Mathematics and the embodied mind

One of the things I need to consider is what is mathematics and where it comes from? One often hears the Platonist's kind of idea that mathematics exists 'out there' independant of human existence, that it is somehow fundamental to the universe, like the parts of a clock, allowing it to happen, that concepts such as the number pie have an existence beyond human thought. This idea of mathematics is similar to a belief, it is not proven, or testable. It also does not really answer the question of what it is.

An alternative view is that it is something that arises form within, something that is in part determined by our biology, and then later by our culture and mathematics as a cultural discourse. At the moment I am reading Lakoff and Nunez, "The Emodied Mind - What is Mathematics Really". It seems to me that the essential argument of the book is that mathematics is based on a series of increasing abstract conceptual methaphors that are originally grounded in the physical, and everyday experience of individuals. For example the natural 'hard wired' instincts of for example being able to conceive of a discrete object with an inside and an outside, the ability to put things into groups or piles, the ability to subitize (instantly recognise how many objects there are in a group - up to four in most people although I have heard of certain cases of autism where inidividuals are able to instantly identify larger numbers - I think Oliver Sachs talks of a group of twins where this is true.

At the moment I am just reading the chapter on arimthmetic, and the origins of addition, substraction, multiplication and division (I have often thought of all of these as just forms of addition - they can all certainly be expressed in terms of addition. Lakoff and Nunez go on later to talk of various metaphors such as the number line. There is no real number line - it is a metaphorical tool to think about number.

So in sum, as it appears to me, mathematics is a particular type and series of increasingly abstract and complex metaphor grounded on daily experience and the way the mind and body work. Of course I've yet to read more of this theory.

Additionally what makes this type of metaphorical symbolic thought different from other forms of thinking?

Why is this important in my research? Because I need to understand how we understand.

Getting back into it - Steps

At the moment I am having to edit, change and overhaul two pieces of my work. These are:

• a draft of a paper relating to interaction with computer eductational content
• reworking my upgrade document for my PhD

I find this difficult for the following reasons:

• difficulty getting back into the data
• deciding between editing and re-writing
• feeling overwhelmed by feeling I have too much to do

I find the feeling of being overwhelmed by too much, and hence feeling flustered and fogged, an experience that I often get in research. Certain things make this condition likely to happen, such as the complexity of the data, the feeling that there are innumerate papers that you should be reading, the pressures of other things in your life, the complexity of the stored data on your computer (where is it all?- I literally have thousands of files relating to my data, usually in many versions) , the juggling of ideas, theory and data, overcoming mental inertia, the multitasking nature of it all (I am actually going off the concept of multitasking somewhat) . So one of the problems is finding where you are, taking stock, and breaking down the complex large task into smaller units.

This type of writing needs time, time to consolidate, think, re-establish your immersion in the data. Getting to that state of immersion is not, for me that easy.

Anyhow in my current position, of 'getting back into' these activities I have just written a series of steps (like quanta, packets of action) thus breaking up these complex tasks. Let's see if it works.

Step 1, for the content paper is simply to find and read my last version of the paper and make highlights where necessary. I probably haven't read this for some time. The aim of this is to try to get me back 'into' the paper. Anyway in my next entry I will talk more about these steps, and if this method helps.

Introduction

This blog is about my experience as a professional researcher and also as a part-time PhD student. It is about the struggle of research. The struggle of writing, reading, thinking and developing ideas and a critical way of thinking. Hopefully it is about networking, developing and dealing with problems. It is about my inner demons, or angels, however you decide to look at them, or how they are framed by the context...for example is the inability to write disguising an internal struggle and formation of ideas that has yet to be expressed via the writing. I will also be putting forward ideas and views that are spin offs from my research and general thinking. I like to take ideas that are generally accepted and question them.

To say is to think?

Are the acts of writing and talking ways of allowing thought to be concretised, solidified, rather than a vague wish wash of ideas?

So what is my research about?...in brief terms :

As a researcher: education and technology - currently in distance learning

As a PhD student: maths education - particularly in a technological context although the prime focus is not on technology per se.