So here it comes… We’re about to look at why the idea/concept of a ‘self’ could be one of the greatest human delusions of all time. I know… It’s a pretty tall order. But still, it’s one that has been slowly changing the way I view things here on this wondrous home of a planet over the last few months. But before I share with you my journey – one that demonstrated to me how the seemingly obvious certitude of an ‘I’, or my ‘self’, might really be only a flawed assumption, which in turn became an illusion bourn from grammatical syntax – I would like to introduce another story… One that lays out the ground work between the two extremes of certainty and uncertainty, making evident that any definite human knowledge is, at its core, not a definite as we’d sometimes like to think… And, thus, all certitudes that we might presume or cling to become subject to uncertainty.
The story here is about an Austrian logician, who, despite his untimely death, still remains to this very day a great hero and inspiration to me. His name is Kurt Friedrich Gödel (b. 1906, d. 1978)… His ideas were revolutionary in the field of logic and shook the foundations of mathematics, providing insights into the limitations of what can be known. In fact, I believe some of his insights might also demonstrate – in a parallel sort of way – how what we think we know about our ‘selves’ might actually not be what is the actually case… In fact, it might go one step further and demonstrate something rather unexpected. But I digress…
For the moment, I would simply like to leave you with this great BBC radio documentary, narrated by Melvyn Bragg, that clearly and elegantly describes the life and work of Kurt Gödel, a great friend and college to the late Nobel prize physicist, Albert Einstein.
Gödel’s Incompleteness Theorems
Melvyn Bragg and guests discuss an iconic piece of 20th century maths – Gödel’s Incompleteness Theorems. In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations, called axioms, had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox.
Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so Gödel changed the way we understand what mathematics is and the implications of his work in physics and philosophy take us to the very edge of what we can know.
With Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol.
To find out where I sourced this documentary from, please click here.
Or to find out more about Melvin Bragg, then please click here.
To read more about Gödel’s proof, then please follow this link to a brilliant article from Science magazine, entitled “Separating Truth from Proof in Mathematics”.
May 2, 2010
Language… Meaning… Understanding… It’s all about higher concepts ‘globing’ together to create the aspects of cognition, via modes of analogy, that we all use in our everyday lives to impart meaning to, and thus construct, the world that we ‘know’ around us.
Here in this talk, Hofstadter pertinently demonstrates his encyclopaedic knowledge about the development of human language and how the meaning behind words manifest, as concepts develop from their base level ideas, for example “ball,” into higher levels of complexity, as new words are developed to further complement and describe these basic parental precepts – perhaps stemming from new inventions which are driven by new discoveries, from both the empirical and non empirical fields of cognition – into aspects of “roll,” “wheel,” “car,” “moving,” “hovercraft,” “floating,” “flying,” etc… In this endless game of semantic development and lexical evolution, we begin to glimpse at the inherent emptiness behind the words we all so readily use in our lives, and, thus, see how they are really nothing more than eloquent “grunts” that contain mental images of meaning that allow us Human Ape men/women to understand one another and get our ‘points’ across to each other.
In many ways this is a good point of entry for us to see and to begin to understand how words and their meanings come about… From there we can then see that mental categories begin to shape the axiomatic world in which we live. Once we can understand this, we might have a better chance to really grasp the fundamental aspects that lie behind both the Buddhist idea of “Emptiness” and Kurt Gödel’s “Incompleteness Theorems.” *
Interestingly enough… As Hofstadter discusses “word blends” and “phrase blends,” I think we can begin to see a pertinent analogy between feedback loops of all sorts i.e. language here randomly mutates into simple amalgamations of “originality,” much like “video feedback loops” create modified patterns of slightly iterated imprints of what was only just on the visual screen.
Regarding language… This evolution and development of lexical complexity stems from seemingly random conjoining of phonemes, subtle phonetic variances and little – or even crass – syntactical errors, which mostly stem from when two ideas intermingle within the mind of the speaker and are thus ejected into the conversation stream without too much consideration. This process allows a rich source of new etymological meanings to flourish and develop within – initially – small social circles of friends/colleges… Or if particularly ‘catchy,’ they might then spread across wider groups as successful “memes” via infectious minds through any form/medium of social communicability.
In many ways it is this type of evolutionary self-similarity that keeps language alive and “thinking” on its toes – always forcing it to move forwards into new realms of functionality to suite the current semantic landscapes of our ever-changing, ever-evolving social networks and scientific/technological habits. Within these linguistic and memetic structures we may even find multidimensional configurations where complex patterns modulate old ideas into modern modes of ever more complex types of understanding… Old frameworks of thinking are slowly battered into new designs, and then the two co-exist in a sort of symbiosis with one another. And ever iterating forms of lingual cunningness flow from out lips… Just as the Mandelbrot set increases in complexity the further we zoom into its boundary, so language seems to increase in complexity the further We – as human beings – progress in developing ideas, our knowledge database, our inventions and with new observations… In many way these two particular types of pattern i.e. aural language and visual fractals, run parallel to one another in similar veins of iterative novelty. One is mimicking the other… Except it is not an “exact” replica… It is merely uses the same iterative mathematical ideas to regenerate and reorganise itself with.
Here Hofstadter describes a process where two ideas are torn apart and allowed to intermingle in the speaker’s own fractal mind, thus recombining/assimilating into an endless array of sometimes intentional, but probably mostly unintentional, hip analogies. Analogies are all about self-similarity. Hence, in my mind I become some strange feedback loop, reiterating what I have already heard and seen in my life thus far, remixing, recombining and experimenting with neoteric verbal adage to describe new modicums and meanderings concerning my experiential existence… And thus, through my will alone, my “I” become a Möbius strip of etymological and memetic reform, playing with all of you – my iterated equals – in evolution and natural selection’s ancient game.
To find out more about Douglas Hofstadter, please click here.
* This exposé about the illusion of self and the delusion of most types of knowledge – in the light of the Buddhist precept of “Emptiness” and Kurt Gödel’s “Incompleteness Theorems” – is coming in a future blog…