Gotama taught that in self-examination, we come to understand that our perspective is always changing, and the world is always changing as well. He further taught that change is itself subject to change. This is a profound hypothesis: if all that is subject to change must have begun, and must end, then the conditions of beginning and ending are themselves subject to change; the implication is that we have tremendous control over our own self, our nature, our world. It is this control which necessitates our compassion for every being and non-being, including ourselves - that teaches all beings are truly equal. However, mathematically proving the logic of this hypothesis required an advanced system of logic not yet available to Gotama - one which Muhammad Ibin Musa Al-Khwarizimi helped to innovate.
Today we celebrate the achievements of Muhammad Ibin Musa Al-Khwarizimi, who invented both digital mathematics and the logical concept of the "equation," expressed through his sublime method of "al-gebra." Perfectly conceptualizing the understanding of variable truth, co-dependence and co-arising and co-termination, algebraic equations permit us to understand not only the limitations of our knowledge, but provide the tools by which we can infinitely expand our knowledge. Digitalization advanced fractional and rational thought into realms of imagination and abstraction, permitting the multidimensional analysis required to accurately understand the dimensional boundaries of relevancy. Al-Khwarizimi independently proved the system of conscience based upon logic hypothesized by the Buddha Gotama.
Al-Khwarizimi's success was built upon previous innovations made by others: integral numbers, negatory and quaternary logic, and numerous other concepts and methods. Integral numbers, especially though, were required to understand that quantities could be divisible and atomistic in nature, and negatory quaternary logic was especially required the potential for known quantities to be dependent upon numerous interacting factors. With algorithmic mathematics, the factors affecting such variables could now be understood as constant truths. His "algorithms" laid the foundation for "calculation" and modern "computing."
He introduced the world to hindu numbers (0,1,2,3,4,5,6,7,8,9), and the hindu decimal point (.). But then he discovered how to use them in new, advanced ways. "When I consider what people generally want in mathematics, I found that it always is an unknown number. I also observed that every number is composed of units, and that any number may be divided into units. Moreover, I found that every number which may be expressed from one to ten, surpasses the preceding by one unit: afterwards the ten is doubled or tripled just as before the units were: thus arise twenty, thirty, etc. until a hundred: then the hundred is doubled and tripled in the same manner as the units and the tens, up to a thousand; ... so forth to the utmost limit of numeration."
His revolutionary method permitted the understanding of trigonometry, spherical geometry and geography required to better navigate our globe for the purposes of exploration and trade, bringing numerous and different people together: now, trade routes could be charted that were faster, more reliable and more profitable. Applying his new logic to geography, he discerned that the continents of land were surrounded by oceans - and was not afraid to leave blank those places on a map he did not have enough information to know certainly: there is a confidence that comes with algorithmic calculation that sooner or later, all unknowns will be discovered.
His work in commercial science did not end with improving the speed of long-distance transportation through trigonometry. He also developed the method of "accounting," demonstrating that all commerce and industry can be understood through numerical analysis by algebra. "Commercial and industrial activities involve only two ideas and four numbers: the ideas are quantity and cost; the four numbers are unit of measure, price per unit, quantity desired and cost of the same."
From such analysis, long-term profit trends could be observed, and he developed a logical basis for business ethics: since all quantities can be divided, and the effects of unfair trading practices can be seen to result in diminished long-term profits, they should be divided fairly. But more importantly, there were implications for short-term profits as well.
This had a tremendous effect on law and contracts, and an increase in Justice. One question which was posed to him was, "if a man is hired to work in a vineyard 30 days for 10 dollars and he works six days, how much of the agreed price should he receive?" Al-Khwarizimi demonstrated an application of his new commercial and industrial mathematics: "It is evident that since days are one-fifth of the whole time; and it is also evident that the man should receive pay having the same relation to the agreed price that the time he works bears to the whole time, 30 days. The month, i.e., 30 days, represents the measure, and ten represents the price. Six days represents the quantity, and in asking what part of the agreed price is due to the worker you ask the cost. Therefore multiply the price 10 by the quantity 6, which is inversely proportional to it. Divide the product 60 by the measure 30, giving 2 Dollars. This will be the cost, and will represent the amount due to the worker."
Though a Muslim, he was convinced that the science of mathematics and ethics was independent of any religious or cultural norm and convinced his people to seek rational, objective truths and a logical basis for conscience. However, because he was a Muslim, Christian Europe did not adopt his methods of arithmetic, accounting, or the ethical standards these implied, or even the Hindu numbers these methods used: there was fear that it was a Muslim system using Hindu numbers, and would be heretical to their moral beliefs. It took a cultural revolution in Europe before the foundation of mathematics, the concept that quantities and truth exist independent of any religious or cultural context, permitted AL-Khwarizimi's algebra and accounting methods to be employed.
This revolution first occurred in Italy. The Italian nations (Italy at the time was not a unified country) had the greatest commercial trade with the several Muslim nations which had adopted the system of numbers, mathematics and accounting developed by Al-Khwarizimi. It was through such trade that partnerships were developed between men of very different cultures: these partnerships required a mercantile code independent of either Christian Europe or Muslim Arabia: Christians would not be subjected to Muslim commercial codes, and Muslims would not be subjected to Christian commercial codes. What they needed was something that was non-thesitic, and fair. They soon discovered Al-Khwarizimi's very logical and very fair system for accounting, division of profits, and coordination wasn't Muslim or Christian, or Hindu, or tainted with any religious practice - it doesn't matter if you are Christian or Muslim or Hindu: the shortest distance between two points is a straight line, and the fairest distribution of profits requires digital and algebraic arithmetic.
Such a partnership resulted in the adoption of a non-theistic mercantile code, but also quickly resulted in the adoption of a non-theistic culture as well: This revolution in culture was not based on religion or ethnicity, but upon fairness, cooperation and conscience - through logical conscience. In the same way, the Arabian traders brought this system to all their other trading partners around the world. Logic - and the conscience it both precipitates and requires - is truly the world's human culture.
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