Structural Mathematics...

[Mike 5]

STRUCTURAL MATHEMATICS...

This phrase is on my mind recently. I have not trained formally in mathematics, however my mother was a weird and powerful mathematics teacher, I knew about fibonacci and the golden section almost before I could read...

Is there an existing branch of mathematics with this name - Structural Mathematics?

Structures fascinate me, and by structures I tend to mean that I think with my fingers, so structures are connected linked things and models that for me I think about primarily using the tactile and sensual abilities of skin muscle and skeleton, secondly the acoustic, and only finally the visual.

Of course geometry is about structures and I believe historically it was seen once as a deeper truth than many things we now trust as true. But geometry assumes flat planes, dimensionless points, linear equidistance, and my thinking finds these ideas just blinkered and flat.

My website and default online identity and pen name is Digital Witchdoctor, which does not sound mathematical, but for me digits - fingers, are the essence of how I think, and what makes my thinking tangible and occasionally clearly explained. (And generally mystifying - I found through NLP that most people can make visual images and memories in their minds at will, and I cannot! So my bullshit detector finds normal ideas "flat", others find my ideas won't fit onto the paper or surface they think upon?)

This is an important question for me. I still consider mathematics as a safe refuge from doubt and uncertainty, and the essence is that in mathematics, truth is clear, it is not decided by priests, it is simply and obviously true equally to all who care to think.

But I am never interested in numbers, really. Most "mathematicians" apply their logic to what I see as utterly false number lines because I cannot touch zero nor infinity, and the need to think in x,y,z co-ordinates is inefficient and clumsy. I have no reason to think on flat planes using x y z co-ordinates, as visual people may prefer. I need thoughts I can manipulate digitally - that is with my fingers, and I test the resilience ad elasticity and structural and sculptural forms of thoughts, I seek the umbilical connections and hidden inflexibilities.

In that I consider myself some form of mathematician. The best phrase I can find is Structural Mathematics.

Comments?

[baudrunner]

The building of a melody or the evolution of a song, in my experience chord progressions on my guitar, the structural mathemathics of music? I had a friend over the other day with a mellow voice and an ear for music and at the time I was playing my own version of this oldie or that goldie or just off on a tangent of my own and he kept asking me whether I knew this song or that, or anything by this group or that (surprisingly, he knew most of the words to "Chances Are" by Johnny Mathis), but I couldn't satisfy him for the most part because as a rule I straddle my own link to music, and I am invariably exploring an original progression of my own construction. I have no real interest in the musical meanderings of other composers because when I do analyze other arrangements I usually come up with a more pleasing version myself and off I go. Structural mathematics, who needs the math when we can just play the music? If what I do is a science then let it be the study of the "resonant concordance of progressive compatible waveforms within the auditory range". Kinda rolls off the tongue. Mathematics belongs to people who like to play with numbers and symbolic equations. It explains things but doesn't always have ideas that are according to the rules of nature. Being wrong in music is merely striking discordant notes and they can be corrected in real time. Being wrong in mathematics means occasionally having to recant, and admit that what was thought to be true turns out to be false. Mind you, music isn't going to help you win at casino gambling like Mandelbrot theory might. But it makes for a nice break.

I found through NLP that most people can make visual images and memories in their minds at will, and I cannot!

You have my sympathies. It is largely through visual imagery that I think. I have had a few too many hard knocks on the left side of my brain, and am by nature a right-brained person anyway and I understand the difference, you're not the first person I've met (one way or the other) who has told me the same thing. The irony is, you'd make the ideal mathematician. Visual imagery allows the storage of a complex idiom or idea into a fleeting symbolic engram. This allows for the recall of memories from the earliest times of one's childhood, and the playing back of a sequence of events like a motion picture "in the back of my mind". Frankly, I don't know how you think. Your writing style has led me to conclude that your perception of a "Theory of Everything" is a statement all about everything that you can regurgitate in one fell swoop after taking one long, deep breath. I know it ain't that.

[Mike 5]

Mathematics belongs to people who like to play with numbers and symbolic equations. It explains things but doesn't always have ideas that are according to the rules of nature.

No no no - you are spot on to talk about music as structural mathematics, in a way MUSIC has structure that is mathematical, and I learnt music from the paper rolls of an automated (suction powered) player piano when I was very very young. Mathematics is a way of structuring truth mechanically, for me, I only wish I could express that more clearly. Mathematics does not belong to people who avoid confrontation and truth. Yes part of the comfort of maths is the escape from challenges in reality, and psychologically maths is perfect when the world is tough - but playing with numbers and symbolic equations is the kindergarten of mathematics surely.

Applying the same structural clarity to reality itself is grown up maths. Anyone who expresses the unruly details of reality within mathematics is awesome - Newton of course, Einstein, Bezier, Fourrier, Pythagoras... Goedel? Penrose (in parts)... Goodness these giants weren't playing with numbers or symbols, but sure we'd need a telephone directory for those who settle for intangible mathematical games

[Mike 5]

You have my sympathies. It is largely through visual imagery that I think.

Well, naturally, deepest sympathies for you too. We all have our cross to polar bear. Visual imagery is so incomplete and superficial, but my first reaction on discovering I was different to most people was %*&*%! To think I got through education using only touch and hearing! All that revision for school exams! But now, I am SO glad I had such a training.

OVer a long while I realised that visual memory is generally very approximate and patchy. Studies have shown how dubious visual memory often can be. But look at this quote from Einstein, sometimes visual imagination is very clear and powerful, if limited:

" … words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be voluntarily produced and combined... The above mentioned elements are, in my case, of visual and some of muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be reproduced at will."

Albert Einstein, Letter to J. Hadamard, 1945

Einstein declared he would NEVER begin to understand fluid dynamics, nor the calculations needed. To me fluid dynamics is where we must start and then navigate back to the simpler stillness with one single and consistent theory.

IN contrast apparently to Einstein, Language is very close to my heart. And my own subjective experience of my own mind, is very fluid, operating in several languages, including linguistic structural forms such as jazz progressions. Improvisation of all kinds is basically so similar to language, and my HATRED of Wittgenstein is not simply because he was a w%**%ker, but he could sight read music ridiculously fluently, which clearly distorted his ideas of symbols as shallow and simplistic meanings. My experience of music has shaped my experience of life and thinking - I prefer Paul Ricoeur's Conflict of Interpretations, ideas of developing exegesis of meaning, meaning as flow and juxtaposition.

NLP of course was the first real approach to codify the three basically different styles of cognition (VAK, or five senses make VAKOG) in modern times. NLP distinguishes different styles of thought, as NeuroLinguistic Algorithms. The ancient Veda's had somewhat similar categories (Vata = sensual & audio, Pitta = visual, Kapha = emotional/kinaesthetic??) and theories (observer & thing observed & the process of knowing...)

ANYWAY - back on topic here

Anybody else every heard of Structural Mathematics, and would I be correct to assume my flavour of thinking and ideas are indeed conveniently named by these two words?

[baudrunner]

Sorry, any references to Structural Mathematics in the mainstream deals with form and integrity, all to do with boring numbers. It is actually an engineering disciline. However, you have friends in the structural reality debate.

You'll probably find this article interesting.

The purpose of this paper is to develop a philosophical tool and argue that it can be used to address certain puzzles in the philosophy of logic and mathematics.

It is natural to suppose, for instance, that ‘the number of unicorns is 0’ carries commitment to the number zero. But whether or not non-philosophers take assertions of this sentence to be true depends on whether they believe that the world contains unicorns, not on whether they believe that the world contains numbers.

I found a continuation of the structural realism debate which concerns the epistemological question about the nature of scientific knowledge, and represents analytic philosophy of science. I don't know where you'd find the thesis but here is a 14 page short.

There will probably never be a shortage of philosophizing on the relationship between practical science and abstractions in mathematical ways of thinking not using numbers, ie. linking reality to probability theory, after all there is no empiricism in the art of philosophy is there? But philosophy is not Einsteinian thinking, and even Einstein had problems with the ostensible versus the real, ie. in the study of fluid dynamics do you remember being wrong about the Bernoulli effect on the dynamics of flow? Never expect the expected in this reality. It's probably comfortable being mathematical without the numbers but it is decidedly impractical. It needs a new name.

[AntonioLao]

Structures fascinate me, and by structures I tend to mean that I think with my fingers,

Now that you mentioned it, my question is why do we have exactly five fingers not 4 or 6? Or what can we do better with lesser or more fingers?

[Guille]

Now that you mentioned it, my question is why do we have exactly five fingers not 4 or 6? Or what can we do better with lesser or more fingers?

we would play the piano better with 6 fingers but play tennis better with 4. I'm a better tennis player than piano player (the only good thing I od in music is composing), so I'm nearer to loose a finger than to gain one. Others are nearer to gain a finger.

[AntonioLao]

we would play the piano better with 6 fingers but play tennis better with 4.

The value of the objective function of playing piano is 6, of playing tennis is 4. The objective function with a value of 5 is for playing what?

[Guille]

The value of the objective function of playing piano is 6, of playing tennis is 4. The objective function with a value of 5 is for playing what?

Our hands as they are, with 5 fingers, their lengths and withds ,and shapes, and the palm too, it evolved from: first grabbing better to the trees and second working with stones. In fact, paleontologists say recently that our hands were the basic factor for us to become intelligent beings, the said it was the ultimate cause of it.

[Mike 5]

Sorry, any references to Structural Mathematics in the mainstream deals with form and integrity, all to do with boring numbers. It is actually an engineering disciline. However, you have friends in the structural reality debate.

...even Einstein had problems with the ostensible versus the real, ie. in the study of fluid dynamics do you remember being wrong about the Bernoulli effect on the dynamics of flow? Never expect the expected in this reality. It's probably comfortable being mathematical without the numbers but it is decidedly impractical. It needs a new name.

Nice references Baudrunner - thanks.

I jut did a websearch on "structural mathematics" and saw that many universities in the UK and the US cover "finite and structural mathematics" but I could not find any specific references to what they mean by "structural mathematics".

Lot of references to geodesic structure - spot on I say - and this weird idea about using 60 degrees instead of 90 degrees to map space, at least I think that is waht this is about:

http://www.rwgrayprojects.com/synerg...s02/p0000.html

A study of the microbiological structures, the radiolaria, will always show that they are based on either the tetrahedron, the octahedron, or the icosahedron.

As for Einstein - I only heard a quote where he says he could never grasp fluid dynamics, and thought, uhuh, that is EXACTLY the problem with Einstein, apart from his fixation with x,y,z, co-ordinate geometry which then melted into gaussian (salvador Dali) forms of drunken x, y, z geometry.

My idea is to think through a third theory or relativity using rotational co-ordinate geometry - where things are positioned as they APPEAR to an observer at any point, with reference to rotation, the decision of where our axis of rotation is, and the practical assumption to all incarnated beings actually in physical form to observe anything must be on a rotating gravity bound planet anyway...

Well, baudrunner, from what you say, I conclude that the term Structural Mathematics as such, is possibly used or possibly understodd as a form of physical description of space that is nothing to do with numbers. Thanks.