Comments

  • Infinity
    I can think of 1,2,3 as instantaneous, so also 1,2,3,... which makes the latter the same as N.

    What babble, but entertaining. :cool:
  • Infinity
    ↪Banno
    I'm not familiar with
    .9̇ — Banno
  • Infinity
    0.9̇ really does equal 1 — Banno

    Really? 0.999... = 1 ?

    Ask ChatGPT about the popularity of NSA. It is on target.

    Consider the following two ways to represent the natural numbers, "1, 2, 3, ...", and "N". Would you agree that these two symbolizations each signify something different? — Metaphysician Undercover

    Depends on whether the first symbolism is time dependent. Does counting actually require temporal steps. Can you think of 1,2,3 as instantaneous? Just speculating.
  • Infinity
    OK. I see that "choice sequence" arises in mathematical constructivism. All these years and never came across it. Flipping a coin over and over.
  • Infinity
    I notice numerous posters have the same attitude: that math is somehow immune from philosophical inquiry, and that if it's all built on nonsense, that's ok. I think it's really unfortunate that people got that impression. It's arrogant ignorance — frank

    Not at all. But philosophically examining mathematics requires knowing something of the subject. Otherwise it becomes a babble of word definitions. Philosophy of mathematics as an academic subject is certainly alive and well, practiced by those familiar with foundations and at least something of the branches of math.

    That is not to say philosophical discussions of math here on TPF is inappropriate, but merely speculative and more concerned with how words are interpreted. That's fine. Actually, I am curious about "choice sequences" - an example perhaps?
  • Infinity
    I'm really not. I learned calculus in an engineering setting. It never really occurred to me that anyone thought the sum of a convergent series actually equals the limit. At face value, that really makes no sense. It turns out Newton would agree with me. Leibniz would not. So this conflict is at the beginning of this kind of math. Since people have been struggling with it for like 300 years, you should cut me some slack for trying to get it — frank

    I feel your pain, but it is the result of applying a philosophical approach to mathematics. Philosophers love to dwell in the past and compare one master with another, one ancient idea with another. Mathematics is a social agreement and looks forward, not backward. I've taught engineering calculus, although its been quite a while ago, and the notion of the convergence of, say a power series, is fundamental. An analytic function is defined by convergent power series.
  • Infinity
    I'll defer to your experience. My understanding is that what I said holds for classical convergence in Real Analysis — Banno

    Keep up the good work!
  • Infinity
    For a convergent series the sum is defined as the limit. There is no residual “infinitely small difference” between the sum and the limit. The sum is the limit. Partial sums are less than the limit, but their difference goes to zero in the standard real number system — Banno

    There is a branch of mathematics called Numerical Analysis which, among other tasks, attempts to predict how far out one has to go in an infinite expansion to achieve an approximation of the limit to a specified degree of accuracy. I wrote some papers about this topic concerning continued fraction expansions. For example:

    https://www.researchgate.net/publication/303490331_An_error_estimate_for_continued_fractions

    There are various infinite expansions beyond sums: Infinite series, infinite products, infinite compositions, infinite continued fractions, etc. as well as infinite sequences arising from other algorithms.
  • Infinity
    How could "the next step" not imply "a thing happening in time"? — Metaphysician Undercover

    Good point. Does a typical mathematical sequence imply motion in time?
  • Infinity
    So apples are countable, but numbers aren't. — frank

    :joke:

    Oh oh, the set {1,2,3} has 3 numbers. :gasp:
  • Infinity
    ↪Banno
    As I have mentioned before, the interpretation I have used for years is that infinity means boundlessness, not a cardinal number. As for transfinite entities of greater cardinalities than the reals, I have encountered only one theorem in functional analysis that requires their use - and even there by altering the hypotheses a tad one escapes that situation.

    There is a "point at infinity" in complex analysis that arises when the complex plane is mapped onto the Riemann sphere. But it is simply the north pole of the sphere.

    I wonder if and when physics will find uses for transfinite objects. Perhaps it already has.
  • The Death of Local Compute
    I once used VB6 to design and run programs on my computer, but one day it was gone from my computer, taken away by Microsoft. In its place was a cloud based language that seemed incomprehensible. I found and bought Liberty Basic - no subscription.

    I also used Mathtype, purchased and installed. Nowadays when I open it up it tries to get me to subscribe to the latest version.
  • Infinity
    Again, this is wrong. The incoherence is internal to mathematics. The notion of "infinity" used by mathematicians themselves, is contradicted by the predication they make, when they propose a "countable" infinity — Metaphysician Undercover

    countable

    It all depends on how one defines "countable"
  • Infinity
    ↪Magnus Anderson
    The sets {1,2,3,...} and {2,4,6,...} are in one to one correspondence, satisfying the acceptable mathematical notion of "same size". But what happened to the odd integers in the second sequence?

    Read a math book or two.
  • Is there anything that exists necessarily?
    There is a broader notion of necessity as what is true in all possible worlds - that two and two is four. — Banno

    (2+2)mod3=?

    There are theorems in math having hypotheses that are both sufficient and necessary.

    Just nit picking.
  • Merry Christmas and Good Luck!
    ↪javi2541997


    A really nice gesture. Happy holidays, my friend!
  • Let's quantify phenomenology!
    ↪Pneumenon
    Reading this the first time, what comes to mind is a circle with a number of radii, each one a quality. Then a phenomenon corresponds to a curve on the interior of the circle, passing through each radius once. When the phenomenon changes slightly the curve is shifted slightly. A real number scale on each radii then provides a sequence of real numbers that "describe" the phenomenon. If the qualities are entirely separate then a shift in one doesn't affect the others.

    On further thought, a simple functional scale might be better, with the horizontal axis the various qualities and the vertical axis the number corresponding to those qualities. If the qualities were to form a kind of continuum, then elementary calculus might be possible. Who knows.

    Spaces and manifolds seems a tad esoteric in this context, with number scales somewhat abstract.

    Just off the top of my noodle.
  • Is there a right way to think?
    It is normal for me to think of both sides of an argument, not because I want to, but it just happens. — Athena

    I, too, have this personal trait. Particularly in political conversations. But also as a mathematician, attempting to conjure up counterexamples before committing to a lengthy proof.
  • Should People be Paid to Study, like Jobs?
    jgill, do you even know about socrates? He wasn't a mathematician. So, this is actually expected: you specialized in mathematics, and you didn't read what I said carefully enough to ask yourself what i meant by a "socratic role of constant truth seeking".

    Let me help you: legend has it that Socrates conducted his philosophy not by studying quietly, but by questioning people in dialogues. If you don't wait your turn to speak in a university setting, people largely just consider you to be a pain in the ass, and according to the stories about Socrates, that's what happened to him, and apparently he was given a death sentence for it. Part of this was because he didn't succumb to pressures to only speak about and discuss one subject matter, he was interesting in much broader and ephemeral ideas than mathematicians. He was mostly interested in particular ideals, such as justice.     — ProtagoranSocratist

    Of course I know what the Socratic method is. I encouraged dialogue you describe in my classes. But teaching math requires transmitting specific ideas, hopefully encouraging dialogue. This was rarely the case in beginning courses, but more advanced topics available after the student absorbs the basics provide a setting for discussions. And, yes, math is less ephemeral and much more focused than what you must have in mind.

    If you don't wait your turn to speak in a university setting, people largely just consider you to be a pain in the ass, — ProtagoranSocratist

    Or very impolite at best.
  • Should People be Paid to Study, like Jobs?
    They are valued because they cannot be bought, and it's pretty hard to give people money for intellectual work without biasing that intellectual work (although we do try, and one example would be university tenure). — Leontiskos

    Of course, professors are given tenure because their work upholds the goals of the institution: a professor will never be given tenure if they play a Socratic role of constant truth seeking. All institutions are fairly political in nature.     — ProtagoranSocratist

    Oh, baloney. I got tenure and a full professorship fairly quickly while periodically publishing on virtually any topic I wished as a mathematician - constant truth-seeking. I suspect you are referring to the Humanities, where political or politico-philosophical cliques abound. And perhaps the elite institutions. I taught in a branch of a state university.
  • Why Not Nothing?_Answered
    ↪ucarr
    In your mathematical analogies do you consider "0" to be nothing (in some sense)?
  • Ennea
    I chose 9 because it has a symbolic significance of finality.

    Explain, please.     — Dogbert
  • How LLM-based chatbots work: their minds and cognition
    Pardon me for breaking in, but as a retired professional mathematician I have observed in short conversations with Chatgpt what I would otherwise guess to be original thinking. The topics were far out of the popular realm and involved extending a process into new territory. I was impressed. But I realize caution is advisable.
  • What Difference Would it Make if You Had Not Existed?
    A nullification of the butterfly effect. — jgill

    It strikes me as wishful thinking or a useful narrative device rather than a genuine possibility.     — Banno

    (From a personal perspective, someone would have come along a little later and advocated turning rock climbing into an athletic, gymnastic sport. No question.)
  • What Difference Would it Make if You Had Not Existed?
    It's a little off topic, but Stanislaw Lem, the Polish SciFi author, had a theory of alternate histories that dealt with events rather than individuals. Social events, such as the rise of the Nazi party would not be eliminated by simply requiring Hitler to die, let's say, when a teenager. Or not be born. The effect of a single life would be absorbed and discarded as time rolled on. A nullification of the butterfly effect.

    I can't find a reference, but recall seeing this some time back.
  • What Difference Would it Make if You Had Not Existed?
    ↪Jack Cummins
    The Butterfly Effect carried to unimaginable complexities. Nature is a fantastically intricate dynamic system. The effect of not being born moves both ways in time and looking backwards brings up whether time actually has a beginning.
  • Psychological Impact of the Great Depression
    ↪Athena
    My father didn't know his father who died in a mining accident about 1912. Dad had several siblings but he was the only one to leave the coal mines behind. He had his mother save his pay for tending the underground donkeys and after he graduated high school he attended Penn State for a year, then went into the deep south to continue his education, working as a campus cop to support himself.

    Dad's mother was a resourceful woman. She turned her shotgun house into a small grocery store and supported herself and her children for years. The store was still open in the 1960s. She lived to 94 or so. I only met her once when we drove from Alabama to Pennsylvania for a visit in the late 1940s. That was considered a big deal and the local newspaper had an article about our adventure.

    I don't recall either of my parents complaining bitterly about the Depression. They minimized their needs and adjusted as best they could. When WWII came along Dad was offered a commission in the Navy, but he had a health problem and turned it down. After the end of the War he became chief statistician for the War Assets Administration for a brief period. Then on to academia.
  • Psychological Impact of the Great Depression
    My mother, a Southern Belle from Alabama, and my father, from a coal mining town in PA, were both born in 1910. My father became an academic but in high school he worked nights in a coal mine taking care of the donkeys and doing his homework.

    The only time my mother worked was when Dad was getting his final grad degree at the U of Texas around 1950, and she played the piano for a womens' PE class. At the height of the GD one summer Dad got a teaching job at a small college in Arkansas where he was not paid but given room and board. Mom and Dad would happily reminisce about the huge bowls of grapes at each meal.

    Mom was quite content with her role as wife and mother (just me), although she had a BA in education.
  • please advise me
    There may not be a lot of interest in the GD here. I was attracted to the thread because I was born during that time and have vague recollections from pre and early WWII days. I suggest letting it ride the Front Page wave and see if it passes away at the bottom or is revived.
  • Psychological Impact of the Great Depression
    I was glad when my X left and filed for divorce, but I don't see that as the best possible outcome for the family. From my point of view, men thought women's liberation meant they no longer had family responsibility. They walked away, leaving the women with hurt and angry teenagers. I don't think that was a good thing. Today, it makes my heart happy to see a man in the park with his children. I am hoping the younger men are better husbands and fathers than when there was too much division between what men and women did. — Athena

    I insisted on custody of our 9 year old daughter. My ex wife spread her wings and did well, now married and retired. My daughter is business manager of a large academic/professional school in a institute in NYC. She will retire in the next few years, as will her husband.

    When you are handed lemons make lemonade.
  • Identification of properties with sets
    Pardon the intrusion. I haven't read all the posts. You have a set {1,3,5} , and then you have another set that has as elements the properties shared by the elements of the first set. If this derived set is a singleton, then one could identify the elements of the first set.

    Not really set theory, otherwise we would need TonesinDeepFreeze.
  • Psychological Impact of the Great Depression
    ↪Athena
    I was born during the Great Depression. My parents became very frugal, and I have always been conservative in my wants and needs. Except my father went to town one day and bought a new Buick sedan (1938) for about $900.! My mother never forgave him for that. But I learned to drive in that car 13 years later.

    I am reading my post, and I am thinking, women's liberation happened! — Athena

    Indeed it did. My wife fell under its spell and I supported her by attending meetings with her. As frequently happened during that time we ended up divorcing. We drew up the papers ourselves. It was painful at the time, but good for both in the long run.
  • What is a system?
    For what its worth I'll toss in a definition of a mathematical system:

    "A mathematical system consists of:

    A set or universe, U.

    Definitions: sentences that explain the meaning of concepts that relate to the universe. Any term used in describing the universe itself is said to be undefined. All definitions are given in terms of these undefined concepts of objects.
    Axioms: assertions about the properties of the universe and rules for creating and justifying more assertions. These rules always include the system of logic that we have developed to this point.
    Theorems: the additional assertions mentioned above."

    Al Doerr & Ken Levasseur
    University of Massachusetts Lowell
  • Time_Distance_Dimension
    Within an infinite series, you can keep changing the scale of your numerical progression so that you'll never exit a bounded infinity. Enlarge the scale and you immediately exit the bounded infinity. Might this be the way out of Zeno's Paradox? — ucarr

    Are you talking about a series or a sequence? What is a bounded infinity?
  • One Infinite Zero (Quote from page 13 and 14)
    ↪jgill
    I also find it hillarious that you claim to be a mathematician yet have no idea about fundamental truths in physics which I mentioned earlier. This must be a parody.     — Illuminati

    You mean the sacred nature of OIZ ? This is a fundamental truth? This sounds more like a cult.

    One can appreciate the theories about the origins of the universe without worshiping them.
  • One Infinite Zero (Quote from page 13 and 14)
    You are going off topic because you have no arguments — Illuminati

    Astute of you. True. How does one argue against the magic of "0IZ" ?
  • Time_Distance_Dimension
    "Infinite series" caught my attention.
  • Time_Distance_Dimension
    A dimension is a time-zero unification of an infinite series from a baseline dimension upwards to the next higher dimension — ucarr

    You'll have to be more specific. Put this in math terms.
  • One Infinite Zero (Quote from page 13 and 14)
    The One means that there is no other One, it is Unique and Simple. It is composed only of itself and it is Alone and All-one (everything and everyone) — Illuminati

    I am very old. I apologize, but when I read something like this I tend to fall asleep. Is this supposedly enlightening? Is there a Zen moment of Aha!! ? Why do you write something like this over and over? Does meditation help making this pronouncement astounding?

    Finally, why is this on the forum page and not in the Lounge? Moderators?
  • Bannings
    ↪Baden
    Very appropriate. It was trying keeping up with the many non-properties of nothingness.
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