• Which books have had the most profound impact on you?
    Introduction to Topology and Modern Analysis by George F. Simmons (1963)
  • What is your understanding of philosophy?
    As a math person, I view philosophy as rigorous speculation, which I do all the time (or so my wife tells me). Not much use for philosophers of Olde, but that's just me.
  • Question about relationship between time as discussed in Relativity in Physics, and time perception
    . . . most physicists today don’t use the word “mass” in that sense, though they used to, and your paper does. — Pfhorrest

    Well, I learned something. And "most physicists" might be an understatement: the Wikipedia page on relativistic mass almost never gets a view.
  • If Wittgenstein were alive today...
    Whatever he might say we might not understand.
  • Question about relationship between time as discussed in Relativity in Physics, and time perception
    ↪tim wood
    Yes, my point was to clarify why your video and jgill’s paper seem to conflict.     — Pfhorrest

    I wasn't aware of a conflict since I don't watch Youtube videos very much. What's the conflict?
  • Indigenous Philosophy Resources
    I never thought of Native Americans having philosophies rather than simply beliefs, but, then, the word "philosophy" can be interpreted in more than the classical sense.
  • Question about relationship between time as discussed in Relativity in Physics, and time perception
    Fermilab — tim wood

    Reminds me that when I was at the U of Chicago 1958-59 each day I would walk past Stagg Stadium and peer into the fenced off area beneath it that housed The Chicago Pile-1. A small simple plaque on the fence paid homage to its creation.

    All that's gone now.
  • What's your favorite Thought Experiment?
    If you call that few if any, well... — ssu

    Wow! That's pretty impressive. I didn't think the AOC ventured much beyond set theory. Some time back fishfry mentioned Zorn's lemma (or transfinite math) regarding the proof of the Hahn-Banach theorem in functional analysis, but when I checked my ancient class notes I found that a minor change in the hypotheses eliminated that need. The closest I ever came in the examples you cite from Wiki is the basis of vector spaces, and even there it didn't come into play in the stuff I explored.

    Thanks for the info. :cool:
  • Question about relationship between time as discussed in Relativity in Physics, and time perception
    Mass in Special Relativity

    Good point.
  • Question about relationship between time as discussed in Relativity in Physics, and time perception
    Light and other massless particles must travel at light speed, but objects with mass can travel at varying speeds - up to but not including the speed of light? — RolandTyme

    Probably the word "particles" can be misleading. They are not like tiny BBs. If light is a field a particle might mean a ripple in the field. From this perspective, a comparison with the passage of a spaceship could be inappropriate. A physicist, like Kenosha Kid, could comment with authority. I'm a novice. :cool:
  • What's your favorite Thought Experiment?
    A colleague of mine tried teaching the subject at the U of Colorado some years ago, and neither he nor his students benefited. — jgill

    Who benefits from the History of Math or the Philosophy of Math? Not many I would say.

    Usually students aren't interested in the fascinating history of a debate in mathematics.     — ssu

    It's not a math history course. It's a sophisticated real analysis course, including calculus, based upon a rigorous concept of infinitesimals.

    For example, just how many different fields of math can you find something similar to the Axiom of Choice? — ssu

    I'm not up to speed in contemporary abstract math, particularly foundations, but I would guess few, if any. fdrake or fishfry might be able to answer your question.
  • Question about relationship between time as discussed in Relativity in Physics, and time perception
    In order for one hour of external observer's time to correspond to a half hour of traveler's time the ship needs to be moving at roughly 161,076 miles per second. This is impractical in a period of chip shortages.
  • Can it be that some physicists believe in the actual infinite?
    I think I said "inherent order", but I don't quite understand the point to making the difference. — Metaphysician Undercover

    Inherent order is a wider concept, applying in particular to biological systems and natural phenomena. Ordering is more specific having to do with listing. I think you are discussing the latter.
  • What's your favorite Thought Experiment?
    Of course, that is then called non-standard analysis — ssu

    Not a "simple" "intuitive" with "beautiful reasoning" in my opinion. If it were you would see more of it in college curricula. The Leibniz notion is interesting, admittedly. A colleague of mine tried teaching the subject at the U of Colorado some years ago, and neither he nor his students benefited. :cool:
  • What's your favorite Thought Experiment?
    I might be wrong, but I think Math is so beautiful, that to a such essential part of mathematics, there perhaps is a simple intuitive and beautiful reasoning — ssu

    Cauchy and Weierstrass did just that. Cauchy: "When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the limit of all the others."
  • Can it be that some physicists believe in the actual infinite?
    The issue I'm concerned with is the question of whether a thing without inherent order is a logically valid conception. — Metaphysician Undercover

    Sorry, I haven't kept up. Are you speaking of inherent order or inherent ordering?
  • Is it better to learn things on your own?
    In theory you can pick up a math book and start grinding through the definition/theorem/proof exposition and work hard on the problem sets. In reality, a good teacher makes all the difference. It's very difficult to go it alone — fishfry

    Yes, indeed. Even with a good instructor you can find yourself reading a paragraph over and over until its meaning sinks in. It's no picnic. You should always read a math book with pen and paper at hand. It's not like reading a novel.

    I've known literary autodidacts, but one thing they may miss is not having their writings carefully criticized. It's hard to see our own work through another's eyes.
  • Suggested typical titles for a new discussion in TPF
    If I Can't Can Kant?
  • Can it be that some physicists believe in the actual infinite?
    I don't want to distract from this fascinating and delightfully lengthy discussion, but to return to the title of the thread: Physicists and infinity
  • How do we perceive time?
    Here's a math note I wrote a few years ago on the subject. Nothing of any real significance, just playing around. :cool:
  • The movie, "Altered states" meaning?
    Renegade, a French film about the American wild west, is one of my favorites. Some really neat hallucinated snakes.
  • How Do We Measure Wisdom, or is it Easier To Talk About Foolishness?
    One aspect of wisdom, particularly in the elderly, is to have learned from one's mistakes. Another is to know one's limitations. The latter expressed by the philosopher Layton Kor fifty years ago. :chin:
  • Temporal quantum salvation by Jesus
    Could be called, Salvation in a Block Universe. Kudos for the authors for conjuring up the unanticipated.

    Were it not so well written I might suspect it came out of a community college in Oklahoma.

    What has become of Oxford? But then it must be hard to explore anything original in theology.

    But what do I know? Not much. :roll:
  • Logical proof the universe cannot be infinite
    I don't get this. How could a 900x900 pixel image show the entire universe or even a small part of the universe? — T Clark

    The OP essentially assumes the conclusion, then attempts to "prove" it. :roll:
  • Can the universe be infinite towards the past?
    ↪Manuel
    It's a dynamical system in C that is observed in the computation of an analytic continued fraction when evaluated by backward recursion:


    In this instance where . If it has a bearing here or for time dilation at the event horizon of a black hole is problematic. :chin:
  • Can the universe be infinite towards the past?
    If the Big Bang is true and complete, how can we speak of time before that? — Manuel

    You probably can't. The question then becomes, Is it possible that time evolved in a way that conflicts with current analysis and provides a path back in time that is unbounded, even to the moment of the BB?

    I know, sounds absurd. But I have been looking at a dynamical system in C in which, starting at a particular past moment, one analyzes a sequence that begins at n and devolves to 1, then begin at a larger n at the same starting point, etc.

    Just musing.
  • Can the universe be infinite towards the past?
    It may be possible that there was an initial moment and yet time extends infinitely into the past. Think time dilation and the Big Bang. Just ruminating, pay no mind.
  • Can it be that some physicists believe in the actual infinite?
    The set of all primes between one and twenty-one has no order dependent upon its definition. However, when I begin to write down the elements of the set I establish an order in which they appear. :roll:

    What more needs to be said? (but I am a victim of naive set theory)
  • Hole in the Bottom of Maths (Video)
    Now, let's look at a certain kind of arithmetical sentence. These are sentences in the language of arithmetic all of whose quantifiers are bounded. — TonesInDeepFreeze

    Thanks. Certainly in the study of combinatorics there are conjectures in which all possible cases are finite in number and a computer program can do the job. Like the four color problem.
  • Integrated Information Theory
    Yet, Tononi’s original IIT concepts and predictions do appear to be bearing out in various neurological studies. In 2013, Adenauer Casali and colleagues completed a study that showed it was possible to use the IIT framework within an EEG paradigm for measuring consciousness in some patients. — Gina Smith
  • Hole in the Bottom of Maths (Video)
    ↪TonesInDeepFreeze
    Perhaps you could elaborate on computational proof. When I conjecture a theorem in complex analysis I usually turn to the many programs I've written for examples that will either suggest the conjecture is true or abruptly halt the process - if only temporarily - by demonstrating it is false in a particular case.

    I don't think this is what you are discussing, however. I'm trying to see the link between actual mathematics and foundational mathematics in this regard.
  • Hole in the Bottom of Maths (Video)
    I can't recall learning of anything in classical analysis (complex or real) affected by incompleteness, but that doesn't mean much since I have been out to pasture for many years and my memory is imperfect. If one of you comes across something please post. :chin:
  • Is ReserachGate dead ?
    Researchgate seems to be functional with my account.
  • Can it be that some physicists believe in the actual infinite?
    Yes, it seems like mathematics has really taken a turn for the worse. If you really believe that mathematicians are aware of this problem, why do you think they keep heading deeper and deeper in this direction of worse? I really don't think they are aware of the depth of the problem — Metaphysician Undercover

    Yes, it certainly looks like that faulty brick in the foundations of math will surely cause the giant structure to collapse. I wish I had known this before becoming a mathematician. :cry:
  • Godel, God, and knowledge
    If we can know God perfectly, we can prove everything in mathematics once we fully know him and Godel's theorem will not apply. — Gregory

    If you were to know God perfectly, mathematics is irrelevant. Especially if that "everything" includes things that mere mortals have deemed false. Just relax and savor the bliss. :love:
  • Can the universe be infinite towards the past?
    . . . when physicists talk about infinity they usually mean something entirely different than the way mathematicians use the term. They usually do mean unbounded — fishfry

    I side with the physicists on this.
  • Hole in the Bottom of Maths (Video)
    A philosopher of mathematics might consider this a serious issue. However, many mathematicians ignore it. But who knows about the future?

    Remember, math is not like constructing a skyscraper, putting in a firm foundation before building the edifice. In math the edifice was largely in place, and the foundations were added afterwards.
  • Can it be that some physicists believe in the actual infinite?
    ↪fishfry


    Gowers: "The “two cultures” I wish to discuss will be familiar to all professional mathematicians.Loosely speaking, I mean the distinction between mathematicians who regard their central aim as being to solve problems, and those who are more concerned with building and understanding theories"

    This is very well said. Of course the distinctions are not clean cut. And the following resonates:

    Atiyah: "Some people may sit back and say, “I want to solve this problem” and they sit down and say, “How do I solve this problem?” I don’t. I just move around in the mathematical waters, thinking about things, being curious, interested, talking to people, stirring up ideas; things emerge and I follow them up. "
  • Godel, God, and knowledge
    Now if we are filled with divine knowledge in a mystical experience, why would Godel's argument prove we couldn't prove all of mathematics while in that state of rapture. — Gregory

    What are thoughts that we should capture
    While in the throes of blissful rapture
    That soothe the pain of incomplete
    With certain knowledge
    Now replete
  • Can it be that some physicists believe in the actual infinite?
    And, modern physics looks at time as the fourth dimension of space — Metaphysician Undercover

    A bit of vaudeville relief :lol:
Home » jgill