Thread: Singularity

Another way of looking at it.

One of the things which people can imagine, and Rene Descartes, who worried quite a lot about what he could imagine, quite excelled at it, is called mathematics. I don't think anybody should try to dispute that mathematics are entirely imaginary, or at least, only existent in the human mind. Nor should they dispute, in my opinion, that, oddly enough, math does seem to be able to create useful descriptions of 'natural phenomena.' These phenomena are, for convenience, assumed, though maybe not initially by Descartes, to be not entirely imaginary. Due to the limitations of human understanding, this is not provable, mathematically or otherwise, but for most people, eventually even Descartes, I think, it's an article of faith.

Over the last several centuries, considerable effort has been given to developing and confirming this correspondence between the logic of mathematics and the assumed actuality of the universe, with such good result that in the last couple centuries some research has reversed the process and looked to invent the mathematical explanation first, to find a clue to the underlying natural processes. First probably in early chemistry, where we find things like the gas laws and stoichiometery first suggested to their discoverers by the elegant simplicity of the arithmetic. Two great triumphs of modern science came in this fashion, in the microcosmic realm of particle physics, a mathematical description called quantum mechanics, and, on the cosmic scale, general relativity. Great swaths in both these arenas are considered totally confirmed experimentally but by no means all, much of the math is still speculative and reconciliation between the two systems is still problematic. There is no rule that things mathematical must be real, as far as can be seen, it is simply our good fortune that quite a bit of it works out. There is also considerable leeway, the massive calculations of general relativity for instance, create dozens of alternate universe models, some of which must seemingly be wrong, unless some new math provides a connection. At present the reiterative calculations of general relativity, which give useful correspondence to cosmic evolution over most of their values, sometimes reach a point of mathematical absurdity, where values zero out or become infinite and for which no useful physical correspondence can be imagined. (In the case of black holes, resort to quantum mechanical calculation provides amelioration and black holes were discovered to exist.) That's what the singularity is. It's just the current end of our mathematical description. Doubtless, we'll invent more. In the mean time, speculations of its import are, so to speak, somewhat groundless, particularly those partaking of a metaphysical hue.

Yeah, right.

I can accept this as the poetic beauty of math...but at the same time if it makes no sense to me, then can I disregard the beauty for ugliness? Yes, I can.

Simplify it. Give us the impetus behind it that drives such a math. The impetus behind it is what is important. Simplification.

Thanks much for your thoughts Draxia. I don't think it is simple though. I think it's really complex and really hard and will take considerable study. Personally, I love that. pp

You mention 'the elegant simplicity of the arithmetic' but go on to confuse complexity with difficulty. For one with the patience to investigate step by step, the equations of relativity and quantum mechanics will unravel and reveal their internal 'elegant simplicity', and those terminal points of zero and infinity mark the limits, not of the math, but of our own ability to find the path that will lead to the next level of understanding. From simple addition, to the solution of linear equations, to Simpson's Rule, to Schrödinger's Equation, and beyond to where we are today and where we will be tomorrow we walk step by step and plant milestones along the way to show those who follow, 'Thus far we came, now go ye farther'.

In the mean time, speculations of its import are, so to speak, somewhat groundless, particularly those partaking of a metaphysical hue.

I do not entirely understand what "somewhat groundless" means. If you are requesting a critique of your writing, that might be something you would want to adjust--also a couple more paragraph breaks would be helpful, though I certainly can't diss the general cohesiveness of your argument and your writing style, which are impressive.

Moving on: Consideration of "the singularity" is of course a keystone of Middle Eastern as well as Western occultism; naturally, of course, the average person--even a highly intelligent and well-educated person such as yourself--is not likely to know much about that, given that this type of spirituality is "occult" (i.e., kept hidden), and conventional spirituality most often concerns itself with making things more complicated and confusing instead of simpler.

If you have spent time researching the metaphysical aspects of the singularity and have not so far encountered these teachings, please accept my apology. If you have not done so--which is my suspicion, based on the phrase "somewhat groundless"--please feel free to message me and I can point you toward some material you can read on line which might help that part of your research. (NOTE: I'm not in the least interested in influencing your point of view about anything, but only offering to help your research.)

Otherwise I think this is a good beginning to an interesting discussion. Is this intended as an essay, or part of some larger work...?

Organizationally, as Scarlett_156 noted, judicious use of paragraph breaks would help greatly in "spreading out on the table" your premise and argument. Please allow me a hypocritical note - as much as I think that commas (one of a writer's few methods to provide inflection and accent) are underused all too often, several of your sentences contain (perhaps unnecessary) qualifying clauses, set off by commas, which can lead to confusion, depending on your reader. Hypocritical because, when writing non-fiction, I find myself, like you, using qualifying clauses to ensure that my point is precise and unquestionable. When I find myself overusing those clauses, I try, not always successfully, to limit them. (See what I mean?)

The term, 'singularity', used originally in mathematics in the 19th C., is not only now used in the field of the occult, but also, for purposes of clarity, in present-day university physics classes, especially in analysis of the simple motion of non-rotating bodies. Further, the term is used more frequently in astrophysics, cosmology, and astronomy to pinpoint one possible origin of the universe.

From a philosophical perspective, the reality, i.e., natural laws, that requires the use of mathematics to understand, have most probably existed since the beginning of time (explosion of the singularity - without motion, there is no time). Mathematics is simply a construct, of human design, to measure the results of those laws. No doubt, long before Descartes (the namesake of Cartesian geometry, et al) relatively primitive mathematical principles were used by such as Hero(n) of Alexandria, the first, true recorded inventor of the steam engine, builders of the pyramids (on several continents), etc. Even a cat, jumping from floor to window sill, uses the principles of mathematics - perhaps primitive, perhaps not - to gauge the correct angle and velocity with which to propel himself. One could argue that the cat, like athletes, hikers, Nascar drivers, etc. use the principles of natural law, not the principles of mathematics; however, if one allows that natural laws exist, there is no principle of natural law - it just is. The principles of mathematics is the human construct that allow us to understand, e.g. measure, predict, the effects of those laws.

As Garza notes, the 'elegant simplicity' is revealed to us, and by us, step by step. Even Einstein, in trying to reconcile his famous equation, had trouble until he imagined that 'C', the speed of light, is, contrary to foregone conclusions, mutable, a possibility that has since been proven true. Not only elegantly simple, but pointing out the hurdles that humans construct in front of their own progress. Additionally, it points out the result of trying to ascribe principles to natural law - they are what they are, perhaps the realization that drove Einstein in his unproductive search for a unified field theory. In the current pursuit of string (or superstring) theory, the existence of eleven, or perhaps thirteen, dimensions will prove more elegant than our Newtonian understanding of four, three physical and time.

"There is no rule that things mathematical must be real, as far as can be seen, it is simply our good fortune that quite a bit of it works out."

Probably, one of my three heroes, Carl Sagan, were he still around, would argue with that statement. He would probably argue that hard work, deep thought, mathematical creativity, and testing of hypotheses is the reason that "quite a bit of it works out," not "good fortune".

Unaware of your intended audience, I still applaud your undertaking of a (primarily) philosophical area and the possible direction(s) to which it can lead.

These are all laudable observations against which I would never dream of making an argument, but would only like to add that my own research has demonstrated that the metaphysical concept of singularity preceded the development of certain scientific advances--for example, the discovery of the potential of controlled thermonuclear reaction--and was to all appearances instrumental in the development of those advances, though this is of course never explicit in the available documentation--you have to do stuff like read biographies and so on, to find out what those guys were into as far as their beliefs. (And that's maybe what you ought to do in this case, rather than take my word for it--your own research may lead you in an entirely different direction. Reading biographies of people who've had important ideas and made important discoveries is always a good time... er, unless the biography is poorly written. But that's another subject.)

Although metaphysics has for some while played around with the concept of the singularity, the idea sort of exploded onto the metaphysical scene in the mid-to-late 1880s, concurrently with a great many startlingly new concepts in art and literature. Within a couple of decades these innovations were starting to be entertained by scientific minds. Many unprecedented scientific discoveries followed.

String theory is a really interesting area of study, but may lead you quite a distance from your intended goal--just sayin. (LINK: Maybe the math behind string theory is overrated anyway) I just googled the phrase "string theory news" and picked something off the first page.

I will note in closing that the Romulans use a singularity to power their interstellar drive systems. Those jerks! They always get the newest stuff first.

As early as the 1840's, the concept of technological singularity was railed against by some, as the potential cause of the downfall of the human species as an outgrowth of mechanical calculators. In fact, the possibilities have been the fodder of fictional novels and movies for decades. The concept of singularity, if not the specific word, was singular in the mind of Siddhartha Gautama some 2400 -2500 years ago. He desired to permanently rid himself of all desire, to reach personal singularity, an aim that led to its own, obvious paradox. Although I've learned that the only absolute in reality is that there are no absolutes, I've also learned that academic philosophy is paradox. Some might argue, for example, that black holes are absolute, allowing nothing to escape their gravitational pull; yet, only recently, has evidence - not proof but evidence - suggested that some particles do indeed emanate from black holes.

Still, it shouldn't be surprising that the concept of singularity, regardless of the specific word used, would precede technological achievement since philosophy is the progenitor of knowledge; hence, PhD - Philosophiae Doctor - in so many disciplines. We wonder and question before we know.

In return for your suggested readings, I will suggest that, short of university-level physics classes and labs, you might benefit from reading a couple of Brian Greene's books, describing what is known about some Newtonian and quantum physics as well as the fundamentals of string theory, as opposed to beliefs of historical figures, for the general reader. (He has yet to write his autobiography.)

String theory, in itself, is elegant and, if someday supported (one hesitates to say proved) by evidence and rational, scientific thought, makes sense, regardless of one's goal. That is, it is what it is (as pointed out in the page you cited), regardless of goals or beliefs of historical figures, e.g., Cardinal Bellarmine vs Galileo's findings, or the Romulans . The alternative is the "velvet inquisition" whereby beliefs drive research to reach preordained goals and conclusions to support those same 'beliefs'. We see the results of such thinking around the globe today. Interestingly, the page you cited does not argue against string theory but expresses some doubt, even Greene's, that current mathematical modelling is up to the task, echoing what ppsage noted in his original post.

Various entities will claim that "string theory" has been debunked--like you, I'm not sure that is entirely the case. It's possible that like you said, it's gonna sit around for awhile until some really smart person picks it back up again, and the reason some smart person will pick it back up again will doubtless be that he or she has figured out some practical use for it besides fueling the creative impulses of science-fiction writers. Science still fiddles with the singularity because of its demonstrated practical potential--look how much green got sunk into that Hadron collider thing.

There are a few models in the natural world that SEEM (the word here is "seem") to harmonize with such a theory, and certainly like a lot of people I've spent a significant portion of my leisure time--even to the point of getting in trouble at work for it--playing with various computer models of Goedel's theorem(s) to discover not scientific but metaphysical truths. (I know: What a waste of time! lol what can I say?) Everybody was all crazy for string theory up until a few years ago, it's true. That surfer dude kinda blew us all out of the water, though. (Get it? Surfer dude "blowing us out of the water"??? eh? eh? )

Concerning 'debunking' of string theory, the GOP candidate for Senate, in Delaware, Christine O'Donnell, stated that evolution, as a theory, is a myth - essentially 'debunked'. There will always be a fringe element who, for reasons that they don't even understand (but others do), wish to prematurely pull the shroud of ignorance over scientific research (see the example in my immediately previous post). Unfortunately, many will view her as an authority on the subject. (She garnered 40% of the vote which isn't too bad - that's 80% of those with lower-than-average I.Q. who voted for her .)

I'm sure that researchers at CERN's LHC project at Geneva would be interested in even one model in the natural world, necessarily existing in at least eleven dimensions, that harmonizes or coincides with string theory. That would be a breakthrough!

I assume you were thinking of Gödel's Theorems, his second of which is an excellent example of my previous statement, "academic philosophy is paradox."

^^^ Because of course we're NOT talking about science, metaphysics, or anything close to it. We're taking shots at people we don't like, aren't we? ROFL.

How I love the internet.

Hmm . . . interesting - I was still talking about the pursuit of scientific inquiry. I simply used her statement as an example of one who wishes to cover rational scientific and mathematical inquiry, exemplified in ppsage's original post, with the shrouds of feigned knowledge and buffoonery, two of the illegitimate children, along with ignorance, of stupidity, a choice which she displayed with aplomb. IGYN!

If we insist on interpreting the evaluation of statements by public figures as disliking them, we run the risk of marginalizing rational evaluations, regardless of their validity, and dismissing any significance they may have - another device of the 'velvet inquisition.'

I'm pleased that my little piece has found a slight audience and thank everyone who’s taken the time to comment. It is intended to be convoluted and I'm afraid suggestions to make it "easier" are taking it a bit too seriously. While I don't really know how correct it is and there is certain to be always imprecision in so generic a presentation, there are underlying thoughts embedded here which I, at least, would usually stick to. But a good deal of the point is also to recognize in them an element of subjective pomposity, and to caution against its hypnotic replication.

My phrase "the elegant simplicity of THE arithmetic" is intended to refer to the notion of integer multiples implicit in quantum deductions generally and to it's possible rudimentary expression in the discovery of the stoichiometric principle underlying molecular combination, the simplicity lying in the process of multiplication by positive whole numbers and not referring at all to an idea that mathematics in general is necessarily either simple or elegant, a position to which I do not wish to be adhered.

I also would opine that it's uselessly imprecise to consider that a cat is obeying mathematical principles when jumping to a perch. My thought in this piece was to express the idea that mathematical principles, if they are anything, are things like the rules of addition and the assumptions of the geometries, completely abstracted from the experiences of counting and measuring, which nevertheless perhaps inspired some of them. Values from the measurement of cats jumping might suggest principles, if we're going to use this word, theorems might be more precise, of physics, for which we might then find particular mathematical expressions by which to calculate values for additional cases which might then be experimentally verified. That particular expression would in no way constitute a mathematical principle, but it might embody one of physics. If it is, for instance, a very fast cat, the expressions derived from Newton's physics' principles might be inadequate and resort to those of a relativistic nature might be required, a very different physics' principle but the same mathematical ones would apply, to guide making the calculations.

Similarly, mathematical singularities are simply values for which the result of a mathematical expression is undefined, division by zero being the everyday example. The use of the term singularity as that from which the Big Bang arises is of this nature as is that at the heart of black holes. There are, of course, presumably physical realities at these points and, presumably, sensible mathematical expression of the physics' principles underlying them will be developed. I still consider the simple semantic confabulation of these technical details with those of metaphysical speculation to be somewhat groundless. That was ironically expressed and really implies that I consider it wholly absurd. I would, however, be interested to hear a less ambiguous definition of the term as used in the musings of occult metaphysics.

Again, my thanks to everyone who's commented. In appreciation, pp.

If any of you have difficulty with understanding math get hold of a copy of The Trachtenberg Speed Maths.(Trachtenberg, a brilliant engineer with an ingenious mind, originated his system of simplified mathematics while spending years in Hitler's concentration camps as a political prisoner. Conceived in tragedy and amidst brutal hardships, this striking work cannot be separated from the life of its originator for it is quite possible that had Professor Trachtenberg's life run a more tranquil course he might never have conceived the system which has eliminated the drudgery so often associated with arithmetic).For years I had great difficulty with math. After reading this work it was like my mind was opened to a mathematical universe.