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Is high-order Mathematics an art or a science?
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Heather
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Nov 21, 2016 04:48AM
Your thoughts?
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Well, Leah, I wasn't even sure what "high-order" mathematics was so I had to look it up.I found that they are really related to one another. My first thought when I read this question was Leonardo da Vinci Vitruvian Man. We all know that he was more than just an artist, he was the definition of Renaissance man dipping into all areas. His painting of the proportionate human body was the first clue that makes me think that high-order mathematics is both.
I found this:
"Leonardo’s famous drawings of the Vitruvian proportions of a man’s body first standing inscribed in a square and then with feet and arms outspread inscribed in a circle provides an excellent early example of the way in which his studies of proportion fuse artistic and scientific objectives. It is Leonardo, not Vitruvius, who points out that ‘If you open the legs so as to reduce the stature by one-fourteenth and open and raise your arms so that your middle fingers touch the line through the top of the head, know that the centre of the extremities of the outspread limbs will be the umbilicus, and the space between the legs will make and equilateral triangle’...Here he provides one of his simplest illustrations of a shifting ‘centre of magnitude’ without a corresponding change of ‘centre of normal gravity’. This remains passing through the central line from the pit of the throat through the umbilicus and pubis between the legs. Leonardo repeatedly distinguishes these two different ‘centres’ of a body, i.e., the centers of ‘magnitude’ and ‘gravity"
http://leonardodavinci.stanford.edu/s...
Leah wrote:
"Heather, that's a great answer -- when I first heard of and saw the Mandelbrot set of fractal geometry, I began to suspect that mathematics might be one way of creating art. The more I learn about mathematics, art, proportion, shape and form, the more convinced I am that the practice of high order mathematics is a creative act, in part because of the rigorous demand for logic, proofs, and elegance in the solution. But I might be wrong: although your connection of mathematics and art using Da Vinci's illustration gives me a frisson of hope!!"
I remember that Michelangelo's David is a rather large statue. And the pedestal on which he stands is above the viewer's head. For this purpose he deliberately 'adjusted' the proportions of the human body to create the illusion of it being directly proportional from a lower view-point. i.e. his arm holding the rock is longer than a normal arm would be, but seeing it from below, it looks natural.High-order thinking with mathematics put into art, I believe, is genius!
Being raised by a Mathematics teacher who is one of many in our extended family, I have likely heard more math based conversations than one human dare be subject to under normal cruel and unusual punishment clauses per the U.S. Constitution.That said, I can certainly appreciate the artistic appeal of higher order Mathematics with respect to chaos theory, fractals, symmetry, sacred geometry, Fibonacci sequences, etc.. Still Math seems to a beast all of it's own accord. The need for explanation and order extends into cultural phenomenon such as Feng Shui too.
On the Science side, my engineering education and career experience have proven that Math is the basis for capture, recording, expression and projection of the wonders and phenomenon to be explained in our tactile world. Math is completely foundational to Science that again it almost appears fundamental and outside of Science too.
Taken to yet another tangent, Math also has instrumental (no pun intended) implications on the creation, comprehension and performance of music. Thus, the calculus involved in tempo, intensity, inflection, vibrato and camber simply scintillate the auditory palette in a way that only art can stir the soul along with other various and sundry sensations.
Ultimately, the thriving contrarian in me insists that Math is all and none of the above and the Mathematician in you felt the need to compartmentalize, assign and thus model the nebulous concept of higher order Mathematics into a genus or species. Yet, the act of doing so is a rather scientific approach in and of itself. None the less, I trust this opening contribution evokes a chuckle or two at a minimum! Cheers!
You are clearly an engineer, Scott. And I am clearly not! Most of what you wrote went over my head but I appreciate your eloquence and it was pleasing to read, though I didn't understand most of it.The one paragraph you did mention resonated with me (no pun intended) in that I am a musician myself.
Scott wrote: "Taken to yet another tangent, Math also has instrumental (no pun intended) implications on the creation, comprehension and performance of music. Thus, the calculus involved in tempo, intensity, inflection, vibrato and camber simply scintillate the auditory palette in a way that only art can stir the soul along with other various and sundry sensations."
Most, if not all of us know that Beethoven was deaf. How did he compose such masterpieces? I've known that math was involved but I found this short, very interesting little video explaining how math is intricately related to how he composed his music, specifically Moonlight Sonata in this video. Check it out!
http://ed.ted.com/lessons/music-and-m...
Astonished by the insightful quality of that link you shared and thankful (I think ???) of the kind words you shared regarding my post. A little befuddled to hear that my words missed their mark of the proverbial apple theoretically placed on ones head. Lol!From what I've heard of Beethoven, he actually relied on sensing the vibrations in the wooden floors by placing his ear against them as his newest compositions were played with the onset of deafness. Likely hearsay though makes for delightful visualization none the less.
As luck would have it, began dabbling with writing a bit of music myself last night though wish I'd had seen your response as well.
I believe I read somewhere that you are a pianist? Hope to one day hear your work. Unfortunately, I've never found my motor skills sufficient to hone the craft if instruments beyond my voice. Truly enjoy singing though and managed to avoid liable lawsuits from karaoke performances to date!
Forgive the rabbit hole I appeared to dive into there in shameless self divulgence please.
This site and quite frankly the facilitator has triggered something me yielding this boon of the day!Trust you may enjoy the visuals and narrative as much I did!
http://www.sacred-geometry.com/openin...
Scott wrote: "This site and quite frankly the facilitator has triggered something me yielding this boon of the day!Trust you may enjoy the visuals and narrative as much I did!
http://www.sacred-geometry.com/o..."
That was clearly fascinating, Scott! If described by a lay-person, it wouldn't make much sense not being additionally explained in mathematics, specifically geometry. Admittedly, this I can believe both in the earthly, what we experience presently, and also the spiritual realms.
One basic, perhaps selfish question, is the metaform and or heart connection pendant something one can purchase or find? Or is it fabricated for experimental purposes only? These could really be used for the good energy within us! Even suggesting using the portions of the brain that are now inaccessible or in other words, a higher power or state of consciousness.
Another question relating to the art of these conclusions, is the 'three dimensional' source found in any sculpture? Or is it specific to a certain form? I wasn't clear on that point.
I'd be interested to know. Thank you for sharing that!
Elated to hear you too found magic in the article. Thanks for bringing the marketing like aspect of the pendant to my attention. Initially I glossed over that and it certainly was not my intention. Seems like a powerful piece though I know nothing more about it.However, I can attest to the work of a near and dear friend at Sovereign Alliance. She produces a pendent called a Serah Key that knocked me off my feet as I experienced it! Here is the link...
http://www.sovereign-alliance.com/pro...
Need to re read regarding the three dimensional source though I believe it refers to the Fibonacci Sequence ant that is sometimes found in rock formations. Will re read and continue comments in another post as time allows.
Scott wrote: "Elated to hear you too found magic in the article. Thanks for bringing the marketing like aspect of the pendant to my attention. Initially I glossed over that and it certainly was not my intention...."Thank you for that information, especially the link to not only read more about how the Heart Connection works, but also how I can acquire one myself!
I look forward to what you've found through your investigation regarding the three dimensional source. I am learning a lot more about mathematics in general as this is not one my strong points.
New algorithm helps uncover forgotten figures beneath Da Vinci paintingby Caroline Brogan, Martin Sayers and Mariana Kneppers, Imperial College London
Imperial and National Gallery researchers have used a new algorithm to help visualise hidden drawings beneath Leonardo Da Vinci's Virgin of the Rocks.
Imperial College London's Professor Pier Luigi Dragotti and National Gallery's Dr. Catherine Higgitt used the new algorithm combined with a technique called macro X-ray fluorescence (MA-XRF) scanning, which maps chemical elements within paintings.
In doing so they revealed, more clearly than ever before, the hidden figures that Leonardo first drew before changing his design to the one that he eventually painted. These included abandoned images of an angel and the Infant Christ.
Professor Dragotti, of Imperial's Department of Electrical and Electronic Engineering, said: "It was like looking for a needle in a haystack, but such a great feeling to see the wings and head finally uncovered."
More recently the team used MA-XRF to non-invasively scan each pixel of the painting to detect different chemical elements within the materials Leonardo used in the painting.
They found that the drawing for the hidden first composition contained zinc, making it possible to reveal more forgotten figures—including the Infant Christ and a winged angel at the right where now only landscape is visible.
At Imperial, Professor Dragotti developed the algorithm to automatically process the huge amount of data from the MA-XRF scans, improving on the existing, more manual methods and producing better, more reliable images to help them visualiz the data.
He said: "Each pixel contained different amounts of each element, within various layers. We analyzed each pixel individually before combining them to see all the underdrawings in the painting. This revealed a much sharper image of the angel and baby."
Dr. Higgitt said: "Before, we were getting very weak signals from the zinc within the painting due to its overlap with other elements, but the algorithm has given us more confidence in the signals that relate to the underdrawing."
"It's been a rewarding experience to learn about and combine our different fields. The findings could also help us to reach out to more varied and unexpected audiences."
Art and Artificial IntelligenceThe researchers say their bespoke technique could be applied to data from other paintings, making analysis of artworks more user-friendly and letting data be accessed more easily by, for example, art students and galleries.
Professor Dragotti will now look to combining imaging techniques and artificially intelligent algorithms to extract more hidden information from paintings.
Explore further:
Scientists pioneer new way to analyze ancient artwork
https://phys.org/news/2017-12-scienti...
