Some Weird Stuff

Richard Feynman

For any person wishing to carry a mapper's strengths into the workplace, the life and work of the physicist Richard Feynman is worth studying. He told stories. The Spencers' Warbler was a bird identified for him by his father. The name was made up. His father then made up names for the bird in many other languages, and pointed out that young Feynman knew no more than when he started. Rote-learning names of things means nothing. Only looking at what the bird itself is doing tells one anything about it.

He was utterly honest and saw through artificial complexity by always insisting on simplicity and facts. See his personal version of The Challenger Report, contained in his book What Do You Care What Other People Think?.

He used simple, humorous, curious language, filled with little pictures and enthusiasm. His techniques for puncturing pomposity were unrestrained.

His Lectures on Computation have recently been published, and are worth reading, as is everything he ever published, from Six Easy Pieces, to the Red Book Lectures. James Gleik's Genius and the Gribben's Richard Feynman are rewarding biographies.

Get hold of his stuff and read it.

George Spencer-Brown

The Laws of Form, by George Spencer-Brown is a little book of mathematics and commentary that is described by modern logicians as containing a form of `modal logic', characterised by having the rules of the logical system applying differently in different places, in a manner defined by the rules of the logic itself.

From the point of view of a programmer, there are two aspects to this book that will certainly stimulate thought. In the main text, the author shows how to do predicate logic with just one symbol, offering a deeper view of `fundamental' logical and computational operations such as NOT, OR AND, XOR than one might have guessed existed.

Then there are the notes, simple and profound thoughts that one returns to again and again, often informed by the technique of doing predicate logic with one symbol, that can be thought of as simply cutting a single plane into two pieces, so that there are two distinguished things, and thus something to talk about. For example, the author says,

In all mathematics it becomes apparent, at some stage, hat we have for some time been following a rule without being consciously aware of the fact. This might be described as the use of a covert convention. A recognisable aspect of the advancement of mathematics consists of the advancement of the consciousness of what we are doing, whereby the covert becomes overt. Mathematics is in this respect psychedelic.

Or try,

In discovering a proof, we must do something more subtle than search. We must come to see the relevance, in respect of whatever statement it is we wish to justify, of some fact in full view, and of which, therefore, we are already constantly aware. Whereas we may know how to undertake a search for something we can not see, the subtlety of the technique of trying to `find' something which we already can see may more easily escape our efforts.

Or,

Discoveries of any great moment in mathematics and other disciplines, once they are discovered, are seen to be extremely simple and obvious, and make everybody, including their discoverer, appear foolish for not having discovered them before. It is all too often forgotten that the ancient symbol for the prenascence of the world is a fool, and that foolishness, being a divine state, is not a condition to be either proud or ashamed of.

Unfortunately we find systems of education today which have departed so far from the plain truth, that they now teach us to be proud of what we know and ashamed of ignorance. This is doubly corrupt. It is corrupt not only because pride is in itself a mortal sin, but also to teach pride in knowledge is to put up an effective barrier against any advance upon what is already known, since it makes one ashamed to look beyond the bonds imposed by one's ignorance.

To any person prepared to enter with respect into the realm of his great and universal ignorance, the secrets of being will eventually unfold, and they will do so in a measure according to his freedom from natural and indoctrinated shame in his respect of their revelation.

In the face of the strong, and indeed violent, social pressures against it, few people have been prepared to take this simple and satisfying course towards sanity. And in a society where a prominent psychiatrist can advertise that, given the chance, he would have treated Newton to electric shock therapy, who can blame any person for being afraid to do so?

To arrive at the simplest truth, as Newton knew and practiced, requires years of contemplation. Not activity. Not reasoning. Not calculating. Not busy behaviour of any kind. Not reading. Not talking. Not making an effort. Not thinking. Simply bearing in mind what it is one needs to know. And yet those with the courage to tread this path to real discovery are not only offered practically no guidance on how to do so, they are actively discouraged and have to set about it in secret, pretending meanwhile to be diligently engaged in the frantic diversions and to conform with the deadening personal opinions which are being continually thrust upon them.

As a beautiful summary of the mapper/packer communication barrier that we have discussed at such length, one can hardly do better than that! Finally, there is a vision of the power of the mapping cognitive strategy, as it continues to seek for ever deeper structure behind the phenomena it regards, offered by way of what we get by making a single distinction in the void,

We are, and have been all along, deliberating the form of a single construction ... notably the first distinction. The whole account of our deliberations is an account of how it may appear, in the light of various state of mind which we put upon ourselves.

Elsewhere he says,

Thus we cannot escape the fact that the world we know is constructed in order (and thus in such a way as to be able) to see itself.

Richness from ultimate simplicity. The limit of complexity cancellation, and the art of using the triangle of creativity to place the Knight's Fork of our perception at the correct level of abstraction for our purposes. As programmers, we work in, and by our every deed prove the unification of, exactly the same creative space as the most abstracted of mathematicians and lyrical of poets. Remembering George Spencer-Brown, look at this poem by Laurie Lee, and ask if your code has ever drawn structure from domain, done all that has to be done, and outroed so perfectly?

Fish and Water

A golden fish like a pint of wine
Rolls the sea undergreen,
Glassily balanced on the tide
Only the skin between.

Fish and water lean together,
Separate and one,
Till a fatal flash of the instant sun
Lazily corkscrews down.

Did fish and water drink each other?
The reed leans there alone;
As we, who once drank each other's breath,
Have emptied the air, and gone.

Physics Textbook as Cultural Construct

We are regularly invited to see the world in a certain way, by users who believe they understand their world, by style and approach gurus, by our own preconceptions. We are continually challenged to see the world as it is, such that we make its representations in our systems as simple as possible. Just as one has to see the quality plateau (albeit only once) before one can recognise it, so one has to `Walk around the side of the Gone With the Windbreak and see how many times they lit the fire'; one has to see a supposed solid reality questioned, before one can know what this is about.

There can't be much more solid than A Level Physics: anyone who says that that is a cultural construct, a social agreement between cynical physicists to make the world obscure to civilised people with media degrees would clearly have to be off their rockers. The strange thing is, some people genuinely do argue that the laws of physics are made up by physicists rather than discovered, and they should be constrained to make them up differently!

Th real tragedy for these prattling fools is that if only they were to study some physics, they might have discovered that although the laws of physics were in place long before the physicists that study them and are quite independent of the opinions of the physicists, the perception of the universe that we draw from these laws may well be a cultural construct.

To explain this amazing claim, we need to refer to three physicists. Isaac Newton discovered modern mechanics, and actually recorded his discoveries mainly in Latin prose, not in the symological style we use today. That was invented by the Victorian Oliver Heavyside, and what we usually refer to as `Newtonian' physics is nearly always in fact the Heavyside rendition of Newton's physics. Richard Feynman was a physicist of modern times, who attempted to summarise what was known as elegantly as he could for undergradultes in the Red Books. Where things get interesting is when we compare the ordering of the tables of contents in the Principia of the genius Newton, the parts of the genius Feynman's Red Books that were known to Newton, and the parts of Advanced Level Physics by Nelkon and Parker (the standard British textbook), again that were known to Newton.

Principia

• Newton's Three Laws of Motion
• Orbits in gravitation (with raising and lowering things)
• Motion in resistive media
• Hydrostatics
• Pendulums
• Motions through fluids.

Red Books

• Energy
• Time and distance
• Gravitation
• Motion
• Newton's Three Laws
• Raising and lowering things
• Pendulums
• Hydrostatics and flow.

Advanced Level Physics

• Newton's Three Laws
• Pendulums
• Hydrostatics
• Gravitation
• Energy

What seems to be distinctive about Advanced Level Physics is that its mechanics builds up the complexity of the equations of Heavyside's system, wheres the two other works are motivated by different intents.

Newton starts with his Three Laws, while Feynman gets energy into the picture really early and leaves the Three Laws until later. But once they have defined some terms to work with, both geniuses start by telling us of a universe where everything is always in motion about everything else, and then fill in that picture. They do this long before they discuss pendulums, which are arithmetically much easier, but are a special case compared to the unfettered planets in their orbits.

Advanced Level Physics puts pendulums before gravitation, indeed deals with the hydrostatic stuff both geniuses leave until very late, before it even mentions gravitation, by which time, we suggest, the student has learned to perform calculations in exams as efficiently as possible, but has possibly built a mental model of a universe of largely static reference frames with oddities moving relative to them.

Algebraically inconvenient though it may be (and while Newton's prose might not be influenced by algebraic rendition, Feynman obviously had to consider it), both geniuses want to get the idea that everything moves, in right at the start.

Might it be possible to learn even physics the wrong way, and end up able to do sums concerning the goings on within the universe, but still with a warped and confused view of it?

Are Electrons Conscious?

In The Quantum Self, Danah Zohar considers some questions relating to the nature of consciousness. One idea from consciousness studies suggests that the phenomenon of consciousness emerges from complex relationships between things that are not, in themselves, conscious. This begs the question of how little consciousness one can have. Can an electron, jigging about and doing its mysterious, wavicle thing, be a little bit conscious?

We have raised Zohar's question not to attempt to answer it directly, but to try to approach it from another direction. And as with all this `Weird Stuff', the intent is not to provide information, but to demonstrate just how close the day to day work of a programmer really is to the highest arts and the deepest mysteries.

We will start by doing you the courtesy of assuming you are conscious. Imagine you make a study of synchronised processes sharing resources. As a good mapper, you research the literature, and contemplate what others have said. You also try some experiments yourself. Pretty soon you start to see the deep invariant patterns, both successful ones and unsuccessful ones. You come to realise that a potential deadlock situation is a potential deadlock no matter how it is decorated with complexity. You also come to recognise a potential livelock when you see one.

For those readers that have not made this study, please note that you should, as too many programmer hours are wasted on this stuff, but here's a summary of deadlock and livelock. A deadlock arises when two (or more) processes end up halted, mutually waiting on each other. For example, one process might acquire exclusive access to the customer database, while another acquires exclusive access to the stock database. Then each process attempts to get exclusive access to the database it hasn't got. Neither processes' request can be fulfilled, because the other process already has the exclusive access requested. So the database manager just leaves both calls pending, both processes asleep, until the requests can be fulfilled. Of course, this will never happen, because neither sleeping process can relinquish the database it already has, so both sleep forever. The easiest way to avoid this situation on a real project incidentally, is not particularly clever. The word customer sorts before the word stock, so make it a mass drinks buying offense to ever acquire the stock database before the customer database, even if this means that situations emerge where one only has access to the stock database already, and so one has to relinquish stock, acquire customer, acquire stock. It's worth it and let's face it, either access will be granted instantly or some other necessary process will get in there and the cycles will be used well.

A livelock is a kind of variation of a deadlock where (for example) each process returns with a failure code instead of sleeping, and tries to help by relinquishing the resources it has got and then carrying on with its shopping list. So both processes chase each other's tails until one or the other manages to get enough cycles in one go to acquire both resources at once, and break the cycle.

So now you know livelocks. From bitter experience you know livelocks, and you recognise a potential livelock when you see one. Now imagine you are planning to meet a friend. You aren't sure which of two bars you will want to meet in, because one or the other is always lively when the other is like a morgue, and you can never tell which way around it will be. You don't know which of you will arrive first. The two bars are on opposite sides of the same city block. Of course, you know livelocks. As a furry animal running around planet Earth you aren't going to have your say, opportunities to mate, reduced by a stupid livelock wherein you both chase around in circles between the two bars looking for each other. When you make the date, you are the person who says, `And if you want to check the other bar, walk around the river side of the block so I'll see you if I pull the same trick!'

That's you. It's the kind of person you are. The person you are going to meet has already been attracted by this simultaneously imaginative and sensible aspect of your character, and approves the plan.

So what we understand and what we are are intertwined. When you understand livelock, understanding of livelock becomes a part of your consciousness - the awareness that this universe does that kind of stuff, so you deal with it.

Now imagine that you are asked to look at the information flows around a major corporation, and propose a network management algorithm that optimises corporate bandwidth. You perform a mapper study, as you did with livelock, and eventually you experience insights (problem quakes) that allow you to see an elegant, robust and extensible network management strategy.

Now this strategy, just like livelock, is a part of you. When you see bits of the problem repeated elsewhere, bits of your strategy will be obviously applicable, although at the time, you may swear blind that `It's just so!', and be unable to say why. So when you subsequently capture your elegant, succinct understanding in a programming language and set it running, to what extent is there a copy of a little bit of you running the corporate comms, 24 hours a day?

This is a deep question, and not at all easy to understand. To see it explored somewhat, look at Marvin Minsky and Harry Harrison's science fiction novel, The Turing Option.

For the traditionally philosophically minded, we might make an additional observation in this regard. Usually the essential, such as the Platonic abstraction of `two-ness' is never seen directly, but only through the phenomenal, such as two dogs, two legs or eyes. It is usually considered that the essential in some way proceeds the phenomenal, because the abstraction of two-ness remains even when there isn't a pair of anything in view. The phenomenal is usually, if covertly (in Spencer-Brown's use of the word) seen as proceeding from the essential.

Now consider what happens in the writing of a one-bit program. The triangle of creativity, comprising problem dynamics, system semantics and desire, is certainly phenomenal, because it takes place in the head of the programmer, who has to be actually and physically in existence. However, the triangle of creativity leaves as its product the Knight's Fork, which is an essential mapping of problem dynamics to system semantics. The Knight's Fork, which is essential, in this case is in the image of, and proceeds from, the triangle of creativity, which is phenomenal. Could this reversal of the usually accepted direction of ontological priority be connected with the strange way that a ROM chip gets a peculiar kind of negative entropy added to it as it passes through our hands?

Teilhard de Chardin and Vernor Vinge

Pierre Teilhard de Chardin was a palaeontologist and Jesuit who wrote The Phenomenon of Man in the mid-1950's. By deducing a pattern from fossil evidence and filling in the black-box properties of the parts of his model that he didn't understand with semi-allegorically, semi-religiously worded speculations, he arrived at an unusual view of evolution that proposed a predictable direction of its future course. Although Teilhard de Chardin's thought was very peculiar at its time, his ideas have been sliding towards the centre of some peoples' view of what is happening with technology at the moment and the universe in general. The work hasn't changed, its just that we are picking up evidence suggesting that the mental model of evolution that it proposes happens to be close to the truth.

Teilhard de Chardin identifies a raising in complexity of forms, first with the aggregation of atomic matter in the formation of planets (geosphere), then upon the geosphere the appearance of life (biosphere), then the development by life of consciousness. He suggests that the next stage is the interaction of conscious units to create a `noosphere', which will be a whole new ballgame using the underlying minds as a platform, as the minds use the brains and the brains use the molecules. The behaviours and relevant environmental influences of minds, brains and molecules are totally different, and we can expect the next stage to be no different.

He suggests that there does not have to be any coercion involved in the necessary adoption of co-ordinated states by enough individual minds for an aggregate identity to form - perhaps this is what we see in a `gelled team', which shares a mental model about what the hell is going on. He proposes that the ultimate confluence will be what he calls the Omega Point, where co-ordinated interaction of the constituent minds of the noosphere overwhelms non-coordinated action and a new state emerges.

He was not without his critics - Sir Peter Medawar wrote a scathing attack that focussed on the language changes at the interfaces between the solid evidential parts of the argument and the processes of unknown mechanism fitted in between them. In particular Medawar became very excited about Teilhard de Chardin's use of the word `vibration' where it was clear that the words `coupling' or `constraint' could have been used, and might not have excited Medawar quite so much. The trouble is, mappers have to work with things they don't understand, so the language inevitably gets a little fluffy in places. That's where new theories come from (and one might say that a program is the programmer's theory of the problem domain). Unfortunately this kind of language drives some people crazy, even though most of the good stuff has some of it kicking around, if only in the form of saying that things `want' to do this or that, and filling in the unknown mechanism with an anthropomorphism that is just as silly, applied to an electron, let alone an ant, as proposing an `ineffable spirit', but is for some reason more acceptable.

For an extreme example, listen to Newton, slagging off the bits he could see were missing from his own physical picture, but could not explain the mechanism of (which was the whole point of course)...

Of course, it's a well known fact that Newton spent much of his life `messing around with theology'!

Vernor Vinge is an Associate Professor of Mathematical Sciences at San Diego State University, and one of the best science fiction writers around. In his famous `Singularity Paper', (use the WWW and the SF books Across Realtime and A Fire Upon the Deep, he proposes that the intelligence of beings on this planet will increase, either by improving human brains genetically, or by giving them hardware enhancements, or by building new trans-human computer architectures. After this, networking and a new agenda that comes from seeing more will create a world that we are inherently incapable of imagining in our current state.

There is a striking similarity between the ideas of Teilhard de Chardin and Vinge, only by moving evolution into the fast-burn of software, we shrink the millions of years of organic evolution required by Teilhard de Chardin for the construction of the noosphere to the thirty proposed by Vinge.

But don't take our word for any of this stuff - check it out, see if it gives you a new perspective on what the universe is doing when you are programming, and above all, think about it if only for practice!

Society of Mind

Marvin Minsky proposed in The Society of Mind that the phenomenon of human consciousness emerges from the interaction of numbers of unconsciousness processing agents that run like co-proccesses in the brain, each with its own triggers and agendas. The agents are then connected up and arbitrated via a `nettiquette' that allows them to determine the course of action the organism as a whole will take. When we feel ourselves exercising free will in pursuing our whims, we are in fact simply enacting a decision that has already been arrived at by the collective of agents. The model certainly has its attractions, and gives a basis for the drives that we use our creativity and intelligence to accomplish, but doesn't seem to give a useful description of the creativity and intelligence themselves. With these generalised cognitive faculties, the brain seems to be used as a directable general purpose pattern recognition device whose internal representations are coupled to the sensory components indirectly, at least such that the abstract and the concrete can be considered in the same terms.

The relationship between the society of mind model of cognition and motivation and the general purpose faculties mirrors the relationship between what we have called the packing and mapping strategies, and there is a further parallel with two simple approaches to managing data in computer system design.

Hash buckets operate by abstracting some sort of a key out of the data - perhaps by taking a 20 character name field and adding up the numeric value of all the characters. That number can then be used to index into a table and find the full record. Real hashing algorithms are designed to maximise the spread in the resulting number from typical input data, and must cope with situations where the hash bucket is already full by putting references to several records in them, such that retrieval involves then checking the full key on each record in the bucket. Hash buckets are often very effective in simple situations, and are reminiscent of packing, where some abstraction of the situations encountered is used to trigger `appropriate action'. In packing, hash collisions seem to be poorly handled. They will not even be noticed unless one or more participants will suffer short term loss due to `appropriate action'. Then an `argument' will ensue, where one packer points to one way of abstracting the hash key from the situation and argue that it is `the case', while another will point to another hashing algorithm and argue that no, their way is `the case'. This is not productive and shows a breakdown of the strategy above a certain level of problem complexity, where we are just trying to cram too much variation into too few hash buckets and have not developed the skills to do the significant amounts of full key examination that is then necessary.

Object models allow the data structures held in the computer to grow in complex and dynamic ways, constrained to the semantics of the modelled objects. The shape of the whole data structure can change completely during processing, and retrieval always stays `natural' in that the data are where they `ought' to be - they are all directly associated with an appropriate other datum. Hence there is no complexity introduced by a foreign algorithm such as hashing to be cancelled by something else such as exhaustive key comparison. Above a certain level of complexity, object models are more suitable than hash buckets, but there is no doubt that they are actually harder to implement. The reason why we can use them at low cost today is that we get a lot of specialist support from our languages for describing objects, and our operating systems for free memory management. Object models seem so similar to the mapper strategy that we have described mapping as the attempt to construct a viable object model of the problem domain.

These parallels between functional (society of mind and pattern recognition), subjective descriptive (packing and mapping) and computational (hashing and object modelling) models of consciousness suggest that there may even be a neurological correlate to the mapping and packing strategies we have described. We certainly know that early stimulation of infants causes increased neuron growth and interconnection in infant brains, and this correlates with higher `intelligence' (whatever that may be) in adult life. Whatever `intelligence' is, the kind of cognitive and problem solving skills that are tested have little place in the Taylorist, packer workplace, where the whole idea is to deskill and constrain behaviour.

Perhaps the question at the start of the Information Age is: `What part of your brain is it appropriate to use at work?'

Mapping and Mysticism

Right at the beginning, we looked at two different ways of going about solving problems. Packing was characterised as a socially conditioned habit of accreting `knowledge packets' that specify `appropriate action', and not examining or reconfiguring the relationships between the knowledge packets. The strategy degenerates into kludging reality to fit the known packets and blaming luck when things go wrong. Mapping on the other hand, involves putting investment into building an internal object model of the world as it is perceived and getting leverage by identifying deep structure. Mapping can be developed by learning techniques that help the exploration of conceptual spaces and help one recognise what it is that one is actually seeing happening in front of one's own eyes, by recognising the deep structure patterns in the goings on. Mappers can respond flexibly and are the only people in a position to propose new approaches. They can learn vastly more quickly than packers, and unless they are seeing deep structure, they are seeing as yet unsolved mysteries. The experience of mappers and packers may be quite different, in exactly the same circumstances.

Mapping is the natural state of people, and everyone is a mapper at heart. Unfortunately, societies the world over developed an alternative, which we have called packing, possibly at around the same time as we discovered agriculture approximately 6,000 years ago. It could not have been before that - a pre-agrarian packer confronting a wild animal on the hunt could hardly have fared well by sticking his nose in the air and claiming that the animal was failing to follow procedure!

The alternative involves convincing people that good living consists of following prescribed procedures, and supressing any alternatives. It must have brought benefits to new societies based around the raising of crops, where significant tedious work must be done in the fields, and if things are tight, the only thing one can do is plod, plod, plod, until harvest when more crops will be available. Packing thus involves socialising the young into the packer mindset, and constructing a society where reality consists of the packer approach and a set of knowledge packets, and nothing else. Any person who suspects that there may be other ways of looking at things is then at odds with every member of the society he or she finds themselves in, at odds with the inefficiencies of packer society and the ritualised manner that even social occasions are brought down to. The dissenter may be ascribed weird properties such as magical powers if they are lucky enough to implement some common-sense ideas, or madness if the surrounding packers manage to sabotage their deviation in time. Most people would not even believe that any way of approaching the world other than packing could even exist.

Today, there is little call for stoop labour in the developed world, but a significant need for fully aware people to create the new programs that will run our automation. Only natural mappers have the pattern recognition skills essential for writing computer programs.

For much of its existence, the packer strategy has probably served its users pretty well, keeping order in the fields and early factories, and ensuring that the simple manual labour that was essential to survival was performed. In the subsistence conditions that prevailed, perhaps the literary arts could have been better served, but since the invention of the printing press, there have actually been more poets than printing presses, so perhaps there has not even been a great cost there. But by the start of the 20th century, the age of industrialisation had made packing a dangerously inefficient strategy. We were just too wealthy. Our engines could allow us to do things undreamed of by previous generations, and we needed understanding to guide our use of them. Trapped in a packer mindset, and in possession of knowledge packets inappropriate to industrialised societies, Europe was torn apart as millions went to war with internal combustion engines, tracked vehicles, barbed wire, machine guns, mustard gas, aeroplanes and other equipment that distorted the pre-industrial knowledge packet that `War is an extension of diplomacy by other means' out of any reasonable diplomatic definition of objectives, on grounds of cost alone.

Now the cracks are really starting to show. We have achieved the dream of ages, and have abandoned the need to work for millions, freeing up their time to do want they would wish. Yet we see this as unemployment, and furthermore we keep millions working away in what used to be low-overhead jobs, just manipulating the tokens of an agrarian economic system. There are so many of these non-productive jobs that it is actually hard to see it, but every supermarket checkout operator, bank cashier, ticket inspector, financial advisor, tax collector, accountant and on and on is in fact engaged in non-productive labour. Only a tiny fraction of the population are doing any work necessary for the maintenance of our material lifestyles, yet still we believe ourselves to be in scarcity!

Even the currently visible stresses, far worse than any in history (packing always leads to a kind of stupidity when decsions about unusual circumstances have to be made), cannot point the way back to mapping in packer language. One might say that it is a function of packer language, evolved over millenia, to prevent the discussion of mapping! So in times gone by, returning to mapping must have been very rare indeed. If the effectiveness or acceptability of a mapping approach to a problem is a matter of opinion, the opinion of the majority of packers will always be that it doesn't matter that the result was obtained, because it wasn't done `properly'.

Only today is there a real opportunity for an individual to practice mapping and get the realistic feedback that is essential for learning. That is because only mappers can program computers. If a person, still in the packer mindset, follows the procedure and translates a requirement, the result is likely to be a mess. At this point, he or she could blame the compiler, the operating system or the user, but possibly might just recognise that the computer really is, with utter faithfulness, reflecting what it has been told. So the individual can accept that it is they, and they alone, that must understand the problem dynamics and system semantics. Here begins many late nights, and the opening of the road to really thinking, rather than performing the abberation that is packing, and which the packer majority calls normal.

From this perspective, it's interesting to look at several strands of previous thought that attempt to describe the experience of mapping in cultures where one cannot just say `The program works!', and have a very strong argument on one's side, in language that mappers can understand in terms of shared subjective experience of playing with representations of reality in one's head until they are correct enough to be useful, and which packers cannot understand at all. Perhaps it is not surprising that many great programmers have interests in these strands of previous thought..

We have already discussed the nature of alchemy as an internal journey that changes the operator's view of the world - the basic technique of mapping. Alchemical traditions likely spread into Europe from Moorish Spain through people like Roger Bacon.

In In Search of the Miraculous, PD Ouspensky records some conversations with GI Gurdjieff, which took place in Russia in 1915. A strange figure who made a remarkable impact, Gurdjieff told that he had spent many years studying mystical traditions, Ouspensky records,

In all there are four states of conciousness possible for man... but ordinary man... lives in the two lowest states of conciousness only. The two higher states of conciousness are inaccessible to him, and although he may have flashes of these states, he is unable to understand them, and he judges them from the point of view of those states in which it is usual for him to be.

The two usual, that is, the lowest, states of conciousness are first, sleep, in other words a passive state in which man spends a third and very often a half of his life. And second, the state in which men spend the other part of their lives, in which they walk the streets, write books, talk on lofty subjects, take part in politics, kill one another, which they regard as active and call `clear consciousness' or `the waking state of consciousness'. The term `clear consciousness' or `the waking state of consciousness' seems to have been given in jest, especially when you realise what clear consciousness ought in reality to be and what the state in which man lives and acts really is.

The third state of conciousness is self-remembering or self-consciousness or conciousness of one's being. It is usual to consider that we have this state of consciousness or that we can have it if we want it. ur science and philosophy have overlooked the fact that we do not possess this state of consciousness and that we cannot create it in ourselves by desire or decision alone.

The fourth state of consciousness is called the objective state of consciousness. In this state a man can see thinngs as they are. Flashes of this state of consciousness also occur in man. In the religions of all nations there are indications of the possibility of a state of consciousness of this kind which is called `enlightenment' and various other names but which cannot be described in words. But the only right way to objective consciousness is through the development of self-consciousness. If an ordinary man is artificially brought into a state of objective consciousness and afterwards brought back to his usual state he will remember nothing and he will think that for a time he had lost consciousness. But in the state of self-consciousness a man can have flashes of objective consciousness and remember them.

The fourth state of consciousness in man means an altogether different state of being; it is the result of long and difficult work on oneself.

But the third state of consciousness constitues the natural right of man as he is, and if man does not possess it, it is only because of the wrong conditions of his life. It can be said without any exaggeration that at the present time the third state of consciousness occurs in man only in the form of very rare flashes and that it can be made more or less permanent in him only by means of special training.