>Outside of the prohibitively expensive alternative of private tutors, admission to one of these schools was the only means to learning the secret code that opened the doors of opportunity.
Mathematics is built around a similar sort of cipher. Even learning from textbooks is not enough to truly penetrate the collective knowledge stored in the symbols of math. The symbols change from sub field to sub field and in a certain sense encrypt the knowledge from one who has not read all preceding papers.
It makes me wonder if one could perform some sort of cryptanalysis on these documents as a method of understanding.
I did Math in undergrad. I hung out with grads and profs a lot, and of course the bright undergrads who would become the grads and profs who apprehended mathematical concepts far quicker than I ever could. It became clear to me partway through my freshman year that mathematics is an extremely social activity. The books are gappy, the exercises are more open ended than you'd think for something that has a single answer, the lectures are best when they are conversations, and the best place to learn something is at the chalkboard with a cup of tea in hand as someone scratches out a diagram composed of all intuition and no logic that makes you go "aha!"
I think all barriers of language are social barriers.
>It became clear to me partway through my freshman year that mathematics is an extremely social activity.
I think many fields are like this, and the "dream" of ending selective residential colleges (which are designed to facilitate this kind of social study) in favor of MOOCs may not be so idyllic.
Definitely, definitely. The idea that individuals achieve through individual means individual rewards does not explain any of my experiences with any of my activities-- especially the ones I get paid for.
I want something similar for programming language operators. There are so many operators that do distinct things in different languages. For example: ":", ":=", "=", "::", "->", "{}", "()", "[]" etc. may be slightly or entirely different between two languages.
Because there's a lower barrier to entry to creating a new syntax than there is to creating a new branch of mathematics, the programming syntax page would be immensely larger than the Wiki page for mathematical symbols, possibly even warranting a dedicated website.
I cannot say anything about the concrete assertions the author makes. He's using artful language to say a scientific thing; a scientific thing that cannot be verified. What I can say is that I see a theme: A theme of unity opposed to distinction. In a world where experts are specialized, people are atomized into rational actors, inquiry cut up into disciplines and schools, classes stratified into hierarchy, the Earth parceled out into privacies, and the most lauded brains in the world the most bifurcated, Da Vinci's life and mind must be unintelligible.
His brain was mixed up; his life was mixed up. Where Da Vinci ended and the world began was no where to be found. His interests saw no division, his talents no distinction. He degraded himself, rolled in the dirt, put his roots there and grew taller than the ivory tower. He without lineage outgrew any line; he came from the tenebrous muck of the world and left for the heavens.
Maybe you're exaggerating a bit on specialization? Unless humans reach immortality (or you live alone in a world), there's no other solution for progress. Most modern specialists out there actually know superficially a broad number of fields (and any of them likely much better than Da Vinci ever knew), but must specialize in one to optimize progress. There's only so much time to reach the frontier of progress, and you need to be at least reasonably quick to get there, lest your work be made obsolete by others before it's even published.
I don't think any expert should be unhappy for "missing out on knowledge" of many fields, because knowledge is infinite -- he should instead be happy to know the essential knowledge of some fields and be able to expand the frontier of human knowledge, which I believe is more satisfying than just soaking up results of all is out there (and probably can pay your lunch).
In popular words, "Jack of all trades, master of none" (unless you're in the middle ages).
The segregation of knowledgeable people into sets of experts based on domains of expertise is more the problem than individuals specializing. People will doggedly pursue answers to their questions without such rigid social structures, but it prevents the interaction between people that would otherwise fruitfully cooperate together. These structures, I believe, mostly serve political and bureaucratic functions rather than the facilitation of human inquiry. We like to pretend our institutions are optimized for their ends, but usually they're optimized for the allocation of resources and power. Cutting people up into experts, giving them titles, making them clique together, impairs them but it makes them 'easier to manage'.
Ah now I can see a more valid point. The problem is not so much that people specialize in certain problems/'issues'/fields/tools/..., it's more that the fields are arbitrarily drawn and rigid. That I can agree with.
"People will doggedly pursue answers to their questions without such rigid social structures" -- that is a good observation imo, and I think science progresses best when it is oriented around problems. The specialization then comes as devoting large amounts of time to a deep understanding of the problem and the different tools necessary to get it solved. But perhaps it's only natural (or human nature) to split tools into categories to study them separately and effectively, and be able to draw upon people who know those tools very well.
Who else thinks the "Mona Lisa" painting is crap? It's always been overrated, and seeing it live did nothing to change my impression. Not to disparage da Vinci's corpus ... but just sayin'.
Look at the comparison of detail on the dresses. Look at the hands, and the slightly darker color where the light doesn't reach as strongly on the tips of her right hand. Look at the small details on her face like the lines around her cheek bones -- Leonardo was making striking advancements about how to make portraiture more realistic.
We can copy his techniques fairly easily, but creating the techniques is hard.
Understanding the context of art is frequently as important as direct experience. Jackson Pollack has been decried as an alcoholic fraud by some, but like Da Vinci, it is the techniques he pioneered as much as his works that are fascinating. There was a study that claimed he (Pollock) represented fractals, even Chaos theory in some of this work. http://phys.unsw.edu.au/phys_about/PHYSICS!/FRACTAL_EXPRESSI...
> Jackson Pollack has been decried as an alcoholic fraud by some, but like Da Vinci, it is the techniques he pioneered as much as his works that are fascinating
Throwing paint at the wall like a baby projectile-vomitting rainbow-colored Gerber puree'd carrots?
Leonardo da Vinci was not a pacifist (second paragraph). As linked here on Hacker News, he designed weapons of war and bragged how great they would work, He was essentially an "arms dealer."
In his words:
"...I have methods for destroying every rock or other fortress, even if it were founded on a rock, etc.
Again, I have kinds of mortars; most convenient and easy to carry; and with these I can fling small stones almost resembling a storm; and with the smoke of these cause great terror to the enemy, to his great detriment and confusion. ..."
He was opposed to war but made war machines to pay the bills. Besides there's a certain logic to avoiding war by being more heavily armed than your neighbours.
By the time the bomb was tested, Nazi Germany had already surrendered (VE Day, May 8. Trinity test, July 16). And Stalin had already agreed to get involved in Asia.
If he wanted to go all the way to the Atlantic, why did he stop at Elbe and spend time negotiating at Potsdam.
I thought this left/right brain stuff was considered pseudoscience at best. Granted, there is more to this article, but I find it somewhat hard to take seriously.
27 comments
[ 3.6 ms ] story [ 78.4 ms ] threadMathematics is built around a similar sort of cipher. Even learning from textbooks is not enough to truly penetrate the collective knowledge stored in the symbols of math. The symbols change from sub field to sub field and in a certain sense encrypt the knowledge from one who has not read all preceding papers.
It makes me wonder if one could perform some sort of cryptanalysis on these documents as a method of understanding.
I think all barriers of language are social barriers.
I think many fields are like this, and the "dream" of ending selective residential colleges (which are designed to facilitate this kind of social study) in favor of MOOCs may not be so idyllic.
And this one can help you search that page if you can't copy-paste a symbol (like if you are reading from a physical text):
http://detexify.kirelabs.org/classify.html
I want something similar for programming language operators. There are so many operators that do distinct things in different languages. For example: ":", ":=", "=", "::", "->", "{}", "()", "[]" etc. may be slightly or entirely different between two languages.
Because there's a lower barrier to entry to creating a new syntax than there is to creating a new branch of mathematics, the programming syntax page would be immensely larger than the Wiki page for mathematical symbols, possibly even warranting a dedicated website.
His brain was mixed up; his life was mixed up. Where Da Vinci ended and the world began was no where to be found. His interests saw no division, his talents no distinction. He degraded himself, rolled in the dirt, put his roots there and grew taller than the ivory tower. He without lineage outgrew any line; he came from the tenebrous muck of the world and left for the heavens.
I don't think any expert should be unhappy for "missing out on knowledge" of many fields, because knowledge is infinite -- he should instead be happy to know the essential knowledge of some fields and be able to expand the frontier of human knowledge, which I believe is more satisfying than just soaking up results of all is out there (and probably can pay your lunch).
In popular words, "Jack of all trades, master of none" (unless you're in the middle ages).
"People will doggedly pursue answers to their questions without such rigid social structures" -- that is a good observation imo, and I think science progresses best when it is oriented around problems. The specialization then comes as devoting large amounts of time to a deep understanding of the problem and the different tools necessary to get it solved. But perhaps it's only natural (or human nature) to split tools into categories to study them separately and effectively, and be able to draw upon people who know those tools very well.
For reference: https://en.wikipedia.org/wiki/Mona_Lisa#/media/File:Mona_Lis...
It was painted around 1503. Compare to something around the same time -- Lorenzo Di Credi -- http://lj.rossia.org/users/marinni/418072.html
Look at the comparison of detail on the dresses. Look at the hands, and the slightly darker color where the light doesn't reach as strongly on the tips of her right hand. Look at the small details on her face like the lines around her cheek bones -- Leonardo was making striking advancements about how to make portraiture more realistic.
We can copy his techniques fairly easily, but creating the techniques is hard.
On a tangent, this is the soundtrack to the eponymous movie, Pollock by composer Jeff Beal. Give it a listen, while taking a look at some of Pollock's catalog: https://www.youtube.com/watch?v=oD0nFjjUCQo&list=RDoD0nFjjUC...
Like nwatson, I wasn't moved the first time I saw Mona. But understanding her history brought her to life the next time we met.
Throwing paint at the wall like a baby projectile-vomitting rainbow-colored Gerber puree'd carrots?
In his words:
"...I have methods for destroying every rock or other fortress, even if it were founded on a rock, etc. Again, I have kinds of mortars; most convenient and easy to carry; and with these I can fling small stones almost resembling a storm; and with the smoke of these cause great terror to the enemy, to his great detriment and confusion. ..."
http://www.theladders.com/career-newsletters/leonardo-da-vin...
If he wanted to go all the way to the Atlantic, why did he stop at Elbe and spend time negotiating at Potsdam.
http://www.smh.com.au/articles/2002/12/11/1039379883809.html