Le 20-juil.-06, à 18:07, John M a écrit :
I appreciate your efforts to 'enlighten' me (and maybe others as well). my case there is more ignorance interfering with the explanations and I will re-re-read your post before I come to a conclusion.
As I tried to tell, when you "matter-of-factly" handle concepts of your 'daily bread' I have to search after for some meaning I can assign as a key to 'read on'.
Even the cardinal points in your theory are not functional parts of my mi nd-content (UD, YesDr, even 'comp') but I get lost with G and G', even I have to translate for my own vocabulary the 1- and 3- features or expressions from 'logics'. All these are raining down in your sentences and I cannot ask you not to use them: I use MY 'words' just the same and others ask back many times using for themselves in other meanings.
The field of logic is not so well known, as compared to algebra and calculus. Not your fault.
There are very few math\ematically gifted minds among us and it does not help what a post yesterday stated that "everybody can learn math (thinking) if diligent". You as math teacher may know pupils who "just CANNOT get it.
I guess such pupil exists, but I cannot decide, and I don't think the pupil can decide, except for his taste.
The fraction of humanity cursed with mathematical imparement (ha ha) looks down to the rest of us, a natural defence of the minority.
Many greeks seemed to have fallen in love with numbers when their discovered that the sum of the first even numbers give always perfect square:
1 = 1
1 + 3 = 4
1+ 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
A simple drawing can explain why it is necessarily so, thus that is a law of numbers. Is that not cute? But math is just not in fashion today for contingent reasons. Like music, it helps developing the taste and educating it as early as possible.
A special case the 'applied math' you mentioned.
Mostly physicists (and other scientists as well) - thinking in limited models - learned math and aooky itg equationally to a
quantized system of their model-view. It elevates the model content to 'total'
I hear that feeling. Incompleteness provides a sort of vaccine against that "total" apprehension!
and the imperfections from neglectimg the 'rest of the world - beyond the model's boundaries' lead to paradoxes and orher misconceptions over millennia.
Yes. And I would say, perhaps naively, that now that we know that numbers are antireductionist, we should not fear to come back to some Pythagorean Greek rational theologies. Ah! Perhaps we should wait more people get that point, but then I should advertise more for math ....
I have some understanding in the math0thinking, my problem is that I did not 'learn' and 'continue' enough math after that rudimentary conventional domain necessary for the Ph,D exam as 'elective'.
You don't need to say. I have myself been disgusted of logic during ten years, and it is only a very special set of circumstances that throws me back in partially.
I am a platonist: if you don't find time for math in this life, prepare yourself to do math in the next one (and take this with a graint of salt ;)
In my practical polymer R&D including numerous implementations and consulting I did not need 'math' and so it faded over all those decades. I never lear\ned theo. logics.
I think I am not the worst candidate for what I proposed, yet it may be more than the burden you might take on.
Sorry if I wasted your time and consideration.
You didn't, best
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