Transfinite Mind - Dr Grahame Blackwell

Transfinite Concepts

Origins of transfinite thinking (below)

The term 'transfinite' was coined by Georg Cantor, a German mathematician of the mid-19th to early 20th Century. Cantor recognised that, beyond the limits of finite numbers, there is not just one massive unknown and unknowable number, which everyone refers to as 'infinity'. Rather, there's a whole hierarchy of numbers beyond the finite, which he labelled Transfinite Numbers. He defined mathematical rules for these numbers, and for Transfinite Sets of numbers.

Cantor's revolutionary ideas were, not surprisingly, resisted by a number of the top mathematicians of his time. The idea of an infinite field of numbers with their own arithmetic operations beyond finite limits - where everyone had thought there was just one incomprehensible 'infinity' - wasn't easy to swallow. Nowadays, though, Cantor's work is viewed very positively as a major paradigm shift in mathematical thinking.

The concept of transfinite measure, and of transfinite awareness, is directly transferable into the real world of matter and energy. The universe is conventionally seen as being made up of matter - in large chunks, smaller chunks and spread about as gases or plasma - and energy moving within and between those collections of matter. But modern physics is increasingly showing that this is a rather simplistic view.

At the sub-atomic level the particles that make up the objects of our everyday lives act in ways that are, quite literally, unmeasurable. Heisenberg's Uncertainty Principle tells us that for any two associated 'observables' (for example, position and momentum) of a sub-atomic particle, such as an electron, the more we know about one measurement the less we can know about the other.

Added to this, both a photon of light and a particle such as an electron are known to sometimes take multiple paths from their source to their destination. Block one of those paths, or attempt to identify which path has been taken, and the results are quite bizarre. Before fixing on a particular destination, that photon or electron samples a potentially infinite number of places to land, since each travels as a wave.

Even locality isn't a given - the idea that things are in particular places. There's plenty of scientific evidence to indicate that matter is nonlocal, or even alocal - that is, the concept of place doesn't exist outside our perception. The idea that I'm here and you're there, and the savage dog you can see is on the other side of that fence, may be just a convenient bookkeeping notation.

As if that's not enough, travel at very high speed or get into a strong gravitational field and time itself begins to behave oddly, slowing down more and more as those effects increase. Relativity Theory even proposes that the same two events can happen in different order for two observers. It seems there's not even a time and place you can call 'here and now'.

This other side of material reality - this absolute reality that lies beneath the veneer applied by our senses - is truly transfinite. It goes beyond the finite limitations of particles, objects and events, beyond the finite intervals of distance or time, beyond any clear precise definitions of 'here' and 'there', 'now' and 'then'. But it doesn't simply drop into some vast amorphous infinity that embraces all that we can't put a number to. Far from it. This true reality has a higher order of definition, a well-defined hierarchical structure, a 'countability' that's there for the asking - if we're prepared to step beyond the limitations of our physical senses.

Our senses are tools designed by the evolutionary process to increase our chances of survival. Just as we've developed hands to manipulate physical objects and a digestive tract to collect nutrients from the food that we eat, so we've developed ears and eyes to collect useful information from pressure-waves and electromagnetic waves in our environment. It's fair to assume that the frequency ranges picked up by these organs are the ones best suited to optimise our chances of survival.

Obviously the mental impressions evoked by these and other senses are simply the brain's interpretation of the messages it receives. As an illustration, we know that bats use high-frequency sound to find their way around and to catch their food. There's no way they could move as they do if they simply heard those sounds and had to work out what they meant. Clearly they have some very sophisticated processing equipment inside their skulls that gives them pictures of their surroundings, and their food, based on those sounds. What might those pictures look, or feel, like? Should we regard the pictures we get as more real than theirs?

Bat reality, human reality - or insect reality, which in many cases includes ultraviolet vision (what colour do they see that as?). Which of these is the true reality? The answer, of course, is none of them. All are maps, aids to survival, tailored to the specific needs of each of those species.

Perception, then, is totally reliable for giving us the information we need for our day-to-day existence, in the form that's most useful to us. Perception didn't evolve in order to show us what the universe is made of or how the universe is put together and how it ticks. To figure that out we have to think outside the box of finite sensory limitation, to think transfinitely.

The mind - your mind, my mind - is innately transfinite. It has the ability to embrace concepts, realities, beyond the limitations of our physical senses. But just as a strong light or a flickering TV image constantly draws our attention, so the steady stream of input from our senses is constantly telling us that this is the reality, this is what we need to know.

A guiding principle of transfinite mind is "A map is not the territory it represents" (Alford Korzybski, Science and Sanity, 1933). The territory represented by our mental map of reality is radically different from that map, just as a real hill is quite different from a flat sheet with a series of contour lines on it.

The challenge for such a mind is to look beyond the window-dressing of the physical senses, to discover the amazingly beautiful underlying structure of the universe in which we live, of which we are part.

The rewards, on three fronts, are potentially very, very great.

[As detailed here.]