studenttag:www.thusspakeak.com,2013-08-07:/student//122022-04-08T15:37:08ZMovable Type 5.2.13On Pitfalltag:www.thusspakeak.com,2022:/student//12.3692022-04-22T19:00:00Z2022-04-08T15:37:08Z
Recall that in the Baron's latest wager, Sir R-----'s goal was to traverse a three by three checkerboard in steps determined by casts of a four sided die, each at a cost of two coins. Moving from left to right upon the first rank and advancing to the second upon its third file, thereafter from right to left and advancing upon the first file and finally from left to right again, he should have prevailed for a prize of twenty five coins had he landed upon the top right place. Frustrating his progress, however, were the rules that landing upon a black square dropped him back down to the first rank and that overshooting the last file upon the last rank required that he should move in reverse by as many places with which he had done so.
student
Recall that in the Baron's latest wager, Sir R-----'s goal was to traverse a three by three checkerboard in steps determined by casts of a four sided die, each at a cost of two coins. Moving from left to right upon the first rank and advancing to the second upon its third file, thereafter from right to left and advancing upon the first file and finally from left to right again, he should have prevailed for a prize of twenty five coins had he landed upon the top right place. Frustrating his progress, however, were the rules that landing upon a black square dropped him back down to the first rank and that overshooting the last file upon the last rank required that he should move in reverse by as many places with which he had done so.
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On A Generally Fractal Familytag:www.thusspakeak.com,2022:/student//12.3742022-03-18T19:00:00Z2022-03-18T19:57:39Z
Recently, my fellow students and I have been caught up in the craze that is sweeping through the users of Professor B------'s clockwork calculating engine; namely the charting of sets of two dimensional points that have fractal planar boundaries, being those that in some sense have a fractional dimension. Of particular interest have been the results of repeated applications of quadratic functions to complex numbers; specifically in measuring how quickly, if at all, they escape a region surrounding the starting point, by which charts may be constructed that many of the collegiate consider so delightful as to constitute art painted by mathematics itself!
student
Recently, my fellow students and I have been caught up in the craze that is sweeping through the users of Professor B------'s clockwork calculating engine; namely the charting of sets of two dimensional points that have fractal planar boundaries, being those that in some sense have a fractional dimension. Of particular interest have been the results of repeated applications of quadratic functions to complex numbers; specifically in measuring how quickly, if at all, they escape a region surrounding the starting point, by which charts may be constructed that many of the collegiate consider so delightful as to constitute art painted by mathematics itself!
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On A Day At The Racestag:www.thusspakeak.com,2022:/student//12.3572022-01-21T20:00:00Z2022-01-21T19:59:11Z
Most recently the Baron challenged Sir R----- to a race of knights around the perimeter of a chessboard, with the Baron starting upon the lower right hand square and Sir R----- upon the lower left. The chase proceeded anticlockwise with the Baron moving four squares at each turn and Sir R----- by the roll of a die. Costing Sir R----- one cent to play, his goal was to catch or overtake the Baron before he reached the first rank for which he would receive a prize of forty one cents for each square that the Baron still had to traverse before reaching it.
student
Most recently the Baron challenged Sir R----- to a race of knights around the perimeter of a chessboard, with the Baron starting upon the lower right hand square and Sir R----- upon the lower left. The chase proceeded anticlockwise with the Baron moving four squares at each turn and Sir R----- by the roll of a die. Costing Sir R----- one cent to play, his goal was to catch or overtake the Baron before he reached the first rank for which he would receive a prize of forty one cents for each square that the Baron still had to traverse before reaching it.
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Finally On A Clockwork Contagiontag:www.thusspakeak.com,2021:/student//12.3492021-12-17T20:00:00Z2021-12-17T20:38:26Z
Over the course of the year my fellow students and I have spent our free time building mathematical models of the spread of disease, initially assuming that upon contracting the infection a person would immediately and forever be infectious, then adding periods of incubation and recovery before finally introducing the concept of location whereby the proximate are significantly more likely to interact than the distant and examining the consequences for a population distributed between several disparate villages.
Whilst it is most certainly the case that this was more reasonable than assuming entirely random encounters it failed to take into account the fact that folk should have a much greater proclivity to meet with their friends, family and colleagues than with their neighbours and it is upon this deficiency that we have concentrated our most recent efforts.
student
Over the course of the year my fellow students and I have spent our free time building mathematical models of the spread of disease, initially assuming that upon contracting the infection a person would immediately and forever be infectious, then adding periods of incubation and recovery before finally introducing the concept of location whereby the proximate are significantly more likely to interact than the distant and examining the consequences for a population distributed between several disparate villages.
Whilst it is most certainly the case that this was more reasonable than assuming entirely random encounters it failed to take into account the fact that folk should have a much greater proclivity to meet with their friends, family and colleagues than with their neighbours and it is upon this deficiency that we have concentrated our most recent efforts.
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On Triumviratetag:www.thusspakeak.com,2021:/student//12.3562021-10-15T19:00:00Z2021-10-15T18:50:55Z
When last they met, the Baron invited Sir R----- to join him in a wager involving a sequence of coin tosses. At a cost of seven coins Sir R----- would receive one coin for every toss of the coin until a run of three heads or of three tails brought the game to its conclusion.
To evaluate its worth to Sir R----- we begin with his expected winnings after a single toss of the coin.
student
When last they met, the Baron invited Sir R----- to join him in a wager involving a sequence of coin tosses. At a cost of seven coins Sir R----- would receive one coin for every toss of the coin until a run of three heads or of three tails brought the game to its conclusion.

To evaluate its worth to Sir R----- we begin with his expected winnings after a single toss of the coin.
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Further Still On A Clockwork Contagiontag:www.thusspakeak.com,2021:/student//12.3482021-09-17T19:00:00Z2021-09-17T18:57:14Z
My fellow students and I have spent the past several months attempting to build a mathematical model of the spread of disease, our interest in the subject having been piqued whilst we were confined to our halls of residence during the epidemic that beset us upon the dawn of the year. Having commenced with the assumption that those who became infected would be infectious immediately and in perpetuity we refined our model by adding a non-infectious period of incubation and a finite period of illness, after which sufferers should recover with consequent immunity and absence of infectiousness.
A fundamental weakness in our model that we have lately sought to address is the presumption that individuals might initiate contact with other members of the population entirely by chance when it is far more likely that they should interact with those in their immediate vicinity. It is upon our first attempt at correcting this deficiency that I should now like to report.
student
My fellow students and I have spent the past several months attempting to build a mathematical model of the spread of disease, our interest in the subject having been piqued whilst we were confined to our halls of residence during the epidemic that beset us upon the dawn of the year. Having commenced with the assumption that those who became infected would be infectious immediately and in perpetuity we refined our model by adding a non-infectious period of incubation and a finite period of illness, after which sufferers should recover with consequent immunity and absence of infectiousness.
A fundamental weakness in our model that we have lately sought to address is the presumption that individuals might initiate contact with other members of the population entirely by chance when it is far more likely that they should interact with those in their immediate vicinity. It is upon our first attempt at correcting this deficiency that I should now like to report.
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On The Fours Reawakenstag:www.thusspakeak.com,2021:/student//12.3552021-07-16T19:00:00Z2021-07-16T18:57:00Z
Recall that the Baron's latest game involved he and Sir R----- each casting four four sided dice. For each pair of dice formed from one of the Baron's and one of Sir R-----'s with matching faces, Sir R----- should have received thirteen coins having given twenty eight to play.
student
Recall that the Baron's latest game involved he and Sir R----- each casting four four sided dice. For each pair of dice formed from one of the Baron's and one of Sir R-----'s with matching faces, Sir R----- should have received thirteen coins having given twenty eight to play.
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Further On A Clockwork Contagiontag:www.thusspakeak.com,2021:/student//12.3472021-06-18T19:00:00Z2021-06-18T18:58:36Z
When last we spoke, I told you of my fellow students' and my first attempt at employing Professor B------'s wondrous computational engine to investigate the statistical properties of the spread of disease; a subject that we had become most curious about whilst confined to our quarters during the epidemic earlier this year. You will no doubt recall that our model assumed that once someone became infected their infectiousness would persist indefinitely, which is quite contrary to the nature of the outbreak. We have since added incubation, recovery and immunity and it is upon these refinements that I shall now report.
student
When last we spoke, I told you of my fellow students' and my first attempt at employing Professor B------'s wondrous computational engine to investigate the statistical properties of the spread of disease; a subject that we had become most curious about whilst confined to our quarters during the epidemic earlier this year. You will no doubt recall that our model assumed that once someone became infected their infectiousness would persist indefinitely, which is quite contrary to the nature of the outbreak. We have since added incubation, recovery and immunity and it is upon these refinements that I shall now report.
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On Twenty-Ninertag:www.thusspakeak.com,2021:/student//12.3542021-04-16T19:00:00Z2021-04-17T16:45:50Z
The Baron's most recent wager set Sir R----- the task of placing tokens upon spaces numbered from zero to nine according to the outcome of a twenty sided die upon which was inscribed two of each of those numbers. At a cost of one coin per roll of the die, Sir R-----'s goal was to place a token upon every space for which he should receive twenty nine coins and twenty nine cents from the Baron.
student
The Baron's most recent wager set Sir R----- the task of placing tokens upon spaces numbered from zero to nine according to the outcome of a twenty sided die upon which was inscribed two of each of those numbers. At a cost of one coin per roll of the die, Sir R-----'s goal was to place a token upon every space for which he should receive twenty nine coins and twenty nine cents from the Baron.
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On A Clockwork Contagiontag:www.thusspakeak.com,2021:/student//12.3462021-03-19T19:00:00Z2021-03-20T04:29:20Z
During the recent epidemic, my fellow students and I had plenty of time upon our hands due to the closure of the taverns, theatres and gambling houses at which we would typically while away our evenings and the Dean's subsequent edict restricting us to halls. We naturally set to thinking upon the nature of the disease's transmission and, once the Dean relaxed our confinement, we returned to our college determined to employ Professor B------'s incredible mathematical machine to investigate the probabilistic nature of contagion.
student
During the recent epidemic, my fellow students and I had plenty of time upon our hands due to the closure of the taverns, theatres and gambling houses at which we would typically while away our evenings and the Dean's subsequent edict restricting us to halls. We naturally set to thinking upon the nature of the disease's transmission and, once the Dean relaxed our confinement, we returned to our college determined to employ Professor B------'s incredible mathematical machine to investigate the probabilistic nature of contagion.
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On Tug O' Wartag:www.thusspakeak.com,2021:/student//12.3362021-01-15T20:00:00Z2021-01-15T19:57:54Z
The Baron and Sir R-----'s latest wager comprised of first placing a draught piece upon the fifth lowest of a column of twelve squares and subsequently moving it up or down by one space depending upon the outcome of a coin toss until such time as it should escape, either by moving above the topmost or below the bottommost square. In the former outcome the Baron should have had a prize of three coins and in the latter Sir R----- should have had two.
student
The Baron and Sir R-----'s latest wager comprised of first placing a draught piece upon the fifth lowest of a column of twelve squares and subsequently moving it up or down by one space depending upon the outcome of a coin toss until such time as it should escape, either by moving above the topmost or below the bottommost square. In the former outcome the Baron should have had a prize of three coins and in the latter Sir R----- should have had two.
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Finally On A Very Cellular Processtag:www.thusspakeak.com,2020:/student//12.3272020-12-18T20:00:00Z2020-12-18T19:55:36Z
Over the course of the year my fellow students and I have been utilising our free time to explore the behaviour of cellular automata, which are mechanistic processes that crudely approximate the lives and deaths of unicellular creatures such as amoebas. Specifically, they are comprised of unending lines of boxes, some of which contain cells that are destined to live, dive and reproduce according to the occupancy of their neighbours.
Most recently we have seen how we can categorise automata by the manner in which their populations evolve from a primordial state of each box having equal chances of containing or not containing a cell, be they uniform, constant, cyclical, migratory, random or strange. It is the latter of these, which contain arrangements of cells that interact with each other in complicated fashions, that has lately consumed our attention and I shall now report upon our findings.
student
Over the course of the year my fellow students and I have been utilising our free time to explore the behaviour of cellular automata, which are mechanistic processes that crudely approximate the lives and deaths of unicellular creatures such as amoebas. Specifically, they are comprised of unending lines of boxes, some of which contain cells that are destined to live, dive and reproduce according to the occupancy of their neighbours.
Most recently we have seen how we can categorise automata by the manner in which their populations evolve from a primordial state of each box having equal chances of containing or not containing a cell, be they uniform, constant, cyclical, migratory, random or strange. It is the latter of these, which contain arrangements of cells that interact with each other in complicated fashions, that has lately consumed our attention and I shall now report upon our findings.
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On We Three Kingstag:www.thusspakeak.com,2020:/student//12.3342020-10-16T19:00:00Z2020-10-17T10:39:14Z
Recall that the Baron's most recent game involved advancing kings from the first and last ranks of a three by three chequerboard in a pawn-like manner until either he or Sir R----- reached the opposing rank or blocked all of the other's kings from moving, having the game in either eventuality.
student
Recall that the Baron's most recent game involved advancing kings from the first and last ranks of a three by three chequerboard in a pawn-like manner until either he or Sir R----- reached the opposing rank or blocked all of the other's kings from moving, having the game in either eventuality.
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Further Still On A Very Cellular Processtag:www.thusspakeak.com,2020:/student//12.3202020-09-18T19:20:20Z2020-09-18T18:50:21Z
My fellow students and I have lately been spending our spare time experimenting with cellular automata, which are simple mathematical models of single celled creatures such as amoebas, governing their survival and reproduction from one generation to the next according to the population of their neighbourhoods. In particular, we have been considering an infinite line of boxes, some of which contain living cells, together with rules that specify whether or not a box will be populated in the next generation according to its, its left hand neighbour's and its right hand neighbour's contents in the current generation.
We have found that for many such automata we can figure the contents of the boxes in any generation that evolved from a single cell directly, in a few cases from the oddness or evenness of elements in the rows of Pascal's triangle and the related trinomial triangle, and in several others from the digits in terms of sequences of binary fractions.
We have since turned our attention to the evolution of generations from multiple cells rather then one; specifically, from an initial generation in which each box has an even chance of containing a cell or not.
student
My fellow students and I have lately been spending our spare time experimenting with cellular automata, which are simple mathematical models of single celled creatures such as amoebas, governing their survival and reproduction from one generation to the next according to the population of their neighbourhoods. In particular, we have been considering an infinite line of boxes, some of which contain living cells, together with rules that specify whether or not a box will be populated in the next generation according to its, its left hand neighbour's and its right hand neighbour's contents in the current generation.
We have found that for many such automata we can figure the contents of the boxes in any generation that evolved from a single cell directly, in a few cases from the oddness or evenness of elements in the rows of Pascal's triangle and the related trinomial triangle, and in several others from the digits in terms of sequences of binary fractions.
We have since turned our attention to the evolution of generations from multiple cells rather then one; specifically, from an initial generation in which each box has an even chance of containing a cell or not.
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On May The Fours Be With Youtag:www.thusspakeak.com,2020:/student//12.3162020-07-17T19:00:00Z2020-07-17T18:57:35Z
In their most recent wager Sir R-----'s goal was to guess the outcome of the Baron's roll of four four sided dice at a cost of four coins and a prize, if successful, of forty four. On the face of it this seems a rather meagre prize since there are two hundred and fifty six possible outcomes of the Baron's throw. Crucially, however, the fact that the order of the matching dice was not a matter of consequence meant that Sir R-----'s chances were significantly improved.
student
In their most recent wager Sir R-----'s goal was to guess the outcome of the Baron's roll of four four sided dice at a cost of four coins and a prize, if successful, of forty four. On the face of it this seems a rather meagre prize since there are two hundred and fifty six possible outcomes of the Baron's throw. Crucially, however, the fact that the order of the matching dice was not a matter of consequence meant that Sir R-----'s chances were significantly improved.
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