An Overview of the History of the development of Math
An Overview of the History of the development of Math
The Impact of Zero
The Impact of Zero
2 The very beginning as we know it
Stone age mathematicians were a bit more rugged than modern ones. Instead of whiteboards, they used wolves.In the 1930’s, archaeologist Karl Absolom unearthed a 30,000 year old wolf bone in Czechoslovakia.The interesting thing is that this bone had notches carved into it. An even more interesting thing is that these notches were arranged into groupings of five for a total of 55 notches.This IS a quinary system. Today we use the decinary.
Stone age mathematicians were a bit more rugged than modern ones. Instead of whiteboards, they used wolves.In the 1930’s, archaeologist Karl Absolom unearthed a 30,000 year old wolf bone in Czechoslovakia.The interesting thing is that this bone had notches carved into it. An even more interesting thing is that these notches were arranged into groupings of five for a total of 55 notches.This IS a quinary system. Today we use the decinary.
3 Images digitally enhanced
2003 at the Deutsches Museum in Munich, Germany
2003 at the Deutsches Museum in Munich, Germany
4 Zero – A mysterious concept
Zero is powerful because it is infinity’s twin.They are equal yet opposite, yin and yang.Throughout history this number has been feared, hated, and outlawed.The biggest questions in science and religion are about nothingness and eternity, the void and the infinite, zero and infinity. The clashes over zero were the battles that shook the foundations of philosophy, of science, of mathematics, and of religion. Underneath every revolution lay a zero and an infinity
Zero is powerful because it is infinity’s twin.They are equal yet opposite, yin and yang.Throughout history this number has been feared, hated, and outlawed.The biggest questions in science and religion are about nothingness and eternity, the void and the infinite, zero and infinity. The clashes over zero were the battles that shook the foundations of philosophy, of science, of mathematics, and of religion. Underneath every revolution lay a zero and an infinity
5 Zero was at the heart of the battle between East and West. Zero was at the center of the struggle between religion and science. Zero became the language of nature and the most important tool in mathematics. And the most prof0und problems in physics – the dark core of a black hole and the brilliant flash of the big bang are struggles to defeat zero.Humanity could never force zero to fit its philosophies. Instead, zero shaped humanity’s view of the universe.
6 The Power of ZeroSept 21, 1997, the billion dollar missile cruiser, the USS Yorktown, was completely disabled by zero.A new software update controlled the engines. In one part of the program, there was a division by zero; a mistake.When the program attemptedto divide by zero the systemcrashed and 80,000horsepower instantly becameworthless.
7 The Beginning People first developed a name for one and many.
Some languages still have this shortcoming. The Siriono Indians of Bolivia and the Brazilian Yanoama people do not have words for anything larger than three; instead, these two tribes use the words for many and much.
Some languages still have this shortcoming. The Siriono Indians of Bolivia and the Brazilian Yanoama people do not have words for anything larger than three; instead, these two tribes use the words for many and much.
8 Because of the nature of numbers, they can be added together to create new ones.
Clever tribesmen began to string number words together……one, two, two and one, two and two, two and two and one, and so on.This was the first binary system.A south american binary system developed into a quinary system by saying that two and two and one was “this is my hand all together.” The word “hand” was then used in many cultures. It is still used to determine a rough estimate of the height of a horse.
Clever tribesmen began to string number words together……one, two, two and one, two and two, two and two and one, and so on.This was the first binary system.A south american binary system developed into a quinary system by saying that two and two and one was “this is my hand all together.” The word “hand” was then used in many cultures. It is still used to determine a rough estimate of the height of a horse.
9 In English, eleven and twelve come from “one over ten” and “two over ten” Meaning one more than ten and two more than ten.Thirteen three and tenFourteen four and tenFifteen five and tenI think you get the point.This base of ten was used by the Germanic protolanguages.
10 The French…those strange people
Used a base twenty….Quatre vingt four twenties eightyQuatrevingt dix four twenties and ten ninetyA base twenty system is called a vigesimal number system.
Used a base twenty….Quatre vingt four twenties eightyQuatrevingt dix four twenties and ten ninetyA base twenty system is called a vigesimal number system.
11 In the past, no one needed to express a symbol for nothing
In the past, no one needed to express a symbol for nothing. Zero was not a useful concept. Its representation wasn’t needed. You just didn’t have zero sheep. You had no sheep.As society progressed, scribes needed symbols for larger groupings of numbers.5,000 years ago, the Egyptians used a system in which pictures stood for groups of numbers. A single vertical mark was one unit. A heel bone represented ten. A swirly snare stood for 100.
In the past, no one needed to express a symbol for nothing. Zero was not a useful concept. Its representation wasn’t needed. You just didn’t have zero sheep. You had no sheep.As society progressed, scribes needed symbols for larger groupings of numbers.5,000 years ago, the Egyptians used a system in which pictures stood for groups of numbers. A single vertical mark was one unit. A heel bone represented ten. A swirly snare stood for 100.
12 The AbacusInstead of writing down 125 tick marks, the Egyptians could write down one snare, two heels, and five vertical marks.In order to perform calculations, colored ropes or an abacus was used.Numbers were primarily used by merchants. A calendar system was developed later. At this time, 5000 years ago, all calendars were lunar. The Egyptians had a lunar calendar 6000 years ago.
13 Lunacy The length of a month was the time between full moons.
This time, however, varied from 29 or 30 days.12 lunar months added up to 354 days, 11 days short of a solar year.
This time, however, varied from 29 or 30 days.12 lunar months added up to 354 days, 11 days short of a solar year.
14 13 lunar months yielded 19 days too many
13 lunar months yielded 19 days too many. Using the moon to determine when to plant and harvest crops became a problem because the seasons drifted after only a few years.
13 lunar months yielded 19 days too many. Using the moon to determine when to plant and harvest crops became a problem because the seasons drifted after only a few years.
15 The ancient egyptians developed a solar calendar 6000 years ago
The ancient egyptians developed a solar calendar 6000 years ago. This calendar, based on the position of the sun in the sky and the stars at night, proved to be far more accurate for determining when to plant and harvest. They only performed their calculations up to the year 2012, which is why so many “doom sayers” proclaim that the world will end at this time.
The ancient egyptians developed a solar calendar 6000 years ago. This calendar, based on the position of the sun in the sky and the stars at night, proved to be far more accurate for determining when to plant and harvest. They only performed their calculations up to the year 2012, which is why so many “doom sayers” proclaim that the world will end at this time.
16 The Egyptians had quickly become masters of mathematics
The Egyptians had quickly become masters of mathematics. They had to, thanks to an angry river. Every year the Nile would overflow its banks and flood the delta.
The Egyptians had quickly become masters of mathematics. They had to, thanks to an angry river. Every year the Nile would overflow its banks and flood the delta.
17 The good news was that the river deposited rich, alluvial silt all over the fields. The bad news was that the river destroyed boundary markers that farmers used to determine what land belong to them. The ancient pharaohs assigned surveyors to assess the damage and reset the boundary markers, and thus geometry was born.
18 Greek System (2000-86 BC) The Greeks used letters. Greek Timeline
H (eta) stood for hekaton 100M (mu) stood for myriori 10, the myriad
H (eta) stood for hekaton 100M (mu) stood for myriori 10, the myriad
19 Greeks and RomansThe Greek system was a step forward from the Egyptian system because it used fewer symbols to represent larger numbers.The Romans took over the Greek empire and supplanted the Greek system for a much less advanced numeral system.
21 The BabyloniansTheir style of writing was actually the most sophisticated of the time. With their insight, zero finally appeared in the east, in the Fertile Crescent of present day Iraq.
22 Present Day Fertile Crescent
23 Babylonians – 1550 BCThe Babylonian Empire used a base sixty numeral system. ( sexagesimal )This was very odd since at the time many other societies had already chosen 5, 10, or 20 as base systems.
24 BabyloniansA single symbol could represent 1, 60, or The user had to know what the symbol basically represented. It was to them a form of code.To help with this code they used an abacus as did many cultures of this time.Japan sorobanChina suan-panRussia s’chotyTurkey coulbaArmenia choreb
25 The AbacusThe abacus relied on sliding stones to keep track of amounts.The words calculate, calculus, and calcium all come from the Latin word for pebble: calculus.Electronic Printer Abacus | 1990 Designer: David Shaw Award: 1991ID Magazine Annual DesignReview Selection
26 BabyloniansZero was used only as a placeholder for the counting system. Zero was represented by two slanted wedges. Zero to them was a digit, a placeholder, not a number. It had no value.The zero didn’t have a spot on the number line. It was just a symbol. It didn’t even have a place in the hierarchy of numbers. Even today, look at a keyboard, the zero comes after the nine, not before the one where it belongs. On an old phone or a cell, it is at the bottom after the nine as well. So why does zero come after nine? We start counting with ONE.
27 The Mayans BC to 1450 ADDivided their year into 18 months of 20 days each. This totals 360 days. A special period of five days at the end, called Uayeb, brought the count to This tells us that they definitely used a solar calendar.They did something that no one else did though, they started counting at zero. The first day of the month of ZipUnfortunately, we got our calendar from the Egyptians and Romans.
28 Mayan Counting System
29 Mayan Symbol Numbers
30 Mayan pictographs (glyphs)
31 The Babylonians and the Mayans were the first societies to use zero
The Babylonians and the Mayans were the first societies to use zero. The Greeks feared zero.To the Greeks, zero was linked to the void. Most ancient people believed that emptiness and chaos were present before the universe came to be. The Greeks claimed that Darkness was the mother of all things and from Darkness sprang Chaos. The two spawned the rest of creation. The Hebrew creation myths say that the Earth was chaotic and void before God showered it with light and formed its features.
The Babylonians and the Mayans were the first societies to use zero. The Greeks feared zero.To the Greeks, zero was linked to the void. Most ancient people believed that emptiness and chaos were present before the universe came to be. The Greeks claimed that Darkness was the mother of all things and from Darkness sprang Chaos. The two spawned the rest of creation. The Hebrew creation myths say that the Earth was chaotic and void before God showered it with light and formed its features.
32 The Hebrew phrase tohu v’bohu stands for formless and empty
The Hebrew phrase tohu v’bohu stands for formless and empty. It is in Genesis 1:2Tohu, short for Tehomot, was a Semitic dragon that was present at the birth of the universe and whose body became the sky and earth.Bohu, for Behomot, was the famed Behemoth monster of Hebrew legend.The Norse myth tells of an open void that gets covered with ice, and from the chaos caused by the mingling of fire and ice was born the primal Giant.Emptiness and disorder were the primeval, natural state of the cosmos, and there was a nagging fear that at the end of time, disorder and void would reign once again. Zero represented that void.
The Hebrew phrase tohu v’bohu stands for formless and empty. It is in Genesis 1:2Tohu, short for Tehomot, was a Semitic dragon that was present at the birth of the universe and whose body became the sky and earth.Bohu, for Behomot, was the famed Behemoth monster of Hebrew legend.The Norse myth tells of an open void that gets covered with ice, and from the chaos caused by the mingling of fire and ice was born the primal Giant.Emptiness and disorder were the primeval, natural state of the cosmos, and there was a nagging fear that at the end of time, disorder and void would reign once again. Zero represented that void.
33 Why???Zero misbehaves.Add a number to itself and it changes. One plus one is two. Two plus two is four, three plus three is six and so on.Zero plus zero is zero.It misbehaves.To the Greeks, zero violated the Axiom of Archimedes, which states that if you add something to itself enough times, it will exceed any other number in magnitude.
34 Zero is just bad It refuses to get bigger.
It also refuses to make other numbers bigger.Add one and two and you get three, a larger number.Add zero and two and you get two, the same number you started with.Zero had no substance, and it was a frightening concept in ancient times.Multiplication and division with zero stumped ancient mathematicians and philosophers.
It also refuses to make other numbers bigger.Add one and two and you get three, a larger number.Add zero and two and you get two, the same number you started with.Zero had no substance, and it was a frightening concept in ancient times.Multiplication and division with zero stumped ancient mathematicians and philosophers.
35 In the realm of numbers, multiplication is a stretch. Literally.
Imagine multiplication as if it’s a rubber band number line. Multiply three by two and you get six, which is twice as big as three. You stretched the number line. Divide six by two and you get three, division relaxes the number line.But what happens when you multiply by zero? You just broke the rubber band. The answer is zero and the number line has collapsed.
Imagine multiplication as if it’s a rubber band number line. Multiply three by two and you get six, which is twice as big as three. You stretched the number line. Divide six by two and you get three, division relaxes the number line.But what happens when you multiply by zero? You just broke the rubber band. The answer is zero and the number line has collapsed.
36 Think of it like this…. Multiplying two numbers represents an area.
2 times 2 is four. The area of a square with sides equal to two is equal to four units.If you try to determine the area of a square with sides 2 and 0, there is no area. You are left with nothing, zip, nada, zilch.
2 times 2 is four. The area of a square with sides equal to two is equal to four units.If you try to determine the area of a square with sides 2 and 0, there is no area. You are left with nothing, zip, nada, zilch.
37 Now it gets scarier Division is the opposite of multiplication.
When you multiply something by zero you get zero.But when you divide by zero you get….what???1/0 = infinity. On your calculator you get an errorZero can go into one an infinite number of times and never equal one.
When you multiply something by zero you get zero.But when you divide by zero you get….what???1/0 = infinity. On your calculator you get an errorZero can go into one an infinite number of times and never equal one.
38 Zero clashed with one of the central tenets of Western philosophy, a dictum whose roots were in the number philosophy of Pythagoras and whose importance came from the paradoxes of Zeno. The whole Greek universe rested upon this pillar: there is no void.The Greek universe, created by Pythagoras, Aristotle, and Ptolemy, survived long after the collapse of Greek civilization. In that universe there is no such thing as nothing. There is no zero. Because of this, the West could not accept zero for nearly two millennia. The consequences were dire. Zero’s absence would stunt the growth of mathematics, stifle innovation in science, and incidentally, make a mess of the calendar. Before they could accept zero, philosophers in the West would have to destroy their universe.
39 The Origin of Greek Number Philosophy
Hippasus of Metapontum stood on the deck, preparing to die. Around him stood the members of a cult, a secret brotherhood that he had betrayed. Hippasus had revealed a secret that was deadly to the Greek way of thinking, a secret that threatened toundermine the entire philosophy that the brotherhood struggled to build. For revealing that secret, the great Pythagoras himself sentenced Hippasus to death by drowning.
Hippasus of Metapontum stood on the deck, preparing to die. Around him stood the members of a cult, a secret brotherhood that he had betrayed. Hippasus had revealed a secret that was deadly to the Greek way of thinking, a secret that threatened toundermine the entire philosophy that the brotherhood struggled to build. For revealing that secret, the great Pythagoras himself sentenced Hippasus to death by drowning.
40 The Greek Mathematical Cult
The leader of the cult was Pythagoras, an ancient radical. According to most accounts, he was born in the sixth century BC on Samos, a Greek island off the coast of Turkey famed for a temple to Hera and for really good wine. He was firmly convinced that he was the reincarnated soul of Euphorbus, a Trojan hero. This helped to convince him that all souls transmigrated to other bodies after death. For this, he was a vegetarian.
The leader of the cult was Pythagoras, an ancient radical. According to most accounts, he was born in the sixth century BC on Samos, a Greek island off the coast of Turkey famed for a temple to Hera and for really good wine. He was firmly convinced that he was the reincarnated soul of Euphorbus, a Trojan hero. This helped to convince him that all souls transmigrated to other bodies after death. For this, he was a vegetarian.
41 PythagorasPythagoras was a powerful speaker, a renowned scholar, and a charismatic teacher. He was said to have written the constitution for Greeks living in Italy. Students flocked to him.Pythagoras the SamosanOn the isle of Samos
42 The PythagoreansThe Pythagoreans were a cult. They were the followers of the ideas of Pythagoras. They believed that all disease is caused by indigestion, that one should eat raw food and drink only water, and that one must avoid wearing wool. At the center of their philosophy though was an important concept: All is Number.
43 The PythagoreansThe Greeks inherited their mathematics from the Egyptians. As a result, there was no distinction between shapes and numbers. Every number-shape had a hidden meaning and the most beautiful were sacred. The mystical symbol of this cult was the pentagram. A five pointed star that gave them a glimpse into the infinite.
44 The PentagramNestled within the pentagram are an infinite number of pentagramswith the exact same proportion. Hidden within the lines of the star was, to the Pythagoreans, the ultimate view of the universe: the golden ratio.
45 MusicTo Pythagoras, playing music was a mathematical act. The harmony of the monocord was the harmony of the universe.This philosophy led to the earliest model of the planets. Pythagoras argued that the earth was at the center of the universe with the sun, moon, planets, and stars orbiting around it each pinned inside a sphere. The ratios of the sizes of the spheres were nice and orderly. As the spheres moved, they made music. The outermost planets moved the fastest and made the higher pitched notes.
48 All together, the planets and stars made a “Harmony of the Spheres”.
Modern musicians have taken this concept and created an entirely new genre of music.Relaxation music, meditation, sleep therapy, hypnotherapy, massage therapy, massage therapists, teachers, spiritual experiences, cancer clinics, and acupuncture ….to name a few.
Modern musicians have taken this concept and created an entirely new genre of music.Relaxation music, meditation, sleep therapy, hypnotherapy, massage therapy, massage therapists, teachers, spiritual experiences, cancer clinics, and acupuncture ….to name a few.
49 Artists and architects today make use of the golden ratio because it is aesthetically pleasing to the eye. This ratio governs the work of many buildings, musical works, and works of art.Some historians and mathematicians argue that the Parthenon, the Athenian temple, was built so that the golden ratio is visible in every aspect of its construction.
50 The Parthenon
51 The Nautilus
52 The Counterclockwise grooves of a Pineapple
53 More Apparent – The Pinecone
54 Sunflower Seeds
55 Modern Art (Comic Books)
56 As late as Shakespeare’s time ( ), scientists and the general public talked about the revolutions of the orbs of different proportions and discussed the heavenly music that reverberated through the cosmos.Kepler, Galilio, and Newton changed this.
とても興味深く読みました：
再生核研究所声明353（2017.2.2） ゼロ除算 記念日
2014.2.2 に 一般の方から100/0 の意味を問われていた頃、偶然に執筆中の論文原稿にそれがゼロとなっているのを発見した。直ぐに結果に驚いて友人にメールしたり、同僚に話した。それ以来、ちょうど３年、相当詳しい記録と経過が記録されている。重要なものは再生核研究所声明として英文と和文で公表されている。最初のものは
再生核研究所声明 148（2014.2.12）: 100/0=0, 0/0=0 － 割り算の考えを自然に拡張すると ― 神の意志
で、最新のは
Announcement 352 (2017.2.2): On the third birthday of the division by zero z/0=0
である。
アリストテレス、ブラーマグプタ、ニュートン、オイラー、アインシュタインなどが深く関与する ゼロ除算の神秘的な永い歴史上の発見であるから、その日をゼロ除算記念日として定めて、世界史を進化させる決意の日としたい。ゼロ除算は、ユークリッド幾何学の変更といわゆるリーマン球面の無限遠点の考え方の変更を求めている。― 実際、ゼロ除算の歴史は人類の闘争の歴史と共に 人類の愚かさの象徴であるとしている。
心すべき要点を纏めて置きたい。
１） ゼロの明確な発見と算術の確立者Brahmagupta (598 - 668 ?) は 既にそこで、0/0=0 と定義していたにも関わらず、言わば創業者の深い考察を理解できず、それは間違いであるとして、１３００年以上も間違いを繰り返してきた。
２） 予断と偏見、慣習、習慣、思い込み、権威に盲従する人間の精神の弱さ、愚かさを自戒したい。我々は何時もそのように囚われていて、虚像を見ていると 真智を愛する心を大事にして行きたい。絶えず、それは真かと 問うていかなければならない。
３） ピタゴラス派では 無理数の発見をしていたが、なんと、無理数の存在は自分たちの世界観に合わないからという理由で、― その発見は都合が悪いので ― 、弟子を処刑にしてしまったという。真智への愛より、面子、権力争い、勢力争い、利害が大事という人間の浅ましさの典型的な例である。
４） この辺は、２０００年以上も前に、既に世の聖人、賢人が諭されてきたのに いまだ人間は生物の本能レベルを越えておらず、愚かな世界史を続けている。人間が人間として生きる意義は 真智への愛にある と言える。
５） いわば創業者の偉大な精神が正確に、上手く伝えられず、ピタゴラス派のような対応をとっているのは、本末転倒で、そのようなことが世に溢れていると警戒していきたい。本来あるべきものが逆になっていて、社会をおかしくしている。
６） ゼロ除算の発見記念日に 繰り返し、人類の愚かさを反省して、明るい世界史を切り拓いて行きたい。
以 上
追記：
The division by zero is uniquely and reasonably determined as 1/0=0/0=z/0=0 in the natural extensions of fractions. We have to change our basic ideas for our space and world:
Division by Zero z/0 = 0 in Euclidean Spaces
Hiroshi Michiwaki, Hiroshi Okumura and Saburou Saitoh
International Journal of Mathematics and Computation Vol. 28(2017); Issue 1, 2017), 1-16.
http://www.scirp.org/journal/alamt http://dx.doi.org/10.4236/alamt.2016.62007
http://www.ijapm.org/show-63-504-1.html
http://www.diogenes.bg/ijam/contents/2014-27-2/9/9.pdf
http://www.ijapm.org/show-63-504-1.html
http://www.diogenes.bg/ijam/contents/2014-27-2/9/9.pdf
再生核研究所声明371（2017.6.27）ゼロ除算の講演― 国際会議 https://sites.google.com/site/sandrapinelas/icddea-2017 報告
http://ameblo.jp/syoshinoris/theme-10006253398.html
1/0=0、0/0=0、z/0=0
http://ameblo.jp/syoshinoris/entry-12276045402.html
1/0=0、0/0=0、z/0=0
http://ameblo.jp/syoshinoris/entry-12263708422.html
1/0=0、0/0=0、z/0=0
http://ameblo.jp/syoshinoris/entry-12272721615.html
再生核研究所声明311（2016.07.05） ゼロ0とは何だろうか
ここ２年半、ゼロで割ること、ゼロ除算を考えているが、ゼロそのものについてひとりでに湧いた想いがあるので、その想いを表現して置きたい。
数字のゼロとは、実数体あるいは複素数体におけるゼロであり、四則演算で、加法における単位元（基準元）で、和を考える場合、何にゼロを加えても変わらない元として定義される。積を考えて変わらない元が数字の１である：
Wikipedia:ウィキペディア：
初等代数学[編集]
数の 0 は最小の非負整数である。0 の後続の自然数は 1 であり、0 より前に自然数は存在しない。数 0 を自然数に含めることも含めないこともあるが、0 は整数であり、有理数であり、実数（あるいは代数的数、複素数）である。
以下は数 0 を扱う上での初等的な決まりごとである。これらの決まりはxを任意の実数あるいは複素数として適用して構わないが、それ以外の場合については何も言及していないということについては理解されなければならない。
加法:x + 0 = 0 +x=x. つまり 0 は加法に関する単位元である。
減法: x− 0 =x, 0 −x= −x.
乗法:x 0 = 0 ·x= 0.
除法:xが 0 でなければ0⁄x= 0 である。しかしx⁄0は、0 が乗法に関する逆元を持たないために、（従前の規則の帰結としては）定義されない（ゼロ除算を参照）。
実数の場合には、数直線で、複素数の場合には複素平面を考えて、すべての実数や複素数は直線や平面上の点で表現される。すなわち、座標系の導入である。
これらの座標系が無ければ、直線や平面はただ伸びたり、拡がったりする空間、位相的な点集合であると考えられるだろう。― 厳密に言えば、混沌、幻のようなものである。単に伸びたり、広がった空間にゼロ、原点を対応させるということは 位置の基準点を定めること と考えられるだろう。基準点は直線や平面上の勝手な点にとれることに注意して置こう。原点だけでは、方向の概念がないから、方向の基準を勝手に決める必要がある。直線の場合には、直線は点で２つの部分に分けられるので、一方が正方向で、他が負方向である。平面の場合には、原点から出る勝手な半直線を基準、正方向として定めて、原点を回る方向を定めて、普通は時計の回りの反対方向を 正方向と定める。これで、直線や平面に方向の概念が導入されたが、さらに、距離（長さ）の単位を定めるため、原点から、正方向の点（これも勝手に指定できる）を１として定める。実数の場合にも複素数の場合にも数字の１をその点で表す。以上で、位置、方向、距離の概念が導入されたので、あとはそれらを基礎に数直線や複素平面（座標）を考える、すなわち、直線と実数、平面と複素数を１対１に対応させる。これで、実数も複素数も秩序づけられ、明瞭に表現されたと言える。ゼロとは何だろうか、それは基準の位置を定めることと発想できるだろう。
― 国家とは何だろうか。国家意思を定める権力機構を定め、国家を動かす基本的な秩序を定めることであると原理を述べることができるだろう。
数直線や複素平面では 基準点、０と１が存在する。これから数学を展開する原理を下記で述べている：
しかしながら、数学について、そもそも数学とは何だろうかと問い、ユニバースと数学の関係に思いを致すのは大事ではないだろうか。この本質論については幸運にも相当に力を入れて書いたものがある：
19/03/2012
ここでは、数学とは何かについて考えながら、数学と人間に絡む問題などについて、幅.広く面白く触れたい。
複素平面ではさらに大事な点として、純虚数i が存在するが、ゼロ除算の発見で、最近、明確に認識された意外な点は、実数の場合にも、複素数の場合にも、ゼロに対応する点が存在するという発見である。ゼロに対応する点とは何だろうか？
直線や平面で実数や複素数で表されない点が存在するであろうか？ 無理して探せば、いずれの場合にも、原点から無限に遠ざかった先が気になるのではないだろうか？ そうである立体射影した場合における無限遠点が正しくゼロに対応する点ではないかと発想するだろう。その美しい点は無限遠点としてその美しさと自然さ故に１００年を超えて数学界の定説として揺るぐことはなかった。ゼロに対応する点は無限遠点で、1/0=∞ と考えられてきた。オイラー、アーベル、リーマンの流れである。
ところが、ゼロ除算は1/0=0 で、実は無限遠点はゼロに対応していることが確認された。
直線を原点から、どこまでも どこまでも遠ざかって行くと、どこまでも行くが、その先まで行くと（無限遠点）突然、ゼロに戻ることを示している。これが数学であり、我々の空間であると考えられる。この発見で、我々の数学の結構な部分が修正、補充されることが分かりつつある。
ゼロ除算は可能であり、我々の空間の認識を変える必要がある。ゼロで割る多くの公式である意味のある世界が広がってきた。それらが 幾何学、解析学、代数学などと調和して数学が一層美しい世界であることが分かってきた。
全ての直線はある意味で、原点、基準点を通ることが示されるが、これは無限遠点の影が投影されていると解釈され、原点はこの意味で２重性を有している、無限遠点と原点が重なっている現象を表している。この２重性は 基本的な指数関数y=e^x が原点で、0 と1 の２つの値をとると表現される。このことは、今後大きな意味を持ってくるだろう。
古来、ゼロと無限の関係は何か通じていると感じられてきたが、その意味が、明らかになってきていると言える。
２点から無限に遠い点 無限遠点は異なり、無限遠点は基準点原点の指定で定まるとの認識は面白く、大事ではないだろうか。
以 上
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