About thinking geometrically
December 19th 2006 02:50
* I'm having probs tracking down a reference, but I think it was Feynman. I think it was Feynman who, when listening to an argument, envisaged a ball with knobs on it. In some strange way -- I'm sketchy on the details -- the knobs represented points, and would allow him to spot contradictions, which would correspond to spatial violations like trying to double knob the same spot.
* Students are taught to structure their essays with a "thesis statement" at the beginning, then a "topic sentence" to start each paragraph. And in studying for exams, they're taught to "mindmap" and to "cluster" -- to draw and memorize webs of ideas.
* I find myself using visual metaphors to picture particular concepts ("time is like a river"), and to picture argument structures and moves ("trying to join, but can't make the two ends connect"; "looking over the wall into a truth"). Depending on context, I might imagine a pyramid, or overlapping coloured sheets, or graphs of all kinds, or Venn diagrams, or tree diagrams, or flowcharts...
There are reasons that any sentence follows any other. There is a logic. There are implied connectives. And where the connection is mysterious, there is still implied to be one.
Even if the speaker is mad, there's a psychological cause and effect.
This sentence defines the scope of a term in that, this pre-empts a problem caused by that, this puts that into a more memorable form, this sheds light on that's relation with another matter, this parallels that and both relate to a past or future sentence...
In a well-crafted paragraph, there is a necessity -- each succeeding sentence filling some need created by one of the previous.
Operators like "and", "if... then", "or" might be insufficiently finely grained to differentiate the types of relation. And words like "therefore", "because", "except" scratch the tip of the iceberg.
When one focuses on language as content, ignoring all the other functions it serves, the logic of connection seems mainly a matter of practicality. There is some need -- like defining scope, like pre-empting problems -- that causes the caveman to utter two syllables in place of one.
Failure to understand a speech might often be failure to see the connectives, the usage implications.
The dream of neatly plotting every proposition -- sketching the argument geometrically. And if I disagree with you, I can see exactly where you went left and I went right: "I think this particular proposition is true, and you think it's false."
Perhaps the turning point, the fork, is a matter of methodology. You take this attitude to evidence, and I take that.
Disagreements could then be shown as a mistake on the part of one party or the other (perhaps from bias or emotion). Or they could be traced to a point where there's genuinely no reason to go left or right, where one has existential freedom.
Bu the idea will remain a fantasy.
On the one hand, there's Quinean concerns. It seems false that you can reduce arguments to "basic propositions". And, similarly, whenever one does choose left or right, it's always for a variety of reasons. Beliefs travel in groups, not singly. When you take on someone's argument, it might be a question of misinformation about a fact -- that's the easy case. But what if you find yourself conflicting with a whole world view, a whole system of mutually supporting ideas?
On the other hand, there's practical concerns. Geometrical thinking is useful in small doses. But is it even possible, other than diffusely, to arrange the whole of an argument on a ball or a tree, or to see how all of it connects with all of what you believe? The art of listening, in most people, seems to take place irrespective of conscious imagery -- you simply listen, then respond based on what you've absorbed.
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article Mind map.
* I find myself using visual metaphors to picture particular concepts ("time is like a river"), and to picture argument structures and moves ("trying to join, but can't make the two ends connect"; "looking over the wall into a truth"). Depending on context, I might imagine a pyramid, or overlapping coloured sheets, or graphs of all kinds, or Venn diagrams, or tree diagrams, or flowcharts...
***
There are reasons that any sentence follows any other. There is a logic. There are implied connectives. And where the connection is mysterious, there is still implied to be one.
Even if the speaker is mad, there's a psychological cause and effect.
This sentence defines the scope of a term in that, this pre-empts a problem caused by that, this puts that into a more memorable form, this sheds light on that's relation with another matter, this parallels that and both relate to a past or future sentence...
In a well-crafted paragraph, there is a necessity -- each succeeding sentence filling some need created by one of the previous.
Operators like "and", "if... then", "or" might be insufficiently finely grained to differentiate the types of relation. And words like "therefore", "because", "except" scratch the tip of the iceberg.
When one focuses on language as content, ignoring all the other functions it serves, the logic of connection seems mainly a matter of practicality. There is some need -- like defining scope, like pre-empting problems -- that causes the caveman to utter two syllables in place of one.
Failure to understand a speech might often be failure to see the connectives, the usage implications.
***
The dream of neatly plotting every proposition -- sketching the argument geometrically. And if I disagree with you, I can see exactly where you went left and I went right: "I think this particular proposition is true, and you think it's false."
Perhaps the turning point, the fork, is a matter of methodology. You take this attitude to evidence, and I take that.
Disagreements could then be shown as a mistake on the part of one party or the other (perhaps from bias or emotion). Or they could be traced to a point where there's genuinely no reason to go left or right, where one has existential freedom.
***
Bu the idea will remain a fantasy.
On the one hand, there's Quinean concerns. It seems false that you can reduce arguments to "basic propositions". And, similarly, whenever one does choose left or right, it's always for a variety of reasons. Beliefs travel in groups, not singly. When you take on someone's argument, it might be a question of misinformation about a fact -- that's the easy case. But what if you find yourself conflicting with a whole world view, a whole system of mutually supporting ideas?
On the other hand, there's practical concerns. Geometrical thinking is useful in small doses. But is it even possible, other than diffusely, to arrange the whole of an argument on a ball or a tree, or to see how all of it connects with all of what you believe? The art of listening, in most people, seems to take place irrespective of conscious imagery -- you simply listen, then respond based on what you've absorbed.
***
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article Mind map.
| 81 |
| Vote |
Add To: 
Subscribe to this blog
Comment by Norm
Consumption Malfunction
Equal and Opposite
Arses and Elbows
Footy Power
Failure to understand a speech might often be failure to see the connectives, the usage implications.
So very true(if I'm connecting correctly).
So much is good about this piece.
Carry on old chap,
Norman
Comment by Damo
For the Sake of Argument
My Apologetics
Listening is sometimes the hardest thing to do when you hearing something that you don't want to hear.
There is also the problem of noise both external in internal noise that constantly tries to distract you.
I think that language is poetic more than mechanical. It can produce beautiful words but has trouble explaining what we actually think. Yet I do find it is sometimes easier to deconstruct and argument based upon baddly chosen words than it is to build a positive arguament.
I do like the image you used. Have tou ever used it?
Comment by Adrian
Philosophy Blog
Norm -- hope you don't mind my saying this, but I reckon that connection is something that you're a master of. Violation of connection rules or surprising connections or strange, surreal connections seem to be one of your trademarks.
Damo --
The problem of noise is Plutarch in a nutshell, I reckon. And have never used mind-mapping myself
The connection between language and thought is something that in itself I find very difficult to talk about. So I can't really comment on to what extent words explain thought, though I'm dubious that they do... I'm dubious about the idea of a "language of thought", and I'm more inclined to think of words as tools than as pictures (so that there's no real question of correspondence with thinking).
Comment by Norm
Consumption Malfunction
Equal and Opposite
Arses and Elbows
Footy Power
Adrian, thanks for looking kindly on my unlawful activities.
I also lean towards seeing words as tools.
Sipping coffee,
Norm.
Comment by Damo
For the Sake of Argument
My Apologetics
I are to agree words are tools.
Some are sharp, others blunt, others colourful and others confussing
Comment by evan
My friend understands the world as music.
Various items usually for a whole that is greater than the sum of its parts. They come to us all-at-once, not one at a time to suit those of an analytical persuasion.
Many thanks for your post.
Evan
Comment by Adrian
Philosophy Blog
I don't have much to say to it, but I think that the thought "They come to us all-at-once, not one at a time to suit those of an analytical persuasion." is provocative.
It could furnish the basis of insights into the nature of subjective experience, and into how the brain works...