In its most specific meaning, the term correlation is associated with statistics. This is a classical story we all know. However, it is still a story that needs to be told and criticized because it claims neutrality and objectivity while it is an act with a political meaning. What more needs to be told? As we are leaving traces behind, correlations are only one of the possible constructions that can be made on those traces. The correlated human is only a small part of the traceable human whereas the latter seems to be a more interesting and challenging one. (Maybe we should consider to rename our ’transversal theme’?) Generally speaking, traces as such are neither good nor bad but they can be used in different ways. One tends to have a rather negative view on the matter, however, we will look at the problem from the bright side. In a first example we shall elaborate on ’mathematical traces’. They lead to a better understanding of mathematics. Within the context of the classroom they will alert students of the relativity of mathematical truth and knowledge and it puts mathematics back in a humanised perspective. In a second example we want to plea for traceability in the political context. Within the scientific context, traceability is a precondition whereas in the political (and social - cultural) context it is rather seen as potential threat to human rights and privacy. Finally we shall elaborate on the eventual comparison between sciences and politics.

The pleasure to walk on earth, leaving your traces (behind) slide

Karen Fran?ois

In line with the talk of Hans, in this presentation I shall try to look at the correlated or traceable human from the bright side. But not before saying something about the classical interpretation of the correlated human.

In this presentation I shall elaborate on:
slide
Correlation: from a mathematical matter of fact to a mathematical matter of concern
The correlated human which is only a small part of the traceable human
The bright side:
Mathematical traces and the history of mathematics
Traces in sciences and politics

Let us start with the classical meaning of correlations. slide

A correlation is often seen as a mathematical matter of fact
Often used in psychology, social and political sciences
To explain, to predict, to proof something …

To me a correlation is a mathematical matter of concern.

I will show you some maters of concern using statistical correlation. slide

Correlation is a statistical technique which can show whether and how strongly pairs of variables are related.

A correlation is a linear relation between the values of the variables.

For example, height and weight of people are related. (photo) slide

However some correlations have no meaning. Slide J

For example, the size of shoes and mathematical understanding / mathematical problem solving
Another example is the significant correlation between human birth rates and stork population sizes. (une cigogne)

slide

The main result of a correlation is called the correlation coefficient (or "r").
It ranges from -1.0 to +1.0. The closer r is to +1 or -1, the more closely the two variables are related.
If r is close to 0, it means there is no relationship between the variables. If r is positive, it means that as one variable gets larger the other gets larger too. If r is negative it means that as one gets larger, the other gets smaller (often called an "inverse" correlation). In Dutch we call it a negative correlation.

It is possible to calculate the correlation coefficient from whatsoever data, where we have at least two variables and a variety of soft-ware packets is available where you have only to ’double click’ to calculate correlations.

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On the other hand there can be a perfect functional association between variables although the correlation coefficient is == ZERO

http://noppa5.pc.helsinki.fi/koe/flash/corr/corrx2-en.html

The classical correlation technique does not work well with a non-linear or a curvilinear relationships (in which the relationship does not follow a straight line). An example of a curvilinear relationship is age and health care. They are related, but the relationship doesn’t follow a straight line. Young children and older people both tend to use much more health care than teenagers or young adults.

However there are statistical procedures to transform a non-linear relation into a linear one.
e.g. multiple regression

Another mater of concern is the types of data. slide

Like all statistical techniques, correlation is only appropriate for certain types of data. Correlation works for data in which numbers are meaningful, usually quantities of some sort. Stricto senso it cannot be used for purely categorical data, such as gender, political party, religion, nationality, IP number or favourite colour.
In statistical terms, there is a difference between correlation and associations where the latter is used for ordinal (rating scales) and nominal scales.
The term correlation is used for ratio scale and interval scale

Rating scales are a controversial in-between case. The numbers in rating scales have meaning, but that meaning isn’t very precise.
They are not like quantities (e.g. euros) where the difference between 1 and 2 is exactly the same as between 2 and 3.
With a rating scale, that is not really the case. For example, the taste of coffee is disgusting, bad, normal, good or excellent. Or maybe one can say, it has ’no taste’. What does it mean?

Most statisticians say one cannot use correlations with rating scales, because the mathematics of the technique assume a ratio scale.
However, many survey researchers do use correlations with rating scales, moreover, nominal scales are often used. For example nationality, religion, mother tongues or gender. They only have to transform or rename the categories into numbers where for example man and woman are renamed as 1 (for man) and 2 (for woman). In the case of gender it is always this kind of translation (and is was Simone de Beauvoir who explained why women are Le deuxi?me sex).

How to present data slide
Voorbeeld van jean paul (inkomsten ratio)

How to understand correlation coefficient slide

While correlation coefficients are normally reported as r = (a value between -1 and +1), squaring them makes them easier to understand. The square of the coefficient (or r square) is equal to the percent of the variation in one variable that is related to the variation in the other.

After squaring r, ignore the decimal point. An r of .2 means 4% of the variation is related (.2 squared =.4).An r of .5 means 25% of the variation is related (.5 squared =.25). An r value of .7 means 49% of the variance is related (.7 squared = .49).

In social and political sciences, low correlation coefficient (0.2 - 0.3 e.g. are often used) to explain, to conclude …

Normally, a correlation goes together with statistical significance. slide

In spoken or in normal language, "significant" means important, while in Statistics "significant" means probably true, it means: it is not by coincidence, not due to chance.

Significance levels show you how likely a result is due to chance. The most common level, used to mean something is good enough to be believed, is .95. This means that the finding has a 95% chance of being true. However, this value is also used in a misleading way. No statistical package will show you "95%" or ".95" to indicate this level. Instead it will show you ".05," meaning that the finding has a five percent (.05) chance of not being true, which is the converse of a 95% chance of being true. To find the significance level, subtract the number shown from one. For example, a value of ".01" means that there is a 99% (1-.01=.99) chance of it being true.

When statisticians say a result is "highly significant" they mean it is most probably true. They do not (necessarily) mean it is highly important.

I am wondering if there is a correlation between importance and truth!

A key thing to remember when working with correlations is never to assume a correlation means that changing one variable causes a change in another variable. A correlation is no indication for a causal relation.
In his talk on correlated human in May last year, Serge was criticising the way in which statistics was used to explain crime, based on correlations with socio cultural variables and even with biological variables referring to Lombroso.

Slide So far so good. This is a classical story we all know. However, it is still a story that needs to be told and criticized because it claims neutrality and objectivity while in reality it is an act with a political meaning. A correlation is no matter of fact, instead it is a mathematical matter of concern
The central question remains:
What kind of information do we have when we are looking for correlations?
For example
There is a correlation between nationality and crime
There is a correlation between nationality and school results
What do we have to do with this information?

The correlated human as only a small part of the traceable human slide

In its most specific meaning, the term correlation is associated with statistics. In one of our VUB seminars, I gave a brief overview of the development of our concept ’correlated human’ which was in the early beginning ’the correlated man’. This was our first change inspired by political correctness.

Is the correlated human all that new?
The differences between the correlated and the traceable human.

Quantitative aspect, increase in scale: the phenomenon of leaving traces has been enormously enlarged/ extended? There is a growing traceability.

The application: is extended from demographic, political purposes to juridical tools (for example the use of correlations to proof something) and to commercial purposes (insurance, advertising, profiling customers to predict there behaviour, …). There are more applications, uses and misuses mentioned by Serge, Mireille and Wim.

The generation of data: used to be organised for specific purposes, e.g. research, but nowadays data are generated automatically, as a part of our daily life (by using internet, chip cards, mobile phone, …).

The temporal aspect: generation and processing of data goes faster and faster, every minute we leave traces behind that can be -and are- used.

The constitutional aspect: the traces we leave behind do have an impact on the construction of our identity. In fact we are determined by our traces. We may have the illusion to be free in our choices, in reality we are determined by our previous behaviour.

The questions remains 1) if the lost of freedom has to be seen as a negative aspect and 2) if it is still a pleasure to leave your traces behind when you know that they are constitutive for your identity.

A last difference between correlations and traces:

As we are leaving traces behind, correlations are only one of the possible constructions that can be built on those traces. The correlated human is only a small part of the traceable human whereas the latter seems to be a more interesting and challenging one. Maybe we should consider to rename our ’transversal theme’?

Suggestion slide
Maybe we should consider to rename our ’transversal theme’?

The bright side slide

Mathematical traces
Generally speaking, traces as such are neither good nor bad but they can be used in different ways. One tends to have a rather negative view on the matter, however, we will look at the problem from the bright side.
Mathematical traces are erased much more than any other traces.
I will give three example of mathematics education.
The erasing of history of mathematics
The erasing of constructional aspects of mathematics
The erasing of values in mathematics

Firstly slide
Looking for mathematical traces, the history of mathematics is the most obvious one. However all historical traces are erased in mathematics education.
If we are looking at the curriculum of mathematics educations we find little room for a history of mathematics and even if this topic is addressed, it is presented as illustrative background information that pupils don’t have to study because it takes no part of the attainment targets.

There is an interesting view on history of mathematics in the preface of the curriculum. However at the level of the attainment targets there is little to find.

View
The history of mathematics helps pupils to understand that mathematics is an important aspect and component of culture, both in the past and the present.
Mathematics in the past developed via many cultures. Due to the emphasis of this development, pupils will gain the knowledge that mathematics is a dynamic process.

There is not only the gallery of great mathematicians (even women)
There is also a history of for example the number zero, the origin of algebra, … and so on.

Secondly slide
There is the erasing of the traces of construction.

Within education, mathematics is handed down as if it were made up of absolute truths and certain knowledge where the deductive methods provides the warrant for the assertion of mathematical knowledge.
Mathematics is often presented as a purely deductive science. So, using a technique oriented curriculum, the rules must be learnt, the procedures accepted and the skills practised. It doesn’t matter what the learner brings to the situation, the mathematical result is always the same.

In the words of my colleague Ard Van Moer
A good mathematics teacher is not only able to solve mathematical problems, (s)he is also able to explain how mathematical problems are solved. Many teachers are, however, able to solve mathematical problems without knowing or understanding how they solve these problems. Problem solving often involves unconscious or intuitive mental processes.

Unfortunately, in a technique oriented curriculum there is no room to practice mathematical intuition. Mathematics education is more focussed on learning rules and procedures to make deductions.

Thirdly slide

There is the erasing of the values in mathematics.
The implicit values in mathematics are the hidden traces of mathematics.
In literature there are several sets of values in Mathematics investigated.

I refer to Paul Ernest
Paul Ernest inquires on the inherent values.
Abstract is valued over concrete
formal over informal
objective over subjective
justification over discovery
rationality over intuition
reason over emotion
general over particular
theory over practice
the work of the brain over the work of the hand,
and so on
(Ernest 1991: 259)

The mathematics which is taught is presented as being value-free. Mathematics is dehumanised, depersonalised and decontextualised.
The mainstream of the current implicit philosophy of mathematics is still a rather absolutist one, regarding mathematical truth as absolute and certain.
There is no attention paid to reflection, critical attitudes, nor to the social construction of mathematics or the cultural variety of mathematics.

To enculturate our learners properly, we should teach the traces of mathematics. What is interesting to me is to make the inherent values explicit so that teachers are conscious of what they teach.

Conclusion slide
One statement
We should implement mathematical traces into mathematics education
History
Construction
Hidden Values

We should implement mathematical traces into mathematics education e.g. the history of mathematics, how mathematics is constructed, …) and we have to make hidden values explicit.
These operations should lead to a better understanding of mathematics. Within the context of the classroom they will alert students of the relativity of mathematical truth and knowledge and put mathematics back in a humanised perspective.

Traces in sciences and politics slide

Within the scientific context, traceability is a precondition whereas in the political context it is rather seen as potential threat to human rights and privacy.

In his talk, Hans was referring to the continuous traceability in science.
Doing scientific work, it’s a precondition to leave your traces behind in such a way that one could see how scientific things were invented or discovered.
In the case of science we build up our traces, for example in our list of literature, footnotes and in a citation index. The more traces we leave behind to more respect we get.

Within the political context, traceability is rather seen as a potential threat to human rights and privacy.
Why is there such a gap between those two areas?

Internet is one of the most clear places where people leave their traces behind.
More and more communication passes through the Internet.
People increasingly disclose there needs and desires on the Internet by leaving traces behind.

If politics is the representation of the multiple needs and desires of people, why shouldn’t human traces be the basic to build our political process on?

There are two aspects that I want you to keep in mind while looking at traces from the bright side.

1) Internet users should be informed and their consent should be sought for storing their traces on the Internet.
2) If we are looking for the use of the internet within a democratic world system we have to be aware that only the happy few have access to the virtual world.

http://www.uis.unesco.org/ev.php?ID=5514_201&ID2=DO_TOPIC slide

http://www.internetworldstats.com/stats.htm

General conclusion slide
Correlations are matters of concern.
Suggestion: Maybe we should consider to rename our ’transversal theme’?
We should implement mathematical traces into mathematics education

One question
How to use traces in the political process which is the representation of humans needs and desires instead of a potential threat to human rights and privacy.