In the beginning of the course, we discussed “NGD”. The two areas of “NGD” that we focused on were number and geometry. Number is discrete, finite, time, or sound. Geometry is continuous, infinite, space, or vision. Bronowski mentioned how “it’s said that science will dehumanize people and turn them into numbers” (374). This tragically became true during the Holocaust where people were no longer considered human beings, but rather numbers. We discussed various mathematical topics concerning numbers like the well-ordering pair. In the well-ordering pair, ever subset has a least member. There are also figurative numbers, squared numbers, and even Pythagorean triples. In an earlier section of The Ascent of Man titled “The Music of the Spheres” Bronowski taught us more about numbers and their origin in the section that states: …show more content…
From that fundamental step, many cultures have built their own number systems, usually as a written language with similar conventions. The Babylonians, the Mayans, and the people of India, for example, indented essentially the same way of writing large numbers as a sequence of digits that we use, although they lived far apart in space and time (155). This means that although the specific numbers systems may vary from culture to culture, the basic concept that one thing plus another thing means you have two things is seemingly
natural numbers are labeled 1, 2, 10, 11, 12, 20, 21, 22, 100, and so forth.
Mesopotamia used cuneiform to communicate information about their crops and about taxes. Daily events, trade, astronomy, and literature were scribed onto clay tablets. According to the website on Ancient Mesopotamia, “Numbers were represented by repeated strokes or circles” (Ankita Bhugra, 2013). The cuneiform are similar to, but more abstract than the Egyptian hieroglyphics.
The writing system that we know today as cuneiform was created by the Sumerians in Mesopotamia around 3500 B.C.E. within the Uruk Period. The region of Sumer is commonly considered the cradle of civilization. Being located in between the Tigris and the Euphrates rivers, Sumerians were skilled farmers, sailors, and traders. The land was very fertile which led to the flourish of trade. With the increase of trade there was a need to keep track of it all. The economic necessity called for the need to keep track of all agricultural wealth. The start of writing was used to record goods such as jars of oil, bushels of barley, and ...
Fundamentally, mathematics is an area of knowledge that provides the necessary order that is needed to explain the chaotic nature of the world. There is a controversy as to whether math is invented or discovered. The truth is that mathematics is both invented and discovered; mathematics enable mathematicians to formulate the intangible and even the abstract. For example, time and the number zero are inventions that allow us to believe that there is order to the chaos that surrounds us. In reality, t...
In this system, the value of a number is determined both by the symbol that represents the number and where that number is positioned within a larger number. This system made it possible for Maya scribes to express large numbers using only a limited number of symbols. The numerical system used by ancient Romans, Roman Numerals, was much less efficient than the Maya system of place value. In the system of Roman Numerals, place holders did not exist, more symbols were just added to express a larger number. In the Maya system, glyphs represented numbers. The bottom row in the glyph represented the numbers one through nineteen. The second row from the bottom in the glyph represented the twenties column. The third row represented the four hundreds column, and so on. The concept of zero was essential in the development of a system of place value because it held the position of quantities that were not
It is believed that zero originated in three separate places—Mesopotamia, India, and Mesoamerica. In Mesopotamia the first recordings of zero was in 300 BCE. For them, zero was just a placeholder between numerals in a number such as 502 and never had an actual numerical value. Similarly, the Mayans in 350 CE independently began using zero, but just like Mesopotamia it was strictly for place holding (www.mediatinker.com). In 500 CE, Ancient India created the first known actual concept of zero. In 628 CE, the Indian mathematician Brahmagupta wrote the rules of zero in his book Bramhasputha Siddhanta. In this book the rules he alludes to are one, zero doesn't change the value to number when added or subtracted, and two, when zero is multiplied with a number the value becomes nothing (www.xslv.org).
Number systems have been around since the beginning of human civilization. In the early history of mathematics, people came up with systems for counting known as bases. A base is the foundation upon which a number system was built. For example, the Mesopotamia Sumerians had a base 60 system, and some pre-Columbian civilizations used a base 20 system. Today, a base-10 system is used. Centuries ago, one of the most essential systems was invented: base-2. Also known as Binary, it has many useful applications, including in computer science. The Binary system was invented by Gottfried Leibniz, a German mathematician and philosopher, in the 1700s.
Leonardo Fibonacci was one who introduced the Hindu-Arabic number system into Europe. This number system is the one we still use today, based on ten digits with its decimal point, plus the symbol for 0. Again, these numbers are 0-9 with the decimal poi...
Tubbs, Robert. What is a Number? Mathematical Concepts and Their Origins. Baltimore, Md: The Johns Hopkins
Hieroglyphics were a traditional form of writing used by the Egyptian people. These carvings are one of the earliest examples contributing to current knowledge of ancient Egyptian mathematics. Inscriptions of early hieroglyphic numerals can be found on temples, stone monuments and vases. Such carvings typically include groups of inscriptions. Although hieroglyphs indicate the use of mathematics in early Egyptian civilization, they shed little light on any ...
One of the most debated questions throughout human history concerns whether or not math, one of the most useful areas of knowledge, was discovered or invented. Of course, many people have evidence and theories to what they think proves either side, yet the question still remains unanswered. When analyzing this question, it is important to fully understand the difference between the terms “discovered” and “invented”. Discovered can be defined as finding something or someone either unexpectedly or while searching. This is contrasted against the definition for invented which can be defined as creating, designing or producing something that has not existed before. With such different meanings, one must question how it is still unknown whether or not mathematics was found among nature or created in the mind. When developing something so basic as the number systems, did the human race invent math or simply discover the coding already written into the universe? Was math created to describe occurrences in nature or was it the reason patterns in nature occur? To put it more simply, does or does not math exist independent of humans? Did it exist before humans came along, and will it continue to exist after their extinction? There does not seem to be an agreed upon conclusion for these questions, however, it is important to analyze both sides of the argument. Overall, the best question to ask is, how do we know whether or not math is discovered or invented? Using various ways of knowing, examples, theories, and ideas both sides are exposed and reveal that they both are supported by plausible evidence and theories.
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
The abstractions can be anything from strings of numbers to geometric figures to sets of equations. In deriving, for instance, an expression for the change in the surface area of any regular solid as its volume approaches zero, mathematicians have no interest in any correspondence between geometric solids and physical objects in the real world. A central line of investigation in theoretical mathematics is identifying in each field of study a small set of basic ideas and rules from which all other interesting ideas and rules in that field can be logically deduced. Mathematicians are particularly pleased when previously unrelated parts of mathematics are found to be derivable from one another, or from some more general theory. Part of the sense of beauty that many people have perceived in mathematics lies not in finding the greatest richness or complexity but on the contrary, in finding the greatest economy and simplicity of representation and proof.