TOK 4/26/10

1. Possibly Pythagoras defined reality as math because it is the closest idea to absolute truth. The consistency and the objectivity that fashions math contradicts with subjective truth and its emotion-contorted views.

Maybe he just simply perceived reality to revolve around math and numbers. Such as the patterns in everyday life and nature, like planet rotations and birthdays.

2. I am slightly reluctant to accept the mathmatician's claims, because I still need to know more about math in reality to firmly believe underneath it all, math is reality. However, math does seem to be resolute in nature, considering that there are routine patterns in our everyday lives. Such as the use of math in scientific ideas like seasonal patterns, and temperaments predicted by date of birth.

One thing scientists say is that women with waist-size 60-80% of their hips are by calculation the most beautiful in proportion. Among millions of subjective people, one is bound to find the 60-80 proportion unsightly. Math can be reality to a certain extent, but math can never reign over the realm of opinions or emotions.

3. Math is discovered because if no emotions are involved creativity is not involved. There is an underlying notion of math in nature and in the world that leads mathmaticians to discover a theorum. However it takes an alert mind and receptive logic to actually formulate a complex theorum such as quadratic formula (baffling for me).

4. Well if a student is to enter a prestigious academy of math they should know geometry. I agree completely with Plato.

5. Plato may have taught reality to his math students. The logical students branched off by discovering formulas for themselves.

6. Immanuel Kant stated that humans are limited in knowledge, and only have access to the realm of math and science. He probably believed this because people can not have access to metaphysics, which is like getting access to the absolute truth. He stated that people are constrained by what can be experienced, and metaphysical experiences, beyond the natural world, is practically impossible.

7. Frege deals with the language ways of knowing because his major was semantics.

A) “Subtract B from both sides” – You can’t subtract random numbers from each other.

B) The hole comes from strange configurations.

C) Miss Miranda can take the apple.

No D

E) It can be done by ordering them by 29.

F) It is simple if the connections go around the whole picture.

G) It has to be 6 because 4 X 4 is 16.

H) 7 Regions?

20-April-10 HMW: Mathematical Knowledge

1. How might the misleading information slant a reader's perspective (if the reader is not careful)? http://googleearthdesign.blogspot.com/2008/10/misleading-graph-bbc-on-house-prices.html//////// The misleading information is a very subtle tactic or mistake concocted by BBC. The simple, yet devious change of size would have definitely been crafted to make the searing information slightly less dreadful. However the significance is minimal (from what I assumed), because the downfall is very sharp anyways. If the news station deliberately intended to mislead readers, they may have had harmless intentions to regain the hopes of the nation.
2. Why might someone want to slant information on purpose? As the smartest living creatures on Earth with a fathomless emotional capacity, humans have an expansive inherent drive, mainly the desire for success, love, truth, and pleasure. With these compelling emotions, humans have many reasons why they would deceive others to gain what they want; drives such as purely capitalist motives or even purely self-empowering intentions.
3. What can you do to protect yourself from purposeful (agenda-driven) misinformation?The most one can do is be fully aware of the different techniques that people can utilize to promote indirect propagandas. Through online exercises, one can learn to view graphs in a more adept and alert manner. Other techniques that one can follow, is rationally questioning the motives of politicians; instead of being gullible and pervious to all persuasions. These skills of identifying propagandas are typically inborn or learned through maturation, however after thoroughly reading hints on defending oneself from agenda-driven information, one can learn to be less oblivious.

16-4-10 HmW: Freakonomics

What might the authors' research into statistics and names suggest about social standing and advancement? Howtrue are their findings (ie: if I have a rare name, does that mean I will become a criminal?)?

The authors of the articles propose an interesting inquiry; is life determined by one's name? With many references to the siblings, Winner and Loser, people dispute that names may determine lifestyle of the nameholder. Ironically, Loser procured a lucrative carreer as a detective, and Winner was incarcerated numerous times and was liable to a police track record.

The evidence alone can not determine the conclusion of the question, but there are many other interesting observations proposed by others. Another freakonomics reader mentioned the racial differences when determining names. The prospects of African girls receiving unique "non-white" names were increasingly common, with more than 50% chance of having a quintessential African monikers, such as Laquisha. African children that received these names were typically given by their single teen mothers of a destitute community. This observation may direct the question in to a more coherent direction, considering that because people who receive un-white names tend to be Africans born in to impoverished circumstances that does raise higher chance of becoming criminals. The idea can be succinctly summed up with the author's final quotes, "DeShawn's name is an indicator—but not a cause—of his life path."

Although Loser and Winner's profile is very limited; it is apparent that Loser may have tried harder in life than Winner. Loser had to earn enough respect through his actions to cover the damage of his name. Winner already seemed to be a success; to anyone who saw his name only. Although names may direct the person in to a certain direction, each person does have an underlying identity that can control whether or not if they will choose to follow the path led by their name.

But the prospects of a person with an interesting name to become a criminal was high, mainly because many of these people were born in to a disadvantaged lifestyle, which does raise the likelihood of becoming a criminal.

14-April-10 HMW: Mathematical Knowledge

2a. Should deductive reasoning be used to determine how smart someone is? Why or why not?

Honed deductive reasoning skills are highly practical because they offer certainty in life. However a test that measures knowledge through a deductive reasoning test seems alot like inductive reasoning. The test begins with a subject too specific, omitting the muti-facetted amplitude of an individual's brain. Knowledge breeds too broad a scope to be analyzed through a narrow peephole.

A deductive reasoning test should stick to testing the deductive aptitude of a person, not the sum up of the person's mental capacity. Many times a person's IQ is determined through a deduction test, and it is mainly because people believe that because deduction is so efficient, the test would be very reliable itself.

Another aspect of deductive reasoning tests that limits the accuracy of the techniques is how there usually is a time constriction. Each person grasps ideas and solves problems differently, but time should not determine whether the person is more intellectually capable. For example, Thomas Edison vied for creating the first light bulb, and he did, after countless years of scrapping and re-scrapping his work. After he created the light bulb, the world thanked him for the ground-breaking innovation; unconditional of the years it took him. It was not the fastest, smartest student in Edison's class that created the lightbulb, but it was Edison; the child that was kicked out of class because teachers thought he was "annoying and incapable".

Deductive reasoning can easily be referred to as the highest frame of knowledge, but it is something that can not determine the complete make-up of a person's knowledge. Without imagination and inspiration, deductive reasoning is nothing more than a cold and endless game of calculations.

2b. Can math be beautiful? What is the most beautiful thing about math?

One of the few rare times I heard that math was beautiful was in a TV show when a character on the show disclosed a pedantic speech on education stating, "Math is beautiful beacuse it can be understood by all languages." The beauty of math is solely depicted by perception. Math can be highly attractive to a girl with OCD because of the precision and organization that math supplements. Math can be beautiful to a precocious child who relates theorums with the missing pieces in his life.

To me, math is beautiful because of the remarkable outcomes people fulfill through their advanced rendering of math. I'm always curious to understand how buildings can be so perfectly symetrical without flaws, or how images can be transported throughout the world with the correct use of powerlines, or even today, through a wireless "portal". Amazingly, these innovations began as a simple idea, which evolved in to innumerable calculations and logistics, succeeded by the ideas advancing into the physical world. Overall the most beautiful feature about math is how people can apply it in to reality, like synthetic a priori.

3a. Is math discovered or invented? Explain your answer.

The axiom that math is rational wholly supports the proposition that math is discovered. The comforting stabilty that math exudes, is derived from the belief that math is not created. Inventions are molded by the perspective of an individual; therefore revealing the disparity between human invention and natural existence. Of the two categories, math has more traits that gravitates towards natural existence.

There are many times people juxtapose math to nature, because math is abstractly fabricated in to reality, similar to the functions of nature. Riemannian's geometry accurately portrays how math is found.

If math was a simple game... theorums would be the puzzle pieces scattered across a table; or less discretely, puzzles that were dispersed throughout the world in the beginning of the universe. Every piece exists but it takes a lot more than existence to correctly position each apparatus in to the big picture of truth. People of all occupations would collaborate to solve different areas of the puzzle. Luckily for the players, each puzzle exists; but sometimes a piece seems to be in the right place but actually inserted incorrectly, like Euclid's postulates.

Generally speaking, math is unearthable, and not spontaneously created by the human mind. However, a symbiotic relationship between human's emotional creativity and natural relativity produces phenomenal physical results, such as architecture and technology.

3b. Does perception play any role in mathematics? How?

Different perceptions allow different mathmaticians to work together to compose more accurate theories. More than a millennium ago, Euclid proposed his 5-main postulates. However in the 19th century, Riemannian utilized Euclid's laws to determine that each concept of Euclid could be disproved using the globe.

Ideas that are compressed by a limited scope can set the foundations for further discovery. Riemannian's geometry may have not been compelled to find a solution for Euclid's law, if it did not exist in the first place. When it comes to math, or other subjects, an infusion of distinctive approaches can cultivate in to a more accurate view of reality, or any other goal.

3c. How is mathematics like a language?

Mathematics can be a language. Theorums can be abstractly related to our lives. It is like a girl calling her best friend her complementary, or even supplementary.

Literally speaking, math can also be a language through coding.

In a (Christian) spiritual sense, it can be seen as a communication from God; at the least Dan Brown thinks so. For the Aztecs, the numbers on calendars and dates are messages from their higher power revealing, revelations upon the Earth.