Anti-mathematics is not a body of rhetoric intended to attack mathematics, but a. new 100% abstract discipline —hitherto overlooked— running parallel to, and requiring much support from, mathematics. (Mathematics is needed frequently as its natural meta-language.) Anti-mathematics studies the logic of wholly transient objects, I.e abstract objects constructed by the reification method out of pure chaos.
The objects of anti-mathematics seem to be much more ‘real’ than those of mathematics, because they are actively changing all the time, moving about vis-a-vis other anti-mathematical objects, and causing surprises.
Mathematics, by contrast, is often said to be the study of timeless objects… a neat description, but one which incidentally rests on the unobvious supposition that ‘timelessness’ exists in the real world. [There seems to be a supposition lurking in modern orthodox physics that an electron or a proton exists for ever and ever.]
A mathematical object, e.g. the real number e, is literally only an ‘object of attention’ or, if you prefer, a ‘reification’ which has been certified by the mathematic consensus: and if the activity of mathematics or the mathematic consensus disappeared all traces of it (e) would go as well. So the so-called ‘timelessness’ of e is relative to the provisional existence of human beings. When we say the objects of mathematics are timeless, we specifically mean that there are no timed qualifications involved in their conception: they are time-independent.
We could, equally say that the Eiffel Tower is timeless… meaning that it does not have an explicit life or lifecycle. To claim that it will continue to ‘exist’ … ‘for ever’ is however a form of grandstanding, because it is easily said and is wholly, absolutely, unverifiable. There is a similar situation in mathematics. The convention exists that we assume that the human race will continue to survive indefinitely, and that mathematics will continue to be recognised as a serious endeavour indefinitely. The number e is of course unaffected by the passage of time as such, but to assume that it will continue to be in circulation or recognised for ever is a human conceit.
Similarly when we say that the natural numbers extend to infinity, we are only saying that the set of those we recognise is open-ended. It is a ‘form of words’ which makes infinity sound like a destination, when it is actually intended to signal that there is no definitive destination.
Timeless objects are therefore essentially a human invention, or if you prefer, a rather bravura assumption. The comparison with anti-mathematic objects makes the latter look relatively feet-on-the-ground, because we certainly do recognise genuine transient objects, like bubbles, petals, splashes and flashes.
The fundamental reification process for simple anti-mathematical objects is to seize on instances when a particular sequence, say /_/_\_\ occurs accidentally three times in the whole of the visible tally track record, (or within some well-defined part of it) and then maintain this immediately (or after a named number of jumps) by identifying the nearest /, then the nearest _ then the nearest / again, then the nearest _, the nearest \… etc. This is a demanding procedure to follow, and, in effect, it requires a demanding effort of willpower. (There will be a considerable sprinkling of cases, though, when the nearest tally required is in fact simply the next tally in the basic sequence currently under the spotlight of attention.)
But the process summarised above is also extendable to ‘second nearest’ at each decision point, or ‘third nearest’, etc…. and indeed to cases when the nth nearest is picked-out where the value of n is determined by a natural number algorithm like 2n-1 or 5n-4…
If we conceptualise a “simultaneous mass reification” of all these options taken together —and treating the simplest definitions as the ‘strongest’— we end up with a distinctive anti-mathematical object moving erratically through space surrounded by a kind of field of less strongly reified, shadowy copies. This unmistakably reveals an uncanny outline similarity to particle physics.
It is important to bear in mind here that the reification of anti-mathematic objects on this penultimate level is unique, because their construction is wholly super-imposed —by human intervention— onto the basic sequences. On a higher level of the explanatory system, say the rth level, by contrast, the characteristic anti-mathematic objects are composed of objects of the r-1th level with pre-existing patterns-of-behaviour. So, in this more general case, the reification of r-level objects depends on two distinctive sources: first, the ordinary logical implications of specially organised sets of r-1 level objects, plus, second, a new humanly imposed component.
[This ‘new humanly imposed’ component is needed to contribute towards bringing about the architecture needed to end up with sentient beings-with-freewill at the final (top) layer… that is, the human agents capable of being the source of the total willpower holding the whole together.]
This morphology is needed to explain how each higher level of the explanatory structure can have qualities and forms of behaviour which are much more than the sum of their parts. [There is a well-known objection to any kind of scientific ‘explanation by deconstruction’ which points out the banality and determinism of the kinds of behaviour one can expect to emerge from the mere aggregation of mechanical components. Adding an extra humanly-imposed component at each level gets round this difficulty.]
The ’humanly imposed component’ being described here is not, however, a stealthy device intended to import some tincture of ‘psycho magic’ into the system. It’s method of operation is simply to apply reification by the selective attention method onto unusual patterns of level r-1 objects which will inevitably occur as a result of random variation. (This is the selective attention method previously described on level 2 when three random instances of the pattern /_/_\_\ were seized-on and subsequently imposed —i.e. made to continue— by willpower. The transience of such objects results from the mechanism for their disappearance, as described in an earlier blog.)
So here are some indications of how a scientific research programme can be built round the project to discover an anti-mathematical anthropic model of the universe. Each individual in such a model is responsible existentially for her or his own world, but of course the reifications needed to do this are universal and are going to produce lots of other sentient, responsible existential agents. So we are saved from solipsism by the essential symmetry of the process. It is also likely that there will be by-products of the advanced reifications needed… ones which will explain the distant galaxies, not to mention plants and animals.
CHRISTOPHER ORMELL 1st February 2023