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Post by Eugene 2.0 on Oct 4, 2023 15:52:31 GMT
While thinking we're bearing a thought in the mind. Whether or not it's separated or plugged somehow into our brains, or maybe it's planted there, or the structure of the thought looks like a wire mesh, it is not what I am asking, but what I want to ask is – can a thought be partial there, in the mind?
Or shortly, can we think partially? Can we bear a half of a thought in our mind? My intuition says me it's impossible. On the other hand, why not to try to imagine this, especially having some close to it examples?
"What does that?" "Someone did something" "He went there"
These and similar phrases are almost empty without any contexts.
Okay, at least we can understand what "Who is the one?" or "That does it" mean in some situations. What about these cases:
"That". "He". "Went?"
We can try to comprehend these ones, but I doubt it helps much.
Besides, we get our thoughts in a head to go fluently. I mean for a thought it must be completed. Any incomplete thoughts don't look as we understand them by ourselves.
I guess this last point is a key one: no halfed thoughts can be understood by ourselves. Since that is true, incomplete thoughts are not thoughts. Doesn't it mean each though that appears within heads of ours does it simulateously as a whole?
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Post by Eugene 2.0 on Oct 19, 2023 22:56:07 GMT
Seems like it was said by Socrates himself. Surely, different languages, one destination – all and more risk to repeat the path of the Babel Tower builders. Also I wonder what attracted Avicenna, Descartes, and some other mathematicians to prefer algebra to other forms? Descartes did analytic geometry, trying to find ways how to convert geometrical shapes, figures, and forms into algebraic sequences. Why that alphabet path was preferable? Sense? Thoughts correlation or something? I know here I cannot be sure, it's nothing, but an intuition of mine. This, however, is what I think is hiding between the lines – the glue that ties the lines up together as the ether.
Real geometry is perfection at its simplest. So those that cannot appreciate it as a foundation, will lack essential logic in all their thinking.
In real terms, geometry is just the easiest way to visibly demonstrate set theory.
Agree that geometry works as perhaps one of the best ways to demonstrate the Set Theory (the Vehn's diagrams demonstrate it). But, it is for us only. I mean geometry illustrates it for us, for those who have the eyes. Hellen Keller (as it is in "The Miracle Worker" play) was deaf, and blind, so she had to visualise things in her way. I understand algebraic way of imagination as something that even some computer are able to read it (however without visualising it). A computer understands 1's and 0's, a blind person is able to understand the Braille Language. But the blind person is unable to be certain about his visualisations, or at least I wouldn't claim this. ("Johnny Got His Gun" 1971 confirms it.) Geometry looks like to be more preferable, than algebra. I would agree with it especially accepting grades, shades, or anything analogue (non-discreet) as what is able to demonstrate the power of Geometry on its applications to the reality. Briefly, we measure things with things, and what we do in such cases is Geometry. We can just to measure things, so all what we need is Geometry in such cases. Contrary to that algebra allows us to use some symbols, and with it to do more operations at the same time, than it is about Geometry. (Not in any case, but I believe this is how it things are.) Calculating is easier, than drawing or imagining numbers, things, and therefore to get the result. The last one attitude (thought) makes me think that a thought lies nearer to algebra, than to geometry is that, it is made with symbols, not with images. So it might be that the art is closer to geometry, while science is closer to algebra. An abstraction can package different squares, triangles, rounds, or pyramids into one or few formulas (and what is also must be true is that none formulas without visualisation of it (i.e. unpackaging it) is unempty). I am not against Geometry (in school I loved Geometry much more, than Algebra), but I still prefer to think of thoughts as about something that is closer to algebra. Thus, thinking we operate symbols more, than images.
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Post by jonbain on Oct 22, 2023 7:47:13 GMT
Real geometry is perfection at its simplest. So those that cannot appreciate it as a foundation, will lack essential logic in all their thinking.
In real terms, geometry is just the easiest way to visibly demonstrate set theory.
Agree that geometry works as perhaps one of the best ways to demonstrate the Set Theory (the Vehn's diagrams demonstrate it). But, it is for us only. I mean geometry illustrates it for us, for those who have the eyes. Hellen Keller (as it is in "The Miracle Worker" play) was deaf, and blind, so she had to visualise things in her way. I understand algebraic way of imagination as something that even some computer are able to read it (however without visualising it). A computer understands 1's and 0's, a blind person is able to understand the Braille Language. But the blind person is unable to be certain about his visualisations, or at least I wouldn't claim this. ("Johnny Got His Gun" 1971 confirms it.) Geometry looks like to be more preferable, than algebra. I would agree with it especially accepting grades, shades, or anything analogue (non-discreet) as what is able to demonstrate the power of Geometry on its applications to the reality. Briefly, we measure things with things, and what we do in such cases is Geometry. We can just to measure things, so all what we need is Geometry in such cases. Contrary to that algebra allows us to use some symbols, and with it to do more operations at the same time, than it is about Geometry. (Not in any case, but I believe this is how it things are.) Calculating is easier, than drawing or imagining numbers, things, and therefore to get the result. The last one attitude (thought) makes me think that a thought lies nearer to algebra, than to geometry is that, it is made with symbols, not with images. So it might be that the art is closer to geometry, while science is closer to algebra. An abstraction can package different squares, triangles, rounds, or pyramids into one or few formulas (and what is also must be true is that none formulas without visualisation of it (i.e. unpackaging it) is unempty). I am not against Geometry (in school I loved Geometry much more, than Algebra), but I still prefer to think of thoughts as about something that is closer to algebra. Thus, thinking we operate symbols more, than images. That's an extremely well thought-out and written post.
The line between algebra and geometry being a tricky one to define.
But it seems that the first step from geometry to algebra is when we introduce time. Of course algebra then goes beyond this, but geometry is all about space alone.
That makes geometry the foundation.
But how we define time, is the next phase, and of course the Einsteinians have turned algebra into a laughable farce on a good day.
Proof for THAT, is here:
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Post by Eugene 2.0 on Nov 2, 2023 14:43:54 GMT
Agree that geometry works as perhaps one of the best ways to demonstrate the Set Theory (the Vehn's diagrams demonstrate it). But, it is for us only. I mean geometry illustrates it for us, for those who have the eyes. Hellen Keller (as it is in "The Miracle Worker" play) was deaf, and blind, so she had to visualise things in her way. I understand algebraic way of imagination as something that even some computer are able to read it (however without visualising it). A computer understands 1's and 0's, a blind person is able to understand the Braille Language. But the blind person is unable to be certain about his visualisations, or at least I wouldn't claim this. ("Johnny Got His Gun" 1971 confirms it.) Geometry looks like to be more preferable, than algebra. I would agree with it especially accepting grades, shades, or anything analogue (non-discreet) as what is able to demonstrate the power of Geometry on its applications to the reality. Briefly, we measure things with things, and what we do in such cases is Geometry. We can just to measure things, so all what we need is Geometry in such cases. Contrary to that algebra allows us to use some symbols, and with it to do more operations at the same time, than it is about Geometry. (Not in any case, but I believe this is how it things are.) Calculating is easier, than drawing or imagining numbers, things, and therefore to get the result. The last one attitude (thought) makes me think that a thought lies nearer to algebra, than to geometry is that, it is made with symbols, not with images. So it might be that the art is closer to geometry, while science is closer to algebra. An abstraction can package different squares, triangles, rounds, or pyramids into one or few formulas (and what is also must be true is that none formulas without visualisation of it (i.e. unpackaging it) is unempty). I am not against Geometry (in school I loved Geometry much more, than Algebra), but I still prefer to think of thoughts as about something that is closer to algebra. Thus, thinking we operate symbols more, than images. That's an extremely well thought-out and written post.
The line between algebra and geometry being a tricky one to define.
But it seems that the first step from geometry to algebra is when we introduce time. Of course algebra then goes beyond this, but geometry is all about space alone.
That makes geometry the foundation.
But how we define time, is the next phase, and of course the Einsteinians have turned algebra into a laughable farce on a good day.
Proof for THAT, is here:
Oh, now I see, that's true. Time is the most important component for geometry to turn it into music! As Pythagoras supposed! It's also according to the start of Bible, where it reads: "In the beginning Gods create Heavens and Lands".
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