One Sunday morning, following the visiting speaker’s sermon that dealt in some way with the beautiful, the service leader asked members of the congregation to put forth the things they found beautiful. Finally, a retired professor of physics stood and asked whether anyone found mathematics beautiful. No one admitted to it.
As someone who finds beauty in a lot of different things - music, art, nature – I was made to ask myself whether I had ever found beauty in any mathematical formula and decided that it had never happened. It turns out that for mathematicians there are beautiful formulas and ugly formulas, and a beautiful formula causes the same area of the brain to be stimulated as listening to Bach or viewing a Van Gogh does in many of the rest of us.
Mystified, I went in search of explanations of mathematical beauty, and this article in BBC News by James Gallagher explains it as well as it can be made understandable to those of us who are mathematically inert.
On an intellectual basis I get it. Certain seemingly unrelated mathematical concepts like, pi, imaginary numbers and prime numbers may be shown to be related in mathematical equations, and the more concise that demonstration the more beautiful. Thus Euler’s equation,
reveals an unexpected relationship between all of these conceptual numbers. The value e, like pi, is an irrational number that is approximately 2.71828, and like pi it is a mathematical constant. The value I is the unit imaginary number and is equal to the square root of (-1). As one mathematician explained the beauty of Euler’s equation, it in the most concise manner explains the relationship between the constants.
Another mathematician when discussing the equation that expresses the fact that any prime number divisible by four with a remainder of one is the sum of two squares was beautiful, but not especially for the equation. In his words that equation is like the final chord in a symphony. The derivation is the symphony.
I understand that on an intellectual basis, but not on the emotional basis that occurs with art or music.
Last evening we were watching television and Lynn paused the recording while she answered a phone call. The image on the screen was of a beautiful, rocky coastline, and it reminded me that when I first read, in the mid-1970s, about fractal geometry and Mandelbrot Sets they were beautiful, not for the equations, which just look like equations to my eye, but for what they represent when expressed visually.
The equations of fractal geometry - which were impossible to perform before computers because they involve continuous equations in which the result of the first equation is entered into the second, the result of which is entered into the third out to infinity - are beautiful because they express the real world.
“"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."
Benoit Mandelbrot
I like this.
I use math all the time when doing sculptures.
from concept drawing ..... praportions
to making patterns ......... graphing to full scale
to exact measurements/fitting ........... not always with rule ... sometimes string or paper line
layout ................... using mock up pattern no details
making shipping crate ........... sizing and construction
math is very important in my way of producing art
when making my ceraminc flowers ... I have sized multiple amounts of clay for petal production, not exact but close enough
after assembling flower petals to make flower, there is a scheduled amount of time needed to dry before bisque firing that is regulated by temp and firing time.
mixing of glazes .... exact measurement by weight for specific measure of water
kiln firing .... exact control of temperature and time of firing noting increase of temp in kiln on scheduled rate
cooling time .... specific schedule for no heat top closed, top cracked open, top propped open with spacer and time to remove finished product after firing and cooling times
and a recording of outside temp, time/date, list of bisque or glaze fired objects
time schedule check list ... progress report
I cannot get away from math as it is integral to my process
Certainly for graph-able functions, I assume that a mathematician can see the graph without doing the plotting. If so, I certainly could see how those equations would be beautiful.
it makes it easier to upsize in as close to being same.
graphing the original drawing and transferring block by block to full size with some adjustments on finish product.
it's not an exact science but it works.
the same is applied in paintings that use taping to provide clean edges/straight line
(modern art/cubist)
there is a mathematical equation in most things ...
poetry ... stanza, rhyming measurement
haiku ... syllable count
cross word puzzles ... only so many spaces to work in
numbers numbers everywhere!
i do a lot of calculations in my head in respect to size and weight based on past results.
have to take size and weight in consideration for shipping venues.
tabg, thanks for commenting. I use math in much the way that you do with ceramics. a^2 + b^2 = c^2 to see if your picture frame is square, and a lot of ways, but I don't look at some elegant mathematical proof - abstract math - and say that is beautiful.
In that way I feel like a tone deaf musician, that knows which strings to pluck, but not without someone else writing the music. I think real mathematicians are alternately wired. They see the answer in advance of the proof.
JMac, I like that image. I read chaos theory back in the 90s and tried to explain to my partner how it applied to everything from weather patterns to the stock market, left a book on his desk and picked it up after it lay in the same place for six months. He was a trader and I think it bothered him to think that the movements of the market over time were basically increasingly unpredictable.
i see my finished product before setting pen to paper .
i work my way in reverse order ... knowing the end result, knowing what will work and what won't then applying that knowledge to paper and so all the way back to raw material.
i have a close to exact knowledge of every piece of stock inventoried and where it is.
anal perhaps but very effective.
"i work my way in reverse order"
Sort of like visualize the David and then take away everything that is not him?
I came to love the elegance within mathematics as a child discovering the mysteries of the number 9. Later, in the 8th grade, algebra fascinated me, and the next year, geometry had me in its grip.
As a musician, I readily understood and admired the number relations within time and tempo and the structure of tones. It still serves me well when I want to transpose a tune from one key to another, or figure out the chord patterns or harmonies behind a melody line.
It was well after most of my formal schooling was done that I found even more to love. In preparation for transferring my New York State teaching certs to Washington State, I found I needed 6 college credits of mathematics above and beyond the 6 credits I had when I got my Art degree. The options were either to enroll in two expensive and time-consuming college courses, or try to teach myself and take a qualifying exam. I chose the latter, and had a ball learning it. Trigonometry and more algebra! Set and number theory! Probability! Whoooo! Gloriously logical and so beautifully constructed.
So, yep. mathematics can be beautiful.
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