In response to : http://www.fromquarkstoquasars.com/why-math-is-the-language-of-the-universe/
Why Math is the "Language of the Universe":
First, lets start off with a few quotes
“Mathematics is the language with which God has written the universe.”
― Galileo Galilei
"Number rules the universe."
―Pythagoras
"Go down deep enough into anything and you will find mathematics."
―Dean Schlicter
"Mathematics directs the flow of the universe, lurks behind its shapes and curves and holds the reins of everything from tiny atoms, to the biggest stars."
― Edward Frenkel
“The interaction between math and physics is a two-way process, with
each of the two subjects drawing from and inspiring the other. At
different times, one of them may take the lead in developing a
particular idea, only to yield to the other subject as focus shifts. But
altogether, the two interact in a virtuous circle of mutual influence.”
― Edward Frenkel
The latter quote especially emphasizes the distinction between physics and mathematics. Both influence each other, but more importantly is being able to describe the physical with math. The fact that we as humans are smart enough to take what we saw thousands of years ago with just our eyes and create this abstract idea called mathematics is astonishing. Euclid was only armed with a straightedge and a compass in his book Elements in which he laid the foundations to geometry that we still use today. Throughout history it seems that every once in a while, someone sees the power and the freedom of mathematics and utilizes it to the fullest extent. These geniuses that had the ability to see what math could do are foundational to the abstract idea itself. Without the groundwork set before us, there would be nothing to climb.
This leads to the idea of mathematics in different cultures here on Earth and far far away from our home here on Earth. That is, can mathematics be different here on Earth in other places and is there a universally accepted mathematics? First we will examine the Earthly mathematics. No matter where you go on this planet, 2 + 2 will always equal 4. It does not matter if you are in Michigan or Australia, this will always be true. Granted things in different places are expressed with different symbols and objects, but the validly and logic of mathematics will still be there. When we start to ponder about alien lifeforms further away from us then we can ever our imagine is when things get interesting.
We have developed this notion of gravity which is about 9.80665 m/s2 on this planet, but what happens if we go three hundred million light years away from here? Nobody has ever traveled this far and knows what is out there. The physical laws we have established here may be different in other places. I do not think that the way we express these quantities is different from other beings, but the numbers may be slightly off. We can argue about the numbers and the physics, but we cannot argue about how it is explained and expressed.
Its been said many times how much math is around us. Lurking and stalking behind, and in front of us, we sometimes forget how much and how great math is. Easily overlooked, we would not be where we are today without the advancements. The only way we advance through this realm of numbers is to keep building from what we already know, and understanding that we could not of done it without the tools and discoveries that were presented to us by the great minds before us.
Sunday, February 16, 2014
Monday, February 10, 2014
Mi Casa..Su Casa
What is the role of the house of wisdom in math history?
Bayt al-Hikma meaning the house of wisdom was built in Baghdad around 810 AD and is an institution in the Islamic Golden Age responsible for bringing together great thinkers to form and collect ideas. Founded by Caliph Harun al-Rashid and passed down to his son al-Ma'mun in 813, the house of wisdom is a central figure of the Islamic Golden Age. For the next four hundred years scholars would start the process of taking the knowledge at that time from around the world and translating it into Arabic. The role of the House of Wisdom was the same as the Library of Alexandria in Egypt in the sense that these were very large institutions created to harvest the knowledge of what we as Humans had found out up to that point. When we have all of the resources that our ancestors had provided for us in one place, we can then begin to form new ideas and build off our previous ones. The House of Wisdom was this place with these resources at our fingertips.The House of Wisdom was responsible not only for great mathematics, but great findings in other fields like astronomy, medicine, chemistry, geography, and many more. Sadly, in 1258 Mongol armies led by Hulagu Khan would destroy the house of wisdom in Baghdad, Iraq. This was a bloody siege and it is said that the Tigris river ran black from the ink from the enormous quantities of books that were thrown it to the river and red from the blood of all the scientists and scholars who were killed.
To name a few significant House of Wisdom attendants known for their mathematics would be not at all difficult. The first one that comes to mind is Muhammad Al-Khwarimi who in the 9th Century was responsible for the strongly advocating the use of the Hindu numeral system (0,1,2,...,9) and also responsible for ideas in algebra relating to reducing, equality, and solving polynomials up to second degree. Another significant mathematician would have to be Muhammad Al-Karaji from the 10th Century who did extended work in algebra introducing the theory of algebraic calculus and also being the first to prove an idea using what we know today as mathematical induction. Thābit ibn Qurra was also a major contributor in the house of wisdom with his ideas in astronomy, physiscs, and mathematics. Thābit ibn Qurra's contribution to the area of mathematics includes finding an equation for amicable numbers, working on number theory and using ratios to describe geometrical quantities, and he also used the idea of exponential series to solve a chess board problem. Another hugely important figure in the house of wisdom is Omar Khayyám. Omar was not just limited to mathematics, he also contributed largely to astronomy, poetry, and philosophy. His work in mathematics is one of the best in the house of wisdom. He is responsible for classifying all cubic equations to a method (25 types), he also worked on the triangular array of binomial coefficients now known as Pascal's triangle, and generalized the method of completing the square to solve all quadratic equations, and did work in geometry on the theory of proportions. This is only a sample of the work that Omar Khayyám did. He is definitely the top dog of mathematics for the house along with Al-Khwarimi.
My favorite thing that spawns from all this mathematics that is being compiled and processed at this time is the art. Specifically, the tessellations that are used in mosques. One must understand that in Islam, the depiction of any religious figure is strictly forbidden which means no kind of being should be placed on the walls of worship or anywhere for that matter. What this meant is that people had to be creative enough to paint beautiful things without beings. As a result, these tessellations that involve a lot of geometry are used. The aesthetics behind these figures is the symmetry. Why they look so appealing is because of the symmetry. Most humans appreciate symmetry and we like these kinds of objects. Maybe the reason why we like a circle so much is because of its infinite symmetries.
My favorite tessellation: http://www.thelck.com/patterns/tenPointStar.html
(ten-pointed star)
Sources:
http://www.amnh.org/exhibitions/past-exhibitions/traveling-the-silk-road/take-a-journey/baghdad/house-of-wisdom
http://archive.thedailystar.net/newDesign/news-details.php?nid=234148
http://www.theguardian.com/education/2004/sep/23/research.highereducation1
Bayt al-Hikma meaning the house of wisdom was built in Baghdad around 810 AD and is an institution in the Islamic Golden Age responsible for bringing together great thinkers to form and collect ideas. Founded by Caliph Harun al-Rashid and passed down to his son al-Ma'mun in 813, the house of wisdom is a central figure of the Islamic Golden Age. For the next four hundred years scholars would start the process of taking the knowledge at that time from around the world and translating it into Arabic. The role of the House of Wisdom was the same as the Library of Alexandria in Egypt in the sense that these were very large institutions created to harvest the knowledge of what we as Humans had found out up to that point. When we have all of the resources that our ancestors had provided for us in one place, we can then begin to form new ideas and build off our previous ones. The House of Wisdom was this place with these resources at our fingertips.The House of Wisdom was responsible not only for great mathematics, but great findings in other fields like astronomy, medicine, chemistry, geography, and many more. Sadly, in 1258 Mongol armies led by Hulagu Khan would destroy the house of wisdom in Baghdad, Iraq. This was a bloody siege and it is said that the Tigris river ran black from the ink from the enormous quantities of books that were thrown it to the river and red from the blood of all the scientists and scholars who were killed.
To name a few significant House of Wisdom attendants known for their mathematics would be not at all difficult. The first one that comes to mind is Muhammad Al-Khwarimi who in the 9th Century was responsible for the strongly advocating the use of the Hindu numeral system (0,1,2,...,9) and also responsible for ideas in algebra relating to reducing, equality, and solving polynomials up to second degree. Another significant mathematician would have to be Muhammad Al-Karaji from the 10th Century who did extended work in algebra introducing the theory of algebraic calculus and also being the first to prove an idea using what we know today as mathematical induction. Thābit ibn Qurra was also a major contributor in the house of wisdom with his ideas in astronomy, physiscs, and mathematics. Thābit ibn Qurra's contribution to the area of mathematics includes finding an equation for amicable numbers, working on number theory and using ratios to describe geometrical quantities, and he also used the idea of exponential series to solve a chess board problem. Another hugely important figure in the house of wisdom is Omar Khayyám. Omar was not just limited to mathematics, he also contributed largely to astronomy, poetry, and philosophy. His work in mathematics is one of the best in the house of wisdom. He is responsible for classifying all cubic equations to a method (25 types), he also worked on the triangular array of binomial coefficients now known as Pascal's triangle, and generalized the method of completing the square to solve all quadratic equations, and did work in geometry on the theory of proportions. This is only a sample of the work that Omar Khayyám did. He is definitely the top dog of mathematics for the house along with Al-Khwarimi.
My favorite thing that spawns from all this mathematics that is being compiled and processed at this time is the art. Specifically, the tessellations that are used in mosques. One must understand that in Islam, the depiction of any religious figure is strictly forbidden which means no kind of being should be placed on the walls of worship or anywhere for that matter. What this meant is that people had to be creative enough to paint beautiful things without beings. As a result, these tessellations that involve a lot of geometry are used. The aesthetics behind these figures is the symmetry. Why they look so appealing is because of the symmetry. Most humans appreciate symmetry and we like these kinds of objects. Maybe the reason why we like a circle so much is because of its infinite symmetries.
My favorite tessellation: http://www.thelck.com/patterns/tenPointStar.html
(ten-pointed star)
Sources:
http://www.amnh.org/exhibitions/past-exhibitions/traveling-the-silk-road/take-a-journey/baghdad/house-of-wisdom
http://archive.thedailystar.net/newDesign/news-details.php?nid=234148
http://www.theguardian.com/education/2004/sep/23/research.highereducation1
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