I am not sure metaphysics is an appropriate initial approach to discussing what appears to be incontrovertible fact: ‘Now’ doesn’t seem to exist. Nevertheless, such an approach is both instructive and as unavoidable as the need to bring in quantum mechanics which, as will soon become apparent, leads to the same conclusions.
“Now, wait a minute” you protest, which is exactly my point. Wait a minute, and now has fled, wait a second and now is lost, wait an instant and now has slipped our grasp, wait a nanosecond and now is past … indeed, if we live in the ‘now’, how long does one have to wait, precisely, before ‘now’ becomes ‘then’?
Similarly, if we come at it from the other side, from the direction of that which has yet to happen, the future, there is an equivalent problem – is it possible to determine the precise moment in time when the future ‘happens’? That is, is there a rigorous way to define ‘now’? Somehow we perceive the unfolding of events as they come closer to us in time with an increasing degree of certainty that they are going to occur, yet the duration of the occurrence itself appears to be arbitrarily short.
(Relativity, relativistic effects, and frames of reference must be admitted to this discussion at some point. Is it the case that each of us is fixed on or within some immovable referential plane or space, and time flows across, through or around us – as rocks in a river? Or is time the referential sea and we the ships, our wake and wastes the only evidence of our passing?)
So here’s the rub – we seem to live in the present, the past over and done, the future yet to be; we admire the view, smell the roses, drink deep the heady wine of a lover’s touch. But if we examine the present too closely, we cannot help but become increasingly uncomfortable the more precisely we try to define ‘now’.
Foregoing a more rigorous treatment (for now), it seems that ‘now’ is simply where the future becomes the past – a seamless interface between an arriving future and a departing past, both of which may be described in probabilistic terms: the probability that a future event will occur is inversely proportional to the length of time remaining before it occurs. Likewise, the probability that a past event actually occurred (and is not a figment of our imagination) is inversely proportional to the length of time after it (may have) occurred.
Look at it this way: The probability of an event occurring (or has occurred) (ρe) approaches certainty (i.e., 1) as the amount of time before (or after) the event occurs (te) approaches zero (0).
In a Cartesian coordinate system (i.e., on a graph), with the x-axis representing time (the zero point, t0, being “now”), any curve representing the future becomes asymptotic to y as it approaches t0, just as any curve representing the past is also asymptotic to y at t0. The questions “will it happen” and “did it happen” are, in a probabilistic sense, equal (or equally indeterminate) at t0, leading us to observe that “now” cannot be rigorously defined.
While that conclusion of indeterminacy of an event occurring appears nonsensical, it is deserving of serious consideration, especially given that certain recent research argues persuasively that time may, in fact, be discrete vice continuous. Just as matter and energy appear to have irreducible minimums, so too, goes the argument, does time.
Granted, a quantum of time, it is argued, is rather small (on the order of 10-43 second), nevertheless it is claimed to be finite, and therefore discrete.
Consider the occurrence of an event as a function of awareness as defined by sensory inputs. Sight, sound, smell, taste, and touch are the five most commonly defined human senses, but without getting into metaphysics there are others. One that is unlikely to generate objection is the ability to sense electrical fields of sufficient strength, or more generally radiation of particular wavelengths. Indeed, recent investigations appear to show that humans have a latent ability to sense magnetic fields. To attempt to lump these senses into any of the other five mentioned (such as touch or sight) does not withstand close examination, except possibly in overlap areas where one sense transitions into another (e.g., it has been rigorously shown that the sense of smell affects the sense of taste).
In a similar vein I ask whether or not there is a sense of time. From a purely physiological perspective the aging process alone clearly shows that our bodies are “aware” of the passing of time. (Indeed, whether or not something is deemed “alive”, or to be imbued with the characteristic called “life”, seems to be another term that does not have an unambiguous definition. One of the more intriguing approaches to the definition of “life” includes a necessary characteristic called “death”.) However, “awareness” is a term that appears to need better definition, especially with regard to time.
What is “awareness”? Actually, this is not a simple question at all. Most researchers that address the question seem to focus on different aspects of “cognitive function” – that is, the complex electrochemical interactions that occur in various areas of the brain that may be classified as “thought”. But “awareness” remains an elusive characteristic that seems to defy all attempts to pin it down (like “life”). Some have noted that “self-awareness” may start with the ability to recognize the object in the mirror as oneself, but beyond that relatively simplistic definition lies a vast region of ambiguous, fuzzy, and poorly defined terrain. A rigorous definition is not yet in sight – at least, one that doesn’t leave a significant residue of unease.
One of the bigger obstacles to understanding “awareness” is the argument that awareness is somehow extra-corporeal. If awareness does not arise from measurable physical processes (even if we do not yet know what to measure or have the tools to measure them), then science is out and mysticism is in. It is not that mysticism is necessarily bad, it is simply that mysticism is not subject to independent (i.e., objective) confirmation.
Mysticism, for the most part, is systematic, consisting of defined rituals, processes, and procedures whose purpose is to produce specific outcomes or results, which seems not to differ from scientism. Where mysticism ends and science begins is not always as clear as some would have you believe. In fact, one of the more memorable and often repeated statements attributed to Arthur C. Clarke, a respected scientist and author, is “any sufficiently advanced technology is indistinguishable from magic.”
In his statement, Clarke was referring to the outcomes of processes, and used the term “magic” in its true mystical sense rather than that of a parlor trick or sleight of hand. Scientists, however, point out that the outcomes of processes based on science are (with a high degree of certainty, albeit usually not absolutely) unambiguous, predictable, and reproducible. That does not currently appear to be the case with mysticism.
Clarke’s statement was also explicitly erected on a foundation of current technology, yet may be considered true whenever “current” is, and on whatever plane “technology” occupies at that moment. Wherever one stands, it seems unequivocal that there will always be more advanced technologies to be pursued, and while Clarke as scientist might find it uncomfortable to defend, ultimately the most significant difference between technology and magic may simply be one of spelling.
To see why that may be true, reflect on the fact that those who believe in (or practice) true magic attempt to apply specific processes, however contrived, to achieve specific outcomes, however defined. Lack of reproducible success of itself does not invalidate mysticism, just as failed experiments do not necessarily invalidate scientism. Other than the perception that certain terms (magic, mystic, etc.) are currently deemed pejorative, the only reason science claims supremacy over mysticism has to do with science’s seeming ability to replicate, and to some degree anticipate (but see below), real world outcomes based on measurable inputs and defined processes.
In fact, as uncomfortable as it might be for a true mystic to accept, should they become capable of reproducing specific outcomes from measurable inputs and defined processes, they will have transitioned from the mystical to the scientific, from magic to technology. The spelling changes, both literally and figuratively (pardon the pun).
I suppose I should explicitly recognize organized mysticism – religion – and proffer my apologies should any in the spiritual realm take offense. To balance the equation, I also offer my apologies to any in the secular realm similarly offended. I accept my place as equal opportunity offender.
What of the assertion “there will always be more advanced technologies to be pursued,” made above? There are those scientists who believe in a thing called the “Grand Unification Theory” – that somewhere out there, yet to be discovered, is a theory that will stand as the root of all science, upon which all other theories can be built, and beyond which no other theories are necessary. Ultimately, according to them, there will come a time when there will NOT be more advanced technologies to be pursued.
Well … perhaps regrettably, they seem to have been proven wrong some time ago – by one of their own.
The following is from The Exploratorium, found online at http://www.exploratorium.edu/complexity/CompLexicon/godel.html (© 1996)
Kurt Gödel (1906-1978)
In 1931 the mathematician and logician Kurt Gödel proved that within a formal system questions exist that are neither provable nor disprovable on the basis of the axioms that define the system. This is known as Gödel’s Undecidability Theorem. He also showed that in a sufficiently rich formal system in which decidability of all questions is required, there will be contradictory statements. This is known as his Incompleteness Theorem.
In establishing these theorems Gödel showed that there are problems that cannot be solved by any set of rules or procedures; instead for these problems one must always extend the set of axioms. This disproved a common belief at the time that the different branches of mathematics could be integrated and placed on a single logical foundation.
Alan Turing later provided a constructive interpretation of Gödel’s results by placing them on an algorithmic foundation: There are numbers and functions that cannot be computed by any logical machine.
More recently, Gregory Chaitin, a mathematician working at IBM, has stressed that Gödel’s and Turing’s results set fundamental limits on mathematics.
These results, along with quantum uncertainty and the unpredictability of deterministic (chaotic) systems, form a core set of limitations to scientific knowledge that have only come to be appreciated during this century.
Many scientists (of whatever persuasion) still do not seem to fully appreciate the depth, the breadth, nor the impact of Gödel’s theorems. A Grand Unification Theory may never be possible unless, of course, it permits exceptions or contradictions – and what sort of Grand Unification Theory would that be? On the other hand, there appear to be no inherent limitations on how close one can come to such a theory, so the efforts to develop such should not be abandoned or belittled.
Let’s take a closer look at the Gödel theorems and their interpretations by Turing and Chaitin. Scientists tend to be rather bound by their specific disciplines, which serves them well within the confines of their particular systems but inherently limits their willingness to address questions perceived as falling outside their area of expertise, or those which bridge disciplines.
Specialization has both benefits and costs. Both Turing and Chaitin saw the limits imposed by the Gödel theorems, but appear to have stopped short of appreciating what amounts to a broader interpretation.
An Infinite Nesting:
Herein is postulated the Infinite Nest Theorem, which is nothing more than a restatement that puts Gödel in context: any rigorously defined, sufficiently rich axiomatic system is a subset of some other rigorously defined, sufficiently rich axiomatic system.
A few moments reflection leads to the conclusion that limits (broadly defined) therefore do not exist – our universe is a subset of another universe, which is a subset of another universe, etc.. To be sure, limits to “scientific” knowledge may exist, but since science is a subset of another more inclusive system, those limits may be seen as relatively narrow and purely contextual.
It sort of boggles the mind, it does, especially when one realizes that logic itself must then be a subset of some more inclusive system. (In a sense this is not news – the prefix “meta-“ explicitly refers to a transcendence of the ordinary and has been in use for a long time. Consider, for example, “physics” vice “metaphysics”. Granted, physicists do not generally categorize themselves as a special class of metaphysical practitioners, but still ….)
What does “rigorously defined” mean? Simply that a set of initial conditions are agreed upon, from which rules are then derived to explain the operations of the system.
One shouldn’t get too bent out of shape by this – the existence of more inclusive systems does not, in and of itself, discredit that which can be proven within the system you are embedded in, so long as your proofs conform to the axioms of your system. It does mean, however, that by definition any such proof is an example of a special case in a more inclusive system.
Neither science nor logic are invalidated by being placed within the context of a broader system. It does mean, however, that a smug assumption of infallibility may not be the most desirable evolutionary trait, regardless if you are scientist or mystic.
If this bothers you it simply means you are limiting your thinking and conceptual space unnecessarily. The colloquialism “think outside the box” is as good an admonition as any – loosen up.
Of course, “thinking outside the box” brings its own set of challenges and constraints, not the least of them being the necessity of defining context – if one is “outside” the box where, exactly, is one standing? Having both feet planted firmly in mid-air would appear to be another of those less than desirable evolutionary traits. And what of those other poor sods left behind in the box? What is to be done about them? How does one go about lifting them out into the rarefied and heady realms of new thought?
Folks, it isn’t easy, and it is rarely appreciated:
On the Origins of War:
Take a minute and imagine, if you will, a squaliquemusplupaka. Yes, that is the correct spelling and it is pronounced “squaw-LEE-kay-moose-plu-paw’-kaw”.
Now, if you were able to do so I must regretfully inform you that whatever you had (or have) in mind is most assuredly not a squaliquemusplupaka – it is a nonsense word without meaning, although we certainly have the ability to assign meaning to the term if we choose to do so.
In fact, please do so – assign a meaning to squaliquemusplupaka, and take the time and make the effort to assign a meaning that is unique and non-trivial. This exercise is itself non-trivial, as one discovers rather early in the effort – red is ‘red’, round is ’round’, and neither are squaliquemusplupaka. Likewise social, religious, scientific, and other concepts that already have existing descriptors are not squaliquemusplupaka, so you are going to have to work at this one.
While you are engaged in that effort, let us consider a couple of existing non-trivial terms that most of us would deem to be unique and well defined, such as ‘teamwork’ and ‘common sense.’
Looking first at ‘common sense’ we quickly discover that while the term appears to mean that which is sensible to a community of people, in actual application we find what is sensible to one is often nonsense to another – common sense requires a common (i.e., shared) background, common beliefs, common intelligence, and so on. There was a time when ‘common sense’ held that the Earth was the center of the universe – everybody ‘knew’ it was true from basic observations of the celestial bodies, all of which appeared to rotate around the earthbound observer. It turns out that common sense seems to work reasonably well in relatively small or closed communities (i.e., within one formally defined axiomatic system), but otherwise may not be so ‘common’, and worse, common sense changes over time and with the accumulation of experience.
What about a term such as ‘teamwork?’ While there are several meanings, the shared concept is working together to reach a commonly agreed upon goal. However, to actually accomplish something using teamwork requires making the term operational. Let us look at two operational definitions of teamwork. The first is the ‘common yoke’ analogy – we are all pulling the load together (and it is understood we are all pulling in the same direction!). The second is like unto the first – we are all cooperating to reach the same goal.
Here is the rub – what if your definition of teamwork is that of the ‘common yoke,’ and mine is the ‘cooperating’ definition? While ‘cooperating’ may occasionally mean everyone literally does the same thing at the same time to lighten the load, it more often means (to me) a coordinated effort to maximize results, with everyone doing different but related tasks. Even where our individual strengths (and possibly interests) are equal, to maximize efficiency usually requires splitting up the workload and attacking it in a multi-pronged (parallel) fashion rather than serially.
“But that’s just common sense,” you intone, “everyone knows that!”
Well, no, everyone doesn’t know that. Assume we are in business together and my areas of responsibility are operational and yours are administrative. Think of the consequences if you are constantly trying to help me out in operational areas because you believe in the common yoke meaning of teamwork. Your intentions are good and noble, but I may well see your attempts to help as interference, a lack of trust or belief in my ability to adequately perform my work, and a dereliction of your responsibilities in the administrative arena.
On the other hand, if I avoid assisting you in your work, trusting in your ability to do the work in a professional manner, and focus on my own work responsibilities (i.e., if I avoid “interfering” in your work), there is an excellent chance that you will get upset because I am not conforming to your expectations regarding teamwork.
Not only are there people who have a different ‘common sense’ about teamwork, there are some who would deny there are any other legitimate definitions of the term than the one they use. It gets worse. There are some who simply do not have the requisite neural linkages to comprehend that alternative concepts or definitions can exist – that is, to them, ‘teamwork’ is (for example) ‘common yoke,’ and cannot be anything else. Whatever you mean by ‘cooperate’ or ‘working together’ is squaliquemusplupaka to them.
To broaden the discussion we first must point out that not having the requisite neural linkages to comprehend any given concept does not necessarily mean one has a low I.Q. or is otherwise mentally aberrant. We all suffer from this type of mental deficiency one way or another, but by its very nature our conceptual blindness is totally and completely unknown to us – we are blind to our own blindness.
We are faced with the potential of both Type I (commission) and Type II (omission) errors here. When others use terms we know and to which we have attached meaning, we automatically apply our meaning to the term whether or not it is the same meaning the other has attached to the term. Only to the extent we have a shared cultural, linguistic, or experiential background is it likely we have enough overlapping meaning to permit us to functionally communicate. On the other hand, when others use terms we clearly don’t understand (squaliquemusplupaka), we often craft responses that force re-expression using terms more familiar to us, but which may misrepresent the true meaning of the original term – a common problem between native and non-native speakers of a language.
Content vice Context:
A native Chinese speaker who is bilingual in, say, Cantonese and English, may often suffer confusion and frustration when talking to a native American English speaker, especially in a close-knit business environment. Generally, Cantonese does not make use of tense, gender, or case. Instead, the speaker includes additional terms that explicitly provide the necessary details of when, how many, etc., to the listener. The listener not only expects but requires the speaker to provide those details, and may become linguistically disoriented, intellectually frustrated, and even emotionally upset, if those details are not provided. The native Chinese speaker has the duty and accepts the responsibility of providing clear, complete, and accurate statements, and will generally strive to avoid any possibility of error or misunderstanding. The native Chinese listener cannot legitimately be held accountable for performance if the speaker’s directions are incomplete or can be too easily misinterpreted. Both sides understand this as ‘common sense’ – content, specific content, is critical to clear communication, while implied or assumed context plays a relatively minor role.
An American English speaker, on the other hand, may well become upset and even angry when conversing with a native Chinese language listener. Spoken English is highly ambiguous, connotative, and heavily dependent on context, not to mention loaded with idiomatic expressions, such as the one just used. Consequently, the native English listener becomes adept at interpreting the speaker’s intention and meaning – the listener accepts the responsibility of properly interpreting and understanding the speaker’s message, and therefore also accepts performance accountability. There is almost a game element involved – properly interpreting the speaker’s language to discern their intent. In this sense, context often outweighs content.
Thus, if you are an American speaker, your expectation is the listener will 1) make the attempt to interpret your meaning, 2) properly identify and incorporate the context of the spoken words into their interpretation, and 3) actually be able to properly discern or interpret your intentions, even if your particular words are ambiguous or less than precise – ‘common sense’ to the American. Unfortunately, this is not at all what a native Chinese language listener expects – their expectation is the speaker has the duty and responsibility to provide a clear, accurate, and unambiguous statement, and therefore they have no need to interpret the speaker’s intent – indeed, to make such an attempt would be an unwarranted violation of the speakers dignity – ‘common sense’ to the Chinese.
Mike: “Chan Fai, when you go out again can you stop and pick up some copy paper? Thanks.”
Chan Fai: “Who is giving us copy paper? What is their address?”
Mike: “Sorry – I meant we need to buy some copy paper. I suggest the office products store.”
Chan Fai: “Do you want me to go now and buy copy paper?”
Mike: “No, before you come back from your next delivery.”
Chan Fai: “Okay, after I go to the bank I will come back and do my delivery, so I will buy the copy paper before I come back from my delivery.”
Mike: “Well, why don’t you stop on your way to or from the bank?”
Chan Fai: “Why do you want me to stop when I go to the bank?”
Mike: “I just told you – to buy copy paper.”
Chan Fai: “Oh, okay, I will buy copy paper after I go to the bank, then. How much copy paper do you want me to buy?”
Mike: “I think a couple of reams will do.”
Chan Fai: “So, you want me to buy two reams of copy paper before I come back from the bank. Do you want letter size or A4 size?”
Mike: “Chan Fai, we have never in the three years we have been in business used anything other than letter size. Please get the letter size.”
Chan Fai: “But maybe you want to send a letter to China. We sold to China before. Okay, what thickness? In Hong Kong we use grams for the weight of the paper.”
Mike: “Standard weight for business paper in the US is 20 pounds, and since the one time we tried 24 pound paper it jammed the copy machine, we need to stick to 20 pound paper.”
Chan Fai: “Okay. I will get brighter paper also, what do you think?”
Mike: “Frankly, Chan Fai, at this point I don’t care how bright or what color it is, just get the paper.”
Chan Fai: “You want colored paper? What color do you want?”
On the other hand, the responsible native Chinese language speaker feels compelled to provide a level of detail that the English listener may well find aggravating and possibly insulting – the English listener quickly discerns the speaker’s intent, but the speaker continues to pile on layers of detail to the point the English listener begins to believe the speaker thinks they are incompetent. Again, the native Chinese language speaker is simply attempting to perform his duty as best as possible, and expects the listener to appreciate such effort – when the English listener expresses frustration, the Chinese speaker may well feel slighted, or worse.
Restating my earlier discussion on teamwork, if I have a ‘team’ concept of cooperation I may become upset if someone else jumps in to help me complete my task when they have a different team assignment. Conversely, the person with a ‘common yoke’ concept of cooperation may become upset if I don’t jump in to help them complete their task, even if I have a different team assignment. Common sense can easily lead to conflict.
So, back to squaliquemusplupaka. Have you arrived at a clear and unambiguous meaning for the term? Okay, good. Now turn to the person sitting next to you and introduce them to the word and its meaning – and I would encourage you to use an example or two to clarify the definition and ensure comprehension. (It might be advisable to do this with someone you know. Reactions of strangers to this sort of thing are highly unpredictable and occasionally ugly.)
Now let us assume that your friend thinks this is an extraordinarily interesting word, brilliantly conceived, with a truly insightful definition that profoundly illuminates previously darkened corners of their existence, and shares it with a wide circle of others. What is the likelihood that after one week in the field, the word will have the same meaning and be used precisely as you originally intended?
My guess? Zero to none. Word usage and meanings change rather often, further confounding fond hopes of establishing a common ground on which to build relationships. You undoubtedly have quickly grasped the concept that content changes to accommodate context, yet context can only be understood in relationship to content. My apologies if I have belabored the obvious.
Now, what about “the origins of war” that started out this section? What? You don’t get it yet? What is the matter with you? It was made perfectly clear, unambiguous, simple, even brilliant … common sense, really.
On Time … or not:
So far it seems to me that somebody has a lot of explaining to do about why there is such a lack of clarity on some rather significant terms – “now”, “life”, “awareness”, “time”, “scientism” verses “mysticism”, “war”, “squaliquemusplupaka”.
One nice thing about ambiguity, however, is that it does open the door to creative thought. Take time, for example. Earlier in this essay we mentioned research suggesting time may be discrete vice continuous. At the quantum (or sub-quantum) level this may be a significant matter, but at the macroscopic level on which we all live it seems to have little if any noticeable effect. So what’s the big deal?
The big deal is the apparent need to invoke the concept of time to understand terms like “now”, “life”, “awareness”, and other words that help us grasp and respond intelligently to “reality” (sorry – that is one nasty, ugly word, but I had to use it).
Error, invalid term. World.com file corrupt. Reboot reality? [Y/N]
One of the problems with the concept of “now” is that we seem to experience it. Therefore, now appears to require that time not take a vacation right at the crucial juncture between future and past. If instead we insist that now has finite duration, then a process reminiscent of that used in Zeno’s Paradox must ultimately bring us to some minimal, indivisible duration of time, at which point Achilles crosses the finish line, Zeno is considerably embarrassed, the paradox evaporates, and the figure 10-43 second seems as good as any (this actually has a name – it is called Planck time, tP, and is roughly equal to 5.391 x 10-44 second … roughly).
Planck time is a curious thing, actually. It is defined as the time it takes a photon of light (which is defined as having zero mass) traveling in a vacuum to traverse the distance of one Planck length, a Planck length being about 10-33 centimeters (1.616 x 10-35 meters – a Planck length is posited as an irreducible minimum distance). Anything less than Planck time is meaningless since it is the fundamental unit of time, indivisible, and therefore it is not possible to transmit any information in less than one unit of Planck time. Here’s the curiosity – below the Planck scale (i.e., Planck time and Planck length), it can be said that space-time as we know it does not exist, since no time exists less than one unit of Planck time, and no distance exists less than one Planck length.
To be sure, a physicist would prefer the term ‘undefined’ be substituted for the phrase ‘does not exist’, but that seems to be splitting hairs – which at this level appears to be prohibited. On the other hand, the reason the term ‘undefined’ is preferred by those of a scientific bent is because they also prefer to hedge their bets (science and magic are a little hard to tell apart at the quantum level). Logic (and Zeno) insists that anything with finite duration or length (no matter how minuscule) can be subdivided … unless, of course, you mumble the proper incantation and define it away. Poof. Magic!
Well, if we are going to do magic I would prefer time travel or psychic powers (the ability to foretell the future). Let us, for arguments sake, assume that time is indeed continuous and not discrete, which means it is possible to make a unit of time arbitrarily small – smaller, even, than Planck time.
In fact, I choose as the unit of time I will use for this discussion as being of zero duration. It is equivalent to a point on a line – no length, but an infinite number of them together define a line of measurable length. In the same way a unit of time with no duration can be grouped together with an infinite number of other units of time to define a time line of measurable duration. I know – that sounds nonsensical but then so does a finite unit of length that cannot be subdivided. Oh, well.
Okay. If, on the one hand, ‘now’ (by definition) is simply the interface between the past and the future, having time duration of zero, and, on the other hand, we are ‘aware’ of events as they occur, then it must be that our awareness spans some finite duration of time that extends both into the future as well as into the past.
While few consider a claim of hindsight to be remarkable, most would reject any claim to foresight as nonsense and the province of those who practice mysticism, sometimes referred to as ‘charlatans’.
Rejecting foresight, however, requires we accept that all we experience as “now” is actually “past” and, in addition, we therefore cannot possibly have any ability whatsoever to anticipate future experience – e.g., the only way to hit a thrown pitch is to swing a bat randomly (okay, so the evidence of the truth of that statement can be found in most Little League games, but as far as I’m concerned they are exceptions). This is, of course, nonsense. We can and do anticipate future events based not only on our own observations and sensory inputs, but on the reports of others as well. We all have ‘foresight’ – the ability to foretell the future. Stray bullets and meteors aside, most of us are probably willing to allow that, if we define foresight as the ability to anticipate future consequences of currently perceived events, then we indeed can see into the future. The only discussable issue might be “how far?” into the future we will permit the definition to apply which leads, naturally, into a brief discussion of savant syndrome and a few comments on normal distributions before we get back to probability and asymptotic curves.
[TO BE CONTINUED]