A recursive method based on successive computations of perimeters of inscribed regular polygons for estimating π is formulated by employing the Pythagorean theorem alone without resorting to any trigonometric calcula...A recursive method based on successive computations of perimeters of inscribed regular polygons for estimating π is formulated by employing the Pythagorean theorem alone without resorting to any trigonometric calculations. The approach is classical but the formulation of coupled recursion relations is new. Further, use of infinite series for computing π is explored by an improved version of Leibniz’s series expansion. Finally, some remarks with reference to π are made on a relatively recently rediscovered Sumerian tablet depicting geometric figures.展开更多
Two years ago I had a chance to read four unpublished Sumerian texts newly housed in the Okayama Orient Museum, Okayama-shi, Japan. With the generous permission of Prof. Dr. Taksahi TANIICHI, Director General of the M...Two years ago I had a chance to read four unpublished Sumerian texts newly housed in the Okayama Orient Museum, Okayama-shi, Japan. With the generous permission of Prof. Dr. Taksahi TANIICHI, Director General of the Museum, I offer three of the texts below.展开更多
The author centers on writing seen both as a human ability and a transcription of oral language,and yet she very heavily refuses there to be any continuity from oral to written language,though once or twice what she s...The author centers on writing seen both as a human ability and a transcription of oral language,and yet she very heavily refuses there to be any continuity from oral to written language,though once or twice what she says,like in her fifth step about“assigning sounds to signs”,is exactly the reverse of what Homo Sapiens did when he developed writing:he assigned signs to sounds.No matter what way it works for a decipherer,and for Homo Sapiens when he developed some writing system for his/her/their language,and his/her/their language alone in 6-8,000 BCE,the connection between an oral language and its written version is connected,but flexible so that it can be easily replaced by another written code for the very same oral utterances,like the Phoenicians developing the first real consonantal alphabet to replace,for Semitic languages,the Cuneiform writing of the Sumerians(Indo-Iranian)and Akkadians(Semitic),and later on the Greeks adding the vowels of Indo-European languages to the Phoenician alphabet that only had“alep”and only when it was the initial sound or letter of a word.She alludes to signs in painted caves,hence going back to 45,000 BCE,and all over the world,but she does not exploit it.She acknowledges there were six cradles in the world and does not give them in chronological order,hence does not link them to the general evolution of the concerned human groups,and she neglects the fact that Egyptian writing and Sumerian writing developed at the same time or so but with a strong link between them:the Akkadians were the scribes of the Sumerians and they were Semitic like the Egyptians,whereas the Sumerians were Indo-Iranian coming down from the Iranian Plateau and settling in Mesopotamia before moving on.She mistakenly declares them Turkic,or speaking Turkish,an agglutinative language.Mutations selected naturally transformed the foot,the larynx,the respiratory system,the articulatory system,the subglottal zone,and its innervation of the pre-Sapiens Hominins concerned to enable Homo Sapiens to become what they are,long-distance bipedal fast runners.The development of oral language is a collateral consequence of these mutations.As soon as Homo Sapiens started using durable medium for their representational and entoptic geometric or other diacritic elements we have to follow Genevieve von Petzinger and state that these are signs and they have a function,counting for the repetitive elements,and all of these rockface paintings were there to illustrate the story the painters or other special individuals(probably sha-women and a few shamans)who could speak to the spirits behind the rockface were telling the fascinated audience.The lack of phylogeny blocks the real vision necessary to understand these facts and the fact that the reference to“bureaucracy”in big cities was the cause of this development,according to Silvia Ferrara.The people who specialized in remembering data,could we call them a bureaucracy in 2023,with the highly pejorative paradigmatic meaning the term conveys?Of course not.Where did the people who developed some writing system come from?What language or languages did they speak?Writing was not a discovery because it was not found on a tree or in a cave.Human writing was not an invention because there is no break from pure oral language to written language via representational drawings,and iconic first,totally abstract then signs used to transcribe the oral language into a durable(the media)and sustainable(to be learned by anyone and taught to anyone)script.We have to take the high road leading to discovering the phylogeny of language starting in 475,000 BCE and still developing.展开更多
文摘A recursive method based on successive computations of perimeters of inscribed regular polygons for estimating π is formulated by employing the Pythagorean theorem alone without resorting to any trigonometric calculations. The approach is classical but the formulation of coupled recursion relations is new. Further, use of infinite series for computing π is explored by an improved version of Leibniz’s series expansion. Finally, some remarks with reference to π are made on a relatively recently rediscovered Sumerian tablet depicting geometric figures.
文摘Two years ago I had a chance to read four unpublished Sumerian texts newly housed in the Okayama Orient Museum, Okayama-shi, Japan. With the generous permission of Prof. Dr. Taksahi TANIICHI, Director General of the Museum, I offer three of the texts below.
文摘The author centers on writing seen both as a human ability and a transcription of oral language,and yet she very heavily refuses there to be any continuity from oral to written language,though once or twice what she says,like in her fifth step about“assigning sounds to signs”,is exactly the reverse of what Homo Sapiens did when he developed writing:he assigned signs to sounds.No matter what way it works for a decipherer,and for Homo Sapiens when he developed some writing system for his/her/their language,and his/her/their language alone in 6-8,000 BCE,the connection between an oral language and its written version is connected,but flexible so that it can be easily replaced by another written code for the very same oral utterances,like the Phoenicians developing the first real consonantal alphabet to replace,for Semitic languages,the Cuneiform writing of the Sumerians(Indo-Iranian)and Akkadians(Semitic),and later on the Greeks adding the vowels of Indo-European languages to the Phoenician alphabet that only had“alep”and only when it was the initial sound or letter of a word.She alludes to signs in painted caves,hence going back to 45,000 BCE,and all over the world,but she does not exploit it.She acknowledges there were six cradles in the world and does not give them in chronological order,hence does not link them to the general evolution of the concerned human groups,and she neglects the fact that Egyptian writing and Sumerian writing developed at the same time or so but with a strong link between them:the Akkadians were the scribes of the Sumerians and they were Semitic like the Egyptians,whereas the Sumerians were Indo-Iranian coming down from the Iranian Plateau and settling in Mesopotamia before moving on.She mistakenly declares them Turkic,or speaking Turkish,an agglutinative language.Mutations selected naturally transformed the foot,the larynx,the respiratory system,the articulatory system,the subglottal zone,and its innervation of the pre-Sapiens Hominins concerned to enable Homo Sapiens to become what they are,long-distance bipedal fast runners.The development of oral language is a collateral consequence of these mutations.As soon as Homo Sapiens started using durable medium for their representational and entoptic geometric or other diacritic elements we have to follow Genevieve von Petzinger and state that these are signs and they have a function,counting for the repetitive elements,and all of these rockface paintings were there to illustrate the story the painters or other special individuals(probably sha-women and a few shamans)who could speak to the spirits behind the rockface were telling the fascinated audience.The lack of phylogeny blocks the real vision necessary to understand these facts and the fact that the reference to“bureaucracy”in big cities was the cause of this development,according to Silvia Ferrara.The people who specialized in remembering data,could we call them a bureaucracy in 2023,with the highly pejorative paradigmatic meaning the term conveys?Of course not.Where did the people who developed some writing system come from?What language or languages did they speak?Writing was not a discovery because it was not found on a tree or in a cave.Human writing was not an invention because there is no break from pure oral language to written language via representational drawings,and iconic first,totally abstract then signs used to transcribe the oral language into a durable(the media)and sustainable(to be learned by anyone and taught to anyone)script.We have to take the high road leading to discovering the phylogeny of language starting in 475,000 BCE and still developing.
