East Meets West Logic...

[Lloyd Gillespie]

Carthage__Eastern Empire Rises In The West...

Carthage (Arabic: قرطاج Qarṭāj‎, Ancient Greek: Καρχηδών Karkhēdōn, Berber: ⴽⴰⵔⵜⴰⵊⴻⵏ Kartajen, Hebrew: קרתגו‎ kartago, Latin: Carthago or Karthago, from the Phoenician Qart-ḥadašt קַרְתְּ חַדַשְתְּ meaning New City, implying it was a 'new Tyre'[1]) refers to a series of cities on the Gulf of Tunis, from a Phoenician colony of the 1st millennium BCE to the current suburb outside Tunis, Tunisia.

The first civilization that developed within the city's sphere of influence is referred to as Punic (a form of the word "Phoenician") or Carthaginian. The city of Carthage is located on the eastern side of Lake Tunis across from the centre of Tunis. According to Roman legend it was founded in 814 BCE by Phoenician colonists from Tyre under the leadership of Elissa (Queen Dido). It became a large and rich city and thus a major power in the Mediterranean. The resulting rivalry with Syracuse and Rome was accompanied by several wars with respective invasions of each other's homeland. Hannibal's invasion of Italy in the Second Punic War culminated in the Carthaginian victory at Cannae and led to a serious threat to the continuation of Roman rule over Italy; however, Carthage emerged from the conflict at its historical weakest after Hannibal's defeat at the Battle of Zama in 202 BCE. After the Third Punic War, the city was destroyed by the Romans in 146 BCE. However, the Romans refounded Carthage, which became one of the three most important cities of the Empire and the capital of the short-lived Vandal kingdom. It remained one of the most important Roman cities until the Muslim conquest when it was destroyed a second time in CE 698.



Legends of the foundation
Queen Elissa (Dido)
According to Roman sources, Phoenician colonists led by Queen Dido (Elissa) founded Carthage in 814 BCE. Queen Elissa (also known as "Alissar", and by the Arabic name[7] اليسار also اليسا and عليسا), was an exiled princess of the ancient Phoenician city of Tyre. At its peak, the metropolis she founded, Carthage, came to be called the "shining city", ruling 300 other cities around the western Mediterranean and leading the Phoenician (or Punic) world.

Elissa's brother, King Pygmalion of Tyre, had murdered her husband, the high priest. Elissa escaped the tyranny of her own country and founded the "new city" of Carthage and subsequently its later dominions. Details of her life are sketchy and confusing, but the following can be deduced from various sources. According to Justin, Princess Elissa was the daughter of King Matten of Tyre (also known as Muttoial or Belus II). When he died, the throne was jointly bequeathed to her and her brother, Pygmalion. She married her uncle Acherbas (also known as Sychaeus) the High Priest of Melqart, a man with both authority and wealth comparable to the king. This furthered rivalry between religion and the monarchy. Pygmalion was a tyrant, lover of both gold and intrigue, who desired the authority and fortune enjoyed by Acherbas. Pygmalion assassinated Acherbas in the temple and kept the misdeed concealed from his sister for a long time, deceiving her with lies about her husband's death. At the same time, the people of Tyre called for a single sovereign, causing dissent within the royal family.

The mention of Queen Elissa (Dido) in Virgil's Aeneid
In the Roman epic of Virgil, the Aeneid, Queen Dido, the Greek name for Queen Elissa, is first introduced as an extremely respected character. In just seven years, since their exodus from Tyre, the Carthaginians have rebuilt a successful kingdom under her rule. Her subjects adore her and present her with a festival of praise. Her character is perceived by Virgil as even more noble when she offers asylum to Aeneas and his men, who have recently escaped from Troy. A spirit in the form of the messenger god, Mercury, sent by Jupiter, reminds Aeneas that his mission is not to stay in Carthage with his new-found love, Dido, but to sail to Italy to found Rome. Virgil ends his legend of Dido with the story that, when Aeneas tells Dido, her heart broken, she orders a pyre to be built where she falls upon Aeneas' sword. As she lay dying, she predicted eternal strife between Aeneas' people and her own: "rise up from my bones, avenging spirit" (4.625, trans. Fitzgerald) she says, an obvious invocation of Hannibal.

[Lloyd Gillespie]

Alan Turing__The Uncomputable...

Turing turned to the exploration of the uncomputable for his Princeton Ph.D. thesis (193, which then appeared as Systems of Logic based on Ordinals (Turing 1939).

It is generally the view, as expressed by Feferman (198, that this work was a diversion from the main thrust of his work. But from another angle, as expressed in (Hodges 1997), one can see Turing's development as turning naturally from considering the mind when following a rule, to the action of the mind when not following a rule. In particular this 1938 work considered the mind when seeing the truth of one of Gödel's true but formally unprovable propositions, and hence going beyond rules based on the axioms of the system. As Turing expressed it (Turing 1939, p. 19, there are ‘formulae, seen intuitively to be correct, but which the Gödel theorem shows are unprovable in the original system.’ Turing's theory of ‘ordinal logics’ was an attempt to ‘avoid as far as possible the effects of Gödel's theorem’ by studying the effect of adding Gödel sentences as new axioms to create stronger and stronger logics. It did not reach a definitive conclusion.

In his investigation, Turing introduced the idea of an ‘oracle’ capable of performing, as if by magic, an uncomputable operation. Turing's oracle cannot be considered as some ‘black box’ component of a new class of machines, to be put on a par with the primitive operations of reading single symbols, as has been suggested by (Copeland 199. An oracle is infinitely more powerful than anything a modern computer can do, and nothing like an elementary component of a computer. Turing defined ‘oracle-machines’ as Turing machines with an additional configuration in which they ‘call the oracle’ so as to take an uncomputable step. But these oracle-machines are not purely mechanical. They are only partially mechanical, like Turing's choice-machines. Indeed the whole point of the oracle-machine is to explore the realm of what cannot be done by purely mechanical processes. Turing emphasised (Turing 1939, p. 173):

"We shall not go any further into the nature of this oracle apart from saying that it cannot be a machine."

Turing's oracle can be seen simply as a mathematical tool, useful for exploring the mathematics of the uncomputable. The idea of an oracle allows the formulation of questions of relative rather than absolute computability. Thus Turing opened new fields of investigation in mathematical logic. However, there is also a possible interpretation in terms of human cognitive capacity. On this interpretation, the oracle is related to the ‘intuition’ involved in seeing the truth of a Gödel statement.

M. H. A. Newman, who introduced Turing to mathematical logic and continued to collaborate with him, wrote in (Newman 1955) that the oracle resembles a mathematician ‘having an idea’, as opposed to using a mechanical method. However, Turing's oracle cannot actually be identified with a human mental faculty. It is too powerful: it immediately supplies the answer as to whether any given Turing machine is ‘satisfactory,’ something no human being could do. On the other hand, anyone hoping to see mental ‘intuition’ captured completely by an oracle, must face the difficulty that Turing showed how his argument for the incompleteness of Turing machines could be applied with equal force to oracle-machines (Turing 1939, p. 173). This point has been emphasised by Penrose (1994, p. 380). Newman's comment might better be taken to refer to the different oracle suggested later on (Turing 1939, p. 200), which has the property of recognising ‘ordinal formulae.’ One can only safely say that Turing's interest at this time in uncomputable operations appears in the general setting of studying the mental ‘intuition’ of truths which are not established by following mechanical processes (Turing 1939, p. 214ff.).

In Turing's presentation, intuition is in practice present in every part of a mathematician's thought, but when mathematical proof is formalised, intuition has an explicit manifestation in those steps where the mathematician sees the truth of a formally unprovable statement. Turing did not offer any suggestion as to what he considered the brain was physically doing in a moment of such ‘intuition’; indeed the word ‘brain’ did not appear in his writing in this era. This question is of interest because of the views of Penrose (1989, 1990, 1994, 1996) on just this issue: Penrose holds that the ability of the mind to see formally unprovable truths shows that there must be uncomputable physical operations in the brain. It should be noted that there is widespread disagreement about whether the human mind is really seeing the truth of a Gödel sentence; see for instance the discussion in (Penrose 1990) and the reviews following it. However Turing's writing at this period accepted without criticism the concept of intuitive recognition of the truth.

It was also at this period that Turing met Wittgenstein, and there is a full record of their 1939 discussions on the foundations of mathematics in (Diamond 1976). To the disappointment of many, there is no record of any discussions between them, verbal or written, on the problem of Mind.

In 1939 Turing's various energetic investigations were broken off for war work. This did, however, have the positive feature of leading Turing to turn his universal machine into the practical form of the modern digital computer.

[Lloyd Gillespie]

Alan Turing__Building A Universal Machine...

When apprised in 1936 of Turing's idea for a universal machine, Turing's contemporary and friend, the economist David Champernowne, reacted by saying that such a thing was impractical; it would need ‘the Albert Hall.’ If built from relays as then employed in telephone exchanges, that might indeed have been so, and Turing made no attempt at it. However, in 1937 Turing did work with relays on a smaller machine with a special cryptological function (Hodges 1983, p. 13. World history then led Turing to his unique role in the Enigma problem, to his becoming the chief figure in the mechanisation of logical procedures, and to his being introduced to ever faster and more ambitious technology as the war continued.

After 1942, Turing learnt that electronic components offered the speed, storage capacity and logical functions required to be effective as ‘tapes’ and instruction tables. So from 1945, Turing tried to use electronics to turn his universal machine into practical reality. Turing rapidly composed a detailed plan for a modern stored-program computer: that is, a computer in which data and instructions are stored and manipulated alike. Turing's ideas led the field, although his report of 1946 postdated von Neumann's more famous EDVAC report (von Neumann 1945). It can however be argued, as does Davis (2000), that von Neumann gained his fundamental insight into the computer through his pre-war familiarity with Turing's logical work. At the time, however, these basic principles were not much discussed. The difficulty of engineering the electronic hardware dominated everything.

It therefore escaped observers that Turing was ahead of von Neumann and everyone else on the future of software, or as he called it, the ‘construction of instruction tables.’ Turing (1946) foresaw at once:

"Instruction tables will have to be made up by mathematicians with computing experiences and perhaps a certain puzzle-solving ability. There will probably be a great deal of work to be done, for every known process has got to be translated into instruction table form at some stage.

The process of constructing instruction tables should be very fascinating. There need be no real danger of it ever becoming a drudge, for any processes that are quite mechanical may be turned over to the machine itself."

These remarks, reflecting the universality of the computer, and its ability to manipulate its own instructions, correctly described the future trajectory of the computer industry. However, Turing had in mind something greater: ‘building a brain.’

Building a Brain...
The provocative words ‘building a brain’ from the outset announced the relationship of Turing's technical computer engineering to a philosophy of Mind. Even in 1936, Turing had given an interpretation of computability in terms of ‘states of mind’. His war work had shown the astounding power of the computable in mechanising expert human procedures and judgments. From 1941 onwards, Turing had also discussed the mechanisation of chess-playing and other ‘intelligent’ activities with his colleagues at Bletchley Park (Hodges 1983, p. 213). But more profoundly, it appears that Turing emerged in 1945 with a conviction that computable operations were sufficient to embrace all mental functions performed by the brain. As will become clear from the ensuing discussion, the uncomputable ‘intuition’ of 1938 disappeared from Turing's thought, and was replaced by new ideas all lying within the realm of the computable. This change shows even in the technical prospectus of (Turing 1946), where Turing referred to the possibility of making a machine calculate chess moves, and then continued:

"This … raises the question ‘Can a machine play chess?’ It could fairly easily be made to play a rather bad game. It would be bad because chess requires intelligence. We stated … that the machine should be treated as entirely without intelligence. There are indications however that it is possible to make the machine display intelligence at the risk of its making occasional serious mistakes. By following up this aspect the machine could probably be made to play very good chess."

The puzzling reference to ‘mistakes’ is made clear by a talk Turing gave a year later (Turing 1947), in which the issue of mistakes is linked to the issue of the significance of seeing the truth of formally unprovable statements.

"…I would say that fair play must be given to the machine. Instead of it giving no answer we could arrange that it gives occasional wrong answers. But the human mathematician would likewise make blunders when trying out new techniques… In other words then, if a machine is expected to be infallible, it cannot also be intelligent. There are several mathematical theorems which say almost exactly that. But these theorems say nothing about how much intelligence may be displayed if a machine makes no pretence at infallibility."

Turing's post-war view was that mathematicians make mistakes, and so do not in fact see the truth infallibly. Once the possibility of mistakes is admitted, Gödel's theorem become irrelevant. Mathematicians and computers alike apply computable processes to the problem of judging the correctness of assertions; both will therefore sometimes err, since seeing the truth is known not to be a computable operation, but there is no reason why the computer need do worse than the mathematician. This argument is still very much alive. For instance, Davis (2000) endorses Turing's view and attacks Penrose (1989, 1990, 1994, 1996) who argues against the significance of human error on the grounds of a Platonist account of mathematics.

Turing also pursued more constructively the question of how computers could be made to perform operations which did not appear to be ‘mechanical’ (to use common parlance). His guiding principle was that it should be possible to simulate the operation of human brains. In an unpublished report (Turing 194, Turing explained that the question was that of how to simulate ‘initiative’ in addition to ‘discipline’ — comparable to the need for ‘intuition’ as well as mechanical ingenuity expressed in his pre-war work. He announced ideas for how to achieve this: he thought ‘initiative’ could arise from systems where the algorithm applied is not consciously designed, but is arrived at by some other means. Thus, he now seemed to think that the mind when not actually following any conscious rule or plan, was nevertheless carrying out some computable process.

He suggested a range of ideas for systems which could be said to modify their own programs. These ideas included nets of logical components (‘unorganised machines’) whose properties could be ‘trained’ into a desired function. Thus, as expressed by (Ince 1989), he predicted neural networks. However, Turing's nets did not have the ‘layered’ structure of the neural networks that were to be developed from the 1950s onwards. By the expression ‘genetical or evolutionary search’, he also anticipated the ‘genetic algorithms’ which since the late 1980s have been developed as a less closely structured approach to self-modifying programs. Turing's proposals were not well developed in 1948, and at a time when electronic computers were only barely in operation, could not have been. Fresh attention to them has been drawn by Copeland and Proudfoot (1996), and they have now have been tried out (Teuscher 2001).

It is important to note that Turing identified his prototype neural networks and genetic algorithms as computable. This has to be emphasised since the word ‘nonalgorithmic’ is often now confusingly employed for computer operations that are not explicitly planned. Indeed, his ambition was explicit: he himself wanted to implement them as programs on a computer. Using the term Universal Practical Computing Machine for what is now called a digital computer, he wrote in (Turing 194:

"It should be easy to make a model of any particular machine that one wishes to work on within such a UPCM instead of having to work with a paper machine as at present. If one also decided on quite definite ‘teaching policies’ these could also be programmed into the machine. One would then allow the whole system to run for an appreciable period, and then break in as a kind of ‘inspector of schools’ and see what progress had been made. One might also be able to make some progress with unorganised machines…"

The upshot of this line of thought is that all mental operations are computable and hence realisable on a universal machine: the computer. Turing advanced this view with increasing confidence in the late 1940s, perfectly aware that it represented what he enjoyed calling ‘heresy’ to the believers in minds or souls beyond material description.

Turing was not a mechanical thinker, or a stickler for convention; far from it. Of all people, he knew the nature of originality and individual independence. Even in tackling the U-boat Enigma problem, for instance, he declared that he did so because no-one else was looking at it and he could have it to himself. Far from being trained or organised into this problem, he took it on despite the prevailing wisdom in 1939 that it was too difficult to attempt. His arrival at a thesis of ‘machine intelligence’ was not the outcome of some dull or restricted mentality, or a lack of appreciation of individual human creativity.

[Lloyd Gillespie]

Alan Turing__Unfinished Work...

From 1950 Turing worked on a new mathematical theory of morphogenesis, based on showing the consequences of non-linear equations for chemical reaction and diffusion (Turing 1952). He was a pioneer in using a computer for such work. Some writers have referred to this theory as founding Artificial Life (A-life), but this is a misleading description, apt only to the extent that the theory was intended, as Turing saw it, to counter the Argument from Design. A-life since the 1980s has concerned itself with using computers to explore the logical consequences of evolutionary theory without worrying about specific physiological forms. Morphogenesis is complementary, being concerned to show which physiological pathways are feasible for evolution to exploit. Turing's work was developed by others in the 1970s and is now regarded as central to this field.

It may well be that Turing's interest in morphogenesis went back to a primordial childhood wonder at the appearance of plants and flowers. But in another late development, Turing went back to other stimuli of his youth. For in 1951 Turing did consider the problem, hitherto avoided, of setting computability in the context of quantum-mechanical physics. In a BBC radio talk of that year (Turing 1951) he discussed the basic groundwork of his 1950 paper, but this time dealing rather less certainly with the argument from Gödel's theorem, and this time also referring to the quantum-mechanical physics underlying the brain. Turing described the universal machine property, applying it to the brain, but said that its applicability required that the machine whose behaviour is to be imitated

"…should be of the sort whose behaviour is in principle predictable by calculation. We certainly do not know how any such calculation should be done, and it was even argued by Sir Arthur Eddington that on account of the indeterminacy principle in quantum mechanics no such prediction is even theoretically possible."

Copeland (1999) has rightly drawn attention to this sentence in his preface to his edition of the 1951 talk. However, Copeland's critical context suggests some connection with Turing's ‘oracle.’ There is is in fact no mention of oracles here (nor anywhere in Turing's post-war discussion of mind and machine.) Turing here is discussing the possibility that, when seen as as a quantum-mechanical machine rather than a classical machine, the Turing machine model is inadequate. The correct connection to draw is not with Turing's 1938 work on ordinal logics, but with his knowledge of quantum mechanics from Eddington and von Neumann in his youth. Indeed, in an early speculation, influenced by Eddington, Turing had suggested that quantum mechanical physics could yield the basis of free-will (Hodges 1983, p. 63). Von Neumann's axioms of quantum mechanics involve two processes: unitary evolution of the wave function, which is predictable, and the measurement or reduction operation, which introduces unpredictability. Turing's reference to unpredictability must therefore refer to the reduction process. The essential difficulty is that still to this day there is no agreed or compelling theory of when or how reduction actually occurs. (It should be noted that ‘quantum computing,’ in the standard modern sense, is based on the predictability of the unitary evolution, and does not, as yet, go into the question of how reduction occurs.) It seems that this single sentence indicates the beginning of a new field of investigation for Turing, this time into the foundations of quantum mechanics. In 1953 Turing wrote to his friend and student Robin Gandy that he was ‘trying to invent a new Quantum Mechanics but it won't really work.’

At Turing's death in June 1954, Gandy reported in a letter to Newman on what he knew of Turing's current work (Gandy 1954). He wrote of Turing having discussed a problem in understanding the reduction process, in the form of

"…‘the Turing Paradox’; it is easy to show using standard theory that if a system start in an eigenstate of some observable, and measurements are made of that observable N times a second, then, even if the state is not a stationary one, the probability that the system will be in the same state after, say, 1 second, tends to one as N tends to infinity; i.e. that continual observation will prevent motion. Alan and I tackled one or two theoretical physicists with this, and they rather pooh-poohed it by saying that continual observation is not possible. But there is nothing in the standard books (e.g., Dirac's) to this effect, so that at least the paradox shows up an inadequacy of Quantum Theory as usually presented."

Turing's investigations take on added significance in view of the assertion of Penrose (1989, 1990, 1994, 1996) that the reduction process must involve something uncomputable. Probably Turing was aiming at the opposite idea, of finding a theory of the reduction process that would be predictive and computable, and so plug the gap in his hypothesis that the action of the brain is computable. However Turing and Penrose are alike in seeing this as an important question affecting the assumption that all mental action is computable; in this they both differ from the mainstream view in which the question is accorded little significance.

Alan Turing's last postcards to Robin Gandy, in March 1954, headed ‘Messages from the Unseen World’ in allusion to Eddington, hinted at new ideas in the fundamental physics of relativity and particle physics (Hodges 1983, p. 512). They illustrate the wealth of ideas with which he was concerned at that last point in his life, but which apart from these hints are entirely lost. A review of such lost ideas is given in (Hodges 2004), as part of a larger volume on Turing's legacy (Teuscher 2004).

Alan Turing: the Unknown Mind
It is a pity that Turing did not write more about his ethical philosophy and world outlook. As a student he was an admirer of Bernard Shaw's plays of ideas, and to friends would openly voice both the hilarities and frustrations of his many difficult situations. Yet the nearest he came to serious personal writing, apart from occasional comments in private letters, was in penning a short story about his 1952 crisis (Hodges 1983, p. 44. His last two years were particularly full of Shavian drama and Wildean irony. In one letter (to his friend Norman Routledge; the letter is now in the Turing Archive at King's College, Cambridge) he wrote:

"Turing believes machines think
Turing lies with men
Therefore machines do not think"

The syllogistic allusion to Socrates is unmistakeable, and his demise, with cyanide rather than hemlock, may have signalled something similar. A parallel figure in World War II, Robert Oppenheimer, suffered the loss of his reputation during the same week that Turing died. Both combined the purest scientific work and the most effective application of science in war. Alan Turing was even more directly on the receiving end of science, when his sexual mind was treated as a machine, against his protesting consciousness and will. But amidst all this human drama, he left little to say about what he really thought of himself and his relationship to the world of human events.

Alan Turing did not fit easily with any of the intellectual movements of his time, aesthetic, technocratic or marxist. In the 1950s, commentators struggled to find discreet words to categorise him: as ‘a scientific Shelley,’ as possessing great ‘moral integrity’. But until the 1970s the reality of his life was unmentionable. He is still hard to place within twentieth-century thought. He exalted the science that existentialists held to have had robbed life of meaning. The most original figure, the most insistent on personal freedom, he held originality and will to be susceptible to mechanisation. The mind of Alan Turing remains an enigma.

[labelwench]

After reading your posts on Alan Turing, the first image that presents itself to me is the physical structure of the human brain, being of two lobes, that each have specific areas of responsibility in compiling and computing the input of our multiple senses, that we might make appropriate response to the circumstances of life, which are in a state of constant flux.

While our inner ear assists in maintaining our upright posture and balance, and we are gravely handicapped in this matter even by a sinus cold, it is the brain that allows us to balance in three dimensions, as it orients us to gravity and light, while co-ordinating the multiple 'involuntary response systems' that provide continuity to our biological integrity.

Tucked between the two lobes, and very small in size, somewhere between a large grain of rice or a small pea, lies the pineal gland, about which we know relatively little.

The Pineal Gland is about the size of a pea, and is in the center of the brain in
a tiny cave, behind and above the pituitary gland, which lies a little behind the root
of the nose. It is located directly behind the eyes, attached to the third ventricle.

Until we learn more about the 'super-computer' (brain) that each of us is born with, and gain an understanding both of the 'default settings' at birth, and the wide range of options that each of us has in our own personal development of these inherent gifts, finding that 'interface' shall remain a challenge.

Language and words are laborious, and a lifetime of experience gained by one, takes much time to preserve for future generations, though it is important that such be done until we learn a better means of transfer.

Somehow we shall unravel the clues, until we can truly 'know ourselves' and comprehend the means by which we can communicate without all the clutter.

Surely at least some of you have known at least one other person with whom words were almost unnecessary?

Regardless of gender or age, every once in a while you meet someone, and something about them lets you know, that they know, too....

Dialogue and sharing, without the usual trappings.

Just like the natural order.

Everything plugs in wherever it fits, and there is a place for everything, although presently this may not be overtly in evidence.

Just ruminating, as ever......

[SteveA]

"…‘the Turing Paradox’; it is easy to show using standard theory that if a system start in an eigenstate of some observable, and measurements are made of that observable N times a second, then, even if the state is not a stationary one, the probability that the system will be in the same state after, say, 1 second, tends to one as N tends to infinity; i.e. that continual observation will prevent motion. Alan and I tackled one or two theoretical physicists with this, and they rather pooh-poohed it by saying that continual observation is not possible. But there is nothing in the standard books (e.g., Dirac's) to this effect, so that at least the paradox shows up an inadequacy of Quantum Theory as usually presented."

I believe a resolution for time in physics is to replace the concept of rates with a sequential ordering of events. The perception of delay appears to be a conscious quality that would not necessarily be physically measurable, but instead that if a theory presents the observations in the correct sequential order (which is in many ways a more detailed representation that I believe can potentially reveal structure on broader scales of time and space), that should be sufficient to verify it, even if the durations of times between events don't agree with consciously measured rates or durations.

I believe the most precise scales of measurement occur when all "independent" sources of information are recorded individually as there would not be a finer scale of measurement for time available, there would be not specific duration of these in time.

For example, if you had a mechanical clock, its motions are determined by many influences that can chaotically interact and you have some motions cancel and some reinforce into the single dimensional measurement of time. By splitting these components of interaction into finer scales and recording them as a sequential order as precisely as possible the precision of the scale is increased and we can potentially even determine scales of time at a resolution finer than these individual events would normally be considered to allow and this occurs indirectly as an ability to favorably bias predictions of which events will occur next. In fact, we may even be able to indirectly see scales of space outside that of quantization by photons.

As a specific example, let's say that we're taking measurements of something in one of three possible states. If we're using a lowest level representation for time, then there would be no additionally finer scale clock to denote times between these states. The transitions between them would be those references.

I'll show an oversimplified example first. Let's say we saw this sequence of events:

11011101101110110

A normal reference for time would simply be to sum as many events as possible into the highest possible "rate", but without retaining information regarding their classes and phase/ordering information, we can miss a finer scale.

In this case we can see that the 1s occur at a rate that is approximately 2 1/2 times faster/denser than the 0s occur.

We could actually construct a finer scale prediction of "where", between these units of time, the 1s and 0s are "at".

If we integrated velocities of 1 and 2/5, we could construct the equivalent of these 1s and 0s cycling through an observational origin in space within a single pathway of space, though we also convert this to these objects moving at identical velocities through different pathways.

If they began at a phase of 1/10th of a cycle, then the times of observation, (relative to a more fundamental unit) would be (p(n) represents the distances to recurring observations at the origin and 'phase0' and 'phase1' represent the offset or initial phase of these and v0 and v1 represent the velocities of these:

t0(n)=(p(n)-phase0)/v0
t1(n)=(p(n)-phase1)/v1

For the zeroes, we have "crossing times" of:

t0(1)= (1-.1)/(2/5)=2.25
t0(2)= (2-.1)/(2/5)=4.75
t0(3)= (3-.1)/(2/5)=7.25
t0(4)= (4-.1)/(2/5)=9.75
t0(5)= (5-.1)/(2/5)=12.25
...

For the ones, we similarly have

t1(1)= (1-.1)/1=.9
t1(2)= (2-.1)/1=1.9
t1(3)= (3-.1)/1=2.9
t1(4)= (4-.1)/1=3.9
t1(5)= (5-.1)/1=4.9
...

If we sort these into a timeline showing the composite, these events would occur in this order:

1(.9),1(1.9),0(2.25),1(2.9),1(3.9),0(4.75),1(4.9), 1(5.9),1(6.9),0(7.25),1(7.9),

1101101110...

A range of possible phase and frequency/velocity estimates at a current moment of an observation could be constructed to dynamically track a continually refined window regarding the likely positions of unobservables (I wonder if that could be done on a molecular scale? Use atomic shell configurations as the "computing elements" to predict photon positions on scales fine enough to be useful?)

But the reality, I believe, is a bit more complex than this and there are additional considerations. The first being that multiple observations of an identical state should be impossible for any version of time that was to be at a foundational level. These units should also be discrete and if all objects moved synchronous to this, but could be observed in parallel, then composite/simultaneous observations as possible, in which case the individual components would not appear to repeat in a regular fashion (though they could still be present within an observation). Also, any prediction based upon these would arise synchronous to these as well as there would be no other "more fundamental" version of time (the unknowns arise from quantities toward macroscale properties, though we can ascribe them to arising from finer scales of interaction, but that would just be semantics).

There's actually a natural progression of forms that would appear to arise from making simultaneous observers of all possible systems synchronized in time (and we can even consider all "random" systems to be included as well - they simply need to be observed in some discrete state at any moment), but I've posted enough regarding this already and I don't want to be too redundant - and I'm still trying to untangle the details more myself.

The main point of this post was simply to point out that there can exist finer scales of time than are detected, by definition, in much of the current physics models (which effectively rely upon an assumption of randomness simply by the manner in which measurements are made - and I think we can do better).

Have fun,
Steve

[Graybeard]

Carthage__Eastern Empire Rises In The West...

Dear Lloyd .... what is this post referring to ??

cool bananas ... greg

[Lloyd Gillespie]

Steve, the reason we can't do better, is the fact we have no sensors to measure below Planck 10^-33cm, and 10^-43t... Any mathematics below these scales are beyond science's physical abilities, and the maths must apply to physical reality, or it ain't science. Physicists and mathematicians know they can do maths below or beyond any physically measurable scales__but, then they're in science-fiction, and that's useless to science. That's why I stay away from sub-Planck and hyper-light scales__They may answer any theories' questions, but they don't pertain to reality. Both Einstein and Wheeler mentioned these facts years ago...

Btw, I don't consider it a paradox__it's just an unmeasurable... Nature don't got no paradoxes... And, nothing disappears upon observation__it changes position faster than we can measure, with our light-speed restricted instruments... I work toward seeing the QM fine structures as flow models__The flow works, for the larger scales, so there's really no giant mystery__we just can't measure it__Exactly...

It's a lot like a lotta' things we don't yet know about our personal realities__which seem beyond our present comprehension__That's what the real metaphysical is__The unknown incompleteness of thought, theories and facts...

The Bio-Law of Give and Receive Action / | \ The Geo-Law of Action and Reaction...

"Math is the #1 necessity, as it only, carries logic to its limits..."

"Self is absolute morality, if we choose it so..."

"Moral logic is the heart of the universe of discourse..."

[Lloyd Gillespie]

Dear Lloyd .... what is this post referring to ??

cool bananas ... greg

It's about how values of lost civilizations of evil, can rise anew, with proper purposeful leadership. Queen Dido's brother was a tyrant who destroyed Tyre, after killing her husband. His sister fled, and refounded her city-state as the world's greatest known empire__at the time... It's about Values Greg, what you seem to be against__Values the West must relearn from the East, if the West is to survive the onslaught of her present scientific, and academic collapse...

The Scientific Values of Unification Axiology...

Esthetics__The Science of Motives, Aims, Goals and Purposes...

The Pursuit of Absolute Value...

Socrates...
Socrates (470-399 B. C.) appeared when sophism was rampant in Greek Society, and he deplored it. For him, the Sophists pretended to know, but in reality they knew nothing. Of himself, he said, "One thing only I know for sure, and that is that I know nothing." Such was the starting point of his plan to reach true knowledge. He sought the basis of morality in the God (daimon) inherent within the human being, and asserted that morality is absolute and universal. Virtue, as taught by him, was a loving attitude of seeking knowledge, and "knowledge is virtue" was his fundamental thought. He also advocated the unity of knowledge and action, saying that once one knows virtue, one should put it into practice without fail.

How can someone obtain true knowledge? True knowledge is not to be poured into a person by others, nor can it be known by an individual alone. Only through dialogue (questions and answers) with others can someone reach true knowledge (the universal truth) which satisfies all people, Socrates thought. He then sought to save Athens from its social disorder by establishing absolute, universal virtues.

Plato...
Plato (427-347 B. C.) thought that there is an unchangeable world of essence behind the changing world of phenomena, and called it the world of Ideas. Yet, since people's souls are trapped in their bodies, people are usually convinced that the phenomenal world is true reality. The human soul previously existed in a world of Ideas, but when it came to dwell in the body, the soul was separated from the world of Ideas.

Accordingly, the soul constantly longs for the world of Ideas, which is the true reality. For Plato, knowledge of Ideas is nothing but a recollection of what the soul knew before coming into the body.

Ethical Ideas included beauty, truth, and goodness, with the Idea of the Good regarded as supreme.

Plato enumerated the four virtues of wisdom, courage, temperance, and justice as the virtues that everyone must have. He felt that those who rule the state, especially, must be philosophers with the virtue of wisdom and an understanding of the Idea of the Good. For Plato, the Idea of the Good was the source of all values. Inheriting Socrates' spirit, Plato sought to find absolute value.

The Necessity for a New View of Value
As seen above, many systems of value have appeared throughout history; in fact, history can be seen as a succession of failed attempts to establish absolute values.

In ancient Greece, Socrates and Plato tried to establish absolute values by pursuing true knowledge. With the collapse of the Greek city-state society, however, the views of value of Greek philosophy also collapsed. Next, Christianity tried to establish absolute values centered on God's love (agape). The Christian view of value ruled medieval society, but with the collapse of medieval society, it gradually lost its power.

In the modern period, Descartes and Kant established views of value centered on reason, as in Greek philosophy; yet, their understanding of God, which was the basis for their views of value, was ambiguous.

As a result, their views of value fell short of being absolute. Pascal and Kierkegaard tried to revive true Christian values, but they fell short of establishing a firm system of value.

The Neo-Kantian school dealt with value as one of the main issues in philosophy, but they completely separated philosophy, which deals with values, from natural science, which deals with facts. As a result, many problems came into being. As scientists have continued to analyze facts in disregard of values, the results have been weapons of mass destruction, the abuse of the natural environment, pollution, and so forth.

Utilitarianism and pragmatism are materialistic systems of value, which makes their views of values completely relative. Analytical philosophy is a philosophy without value. Nietzsche's philosophy and Communism can be described as anti-value philosophies opposing traditional views of value.

Traditional views of value based on Greek philosophy and Christianity are no longer regarded as important today. Traditional views of value have become weak and separated from natural science. Now they have been almost completely eliminated even from the field of philosophy. As a result, society today is in extreme confusion. The appearance of a new view of value that can establish absolute values while revitalizing the traditional systems of value is deeply hoped for. This new view of value should be able to overcome materialism and to guide science with its correct view of value. This is so because value and fact are in the relationship of Sungsang and Hyungsang, and just as Sungsang and Hyungsang are united in existing beings, value and fact are originally united. Unification axiology is precisely that which has appeared to answer this demand of our times.

[Graybeard]

It's about how values of lost civilizations of evil, can rise anew, with proper purposeful leadership.

Why was Phonecia a civilisation of evil ..... pretty well par for the times I would think.

Queen Dido's brother was a tyrant who destroyed Tyre, after killing her husband. His sister fled, and refounded her city-state as the world's greatest known empire__at the time... It's about Values Greg, what you seem to be against__Values the West must relearn from the East, if the West is to survive the onslaught of her present scientific, and academic collapse...

I think you may be merging legend, myth, and reality here. Thomas Jefferson's DNA carried the markers for Phonecia. In my opinion he had values.

cool bananas ... greg