(Hyperlink to Instructor Key at Bottom of Page)
Montréal, March 23, 2000
Physics and Curved Space 101
March 23, 2000
PACS 101 Entrance Exam
1. An engineering team has designed a ten foot by four foot by one foot thick slate domino weighing four tons. A large quantity of dominos has been made so that they can be stood on edge along a straight line with their broad face transverse to the line, as in the usual domino configuration. There are sufficient dominos to go around the full circumference of the earth at a spacing of five feet, ... a flat causeway and pontoon system has been engineered to provide a continuous smooth surface over the 25,000 mile distance.
You are given a piece of chalk, a lever and a car jack, and asked to enter one of the inter-domino gaps, situate the jack assymetrically so that it topples one of the dominos and starts the dynamical sequence. After starting the domino process, you must turn around so that you are facing the first domino in the still standing sequence, and write the equation of motion for the dominos on its slate surface. Should you, ...;
(a) Choose the euclidian space convention for describing the straight line.?
(b) Choose the spherical space convention for describing the straight line.?
(c) Get the hell out of there!
2. You are give the general solution for the dynamical interactions of multiple six-member ensembles of nomads (wandering tribesmen) on an unbounded landscape in which the total available surface area is given by A*(1 + r*(n-1)) where 'A' is the area covered by a single ensemble (one billionth the surface area of the earth), ... 'n' is the number of ensembles, and 'r' is a fraction between 0. and 1.0. You are also given an experimental plan which calls for increasing the number of participating nomadic ensembles from one on up to one billion. You are asked to do a live enactment of this experiment in which the nomadic ensembles are deployed on the surface of the earth. Do you, ....
(a) Keep the solution formulation in the standard euclidian terms where the self-referentiality (dipolarity) of the containing space is assumed to be zero?
(b) Re-develop the solution in non-euclidian terms where reciprocal disposition effects propagating over the horizon and back around again, are accounted for?
(c) Start the simulation, then get the hell out of there!
3. A pool pro (billiards pro) is invited to go on a camping trip with a multi-disciplinary scholar. After a good meal and a bottle of wine they both lay down for the night and go to sleep. Several hours later, the pool pro wakes up, nudges his companion and says: "Look up at the sky and tell me what you see."
The scholar replies: "I see millions and millions of stars."
The pool pro asks; "What does that tell you?"
The scholar ponders things for a moment and then says; Astronomically, it tells me that there are millions of galaxies and billions of planets. Astrologically, I observe that Saturn is in Leo. Horologically, I deduce that the time is approximately a quarter past three. Theologically, I can see that God is all powerful and that we are small and insignificant. Meteorologically, I suspect that tomorrow will be a beautiful day. What does it tell you?"
The pool pro pauses for a moment,... then says; "You dickhead. Some bastard has
stolen our tent."
* * *
Do you explain the divergent modes of inquiry in terms of, ...
(a) Ontological inquiry is innately blind to emergence and subduction which occurs within the domain of inquiry?
(b) The relational interference which informs the senses as to ontogenetic emergence and subduction is destroyed in the process of ontological inquiry? (i.e. Feynman's formulation of Heisenberg's uncertainty principle.)
(c) Orienting one's perception and inquiry to 'shape' (implicit ontogenetic transformation) over 'shots' (explicit ontological facts or events) is a superior strategy whose application goes well beyond eight-ball and snooker?
(d) The scholar is truly a dickhead.
4. You are the captain of one of a flotilla of sailboats out on the open ocean when a magnetic storm erupts and disables all communications and location instruments apart from radar, which all the boats have. The radar tells you only your RELATIVE motion with respect to the other vessels, ... and because of vagaries of wind and current, you have no independent means of segregating your manoevering efforts from the manoevering efforts of the other vessels. You are concerned about collisions in the severe weather and so you need to somehow 'calibrate' the effectiveness of your manoevering tactics to develop a collision avoidance capability. You notice that when you approach a linear 'line-up' of vessels, ... there is total ambiguity as to whether it is 'you' closing on 'them' or 'them' closing on 'you'. After many observations, you determine that the only time you can 'segregate' for sure what 'you' are doing relative to 'them', is when you are surrounded, at all azimuths, by vessels which are either radially receding from you or radially closing on you. That is, you know that your vessel cannot at the same time be approaching multiple other vessels situated at all points of the compass around you, ... nor can your vessel be receding, at the same time, from multiple vessels at all points of the compass around you.
Do you conclude from this;
(a) Relativity means that one's behavior can never be determined in its own right, but only in terms of the behaviors of others? (i.e. the ontogeny of the containing ensemble determines the ontology of its constituency?)
(b) All sailing vessels should be equipped with either GPS systems or no-fault insurance policies?
(c) The best collision-avoidance tactic is to make your boat look like a lighthouse.
5. You are the mayor in a town in which one of the town's most successful business executives, a healthy young female, has been found dead in her apartment. The coroner determines that she has been poisoned, and a homicide investigation is initiated. There are numerous motives being discussed in the town's rumour mill which throw suspicion on several individuals. The District Attorney regards the citizenry in general as being in possession of ontologic facts which are mixed in with 'noise', ... not necessarily intentional falsehoods, but inaccuracies which obscure the truth. The town's most prominent defense attorney, rather than seeing people's testimony in terms of 'facts partially obscured by noise' sees people in terms of ontogenetic canvases which have been written upon by their particular relational experiences.
The DA, in his continuing inquiry with the citizens, ... continues to build signal to noise ratio and is able to exclude several of the theories, ... homing in on the most likely three. While the suspects in two of these theories have credible alibi's which remove them from the scene during the time interval in which the poison would have had to be administered, ... the suspect in the third case had motive and no such alibi. By refocusing more intensively on the testimony of those who knew the movements of both the deceased and the suspect, ... the DA was able to confirm that the suspect's movements during the critical interval had given him ample opportunity to administer the poison to the victim. The suspect was arrested and retained the defense attorney mentioned earlier.
The defense attorney began an inquiry which was reciprocal in its approach to that used by the DA. He began a broad basis of interviews of a general nature, without reference to any 'likely theories', searching for relational patterns of interest. He accepted no facts or theories as he gathered information he excluded nothing. As his database built, a number of the victim's local activities pointed to an ongoing relationship with someone in another country which was not known about by any of the local citizens, but which had been established during the victim's frequent travel abroad. Further investigation showed that the poison had been self-administered, ... implanted in a gift of chocolates given to the victim by her jilted lover abroad. The local suspect was released and the foreign suspect comitted suicide while being pursued by Interpol.
The contrasting 'imaging' approaches used in this case by the DA and the defense attorney were (1) 'exclusionary ontologic filtering' which starts off by assuming the existence of causal truths or 'facts' buried in noise and seeks to build the signal to noise ratio to the point that 'actuality' is cleanly 'imaged' and (2) 'inclusionary ontogenetic synthesis' which makes no initial assumptions but seeks to bring into connective focus, interferential patterns which 'image' the 'opportunity space' from which the ontologic actuality was precipitated.
As the mayor, you recognize how nearly the DA's approach came to convicting an innocent citizen and you make a statement which includes which of the following?
(a) Schroedinger's view that ontologic fact is only apparent and that 'things' must be seen instead as 'canvas' painted with a collection of backscattered relational experience, ... a wavefield which must be 'backward continued' to 'image' the meaning-giving possibility space from whence the ontologic state was precipitated.
(b) Exclusionary filtering methods which must be seeded with initial hypotheses will always yield a hypothesis of maximum signal to noise ratio, ... but will be exposed to the possibility that the appropriate seed hypothesis is never introduced.
(c) The victim was a seductress who had it coming to her, anyway.
6. (Only for those students who have found their C-legs ( 'curved-space legs')).
Discuss how the answers to questions 1 - 5 contribute to the general theory of relativity notion of the primacy of space-over-matter, and how this leads to the notion of 'dipolar' or complex space-time phase information being the fundamental information type in nature, rather than 'real', bivalent information, and show how imagination (i.e. the imaginary component) relates to curved space visualization. Show also how ontogenetic time relates to historical (linear or ontologic) time in the same way as the defense attorney's perception of possibility space relates to the DA's perception of factual space. Lastly, identify the correspondence between the characters involved in the first five questions of the exam, including yourself, with the characters in the following excerpt from Charles Dicken's 'Hard Times', citing supportive examples from your own experience;
'Hard Times' by Charles Dickens, Book the First, Sowing
Chapter 1: The One Thing Needful
'NOW, what I want is, Facts. Teach these boys and girls nothing but Facts. Facts alone are wanted in life. Plant nothing else, and root out everything else. You can only form the minds of reasoning animals upon Facts: nothing else will ever be of any service to them. This is the principle on which I bring up my own children, and this is the principle on which I bring up these children. Stick to Facts, sir!'
The scene was a plain, bare, monotonous vault of a schoolroom, and the speaker's square forefinger emphasised his observations by underscoring every sentence with a line on the schoolmaster's sleeve. The emphasis was helped by the speaker's square wall of a forehead, which had his eyebrows for its base, while his eyes found commodious cellarage in two dark caves, overshadowed by the wall. The emphasis was helped by the speaker's mouth, which was wide, thin, and hard set. The emphasis was helped by the speaker's voice, which was inflexible, dry, and dictatorial. The emphasis was helped by the speaker's hair, which bristled on the skirts of his bald head, a plantation of firs to keep the wind from its shining surface, all covered with knobs, like the crust of a plum pie, as if the head had scarcely warehouse-room for the hard facts stored inside. The speaker's obstinate carriage, square coat, square legs, square shoulders- nay, his very neckcloth, trained to take him by the throat with an unaccommodating grasp, like a stubborn fact, as it was-all helped the emphasis.
'In this life, we want nothing but Facts, sir; nothing but Facts!' The speaker, and the schoolmaster, and the third grown person present, all backed a little, and swept with their eyes the inclined plane of little vessels then and there arranged in order, ready to have imperial gallons of facts poured into them until they were full to the brim.
Chapter 2: Murdering the Innocents
THOMAS GRADGRIND, sir. A man of realities. A man of fact and calculations. A man who proceeds upon the principle that two and two are four, and nothing over, and who is not to be talked into allowing for anything over. Thomas Gradgrind, sir- peremptorily Thomas- Thomas Gradgrind. With a rule and a pair of scales, and the multiplication table always in his pocket, sir, ready to weigh and measure any parcel of human nature, and tell you exactly what it comes to. It is a mere question of figures, a case of simple arithmetic. You might hope to get some other nonsensical belief into the head of George Gradgrind, or Augustus Gradgrind, or John Gradgrind, or Joseph Gradgrind (all suppositious, non-existent persons), but into the head of Thomas Gradgrind- no, sir!
In such terms Mr Gradgrind always mentally introduced himself, whether to his private circle of acquaintance, or to the public in general. In such terms, no doubt, substituting the words 'boys and girls', for 'sir', Thomas Gradgrind now presented Thomas Gradgrind to the little pitchers before him, who were to be filled so full of facts.
Indeed, as he eagerly sparkled at them from the cellarage before mentioned, he seemed a kind of cannon loaded to the muzzle with facts, and prepared to blow them clean out of the regions of childhood at one discharge. He seemed a galvanising apparatus, too, charged with a grim mechanical substitute for the tender young imaginations that were to be stormed away.
'Girl number twenty,' said Mr Gradgrind, squarely pointing with his square forefinger, 'I don't know that girl. Who is that girl?' 'Sissy Jupe, sir,' explained number twenty, blushing, standing up, and curtsying.
'Sissy is not a name,' said Mr Gradgrind. 'Don't call yourself Sissy. Call yourself Cecilia.'
'It's father as calls me Sissy, sir,' returned the young girl in a trembling voice, and with another curtsy.
'Then he has no business to do it,' said Mr Gradgrind. 'Tell him he mustn't. Cecilia Jupe. Let me see. What is your father?' 'He belongs to the horse- riding, if you please, sir.'
Mr Gradgrind frowned, and waved off the objectionable calling with his hand.
'We don't want to know anything about that, here. You mustn't tell us about that, here. Your father breaks horses, don't he?' 'If you please, sir, when they can get any to break, they do break horses in the ring, sir.'
'You mustn't tell us about the ring, here. Very well, then. Describe your father as a horsebreaker. He doctors sick horses, I dare say?' 'Oh yes, sir.'
'Very well, then. He is a veterinary surgeon, a farrier and horsebreaker. Give me your definition of a horse.'
(Sissy Jupe thrown into the greatest alarm by this demand.) 'Girl number twenty unable to define a horse!' said Mr Gradgrind, for the general behoof of all the little pitchers. 'Girl number twenty possessed of no facts, in reference to one of the commonest of animals! Some boy's definition of a horse. Bitzer, yours.' The square finger, moving here and there, lighted suddenly on Bitzer, perhaps because he chanced to sit in the same ray of sunlight which, darting in at one of the bare windows of the intensely whitewashed room, irradiated Sissy. For, the boys and girls sat on the face of the inclined plane in two compact bodies, divided up the centre by a narrow interval; and Sissy, being at the corner of a row on the sunny side, came in for the beginning of a sunbeam, of which Bitzer, being at the corner of a row on the other side, a few rows in advance, caught the end. But, whereas the girl was so dark-eyed and dark-haired, that she seemed to receive a deeper and more lustrous colour from the sun when it shone upon her, the boy was so light-eyed and light-haired that the self-same rays appeared to draw out of him what little colour he ever possessed. His cold eyes would hardly have been eyes, but for the short ends of lashes which, by bringing them into immediate contrast with something paler than themselves, expressed their form. His short-cropped hair might have been a mere continuation of the sandy freckles on his forehead and face. His skin was so unwholesomely deficient in the natural tinge, that he looked as though, if he were cut, he would bleed white. 'Bitzer,' said Thomas Gradgrind. 'Your definition of a horse.' 'Quadruped. Graminivorous. Forty teeth, namely twenty-four grinders, four eye-teeth, and twelve incisive. Sheds coat in the spring; in marshy countries, sheds hoofs, too. Hoofs hard, but requiring to be shod with iron. Age known by marks in mouth.' Thus (and much more) Bitzer.
'Now girl number twenty,' said Mr Gradgrind. 'You know what a horse is.'
She curtsied again, and would have blushed deeper, if she could have blushed deeper than she had blushed all this time. Bitzer, after rapidly blinking at Thomas Gradgrind with both eyes at once, and so catching the light upon his quivering ends of lashes that they looked like the antennae of busy insects, put his knuckles to his freckled forehead, and sat down again.
The third gentleman now stepped forth. A mighty man at cutting and drying, he was; a government officer; in his way (and in most other people's too), a professed pugilist; always in training, always with a system to force down the general throat like a bolus, always to be heard of at the bar of his little Public-office, ready to fight all England. To continue in fistic phraseology, he had a genius for coming up to the scratch, wherever and whatever it was, and proving himself an ugly customer. He would go in and damage any subject whatever with his right, follow up with his left, stop, exchange, counter, bore his opponent (he always fought All England) to the ropes, and fall upon him neatly. He was certain to knock the wind out of common-sense, and render that unlucky adversary deaf to the call of time. And he had it in charge from high authority to bring about the great public- office Millennium, when Commissioners should reign upon earth. 'Very well,' said this gentleman, briskly smiling, and folding his arms. 'That's a horse. Now, let me ask you girls and boys, Would you paper a room with representations of horses?'
After a pause, one half of the children cried in chorus, 'Yes, sir!' Upon which the other half, seeing in the gentleman's face that Yes was wrong, cried out in chorus, 'No, sir!'- as the custom is, in these examinations.
'Of course, No. Why wouldn't you?'
A pause. One corpulent slow boy, with a wheezy manner of breathing, ventured the answer, Because he wouldn't paper a room at all, but would paint it.
'You must paper it,' said Thomas Gradgrind, 'whether you like it or not. Don't tell us you wouldn't paper it. What do you mean, boy?' 'I'll explain to you, then,' said the gentleman, after another and a dismal pause, 'why you wouldn't paper a room with representations of horses. Do you ever see horses walking up and down the sides of rooms in reality- in fact? Do you?'
'Yes, sir!' from one half. 'No, sir!' from the other.
'Of course no,' said the gentleman, with an indignant look at the wrong half. 'Why, then, you are not to see anywhere, what you don't see in fact; you are not to have anywhere, what you don't have in fact. What is called Taste, is only another name for Fact.' Thomas Gradgrind nodded his approbation.
'This is a new principle, a discovery, a great discovery,' said the gentleman. 'Now, I'll try you again. Suppose you were going to carpet a room. Would you use a carpet having a representation of flowers upon it?'
There being a general conviction by this time that 'No, sir!' was always the right answer to this gentleman, the chorus of No was very strong. Only a few feeble stragglers said Yes; among them Sissy Jupe. 'Girl number twenty,' said the gentleman, smiling in the calm strength of knowledge.
Sissy blushed, and stood up.
'So you would carpet your room- or your husband's room, if you were a grown woman, and had a husband- with representations of flowers, would you,' said the gentleman. 'Why would you?' 'If you please, sir, I am very fond of flowers,' returned the girl. 'And is that why you would put tables and chairs upon them, and have people walking over them with heavy boots?'
'It wouldn't hurt them, sir. They wouldn't crush and wither if you please, sir. They would be the pictures of what was very pretty and pleasant, and I would fancy-'
'Ay, ay, ay! But you mustn't fancy,' cried the gentleman, quite elated by coming so happily to his point. 'That's it! You are never to fancy.'
'You are not, Cecilia Jupe,' Thomas Gradgrind solemnly repeated, 'to do anything of that kind.'
'Fact, fact, fact!' said the gentleman. And 'Fact, fact, fact!' repeated Thomas Gradgrind.
'You are to be in all things regulated and governed,' said the gentleman, 'by fact. We hope to have, before long, a board of fact, composed of commissioners of fact, who will force the people to be a people of fact, and of nothing but fact. You must discard the word Fancy altogether. You have nothing to do with it. You are not to have, in any object of use or ornament, what would be a contradiction in fact. You don't walk upon flowers in fact; you cannot be allowed to walk upon flowers in carpets. You don't find that foreign birds and butterflies come and perch upon your crockery. You never meet with quadrupeds going up and down walls; you must not have quadrupeds represented upon walls. You must use,' said the gentleman, 'for all these purposes, combinations and modifications (in primary colours) of mathematical figures which are susceptible of proof and demonstration. This is the new discovery. This is fact. This is taste.'
The girl curtsied, and sat down. She was very young, and she looked as if she were frightened by the matter of fact prospect the world afforded.
* * *
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