Since the concept of ACTIMATICS was introduced into these philosophy-renewal blogs two years ago, there has been some quiet progress in developing the new 100% abstract discipline. This instalment offers an outline account of the current situation. In many ways Actimatics might just as well be called ‘ANTIMATHEMATICS’ because it offers a wholly abstract modelling language suited to mimicking transient existence —an important state quite different from the timeless existence mimicked by mathematics. Discovering Actimatics might be likened to the discovery of the positron in physics (by Carl Anderson at CIT in 1932), the first glimpse of anti-matter.
HISTORY OF ACTIMATICS Actimatics is a wholly new, exciting abstract modelling tool which appeared in a niche publication in the year 2000, has been developed a little during the first two decades of the 21st century, but has been spurned by most logicians and philosophers. It can be built-up using the same kind of definitional-reification methods as mathematics. It has a quite different building block, though. Its basic units are on-going jumping-random sequences of a small set of tally types. The canonical set consists of the four types |, /, _, \. The Original Standard Sequences (OSSs) based on this set might look like this:
This is a snapshot of a particular OSS at a particular moment, because it is continually “popping” —adding new different tallies at the front end (marked >>) and losing tally types at the rear end (marked …).
Actimatics is not a general-purpose modelling kit like mathematics, but a modelling kit tailor-made for modelling the physical universe. It begins with a thought experiment. The ultimate elements of matter must be wholly random like an OSS, because the classic method of explanation used in science is to deconstruct any level of entity (a cell, a nucleus, a molecule…) into its constituent parts, which of course have simpler behavioural patterns than the original. But taken together these parts combine to produce the more complex behaviours we have observed in the original entity. So the governing behaviour patterns of entities on the ladder of scientific deconstructions get simpler and simpler as we go down the system. The ultimate level can only consist of entities with no patterned behaviour at all, i.e. OSSs. If the ultimate level had even a tiny residue of patterned behaviour, this would cry out for further explanation. (This is the principle underlying science: we are provoked to try to explain anything with patterned behaviour.) In which case, it wouldn’t be the ultimate level.
Actimatics is predicated on the unexceptionable assumption that such OSSs exist somewhere “out there” in the physical universe, and in immense quantities. An OSS may be envisaged as a terahedron die with its four faces marked |, /, _, \ which is constantly being shaken: or if you prefer, the position of the valve on the LHS front tyre of a car each time it pulls up to a standstill. (It will then be in one of four possible quarters tagged |, /, _, \. Repetitions are ignored.) Crucially an OSS is the kind of thing which science has no obligation whatever to explain; it is the ultimate kind of thing which can be taken as given.
Space The totality of all possible OSSs, taken together, is the Grand Field. Each OSS has no relationship of any kind with any other OSS, neither spatial nor temporal. It is, however, easy to impose a metric onto this field which serves, as it were, to “club” them together into a coherent space. To do this the simplest method is to mark all the positions —counting back from the front >>— of each tally type. For example, the | tally type shown above occurs in the 3rd, 10th, 13th, 15th, 20th …positions. The fraction ½ is then raised to each of these powers and the total is summed-up. The number thus obtained is the | coordinate of the OSS shown. Each of the other three tally types also have a coordinate calculated in the same way. Let these numbers be denoted w, x, y, z. A second OSS might have coordinates W, X,Y, Z. Now we can define the “distance between” these two OSSs as the square root of the sum of (W-w) 2 + (X-x)2+ (Y-y) 2 + (Z-z) 2. This is entirely relativistic. There are no assumptions about axes or origins. It is a number which we have imposed onto the system, which (we are taking for granted) exists. It turns the Grand Field of OSSs into a coherent space in which the OSSs are moving unpredictably around. This space, mathematical readers will recognise, is three dimensional.
Here we have something which breaks through to new ground: it shows that it is possible for human beings to impose (by adopting strict definitions) a distinct structure onto pure randomness. It is the first unmistakable sign that such a process for obtaining structure can happen. The easy, common assumption that <<nothing can be built on a random substratum>> is plainly wrong.
The Ban Now an OSS might consist of, say, 200 tally events like the example given earlier or it might be more, say 300. The system as a whole is being conceived as an optimum way to model the physical universe. But the tallies which we observed 200 or even 300 jumps ago are very faint events compared with what is happening at the front, live, end of an OSS. Human consciousness is not infinitely sensitive. There is a limit to what we can take in. At Bletchley Park in the 1940s Alan Turing conceived ‘the Ban’ —the slightest amount of information which can be registered by human consciousness. This provides a way of finding how long an OSS should be. The human brain will register past tally-jumps back as far as the Ban. After that any earlier tally jumps will simply not be registered.
A consequence of this thought experiment is that such a modelling system will be both immense and finite in extent. There are 4 x 3299 possible OSSs in a modelling system with 300 tally OSSs.
Another common assumption is that a wholly random substratum cannot possess any energy. The 2nd Law of Thermodynamics surely implies that it must be cold and utterly lifeless? (It seems to have no store of pent-up energy which might be released to make things happen.) But this easy assumption, too, is wrong. If we think of a sequence of tally jumps like | then / then _ then \ as a ‘sweet cycle’, it is possible to find the proportion of a given OSS at a particular moment which is showing fragments of this sweet cycle. For the OSS shown earlier the proportion of the 200 jumps when it is exhibiting bits of the sweet cycle is XXXX. This may be described as a measure of its degree of ‘stochastic spin’ at that moment.
Stochastic Spin Now the sequence | / _ \ is only really one arbitrary way of choosing a basic sequence. We could have called \ _ / | the ‘sweet cycle’ or |_ \/ or \_|/… There are actually six different permutations of the four tally types | / _ \. So we could have nominated any one of these six permutations as defining the ‘sweet cycle’. If we use each of these six possible permutations to calculate the OSS record given earlier, we get six different ‘degrees of stochastic spin’. Of these one will be greatest. This will be defined as the OSS’s topspin at the moment in question. Now computer simulations of this calculation show that, on average, an OSSs topspin is about 4.5% greater than the average. This means that there is a small surplus of spin present throughout the Grand Field. It may sound rather small, but once we multiply it by 4 x 3299 we get a vast reservoir of surplus spin, which is a kind of abstract energy potentially available to make things happen. It comes about because human consciousness is present in the loop, and this enables us to identify each OSS with its topspin.
So here is a second example of distinctive structure emerging from the Grand Field as a result of definitions we have imposed onto the system. It too is directly contrary to the common assumption that structure cannot be built on a random substratum.
Second-level objects The most difficult challenge is to see how the classic way of building scientific explanations can operate on the final level (the OSS level) of the explanatory ladder of levels of explanatory entities. Because the OSSs have no determinate structure, it is difficult to see how this can become the logical explanation for entities on the penultimate level. Here, too, though, a way has been found.
The simplest kind of ‘actimatic object’ on the penultimate level will be represented by a perfectly spinning sequence of tallies such as …\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_\_|_>>. How can we expect something like this to emerge from definitions applied to the Grand Field?
Well, we look first for a moment when a typical OSS has three distinct patches where the sequence is a perfect \_|_. When we spot such an example, we immediately treat it as a “gestation moment”, the birth of a second-level actimatic object of the kind we are looking for. Such a birth moment will occur precisely when a sequence of the kind \_|_ occurs at the front of the OSS in question. We then need the next tally to be a \. It might occur by chance, but if not, we transfer attention to the closest OSS where the next tally is \. We then repeat the exercise for a tally of the kind _… and so on. In this way we create a new actimatic object by the method of reified definition. It is a second-order actimatic object which is not represented by any single particular OSS, but by a sequence of different bits of different OSSs. It is a kind of epi-phenomenon emerging by reified definition on the Grand Field.
It is evident that this method of reified definition can be applied to any repetitive cycle, say something like,
\_|_\_|_\_|_\_|_\_|_\_|_/\/\/\/\/\/\|\_|_\_|_\_|_\_|_\_|_\_|_/\/\/\/\/\/\/\|\_|_\_|_\_|_\_|_\_|_\_|_/\/\/\/\/\/\|\_|_\_|_\_|_\_|_\_|_\_|_>> though when the repetitive section approaches 66 jumps such objects will be very rare, and will cease to be possible beyond 66 jumps. But there is a vast possible field of second-level actimatic objects here to be taken into account.
Transient objects The method for establishing actimatic objects outlined in the previous section would, of course, if operated for a long time, produce an ever-growing number (and hence density) of actimatic objects. To produce a more balanced modelling platform, the density of actimatic objects should remain roughly constant. This points to the need to conceptualise a way for losing actimatic objects. If this can be found, they can avoid being “timelessly there” once they have been established. A method for ensuring this outcome may be described as follows.
If we take the standard set of tally-types |, /, _, \ each one has a “successor” tally-type, the successor of | being /, the successor of / being _ …and the successor of \ being |.
The antithesis of a given second-level actimatic object will be defined as the sequence of successor tally-types to those which represent the given object, because such a tally sequence is automatically wholly different from that of the given object. Now as the wave of tallies signifying a second-level object keeps throwing up the need for a switch of OSS to the nearest appropriate tally-type, the original sequence of (unsuitable tallies) might follow the antithesis pattern and be repeated three times within a 200 tally record. This may be defined as the “cancelling signal” for that particular object. This will be the trigger which announces the demise of the previously established object. The probability of the cancelling signal is exactly the same as the probability of the gestation moment. This should have the effect over a long period that the numbers of a given object genre stay roughly constant. This transcience, built-into the conception of an actimatic object, is obviously necessary, otherwise the total field of actimatic objects will keep growing and growing
Computer operations In the earliest stages of actimatics the preparatory work is naturally mainly conceptual —establishingthe kind of principles and definitions needed. But to develop actimatics professionally —to try to solve some of the outstanding problems of modern physics— it is clear that most advanced actimatics will have to be handled on super-computers, machines capable of tracking the fortunes of large numbers of 200 or 300 tally sequences.
Maximum approach speed Any actimatic object which features in a model of physical reality will of course consist of a structured bundle of tally events, each one traceable to a specific OSS. Now the metric introduced on page 31 is based on the principle that two OSSs will be relatively close when they have a lot of tally jumps in common. When w=W, x=X, y=Y and z=Z the two OSSs have become one OSS. It follows that the most the distance between the two can decrease, is at the rate of one jump per jump. The new tally at the front end >> of the two OSSs is the same, but the “lost” tallies at the far end of the sequence were different tallies. This means that the fastest that two OSSs can ever move towards each other is limited by this logic. It appies equally to the motley, sequences associated with second-level objects and all material objects on the higher levels. This offers a remarkable rationale for the phenomenon that nothing can exceed the speed of light. It is another example of how structure can emerge from reified definitions based on wholly random elements.
The future of Actimatics The advances already posted in this Appendix show, beyond any shadow of a doubt, that actimatics can grow and grow. At present its comparison with mathematics is like that of a shoot emerging (with a tiny root) from an acorn compared with the ancient Robin Hood Oak near Nottingham. The simple spatial metric set out in this Appendix is only the beginning of the story. Once a metric has been established, a hundred more sophisticated successor metrics can be envisaged. The Grand Field is a representation of the matter in the universe, and this is, we know, distributed in a very special, locally concentrated, way; so evidently further metrics will emerge.
The great challenge for science is to understand living matter, which, we know, can produce music (animal song), can detect trace chemicals, can defy the 2nd Law of Thermodynamics, and result, through evolution, in autonomous human creativity and confidence. There is not the slightest hope that a mathematic model of the fundamental physics, however good, could even satisfactorily account for these amazing transcendental indications.
It is, though, reasonable to suppose that an actimatic model of human consciousness is possible. When it has been achieved —which might be 100 years from now— we can turn a secured actimatic model of the universe into a palpably self-generating system, because genuine human creativity can be responsible for the actimatic pre-conditions (reifying definitions) necessary for the existence of everything. This is not a theory implying that the distant cosmos is a figment of our imagination. A future palpable actimatic model of this kind will include the distant galaxies as being just as real as we are. (And their “reality” can only be judged by us relative to our own.)
What is clear is that science can now hope to move forward once more on the front foot, something it has not been able to do with much credibility since the Four Whammies of the post WW2 period. An exciting future dawns, in which quite unexpected, exciting, dramatic explanations may be expected —of many things (and ultimately human consciousness) which have looked like utterly insoluble enigmas since time immemorial.
It may be pointed out that the gap between second-level actimatic objects and quarks might be only two or three levels. Once this gap has been closed, the whole of modern science can be re-interpreted as an actimatic system.
The comparison with mathematical modelling It will be seen from the foregoing that Actimatics can provide an inherently relativistic modelling platform from the beginning. Its basic unit is probably 200 times more complex than that of mathematics (or even 300 times more). It naturally carries a great deal of in-built variability and vivacity. Its models are autonomous, free-standing, working models, unlike those of mathematics, which require the additional application of human imagination to activate them. Most significant of all, it avoids the presence of determinism and an infinitely static, passive, timelessly wooden complexion which mathematics inevitably has. (Mathematics, of course, came into being as something prized for its instrumental uses. It was not conceptualised from the beginning as a platform for modelling the cosmos.)
CHRISTOPHER ORMELL 1st April 2022