Comments

  • Mathematical universe or mathematical minds?
    So what are your thoughts here when one direction looks to track the "deep maths" of Nature and the other choice may be just unphysical pattern spinning? What do we learn if this is the case? — apokrisis

    Motivations vary in the mathematical community. What is common, however, is the drive to explore, sometimes with regard to the mysteries of nature, sometimes within the discipline itself. I'm a spinner.

    But am I right that you argue the complex plane has lessons in terms of the physics of chaos - patterns of convergence~divergence? — apokrisis

    I don't know about the physics of chaos (other than my experiences as a meteorologist ages ago), but the patterns that appear as examples of weak emergence are fascinating.

    what would happen if physics were re-written in the language of intuitionistic mathematics? Would time become “real” again?

    Since computations are done on computers with computable numbers and functions, isn't that already the case? The notion that a non-intuitionistic approach damages the idea of time seems ridiculous. A purely philosophical tragedy.

    But Gisin points out that intuitionistic mathematics could offer a natural way out of the deterministic lockup.

    I've never known a fellow mathematician who claimed to be an intuitionist. The fact that all functions from [0,1] to R are continuous from that perspective is quite unappealing to someone who came up in classical analysis. (Yes, it depends on the definition of "function"). Equating the flow of time with adding more digits to a number seems a bit absurd, at least for me.

    Zoom in on your complex plane with its pattern of curl, and do you start to lose any sense of whether some infinitesimal part is diverging or converging? — apokrisis

    The complex plane itself doesn't have a pattern of curl. It's a vector field based on a complex function that does the job. I have zoomed in up to 10,000X to display fascinating objects purely from curiosity. In the vicinity of an attracting fixed point, no matter the magnification, one sees convergence. It's just a matter of how one writes the computer program.


    One can ask again whether maths made the right pragmatic choice even if Peirce is the metaphysically correct choice? — apokrisis

    I admire Peirce for his thoughts on nonstandard analysis. I once toyed with the idea of teaching a real analysis course from that perspective, but gave it up when a friend at a larger university did just that, with poor results. I find it a bit amusing that when one looks at the standard graphical depiction of a mathematical Category, one sees Peirce's Triangle.
  • Foundational Metaphysics
    . . . almost everyone has a problem with your views of infinity. Now we may all be wrong, and you may be correct. But is it necessary at this time to focus on the infinite as such, or can this be shelved or stated another way that allows your readers to focus on the first premise they can readily accept? — Philosophim

    :up:
  • Should Philosophy Seek Help from Mathematics?
    In India, it seems religion and math went hand in hand. — Athena

    That's an amazing article on Indian mathematics on Wikipedia. Ramanujan, of course, was one of the great geniuses in math. When I was a math prof I would be asked occasionally to teach the survey course in mathematics history - a task none of us relished since no one had the necessary background. It would have been an enormous help had Wikipedia been available!

    How do you guess mathematics might have evolved had it not been for the Romans and Christianity? Or, is it the teaching of math to school age kids that you think should be different? My wife is a retired HS English teacher and she made the same remark about coming up with the right answer without going through all the steps when she was a student. :smile:
  • The mind and mental processes
    ↪jgill

    I put a lot of effort into these posts. If you don't have anything substantive to add, please go to a different thread.     — T Clark

    Sorry. I was feeling frivolous after reading the sandwich vs hotdog thread. :sad:
  • The mind and mental processes
    Ogg Eep did in 100,000 BCE — T Clark

    Alley Oop, perhaps?
  • Is a hotdog a sandwich?
    You guys need to stop joking and start chomping away at this mouth-watering question at the heart of philosophy. :chin:
  • Mathematical universe or mathematical minds?
    ↪apokrisis
    Thanks for the link. Nice paper. I have Penrose's massive book, but have only read bits and pieces. The rotation/translation bit makes sense, although my knowledge of modern physics is weak. I have, in fact, done a fair amount of research involving Moebius (or linear fractional) transformations (that crop up in these physics discussions), but going the pure analysis direction in the complex plane rather than the geometries coming off the Riemann sphere. A non-terminating continued fraction - a kind of analogue of an infinite series - can be perceived as an infinite composition of such transformations (as can a series).

    (We were speaking of fixed points before. I introduced the idea of accelerating the convergence of limit-periodic CFs through the use of attracting fixed points of LFTs back some years ago.)
  • Is a hotdog a sandwich?
    . . . exemplifies a confusion which lies at the heart of philosophy — hypericin

    Wow! That came out of nowhere. :yum: And to think some say that philosophers only look backward.
  • Should Philosophy Seek Help from Mathematics?
    The mystical and math go very well together and I think the Western mind is biased and this bias is like blinders that limit the consciousness of the Western mind. — Athena

    There are about 24,000 math topics on Wikipedia, many if not most by "Western minds". That doesn't sound like the Western mind is terribly limited.
  • Should Philosophy Seek Help from Mathematics?
    ↪jgill
    I think in the West much of Eastern is considered nonsense. But I also think this is more about perspective than fact. Is God outside of nature or is nature God? Should we look for God in everyone? Could our understanding of God affect our understanding of democracy?     — Athena

    I suppose there are psychoanalytic threads woven into the relationships between the gods of ancient Egypt, but, yes, nonsense. On the other hand, some of the spiritual practices originating in the East, like Zen Buddhism, are relevant today. I once wrote a chapter of a book on a certain aspect of a sport being a "mystical art form." :cool:
  • Mathematical universe or mathematical minds?
    There's more magic in complex analysis than in complex arithmetic. :cool:
  • Mathematical universe or mathematical minds?
    And complex numbers make commutative order matter in a way that is "physically realistic" — apokrisis

    Perhaps you are speaking of the canonical commutation rule in QM? Obtained by employing the imaginary number i. Otherwise I see no particular advantage in, say, multiplication or addition over the reals. Of far more interest is Euler's formula and its relation to wave forms.
  • Should Philosophy Seek Help from Mathematics?
    Maybe we should not be divided between those who have made math and science their God and those who have not because we are butting heads — Athena

    I see a more divisive conflict between right-wing Republicans and left-wing Democrats.

    So those who understand stand math as it is taught in the West have valuable information, but we should know they most likely come to the study of math and all other things with closed minds. — Athena

    Not my experience at all. But if you mean entertaining the wisdom of the ancients, like this:

    A distinction must be made between associations of deities and manifestations of a neter principle into other neteru’s principles/forms. For example, it is wrong to assume that Re-Sebek is an association of two deities —

    Yes, perhaps of interest as part of history, but nonsense nevertheless.
  • Doing away with absolute indiscerniblity and identity
    but with eternal inflation, there are guaranteed to be other identical versions of you, and some with only slight differences — Count Timothy von Icarus

    Why? :chin:
  • Negative numbers are more elusive than we think
    Friend, there are many interesting questions and debates involved with the foundations of math . . . The existence of negative numbers is not one of them. — Real Gone Cat
    :up:
  • Rules and Exceptions
    1. is a colloquialism, not meant to be taken seriously.
  • The Ultimate Question of Metaphysics
    Zero, or empty set. is nothing, but it is a type of nothing, or nothing of a specific type of thing. If we proceed to say that the specified type is every type, so that it is nothing of any type of thing, then "every type" is a type. And if types are things, (Platonism), then nothing is something. — Metaphysician Undercover

    I like to make sure statements like this are enshrined on the forum. :cool:
  • Mathematical universe or mathematical minds?
    This is a bold claim... that all pure math is eventually applied. Really? — Pie

    I've commented on this before. ArXiv.org receives 150 - 300 math papers a day, most probably pure math that vanishes into the academic aether after a while having served its purpose, tenure, promotion, prestige within specialties, curiosity, etc.
  • Are dimensions needed because of Infinity?
    ↪alan1000
    There's a one to one correspondence between points on such a line and points in the interior of the cube. You could look it up, it's a simple arithmetic trick involving manipulating the digits of the numbers representing the points.
  • Should Philosophy Seek Help from Mathematics?
    What is not worth the effort? — Athena

    Competing with the wisdom of the ancients, such as:


    Ennead The nine worlds of the Odine Mysteries. The Egyptian Ennead, or company of nine gods and the goddesses, represents archetypal principles that regulate and rule the cosmos through the laws of number. The pharaoh came forth from between the thighs of the divine Nine. — Athena
  • Should Philosophy Seek Help from Mathematics?
    But, you should ask one of the mathematicians here, like jgill or others, who could help you out much more than I ever could. — Manuel

    Not worth the effort
  • Are dimensions needed because of Infinity?
    If its any help, the "number" of points inside a cube is the same as found on one of its defining edges (lines).
  • Who do you want to see as 47th President of the United States?
    Biden reelected — Jackson

    Biden deselected
  • "Philosophy simply puts everything before us,"
    RIP Jackson :sad:
  • The Ultimate Question of Metaphysics
    the fixed point behaviour that anchors renormalisation in quantum field theory — apokrisis

    Beyond my pay grade. :smile:
  • Foundational Metaphysics
    I am not entirely certain that a stable methodological approach can be establish to examine the properties or existence of PoR, but that is something I am currently contemplating — Bob Ross

    Since this seems to lie at the foundations of your paper it would be good to make it a bit clearer what you are talking about. I'll ignore the infinity stuff, that itself is puzzling from a mathematical perspective.

    Another member of TPF has in the past submitted a lengthy and sophisticated essay on a theory of everything (or roughly that), starting with an assumption every fact in the universe can be encoded for use in Turing machines. But doesn't explain how.

    When one doesn't explain clearly at the outset what the fundamentals are or how they can be attained, readers may not be enticed to go further.

    But that's just how I see it. Others here may differ. OK :cool:
  • Evidence of conscious existence after death.
    A waste of philosophical energies. :meh:
  • Should Philosophy Seek Help from Mathematics?
    Quick question, for my benefit: does this applied math give us insight into the nature of the world? — Manuel

    Quick answer: insomuch as there are existing patterns in the world that we identify and attempt to codify with mathematics. But applied math can go any number of directions, like computing the stresses on bridges, calculating the orbit of a satellite, building the pyramids, etc. :cool: Sometimes pure math finds surprising applications, like a result of mine from 1991 that was recently used in a paper on decision making in group environments.
  • Should Philosophy Seek Help from Mathematics?
    Applied math, the kind the gives us theories, usually belong to physics. — Manuel

    Sorry to be picky, but applied math goes beyond physics. Physics, in fact, almost has its own math.
  • The Ultimate Question of Metaphysics
    So fixed points are important as the emergently stable invariances of a physical system. The symmetries that anchor the structure of the self-reconstituting whole — apokrisis

    An example would help. Intriguing.
  • Venerate the Grunt
    Joining the military is a HUGE gamble — Bitter Crank

    It depends on how you join. I was sent to the U of Chicago for twelve months to be certified as a meteorologist (weather officer), all expenses paid plus salary, housing allowance, etc., never wore a uniform. Two and a half more years of not unpleasant duty and out, receiving an automatic GS11 rating should I want to join the Weather Bureau. I have a friend, now a district attorney, who was sent to law school, everything paid for plus salary, etc.,and rose to colonel in the Judge Advocates office. Another friend was sent to medical school to become an MD, all expenses paid plus salary, served a short period an left the service for private practice.

    Then there were those inducted during the Vietnam War. There's your HUGE with bells on it.
  • Should Philosophy Seek Help from Mathematics?
    To use math is to apply mathematics. And to apply mathematics is to treat the thing which you apply mathematics to, mathematically. Therefore to use math is to mathematize the thing you apply it to. — Metaphysician Undercover

    See why I love this forum? :cool:
  • Should Philosophy Seek Help from Mathematics?
    Actually, philosophy should seek help wherever it can be found. :meh:
  • Venerate the Grunt
    Still no one coming forward saying, "I was a grunt and now I am a philosopher"? — jgill

    Did we honestly expect that? — ToothyMaw

    I was being optimistic. Of the 15,000 or so who have joined the site perhaps a few would read the thread and post up.
  • Is this even a good use of the term logic?
    Four in a Row Game
  • Venerate the Grunt
    Friedrich Nietzsche was an artillerist in the German army during the Franco-Prussian War.
  • The nominalism of Jody Azzouni
    My own account of causation is taken from Lewis: A causes B if it is not possible for A to be false and B to be true. — Michael

    This assumes a linear causation chain. I.e., no other cause for B exists. If C also causes B, then A can be false and B true, and still A, like C, causes B. :chin:
  • Foundational Metaphysics
    And I think we agree there is only 1 unbounded infinite, as more than one would be by definition, two bounded infinites — Philosophim

    This essay might get a larger following if all this infinite stuff were in mathematically acceptable nomenclature. Just a thought.
  • The nominalism of Jody Azzouni
    . . . but instead, the world is a "fabric with features". — Marchesk

    A little like quantum field theory. We are excitations in a reality field. Neat.
  • Should Philosophy Seek Help from Mathematics?
    So if using mathematics in a field of study does not constitute mathematizing it, then what does? Is physics mathematized? Is music mathematized? — Metaphysician Undercover

    Yes, I agree, although using simple percentages is near the lower bound of the definition. At this intellectual level grocery shopping might be, "Well, one can is $2, so two cans will be $4".
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