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Jan
Mountain climber
Colorado, Nepal & Okinawa
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I'm copying this over from the other thread.
Jan:
In my experience, understanding means being able to explain something in my own words in a way that any undergraduate, including those from poor educational backgrounds could understand. It means being able to come up with examples relevant to the unique backgrounds of those individuals and to answer questions they have, no matter how naive.
In fact, those naive off the wall questions are often the very ones that have forced me to reconsider why I have thought the way I have other than I read it or heard it from another authority. Some of the most existential questions for me have often come in the simplest, least sophisticated form.
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MikeL:
Jan: . . . in a way that any undergraduate, including those from poor educational backgrounds could understand.
Some of my colleagues would suggest you have low standards.
. . . those naive off the wall questions are often the very ones that have forced me to reconsider why I have thought the way I have other than I read it or heard it from another authority.
Can I get an "Amen, sister" from the congregation?
Students have the damnest way of asking the most embarrassingly difficult questions to answer. It "schools" a teacher.
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My reply:
How you interpret teaching, like everything else reflects context. My job description was to work with highly motivated and disciplined but educationally naive and often ill prepared students. Personally I am glad that I didn't work with more sophisticated but less motivated ones.
This is probably a new thread but one could certainly question the rationale that we only teach to a certain level and tough luck to those who don't reach that level. Maintaining standards or preserving elitism?
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Jan
Mountain climber
Colorado, Nepal & Okinawa
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And jstan, that certainly defines the differences in outlook here - whether one is primarily concerned with how or why.
In the pre agricultural and pre industrial world of most of our evolution, peace chiefs were more highly valued than warriors, so perhaps why was more important than how to our survival?
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jgill
Boulder climber
Colorado
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In the pre agricultural and pre industrial world of most of our evolution, peace chiefs were more highly valued than warriors, so perhaps why was more important than how to our survival? (Jan)
I wouldn't have guessed that, Jan. Thanks. Good comments regarding understanding.
Excellent posts, John S and Ed.
Humanists, what say you?
Sam Harris on the subject?
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Marlow
Sport climber
OSLO
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I'm often able to understand why people do not understand.
And Largo understands nothing...
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PSP also PP
Trad climber
Berkeley
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Understanding in our day to day lives is based on your point of view, ie one persons terrorist is anothers freedom fighter,. So there are infinite understandings all justified by there various points of view. So I think understanding has to have a qualifier in front of it such as limited understanding , conditioned understanding , non bias understanding (is that possible?) .
And then we get back to my favorite: what is this "I" that understands? LOL
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jgill
Boulder climber
Colorado
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I remain curious about what "understanding" means to John S. Listening to Richar F.'s lucid breakdowns per QM provides me usful data about a question I never asked. My question had to do with someone's internal process. If someone would rather not share that process, John S. needs merely to say so. End of story. But deflecting the load onto me, with Tvash and John G. piling on, seems queer - and at any rate, leaves the original qustion unanswered. (JL)
You should describe what you think might be the internal process supporting "understanding." Do you understand no-thingness? How does understanding relate to the illusory "I"? Is it really necessary for the "I" to be present (aware) to "understand"? When my mind is fully engaged in attempting to "understand" I may not be aware of "I" - it might be a hindrance.
This seems a long way from politics & religion vs science.
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BLUEBLOCR
Social climber
joshua tree
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I'm often able to understand why people do not understand.
So if you inject How instead of Why, you'll have two different answers!
Making both questions relevant.
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MikeL
Social climber
Seattle, WA
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I've been lurking on this topic of understanding, and I've been wondering if anyone would go beyond conceptuality, ratiocination, reason, logic, and mathematics in regarding understanding.
There would seem to be much more that would come under "understanding." When I am hungry, I know I am hungry, but there is no logic or reasoning necessary. There is no need for a model or a concept. When I walk into a room and instantly perceive a conflict among the people in the room, there is no need for logic or reason. I just feel it. When a random thought emerges in my mind, I don't look for the reason or the logic behind it. They just show up. If there is no logic to a thought's randomness, then what would I understand conceptually about it? When I feel sadness or jealousy, I don't run around looking for concepts or logic that help me make sense of it. For the most part, when I feel an emotion, I just feel it; an emotion can consume me and run wild as if it had a life all their own. When I breath, I just breath. I don't think about it. The understanding is in the doing of it. My body is understanding itself. Perceptions are understanding. I'd be liable to say that EVERYTHING is understanding. My very consciousness constitutes an ultimate understanding.
I thought Largo's question was not weird or nefarious at all as some of you did.
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jgill
Boulder climber
Colorado
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There would seem to be much more that would come under "understanding." When I am hungry, I know I am hungry, but there is no logic or reasoning necessary (MikeL)
Is there a distinction between knowing and understanding? It's possible to become suddenly angry at something (and know we are angry), but not understand the anger. Here we skirt the issue of free will, but on a simpler level we might have been irritated at something else - and put it out of our conscious mind - and encountering this new thing triggers the anger, irrationally directed.
I may know a person, but not understand him. I may in general know what Feynman talks about, but have little understanding of the underlying complexities, and therefore my "knowing" is limited. JL "knows" a little about Hilbert spaces being used in physics, but probably understands very little. When you know you are hungry, do you really understand the complexities of your hunger?
There are degrees of "knowing" and degrees of "understanding."
On another note: The Masters College, where apparently science serves creationist philosophy:
The Mathematics Department provides a strong and thorough offering in Mathematics as a part of God's creation in a concentrated effort to integrate faith and learning
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yanqui
climber
Balcarce, Argentina
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Even in the fairly rigid frame of mathematics "understand" seems to be a very open ended concept. I think it is an error to equate the concept with "has been proven" and I think it is clear from the everyday usage by practising mathematicians that they do not (in general) make that equivalence. I could post numerous references, just in my area of expertise, where new proofs of established results have appeared in top journals, the justification being that the new proofs could lead to better insights (better understanding) into why the results are true. This is the case even when the new proofs do not immediately lead to new consequences. When I was a student, I recall my advisor complaining that Rudin's proofs were sometimes "too slick for their own good" meaning that although these proofs were short, clever and vaild, they failed to give insight into why the result was true.
There is also the point that mathematicians can understand a result (in the sense of being able to apply it to other cases, or use it to establish new results) with out even knowing (or, at least, being aware of) the proof. This ability to see how known results connect (sometimes in surprising ways) to other parts of mathematics (or even to "real world" applications) is also an important kind of understanding. In some cases, understanding a proof may help us make the unknown connection, but in other cases mathematicians may come to see how this connection works without even thinking about (or understanding) the proof of the original result.
It seems that "understanding" in math has something to do with both seeing why something is true and/or seeing how it connects to other things. There are psychological (even personal or subjective) aspects as to what helps us see or undertand something and I think most working mathematicians can be open to different points of view (in my field we use geometric, algebraic and analytic methods) about what might be the best way to "understand" something.
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Jan
Mountain climber
Colorado, Nepal & Okinawa
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It seems that "understanding" in math has something to do with both seeing why something is true and/or seeing how it connects to other things.
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I immediately thought of the very complex kinship diagrams that we have in Anthropology which are often compared to mathematical equations. At first we simply recorded all the varieties of kinship around the world. Then we began placing them in categories named after the first place they were discovered (Hawaiian, Sudanese, Eskimo, Iroquois, Omaha and Crow systems for example).Then we began to try to understand why they had developed in terms of the environment and historical forces. Omaha and Crow turned out to be transitional forms developed in response to leaving the woodlands and migrating out onto the prairie as a result of eastern Indian tribes being pushed into their territory by the Europeans settling the East and Midwest.
We next tested to see if that hypothesis applied to other groups practicing the same forms. It was quite a surprise to discover that the Sherpas of Nepal practiced Omaha form kinship when first studied 50 years ago. It is even more interesting to see that they practice the Eskimo form only 50 years later. I surmise that they practiced Iroquois 100 years ago. Not being driven from their homeland what could be the cause? I surmise population growth and extreme taxation by the central government caused land and agriculture to be less important and long distance trade to be more important. Going to Tibet and India with trade goods and later mountaineering, was their equivalent of moving out onto the prairie. And now that they own hotels, tea houses and climbing shops, participating in the global cash economy, they share the same form as modern Americans - the Eskimo. This form is thought to have evolved where harsh conditions favor the nuclear family over the extended one ?!
In the meantime at least a dozen articles have been published detailing extremely convoluted explanations of variations of the Omaha system and one is left to ponder if these are anything more than intellectual projections or something important this researcher has overlooked. Likewise, the variations from village to village over a 500 mile swathe of Nepal. Random chance, the influence of different altitudes and ethnic groups, clever linguistic turns of phrases, or something not yet discovered?
Corelating kinship forms with DNA is the next frontier and while I loved walking 500 miles across the Himalaya to interview in village after village, 35years ago, at my current age, I am happy we can take all the samples we need in Kathmandu.
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BLUEBLOCR
Social climber
joshua tree
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^^^That all YOUR understanding!
The truth is, it DOESN"T make it everyone's truth!
Whatever the karma of this accident is, I feel much more optimistic after hearing this news.
^^^Same here!
It's the devils law that one should get what one deserves.
Thank God today we have The Truth in Jesus Christ!
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MikeL
Social climber
Seattle, WA
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Jgill asks about distinctions between knowledge and understanding.
Knowledge would appear to be a clear indication of conceptualization, as it can be codified and communicated in a variety of ways. Some folks have said that conception and perception form one whole--but that knowing is merely believing.
While not necessarily conceptual, understanding appears to be phenomenal and personal, and the result of a process which uses mind objectively.
What of the "nonobjective?" What of the noumenal? Noumenal is neither real nor unreal, and cannot be conceived as a "thing" or as possessing any attribute which is necessarily objective. The noumenal seems to be unbounded and unconditioned. For example, look at yourself. You have conceptual existence, but non-objectively, you are the apparent universe.
The point of talking about emptiness, unreality, non-existence, what is inter-temporal rather than caught in time and space, subjectivity, non-volition, voidness, the results of imagination--is to see everything as an appearance, as a psychic experience, as that which is being lived, as becoming, as verbs rather than nouns, as interdependent, as a mirror which reflects what is looking,to quit seeing yourself as an object, etc.
We are functioning, where noumenality and phenomenality are identical. Perceiving is everything.
"'Seeing, seeing, seeing!' cried Rumi. He was not referring to phenomenality-based observation of objects by subjects, but to noumenally-based in-seeing that is devoid of both."
(Wei Wu Wei)
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jgill
Boulder climber
Colorado
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I am impressed with how sophisticated this discussion has become.
When I was a student, I recall my advisor complaining that Rudin's proofs were sometimes "too slick for their own good" meaning that although these proofs were short, clever and vaild, they failed to give insight into why the result was true (Yanqui)
Thanks for chiming in, Tim. Good to hear from a practicing mathematician. The stuff I did years ago (and which I still putter with) is largely "constructivist" math in the simplistic sense that I tried to avoid indirect proofs, although the entities I "verified" were sometimes a bit vague - like fixed points in certain arguments - and at best approachable by approximations. But "constructivism" in math has many and varied definitions. Occasionally an indirect proof provided a much quicker solution than a longer, more tedious constructive approach - which may have been too complicated to provide any more insight than the quicky.
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Thanks for your insight, Mike.
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Ed Hartouni
Trad climber
Livermore, CA
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I suspect that yanqui and jgill express a dimension to "understanding" that is not usually identified with either mathematics or with science generally, to those who don't practice those disciplines.
My rather short offering about physics is also more nuanced, and the constraint that physicists have is that the logic has to conform with observations of nature. "Understanding" isn't a rote "turning the crank" on an equation. The brutal pedagogy of physics instruction insures that mere memorization of the equations will fail, and only understanding the physical basis of the calculations will succeed.
Looking at an equation, one eventually has practiced this so extensively that the physical implications are extracted. This can take time, Dirac "understood" the Dirac equation many different ways, and other physicists looked at it and found even more divergent "understanding."
However, in the end, the test is to calculate the outcome based on that understanding. And when one cannot do that, it is attributed to not "understanding."
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Jan
Mountain climber
Colorado, Nepal & Okinawa
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Blue-
Clever way to work your theology into this discussion by quoting me from the Cosgrove thread. However, your ideas belong on the religion thread, not here. Not to mention, Christianity is not the only religion to recognize the role of grace. Try reading about Buddhist Boddisattvas.
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jgill
Boulder climber
Colorado
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However, your ideas belong on the religion thread, not here (Jan)
Amen
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BLUEBLOCR
Social climber
joshua tree
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Sorry Jan,
But my synapse wasn't referring to religion VS science. Moreso mind VS mind. Afterall religion is a construct of the mind, Right? So they say..
Subject matter; understanding; knowledge.
Similarly, we understand the number 0.33333... by thinking of it as one-third.
For me, this is where mathematics gets stupid. Understandingly, if you offer me a third of your pizza it's fairly cut-n-serve. The pizza being "one thing" is easily separated into equal amounts. 1/3 of a pie, plus 2/3 of a pie equals one whole pie. Doesn't this surmount to a Truth?
So does 0.33333....etc + 0.666....etc EVER = 1? Truthfully?
If a mathematician separated the pizza, i'd prolly starve to death waiting.
If understanding is ongoing, it wouln't be fair to consider any of it True until we acknowledge it as knowledge? But then is any ONE'S knowledge, everyone's Truth?
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jgill
Boulder climber
Colorado
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For me, this is where mathematics gets stupid
Jake is not amused.
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