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Math and Myth

 
 
Reply Tue 22 Dec, 2009 11:12 pm
Philosophers have long been fascinated with math/geometry. Nicolas Cusanus used a sort of proto-calculus to describe God. Spengler thought that each culture had its own math, and that this was an essential part of its worldview. I personally think that irrational numbers are great symbols for God or what Lacan would call the Real.

I would like an open-ended discussion of the aesthetic/philosophical/mythological side of math. What excites you about math and why? I also think math is a near perfect (if not perfect) sort of language. Numbers allow for a precision that words will not allow. This too I would like to include. So please, indulge me. Share with me what turns you on about this broad subject.
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jeeprs
 
  1  
Reply Wed 23 Dec, 2009 12:41 am
@Reconstructo,
What I like is that number does not exist, and yet nothing could exist without it.

Consider number. Obviously we all concur on what a number is, and mathematics is lawful; in other words, we can't just make up our own laws of numbers. But numbers don't 'exist' in the same sense that objects of perception do; there is no object called 'seven'. You might point at the numeral, 7, but that is just a symbol. What we concur on is a number of objects, but the number cannot be said to exist independent of its apprehension, at least, not in the same way objects apparently do. In what realm or sphere do numbers exist? 'Where' are numbers? Surely in the intellectual realm, of which perception is an irreducible part. So numbers are not 'objective' in the same way that 'things' are. Sure, mathematical laws are there to be discovered; but no-one could argue that maths existed before humans discovered it. Mathematical relationships are indubitably a function of perception; nothing is counted if there is no-one to count.

Therefore I wonder if subject of mathematics is real, in a different way to the reality of ordinary objects of perception. But then, of course, number is intrinsic to the way in which everything is organised.

...this line of thought needs to be developed. But it is derived from Pythagorism, and in fact, there is a whole school of 'numerical mysticism' that derives from it. I have not studied it much yet.
kennethamy
 
  1  
Reply Wed 23 Dec, 2009 12:45 am
@jeeprs,
jeeprs;113696 wrote:
What I like is that number does not exist, and yet nothing could exist without it.

Stand by, I have some more to add.....


Nah! No outrage. You are just using the word, "nothing" as the name of something. Heidegger does that all the time.
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jeeprs
 
  1  
Reply Wed 23 Dec, 2009 12:54 am
@Reconstructo,
Sorry Ken, I edited out my remark by the time you had commented on it, but thanks all the same! (and also for placing me in such illustrious company!)
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Reconstructo
 
  1  
Reply Wed 23 Dec, 2009 01:05 am
@jeeprs,
jeeprs;113696 wrote:


Therefore I wonder if subject of mathematics is real, in a different way to the reality of ordinary objects of perception. But then, of course, number is intrinsic to the way in which everything is organised.


Yes indeed. I think number is imaginary. This is why it's so clean. Because it's transcendental in its way. At the same time, different cultures used numbers in different ways, according to the spirit of their culture. Or so argues Spengler, and I found it convincing. Calculus and Cathedrals. Irrational numbers and Faust.
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jeeprs
 
  1  
Reply Wed 23 Dec, 2009 01:18 am
@Reconstructo,
BUt if number was imaginary, why is it the same for everyone? Does it mean we all have a common 'imaginary realm'? Surely I can't imagine a different 7 to you?
Reconstructo
 
  1  
Reply Wed 23 Dec, 2009 01:22 am
@jeeprs,
jeeprs;113711 wrote:
BUt if number was imaginary, why is it the same for everyone? Does it mean we all have a common 'imaginary realm'? Surely I can't imagine a different 7 to you?


I've always thought Venn diagrams were good on this sort of question. Most of us have 7 in common, but only some of us know what 3x/y means, and fewer still can mess with pi and i. It does seem that integers are part of a common imaginary realm, and also basic operations.

But so much of our human imaginations presumably overlap in many ways. For instance, we are trading letters right now. Maybe number is more basic, as it focus on a sort of quantity-continuum.
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jeeprs
 
  1  
Reply Wed 23 Dec, 2009 01:52 am
@Reconstructo,
No, that's not it. Number has a very specific meaning - an exact meaning. It does not vary from person to person, or from culture to culture. One can have a greater or lesser grasp of mathematics, but the subject does not vary according to whether your grasp of it is good bad or indifferent.

Numbers are real in a different way to 'the cat on the mat' being real. I am interested in whether you can say that numbers are real, but the cat exists.

But in any case, number in general is not imaginary. Nor is it objective. Nor does a nunber exist. But number it real. That is what is interesting about it.
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Reconstructo
 
  1  
Reply Wed 23 Dec, 2009 02:00 am
@Reconstructo,
I see your point, but still, I wonder. Have you looked at Spengler on number? He makes a case for cultural variation. Also, I see math as created. It's basics are perhaps universal/cross-cultural, but I don't see it as axiomatic that the entire structure is universal. Not every culture would invent "i", for instance, and the Greeks were not fond of irrational numbers.
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jeeprs
 
  1  
Reply Wed 23 Dec, 2009 02:23 am
@Reconstructo,
There are culturally distinct mathematical schemes and ways of counting. But that is not what is at issue. Have a look at The Theology of Arithmetic by Proclus. And actually Proclus, Paracelsus, and Plotinus were all significant thinkers in this discipline.

(Footnote: Do you know that one of the most revolutionary discoveries in mathematics was that of zero? I believe it was actually the work of Buddhist mathematicians (although I could be corrected on that.) There is an etymological connection between 'cypher' and the Buddhist term 'sunya' (or emptiness.) The symbol for zero is understood to be derived from the shape of the hole in the seat in which the mast on the arab dows was placed. I love it that you can say 'the Buddhists invented nothing'.)
0 Replies
 
Reconstructo
 
  1  
Reply Thu 24 Dec, 2009 03:37 am
@Reconstructo,
That book looks good. If you care to, elaborate on the number issue. I'm all ears.
0 Replies
 
jeeprs
 
  1  
Reply Thu 24 Dec, 2009 04:37 am
@Reconstructo,
I don't have much. All I have worked out is what to study about it. That, and an intuition, which is very simple but deep.

Think about these words - in-form and in-form-ation. Notice that 'form' is at the centre of both. Form is also related to format. Format depends on ratio which dicates the relationship of each part of the form. Matter is just dumb stuff which only exists by virtue of being in a form. If there were no form, there would be nothing. And the basic parameters of form have been set from the very beginning, because without the form, nothing could be formed. So the idea of form, and in-form-ation, must precede existence. Things can't exist without form. We might think that things 'just evolve' or 'just happen' but without form, everything would be at maximum entropy from the get go, and nothing would exist.

Anyway, here is the original post I created on this topic, in January, on another forum.

Quote:
Here I want to consider whether there is a difference between what is real and what exists.

'Exist' is derived from a root meaning to 'be apart', where 'ex' = apart from or outside, and 'ist' = be. Ex-ist then means to be a seperable object, to be 'this thing' as distinct from 'that thing'. This applies to all the existing objects of perception - chairs, tables, stars, planets, and so on - everything which we would normally call 'a thing'. So we could say that 'things exist'. No surprises there, and I don't think anyone would disagree with that proposition.

Now to introduce a metaphysical concern. I was thinking about 'God', in the sense understood by classical metaphysics and theology. Whereas the things of perception are composed of parts and have a beginning and an end in time, 'God' is, according to classical theology, 'simple' - that is, not composed of parts- and 'eternal', that is, not beginning or ending in time.

Therefore, 'God' does not 'exist', being of a diffrent nature to anything we normally perceive. Theologians would say 'God' was superior to or beyond existence (for example, Pseudo-Dionysius; Eckhardt; Tillich.) I don't think this is a controversial statement either, when the terms are defined this way (and leaving aside whether you believe in God or not, although if you don't the discussion might be irrelevant or meaningless.)

But this made me wonder whether 'what exists' and 'what is real' might, in fact, be different. For example, consider number. Obviously we all concur on what a number is, and mathematics is lawful; in other words, we can't just make up our own laws of numbers. But numbers don't 'exist' in the same sense that objects of perception do; there is no object called 'seven'. You might point at the numeral, 7, but that is just a symbol. What we concur on is a number of objects, but the number cannot be said to exist independent of its apprehension, at least, not in the same way objects apparently do. In what realm or sphere do numbers exist? 'Where' are numbers? Surely in the intellectual realm, of which perception is an irreducible part. So numbers are not 'objective' in the same way that 'things' are. Sure, mathematical laws are there to be discovered; but no-one could argue that maths existed before humans discovered it. Mathematical relationships are indubitably a function of perception; nothing is counted if there is no-one to count.

However this line of argument might indicate that what is real might be different to what exists.

I started wondering, this is perhaps related to the platonic distinction between 'intelligible objects' and 'objects of perception'. Objects of perception - ordinary things - only exist, in the Platonic view, because they conform to, and are instances of, laws. Particular things are simply ephemeral instances of the eternal forms, but in themselves, they have no actual being. Their actual being is conferred by the fact that they conform to laws (logos?). So 'existence' in this sense, and I think this is the sense it was intended by the Platonic and neo-Platonic schools, is illusory. Earthly objects of perception exist, but only in a transitory and imperfect way. They are 'mortal' - perishable, never perfect, and always transient. Whereas the archetypal forms exist in the One Mind and are apprehended by Nous: while they do not exist they provide the basis for all existing things by creating the pattern, the ratio, whereby things are formed. They are real, above and beyond the existence of wordly things; but they don't actually exist. They don't need to exist; things do the hard work of existence.

So the ordinary worldly person is caught up in 'his or her particular things', and thus is ensnared in illusory and ephemeral concerns. Whereas the Philosopher, by realising the transitory nature of ordinary objects of perception, learns to contemplate within him or herself, the eternal Law whereby things become manifest according to their ratio, and by being Disinterested, in the original sense of that word.


That is the extent of the argument at the moment. I have elaborated on it here and there in various threads. But I have found that there is nothing which really contradicts this idea. Of course, all the empiricists won't even consider it because 'it sounds mystical therefore could not be true' (there's a sophisticated piece of empiricism for you.) And also there are probably many who understand it better than me and know what is the matter with this argument.

And for them, I am all ears.

[This is really just my take on Platonism.]
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Reconstructo
 
  1  
Reply Thu 24 Dec, 2009 11:32 pm
@Reconstructo,
Great post. I can see connections between Plato and Jung and Kant, and even Blake, but also distinctions.

I find myself in agreement with that view. Blake thought the Artist was one who didn't waste his time on this "vegetable shadow" but went to the source, the Imagination. Very Platonic of him. One can look at Kant as a sort of despiritualized Plato. Jung is like a peeping tom outside of Plato's house. Of course Jung had his spiritual experiences that made him study the structure of such in the first place.

Lacan used "mathemes" to represent certain parts of the pysche. I'm adopting "o" as a symbol for the ineffable you-tell-me.

Thanks for your post. Good stuff.
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jeeprs
 
  1  
Reply Fri 25 Dec, 2009 03:57 am
@Reconstructo,
It is my intuitive take on Pythagorean and Platonic philosophy. I don't know a lot of the detail but am going to read up on it during 2010, beginning with The Pythagorean Sourcebook which on perusal of the ToC and comments, looks utterly fascinating. Comment from the publisher:

Quote:
the material of this book is indispensable for anyone who wishes to understand the real spiritual roots of Western civilization.
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prothero
 
  1  
Reply Fri 25 Dec, 2009 08:53 pm
@Reconstructo,
It is not just cultures and people that use mathematics. The universe itself seems to have a mathematical representation. A feature that is really quite remarkable but which many seem to just take for granted. As Einstein said "the most incomprehensible thing about the universe is that it is comprehensible" and even more remarkable is the ability to represent its laws in mathematical form. Mathematics may be the least and the most mythical conception of all.
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