# Zero- Book Summary chp 0

1. Sep 8, 2004

### Tom McCurdy

Zero-- Book Summary chp 0

I have to read zero by Charles Seife for Evolution of Scientific Thought Class. I will be posting chapter summaries on this thread as they come

I would really Appreciate it if you tried not to reply to the summaries... if there is a problem or you want to comment please private message me or post a new thread about zero

Chapter Zero

Chapter 0 introduces us to the power of zero by describing a situation when the USS Yorktown was cruising on September 21, 1997 and was brought to a halt when its computer which ran its engines tried to divide a number by 0. The new software the ship was running had the hidden problem in it and just completely shut down the engines and the 80,000 horsepower they provided. It took three hours to get the ships emergency controls attached to the engine and the ship had to “limp” back into port. The last part of this section further introduces some of the conflicts that zero faces. An example would be the birth in the east and its attempt to gain acceptance in the west. The short chapter ends by describing how although zero has faced many problems and rejections, zero always in the end is able to defeat those who oppose it.

2. Sep 12, 2004

### Tom McCurdy

Zero -- Chapter One Summary

Chapter 1
[The Origin of Zero]

Zero was left out of the mathematical framework of early mathematical thought because it simply wasn’t required. Early mathematics was created with the purpose of counting something or monitoring the passage of time.

Life without Zero
Early mathematical systems started with a low base system like binary. They couldn’t count very high so it would be one, two, then many. This system works out the same way our binary system works out, in order to get larger numbers you simply add the smaller numbers. Five for example is just two and two and one. Eventually civilizations learned to count to higher numbers like three causing the chain of events to change to one, two, three, then many. However as civilizations got more advance the ancient systems adopted quinary (base-5) systems more than they did binary systems. This is believed to have happen because of the fact that humans have five fingers on each hand. From this base 5 system there were other popular bases that different groups of people used. There bases mostly consisting of base 5, 10, or 20 systems. As early civilizations started to develop writing and transcribe numbering systems it was very easy to do as the numbering system was already well established orally. Actually the Incas had a way of recording numbers with strings before they discovered writing. The Egyptians was a group of people who created a number system out of pictures representing different amount of numbers in a base 10 system. The Egyptians used the math they developed for practical uses and didn’t have a use for zero. They fixed the calendar problems presented by the lunar calendar with the creation of the solar calendar, with 12 months each consisting of 30 days and 10 day weeks. The Egyptians also valued land ownership to the point that there were grave consequences for using someone else’s land and because of this the Egyptians also invented geometry. However zero was still yet to be found.

The Birth of Zero
Although it was likely that the Greeks learned mathematics from the Egyptians they quickly surpassed their teachers in understanding and improved on the picture based way of counting. Although the Greeks were more sophisticated in their numbering system than the Egyptians, they were not as advance as the Babylonian way of counting. In this system zero was finally discovered in Iraq. The Babylonian system was sexagesimal or base 60. Zero was created as a placeholder that fixed a problem in the base 60 counting system. Without the zero placeholder the symbols used could be interpreted as any number x or that number plus 60^y+x. The zero placeholder allowed the numbers to have specific value, for example it would be like 1 vs 100, the two zeros tell us that the one has a value of 100 or 1 one hundred the second time. The Mayans also used a zero, but they used it for a counting system. Their calendar had 18 menthes each with 20 days in it, however each month had days 0-19, instead of 1-20.

The Fearsome Properties of Nothing
Although it seems strange to be afraid of a number for us today, many ancient people had religious significance with zero or nothingness. Many people believed that zero was synonymous with chaos. Also from a purely mathematical standpoint zero was unique. Until zero if you added to numbers together you would get a bigger number but zero plus anything is zero and zero plus another number is just the other number. Zero also has unique properties for multiplication and division. Dividing by zero for instance allows you to prove anything you want mathematically.

3. Sep 21, 2004

### Tom McCurdy

Zero-- Chapter 2 Summary

Chapter 2-Zero

Nothing Comes from Nothing
Zero was an inherent problem with the Greek Universe because it implied that it was possible for there to be a void. The perceptions and laws of the Greek Universe were built upon the philosophies of Pythagoras, Aristotle, and Ptolemy.

The Origin of Greek Numbering Philosophy
The Greeks took mathematics very seriously, too seriously by today’s standards. One of the chief leaders behind this radical mindset was Pythagoras, a kind of leader of a mathematical cult. Along with the area of mathematics the cult had very strict rules its members had to follow. Any abrasion of a rule would result in major consequences, such as death if one were to question a mathematical law set by the cult. They also followed many other interesting rules, such as only making love to woman in the winter. The Greeks also placed major importance in shapes, which to them were the same as mathematics. They placed special importance on the pentagram and its so called golden ratio it contains. However despite all of Pythagoras success the thing he was remembered most for was the creation of the musical scale. Pythagoras incorporated his idea of music and shapes into many things such as the cycle of the planets motion. He described the planets moving as the went around earth, with the furthest ones moving the fasted and therefore having a higher tone, while the closer ones slower with a lower tone. All together the planets combine to create a heavenly symphony. Pythagoras also ended up killing a member of the brotherhood who let out the secret about irrational numbers, and Pythagoras himself was rumored to be killed instead of crossing through a bean field.

The Infinite, the Void, and the West
This section discusses one of Zeno’s 4 main paradoxes of motion. Achilles and the tortoise, which basically says, if the tortoise has a lead at the start of the race, even though Achilles could run much faster than the tortoise he would never be able to catch up to the tortoise. The argument was that each distance segment could be divided smaller and smaller pieces… essentially forever. And with no concepts of zero, infinity, or limits the Greeks were unable to have the benefits of calculus which is needed to properly solve the problem.
Other philosophies of the times included the atomists who believed the universe was made up of indivisible atoms, who were associated with atheists. Then there were the followers of Aristotle and his view of the universe where he simply rejected zero and infinity calling them figments of mathematician like Zeno’s imagination. However unfortunately for Aristotle his argument had the paradox of requiring creation, zero, or existence forever, infinity, and he chose infinity.
Zeno’s successor was Archimedes, a brilliant mathematician who used notions of infinity with mirror problems that allowed him to create new weapons to protect his city from the Romans. He also was able to figure out if the kings crown was made of pure gold or not by the idea of water displacement vs density.

Blind Dates
This section entails the problems presented by monks who created the AD/BC year counting system. They didn’t know about the existence of zero and ended up starting with 1, this also meant the year before one was -1 because again they did not have zero. Also it turns out the monks calculated the birth of Christ wrong by four years.

The Zeroth Number
This section describes how we incorporate zero into are counting systems today and makes the point that we usually exclude it when counting up but include it when counting down.

The Gaping Void
The monks in the dark ages inherited their fear of zero from the sources they learned the math from which was the old Greek methods.

4. Sep 21, 2004

### Tom McCurdy

Zero-- Chapter 3 Summary

Chapter 3-Zero

Nothing Ventured
Although in the West zero conflicted with their philosophy, zero was widely welcomed in the East in the lands of India and later Arab lands. India was introduced to the concept of zero by the Babylonians who only used zero as a placeholder for dates. However unlike Christianity which tried to completely expel zero with religious argument Hinduism accepted zero and infinity quite readily. According to Hinduism the goal in life is to free yourself from having your soul transmigrate into other people to be reincarnated. To do this you must embrace the nothingness of your soul, so your soul or artman will be free to join the collective consciousness. This collective consciousness is everywhere at once and at the same time nowhere.

Zero’s Reincarnation
Indian mathematician transformed the idea of zero from the placeholder Babylonian view to the idea that zero was a number with a value. After some time the Indian people adopted a Babylonian style of numbering, however instead of base 60 they used base 10 which was easier for calculations. Also with the creation of Algebra Indian mathematicians did something that would have been impossible for Greek mathematicians to do. They gave up the tie between geometry and numbers. This allowed not only for negative numbers but also for zero. Both of which would have been impossible to show with shapes, how do you show a circle with and area of zero or negative five.

The Arab Numeral
Islam took its understandings of mathematics from the Indians, and the West eventually was able to take its understanding of numbers from the Arabic people. This is why our numbering system is usually said to have Arabic roots instead of Hindu roots. The Muslims were quick to adopt the systems from the Hindu people which they conquered, but still had to overcome the teachings of Aristotle which had been spread through the area from the conquests of Alexander the Great. The Muslims chose to say that Aristotle was wrong, and adopted the atomist’s view of the universe.

I am that I am: Nothing
The Jews were the next one to take the leanings of numbers from a group. They took the ideas of the Muslims and incorporated it into their own meanings. A religious leader for the Jews tried to rationalize the creation idea of the universe because of its telling in the bible. Also with the creation of Kabbalah or Jewish Mysticism Jews started to look for hidden codes in the bible, adding up numbers that had either good or evil values (a system that seemed reminiscent of certain practices of Hinduism).

Zero’s Triumph
Leonardo of Pisa, better known as Fibonacci came up with the Fibonacci sequence from a problem about rabbits he posed in one of his books. It basically says if you take a number in the sequence and add it to the number previous in the sequence you will get the next number in the sequence n=(n-1)+(n-2). This soon proved to be the sequence that determined Pythagoras golden ratio.