Mathematics and Ordinary Descrptions of Reality.

Fresco, my friend. I would consider it a favor if you would simply reduce life to it's simplest terms. Beyond that I am simply having a sneezing fit.

Letty,

I understand your request for "simplicity".

Consider another Einstein quotation:

"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality"

What he appears to be saying here is that there is some interplay between our concepts of "mathematics" and "reality" which is worth investigation.

At the simplest level all "naming" of objects is "mathematical" (nominal level) and this has been questioned by philosophers on the basis of the transitory nature of all states (...everything is in flux) The discussion could proceed from there.

fresco, to be frank, I have no idea what Einstein meant, nor frankly, do I care. All, he did was unleash the atomic bomb on the world, and I really think that he didn't intend to do that....but then, maybe he did...what really matters is what we feel when we take our last look at the world...and I can tell you this, my friend. When I look through that veil, I won't be thinking of him...Tesla, perhaps...but then I was always a sucker for Dr. Frankenstein....I'm not being glib, Fresco. I'm just realizing that when we look in the face of infinity, numbers won't matter. Can you dig it, Brit? Once, when I was very young, I sketched a picture of a child, sitting among the rubble of war, petting a dog. That is the miracle to me...out of chaos--order...Remember this, Fresco.It's not the giants that shape our destiny, it's the common man........................................

Letty,

I can commune with your humanity at an emotional level, but I am also intrigued by the "refinements" of our concepts of "order" and "chaos" from a "culture free realm".

Have a look at these (by now familiar) fractal figures generated by relatively simple mathematical processes. They seem to have an almost "clinical beauty" which perhaps informs our "imperfect" attempts to emulate them.

http://www.mbfractals.com/images1.html

I think that what we are really talking about here is the uses of different kinds of language. Any human language employing words (or sounds which stand for something) is likely to elicit an emotional response. Mathematical formulae (also a language) are less likely to do so. But does that make the language of numbers more 'objective' (for lack of a better word)?

I am a great fan of Albert Einstein. I can barely understand some of his mathematical concepts as expressed by long formulae. Sometimes I don't understand any of it. But when he uses human language to express such lovely metaphors as "God does not play dice with the universe"...ah, there is a measure of the man's greatness and clear thinking.

If we reduce human experience to a set of equations, I think we lose some of our humanity

Good morning, Fresco and Andrew.

Fresco, those images were breathtaking. I should look up the meaning of fractal, but I do not believe that I need to do so as the label becomes redundant to the beauty created therein.

The spirals contained in the creations are a reminder of the golden ratio--the golden spiral, that Fibonacci devised to explain beauty geometrically--the curl of the wave--the chambered nautilus--the fetus.....

I think that you have made your case, my friend. I just get frustrated because I'm such a dunderhead at any mathematics.

Yes, you are right. It is about language.

Merry Andrew,

I agree that maths is a type of language, but its "coherence" lies beyond what we can normally aduce to " logic".

Take "complex numbers" for example which have a "real" and "imaginary" component. Only by taking into account both of these components are we able to describe/predict real results for wave phenomena.

The situation gets even more surprising in quantum physics where proposed mathematical variations seem to "cause" the very existence of particles.

There is clearly some form of "metalogical interplay" between mathematics and "reality" which seems to transcend ordinary language.
The question is almost "which is the servant and which the master".

I heard that trees grow and hearts beat in fractal patterns. I also heard somthing about harmonious sounds on a keyboard being akin to fractal patterning, but other than those shallow references I don't know anything about it or it's implications in the world.

Many beautiful theories are too perfect and don't work. This is especially true of theories in sociology and political science. But then you have some simple ones that are consistent throughout the universe. Ex: Pythagorean theorem. Einstien has some theories that work consistently with great accuracy, and Newton's are much simpler but are off by an inconsequential amount.

I don't think we are always classifying unnecessarily, Fresco. There are laws that are consistent throughout our known universe, and we try to discover those laws. Classification is a totally valid means of understanding, especially where it is tested and works (as in physics.)

I'm afraid I can't go into as much depth as you seem to know about this, I am no mathemetician. Quantum physics is very strange.

Portal Star

My general interest is in epistemology and how our "knowledge" evolves. Working hypotheses are used to direct our attention to "new data" and these often emerge from pure math results. This brings up some surprising issues. (For example the equations used to predict for electric power transmission were formulated about rwo hundred years before the advent of electric power !)

I admit to the problem of having to maintain my patience with "ordinary language philosophers" who seem to be unaware that words like "logic" "proof" and "evidence" as related to "reality" seem to me to belong in "the playroom". However I do not feel it essential to be expert in mathematical matters in order to appreciate the naivity of some ordinary language approaches.

Letty,

...just to explain that Einstein's use of "non-Euclidean Geometry" means that his theories required a concept of "curved space" rather than "3-D space of flat planes and straight lines". This is a direct rejection of the Greek axiom that "parallel lines never meet" based on the concept of a "straight line" being (merely) a human cognitive construct. Riemann and Lobachevsky were mathematicians who developed non-Euclidean Gemoetry (Lobachevsky being immortalized in a song of that name by Tom Lehrer http://www.123lyrics.net/t/tom-lehrer/lobachevsky.html )

Loved that song, Fresco. Hilarious! Plagiarize? heh heh..was it Newton who observed that all he had learned was because he had stood on the shoulders of giants? I guess Atlas was the first giant, huh?

Hmmm. As to your explanation of curved space, that was succinct and clear. Thanks. It won't make a physicist out of me over night...but it is something to build on.

Forgive me, Fresco, but I cannot resist this, given your link:




Two and two are four
Four and four are eight
Eight and eight are sixteen
Sixteen and sixteen are thirty-two
Inchworm, inchworm
Measuring the marigold
You and your arithmetic
You'll probably go far
Inchworm, inchworm
Measuring the marigold
Seems to me you'd stop and see
How beautiful they are

sung by Danny Kaye in the Movie Hans Christian Anderson. The children where droning the numbers in the background in a strange minor to major change, and Kaye was outside looking at the flower and singing a sweet, simple tune in a major key. Perfectly lovely.

truth
Fresco, interesting thread. I am a mathematical illiterate so I will not do more than read and learn, but let me say that philsophy is, for me, the use of language to produce "adequate" answers to verbalized questions, and the task of making our verbalized questions increasingly sophisticated. That is to say, to use language to investigate our linguistic formulations of the world and to investigate the nature and limitations of linguistic formulations themselves.
Not being a mathematician, I cannot imagine a mathematically phrased question, nor can I imagine myself being satisfied by a mathematical answer to a linguistically phrased question, especially one fraught with existential meaning or poetic power.
But I do not want to let my mathematical illiteracy push me into a position of rationalizing that inadequacy, in a refusal to appreciate the advantages of the mathematical approach.

JLN

Nice to see you recovered.

This thread is partially an attempt to escape from and to formalize (our) general problems with respondents who rely on "ordinary language".

Try the fractals reference above (in particular the last animation of "Julia Sets" which takes a few minutes to work). This gives some non-specialist insight into current mathematical trends,

Capra cites this as one example of "the mathematics of complexity" required to adequately describe organic structures (which he claims should all be labelled "cognitive"). We have spoken about "states of equilibrium between observer and observed" and Capra's discussion borders on this. It is also significant that he cites Von Forster who we have discussed in connection with "transcending the observer".

Forgive me, but I cannot resist.

The ultimate answer: 42
The ultimate question: What is six times seven?

May Mr. Adams rest in peace.

Fractal,
As much as mathematical science has advanced, as much as "ordinary language" has remained largely stagnant, neither is developed enough to represent a cohesive, complete, cogent, or any other c word, picture of reality.
In my humble opinion (and please forgive me again if I ever sound as if I'm on a tirade- I'm not, its just that I'm abrasive) The evolution of mathematics is just that, an evolution. The same as any other language. Its a work in progress. Not so oddly enough, so is the rest of the universe/reality. As our understanding of the universe changes, the very nature of our relationship to it changes. Yes fractals, and non-Euclidian geometry, along with quantum physics, neuroscience, geology and other sciences have changed the way we talk about the universe, and the way we go about with it. So if you want to get down to the nittiest, grittiest, and tiniest parts of reality- yes, its all math, and no, we have no inkling of how to describe it- yet. So I say lets use the best of what we have got. The big picture takes much more than a thousand words or an infinite set to describe.

My apologies Fresco, I seemed to have addressed you incorrectly. Damn, 1 post and already I screwed up.

Not 6 x 7 but 6 x 9. In base 13, of course. See sig.

Alex,

No apology required - thanks for the contribution.

The particular context in which I raise the "mathematics versus ordinary language" issue is an ongoing one in this forum - that of the relationship between "the observer and the observed." It seems that the Heisenberg issue and its offshoots, together with the ability for computers to deal with complex data have prompted mathematicians to re-consider this fundamental problem. So yes - I agree there is an evolution - but that evolution is not "smooth". This massive chasm of what "actually" constitutes "a description" may be about to be bridged.

truth
Alex, nice comment.