Jeremy, below is an old post I came across. My thinking may have evolved since then, but I yet find it difficult to disagree today, except on a trivial level, with anything I wrote upon this forum about 4 years ago...
Here is a part of that post I wrote last night, but deemed too long too post...
You make the point, RPenner, and I thank you sincerely for the time you took to respond to my earlier post, that one must understand QED in order to derive formulas of possible interest to physicists and I just can't say as I am convinced that this is the case. Such knowledge certainly improves ones odds, and I have been working at frantic pace to educate myself in that area, but is such knowledge either a necessary or sufficient condition to generating such formulas? IF, in fact, the laws of physics apply to patterns of human organization and perception, as Jung, for instance posited, and great Physicist/Thinkers from Pauli to Einstein to Penrose would seem to agree or have agreed, then it stands to reason at least to postulate that for each and every physical phenomeneon there is a mental correlative; that the mental and the material realms can be thought of as bijective mappings of one another.
IF, in fact, this is the case, then, for instance, the concept of the holographic mind, in which every part contains the imprint of the entirety, as a holographic plate divided can yet project the entire image, may not be so farfetched after all. Whether we are speaking of quarks, leptons or bosons, or physics, biology and sociology or cells from the brain, nose or posterior region, the question becomes far more one of perspective and orientation and emphasis than one of objective validity. In other words, one multi-dimensional "crystal," many facets.
And what would be one of the implications IF this were to be the case? And this, as before, is all a question, not an answer, but I believe it to be a worthwhile question to ask... Well, at least in theory, we could study social systems or the psyche or even language to generate hypotheses regarding the workings of the cosmos and vice-versa. But there's a problem, an obvious one to me, and it's something I call "Babelization." Even as knowledge and information explodes in exponential upon exponential fashion according to what Ray Kurzweil termed "The Law of Accelerating Returns" (and long gone are the days when one man or woman can know "everything"), we simply don't have the common argot to effectively communicate across disciplines even when we're speaking the same language.
Biology uses one set of symbols and terms and paradigms. Chemistry another. Physics another. And these are practically sibling disciplines. Now bring in the philosophers and the psychologists and the politicians and sociologists and artists and on and on and you've got a multi-threaded system chalk full of co-evolving strands of knowledge and experience diverging in logarithmic fashion even as we are facing global dangers of unprecedented magnitude: Nuclear proliferation to rogue nations and terrorist groups, Global Warming, dwindling supplies of renewable energy, increasing concentration of wealth in violation of the "Tinbergen Norm" (Tinbergen developed the "Gravity Model of Economics) etc. etc.
An ironic thought, I know, in an age of globalization and connectedness on a scale also unprecedented, and I do not wish to sound alarmist because i have great hope and optimism for the future of humankind also, but the danger is that, as Yeats might have put it, the center cannot hold. All systems may be self-organizing, which I believe to be the case, but unfortunately such self-organization oft times takes violent form and that is something obviously I believe we can agree that most of us want to avoid.
The bottom line is this:
I believe we need to start figuring out some shortcuts to better communication across disciplines (not to mention across race, color, creed, class, etc.) so that we might more effectively "tie it all together" (social string theory, anyone?) before we blow it all apart. And in order to do that, my take is that we need better "algorithms" for understanding and communicating with one another and ought to figure out ways to pool our resources in distributed computing, parallel-processing fashion.
All that said, let me make one point clearly: I do not believe that understanding can come from pure thought alone. But what I do believe is that reason, intuition, imagination, experience, observation, testing etc. are all together a part of the overall equation.
Furthermore, as pertains to my comments regarding a pooling of resources, I believe we must figure out ways to bridge disciplines. Not empiricism, not poetic social theories, but the two in tandem. Not positivism, not phenomenology, but both in tandem. "Hard" and "soft," reason and intuition in tandem. My goal is not to be a mathematician or a physicist, but to learn enough to be able to work with mathematician and physicists.
Another point I'd like to make, you mention the level of mathematics involved, and point it out with a certain amount of judgement associated, but I feel, as you feel with Guest00, that you are missing the thrust of the basic point I am trying to make (although perhaps I have not made it well...). In Vicoish, back to basics manner, I don't believe that one NECESSARILY requires higher levels of complex mathematics to intuit certain knowledge, so much as one requires complex and interdependent and relational patterns of thought.
For instance, one of the beauties of number theory is that one can let the embedded algorithm of the series "do the work" for you. As one need not understand a computer's assembly code in order to use it, one also need not understand prime numbers in order to use public key code, and so on.
Fib numbers, for instance, related obviously to Lucas numbers, and therefore to the powers of phi in compound form (phi^2n + phi^-2n = L^n; phi^2n-1 - phi^-2n-1 = L^n) can be thought, relative to one another, as a flowing series of whole number Pythagorean triples (i.e. a "moving equilibrium" in the vein of some of the premises of functionalist sociology) with each F(2n) equal to F(n-1)^2 + F^(n+1)^2.
Does any of this have application in functionalist sociology? Or with respect to string theory or bit string physics? Or IA? Perhaps, yes. Perhaps no. The answer is that I DON'T know, but, to reiterate a point I have made repeatedly, I believe the inquiry to be more than worthwhile.
We need new approaches, because the old ones are no longer sufficient as Peter Woit, I believe, made amply clear by negation in his book "Not Even Wrong," a critical response to string theory.
In closing, let me simply make reference to the words if Stanford Professor of Physics Emeritus H. Pierre Noyes...
A Short Introduction to BIT-STRING PHYSICS"http://arxiv.org/pdf/hep-th/9707020.pdf
When I first met Ted Bastin in 1972 and heard of the Combinatorial Hierarchy (hereinafter CH), my immediate reaction was that it must be dangerous nonsense. Nonsense, because the two numbers computed to reasonable accuracy — 137 ? hc/e 2 and 2127 + 136 ? hc/Gm 2p — are empirically determined, according to conventional wisdom. Dangerous, because the idea that one can gain insight into the physical world by “pure thought” without empirical input struck me then (and still strikes me) as subversive of the fundamental Enlightenment rationality which was so hard won, and which is proving to be all too fragile in the “new age” environment that the approach to the end of the millennium seems to encourage [84, 86]...
I largely agree with Noyes. For whatever that is worth.