Comments

  • What's the big mystery about time?
    Are you talking about perceiving red and yellow as one simultaneous unity?Joshs

    Perceiving the changing from yellow to red simultaneously. Not quite change, I'll admit.
  • Why Metaphysics Is Legitimate
    As a math person what immediately comes to mind when the word metaphysics arises is Leibniz's notion of the infinitesimal. These tiny things cannot possibly exist, yet they can be used to develop profound mathematical results. There is much more math that is - to my mind - metaphysical. The more abstract, the closer to that category.
  • What's the big mystery about time?
    Is it possible to explain it simply?Watchmaker

    Maybe. Suppose you are looking at the computer screen before you. It is devoid of imagery, but is a continuously changing color from yellow on the left to red on the right. If you allow your eyes to move from left to right there is an element of time change involved. But if you simply move back a bit and look at the entire screen what you see is yellow changing to red as an entity of its own, not requiring a period of time.

    This seems overly simplistic. Banno can do better.

    These are the folk who will explain the ineffable at great length, with no awareness of the irony involved.Banno
    :up: :lol:
  • What's the big mystery about time?
    Time is the activity of pure self-affectingJoshs

    I hope that's not the last word on the subject. :roll:
  • What's the big mystery about time?
    Time and energy are related by observing that, as in space, moving at a fixed rate requires no energy. Whereas if one accelerates by applying a force time will speed up for a stationary observer. So in a peculiar sense physical acceleration accelerates time as well. :chin:
  • Why do Christians believe that God created the world?
    It's almost like you were attacking John Cleese with a banana.Vera Mont

    Which would have made more sense and been far more entertaining.
  • Why do Christians believe that God created the world?
    ↪jgill
    What was the point of that post?
    Bartricks

    When you sober up you'll get it.
  • Why do Christians believe that God created the world?
    If God wants us to know what he is like, then he can do that. And he has, for we can know that God exists . . .Bartricks

    Sunday School babble. Have one more for good measure, then toddle off to beddy bye. :roll:
  • Of Determinacy and Mathematical Infinities
    What an exciting thread this has been! Never a dull moment as we delve into two thousand year-old mysteries. :chin:
  • Of Determinacy and Mathematical Infinities
    A point and any geometric extension are completely dissimilar from each other. It is strange that there is no thing in-between themGregory

    If you are thinking of a line segment between points A and B, then philosophically there really is nothing there - its merely a hypothetical path in Euclidean spaces of shortest length from A to B. We draw it with a pen, but that always gives us a two dimensional version having width. Modern math of course says otherwise.

    Honestly, @apokrisis is the only guy I know around here who's comfortable with this sort of metaphysics,Srap Tasmaner

    I agree. As a biophysicist/philosopher this is the goto guy. Were we talking about foundations/set theory @Tones is the resident expert. Fellow mathematician, @Real Gone Cat for math in general. For modern or theoretical physics I'm not sure who that would be. @Kenosha Kid qualified, but he has left the room. Speak up, anyone.

    The history of "infinity" is over two millennia old and progress over that period was done by philosophers/mathematicians. Were Aristotle to rise from the dust today he would tell philosophical devotees to pay attention to what has been achieved and not to refer to his ancient ideas. Or do you think he would eschew progress?
  • Of Determinacy and Mathematical Infinities
    In sum: You seem to want to investigate notions of infinity in non-mathematical senses or contexts. Fine. But then you'd do well to leave mathematics out of it if you don't know anything about the mathematicsTonesInDeepFreeze
    :up:
  • Of Determinacy and Mathematical Infinities
    Countable in the sense of: one infinite line and another infinite line make up two infinite lines.

    Or: the infinity of real numbers and the infinity of natural numbers and the infinity of transfinite numbers make up three numerically distinct infinities. More technically, make up three numerically distinct infinite sets
    javra

    Certainly you have two infinite lines. And each line has the cardinality of the reals. Also, both lines, together, have that cardinality. And so on. But the "three numerically distinct infinite sets" are not really distinct, in that the set of integers is a subset of the set of reals, etc. So the cardinality of the integers is "less than" that of the reals.

    The real numbers are quite complicated. And I didn't intend to belittle your efforts, but it sounded to me like you were thinking it is possible to count all lines in the plane through some sort of algorithm.
  • Of Determinacy and Mathematical Infinities
    Okay. I certainly don't understand what your stance is on whether or not infinite lines are countable.javra

    Are you talking about a single infinite line being somehow countable? Like the points on the line?

    Or are you talking about the set of all infinite lines being countable?

    Neither are countable. Countable means this is #1, this next is #2, the next is #3, etc. It means some sort of algorithm for actually counting.

    Maybe you are using the word differently. Like "I can be counting on you to do the best you can." Rather than counting 1, 2, 3, ...

    Real Gone Cat is a fellow mathematician.
  • Of Determinacy and Mathematical Infinities
    In other words, “countable” can only hold the valid usage in its mathematical senses when addressing things such as lines. Therefore, the concept of there being “2 lines” is … invalid and nonsensical.javra

    You have reached an absurd conclusion. Of course there can be "two lines". Any finite collection of lines is clearly countable. And there are countable infinite collections of lines such as all lines parallel to the x-axis that pass through y= 1, 2, 3, ....

    What are not countable are all lines in the plane.

    I too wonder how a continuum makes up something discreteGregory

    As the seconds tick by in the continuous flow of time we have minutes and hours which are "discrete".
  • Of Determinacy and Mathematical Infinities
    The definitions can of course be questionedjavra

    I'll say. Go deeper: Countable

    The unit itself - which is a unit only because there are limits or boundaries which so delimit it - can however be counted. A geometric line does not have limiteless or unbounded width; its width holds a set limit or boundary, namely that of zero width. Because of this, one can quantify and thereby count geometric lines on a plane as individual units.javra

    An infinite line is a line, therefore, I suppose, a "unit". But they can't be counted since the points in the Euclidean plane cannot be counted and so pairs of these points - defining lines - cannot be counted.
  • What does "real" mean?
    ↪jgill

    You're a butthead, so we're even.
    frank

    Sorry if I awoke you too abruptly from your nap. :cool:
  • Of Determinacy and Mathematical Infinities
    Can not two points in a plane (with the plane itself determined by a multitude of points) determine a unique line, this as ↪Srap Tasmaner offered? In which case, the line here then has determinants and is thereby not indeterminate (i.e., undetermined)javra

    By Jove, you're getting there! Two points do indeed determine a unique line segment joining those points, But there are lots of line segments including and extending beyond this initial segment, aren't there? The big Kahuna here is extending this segment infinitely in both directions.
  • What does "real" mean?
    Just checking in. 413 posts and still no consensus on what "real" means.

    You are a disappointing bunch. :sad:
  • Of Determinacy and Mathematical Infinities
    Is there any property in taxicab geometry analogous to curvature?Srap Tasmaner

    Taxicab Fun

    What makes them countable if they are completely devoid of any boundaries?javra

    I don't know what you're talking about. Provide an illustration, please. Show me how you count them, 1,2,3,4,5,...
  • Of Determinacy and Mathematical Infinities
    If one can discern the quantity of lines specified, then lines as a whole are indeed countable. Or would you disagree with what I actually said?javra

    So, if I have a countable collection of lines, they are countable? I suppose that's a step in the right direction.

    So for your question about the determinateness of mathematical infinities, you would say here that a line is I guess 'determinate enough' that we can pick it out as an object?Srap Tasmaner

    If it's in a countable collection that would seem to be the case. But if a line is the shortest distance between two points, it could depend upon the metric you are using. For example, in the taxicab metric the shortest distance between two points is greater than in the Euclidean metric.
  • Of Determinacy and Mathematical Infinities
    OP's question is one of whether mathematical infinity - your field I take it - is determinate, indeterminate, or neither?javra

    Set theorists and foundations people might be interested in such distinctions, but for me infinity simply means unbounded. Going back millennia to study what the ancients thought is of historical interest, but there has been progress since then. If that's your goal, then don't even mention mathematics. Once you do you are out of your depth. Not criticising, just fact.
  • Of Determinacy and Mathematical Infinities
    A mathematical infinity (in contrast to metaphysical infinity) is not limited or bounded in only certain respects and is thereby countablejavra

    Oh boy, here we go again . . . :roll:
  • On Thomas Mann’s transitoriness: Time and the Meaning of Our Existence.
    To exist is to be at the present. The pages in the past no longer exist, yet we have learned from them. And the important thing to note is that the pages of the future have no existence until the prior page is turned. The living being, existing at the present, is not the one turning the pages though. The page turning is being forced upon us, and if we do not move to the next page, (which has no existence until the previous is turned), by creating a place for ourselves on that page, or even better, creating a spectacle for others, on that page, then we get forced into the past.Metaphysician Undercover

    Well said, as usual MU.

    At 85 turning a heavy page can irritate an arthritic finger . . . but worth the effort.


    The Moving Finger writes; and, having writ,
    Moves on: nor all thy Piety nor Wit
    Shall lure it back to cancel half a Line,
    Nor all thy Tears wash out a Word of it.
  • What does "real" mean?
    All boils down to the meaning of the concept of "real" and how useful our usage is to avoid fallacies of ambiguity.Nickolasgaspar

    Agree. After almost 200 posts . . . :roll:
  • Does quantum physics say nothing is real?
    You simply refuse to adhere to the rule, and insist on defending all those sinners who have gone before youMetaphysician Undercover

    And there are so many, many of those. My math genealogy alone goes back to Karl Weierstrass (1850s), one of almost 40,000 descendants of that gentleman. And everyday 150 or more papers arrive at arXiv.org . So many sinners, so brief a time . . .
  • Does quantum physics say nothing is real?
    What I am arguing is that mathematicians ought not accept such theorems, I am not trying to say that they don't accept them. So, you providing me evidence that they do accept them, just provides me with inspiration to produce a stronger argument that they ought not do what they do.Metaphysician Undercover

    I just took a moment doing what I do to read this post, and now I feel so guilty. :cry:

    You have no mercy, MU.
  • Does quantum physics say nothing is real?
    What you'd prefer is to say that they do not have any apples . . . calling 0 a quantity is an abuse of the idea of quantitySrap Tasmaner


    ? :roll:
  • Does quantum physics say nothing is real?
    No good. 0+ and 0− are used in limit notation to indicate one-sided limits but have nothing to do with opposites.Real Gone Cat

    Picky picky. Of course they don't. But in the spirit of this discussion they could. There are enough ambiguities in math to satisfy MU. Take for example. What does it mean? A function? A constant force? Depends on the context. ? How about 4x/5y-1 ? If these guys want to play around with nonsense don't poop in their sandbox. :cool:
  • Does quantum physics say nothing is real?
    A curious statement. All the years I've practiced math I can't recall using "opposite" in this way. But I suppose some do.jgill

    ↪jgill

    Major Edit : "Opposite" is perfectly fine when discussing positives and negatives
    Real Gone Cat

    This discussion revolves around the use of the word "opposite" in math. Apart from integers - the focus here - it arises in discussions of geometry, like a side opposite the hypotenuse, or in a complex vector field with an indifferent fixed point - on one side an attractor and on the other or opposite side a repellor. And so on.

    Why not use a pair of these? . They are commonly used in math. You could come up with the first being infinitesimals just to the right of zero, etc.
    There are your "opposites" of zero.

    Does quantum physics say anything about this?
  • Why are people so afraid to admit they are wrong here?
    This user has been deleted and all their posts removed. — Deleted User


    That's an excellent username. And what better way to admit that you were wrong, then to delete all your posts.
    Metaphysician Undercover

    A sort of "Cancel Culture" of TPF.
  • Does quantum physics say nothing is real?
    In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number)Additive inverse - Wikipedia

    A curious statement. All the years I've practiced math I can't recall using "opposite" in this way. But I suppose some do.

    I dunno, I don't really feel that way. I find pre-theoretical intuitions interesting and important. No math without 'em.Srap Tasmaner

    Indeed. Centuries ago.
  • If you could only choose one...
    Proof of something like time travel would be more appealing.
  • Does quantum physics say nothing is real?


    Word games full of sound and fury . . . :roll:
  • Right brained thinking in science...
    Recently I have taken an interest in testing remote viewing.TiredThinker

    Any luck there?
  • Is there any difference between a universal and a resemblance relation?
    Abstract, "pure mathematics" shows that we dream up universal principles (axioms) first, from the imagination, or they come to us intuitively, then we try to force the particulars of specific circumstances to be consistent with the universals. — Metaphysician Undercover

    That's at least in the neighborhood of Sellars's argument and the impasse I expected to reach, that empiricism from a blank slate can't actually get started.
    Srap Tasmaner

    MU makes a good point regarding some highly abstract mathematics. I'll tell the story again of a PhD student writing a fine looking thesis about a certain class of functions, but when asked to illustrate the class by a specific example discovered the class was the empty set.
  • Immanence of eschaton


    Thanks for adding to my vocabulary. I had to look up "eschaton" to see what in the world you are talking about. Now I'm glad I had no knowledge of this word, nor its depressing meaning.

    Psychologically, how can we confront this terminal historical moment we have all been thrust into?hypericin

    Don't Google "eschaton". :roll:
  • Historical Forms of Energy
    Usually the concept of work relates to a change of energy, kinetic or potential. When an object follows a path through a force field, if that field is conservative, the path the object takes from point A to point B is immaterial regarding work; all such paths produce the same work. This idea aligns with Cauchy's Theorem in complex analysis.

    The analogy I recall is two people about the same weight standing before a mountain. One takes off directly to the summit over a series of cliffs, and the other follows a trail that winds round and round the mountain, finally reaching the top. Both have done the same work.

    A sequence of smooth contours in the complex plane I devised that start at zero and end at one grow longer and longer without bound while converging uniformly to the straight line path along the x-axis from zero to one. Set in the backdrop of a conservative force field an object moving from zero to one along the x-axis does the same work as on a contour that could be unraveled and stretched from Earth to Alpha Centauri and beyond.
  • Historical Forms of Energy
    Richard Muller, physics professor emeritus at UC Berkeley, states that energy is the most difficult concept to understand in the basic physics curriculum. It will be interesting to see what people say.
  • Nature of the Philosophical Project
    In what sense inaccessible? Do you mean that generalisation actually ends up cutting its connection to the particular? That shouldn’t happen if it is being done rightapokrisis


    Mathematical Schemes is an example of current levels of abstraction. If I were an algebraist or topologist I would probably see the values therein. This entity aided in solving Fermat's Last Theorem. But its value in real or complex analysis is debatable. Here's an example that, for me, is vague - which you value. For others that vagueness is merely the ectoplasm of math.

    You speak often of systems theory, and in math that begins with dz/dt=f(z,t) in the complex plane. Here the levels of vagueness are low, and chaos may grow out of these scenarios. What scheme theory has to say about this is a question for experts in these areas. But it appears schema theory means something else in biology.

    Schema Theory and the Dynamical Systems Theory are the predominant behavior theories that address how the nervous system produces a movement.

    The Generalized Motor Program Theory (GMP) or Schema Theory and the Dynamical Systems Theory are the predominant behavior theories that address how the nervous system produces a movement. The debate of movement scientist and the contrasts of these theories centers on whether movement is created through hierarchical control in the nervous system (i.e., cortical control) or if movement control is distributed throughout cortical, subcortical, spinal, and even musculoskeletal levels of the nervous system. While compromise between these two theories may be possible, each theory has its respective adamant supporters who will argue for the support of one over the other. In this assignment, you will evaluate these theories to determine which theory you believe is the more plausible explanation.