In life, nothing is the same only similar. We examine here the basics of how this is possible and why mathematics can never describe life modeling.
Why is variation so fundamental to existence?
There is something very enlightening to be found in research into the plague that swept much of the world in the middle ages. Populations of humans were wiped out leaving a few survivors. In Norwich, then the second biggest city in England, only one third of the population survived. There is a lot of written material trying to understand the nature of the plague but the village of Eyam contains the answer to why some people survived.
Constantly, ‘mistakes’ are made in copying genes. A decent time before the plague, it could have happened thousands of years before and probably on many occasions, a ‘mistake’ was made and instead of creating a copy of a particular gene two copies were made instead. Some people had one copy of this gene and some people had two.
Eyam sealed itself off from the outside world when the plague struck. We know exactly who died of the plague and who died later of something else but was alive at the time. Examination of the remains of the villagers show that all the villagers who died had one copy of the gene and all those who survived had two copies. This could explain all world wide death and survival during the plague. The ‘mistake’ in replicating the gene could have happened eons before the plague with no implications. We see gene changes as being problematic but they are part of creating variation. Changes in genes are random and will cause early death in some animals, survival in others and predominantly increase variation across a species. Some genes will sit and wait while others will have immediate effects. A species varies blindly in its gene pool, in which genes are switched on and which ones are not and in how the genes relate to each.
The creation of variation within an animal species exists alongside changes in the nature of the encounters that the animals of the species have. The variation within a species blindly seeks to match changes in encounters. An important tree in the forest is largely wiped out by infection but some survive if they have genetic difference. A new type of insect that breeds in an animals fur and feeds of its blood arrives. Some animals are so weakened that they die as their encounters no longer effectively give food and protection. Others survive because their skins are a bit thicker or they scratch more or their social relations are better and they receive (and give) more grooming or their blood type doesn’t suit the insects etc. Variation and unpredictability is everywhere in nature. It is created in all living things as well as in encounters. The most rapid variation process is to be found in tropical forest where exists the most dense and complex assembly of life.
The easiest way that I find to illustrate the relationship between genes and encounter is to consider the fate of the mountain hare in the High Peak. There are two species of hares in the UK. They are so similar genetically that they can interbreed. The fur of mountain hares changes to white in winter. There is a small population up the road in the High Peak. On one occasion I disturbed one in its winter coat. It ran off through brown heather. It was very conspicuous. There is nothing like the amount of snow over a long enough period of time to explain the survival of the mountain hares in the High Peak. Its encounters with birds of prey and foxes should have wiped it out a long time ago. If, however, you change its encounters by getting rid of its predators then its bizarre survival is secured. It lives in red grouse territory and game keepers kill predators.
The more that an animal species can engage with what the physical, vegetative and animal world contains, the more complex is the life of the species and the individuals within it; who, of course, have to actually live it. This increases the variation and unpredictability of encounters. Life is always ‘playing with the genes’ judged by the ease with which at least some genes change and switch and alter relationships with each other. This randomly generates variation that might be the basis for survival when encounters vary for the species.
Autism
In addition to genetic change autism sheds light on the existence of genes that actually facilitate unpredictability and promote states of indecisiveness. A state of unresolved contradictions and demands. Those with autism have poor and sometimes non existent function in these states.
Autism can be explained as a problem with the exactness/inexactness ‘genes’: the ‘genes’ that set the boundaries of variation. The most obvious characteristic of those with autism is the way that they are limited by over-exactness. To others they appear as obsessional and inflexible. In areas such as numbering mathematics and drawing what the brain initially ‘sees’, their exactness can be generally appreciated. Those children whose inexactness genes are less restricted are able to learn language.
The activity of the‘genes’ of inexactness have degrees of effect. Human beings are infinitely complex and in trying to understand children’s developmental problems we need to explore and think carefully about all biological and social influences. If it is then helpful to identify the child as autistic or aspergers then fine. However, by doing this we have put them in a box. They have the label. They have become, in part an object. What happens when ‘this child’ is like the labeled child but has not yet been ‘diagnosed’, or when ‘this child’ is a bit like them but not bad enough to get the label. What!! We have left reality. There are only multiple degrees and effects.
I have seen and assessed hundreds of children, from two upwards where the ‘autisms’ have helped explain the profound and widespread nature of their difficulties.
Reproduction
Reproduction by combining genes from two animals increases variation. Variation and hence adaptation to changing encounters, can progress at a faster rate.
How did variability and inexactness begin at all?
The simple animal organism (a simple body) will be depending on variable physical and biological registers to directly identify and digest food? From the very beginning of animal life the ability to embrace variation has been crucial to the survival of the individual and through this its species (on the ‘living long enough to breed’ principle).
The simple body will vary in size as it grows and its ‘food’ will also vary in size. The variation in itself as it grows and the variation in the size of its food source, changes both the physicality and the biology of its absorption of ‘food’. It changes with every encounter with ‘food’. It is better off if it becomes inexact.
Let us imagine that the simple animal encounters its food source by two specific registers which are: if it touches me I will grab it and if my ‘digestive juice’ cannot do anything to it I will let go. Sometimes when I encounter my food source I get a little dent halfway down my side. The position of these dents vary. Could the experience of the dent tell me which one I can digest and which one is too big and I need to let go? Every time that I encounter my food source I have to expel the bit that is not recognised by my ‘digestive juices’. When I do this another biological register ‘juice’ reacts to the waste. Could this one help me recognise my food in the first place?
It is genetic variation among the descendants of our simple animal that changes the offspring of this early animal into one that now adds in these two new components. The old and new components working together make the animal more effective and help it to survive.
As evolution progresses variation increases because the more complex the animal the greater the potential variation. The problem is that potential is not the same as the energised physical change involved in encounters. We need to return to the point that in encounters an animal species, even the simplest one, benefits from the inexact. Inexactness can be increasingly useful to the individual and it can be developed by memory change. When identifying a certain plant or animal to eat, it is not possible for a brain to use a specified model or program as all these are life forms and each one is unique. Living things are similar not the same.
At some point in evolution; and therefore in some existing simple animals; a gene or a combination of genes (or some other biological function of genes) developed that actively introduced dysfunction, faults and risky new vulnerabilities to other biological organs also within the animal. Variation has a physical, material home. We can actually see this in the most complex animal of all, us.
It is the ‘gene’ of inexactness that makes animal life possible. It creates spaces. Though unstable and unpredictable inexactness can be built on and acted on. It is a creative match for the unpredictable nature of an animals encounters as it moves through life. Wittgenstein understood this and captured it in his ‘family resemblance theory’ - targeted to word meaning. He has chosen his example so well that its structure is self explanatory.
As evolution continued the amount of biological variation increased. The more complex the animal the more unique are the individual members. We are genetically more similar than many other species but our brain complexity and our deeply social nature leads to infinite possible encounters. Small changes make for the uniqueness of each individual human and the impossibility of predicting the nature of their participation in encounters. Human life has become infinitely complex. In the momentary encounters of your life do you know what your partner will do and say next and can you anticipate the emotions that you will feel afterwards? It is deeply remarkable that we are often able to guess correctly.
We are each unique before we add in the consequences of differences in memory (experience); I.e. the ability to change our nature in response to encounters.
Mathematics
Mathematics is intolerant of unpredictability and is therefore unable to offer up descriptions of life models. It can only function where specific parameters with specific options have been artificially set up.
Mathematics has its animal origins in two different areas of our natural functioning.
The first is in accurate movement, where the integrated movement model of kinaesthesis and vision creates a spatial model that allows the body of an animal, to move without walking or running into things and without falling down voids. The co-ordination of our muscles in relation to physical encounters, is a place where exactness is beneficial. The more exact the better. The life modeling can become so complex and dynamic that it soon outstrips mathematics and computing. Imagine a lion trying to catch a warthog on a specific part of the Savannah. We look at this in detail in the movement and action topic.
The fact that we evolved as one of the throwing and seed eating apes (hominids), with increasingly effective hands, pushed our brains to develop complex life models for movement. At the same time this increased our ability to change our physical and vegetable environment. We came to make physical structures and here we needed to externalise our spatial accuracy into measurement. The resulting activity could be shared socially. It therefore became acts and movements passed on together with how to use invented tools and devices. We then came to record how we used these tools and the measured detail of our structures. Thus we pulled geometry out from our movement models. We look at these in more detail in the movement and action topic. There is no basis here for the a priory existence of mathematics. Neither is there a base in our second source.
The second origin for mathematics lies with the repetition of our perceived or agreed identity of the ‘same’. This is a necessarily clumsy way of putting it because sameness is not a characteristic of life models. In the natural world, and even in the human made physical world, we only have degrees of similarity but we can deem things to be the same and in fact need too if we are to eat all the different looking pears on the tree. Initially repetition was experienced as group size. The usefulness of knowing the size of a group had already led to many animals, particularly primates, linking group size to one (as well as anywhere between two and five depending on the species of primate), some and ‘a lot’. The core meaning clusters behind our use of the words one, two, three, four, five, ‘some’ and ‘a lot’ can be pulled together without language by using life models for action and therefore can be in other animals. See the meaning and grammar topic for more clarity on meaning clusters.
The ‘repetition of the same’ changes after five. Only we can go beyond because only we can count. If you look at the speech and language topic, you will come across the articulation and resulting sounds called phonemes. These are the building blocks of the sequences that make words. The parts of the brain that are involved with the life of these phonemes we have referred to as a phoneme computer as this is the nearest we get to computing. Usually the phoneme sets that constitute spoken words are themselves structured grammatically but this is not the only possibility. Some specific words could be allocated to group size after five as each new ‘same object’ is put into the group. You have to remember the sequence of the words and you have to count in order to accurately identify the number of objects. Children find it hard to learn to count because each said, or thought, word has to correspond to a yet uncounted member of the group and they must not leave any out. They usually learn ‘one to one correspondence’ by actions such as touching and moving objects.
Humans vary in how good their phoneme computers are. The tests for this involve repeating random numbers and nonsense words and also listening and then repeating them in reverse order. There are other variations.
The articulated and sound sequences can also be captured by moving in a set direction across written versions of the numbers. The interaction of spoken and remembered patterns and the capturing of sequences physically form the basis of numeric and algebraic mathematics.
Mathematics has served as a model for rational enquiry and is used extensively in the sciences. When combined with grammar and a selection of closed class words (see the meaning and grammar topic) it takes the shape of logic. It is a tool extracted from our nature that has proved able to facilitate our participation in the material world. It cannot be raised as some kind of a priory form by which humans can engage with all existence and expressions of life.
Within mathematics itself, complexity theory recognises that mathematics is excluded from describing life modeling. In the context of the ‘terms and conditions’ for experienced human life we describe complexity as infinite along with time and space. Further more, algorithms cannot escape decidability and computability.
Wittgenstein was not just a ground breaking mathematician he was also the first to break out of the grip of mathematics. In the context of capturing the structure of meaning he used a family resemblance model.
Wittgenstein was unable to find comprehensive and bounded logical definitions of the meanings of words. He urged that we examine carefully how we use words and he suggested that their meaning holds together in a way comparable with how the members of a family resemble one another. We see family resemblances between people but cannot exactly specify a particular nose shape, the distance between the eyes or gait, build, laugh or ‘smell’. Members of a family, resemble each other without satisfying a set of rules about how the family should present.
We replaced family with a given word sound when describing the complex and personalised world of the meaning clusters that form behind every word and every combination of words. Note that the semantic side of meaning is more rule bound.
See meaning and grammar.
What does it look like when we use family resemblance as a basis for action? We act on family resemblance when we already know that the members of the family in question are related. We do not act on it in the absence of this prior knowledge. In fact we are acting; physically and socially; on the basis that we know that they are related not on the basis that they resemble each other. We do not approach casual acquaintances, let alone total strangers and say things like “could you give this to your relative who lives in Waterloo Crescent” on the grounds that their voices sound the same and that they look similar. Family resemblance theory does not give a picture, or an account of meaning that captures the fact that we act on it.
Though family resemblance theory is helpful it does not include movement modeling, physical action and the complex world of integrated models. In other words it does not allow the real world to be referred to firmly enough to serve as a basis for physical and social action.
We have found ourselves in a place famously described by Douglas Adams. The people of a planet built a vast computer and then gave it the question ‘what is the meaning of life and everything’. The computer was silent for many generations but the day came when it said that it had the answer. A huge gathering, with ‘wired’ distribution around the planet, heard it answer ‘forty two’.
If rational thought has failed as a ‘god’ to worship - I.e unquestioning adherence - how about choosing another. I suggest that intimacy would be the best candidate.
Suggest that you read the Life modeling topic next.