Footnote: The Fallibility of Perception and Reason

I am self-aware. I think, therefore I am. This is necessary and sufficient evidence for me that I exist. I do not need any evidence or assurance, from the vast universe be­yond me, to verify or validate this fact. Notwithstanding, in order to be able to per­ceive myself, I do need a notion of the vast universe that is outside of me.

I can ponder my existence and make consequential deductions about me and also about my relationship with the vast universe that is outside of me. Pondering and deducing require the use of reason. My power of reason seems to be an innate at­tribute of my human consciousness. It works according to what the mathematician and linguist George Boole called The Laws of Thought.

When I reason, however, I do it in terms of abstract concepts and notions. I do not use any formal system of logic. I think the first person attributed with having invent­ed a formal mechanism for reasoning things out, namely logic, is the ancient Greek philosopher Aristotle.

Logic and Deduction

The process of logic or deductive reasoning is popularly illustrated in the quotation "All men are mortal. Socrates is a man. Therefore Socrates is mortal.". This process is formalised as a system of algebra in which a symbol is assigned to each of the propositions.

A = All men are mortal.
B = Socrates is a man.
C = Socrates is mortal.

A graphical representation of these propositions is shown on the right. The big circle 'U' represents the universe. The smaller red circle 'M' within it represents all things mortal. The even smaller yellow circle 'm' within the red circle represents "all men". The little figure 'S' in the middle represents Socrates. Consequential relationships between the propositions are expressed through the log­ical operators "and", "or" and "not". In one conven­tion, the symbol "&" represents "and", "|" represents "or" and "!" represents "not". The popular quotation above can thus be reduced to an algebraic equation C = A & B.

The logical equation C = A & B states that Proposition C is true provided that the Propositions A and B are both true. In the simplest situation, propositions A and B are both what are called primary propositions, which means that they are known by direct observation of the real world. Proposition C is a deduced proposition, which means that you know of its truth or falsity without having to observe its state in the real world. In other words, by the process of deduction, it is possible to know the truth or falsity of a proposition that cannot be directly observed.

The three logical operators &, | and ! are not mere conventions of human language. They are fundamental elements of the entirely natural Laws of Thought, just like the arithmetical operators + − × and ÷. In fact, each of these four arithmetical operators can be expressed in terms of the more fundamental operators "&", "|" and "!". For instance, in arithmetic, we express the sum S of a pair of binary num­bers A and B as S = A + B. We can, however, rewrite this equation in terms of the more funda­mental logical operators as follows:

D = (A | B) & (!A | !B) and C = A & B

Here, D is the resulting value for the current digit position and C is the amount we must "carry" to the next higher digit position.

The above diagram shows how the binary numbers A and B in the least-significant column of an 8-bit register are added together, using logical operators, with the re­sult D placed in the least-significant column below and the amount which must be "carried" to the next column. For example,

if A = 1 and B = 0, then
C = 1 & 0 = 0 [so there is nothing to carry]
D = (1 | 0) & (0 | 1) = 1 & 1 = 1
Note that !1 [not 1] = 0 and !0 [not 0] = 1

We get the same result if A = 0 and B = 1

if A = 1 and B = 1, then
C = 1 & 1 = 1 [so there is 1 to carry]
D = (1 | 1) & (0 | 0) = 1 & 0 = 0

A binary adder is implemented electronically in a computer by wiring together basic logic circuits as shown on the right. There needs to be a repetition of this circuit for each column of a 32-bit register. All but the least significant column needs additional circuitry for adding in the "carry" bit from the pre­vious column. The existence of the electronic adder circuit shows that logic is intrinsic to the way nat­ure's Laws of Thought work. It was not invented by man, but rather, discovered by him.

Clarification: We express our perceptions of physical phenomena in terms of the Laws of Thought [logic and mathematics]. Notwithstanding, these ex­pressions are different and distinct from the objective Laws of Physics which act­ually govern the phenomena themselves. The objective Laws of Physics are fundamentally beyond our senses, perception and reason.

In the case of Socrates discussed above, the whole of each smaller (more specific) class of objects is contained within the more general class. It is merely an instance of the human convention by which we classify a particular object — in this case, Socrates — in terms of a characteristic that it shares with other objects and classes of objects.

Far more interesting and useful cases occur where clas­ses of objects overlap, as shown in the diagram on the left. For instance, if U represents the United States of America, T represents all Texans, R represents Americ­ans who vote Republican and S represents all Americans who did not approve of Saddam Hussein, then the little roun­d­ed triangle in the middle represents Republican-voting Texans who don't approve of Sad­dam Hussein. Cases with overlapping classes can lead to very complex rel­a­tionships and dependencies bet­ween propositions that are difficult — if not impossible — to reason out through verbal argument.

The process of deduction — whether by verbal reasoning or by logical algebra — is to determine the TRUTH or FALSITY of a proposition [Proposition C] that you want to know (but are unable to observe) from the TRUTH or FALSITY of related propositions [Propositions A and B] that you already know because you have observed them. The validity of your deduction depends on the validity of your observations [of Propositions A and B]. The validity of your deduction is therefore a matter of per­ception. It is about whether — and to what extent — you can know the TRUTH or FALSITY of a proposition relating to an external event, object or phenomena that you observe.

The Black and White View

Whatever we observe, we can discover things about it by asking ourselves ques­tions about its appearance and behaviour. All these questions can be reduced to a set of elemental questions, the answers to which are either "yes" or "no". For ex­ample, we can ask "What colour is it?". The answer must be the name of a colour. However, we can reduce this question to a set of elemental questions like "Is it red?", "Is it green?", "Is it blue?". The answer to each of these elemental questions is either "yes" or "no". Another more formal way to do this is to replace questions with propositions, then decide which propositions are TRUE and which are FALSE. For example, we can make the following propositions about an object we are ob­ser­ving: "It is red." "It is green." "It is blue.". Assuming we include propositions for all colours, then only one proposition will be TRUE and all the rest will be FALSE.

Whether an elemental proposition about an observation be true or false has been the basis for logic since ancient times. Today, this yes/no logic represented by 1s and 0s is the principle upon which computers operate.

Many people see the world in terms of this absolute two-state log­ic. They see "facts" as absolutely TRUE or absolutely FALSE. They view each aspect of human behaviour as being absolutely RIGHT or absolutely WRONG. They adhere to a strict syntactical interpret­a­tion of, for example, holy scriptures, which implants within them an austere black-and-white notion of GOOD and EVIL. It engenders a bloody-minded mentality in both company employees and public functionaries who uncompromisingly expedite their interpretations of policies, rules and regulations, knowing full-well of the officially unintended harm and injustice they thereby may inflict on those to whom their interpretations are applied.

But Perception Isn't Perfect

Notwithstanding, this black-and-white two-state logic isn't the principle upon which the real world operates. The reason for this is that human perception is imperfect. The human life-form is not equipped with a divine all-seeing eye that can view the whole universe with perfect vision against an absolute frame of reference. Our im­perfect perception allows each of us to know some things but not others.

We can observe some propositions about our universe to be TRUE and some to be FALSE. However, for the vast majority of proposi­tions about our universe, our powers of observation fail. Conse­quently, we do not know whether they be TRUE or FALSE. Unlike computers, communication links suffer from interference. This fogs signals to greater or lesser degrees, depending on dist­ance and the quality of a connection. In the absence of inter­fer­ence, a receiver will be able to resolve definitely whether a signal is "0" or "1". However, when interference is present, it may not be sure which it is. For this reason, communication links use a three-state logic: "+1", "0" and "−1". When a receiver is unsure of a signal, it asks the transmitter to re-send it. The receiver is thereby able eventually to obtain a good copy of the message.

But even this three-state logic is not sufficient to represent the TRUTH or FALSITY of the propositions we make about what we see in the real world. Four different fac­tors actively diminish the certainty with which we can know the TRUTH or FALSITY of such propositions.

Sense and Interpretation

The first factor is to do with our physical senses. If we are looking at something through a morning mist or in the dusk of night, we do not see it clearly. Our eyes sometimes "play tricks" on us. Any medium that con­veys information from the outside world to one of our physical senses interferes with, and degrades, that in­formation to some degree, even under the most benign conditions. What we see is therefore never a true re­presentation of whatever we are looking at.

The second factor concerns our interpretation of what we see. Throughout life, one accumulates mem­ories of all his experiences. With these, his mind con­structs, and continuously augments, a neural model that sim­ulates his world outside. One interprets what he sees by comparing his current experiences with this neural model. For him to be able to interpret what he sees correctly, his past experiences must contain all the basic elements of what he is seeing. If any of these basic elements be missing, his interpretation of what he is seeing will be inaccurate, and could be com­pl­etely false.

Furthermore, the process, whereby a person's neural model is built and updated, may impose emotional distortion upon the information it receives from the outside world. This is particularly significant regarding how a person's mind interprets the attitudes and intents of other human beings.

I liken this to a sound equaliser with sliding gain controls to allow you to adjust an amp­lifier's gain for each octave of the audio spectrum. If the sliders are adjusted correctly for a given input, you get a well-balanced out­put. If, on the other hand, some of the sliders are significantly far from where they should be, the output is unbal­anced and not pleasant to hear.

Different sliders [different octaves of the audio spectrum] represent the different aspects of human emotion. In the latter case, where some sliders are out of adj­ustment, the person's perception, of that emotional aspect of what he is currently experiencing, is either accentuated or diminished. This results in his neural model of the world [specifically human society] being updated in an emotionally distorted way. This, in turn will cause him to have an even more emotionally-distorted view of his future experiences.

Emotional distortion thus gives a person an increasingly distorted view of human society. It can cause the person to fear people, animals and objects to an extent much greater than is necessary for reasonable levels of caution. It can also work in the opposite direction, giving him a reduced sense of danger.

If emotional distortion exceeds a critical threshold, it becomes super-regenerative. This causes a person to continually re-run horrendous "what if" scenarios that can eventually become part of his neural model of the world and thereby become per­ceived as having really happened. In other words, they become fear-invoked false memories, which, when used as a context for interpreting what he sees, can compl­etely falsify his interpretation of what he is currently experiencing.

Angle of View

The third factor concerns the direction from which an object is being viewed. The object in the picture on the right is almost impossible to recognize. It looks like nothing that could be remotely described as familiar. This is because it is being viewed from a direction from which it is not normally seen.

If, however, you change the angle of your point of view by 90°, it appears as shown on the left. It becomes instantly recognizable as a carving of a man and a woman embracing. This is because it is now being viewed from a direction from which people normally view such things. Unfortunately, it is not always possible to change one's viewing position in order to find a more familiar direction from which to observe something. For example, an astronomer observing the motion of a planet is constrained to make his observations from the surface of the Earth. The Earth is rotating on its own axis and also revolving around the sun. The observer's own motion combines with that of the planet he is observing. This makes the planet's motion appear to the observer to be far more complicated than it really is. It confused the astronomers of the ancient world for a long time.

Each of us is constrained to view others from the point of view of his particular eco­nomic and cultural stations within the social order. Those of us who do not have sufficient means and influence are therefore constrained to view the rest of society from a less amenable angle. Consequently, making sense of it requires of us that much more effort.

Each View Is Different

The fourth factor is to do with the nature of the Universe regarding the funda­men­tal constraints of time and space. It is physically self-evident that no two objects can ever occupy exactly the same position in time and space.

This idea can reasonably be extended to human observers by saying that no two people can occupy exactly the same position in space-time or society. Everybody's experience is different because the lives of no two people have ever followed exactly the same path through time, space and society. Each person's point of view is therefore bound to be different to at lease some degree. It is fundamentally barred from ever being ex­actly the same as somebody else's.

Hence, the precise angle from which each of us views the world is unique. Consequently, each person's perception of the TRUTH or FALSITY of propositions about the world is bound to be differ­ent from everybody else's. Each of us effectively lives in a slightly different person­alised version of the Universe. This is evinced by the fact that no two people can agree perfectly about everything.

This leads people and nations to very different views of some very basic notions. For example, the word "freedom" has somewhat different meanings to different people:

Logical Probability

The indistinctness of human perception requires a more so­phisticated version of logical switch than the two and three-state versions discussed so far. To represent the status of pro­positions relating to our perception of the real world, we re­quire a form of logic that varies infinitely and continuously all the way from definitely TRUE to definitely FALSE. This accom­modates the fact that perceived truth can only ever be a fuz­zy version of the real truth. This type of logic can be regarded as a measure of the probability of the TRUTH or FALSITY of a proposition relating to some­thing in the real world. Instead of stating whether a proposition be TRUE or FALSE, a person guestimates a numerical value between −1 and +1.

For example, a value of +0·5291166 means that through the fog of his senses and the errors of his perception, he estimates, from what he sees, that the proposition is 53% likely to be true. This pertains to a single primary proposition.

But what about a proposition whose probability of being true cannot be directly observed and so must be deduced from other propositions?

Primary propositions are those whose probability of being true can be derived from direct observation of the real world. So to keep the process of logical deduction as simple as possible, all primary propositions must be independent of each other. In other words, variations in the probability of one primary proposition being true must not cause to vary the probability of another primary proposition being true.

When trying to find a set of propositions, whose probability of being true can be observed, in order to deduce the truth probability of one that cannot be observed, they all too frequently interfere with each other's truth probability. How­ever, by breaking down such propositions into one or more simpler ones, we can arrive at a set of primary propositions that are independent of each other.

It's rather like breaking down a loaded question into a set of independent simpler questions, each of which can be fully answered by "yes" or "no".

In the above diagram, I used a scale from −1 to +1, as used in 3-state communi­cations logic. By convention, however, logical probabilities are measured on a so-called 'normalised' scale of zero to unity [0 to 1]. In the following diagram, I have gone a step further by expressing this 0 to 1 probability as a percentage [0 to 100]. This way, a proposition is said to have a percentage probability of being TRUE. But this too is a mere convention. There is nothing fundamental about it.

Suppose I can see the truth or falsity of Propositions A and B directly in the real world. But due to imperfections in my per­ception, senses and instrumentation, I can only be 90% sure that Proposition A is true and only 75% sure that Proposition B is true. However, I need to know the truth or falsity of Propos­ition C, which I am unable to observe directly. I know that the truth or falsity of Proposition A doesn't affect the truth or fals­ity of Proposition B and vice versa. So log­ic­ally C = A & B. So the composite probability that C = A & B be true is given by:

P_C = P_A × P_B = (90/100) × (75/100) = 67·5%

This logical probability must not be confused with the probability of an actual event occurring. Logical probability is different from, for example, the statistical prob­ab­ility with which an actuary predicts real movements in a financial market. It is a probability of perception: not of fact. One's perception of an observed event can be thought of as a mixture of truth and error. For example, if you estimate that a particular proposition be +75% (75% TRUE) then you are saying that your esti­mate, based on what your senses and experiences are telling you, probably com­prises ¾ truth and ¼ error.

The Advantage of Consensus

When many people make considered judgements about their independent observations, what they agree about will be more likely to be correct than what they disagree about. This is because truth originates from the uni­versal reality without while error originates from the process of perception within each individual mind. A much better ap­proximation to truth is therefore always acquired by con­sensus and compromise.

Notwithstanding, for consensus to work, each individual must apply considered and separate thought to what he is observing. Each must be an independent thinker and judge: not a sheep blindly following the dogma of an elite minority or exigent leader. An example of the latter is the dogma that the Earth was flat. This was foisted upon a world of willing sheep by a church that condemned the one man who dared to publish his unfettered empirical observation that the Earth was in fact spherical.

A much better approximation to the truth is always acquired by consensus and compromise. However, this introduces a further element of error. When one makes a judgement as to the probability of an observed proposition being true, the pro­cess takes place entirely within one's mind. It involves nobody else. But consensus and compromise take place between people. This necessitates inter-personal com­munication, which requires the use of language.

The Problem of Language

Language is symbolic. Objects and actions are represented by words. A word al­most always shares no fundamental characteristics with what it represents. For in­stance, neither the sound nor appearance of the word "dog" bears any resembl­ance to the animal that barks. Therefore, to convey accurately a message involving a dog, both the speaker and the listener must have had previous sight or sound of that type of animal. The speaker and the listener must both attach similar experi­ences to the word "dog". A dog is a physical thing. Certainly, a person who has seen any animal with four legs could eventually come to understand — at least in part — what a dog is, even if he had never seen one. However, without ever having seen one, his understanding could never be perfect.

This imperfection becomes far more significant when we consider what a particular speaker means by an abstract notion like "freedom". This is impossible to know exactly unless the listener has direct experience and appreciation of the speaker's life, background and belief system. No two people have ever trodden exactly the same path through life. Each individual's battery of elemental exper­iences is there­fore different. Consequently, no two people can mean exactly the same things by exactly the same words. In any verbal exchange between people, the meaning con­veyed is necessarily fuzzy. Often — especially through the narrow sub-language of bureaucracy — it can become impossible to convey the overall truth without telling detailed lies.

Social Consequences

A stark witness to the way meaning is warped by the fuzziness of human percep­tion and communication is the grand diversity of religions that exist in the world. Even variants of what is purportedly the same faith are often irreconcilably incom­patible. The same is true of political ideologies and schools of academic thought.

If harmony is ever to emerge from this cacophony, each of us must realise that the logic of the real world is fuzzy. We must each make careful observation and sincere independent judgement of the truth probability for all the propositions we en­coun­ter in all areas of human thought and belief. Then all of us must share our obser­va­tions and judgements in a spirit of consensus and compromise. Religious and polit­ic­al dogma will then disappear. Academic egotism will evaporate. Such freedom of thought could lead us to discover things like a solution to the inequities of capital­ism by incorporating within it some ideas from communism, or resolu­tions to the paradoxes of Christianity within the tenets of Buddhism.

Once we all recognise that observed truth has a probability and not a certainty, we can perform the same computations of logical algebra to derive unobservable truths. The same logical operators (AND, OR, NOT) work equally for fuzzy logic as for the inflexible two-state logic of the ancients.

All is Opinion

Nothing spoken or written is fact. Any statement is merely a subjective observation, which is relative to the originator's unique path through the experience of life. It can only ever be an opinion that has a certain probability of being fact. To maxi­mise this probability, many can pool their observations. But this demands that each respect the points of view of others equally as his own.

All observation is relative to the unique path through space, time and the experi­ence of life of each individual. All that is said and written is derived from observ­ation. Consequently, all that is said and written is also relative to each individual's unique experience of life. All that is said and written is therefore, necessarily, in­dividual opinion: not universal fact.

In the context of individual responsibility, the question can never be whether what somebody says or writes is factual or not. It can only ever be a question of whether the speaker is stating an honest opinion or a malicious one. This could have im­plications regarding the validity of established laws relating to slander, libel, mis­representation and defamation. The default assumption about anything that is said or written must always be that it is opinion.

What about True Lies?

I was once arrested by the police. Initially, they were going to arrest me on susp­icion of attempted murder. Then they decided to downgrade it to GBH [grievous bodily harm]. When I was finally arrested, it was on suspicion of having committed ABH [actual bodily harm]. So I have an arrest record.

I was staying the night in the house of a friend. I went to bed. In the middle of the early hours [about 01h45, as I understand it] there was a considerable commotion. The mother of my friend claimed that somebody had hit her hard while she was in bed. I was the prime suspect because I was the only 'stranger' in the house. The police were called. I had to give a statement. Evidence was collected. There was a lesion on the old woman's forehead.

I had, of course, done nothing. At the time the old woman claimed to have been hit, I had been fast asleep. Nonetheless, I was summoned by the police to appear at a police station that was about 80 km from my home. I was arrested on suspicion of having caused the old woman actual bodily harm. I have, to this day, try as I might, been unable to deduce what really happened.

Later, the police told me that I would not be hearing anything further from them. The police offered no further clarification. It was known, as I later discovered, that the old woman was in the late middle stage of Alzheimer's disease. All-enveloping hallucinations are well possible at this stage. I think that in all probability, the whole thing was an all-powerful hallucination resulting from her Alzheimer's condition.

The old woman made a statement to the police about me that was totally FALSE. But was she giving an honest or dishonest opinion? Was she telling the TRUTH while conveying a LIE? Yes, I think her intent was to tell the TRUTH. But she conveyed what was, in fact, a very damaging LIE.

Notwithstanding, I am still left with a totally undeserved arrest record for a serious crime. And society in general assumes that there is never smoke without fire. With an arrest record, I could not go ahead with an application to go to another country to participate in a project on which I had my heart set. Whom do I blame? The police, of course, for arresting me immediately without hearing me freely give my own evidence first. It is the police who really inflicted damages on me, which they were able to do with impunity.

Even honest opinion cannot always convey normally perceivable TRUTH.

But Do We Really Want Truth?

Notwithstanding the above-described tenuous and tempestuous path, which truth must travel, in order to arrive into one's conscious view, does the generic human being really want to know the truth? For all its inconsistencies, mistranslations and creative editing down through the ages, the Judaeo-Christian Bible contains pearls of self-evident wisdom. One such, to my mind, is the following:

This is a rebellious people,
Lying children,
Children who will not hear the law of the LORD;
Who say to the seers, “Do not see,”
And to the prophets,
“Do not prophesy to us right things;
"Speak to us smooth things,
"prophesy deceits".
— Isaiah 30:9-10 NKJV

It is easy to transpose the essence of this verse, into today's world of so-called democratic and autocratic societies, as the universal sentiment of all human be­ings. And the politicians give it to them as an incessant drip-feed of smooth, com­forting, easily digestible lies. Thereby, in this dog-pile world, they are willingly de­luded that all is right and well, despite the war, prejudice, torment, hardship, poverty, disparity and suffering that is clearly taking place before their eyes. Thus, even if our senses, perceptions and communications media were perfect and the pure truth were to arrive intact within us, we still wouldn't see it.

We do not have — either individually or collectively — access to, or use of, sufficient resources to empower us to change our world for the better. We have no choice but to accept it as it is. It is all we have. We are stuck with it. Consequently, We have no motive for mindfully subjecting it to the scrutiny of logical analysis. Yet, one way or another, each of us is an active element of the society in which he lives. Each of us responds to his social environment. Most form a political opinion. But if most don't mindfully consider in detail the state of the world, how can they meaningfully and constructively respond to it? How can they form political opinions?

The answer is that the generic individual doesn't mindfully subject the world to the scrutiny of logical analysis. Nor does he construct and despatch consciously consid­ered responses to the way it treats him. On the contrary, his responses are, for the most part, unscrutinised emotional reactions that are generated covertly within his subconscious mind. They are natural responses that have been honed by accumu­lated experience to maximise his socio-economic survival and betterment.

But because his semantic view of society be generated by emotion does not mean that this view cannot be discussed and shaped through mindful verbal discussion. After all, I would wager that most political dogma is an amalgam of idle opinion­ations that emerge through a Friday night beer haze, bequeathing to their partici­pants a comfortable sense of togetherness, which is a natural human craving.

Part of this comfortable sense of togetherness is a collective desire of self-deception into an enduring real and present sense of well-being: that no matter what is really there before one's eyes, all is normal, right and well. And this is what society wants its leaders to tell them by withholding truth and substituting in its place a babbling stream of comforting believable lies. So it would seem that there's a tangible mech­anism, built into the subconscious mind, that inexorably compels one to believe that his world is a nice place, whether or not this be so.

However, the function of this 'tangible mechanism' within the subconscious isn't limited exclusively to the socio-political sphere. It even distorts rigorous scientific enquiry. An appropriate degree of resistance to change is healthy in the realm of science. Mindful peer review is essential to guard against impulsive erroneous de­ductions. Nonetheless, the same subconscious emotionally-driven collective desire for self-deception into an enduring real and present sense of comfort is alive and well also in science. Any new radical idea — or even hard experimental evidence — which, at first glance, appears to violate established theory, is impulsively rejected.

An example of this, which springs to my mind, is the British Royal Institu­tion's rejection of the ideas and well demonstrated experimental evidence presented by electrical engineer Eric Laithwaite in his 1974 lecture.

It appears to me that this rejection was not based on peer reviewed counter experi­mentation, but was immediate and impulsive on the strength that it 'appeared' to violate Newton's Laws of Motion, which would have forced the scientific establish­ment outside its comfort zone. Thus, after all the imperfections of sense, perception and communication path, plus the fallibilities of thought [discussed later in this essay], one's final view is, in the absence of mindful logical consideration, formed by the whims of one's emotionally-driven subconscious.

The only path to truth is to seek it mindfully, through a process of deliberate and unencumbered logical thought, while remaining perpetually aware of the fallibilities of one's perception, senses and instrumentation. But one cannot expect such truth to be necessarily pleasant or palatable.

The Cosmic Context

Human perception has formed and developed within the context of the terrestrial biosphere. My brain has accumulated, during my life so far, a kind of database of elemental observations, experiences and sufferings. It is in terms of these that I perceive, interpret — and hopefully understand — any new event of observation or experience. Notwithstanding, for me to be able to understand [make sense of] a new event, it must necessarily be analysable in terms of my stock of elemental experiences, which I have accumulated within the context of my life here thus far within the Earth's biosphere.

For example, I live in tropical Brazil. I have never been to Antarctica. Nevertheless, I can construct, from my elemental experiences, a sense or understanding of what the intensely cold climate of Antarctica is like. No doubt I would still be taken by surprise if I ever visited Antarctica. My prior conception would not be 100%. But the difference would only be one of adjustment. It would not be a fundamentally differ­ent concept. Besides, the experience of visiting Antarctica would then add to my internal database of elemental experiences to give me a ready context for visiting Northern Canada or Siberia.

Notwithstanding, my database of observations, experiences and sufferings, that I have directly acquired from my life so far on the Earth, does not equip me fully to analyse and understand what I see far out into the universe beyond the Earth. A period of time, a distance and weightlessness: these I can sort of get a handle on without much trouble. But notions like the origin, size, end and destiny of the uni­verse are not parsable in terms of the elemental experiences with which my earthly life has equipped me.

My mind is nonetheless curious about these things, which is, in itself, a paradox. Why should the conscious "me" be curious about things that are outside the context of my earthly environment? What possible survival value could it have? None that I can see or imagine.

So it appears that the conscious "me" is inherently able and motivated to imagine and consider aspects of the physical universe, which it is unequipped to adequately perceive or understand. This alludes to the possibility that the conscious "me" be outside physical reality, yet is constrained to view anything outside itself exclusive­ly through, or by way of, the physical universe, which it is able to understand only within the limited scope of my terrestrial experiences.

I can contemplate infinity of time and space. I can contemplate a beginning and an end. But my earthly context causes me to ponder on what is beyond the end in the same sense that I would ponder on what is beyond the garden wall. In other words, the ground just continues beyond the end of the garden. And also ponders what is before the beginning in the same sense that, when I was a child, I knew that daddy and mummy were children like me before I was born: before my conscious exist­ence began. The cycle of life was the same.

Nevertheless, even as a child, I could see that the beginning and end of time and space and the notion of nothing as opposed to something were not the same in the context of the universe as they were for things in my terrestrial environment. The conscious "me" could see that although places for the ideas of zero, infinity, begin­ning and end existed within my consciousness, I could not understand them.

I was taught as a child that God created the universe and all that is in it. Of course, what is in the universe is itself the universe. So all is covered by simply saying that God created the universe. The terrestrial context, which formed my mind, always shows that when something is made, it has to be made out of something: some basic material. For example, a house is made of bricks. The bricks were made out of clay. The clay was already there. Similarly, machines are made out of metal. The metal was there already in the ground. Structures and systems are made simply by rearranging stuff, that is already there, according to a prescribed design.

My inherent curiosity prompted me immediately to ask the logical question: out of what did God make the universe? As a child, I was taught that God made the uni­verse out of nothing. This, at the time, I accepted. But later, as an adult, I realised that the whole principle of Creatio ex Nihilo, within the context of all my life ex­per­iences, didn't make sense. It is a nonsense. There has to be some kind of material or medium to carry, or make manifest, a design. This, of course, opens an infinite regression of questions that begin with "Who made God?".

If God made the universe ex nihilo, then God is necessarily outside of, and separate from, the universe of time, space and matter that we perceive. But my inherent curiosity also prompts me to conjecture that perhaps the universe we are able to perceive may not itself be the whole of reality. There are far too many loose ends in physics that appear to us as discontinuities or singularities that could be resolved if we suppose that the universe we can perceive is like the part of an iceberg that is above water and that the iceberg continues below the water line into dimensions that we are fundamentally unequipped to perceive.

Of course, lots of the singularities and discontinuities we encounter in physics result from extrapolating the jurisdictions of laws, which work correctly while in close proximity to our terrestrial context, by vast orders of magnitude into the uncharted territory of the cosmos through many tenuous ladders of speculative observation.

One of these is at the heart of the current speculation about the beginning of the universe being a Big Bang emanating out of nothing at a point singularity. This is a clear case of Aliquid ex Nihilo [something out of nothing], which, in the context of terrestrial experience, is also a nonsense. One cannot comprehend it in terms of one's elements of experience acquired throughout a life confined to the terrestrial biosphere. In this situation, the notion of nothing is simply a linguistic paradox. I take comfort in observing that nature seems to abhor discontinuities and singular­ities and avoids them by imposing — often extreme — terminal non-linearities.

It is essential to note that it is our language of mathematics, which is governed by the laws of thought, that throws up discontinuities and singularities. These laws of thought give us our strictly subjective view of reality from our singular point of view in time and space. Furthermore, like any language, mathematics allows us to create only a symbolic representation of reality: not an analogue of it. To know the true laws that govern reality, we would need an objective view of the universe, through which we could see what is going on from all points in space-time simultaneously. Consequently, the true objective laws of physics are — and always necessarily must remain — fundamentally beyond perception.

The fact that we can only ever have a fallible subjective view of reality means that there are things, within the physical universe, that appear to us as nonsense. There are also structures and behaviours within reality that, in terms of our language of mathematics, are fundamentally non-computable, even though unknowable under­lying laws of physics must exist that are actually governing them.

But to my mind, that's OK. It doesn't bother me. There may or may not be a creator God. Either way, God isn't necessary in order to satisfy my inherent curiosity as to how the universe — and we — came into being. I understand that the language of fundamental terrestrial experiences, with which my life on Earth has equipped me, simply doesn't include, within its semantic vocabulary, some of the elements neces­sary to make sense of some of my objects of inherent curiosity.

All this strongly suggests that the conscious "me" came into being pre-equipped with semantic place-holders for certain concepts and notions about the physical universe that are fundamentally beyond my powers of perception. So they appear to me as paradox or nonsense.

I am conscious that I exist. My sense and perception reveal to me other entities like me and allow me to communicate with them. I sense and perceive, subjectively but reasonably accurately, the everyday environment in which I live. I further sense and perceive, albeit imperfectly, the universe beyond. But in attempting to understand the universe in terms of the elements of my terrestrial experience, my understand­ing is blighted by many discontinuities, singularities, paradoxes and nonsenses.

These precipitate unanswerable questions. Did the universe have a beginning? If so, what was there before the beginning? Was the universe created? If so, who created it? Out of what was it created? What is the size of the universe? Is it expanding? If so, expanding into what? Will it end? Will it collapse? Will it expand forever? Was the universe always here? Is it a looped, manifolded or oscillating continuum of some sort? Can something appear out of nothing? Or is the notion of nothing a physical impossibility or nonsense? Does the universe exist because 'nothing' as such funda­mentally cannot exist? Why does the universe have the form and constituency that it does? Why does the universe exist at all? What's it all about?

Pondering these questions clearly shows that they are being asked from within the narrow scope of terrestrial experience. In fact, human languages are themselves all constrained by human experience in an environment on a planet's surface compris­ing what tends towards a plane in a vertical gravitational field. Any human attempt to understand the universe is thus forever trapped in this Sapir-Whorf hypothesis.

Quantum Uncertainty

I have, thus far, considered only the probability with which we are able to know the truth or falsity of a proposition constructed from what we observe with our own senses. Such observations can only involve things that are big enough to see (with magnification if necessary). On this macroscopic scale, as it is called, I can reason­ably assume that what I see must be an albeit imperfect view of a concrete object­ive reality in which all propositions are, definitively, either true or false.

For example: the proposition "my cat is dead" is necessarily either true or false at any given time in any given place. My cat cannot be both alive and dead at the same time in the same place. In our macroscopic world, the two states-of-being — alive and dead — are mutually exclusive. Due to the fallibility of my perception, I may not be able to see clearly whether my cat is alive or dead. But this has absol­utely no bearing on whether my cat is actually alive or dead.

Notwithstanding, once we venture down into the so-called quantum world, at scales significantly smaller than the wavelength of light, we enter a realm in which facts themselves only have a certain probability of being true. Furthermore, it would seem, a fact can be both true and false in the same place at the same time. In other words, things on this scale can exist coincidently in two mutually-exclusive states-of-being. At least this is my best understanding of what scientists are saying.

Schrödinger's Cat

To illustrate this notion, Erwin Schrödinger made an analogy with a cat, which could be both alive and dead in the same place at the same time. Schrödinger put his cat in a closed box. Also in the box he put a lethal source of gamma rays, which was contained in a radiation proof vessel. He included a mechanism with a random trigger above the container of the gamma ray source. The mechanism could break the container at any random time, thus releasing the deadly radia­tion, which would kill the cat. At any given time, therefore, the cat could be alive or dead.

Since the box is sealed and since the mechanism that breaks the container can trigger itself at any random time, no out­side observer can know, at any given time, whether the cat is alive or dead. To him, the cat has an equal probability of being dead as of being alive.

We must, of course, ignore the strong likelihood that the cat would suffocate any­way in a sealed box. Notwithstanding, the corollary to this scenario is that Schrö­dinger's cat, while it is sealed in the box, is both alive and dead at the same time. It exists in a state of life and in a state of death coincidently.

This is what, I am given to understand, is called a superposition of states. But, zombies notwithstanding, life and death are mutually exclusive states of existence. Consequently, the story of Schrödinger's cat seems to me to be asserting that, at the microscopic scale, a finite-state mechanism can exist coincidently in two mutu­ally exclusive states, which is a logical absurdity. It is no more than a play on words; an implicit self-contradiction.

It is only when the observer opens the box that he is able to see the cat's definite current state-of-being: namely alive or dead. But it gets worse. Schrödinger's ana­logy asserts further that the cat's state-of-being only becomes definite when the observer actually opens the box. In other words, it is the very act of opening the box (the act of observation) which puts the cat into one mutually-exclusive state-of-being (alive) or the other (dead).

This assertion is contrary to all that is, or has been, perceived by human ex­peri­ence. The act of opening the box cannot kill the cat or leave it alive, unless the lid of the box is somehow linked mechanically to the mechanism that breaks the con­tainer of the deadly radiation source, which is understood not to be the case.

The story of Schrödinger's cat asserts that the probability of the cat being alive or dead, when the box is opened by an observer, is an intrinsic attribute of what is being observed; as opposed to being due to imperfections intrinsic to the obser­ver's means of perception. At least, this is how the story has always come across to me.

A Finite-State Machine

In the context of his thought experiment, Schrödinger's cat is a kind of finite-state machine with only two possible states: ALIVE and DEAD. Schrödinger's experiment has the systemic profile of a bomb with a random trigger. It is going to explode but nobody knows when. And when it does, it can never do it again. It can only ever change its state-of-being once. It is non-reversible. Schröd­inger's cat could represent some mechanisms in the microscopic world, such as the decay of a radioactive atom, which, beyond the super-hot core of a giant star, is essentially non-reversible.

Most finite-state mechanisms of the microscopic world appear, however, to be able to change their states-of-being in either direction, and without limit.

My understanding of how such a machine should operate is illustrated on the left. The machine is in its low-energy state. It is hit by a travelling distur­bance (1) which imparts energy to it. This raises (2) the machine to its high-energy state. After a ran­dom delay (3), the machine falls back again to its low-energy state (4). In the process of so doing, the machine creates a fresh disturbance in the space around it, which travels outwards away from it.

To be able to hit the machine into a particular higher energy state, the amount of energy in the incident disturbance (1) must be between certain critical limits. So also must be the period within which this energy is completely delivered to the machine. In fact, the incident disturbance has many other critical parameters such as spin, momentum, relative angle of incidence and so on. Likewise, the para­meters of the emitted disturbance (4) are determined by the precise manner and timing extant when the machine falls back to its lower energy state.

Abstracting the parameters of the disturbances (1) and (4) from their physical em­bodiments, we have input and output messages respectively to and from the finite-state machine. Our model thus becomes a message-driven finite-state mach­ine (or finite-message machine).

The delay before the machine falls back to its lower energy state seems to be random. This suggests to me the pre­s­ence of chaos. The higher energy state may therefore host a complex dynamical process, like a weather system within the Earth's atmosphere. An intrinsic characteristic of comp­lex dynamical systems is their sensitive dependency on in­itial conditions. This, which is also known as the butter­fly effect, could well be the author of this randomness.

Thus the whole machine could simply be a twin-lobed complex dynamical system, which, when hit by an incident disturbance (1) is pushed (2) onto its upper lobe. Then, after an apparently random delay (3), it falls back to its lower lobe, releasing its excess energy as the emitted dis­tur­bance (4). Although the delay appears to be ran­dom, it is deterministic. It's just that the det­er­minism is very complex, thereby creating an ill­u­sion of random­ness.

The butterfly graph is, of course, unrelated to the physical structure of the micro­scopic machine itself. It merely represents the apparent behaviour of the machine from the point of view of an outside observer. My best understanding of the phys­ical embodiments of these microscopic machines is as follows.

I imagine them to be complex 3-dimensional structures of standing waves, held in dynamic equilibrium by opposing force fields, which have differing forms and degrees of non-linearity. Each state-of-being of such a machine is thus a stable or meta-stable standing wave, upon which may be modulated a complex melody of chaotic sub-oscillations. The form of this melody, at any given time, is probably deter­mined by the precise way in which the machine was hit into its higher state. And this determines the amount of the delay before it falls back to its lower state.

Different Worlds

My intuitive difficulty with the story of Schrödinger's cat is that it is a macroscopic analogy of something which takes place on the microscopic scale. Schrödinger's cat, in the context of the story, is a finite-state machine, which can be, at any given time, in one of two possible mutually exclusive states-of-being: alive or dead. In the analogy, it is being used to represent a microscopic finite-state mechanism, such as an atom.

There is, however, one fundamental difference between the macroscopic and the microscopic worlds. And that is the difference in their relationships to light. At the macroscopic scale, a cat's body reflects light. The observer's eye can see this light. The observer's brain can parse the details of the image of the cat conveyed by the light. Thereby the observer can know the cat's state-of-being when he opens the box. He can see whether it is alive or dead. But above all, at the macroscopic scale, the light itself cannot affect or change the cat's state-of-being. The light that falls on the cat, and renders it visible, cannot kill it.

At the microscopic scale, on the other hand, Schrödinger's cat, while in a stable state, does not reflect — or otherwise emit — light, or indeed anything. It conveys nothing about itself to the outside world. To any outside observer, it is invisible. It is as if it doesn't exist. Consequently, an observer — no matter how sophisticated his instrumentation — has no means of knowing in which of its two possible mutually-exclusive states-of-being Schrödinger's microscopic cat currently exists.

Shining light on Schrödinger's microscopic cat would be like trying to make a de­tailed observation of a pebble by bowling a large ocean wave at it. Any reflected energy would be so diffuse that it would convey no detail whatever. Even firing electrons (incredibly small wave-particles) at atoms, as when viewing them through an electron microscope, reveals nothing more than somewhat fuzzy looking balls with nebulous lobes. The degree of detail is vastly insufficient for an observer to be able to discern an atom's current internal state-of-being.

To be able to view an atom in sufficient detail to perceive its internal state, it would be necessary to fire at it wave-particles of such high energy that they would them­selves knock the atom into a different state. It would be like trying to view Schrö­dinger's normal size cat, not by shining light on it, but by firing bullets at it and monitoring how the cat's body deflected them. It is obvious that by doing this, the method of observation would affect the cat's state-of-being. They would kill the cat. Consequently, the observer could not know if the cat had been killed by his bullets or if it were already dead before he made his observation.

Same Fallibility of Perception

The cat is an extreme analogy. An act of observation does not necessarily destroy an atom or smash it into pieces. It simply hits it into a higher energy-state. In the general case, the atom acts towards an observer as a message-driven finite state machine. Systemically, the observer sends an interrogative input message: "What state are you in?". If the machine is in its lower state, this act of observation will kick it into its higher state. After a random delay, the machine emits an answer: "I am in my LOW state", which was, and now is again, true.

It could, however, already be in its HIGH state. Countless particles are flitting about all the time, any one of which could, unbeknown to the observer, hit the atom into its HIGH state. So if, on the other hand, the machine were in its HIGH state when the observer's interrogative message hit it, it would not be able to absorb the energy. It would therefore ignore the message. Nevertheless, after an indetermin­able random delay, the machine must naturally return to its LOW state, thereby emitting an output message saying: "I am in my LOW state".

The observer can never receive a message from the machine saying: "I am in my HIGH state". Consequently, the observer fundamentally has no way of knowing what state the machine was actually in when he asked his question.

When the observer receives a message from the machine, he knows that the mach­ine had to expend energy in order to send it. He can therefore reasonably speculate that the machine has a HIGH energy state from which to fall to a LOW energy state in order to liberate the energy necessary to send the message. The observer can therefore reasonably deduce that the machine has (at least) two finite states, even though he can never know when it is in its HIGH state and for how long it has been so.

Is the observer therefore justified in deducing further that, because he cannot per­ceive which state the machine is in at any given time, then it must be in both states at once? Does it make sense for him to assume that, unless or until he re­ceives a message from it telling him it is in its LOW energy state, then it must necessarily be in a superposition of both its HIGH and LOW energy states?

I think not. Just because the actual state of the machine, at any given time, is fun­damentally unknowable by an observer, does not mean that the machine itself, in reality, cannot be firmly in one or other of its mutually-exclusive states. Just be­cause its state is indeterminable by an observer does not necessarily make it in­definite. The superposition of states exists not in what is being observed but within the perceptual model of what is being observed, as etched within the neural net­works of the observer's brain.

For the most part, the observer's conceptual model is completely isolated from the reality it represents. There is no physical connection between them. It is only in the event of the observer engaging in proactive observation that a fleeting connection is established. Even then, the connection is extremely tenuous and fraught with un­certainty. It is like trying to discern what somebody is shouting at you through a very long tunnel. Thus, although the machine may be signalling that it is in a defin­ite state, the observer can have only a quasi-certainty of what state it is now in. Nevertheless, this uncertainty rests wholly within his perceptual model of what he is observing; not at all within the reality it represents.

The fundamental uncertainty in the observation comes not from within the machine itself. It is entirely due to inadequacies in the means through which the observer receives his information about the machine. It is due to a channel of perception which lacks the necessary and sufficient bandwidth and diversity to convey to the observer all the detail he needs to make a complete and thorough observation of what he is looking at. After all, he can never see the object itself. All he is funda­mentally able to observe is an event precipitated by the object's presumed spon­taneous change of state from HIGH to LOW.

When viewing the macroscopic (or normal) world, I see it through my imperfect senses from what is, in most cases, a disadvantageous angle. What my senses give me, I then interpret against my incomplete and inadequate world-view given to me by experiences gained along my own limited path through space, time and the social order. Finally, I communicate my interpretation, through the chokingly narrow error-prone channel of natural language, to my peers, in order to arrive at some consensus view of what we each saw.

When viewing the microscopic (or so-called quantum) world, my frail human senses themselves cannot even see — or in any way sense directly — what I am looking at. The microscopic world is a dark world. It is illuminated by nothing. Even the inst­rument I use fundamentally cannot capture an image of what I am looking at. All it can relay to my senses is an event, which occurs when the thing I cannot see changes state. Even then, it does not emit an informative event for every type of change of state.

I think of it as watching a game of tennis where I can see the ball but not the players. My task is to observe the size, path, velocity and direction of the ball and thereby determine the structure, function and complete nature of the kind of be­ings playing the game. But it gets worse. I can only observe the ball when it acci­dentally hits me and thereby derive the size, path, velocity and direction of the ball from the impact. These difficulties are nothing to do with the nature of what I am looking at. They are due entirely to the enormous limitations of the only channel available to me through which I am able to look at it.

In all the foregoing, I have treated what is being observed as distinct and separate from the channel through which information about it is conveyed to the conscious­ness of the observer. But are they separate? No. By definition, the whole universe is a single integrated entity. Consequently, what is observed and the chan­nel through which it is observed are all part of the same thing. So they cannot be separated physically. They can only be separated in my mind. So what made me consider them as separate?

From Where I am Looking

As an observer, my consciousness, like everybody else's, is trapped in its own sing­u­larity within the space-time continuum. It is a unique prison, which it shares with no other consciousness. This singularity is the apex — the oldest point — within my past event-horizon. Consequently, whatever I choose to observe, at any other point, I can only view through a fallible chain of perception. My consciousness can never physically go there, however close it may be.

The universe bombards my physical senses with inputs. My body converts these inputs into nerve signals, which stimulate my brain. Within my brain, my mind interprets these signals in the con­text of its evolving neural model of the world out­side. This invokes, within my consciousness, an experience of the physical universe.

Thus, the boundary between my conscious self and what I experience lies somewhere within my mind. As a conscious observer, my universe of experi­ence must therefore include my body with its phys­ical senses, my brain and my mind, which may be regarded as the software running within my brain. It is here that the information interface, between my conscious self and the external phys­ical uni­verse, resides. Consequently, I must always regard my fallible chain of perception as an insep­arable part of whatever I am observing.

On this basis, if I set up an experiment to observe a microscopic phenomenon, such as a particle, I must be aware that I am not, in reality, simply observing the be­haviour of the particle. I am, instead, observing the behaviour of the particle, as modified, modulated and corrupted by that part of my observable universe which forms the chain of perception between the particle and my consciousness.

With My Mind's Eye

This is not, however, the way my conscious mind naturally views the world. On the contrary, it thinks it can transport itself to any location, within space and time, and attach itself directly to any phenomenon it desires to observe. If it wishes to ob­serve the state of a particle, it just wraps itself around the space-time occupied by the particle and observes it from all directions at once. It thus tends to ignore the fact that it is trapped at the point-like apex of my physical event-horizon.

As a result, the focus of my interest, and therefore my attention, is the particle alone. I have no interest in — and consequently tend to ignore or forget — all the intervening space, instrumentation, physical senses and mental interpretation that lies between the particle and my consciousness. In my mind's eye, I see only the particle. And so when I observe my experiment, I tend to passively assume that it is only the particle itself that I am seeing.

In my mind's eye, I have an omnipotent view of all reality. I can see directly any thing in any place at any time from any angle. There is no intervening chain of perception distorting or corrupting my view. Thus, in my mind's eye, I see the particle in only one of its mutually-exclusive states. I see Schrödinger's cat as definitely either alive or dead.

This is because, in my mind's eye, I see what is intuitive. And this intuition is an accumulation of my life-long every-day experiences of how things look and behave in the macroscopic world. On the other hand, if I look at the particle with my physical eyes, I see it in a superposition of its two mutually-exclusive states.

What I'm Really Seeing

But what I am looking at comprises not only the particle itself. It includes also the experimental apparatus, instrumentation, my eyes, my brain and the interpretive mechanisms within my mind. And this far more ample finite-state machine seems to exhibit the strange counter-intuitive behaviour we attribute to the quantum world. Like Schrödinger's cat, it has the ability to accommodate a superposition of two mutually-exclusive states-of-being.

In other words, I see Schrödinger's cat both alive and dead at the same time. By definition "alive" is "not dead" and "dead" is "not alive". If A="the cat is alive" and B="the cat is dead" then A=!B and B=!A. If A=!B then what is the meaning of A&B? Clearly A&B=Ø ("nonsense"). It has no meaning. Consequently, what I am seeing, through my physical eyes and the instruments that are monitoring my experiment, is nonsense.

It is well to note that nonsense is not merely counter-intuitive. Something that is behaving in a counter-intuitive manner is behaving in a way that is different from — but not necessarily incompatible with — all that has been previously experienced. A nonsense, on the other hand, is a behaviour which is wholly incompatible with all that has been previously experienced. The superposition of two mutually-exclusive states is a nonsense. But it is what I am seeing, through my instruments, from my experiment.

From this, I could conclude that the subatomic world is so strange that it is beyond human endeavour to make sense of it. On the other hand, I could suppose that perhaps the information I am receiving from the particle I am observing has some­how become distorted during its journey from the particle to my conscious view of it. Perhaps something along the path followed by the information randomly rever­ses its meaning. Sometimes it gets reversed, other times it doesn't.

This random inversion, within the chain of perception, could be a mechanism with a characteristic analogous to sideband dispersion, as experienced with long-distance radio transmissions in the short-wave bands. It distorts the signal, often to the ext­ent of making it unintelligible.

My grandfather was a signaller during the First World War. Once, when he was short of wire, he rigged a signalling circuit using the River Euphrates as the return cond­uctor. He often related the signaller's joke in which a signaller sent the mes­sage "Enemy advancing on west flank; please send reinforcements." The distortion was so bad over the signal path that the receiving operator heard, "Enemy dancing on wet planks; please send three and fourpence".

This emphasises the importance of considering a chain of perception's ability to distort, or otherwise modify, information emanating from what is being observed. Thus, my chain of perception, from the particle to my consciousness, could be arbi­trarily reversing the sense of some of the information it is conveying. It could even be accidentally picking up a statistical spread of indications from many particles. So these perfectly intuitive possibilities could easily turn a sensible original signal into nonsense.

Thus, as with our human perception of the macroscopic world, uncertainty in what we see of the microscopic world is likewise entirely due to the fallibility of our per­ception. There is no tangible reason to suppose that it be in any part due to counter intuitive or nonsensical weirdness in the nature of what we are observing.

Which View is Relevant?

There exists an objective reality, which is both intuitive and sensible. I can see, with my mind's eye, an uninhibited view of this reality. But I can never see it, as it truly is, with my physical eyes. This is because its appearance, as presented to my con­sciousness, has necessarily passed through an intervening chain of perception, which distorts and corrupts what it passes. This applies on both the macroscopic and microscopic scales. On the latter, the distortion and corruption are so bad that the view conveyed is not only counter-intuitive but is also nonsensical.

But which view is relevant: the sensible objective view I see with my mind's eye, or the distorted and often nonsensical view I see with my physical eyes?

On the macroscopic scale, the two views are mostly reconcilable. I may see planets in the sky doing inexplicable epicycles. Nevertheless, within the context of my intui­tive experience, it is not too difficult to transpose their motion, in my mind's eye, into a heliocentric view of simple orbits. Yet, if I think about it philosophically, the epicyclic view of planetary motion is every bit as valid as the heliocentric view of simple orbits. The only difference is in my position as an observer, which is nothing to do with the real structure and behaviour of what I am looking at.

On the microscopic scale, on the other hand, information is carried by perturb­ations within the fundamental force-fields. Consequently, the way I see the universe with my physical eyes is actually the way the universe is affecting me. In fact, it is what the universe is to me. On this scale, from the point of view of how the universe physically affects me, the objective view of my mind's eye is irrelevant. For me, it doesn't exist.

Which of its two mutually-exclusive states a subatomic particle may be in is, and forever will be, unknown, unknowable and irrelevant. It can never dir­ectly affect me. What is real — what directly affects me — is what arrives at me. And that is a particle in a superposition of mutually-exclusive states. What arrives at me — what hits me — may be a nonsense. But in my universe — the universe that I experience — it is, for me, the unique and complete reality.

Notwithstanding, what is real to somebody else — what directly affects him — is also what arrives at him. Suppose that he, at the same time but through different instruments, is observing the same particle that I am. He will inevitably see it as a different instance of the superposition of mutually-exclusive states. What arrives at him — what hits him — may be a nonsense: but it is a different nonsense. In his universe — the universe that he experiences — it is, for him, the unique and complete [but different] reality.

This difference, in our perceptions of the same thing, results from the fact that each of us is observing it through a different communication channel. And our different communication channels will distort and disperse the information arriving at each of us differently. And that is determined by the fact that we are both subject to the universal exclusion principle: it is fundamentally impossible for us both to observe the same thing from exactly the same place at exactly the same time.

The two different views seen by him and me are what are generally said to be sub­jective views. Each view is subject to the time and place from which it is observed. I and he can only "see" an objective view of what we are looking at in our minds' eyes. And these views should be, theoretically, exactly the same. But we can never know that. What we see in our minds' eyes is necessarily an object within — an isolated component of — an observerless universe.

However, an observer, in this sense, is not necessarily sentient and mindful of what he is doing. Any object within — any component of — the universe, that is affected by the rest of the universe, is, in effect, an observer of it — sentient or not. So, there can be no such thing as an observerless universe.

To any observer, no object of his observation can exist in isolation. Whatever may be the observer's object of interest, he must always necessarily consider it as being a mere part of an integral whole, which comprises his object of interest plus the channel of observation through which he is observing it. In other words, any pheno­menon being observed necessarily comprises the object of interest [the particle] plus the channel of perception, sensation and instrumentation that conveys inform­ation about that object of interest into the observer's conscious mind.

This is what makes the universe relativistic. How we see the universe is relative to where we are within it. But please be aware: the act of any particular ob­server, observing an object, in no way changes that object [unless of course his means of observing it is to bombard it with something]. Relative to a different ob­server at a different time or place, the object is bound to appear different. Nevertheless, the object itself is still inherently the same. The relativity is in the individual mind of the observer and in his channel of observation: not in the object itself or its immediate environment.

Fallibility of Thought

So far, I have only dealt, in any detail, with how information gets from the universe into the human mind. But how well does the mind interpret this information and thereby construct a true conscious view of what has been observed? I have already mentioned how the mind uses logic and language to construct a conscious view of what is observed. This conscious view is a working model of what is observed. But this working model is in no sense a comprehensive mental copy of anything in the outside world. It is merely a low-definition symbolic representation of it.

Consequently, the elements of language — words, grammar, variables and opera­tors — are fundamentally different from the physical elements of the external uni­verse, which they represent. They don't even share the same form or behaviour. The lang­uage-borne model of an ob­served phenomenon is simply a framework — a system of classification and relation — by which the conscious mind tries to get some kind of perceptual handle on the external reality it represents.

To explain my view of how the conscious human mind can on some occasions think logically and correctly, while on other occasions thinking emotionally and errone­ously, it is necessary to examine — to at least some limited degree — the structure and functionality of the human mind. Sigmund Freud, the great psychoanalyst, did this in great depth and made his famous "iceberg" model of the human mind. For my purpose here though, I don't need such a detailed analysis. So a much simpler lower resolution model of the human mind will suffice.

My own very simple not-quite-Freudian model of the mind is illustrated on the right.

The sky-blue part, lit by the sun, is my conscious mind. It exists only while I am awake, during which it contains thoughts that are in full view to the conscious "me". This is why it is shown as a daytime scene in the presence of the shining sun.

The darker blue below represents my subconscious mind, which is beyond my conscious view. It accommodates my basic instincts, moral conscience and acquired knowledge. It also drives my instinctive reactions to threats and events from the outside world.

Following is a description of how, after mindful consideration and subject to the falli­bility of my own perception and reason, the various components of the mind, as shown above in my model, appear to me.

My Mindful Self is the conscious "me" as an individual sentient human being. It is able to think logically, provided it remains continually mindful to do so. Mindfulness — concentrating continuously to maintain my thinking rigorously within the Laws of Thought — is absolutely key to my being able to think logically. In this, I must never assume unobserved context. All primary propositions must be fully proven by direct physical observation and correctly qualified as necessary. But where do the Laws of Thought come from? Where do they reside? I don't think the Laws of Thought are naturally and initially hard-wired into my human brain. I think they originated and exist only within my [ostensibly non-physical] conscious mind.

It is only possible to apply the Laws of Thought through mindful deliberation. By so doing, I have been able, through mindful observation and experience of the outside world, to construct my natural and artificial languages. My natural languages are English, which is my mother tongue, and Portuguese, which I acquired later. My arti­ficial languages are mathematics, in terms of which I am able to build my percep­tion of the Laws of Physics and programming languages, such as C, in terms of which I am able to construct logical machines. These languages, and the knowledge they are used to convey, are stored in my subconscious as Learned Knowledge.

I believe that the fundaments of the human Sense of Morality are also built into The Mindful Self. That is, I do not believe that my Sense of Morality is naturally and initially hard-wired into my human brain. Its fundaments of altruism, empathy and love are diametrically opposed to, and wholly incompatible with, the natural hard-wired Human Instinct, which is essentially "red in tooth and claw" like the natural ecosystem and the modern Capitalist socio-economy. However, although its funda­ments be part of My Mindful Self, I needed to apply them mindfully to construct, within my subconscious memory, My Moral Conscience. This comprises the codes of Good Manners and Benign Behaviour which I must apply continually in my inter­personal encounters and relationships.

Human Instinct is, at least in part, the anithesis of The Mindful Self. Initially, it contains only The Gaian Protocol. Gaia is a name used, by way of literary licence, to personify the Earth's biosphere, as a means of bringing it into sharp focus within the reader's mind. The Gaian Protocol is a set of subconscious reactive procedures, designed by nature, to protect the human life-form and enable it to survive by responding appropriately to the behaviour of its designated niche within the terre­strial environment. Gaia is essentially "red in tooth and claw". I believe that the Gaian Protocol is pre-installed within the human mind. It is probably hard-wired into the human brain. Notwithstanding, the pre-installed version of the Gaian Protocol can become modified, augmented or even perverted by external influences. It can passively acquire, through experience, new operational and defensive skills. It can also, by way of The Mindful Self, have etched into it, through training, protocols that would appear to be dangerously counter-intuitive.

The Auto-reactive Subconscious receives sensory inputs from the outside world and reacts to them instantly and unilaterally, without consulting the Mindful Self. This occurs when the Auto-Reactive Subconscious senses a mortal danger that's so immanent that there is simply no time for The Mindful Self to consider the situation. A prime example of this occurred during World War II when my father, who was about to blow up a bridge, subconsciously threw himself to the ground to avoid what would have been a lethal burst from a German machine gun.

My Reactive Self — like my Mindful Self — is part of my conscious mind. I tend to think of it as my Mindful Self's poor relation. This is because, unlike my Mindful Self, it does not make deductions according to the logical Laws of Thought, but rather according to emotionally driven instinct, which is inconsistent with the logical Laws of Thought. The conscious "me" always defaults back to Reactive Self mode from Mindful Self mode whenever "I" cease or fail to deliberately concentrate on thinking logically. This is why I think that the Laws of Thought are seated in the conscious­ness and not in the brain. The Reactive Self, driven by the human instinct, is in control for most of the time. It is indeed rare for a human to think mindfully. The Reactive Self is king.

The greatest example of the Reactive Self in action is the socio-economy. Practically all decisions relating to my purchase of consumer goods are taken by my Reactive Self. I buy what looks the most saleable from the most well-known household name. I do this even though I know that the well-known household name will manufacture the product to last as close as possible to just after the statutory warranty period. Then I'll have to go out and buy another one. I cannot repair the product because it will be design so as to be as awkward as possible for a user to repair without pro­prietary tools and the necessary parts will not be separately available.

Perhaps I don't consider my purchases logically because to do so would be futile. I do not have the time or means to investigate which products are good, if any. And I suspect that magazine reviews are kind to who are obviously their paying advert­isers or back-handerers.

On the other hand, it would be well possible to make the same consumer product in a way that would enable it to last indefinitely and also be easy to service and repair. But the manufacturer of such would not stay in business very long in competition with the well-known household names. So I must continue to allow the well-known household names to 'rip me off'. I have no power to change this unilaterally. All the well-known household names are vastly more powerful than I am. Each follows a blind strategy of maximizing its profit by maximizing its revenue and minimising its costs. The rules governing a human socio-economy do not limit this maximizing. In other words, there is no negative feed-back mechanism within human instinct. It is simply driven by the raw emotion of greed. The ramifications of this behaviour — accelerating disparity, the imposition of austerity, abject poverty, economic instab­il­ity [boom/bust] and violent social insurrection — aren't logically considered.

Perhaps, driven solely by the raw emotion of greed, those with power simply don't care about their hapless underlings — any more than would a fox in a hen pen. In my considerable experience, the vast bureaucracies and institutions of the modern state also exhibit the psychopathic characteristics of the Reactive Self.

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It is clear from what I have said above, about my view of the human mind, that I see The Laws of Thought and all that is derived from them or through them as hav­ing existence only within the conscious "me" and that they are not founded upon any hard-wiring within the human brain. On the other hand it is also clear from what I have said above, that The Gaian Protocol [or Human Instinct] is hard-wired into the human brain and that all that is derived from it or through it is stored within the subconscious human memory within the brain.

This construct is similar to the Duality Belief that the human being is not exclusively physical, but comprises a physical body and a non-physical soul. To some people, this raises the notion of what I call The God Problem. Religious people may believe that the existence of this 'soul' predicates the existence of what they conceive of as God. However, the non-physical essence within the human consciousness, that ac­com­modates the Laws of Thought and The Moral Conscience, could simply be some kind of universal field of intelligence, like that known to ancient Greek philo­sophers as the Λóγoς [Logos]. Al­though undetectable by human sense or instrument, this field would nonetheless be part of the physical universe.

A corollary to this is that, since what is hard-wired into the human brain is illogical emotion-driven human instinct, then the brain itself cannot be a logical machine. Indeed, all its output, which is not mindfully orchestrated, certainly appears to be illogical. One may cite that neural networks, which are used to construct so-called artificial intelligence, are programs that run on a computer, which is definitely a logical machine. But many types of non-logical mechanism are simulated by com­puter programs. Neural networks are just one of them.

Of course, a multi-layer perceptron, as in the above diagram, could be im­plemented directly as a set of interconnected electronic neurons mounted on a physical printed circuit board. However, it has proven to be quicker and more convenient to implement it as a program in a digital computer.

The Human Brain is an analogue device, comprising a network of around 86 × 10⁹ neurons, which are also strictly analogue devices. It operates according to the Laws of Physics, using weighted networks to construct working analogies of structures and behaviours in the outside world. So unlike a digital computer, neither its struc­ture nor its functionality is based on Logic. It should therefore be no surprise that neither the human brain, nor the basic instinct it embodies, is logical.

Digital computers are frequently deployed to simulate analogue devices. In the late 1960s, I wrote digital computer programs to simulate analogue computers used for flight direction and navigation in aircraft. However, in the case of the human brain, it's the other way round. The brain is a vast analogue device that simulates a logical phenomenon; namely, the Mindful Self, which operates according to the Laws of Thought.

The human brain, as depicted above, is an astronomically large version of the Multi-layer Perceptron, as shown in the previous diagram; except that the human brain comprises of the order of 86 × 10⁹ neurons instead of only 9. Furthermore, a human brain contains many different network architectures: not just that of the perceptron.

The 'digital' [or rather 'logical'] mechanism that is implemented within the human brain is what I have called The Laws of Thought. My perception of these is that of an analogue program, within the brain, that implements a digital soft machine core through which the conscious mind can implement human cultural languages like English, Portuguese and Russian; artificial languages like Esperanto and Lojban and definitive/imperative machine languages like 'C', Ada and Java.

I cannot see how the Laws of Thought could be hard-wired into the human brain biologically. My reluctant conclusion is that they must be induced in some myster­ious way by this intelligence-bearing all-pervading æther, which the ancient Greek philo­sophers referred to as the Λóγoς [Logos]. On the other hand, I imagine that the vocabularies, grammars, operators and variables of cultural, artificial and 'machine' languages reside as objects and functions that are modelled analogically within the neural networks of the brain.

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The reason behind the above brief excursion into the structure and workings of the human mind has been to give focus to The Mindful Self. This is because it is the only part of the human mind that is relevant to the processes of perception and reason. Thus, for the purpose of the remainder of this essay, we can set aside consideration of all the other parts of the human mind. It is The Mindful Self exclusively that drives and manipulates the Objects of Thought.

The Objects of Thought, namely words, are not the objects to which they refer. They are merely labels: tenuous attempts to represent real objects symbolically. And the laws of thought, namely grammar, are not the laws which govern the physical uni­verse. They are merely the linguistical rules which link words together into a sem­antic structure that represents the apparent form and behaviour of the universe.

Even the formal processes of symbolic logic and probabilities are merely an artificial [as opposed to a natural] language, which operates according to the same Laws of Thought: not the Laws of Physics. I have already mentioned mathematics above as one of my artificial languages, along with programming languages such as C. But isn't mathematics the very core mechanism upon which the universe operates? Doesn't mathematics actually define and embody the Laws of Physics?

What About Mathematics?

Isn't mathematics the underlying fundament according to which the physical uni­verse operates? Consider two established scientific observations:

Newton's "law of acceleration": F = M × a and
Newton's "law of gravity": F = G × M₁ × M₂ ÷ r².

Are these not solid objective realities? If so, then we can complete this notion by asserting that the mathematics of the Theory of Relativity be the underlying reality that becomes manifested to our physical senses as the material universe. Equally, however, we could make the same assertion about the mathematics of the Stan­dard Model of Physics.

Notwithstanding, we know that, although the Theory of Relativity and the Standard Model of Physics are pretty good descriptions of different aspects of the physical universe, they are, nonetheless, mutually incompatible. How can two incompatible mathematical models be the real underlying fundament of a single universal real­ity? They can't. They are merely symbolic representations of our respective percep­tions of our macroscopic and microscopic views of the universe. And a symbolic re­presentation is merely a language.

The Theory of Relativity and the Standard Model are nothing more than essays, written in the language of mathematics, which are mankind's best macroscopic and microscopic perceptions of the real universe.

Mathematics is strictly a language. As such, it has existence exclusively within the perceptive mechanisms of the human mind. It is not a real underlying framework upon which the universe itself is built. It is merely a mental framework by which hu­man consciousness tries to get a handle of understanding on the reality of the out­side universe. The real underlying force which drives the universe, and the laws which govern it, are something else. These are unknown to us and will most likely forever remain fundamentally unknowable.

Hierarchy of Operators

The universe does not contain hierarchies. It has — as far as it can be seen — what could better be described as a fractal nature. Hierarchies are structures of human language, used to categorise and classify what we observe, as an aid to making some sense of what we observe. Thus, mathematics has the structure and behav­iour of a language: not of the physical universe it tries to describe.

Consider Newton's "law of acceleration": F = M × a. It has letters which represent the values of three different measurable quantities. It then expresses an observed relationship between these by means of two symbols: = and ×, which represent the relational operators of equality and multiplication. Equality [=] is a fundamental op­erator. Multiplication [×], on the other hand, is a composite operator. It can be broken down into a component structure. It can be replaced by a more complex expression using only the addition operator [+], which is more fundamental than the multiply operator [×]. An example of how this can be done is the following program snippet, which is in C-notation:

F = M; for(i = 0; i < a; i++) F += M;

Of course, this snippet, as it stands, only works if F, M and a are numeric integers: that is, whole numbers of newtons, kilograms and metres per second per second. Notwithstanding, each can be represented by a 64-bit register to whatever fraction­al precision may be required for a practical calculation. The upshot is that any hu­man observation of an observed natural quantity [such as F, M or a] can only ever be expressed in terms of a radix-based system of numbering such as decimal, hex­adecimal or binary. These can never express completely the continuously-variable values of the natural quantities which they attempt to represent.

I have already shown that even the more fundamental addition [+] operator is a composite of logical operations "=", "&", "|" and "!", such that:

A + B ≡ Digit{(A | B) & (!A | !B)} Carry{A & B}

Thus, in the ultimate analysis, it would be possible to express any known Law of Physics in terms of the fundamental logical operators "=", "&", "|" and "!", including all those involving multi-dimensional mathematical operators like grad, div and curl.

These fundamental logical operators, in terms of which all observed physical law can be expressed, are not the ultimate components of the real laws which govern the universe: they are the ultimate components of what George Boole called the Laws of Thought. They are the ultimate fundaments of language. And language has existence exclusively within the conscious mind. Consequently, although language enables the mind to discern the form and behaviour of the universe, it is not, in any sense, the framework of objects and rules upon which the universe itself is built and by which it is driven.

Logical Machines

What about logical machines: computers? These expedite processes, according to the laws of logic, independently of the human mind. They contain circuits com­p­rising components which perform the logical operations "&", "|" and "!". These, in turn, execute programs, which comprise sequences of logical imperatives written as statements of a programming language such as 'C'. Doesn't this behaviour of a mindless machine, constructed entirely of physical material, evince the presence of the Laws of Logic within the material universe?

The materials, of which the most basic components of a computer — its transistors, capacitors and resistors — are made, behave according to the real laws of the physical universe. By observation, science has abstracted and expressed in the language of mathematics, the observed laws and properties which these materials exhibit. Engineers have then used these observed laws and properties to design an order in which to put these materials together to build the transistors, capacitors and resistors with which to construct a computer.

Others then assemble these components into circuits which they design to perform logical operations in the same way as those logical operations are reasoned within the human mind. Thus, the logical functionality of a computer does not come from the observed laws of physics. It comes from the observed laws of thought. And it is put into the computer's circuits by engineers: not by nature.

The materials, of which the transistors, capacitors and resistors are made, could be thought of as bricks. They behave according to the observed laws of physics. The logical functionality of the computer, on the other hand, is a palace built of bricks. The design of the palace is much more than the design of its bricks. The design of the palace came from the mind of the architect: not from the bricks. Another useful analogy is pen and paper. The laws of thought, by which the mean­ing conveyed by words written on a piece of paper are encoded, are nothing to do with the laws which regulate the physical and chemical composition of the paper or the ink, nor even with the laws that govern the mechanics of writing.

Abstract Identities

The languages of Logic and Mathematics are only known to exist within the human mind. They have no tangible counterparts in the outside universe. But can — do — mathematics and logic contain entities that are inherently self-existent: that exist within the human mind but independently of it? What about such things as Euler's Identity?

e^iπ + 1 ≡ 0

This is a grid-locked relationship between what are called universal constants. Two of these constants are the integers 0 and 1 — the only two mutually exclusive val­ues which a logical variable may have. The constants e and π are transcendental numbers, which can never be represented exactly by any numbering system based on an integral radix such as 2, 8, 10, 12, 16. And i = √(−1), a number so bizarre that mathematicians call it "imaginary". Yet these five unlikely bedfellows form the above immutable relationship, which seems to relate logic with multi-dimensional dynamic geometry.

Euler's Identity is not a convention agreed by mathematicians. It just is. As such, it appears to have an existence in its own right. But is it representing something that exists in the physical universe? Or does it merely exist as a semantic construct en­tirely within the human mind? To answer this question, we must examine its com­ponents.

The Exponential Constant e

e≈2·718281828459045 is known as the exponential constant. Consider an object that is continuously shrinking. The rate at which the object is shrinking, at any given instant, is proportional to its volume, at that instant. Its rate of change of volume: (dv/dt)=−kv: its current volume v times a constant of proportionality k, which is called the object's rate of shrinkage. To calculate what its volume will be, after any given lapse of time after you started to observe it, you need to "solve" the differ­ential equation (dv/dt)=−kv for the amount t of time that has elapsed. The math­e­matical "solution" is shown below.

The original differential equation:	(dv/dt)	= −kv
Divide both sides by v and multiply by dt:	(1/v)dv	= −kdt
Integrate both sides of the equation:	∫(1/v)dv	= −k∫dt
Result of integration: [ln=logarithm to base 'e']	ln|v|	= −kt + c
Make both sides of the equation powers of 'e':	eln|v|	= e−kt+c
e to the power ln(number) is simply the number:	|v|	= e−kt × ec
e to the power of a constant is another constant,	so let C	= ec
So the volume of the shrinking object at any time t:	v	= C × e−kt
Evaluate this expression for when t = 0:	v0	= C × e−k0
Any number raised to the power of zero = 1	v0	= C × e0
So C is simply the initial volume when t = 0	v0	= C × 1
So the volume of the shrinking object at any time t:	v	= v0 × e−kt

A practical example of a "shrinking object", in the above context, is water flowing out of a barrel. There is an open tap in the side of the barrel near the bot­tom. Water is emptying out of the barrel through the tap. The rate at which the water flows through the tap, at any given instant, is propor­tional to the pres­sure pushing the water through it. This, in turn, is proportional to the head of water above the tap at that instant, which, in turn, is proportional to the vol­ume of water left in the barrel, at that instant.

From the above analysis, it is easy, at first sight, to suppose that the transcend­ental constant e plays some fundamental role in the dynamic process of a shrinking object whose rate of shrinkage, at any given instant, is proportional to its actual volume at that instant. In other words, it would appear to underpin the real-world mechanism that conducts the shrinking process. But it doesn't.

The universe is not a static object. Neither is it a series of static frames like a movie. It can only exist in a dynamic state. It is a continuous on-going event. You cannot freeze-frame the universe, or indeed, any part of it. Time is a flow. It cannot be stopped. So-called "points in time" are a construct of human consciousness. We can conceive of them only because we possess the faculty of memory from which we can consciously recall semantic representations of past events.

Consequently, the notion of an amount or lapse of time — a number of seconds, minutes or hours — exists only within the human mind. A standard time reference, such as Greenwich Mean Time [GMT], is even more a notion that can exist only within the human mind. The universe makes no reference to GMT or any other artificial time standard. Such standards, or systems of reference, measure what is conceptually a "distance" through time. It is this "distance" that is measured in seconds, minutes and hours: not time itself. This is because the reality of time is a rate of flow. It is a universal rate at which we pass through seconds, minutes and hours. And this rate of flow cannot be measured against anything because it is the most fundamental property of the real universe. It is the ruler against which every­thing else must be measured.

The upshot is that the so-called "solution" to the differential equation (dv/dt)=−kv is not the fundament. The dynamic process represented by the differential equation is the fundament here. The so-called "solution" v=v₀e^−kt is a notion which exists only within the human mind, as a result of its possessing the faculty of memory with which to recall what the situation was like at various "points" in the past. And these "points" are nothing more than snap-shots stored in the memory as the real time in the outside universe relentlessly flows onwards at its immutable rate.

The differential equation (dv/dt)=−kv is, an albeit imperfect, representation of what is taking place in the real universe. Its solution v=v₀e^−kt shows a view in which time is frozen: a thing which, in reality, cannot exist: a thing which can only be const­r­ucted within the human mind by virtue of human memory. The constant e is a component of the "solution" and not of the "problem". Consequently, e pertains not to the real world but to how the human mind perceives the real world. It is a natural universal constant relating to the mechanism by which the human mind tries to get a handle of understanding on what is taking place in the real world.

It appears that the human mind is best able to perceive a dynamic real-world phen­omenon as a static representation, comprising a series of freeze-frame views ext­ending over a prescribed period. In other words, as a time-graph in which, what is perceived as an extent of time, is represented by a physical distance on a piece of paper or monitor screen. Such a static representation is therefore nothing more than a mental template against which the human mind is able to recognise the phenomenon.

Representation, in this form, of a natural phenomenon in which the rate of change of something is proportional to the current instant magnitude of that something, is a curved time-graph x = x₀ × e^−kt, where x₀ and x are the initial and current mag­nitudes of that something, t is the amount of time that has elapsed since observa­tion of the phenomenon began, k is a constant of proportionality and e is the trans­cendental constant.

Notwithstanding, you cannot, in reality, stop the flow of time. Time is a flow. All natural phenomena are, however still they may appear, dynamic. They all involve continuous motion of some kind. Consequently, the real mechanism of nature, which is driving what we are observing, is very simple. It can be more truly repre­sented by the equation: x' = −k × x, where x' represents the rate at which x is changing and k is a simple constant of proportionality. No mysterious transcend­ental number is involved in the real-world phenomenon.

The transcendental constant e is thus part of the grammar of the symbolic langu­age of mathematics, through which we try to get a perceptual handle on certain phenomena we observe in the outside universe. As such, it has real existence and significance exclusively within the human mind.

But what about the dynamic representation of the phenomenon: x' = −k × x. Is this the law that underlies the reality? Not exactly. It gives us a statistical view — an overall view — of what appears to be happening. As such, it is much more a representation of the real universe than the time-graph equation. But this does not mean that this mathematical representation is the underlying motivator of the real phenomenon.

The reality of a phenomenon comprises interactions between nanoscopic entities on a nanoscopic scale. Each such entity interacts with each of its neighbours accor­ding to a particular protocol. This protocol could be simple. Or it could be an inter­action of complex-dynamical states. Nobody really knows. However, the result of all these zillions of interactions, between zillions of nanoscopic entities, gives macro­scopic beings like us a macroscopic view we see as representable by the equation x' = −k × x. But the idea that this equation represents what nature is really doing is an illusion. It too is a mere template, which the human mind sees as fitting snugly around the large-scale effect of a real but unknown relational protocol operating on the nanoscopic scale.

According to what is considered to be pure mathematics, the solution to the differ­ential equation x' = −k × x, namely, x = x₀ × e^−kt is arrived at by considering an infinite number of infinitesimal advances in time. This is considered by many to be the ultimate purity of what is really driving the universe. Notwithstanding, it is evi­d­ent that, at least in the case of the water emptying from the barrel mentioned above, the real mechanism involves zillions of discrete encounters between finite water molecules. Consequently, the reality cannot be the infinitely smooth cont­in­uum depicted by the mathematical solution x = x₀ × e^−kt. It's much more like the iterative jumps of the numerical methods for solving differential equations.

Solutions to differential equations, which involve transcendental numbers and con­t­inuous functions, are considered to be the pure and beautiful work of mathemat­i­cians, which show us how nature really works. Numerical solutions, on the other hand, are considered to be crude "suck it and see" methods used principally by engineers for getting approximate solutions for designing their machines, systems and devices. To my mind, these ideas are the very opposite of the truth.

The beautiful solutions of the mathematicians apply to only a very few special cases. The vast majority of differential equations that represent the behaviours of natural phenomena can only be "solved" by numerical methods anyway. But all cases are equally real. The only generic methods for solving differential equations are therefore necessarily numerical. The key to accuracy is not to use the continua of pure mathematics but to use iterative steps which are as small as the ones nature uses. Of course, for some phenomena, this might involve using steps in time and space as small as the Planck interval [if it really exists], which is problematic.

Notwithstanding, whatever mathematical methods are employed, they are all mere templates, used by the human mind, to try to make sense of what we see; to try to classify or categorise our observations. It's just that the "crude" numerical methods are a bit closer to the way nature actually creates what we see.

The Circular Constant π

A circle is a mental concept. It is constructed, mentally, by moving a fixed-length radial angularly through a com­plete turn within a fixed plane. The ratio between the distance round this mental construction [its circum­fer­ence] and the distance across it [its diameter] is a tran­s­cendental number which mathematicians represent by the Greek letter π. Although π has an approximate num­er­ical magnitude of 3·14159265358979, its true magni­tude, fundamentally, can never be computed exactly in any numbering system with an integral radix.

As a component of the human language of mathematics, π indisputably exists. As such, it can be used, quite effectively, to refer to certain aspects of the shapes of real objects in the outside universe. Thereby we can perceive that many objects in the universe — such as stars, planets and orbits — have a tendency towards roundness. To a somewhat lesser extent, so do objects on Earth, such as trees and flowers.

Notwithstanding, nature does not construct circles — either absolute or approxi­mate — by rotating fixed-length radials through complete turns within fixed planes. On the contrary, nature constructs what we perceive, on the macroscopic scale, as circular characteristics or roundness through what I would call fractal laws or pro­to­cols operating — bit by bit — on a nanoscopic scale.

The real laws of nature, which govern the motion of a planet moving in a circular orbit, are 'unaware' of the concept of a circle. Nature does not consider a circular orbit to be any more significant than an elliptical, parabolical, hyperbolical or rosette-shaped orbit. Indeed, these are all special cases of the mathematically in­expressible meandering orbits encountered in the so-called many body problem of a star wandering through a well populated galaxy.

As far as nature is concerned, a body's path through space is determined entirely by local irregularities in the aetherial flux within the space through which it is pas­sing. Large scale special case notions like circles, ellipses, parabolas, hyper­bolas and rosettes, are mere geometrical templates used by the human mind to try to differentiate between variants of the general case.

Space Within The Mind

These templates are, for most people, based on Euclidean geometry. Euclidean space is a mental frame of reference. And a frame of reference must have an origin, which is the coincident zero-point of the three mutually perpendicular axes. Every place in Euclidean space is defined in terms of its relationship to [distance and direction from] an origin. An origin thus comprises a favoured point and direction in Euclidean space. It is where the observer is located. It is the point at which his con­sciousness is seated: his point of view. So Euclidean space is space which occupies an observer-centred frame. But it is not real space: it is imaginary space, which helps an ob­ser­ver to create a perception of real space.

Within the Euclidean space of his imagination, an observer can construct abstract geometrical objects like lines, circles, ellipses, parabolæ, hyperbolæ, spheres, tet­ra­hedrons, cubes, dodecahedrons and various hybrids of these. He is able to view, scale, translate and rotate them within his mind and thereby use them as gauges to categorise by shape whatever he sees within the outside universe. These geo­metrical structures are what may be regarded as complex nouns or sub­stantives of the geometrical subset of the language of thought.

These somewhat analogical substantives can be represented or symbolised by the language of mathematics. Lines, circles, ellipses, parabolæ, hyperbolæ, spheres, etc. can be represented, within a Euclidean frame of reference, by mathematical formulæ comprising symbolic constants, variables and operators. And π is one of those constants. As such, it pertains to the Euclidean space of the imagination: not to the real space of the real universe. Thus, it is not a property of real space: it is part of an imperfect language in which an observer thinks about real space.

Here within the Earth's biosphere — the environment within which the human mind was developed — the plane and 3-dimensional geometries of Euclid provide a good set of perceptual templates against which to measure and make sense of what we see. But once we look outwards to the stars, it doesn't seem to work quite so well. A more sophisticated template is required.

The relativistic space-time of Einstein provides a more sophisticated template for the vast scales of the stars and galaxies. The geometries of Quantum Mechanics provide a more sophisticated template for the nanoscopic scales of atoms and fun­d­a­mental particles. Yet neither of these is perfect and they are themselves mut­u­ally incompatible. So they cannot be reality. Nor can they represent reality absolutely.

Real space-time, whatever it may be, is not Euclidean. Neither is it Einsteinian nor is it Bohrian. All these are instruments of human perception which exist solely with­in the human mind. The only way we can even express or conceptualise Einsteinian or Bohrian space-time is in terms of our crude Euclidean concepts of space and time. The mathematical constructs of Einsteinian and Bohrian space-time are built of Euclidean conceptual components. The so-called natural constant π is one of these. It is a constant of Euclidean space, which is a thing of the mind; not of the objective reality that is thought to lie beyond the mind in the external universe. Thus π cannot be other than an element of the Laws of Thought.

The circle — and the relationship between its diameter and circumference, π — are very special to Euclidean space. Notwithstanding, the circle is neither here nor there in real space-time. A planet moves in relation to a star in what our minds can only conceptualise as an infinitely fine incremental fashion with the flow of time. The shape of what we perceive as a complete orbit is irrelevant. The chance of it being circular is almost zero. Even the chance of it being elliptical, parabolic, hyper­bolic or even rosette shaped is pretty well equally remote. Any orbit is, in reality, always irregular and meandering: never closed. None of these conceptual geo­met­rical shapes even so much as forms a dynamic attractor for an orbit. Thus π has no part in external reality. It is a property of the way we think and imagine.

The Confabulation of Memory

Our human memory is absolutely indispensable to the process of thought. As such, in considering anything, it has the status of the Prime Axiom. It is assumed. It goes without saying. It is the universal container of our thoughts, knowledge, information and wisdom. It cannot be viewed against, or in terms of, anything. It is our baseline frame of reference. To us, memory is everything. It is — and always has been — essential to our life and survival within our terrestrial environment.

The universe, on the other hand, doesn't have a memory. Because it doesn't need one. Because it has no past or future. It exists solely within a continuously-changing instantaneous present.

A consequence of our human memory is our natural concept of time. Because we remember past events, we see what appears to be an unfolding of history from the past to the present as a static display which we can examine at will. And by seeing the manner in which this unfolding takes place, we can extrapolate this manner or behaviour in order to predict the shape of things to come — our future. This, in turn, gives us a basis for making beneficial decisions and taking the constructive actions necessary to ensure our survival and well-being.

And this has shaped our notion of time. We perceive of time as a period, which we measure in years, months, days, hours, minutes and seconds. But this is not the way the universe 'perceives' time. To the universe, the essence of time is not a per­iod. Rather, it is a flux or flow. It is a rate of change. It is one order of differentiation beyond what we perceive as time.

But with respect to what can you differentiate a period of time? In other words the flow of time is dt/dw, where w is what? Well, nothing. Because the notion of time-flux is the base-line absolute of which we, as humans, are mentally ill-equipped to conceive. The best way I can come up with to think of it is that a period of time is the integral of the rate of passage of time. And the rate of passage of time is the most fundamental universal constant.

By way of example, consider an astronomer looking through his telescope at Mars. He notes the elevation and right ascension at the same universal clock time every night for several years. He then applies the necessary mathematical calculations to transform his observations to a heliocentric view. And lo, he declares to the world that the Planet Mars moves around the Sun in an elliptical shaped orbit.

But an ellipse is a shape that can be expressed as a mathematical formula. Conse­quently, he deduces that the mathematical shape, which was first constructed by using something like a pencil constrained by a loop of string wrapped around two separated pegs, has an independent existence out there in space and is acting as a physical law that is somehow driving Mars around its orbit in this particular way.

So, do the Laws of Mathematics, which I have asserted to be solely a subset of the Laws of Thought, therefore also independently underpin the Laws of Physics? No. Our astronomer, like so many, is a victim of the Confabulation of Memory.

More rigorous observation and deduction persuades us that the orbit of Mars is more complicated than just a simple ellipse. It is a precessing ellipse that traces out a rosette shape when viewed from 'above'. But how many petals does the rosette have? Well, in fact, the rosette isn't even closed. Mars continues on its orbit ad infinitum without ever re-tracing its path. Its orbit is forever open-ended. Further still, the precessing ellipse is modulated continually and unrepeatedly within its orbital plane with a melody of very small perturbations caused by the 'gravitational' influence of every other body in the universe. So it's a distorted ellipse: a somewhat ragged open-ended precessing rosette.

Consequently, although the exact orbit of Mars be deterministic, it appears to us, at its ultimate depth, to be chaotic. Thus it falls into the realm that goes under the misnomer of Chaos Theory, which is more correctly termed Complex Dynamics. As such, it is too complex to be specified completely in terms of our fit-kit of concepts known as the Language of Mathematics.

So let us take a step back and ask: what is the astronomer really seeing when he is looking at Mars through his telescope? He is seeing Mars — all on its own in space. But he sees no orbit. There's no ellipse out there. There isn't even a distorted ellipse or ragged open-ended precessing rosette. There's nothing.

Mars is simply there on its own in space with no strings attached. From there it takes its next infinitesimal step through space relative to all other bodies in the universe. I believe that this step is driven by the magnitude and direction of the vector resulting from the asymmetry in the divergence of the universal time-flux extant within the space currently occupied by the planet.

My conjecture is that this process is governed by a universal mechanism, which our natural human mindset can only perceive as a kind of fractal Law of Physics. The mechanism acts in infinitesimally small jumps within the immediate vicinity of the planet. But these 'infinitesimal' jumps don't just tend towards zero: they are zero. In other words, the mechanism acts within a pure continuum. The cumulative effect of its action, in the long term, within its universal environment, is the distorted ellipse or ragged open-ended precessing rosette that we observe.

The orbit of Mars is thus an object that exists solely within the observer's memory. It was constructed: through deductions made according to the Laws of Thought, from measurements made with reference to the human-decided datums of time, angle and distance from the observer here on Earth. Thus the universe itself isn't mathe­matical in any conventional sense.

The Complex Operator i = √(−1)

The square of plus one is plus one: (+1)² = +1. So, conversely, the square root of plus one is plus one: √(+1) = +1. But the square of minus one is also plus one: (−1)² = +1. So what, when squared, gives minus one? In other words, what is the square root of minus one? It can be neither minus one nor plus one. Of course minus one × plus one gives minus one: (−1) × (+1) = −1. But minus one does not equal plus one: (−1) ≠ (+1). Consequently, neither can be the square root of −1. So the square root of minus one would appear to be an arithmetical paradox.

NOTE: The cause of this paradox is the arbitrary human convention that, while negating a positive produces a negative: −(+1) = −1, positivising a negative does not produce a positive: +(−1) ≠ +1. Thus positive and negative numbers are not logically symmetrical. And an arbitrary human convention is a thing of the mind: not of objective reality.

A clue to the meaning of the square root of minus one is in the fact that it gives the same arithmetical result as minus one × plus one: {√(−1)}² ≡ (−1) × (+1). This suggests that, conceptually, it is mid-way between minus one and plus one. On a scale of pure numbers, that would make it zero. But zero × zero does not give −1. So √(−1) must be mid-way between +1 and −1 in some other sense.

However, as well as being mid-way between +1 and −1 in some sense or another, √(−1), by reason that it produces a result of unit magnitude, must itself have unit magnitude. In other words, although its magnitude be neither +1 nor −1, its mag­ni­tude must — in some other peculiar sense — be 1. But how can this be? How can a number be half-way between +1 and −1 and also have unit magnitude?

If √(−1) indeed be mid-way between +1 and −1, it must have a zero magnitude on the scale of real numbers. Notwithstanding, it could have any finite magnitude along any dimension perpendicular to the scale of real numbers. Consequently, we may conceive of √(−1) as having a unit magnitude on a scale of imaginary numbers that extends along any dimension that is perpendicular to that con­taining the scale of real numbers. Since this scale of imaginary numbers be perpendicular to the scale of real numbers, it follows that the magni­tude of an imaginary number must be independ­ent of magnitudes along the dimension containing the scale of real numbers.

At college, I studied complex numbers [which are 2-dimensional] in one class and vector analysis [which is 3-dimensional] in another class. I always wondered if perhaps the imaginary axis should be a plane which could be used to construct a means of expressing aspects of gyroscopic phenomena, which were little-understood.

Mathematicians represent √(−1) by the letter 'i'. Electrical engineers represent it by the letter 'j' so as not to confuse it with 'i' representing electric current. Thus i² = −1. So 'i' can be conceived as a unit distance along an im­aginary dimension (or line) which progresses at right-angles to the linear dimension (or line) along which we represent real numbers in terms of unit dist­ances.

I have already considered −1 × +1 = −1. Now, what about −i × +i? Well, this is the same as (−1) × i × (+1) × i = (−1) × (+1) × i² = (−1) × (+1) × (−1) = +1. It would thus seem that multiplying a number by +i has the effect of turning it through a right-angle in an anti-clockwise sense, while multiplying a number by −i has the effect of turning it through a right-angle in a clockwise sense. Multiplying a number by +i twice effectively turns it through 180°, which is the same as revers­ing its sign.

Multiplying any number by 'i' does not alter the magnitude of the number. Instead, it changes the number's dimensional or geometrical relationship to other num­bers or magnitudes. Consequently, rather than thinking of 'i' as a number, mathe­matic­ians tend to classify it as a mathematical operator like + − × ÷. This complex operator is used a lot in mathematics, science and engineering, especially to re­present the dynamic relationships between parameters such as voltage and current in both power and radio frequency devices.

But does this mean that 'i' is real? Is it a fundamental element of the external ob­jective reality we refer to as the universe? Or are imaginary numbers also a figment of human imagination?

Perhaps the most practical use of the complex op­erator is in the graphical representation of rela­tionships between the alternating current and vol­t­age in reactive electrical circuits and the electric and magnetic vectors of waves propaga­ting thro­ugh space-time. The adjacent animation shows the dynamic relationship between the elect­ric & mag­netic field vectors of the classical electromag­netic wave as it is passing an observer on its journey through space. One could re-label the axes Voltage and Current to represent the dynamic relation­ship between the voltage and current in an elect­rical circuit containing capacitors and inductors.

Such relationships are dynamic. The phenomena only exist within space and time. If you could, in reality, freeze-frame such a phenomenon, it would collapse instantly into nothing.

Of course, you can draw a static graph showing a freeze-frame representation of the phenomenon at any arbitrary "point in time". Notwithstanding, such a static representation is solely for the purpose of helping the human mind to get a handle on a difficult-to-grasp dynamic phenomenon. But this kind of representation is an entirely artificial notion. It represents a situation that cannot exist in reality.

The complex operator 'i' [or 'j' for electrical engineers] is part of a symbolic means of representing both dynamic animations and static snap-shots of these phen­o­mena algebraically on paper. As such, it is part of a mathematical language used by the human mind to express and manipulate human perceptions of these natural phenomena. Thus 'i' too is a thing of the mind: a participant in the laws of thought. It is not an element of an implied external objective reality we call the universe.

Euler's Identity: e^iπ + 1 ≡ 0

This interlocking relationship between the logical integers '0' and '1' and the so-called natural constants 'e', 'π' and 'i' appears, at first sight, to have tangible exist­ence within the implied objective external reality we call the universe. Notwith­standing, I have shown above that its component elements are all merely part of a linguistic template by which the human mind enables the conscious 'self' to get a handle on that implied objective external reality we call the universe.

And if this be so regarding Euler's identity, then it is probably true of the more com­plex and sophisticated objects which exist within the universe of mathematics such as the beautiful and extensive Monsters of Symmetry.

The universe itself works according to its own rules, which, to us, are largely un­known and which are perhaps even unknowable by virtue of the fact that the hu­man mind is simply not capable of perceiving them as they really are. This is prob­ably because the human mind was — at least from a physical point of view — de­veloped to guide us through our natural environment of the Earth's biosphere, which it does very well. The mystery remains, however, as to how and why the hu­man mind is capable of imagining worlds that are beyond the bounds of observed reality — worlds of fantasy, mystery and disembodied conscious existence.

There are unlimited ways in which the human mind may attempt to gain a cogent view of the reality within which it has being. I have written about two personal views of the universe: here and here. Notwithstanding, these views are mutually incompatible and internally inconsistent. But this is inevitable and is no cause for shame. Human perception is fallible. Consequently, one can never expect it to be consistent. The virtue is in experimenting with perception, not in perfecting it.

The Real Laws of Physics

The real Laws of Physics are immutable: they cannot be changed or influ­enced by the will of man. Consequently, ipso facto, they must be entirely natural. They relate cause with effect. They are, and act, the same in all places at all times throughout the universe. They are an essential element of the very fabric of the universe. They thus can never be broken nor disobeyed.

... except perhaps, as some would try to have us believe, for a very short time in a very restricted part of the universe on 11 September 2001.

Likewise, the Laws of Thought are immutable: they can't be changed or influenced by the will of man, and hence, cannot be disobeyed. Consequently, ipso facto, they too must be entirely natural. They distinguish the difference between what is True and what is False. They relate Observed Truth to Derived Truth. They are, and act, the same in all places at all times throughout the universe. They are borne and act within, another essential fabric of the universe, which the philosophers of ancient Greece knew as the Λóγoς [Logos] and which they perceived as the all-pervading æthereal carrier of intelligence throughout the universe.

So, what is the difference between what I have called our "Laws of Thought" and the real "Laws of Physics"?

The Laws of Thought are the laws by which human perception and reason operate. They manifest themselves and operate only within the human mind. They are the underlying fundaments of cultural languages like English and Portu­guese, artificial languages like Esperanto and Lojban, the natural languages of logic and mathe­mat­ics and programming languages like C and Java. They are our means of expressing how the universe's structure and behaviour appears to us from our particular point of view in space and time.

Cultural languages are subject to a growing number of exceptions to their rules, for such reasons as sloppy use, linguistic ignorance, vowel rotation and parallel evolution of accent and dialect in separate regions, which can only result from arbitrary human activity. Even the artificial languages are unable to describe the universe the way it really is and operates. This is well evinced by the incompatibility between Relativity Theory and The Standard Model of Physics, thereby confirming that artificial languages, like logic and mathematics, are not inherent to the universe itself.

This invariably puts the observer at a very disadvantageous viewing point. For example, suppose I want to study the relative motion of the Earth and the sun. From my physical point of view, the sun orbits the Earth and the planets appear to do so also but in orbits in which each planet often diverts into a little epicycle before continu­ing its main course again. This seems to be overly complicated.

In my quest to simplify my observation, I transpose my point of view to the sun. I look outwards from the sun's point of view. But by so-doing, I effectively attribute to the sun a 'theory of mind', which in reality, it doesn't have. Notwithstanding, I get a view of orbits that are much simpler and understandable. I become the sun, which is located at one focus of the earth's elliptical orbit.

Note, however, that by changing my position and thereby simplifying the mathematics, I haven't changed the real situation at all. I haven't in any way modified the relative motion between the Earth and the sun.

In this case, the formula for the pro­portional radius of the orbit at the true anomaly angle, θ is given by the following formula where φ is the angular offset of the major axis of the orbital ellipse from the angular origin of observation.

r(θ) = a (1 − e²) (1 ± e · cos(θ − φ))

The formula is indeed simpler from a heliocentric viewing point, but it is really a special case of orbits as seem from other places. Besides, it is never going to be completely accurate, even in principle. The orbit of the Earth around the sun is not circular, but neither is it an ellipse, a rosette or a precessing rosette. An orbit isn't even closed. The orbiting body never retraces its path. It is an open ended path. Any real orbit is a complex-dynamical phenomenon. When the combined effect of all bodies in the universe is taken into account, it is fundamentally non-expressible through the language of mathematics.

The real Laws of Physics, on the other hand, are laws that determine the structure and govern the behaviour of the external objective physical universe. They are built into the mechanics of the universe. They are unknown and fundamentally unknow­able by the human mind. But their expressions would be universal and objective; i.e. independent of the observer's viewing point. But they cannot be constructed from the mathematical fit-kit with which we try to formulate expressions to describe such things as orbits in terms of circles, ellipses, rosettes, precessing rosettes or whatever. I can only gain vision of these real Laws of Physics as through a glass darkly. They appear to be complex-dynamical and the best way known so far to represent a complex-dynamical phenomenon is in terms of an iterative difference equation, something like:

x_new → k.f([X].x_old)

...where the iterative period → 0, x_new − x_old → 0 and [X] is a determinant containing all relevant universal metrics. It doesn't seem to matter what the function 'f' is, so long as it's non-linear. It could be something like: x_new → k.x_old(x_old − 1). But we can fundamentally never know what the rule really is.

But having said this, I think the above way of expressing what I think is happening is conceptually frumpy. I would prefer to develop a mathematics whose notions are based one order of differentiation higher with respect to time, in which the funda­mental metrics are not MLT but something along the lines of C[a constant which relates rate of convergence with velocity], I[a constant relating energy and inertia] and F[force]. But I'm now too old.

Conclusion

Human perception is fallible. The view of any observer can only be from one point in space at any given time. His bodily senses — and any instruments he may use to extend their reach — corrupt and distort the information they convey. The mechan­isms of thought, whereby he attempts to understand what his senses deliver, give different mutually inconsistent interpretations at different angles and scales. His emotions and memories further warp and embellish the view he perceives.

But is this bad? I think not. I believe that, if scientists were ever to discover the fun­damental bedrock of the universe, they would find it supremely bland and boring. Notwithstanding, it provides two things that are vital to mankind: 1) the framework upon which he builds his perceptions of reality; 2) the medium through which he may discuss his perceptions of reality with others.

The objective reality of the universe is thus not the end in itself. It is merely the agent that provides the conscious self with the stimulus necessary to construct em­bellished perceptions of what is out there: to construct imaginary objects and views of significance and beauty, which are above and beyond their objective reality.

An example of this phenomenon used to occur along the old tow path by the side of the River Stort in England. Within the largely grassy flood plain was a small coppice of willow trees. As I approached the coppice on a warm sunny afternoon, I reached a point on the path at which, for me, the scene turned magical. The swish of the wind through the grass and the willow leaves. The textures of the tree trunks. The swaying of the branches. I felt that I was in an enchanted wood. It seemed to be aware of me. I was ensconced in another dimension, far far away from the red-bricked suburbia from which I had come.

But this sensation only lasted over a short 3 to 5 metre stretch of the path, just be­fore entering the wooded area. Before or after this short stretch of path, I was just on a flood-plain close to a clump of soulless trees. They were the objective reality. My enchanted coppice was a product of my perception, created by my con­scious mind, embellished by my memories.

Each observer's perception, of the same objective reality, is necessarily different from everybody else's. And these differences provide a motive for discussion. Dis­cussion develops relationship. Thus it would appear that nature's ultimate objective is to facilitate the development of relationships between human beings. And for this to work, it is essential that human perception be fallible.

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© June 2005, Sept-Nov 2014, Jan-Apr 2017, Oct 2023 Robert John Morton
Parent Document | Essence of this article in the form of a poem.