Douglas Hofstadter and his ‘Strange Loops’
Some initially attractive ideas can begin to feel slightly unacceptable after further consideration and, despite the obvious and romantic appeal of pan-psychism for dowsers, BK’s mind (or the thing ‘he’ still thinks of as his ‘mind’ anyhow) couldn’t quite accept the notion wholeheartedly. It felt…..well, rather too easy a solution.
Somewhat surprisingly, a more comfortable alternative came to light from the work of the American mathematician and cognitive scientist, Douglas Hofstadter. His books – I Am a Strange Loop (2007), and the Pulitzer Prize winning study Gödel, Escher, Bach : an Eternal Golden Braid (GEB) (1979) – have both made important contributions to the study of consciousness, even though Hofstadter is essentially amaterialist scientist, as indeed most ‘respectable’ enquirers seem to be these days. Many materialists think that minds originate within our physical brains and somehow emerge from them.
What makes Douglas Hofstadter especially interesting, though, is his unique assertion that paradoxes – logical inconsistencies leading to impossible conclusions – are fundamental to the process of that emergence.
Hofstadter says that each human being is really an individualised point of view, with individual perspectives, which can exist in other media – like a composer’s written out scores, for example – outside of the brain. The most important element in Hofstadter’s argument is that a continuous process of self-reference is critical to the development of consciousness.
This is most significant when it leads to the formation of paradoxical statements, which in turn become what he calls ‘active symbols’ or ‘neurological patterns’. These symbols can be arranged – or else they arrange themselves – into the ‘tangled hierarchies’ of ideas that Hofstadter calls ‘Strange Loops’ and he finds prime examples of them in all of the arts and sciences.
The Dutch artist MC Escher’s famous ‘Waterfall’ lithograph (above) is a good graphical example of a visual tangled hierarchy. The water falls perfectly naturally from the apparent top of the picture downwards through a waterwheel only to continue to flow – once again apparently completely naturally – uphill – to provide the energy for a perpetual motion machine.
We know of course that this is an impossibility in the real world, but somehow there is a compelling ‘rightness’ about what we see. Verbal examples of self-referential paradox abound too, and often have an appealing whimsical quality about them. For example:
‘Do NOT read this sentence!’
‘The sentence following this one is false. The previous sentence is true.’
‘This sentence no verb.’
Thoughts like these somehow stick in our heads and can develop a curious attractiveness of their own, which is often quite difficult to resist. Other forms of the arts, and even the sciences, are not immune either. JS Bach’s Musical Offering and The Art Of Fugue apparently contain deliberate Strange Loops according to Hofstadter, and in his masterful literary tour de force Gödel, Escher, Bach, he describes how the young and relatively unknown Austrian mathematician Kurt Gödel managed, in 1931, to prove that the mighty Principia Mathematica, published by Bertrand Russell and Alfred North Whitehead between 1910 and 1927, was itself riddled with self-reference, the very thing it was trying to expunge from mathematical theory.
The Principia’s primary purpose had been to make mathematical theory completely and consistently logical. However, Gödel said that all complex arithmetical and logical systems contain propositions that simultaneously refer both to the mathematical ideas themselves and to the symbol systems being used to describe them. This runs against even commonsense logic and so paradox is everywhere – including the formation of consciousness according to Hofstadter.
The Emergence of ‘I’?
To cut two very long stories short – and Hofstadter’s two volumes run to almost 1200 pages between them – Hofstadter claims that self-referential elements are inevitable consequences of the complexity of the symbols generated in the human brain.
The self-referring elements combine with the multifarious ways in which the brain symbols interlock to allow us to make comparisons between ideas that seem to have nothing to do with one another at first sight.
So Hofstadter argues we are not born with a sense of ‘I’-ness, but rather that this psychological sense of personal identity emerges gradually as we develop the enormous sets of symbols that we use to construe the world as we grow. Most importantly however, it is only when the symbol sets become rich or dense enough to begin to twist back on themselves (and become Strange Loops) that we form any sense of self at all.
Hofstadter says that in a way we hallucinate ourselves, but hallucinations, of course, can seem completely real to those who experience them.
As a well-worked out theory of consciousness, Hofstadter’s ideas certainly provide hefty amounts of food for thought – but that’s by no means the end of the story. Hofstadter spends a lot of time discussing the idea of soulfulness, and the possibility that the symbols and associations he describes can be somehow shared with other consciousnesses.
In an exceptionally moving account of the sudden death of his wife from a brain tumour, he explains that in some very real sense he had assimilated her points of view into (or even alongside) his own, on so many matters and so thoroughly, that they ceased to be independent perspectives at all. They were so close that the couple became able to see the world, almost literally, through each other’s eyes. Similarly, Hofstadter also believes that the same phenomenon may arise through reading about another person’s thoughts.
It seems then that we may not be completely alone, or wholly isolated, from specific elements of other consciousnesses across both space and time. Perhaps it is true that in some yet undefined fashion, there is something (but only ‘some’ thing) of the pan-psychist lurking quietly in all of us even in double-dyed materialists. BK’s own inclinations are certainly leaning that way more than formerly so, here are some ideas that potentially support this point of view.
Firstly, on discovering Hofstadter’s work, BK noticed (and later discovered that Hofstadter himself had also noticed) a curious similarity between the impact of self-referential sentences and Zen Buddhist ‘koans’ – the Japanese spiritual exercises designed to raise and develop students’ self-awareness or self-consciousness. The well-known koan ‘What is the sound of one hand clapping?’, to which there is no immediately obvious answer, is perhaps not a million miles away from ‘This sentence no verb’.
There is a curious similarity too, at least at first sight, between the idea that our sense of self is a kind of hallucination and the commonly held belief in some Eastern religions – including Buddhism – that ‘the entire world is nothing more than a continuous illusion, which we must shake off in order to discover our true nature’.
And finally, to continue with the Buddhist theme: as far as BK can see, neither the messages on Tibetan Buddhist prayer wheels and prayer flags – some of which fly in his garden for personal reasons – nor the messages on the ‘Sound Dowsing’ labels have any physical connection with their intended recipients. But the intentions behind each of them (and, for all we know, their ultimate effects) do seem vaguely similar.
Looking at this situations from a dowser’s perspective, Albert Einstein’s statement that ‘we cannot solve our problems with the same thinking we used when we created them’ certainly seems to be another insight into the potential depth of these ideas.