Similarities and Differences of Mathematical Systems

Mathematical systems from different cultures were of course different, but they were generally used for measuring: lengths/widths/heights, and time. Some cultures, like the ancient Greeks, were more advanced, and they dove deeper into complicated equations and formulas, such as the Greek mathematician Pythagoras. Cultures used symbols and ideas that made sense to their surroundings: for example, Base 10 comes from the ten digits (fingers) that humans have. Some cultures were more superstitious than others. The Pythagoreans thought that 4 and 10 were numbers to celebrate, especially 10, because it was the "object of a sacred oath." Cultures that lived by the sea might have used seashells for their units, for counting and currency, and their representations (symbols) might look like different shapes of shells. Cultures that lived by the mountains might have symbols that looked like mountains, for example, ^/\^. Almost all groups had some level of mathematic discovery, but some had more advanced ideas than others.

Signs and Symbols of Math and Language

Part of my research is dedicated to the signs and symbols of math and language and how they are similar. In language, letters and characters represent sounds, and they are linked together to form words, which represent meanings. In mathematics, the obvious symbols are numbers, as they are what comes most frequently to mind when we think of math. Decimals, division signs, addition signs, subtraction signs, and multiplication signs are all symbols used commonly used in mathematics; they represent concepts and processes. Mathematical symbols can change numbers entirely, for example, a pointedly placed decimal can alter a number completely (ex. 1234567 and 1.234567). In language, the obvious symbols are letters, which are like the direct cousins of numbers, but there are also punctuation signs, such as quotation marks ("), exclamation marks (!), commas (,), periods (.), and question marks (?). Punctuation can also change meanings: a statement can be changed into a query by adding a question mark at the end. Symbols are things that stand for something else - something that would make sense and would relate to the concept it was representing; representation, association, resemblance. Symbols can be complex or simple (hand-drawn or computerized).

History of Mathematics

I am currently researching the history of the mathematical system that is most commonly used around the world in modern times. I have found out that our math system has roots in ancient Egypt, ancient Greece, and ancient Babylon. Ancient Greek and Indian math was translated into Arabic, then into Latin. Once this was translated into Latin, it spread over Western Europe, and then became the mathematics of the world after a few hundred years. The ancient Greeks were the first known people to work with pure math, and they introduced the concepts of logical deduction. They were highly interested in geometry, and used it to solve problems that algebra could be used for. They discovered irrational numbers in approximately 400 BC., and they were intent on proving that certain mathematical concepts were true. Researchers and mathematicians have predicted that there will be no end in sight for the discoveries of math, based on the progress that has been happening during the present, and also the past. The Greeks like music, because - along with architecture - it created beauty while following the strict rules that they preferred.

ACE References

About. (2010) “Mathematical Symbols: An Overview.” About. Retrieved March 24, 2010, from the Internet: http://math.about.com/library/weekly/aa052502a.htm

Ager, S. (1998-2010). “Gothic Alphabet.” Omniglot. Retrieved February 8, 2010, from the Internet:http://www.omniglot.com/writing/gothic.htm

Koller, J. (2003). “Roman Numerals.” Jurgen Koller. Retrieved March 24, 2010, from the Internet: http://www.mathematische-basteleien.de/romannumerals.htm#top

Merriam-Webster. (2010) “Symbol.” Merriam-Webster. Retrieved March 24, 2010, from the Internet: http://www.merriam-webster.com/dictionary/symbol

No Author, but notated as “Brian.” (2010). “What is the Difference Between a Number and a Numeral?” The Math Mojo Chronicles. Retrieved January 11, 2010, from the Internet:http://www.mathmojo.com/chronicles/2008/08/09/what-is-the-difference-between-a-number-and-a-numeral/

Viadero, D. (2010). “Early-Algebra Push Seen to be Flawed.” EBSCO Host. Retrieved March 24, 2010, from the Internet:http://web.ebscohost.com/ehost/detail?vid=4&hid=102&sid=750e2f69-7484-4460-9452-3cf8ec5d22d1%40sessionmgr110&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#db=aqh&AN=48242701

World Book Encyclopedia. “Algebra.” 2004 edition. (Volume A pg 350).

Your Dictionary.com. (2009). “Roman Numerals.” Love to Know. Retrieved March 24, 2010, from the Internet:http://www.yourdictionary.com/crossword/romanums.html

Digital Citizenship Questions (Homework)

1. Do computers give us more human connections or less human connections?

I think that computers allow more connections to humans, but in a way that makes us less human. Technology becomes unnatural beyond a certain amount of use, in spite of the natural reactions it can bring up. Technology is human, in the sense that it is a natural instinct for people to strive harder to reach goals that would not have been possible decades ago. New forms of technology are being created all the time, and younger generations are adapting to them as if they had lived with them their whole lives. Children and teenagers are able to use new and advanced technology because they have been exposed to computers and digital devices pretty much since they were born. I believe that computers can cause addictions. Some technology, like video games or computer games can become additions and obsessions, and although they may set up acquaintances, they can transform a person into, for instance, a more violent being - the cause of fighting, military, or other not-so-peaceful games. Computers do allow friendships to be held over long distances, when they might not be able to otherwise. In short, computers give us more connections, but at a price.

2. If you had to write 5 rules for internet ethics and manners, what would they be?

1) No crude language - no swearing/inappropriate words.

2) No explicit publicity or information/pictures of/about/belonging to others without consent - copyright terms.

3) No extremely violent technology that could promote similar behaviour in reality - that could mislead children to believe things that aren't true.

4) No false claims - advertisements claiming products or programs/websites to be free when they aren't.

5) No personally prejudiced remarks concerning racism, sexism, religiously biased remarks....

3. Do you think teachers should encourage or discourage multitasking in students?

This question is not easy to answer, as I have no knowledge of the learning atmosphere or the students and their learning styles. Some people learn better if they can focus on one task at a time, while others are able to actively work on different thing at the same time. I think that teachers should encourage multitasking to some extent, because in more cases than not, attempting several tasks at once can stretch the boundaries of one's learning, and stretch how much the mind can accomplish.

4. Write a 6 word story summarizing an experience that you've had "living" online.

Peer pressure created by the unknown.

Hello! Welcome to my blog. I will be using it to post my research and information that I found for my research topic, which is about language and how it connected to almost everything known to mankind. Last term, when I researched another topic, I studied the connections between music and language, and I gained knowledge of many interesting concepts, such as the fact that musical enharmonics are like homophones in language.