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... aps a single stick split lengthwise, held by the parties to a purchase or debt. The two sticks are held parallel, scores are made across both to indicate a count, and, if it is deemed necessary, they are signed or stamped by both parties to guarantee authenticity. Different symbols are usually employed for larger quantities: compare our use of a diagonal slash across a group of four lines to complete a count of five. The two sticks can be compared at any time, and together comprise a difficult to falsify record of the original count, since if the debtor erases notches or the lender adds them, the discrepancy will be apparent. Tally sticks were in wide use throughout historical times, and feel right for Tkumel: the penchant of the Tsolyni for the physical representation for abstract relationships (such as debt) is well known.
It is even possible that conservative organizations trust them more highly than paper accounting methods, as the British Exchequer did until the 19 th century! As rapid calculation is important for many people, the abacus plays an important part in the lives of clerks, accountants and other functionaries. As they are tools of the lower and middle clans, they would not be ornamental, but instead simple constructions of wood, ceramic and stone. One likely arrangement is the employment of the favored color of each God for each digit: 1 (1) is white and of Lord Hill; 2 (2) is sapphire blue and of Lady Avnthe; 3 (3) is scarlet and of Lord Karen; 4 (4) is golden yellow and of Lord Belkhnu; 5 (5) is dark brown and of Lord Sky; 6 (6) is grey and of Lord This; 7 (7) is purple and of Lord Hr; 8 (8) is deep azure and is of Lord Karl; 9 (9) is red-orange and is of Lord Villa; and 10 (0) is emerald green and of Lady Dlamlish. The abacus has taken many forms in our own history.
One possible form for the Tsolyni abacus is a checkerboard, as was in use in China around the 9 th century CE. In this, each digit occupies a space of the checkerboard. The Chinese used certain configurations of small rods to represent each digit; a user might simply use a differently colored token for each, corresponding to the system above. (As there is no need for a token for 10 in a decimal positional system, such boards would incorporate emerald green somewhere in their decorations to retain Lady Dlamlishs good will. ) Efficiency would require an operator to have 9 bins before him, each containing one color of token. Thus, for example, the number 3, 109 would be represented by a scarlet token in the rightmost square of a row (recall that Tsolyni is written right-to-left), a white token in the square to the left, no token in the next square (the absence serving as a placeholder) and a red-orange token in the fourth rightmost square. Such an abacus would require lengthy training for mastery, which is in keeping with Tsolyni ways, but would allow for all arithmetical operations including the finding of square and cube roots. It is interesting to note Georges Ifrahs observation that an abacus can be used for arithmetic without any grasp of zero as a number: leaving a square blank corresponds to a zero digit in that place.
Iraq notes that the Indians had to conceptually reject the abacus representation of numbers to produce our modern decimal system with a zero. This corresponds to the Tsolyni's rejection of zero as a number for general use. Other forms of abc would be necessary for other cultures in which the convenient correspondence of gods to digits did not exist; they may even employ the familiar bead-and-rod abacus, which in different forms is still in widespread use throughout China and Japan. The Salarvyni, in particular, are masters of such devices, but are distrustful of all mathematical abstraction we would be cheated of our last Dn-grain by those using such artifice!
It can thus be tedious dealing with them in contracts where formulae could be used. For example, if a landowner has recently constructed a new grain repository and wishes to sell his grain, only careful measuring of its contents will satisfy a Salarvyni merchant; simply calculating the volume of the repository would be unsatisfactory. Older repositories that the merchant has experience with might eventually be considered trustworthy, so that a conversion of depth of grain to volume could be acceptable. V. Higher Mathematics Again from Swords & Glory, vol. I (Sec. 1. 1010): Practical geometry is indispensable to architects, masons, and some other professions.
It is thus quite well developed. The properties of straight-sided figures are known, including calculations or areas and volumes, and experts can solve similar problems relating to circles, spheres, and cylinders, utilising an approximate value for pi. Beyond this, however, little is known, although it is said that some savants (particularly those of the Living) have been experimenting with simple algebra. The Tinaliya are reported to have more in the way of theoretical mathematics, but these little beings are either incapable of explaining their techniques to humans -- or do not care to do so. Logarithms, trigonometry, calculus, and further varieties and methods of mathematics are all as yet unknown on Tkumel. Straight-sided figures would include squares and rectangles, trapezoids, cubes, etc. ; thus, an extensive collection of formulae has been developed.
Their approximation of would be poor indeed unless, as noted above, fractions are employed; it is probably no more accurate than 22 / 7 in any event. As a general observation, one may note that the limited development of most higher forms of mathematics, the cultural fixation on past authorities, and the disdain for scientific and abstract thought on Tkumel all strongly suggest that proof in the modern (or even Euclidean) sense is little employed. It may not even have been discovered! Ancient India, for example, developed quite a lot of mathematics without being in clear possession of an abstract concept of proof. And even after the Greeks had first developed one, the primary sense of proof for a long time in the West was attached to scriptural rather than scientific argumentation. It strikes us as quite likely that a Tsolyni would be deeply suspicious of a proof with only rational or conceptual presuppositions.
When the young mathematical scholar writes Two lines are parallel if and only if a line drawn perpendicular to one is also perpendicular to the other, his superior at the Temple of This may well respond with the following query: What sage supports these definitions? From what tome do you derive your first principles? And if our earnest geometer lacks an answer, it is not the elder priest who will be seen as the dogmatist and fool, but the younger priest who will be seen as erratic, untrustworthy, and undisciplined in thought, a dreamer rather than a sober researcher. The simple algebra described above is most likely either symbolic, generalized or both: no civilization at the level of advancement of the Five Empires could manage without some means of solving linear word problems.
Without a well-trusted zero, and with no sign of the sophistication needed for symbolic mathematics, it is likely that Tkumelani algebra is rhetorical. A good model for this is found in the non symbolic algebra of the ancient Egyptians. Their primary technique was that of false position, as illustrated below: Given a formula of the form ax + x / b = c, where a, b and c are known, they would guess an answer for x, almost invariably the wrong one. Substituting this value into the left hand side of the equation they would get some value d (generally different to c) on the right hand side. Because the equation is linear, we can use proportions to deduce that the correct value of x is c / d times the false value. This technique would be taught by repetition of age-old examples first concocted by Engsvanyali or even Bednalljan savants (those schooled in the calculus from hi-Thomas and hi-Finney may find this familiar).
Tsolyni mathematicians are culturally unwilling to generalize and consider a mathematical entity from multiple perspectives. Thus, they do not draw graphical representations of either functions or data points, and the Cartesian coordinate system is unknown to them. Consider in relation to this the strikingly different nature of their maps: neither the dot-and-line mercantile maps nor the recondite, subtly sculptured polyhedra of the high cartographer resemble in any way our quasi-Cartesian world maps, though the latter at least contain as much or more information for those trained to receive it. Analytic geometry is evidently not to be found in the Tkumelani mathematical lexicon; this should be kept in mind when reading our speculations on their topology below. While we have come to believe that certain savants have an advanced knowledge of multidimensional shape and structure, the additional idea of a number-like metric on such spaces is clearly beyond them. Statistics, the finding of patterns and predictability in random phenomena, has obvious and troubling theological implications for a Tsolyni.
However, the advantages of statistical techniques would give great advantages to their practitioners: they could make predictions for harvests...
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Research essay sample on Straight Sided Figures Zero As A Number Lord
