use Math 1.0 to manipulate, interpret and compare measurements

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 2.0

No-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 2.0

MATH 1.0

Math 1.0   2 + 2 = 4   YES this is absolute, there is only one answer and that is 4

Math 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 inches

MATH 2.0

Math 2.0 – when simply counting, the results are the same as for Math 1.0

So 2 + 2 = 4   this is absolute, there is only one answer and that is 4

However 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 measurement

This 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



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Lessons for Science from the Mesmer experience

On 07.28.09, In Me, by Barry Mapp

The story of healing – from Mesmer to the Present
In the last blog, I mentioned that most Doctor’s and Scientists appear to practise ‘scientism’ rather than ‘science’. This is NOT a new phenomenon and we can see that this was often the case back in the 1700’s.
Let’s take a look at the story of [...]

The story of healing – from Mesmer to the Present

In the last blog, I mentioned that most Doctor’s and Scientists appear to practise ‘scientism’ rather than ‘science’. This is NOT a new phenomenon and we can see that this was often the case back in the 1700’s.

Let’s take a look at the story of healing from Mesmer and see if much has changed in regard to how scientists perceive healers and healing.

As you read on, focus on what I said previously about scientism – that when practicing scientism, if the observations don’t fit the belief held, than the observations are either (1) ignored (2) attacked as being false or some ‘magic trick’ (3) manipulated to fit the belief.

Because ‘hands-on healing’ (or distance healing or other types of healing) doesn’t fit comfortably with any Newtonian Model of Science, doctors practicing scientism will defend their Scientific Beliefs (using methods 1,2,or 3) rather than pay proper attention to what is actually happening and so don’t properly observe and have no inclination to investigate what they see. Most doctors will simply say ‘there isn’t any evidence that healing works’.

In this example below with a French Royal Commission set up in 1784 to investigate Mesmer’s Healing Technique, there was clear evidence that healing worked at some level – as most of the patients got better.

What wasn’t clear was HOW it worked and a true scientist would therefore want to set up experiments to ascertain the ‘how’.

Instead these commissioners used their expertise to DENY that Mesmer had demonstrated any real effects worthy of further exploration. Only one of the scientists a botanist called (Jussieu) appeared  to value science rather above scientism. See what you think -

The story of healing – from Mesmer to the Present

Mesmer was a scientist and healer living in the mid-1700’s.

Using a technique he described as “animal magnetism” (initially using magnets until he discovered that just using his hands had the same effect), Mesmer’s healing work became fashionable in Paris but irritated eminent physicians and scientists of the time. A Royal Commission, chaired Benjamin Franklin, was set up by Louis XV1 in 1784 to investigate Mesmer’s method.

The Commission’s Report when completed labelled Mesmer a Charlatan.

The crucial evidence cited against his method was that blindfold patients (Mesmer used a “hands off”or “hands-over” healing technique) did not demonstrate the patient bodily rigour that usually happened during his regular treatments. The fact that patients behaved differently blindfolded was evidence enough for the Commission to report that this technique was a sham (though in the blindfolded cases the patients also improved).

The Commission’s viewpoint was that “all could be explained by the patient’s imagination”.

A minority report by the botanist Jussieu dissented from this view and he felt that sufficient evidence had been provided “to make us admit the possibility of the existence of a fluid, or agent, which is communicated from one man to another, and sometimes exercises on the latter a sensible action”.

Who practised the good science? Franklin or Jussieu?

Which theory better predicted the facts – the unseen magnetic-type force proposed by Mesmer, or the Commission’s theory of imagination?

And if imagination was the key, why was this not explored further. Why did the scientists not remain curious as to how this allowed patients to get better (most were patient’s who were put forward by the physicians themselves that had not been helped by the physician’s treatments).

The Commission’s findings raised many questions for valid scientific investigation but the results were merely used for the purpose of discrediting Mesmer and not to advance scientific learning.

Would a Commission investigating healing conclude anything different today?

Probably not! We have some recent possible pointers. In the last 10 years at least one American State was reported to have banned healing (specifically a form called therapeutic touch) in their Hospitals, because researchers “disproved” the theory upon which it was based even though it appeared to have beneficial effects (animal magnetism in 18th Century, energy fields in the 20th Century).

Again not long ago in the UK there was the “scandal” of a healer and the England football team. The healer was “sacked” because of her beliefs and not because she was ineffective in accelerating players recover from injury.

Coming Next:

More on the England football Team Healer (who was sacked), as well a description of some simple experiments that open-minded scientists around the world could quickly and easily undertake in order to validate that healing is for real and that it is worthy of an extensive input of funding for research to the potential benefit of all.

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Scientists and Healers need Open Minds

On 07.27.09, In Me, by Barry Mapp

On the need for scientists and healers to have an open mind
(adapted from an article “The Science of Healing and the Healing of Science” published in Resource Magazine September 2005, Author: Barry Mapp)
We don’t realise how much our existing theories and beliefs prevent us from seeing new things clearly.
How the Scientist’s beliefs stop them seeing [...]

On the need for scientists and healers to have an open mind

(adapted from an article “The Science of Healing and the Healing of Science” published in Resource Magazine September 2005, Author: Barry Mapp)

We don’t realise how much our existing theories and beliefs prevent us from seeing new things clearly.

How the Scientist’s beliefs stop them seeing clearly

A principle of science is that ‘what actually happens’ comes before ‘how do things happen’. Thus the first stage of science comes from observation and experience. Then comes a hypothesis (a preliminary belief), then come experiments to see if the hypothesis holds water. What many scientists actually practice is not ’science’ but ’scientism’ which is the opposite of science – where the belief (the need to know how things happen) comes first and observation (what happens) comes second.

Thus when practicing scientism, if the observations don’t fit the belief held, then the observations are either (1) ignored (2) attacked as being false or some ‘magic trick’ (3) manipulated to fit the belief.

Because ‘hands-on healing’ (or distance healing or other types of healing) doesn’t fit comfortably with the Newtonian Model of Science, doctors practicing scientism defend their theory (using methods 1,2,or 3) and don’t properly observe and investigate the potential phenomenon. Most doctors will say ‘there isn’t any evidence that healing works’.

However any doctor who can suspend judgement about healers and healing long enough to search the world’s literature, will find plenty of published material (but not in the Lancet or the British Medical Journal) demonstrating that healing has “medical” effects worthy of further investigation. So we have to assume that most doctors practice scientism.

How the Healer’s beliefs stop them seeing clearly

Equally “healers” are often unaware how their theories and beliefs prevent them from seeing things clearly and they too must be prepared to change their beliefs if they want to move healing forward.

Scientists and healers suffer from the same problem. They both use outdated concepts or “out-of-context” theories to explain how things happen. (see more about unhelpful ways of thinking here). Healers are often using theories and explanations which go back thousands of years, whilst openly criticising the scientists who cling to Newton’s ideas that are much more recent. We need a pragmatic view of theory. No explanation or model is ever complete or “true”. What is important therefore, is not to argue over who or what is “right”, but to find explanations or metaphors that are useful, that most people can accept, and that allows predictions to be made and theory to be tested.

For example, some healers say that the cause of illness is “evil spirits”. A few hundred years ago or more this may have been a reasonable theory. However today this metaphor is outdated. Other healers invoke their religion, reincarnation, or their “spirit guides” as integral to their healing but none of these are essential to what they do. These beleifs simply provides a stream of potential red herrings (and an uncomfortable feeling) for the scientist. If healers want their form of healing to become mainstream, and thus part of everyday medical practice, they have to conceive explanations that are aligned with present day context and knowledge (even if some of that knowledge is “wrong”). As Newton’s Thinking is still predominant in science, the healer must speak with metaphors that the scientist understands (rather than jumping on the Quantum Theory bandwagon as most are doing – a bandwagon that has yet to starting rolling in the corridors of power)

Coming next: Lessons for science from the Mesmer experience

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Americans value science, but not all of it

On 07.10.09, In Know-What/Why, Non Political Party, by Barry Mapp

On Science and Scientists, Climate change and the Public – who is thinking clearly?
Just seen the results of this survey from Reuters. Of course we always need to take surveys with a pinch of salt, but I find the results of this particular survey  (http://unhub.com/9Vmx) very interesting, particular about current opinions on Climate Change. The [...]

On Science and Scientists, Climate change and the Public – who is thinking clearly?

Just seen the results of this survey from Reuters. Of course we always need to take surveys with a pinch of salt, but I find the results of this particular survey  (http://unhub.com/9Vmx) very interesting, particular about current opinions on Climate Change. The problems with surveys is they only leave us with more questions than provide any answers because they never seem to follow up and ask the really interesting things.

First a summary of the survey results with respect to the ’science’ of climate change:

The survey says that “while 84 percent of scientists say the Earth is getting warmer because of human activity, less than half of the public agrees with that”.

There are two things of interest to tease out from this. Firstly the ‘public’ view.

Is it that the ‘public’ are in denial of the ’science’ or is it that actually they don’t believe in the models that the scientists are using? Now it would be good to survey that. My money is on the fact that most of the public simply don’t believe the models. If so that would be very interesting as well to know why.

The second thing of interest is the viewpoint of the scientists. This survey showed that 16% of the scientists surveyed did not believe the ’science’. From what you read in the media I would have thought that it was fewer than 5% of scientists who did not agree with the interpretation of the ’science’. Again it would be most interesting to know more about the scientists who are the ‘non-believers’

So this survey would have been far more useful if we could have found out something about those ‘public’ that don’t believe the ’science’ of climate change (or rather the way most scientists are interpreting the data). Are they all people who just want to go on decimating rain forests etc? Are they actually people (like myself) who want to stop burning fossil fuels and decimating the planet, but have no confidence in the models that  scientists are using to predict the global effects?

And the 16% of scientists that don’t believe the (interpretation of the) ’science’? Are they all in the pocket of the energy companies? Or are they merely scientists who are concerned that the data is contradictory or selectively taken and the models are inadequate to make predictions?

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