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.
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.
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