Comments

  • The No Comment Paradox
    Why then is there this trend to say "no comment" when silence would've achieved the same thing?TheMadFool
    Silence does not achieve the same thing (even in an online one-on-one conversation).
  • A copy of yourself: is it still you?
    In both cases what decides the identity of the person is memory.TheMadFool
    Of course this is wrong. If the 3D printing process created two persons, both believing being original, which one would you be after awaking?SolarWind
    But nothing is shown wrong by your question. Per the principle they are both "you". But being separate beings, they are different from each other. There's nothing contradictory about it; just as your body has been copied, so has your identity been copied. Now there are two.
  • A copy of yourself: is it still you?
    That is why it was stated that a person is NOT JUST the sum of the particles that make up the person, but it is obvious that they are included.Sir2u
    Actually, no, it's not obvious. Why is it obvious to you?
    The memories and experiences are not all of it either, a person is made up of both molecules and memories.Sir2u
    But being made up of molecules does not entail being a particular set of molecules. A river is made up of molecules, but is certainly not a particular set of them.

    From a subjective perspective, we can easily say we're different persons because we have different points of view. I see what I see not what you see, and vice versa. We can also claim to have an identity across time due to memories of points of view; I remember seeing what that guy who stepped into the kitchen in the last post saw, you do not. So I'm the same guy that stepped into the kitchen in the last post. You aren't that guy.

    Everything I described matches the heart of what these teletransporters (and apparently 3d printers now?) are wanting to get at... personal identity. Were it not for such inconvenient philosophical devices, our identities would simply be tied to our bodies that age from birth to death. But those bodies are living beings; furthermore, we're energy hungry mammals. As such, it's incredibly reasonable to say that this identity-having, identity-maintaining thing that goes from birth to death, which is what we're talking about, is a slow moving stream of molecules, not a lump of them.
    Therefore they cannot be the same person because Person #2 does not have the experience of going into the machine.Sir2u
    Applying the principles above, Person #2 has a distinct point of view from you, so you and Person #2 are different identities. Person #2 remembers being person #1, so Person #2's personal identity connects to the past entity you're calling Person #1 in the same way my identity right now connects to the identity of that guy that walked into the kitchen in the last post. Therefore, per this principle, Person #2 does have the experience of going into the machine.
    Another part of you is actually changing as you grow old, your reconstructed body would be brand new but aged according to the old one. In the art world that would be called a fake.Sir2u
    But a person is a living being not a sculpture.
  • The paradox of Gabriel's horn.
    It seems like you're having the same difficulty with the word "absolute"Metaphysician Undercover
    Actually, it seems you're having problems with the word "acceleration". If an object at rest remains at rest, it is ipso facto not accelerating. Likewise, if an object at rest accelerates, it ipso facto starts moving. But somehow in MU land, absolute means something can stay at rest and still accelerate, so long as it's not accelerating infinitely. Whatever that means.
  • Psychology experiments
    People seem to make up stories as to why they do things and "believe their own shit" so to speak.Gregory
    I think we're talking about different things then. Or not. In your reporting of these experiments, people are confabulating. It's completely untrue that they saw the image "yesterday"; rather, they saw the image moments ago. But what appears to be true is that they were influenced by seeing an image, and their self report of why contains the account of seeing an image.
    Since no one so far has referenced studies in this area, it IS hard to discuss this further nonetheless.Gregory
    Yes; it would be interesting to see the studies. I'm solely describing the report you have given; if you run across particular citations of the experiments I'll be interested (though reserve the right not to comment).
  • Psychology experiments
    Sam Harris mentions these types of studies at the end of this short video:Gregory
    I think you have the wrong video... I've played through this and there didn't seem to be any references to such experiments in them.
    People, just as they feel like they have complete free will, also feel like they know what exactly why they are recalling ideas. However,Gregory
    But the conflict that I'm seeing has nothing to do with a feeling of complete free will, or feeling of knowing why exactly we do things. There were two statements that I quoted. The first claimed that the images were being flashed too quickly for subjects to consciously process. But in the second, the subjects correctly report their motivation of naming that animal as being based on seeing an image of the animal. (Mind you, they incorrectly report the time, but you're not claiming for example that they remember eating chicken last night, or reading about chickens, or watching cartoons about chickens, or having a pet chicken when they were little, or any of a number of alternate potential triggers).
    Maybe the signal made the subject's brain think of chicken and in the subjects mind he remembered something about chickens and believes this alone was the reason.Gregory
    This does not explain why the subject's report is of seeing an image of the chicken.
    However, they are becoming very sophisticated in science where they can tease out these factors and know when something is known (by the subject) subconsciously only and when it's in the conscious mindGregory
    The conflict I see gives some reason to doubt this very thing. Whatever speed these subjects were flashed those images, it was apparently sufficient enough for them to self report seeing images.
  • Psychology experiments
    Anyway, if large such experiments do exist just as here explained, what do you make of them?Gregory
    Well for starters I would like to point out that:
    Basically the experiments flashed images of animals in front of people at a speed they could not consciously process.Gregory
    However each time they were asked why they named that particular animal they said "because I saw a picture of it the other day" or something and very seldom said "i don't know".Gregory
    ...these two things seem to conflict.
  • The paradox of Gabriel's horn.
    Instead of addressing the problem which is the question of what causes the appearance of an infinity,Metaphysician Undercover
    ...and what is that problem?
    the mathematicians create a "fix" to deal with the infinity.Metaphysician Undercover
    ...and how are you fixing that? And why should we trust a guy whining about lack of reality when it's the same guy who claims it takes an infinite amount of acceleration to move an object at rest?
  • The paradox of Gabriel's horn.
    Amazing, the things which mathematicians will come up with, in an attempt to solve their problems, instead of simply recognizing that the dimensional representation of space is wrong.Metaphysician Undercover
    An infinite acceleration is required to go from rest to moving.Metaphysician Undercover
    Nothing more need be said. But it will be said anyway.

    Incidentally, GR and SR use dimensional representations of space. This includes with GR the use of Penrose diagrams, which have multiple infinities.
  • A copy of yourself: is it still you?
    So please enlighten me how it was possible.Sir2u
    Sure. Let's backtrack.
    The "person" is not just the total of the atoms that are arranged to form them.Sir2u
    Call this statement A. I find this statement acceptable. In fact, a person isn't comprised of the same molecules over time; the act of living involves the exchange of molecules (and atoms) with the environment.
    The person is the result of the years of experiences and knowledge acquired.Sir2u
    Call this statement B. I also find this statement acceptable. A person as an agentive entity will in the "approximate now" have experiences. The person through time will notably acquire knowledge and experiences in the form of memories that are shaped by those experiences.
    Person #1 walked into a machine, but never walked out of the other machine. Person #2 is not the same person as Person #1 because he has been reconstructed in in the shape of Person #1 but in a different place and from different molecules.Sir2u
    It's here where I see problems. The first statement here conflicts with statement A; it seems to suggest that a person is just the total of the atoms arranged to form them.

    Also, given the problem statement in the original post, it's quite reasonable to presume that Person #2 would have the same memories as Person #1; i.e., that Person #2 would have the same acquired knowledge and "remembered" experiences as the person who stepped into the machine (Person #1). Under that reasonable presumption, your second statement conflicts with statement B; Person #2 would be a result of the same experiences and knowledge that Person #1 (again being the person who entered the machine) had.

    Also, I find the "different place" thing a bit confusing. I just walked from my kitchen to my desk. I had and acquired some experiences in my kitchen; now I am having experiences at my desk. But obviously I'm in a different place at my desk than I was when I was in my kitchen. I don't think you're presuming I'm a different person at my desk than the person in my kitchen moments ago, but according to the argument you just gave, you're arguing that Person #2 is different than Person #1 because Person #2 is in a different place... perhaps you're missing a time element in your analysis?
  • A copy of yourself: is it still you?
    It is obvious that the person stepping out of the machine never experienced going into it, and the person going in has no experience of getting out.Sir2u
    That's not obvious to me.
  • Free will
    Can you see these other worlds posited by MWI?Olivier5
    MWI doesn't posit that everything you can think of happens. You need to show there actually is a part of the universal wave function with unicorns on it; otherwise you're just fantasizing. It's the same speculative leaps you would have from positing if there's a planet somewhere in the universe with unicorns on it.

    What is the point of this discussion? If you're trying to convince me that MWI is incorrect, you're kind of bypassing everything I hold to be relevant. I think the proper criteria for that (along the view you're arguing) is to show that the SE and the BR is ontic; I don't know how to do that, but certainly arguments from absurdity about universes with flying unicorns are irrelevant.
  • Free will
    Have you considered that quite a few among this infinite number of invisible universes posited by the MWI may contain at least one unicorn, and that these unicorns would then be invisible to us?Olivier5
    Sure, one of those worlds may contain a unicorn, but it would have to be shown that it does to meaningfully discuss it; same with the flying. As for the invisibility part, that sounds like an amphiboly. I've never seen my liver either, but I don't think I can call it invisible based on that.
  • Free will
    All sorts of funny competing hypotheses are consistent with the facts, including that of invisible flying unicorns. But quite often, one of them competing hypotheses is simpler than the others... and it's often the one that assumes the less.Olivier5
    Yes, Oliver5, it is a false equivalence.
    • Invisible (<- assumed property) flying (<- assumed property) unicorn (<- assumed beast).
    • Schrodinger's Equation (<- evidential) + Born Rule (<- presumed)
    • Schrodinger's Equation (<- evidential)
    You're rationalizing it this way, best I can tell:
    • Schrodinger's Equation (<- evidential) + Born Rule (<- presumed)
    • Schrodinger's Equation (<- evidential) + infinite numbers of worlds
    ...but those worlds, again, are already there. They come from that SE part; if you haven't measured exactly where the particle is, there's an amplitude for all possible paths. The Born Rule, as an ontic premise, is positing in addition that there's a process whereby, at some undetermined point, a bunch of those worlds disappear.
  • Free will
    Concluded from an assumption, therefore assumed as well. This is nitpicking.Olivier5
    No, it's accuracy. What you're doing is spinning. The key question here isn't whether we should assume multiple worlds; it's whether we should assume the Born rule. Technically, the multiple worlds are there anyway; they're in the wave function. The photon goes through the left slit and it also goes through the right slit. Think also path integrals and Feynman diagrams.
    And I question the presumption that a new me is born everytime an electron in me changes its orbit. Call me crazy.Olivier5
    It's not craziness, it's just not science.
    Of course. It's also consistent with the existence of invisible flying unicornsOlivier5
    This is a false equivalence. We have good evidence that the Schrodinger equation works. We don't even have a model for when Born rule actually applies (i.e., the measurement problem).
  • Free will
    It assumes the existence of an infinity of worldsOlivier5
    That's incorrect; MWI doesn't assume the existence of an infinity of worlds. Refer to Everett's seminal work "The Theory of the Universal Wave Function". Everett notes that the Born Rule (in the introduction, this is "Process 1") is arbitrary and suspect, and lays out an argument for it. Based on this he tosses the rule out, keeping the Schrodinger Equation ("Process 2"). From here the "many worlds" arise; but they arise from "Process 2".

    IOW, the many worlds are not assumed, they are concluded.
    But the MWI is a ridiculously expensive hypothesis.Olivier5
    It's pushing risk intolerance a little to far in my view.Olivier5
    At this point you're not practicing science.
    How do you control which universe you end up in?Olivier5
    That question presumes that there's an "authentic" identity, and that the issue is to get the "authentic" one to be in the universe you like. I question that underlying presumption.
    The degree to which the MWI is actually usable, practically speaking, in offering greater control is highly debatable.Olivier5
    If it can't, what good is a formally deterministic theory which gives us no additional control? How is it even testable?Olivier5
    That sounds a bit backwards... suggesting that we start at our favorite pet theories of free will, then go looking to science to find justification for it.
    I'd rather go where the data leads me: there is only one world that we know of, and undetermined events happens in it.Olivier5
    But that winds up with two fundamental mechanics in QM instead of one; and one just merely being a result of a guess. Maybe it's a good guess, but it appears unnecessary as well. I would rather actually see evidence one way or the other. You might prefer to include that rule anyway, but don't pretend that's the data leading you... the data is perfectly consistent with both views.
  • Free will
    Except determinism makes enormous claims, like the idea that this post I am now writing was predetermined since the Big Bang.Olivier5
    The concept of "predetermined" is a bit broken. On a deterministic pool table, a cue ball hits a 6 ball, that veers off and hits the 8 ball, and that lands in a pocket. Given the state of the table, and that the cue ball started out with its motion, will the 8 ball sink? Of course it will; that's how determinism works. But predeterminism (especially in the sense applied here) seems to say something distinct, and kind of wrong... something akin to the fact that because the 8 ball sinks due to that cue ball, then the 6 ball had nothing to do with it. But of course it has something to do with it.
    Beside, science has decided on this issue. Modern science is undeterministic, on the whole.Olivier5
    Nope; that's just pop-sci myth. Science has not decided on this issue. Schrodinger's equation in quantum mechanics is completely deterministic. Indeterminism comes from application of the Born rule. Interpretations that propose the Born rule ontic tend to suggest indeterminism (and e.g. are susceptible to the measurement problem); but interpretations such as MWI that propose the Born rule emergent are still compatible with determinism. See the link I just posted to this thread. Which is correct? Nobody knows.
  • Free will
    I'm just saying that if you look at the history, Determinism was just a story concocted by some people with zero evidence to support it.MondoR
    ...that's too hyperbolic to be true. The development of the sciences suggest that the universe follows a set of natural laws. That suggests determinism at least to the degree that we can say there's more than zero evidence for it.
    Believe it if you want, but let's not pretend there is any science behind it.MondoR
    But that is meaningless. To hold that indeterminism is true because nobody proved determinism true is to hold truth to a double standard. If one should have to prove determinism to justify it, one should have to prove indeterminism to justify it.

    The science is not yet decided on the issue. So the rational thing to do, if you appeal to science, is to likewise remain undecided.
  • Free will
    People musing about possibilities. It's the nature of human existence.MondoR
    Sure. But you're a person, right? It's kind of like you're trying to tell people to believe you because, well, those other people, they're just being people.
  • Free will
    Interpretations, is basically a story.MondoR
    It seems very important to you to make sure people realize that everything here is just a story.
  • Free will
    All matter operates as probabilitistic, yet the myth of determinism goes on.MondoR

    https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Comparisons
  • The paradox of Gabriel's horn.
    They are outside the shape, irrelevant, and insufficient for measuring the shape.Metaphysician Undercover
    Your entire response is misguided. The limit is not describing a point in the shape. If it were, it would be an empty concept; the limit would just be a function evaluation. Take:

    The value of this piecewise function at f(1) is 8, as explicitly denoted. But:

    Despite explicitly talking about 1, which is explicitly defined by the bottom piece, the limit is about that top piece, which doesn't even have a value at x=1, nor is there an f(x)=2.
  • The paradox of Gabriel's horn.
    I didn't say anything about dipping below zero. Where did you get that idea from?Metaphysician Undercover
    From this:
    Is there any limit to how small the value can be? NoMetaphysician Undercover

    There is always an infinitude of values between it and zero, so it's really not ever getting any closer to zero.Metaphysician Undercover
    That does not follow. 1 is closer to 0 than 2 is, despite the infinite number of points between 0 and 1.
    Zero is off the scale, it's literally not part of the scale, as it is excluded by virtue of being impossible.Metaphysician Undercover
    I assume by off the scale you mean 0 will never be reached. But that's not required for 0 to be the limit.
    Since there is always that infinity of values between any given value of y, and zero, it makes no sense to say that it is getting closer to zero.Metaphysician Undercover
    Sure it does; but it's a bit more precise than this. The limit specifies that it's possible to get arbitrarily close to 0. "Arbitrarily" here is used in a strong sense that includes all positive distances at once.
  • Free will
    What do you mean it matters that you go to a doctor????MondoR
    I mean that the future state is a function of the current state, as opposed to fatalism, where the current state is irrelevant to the future state.
    It's already Determined. There is no choice.MondoR
    Why not?
    Determinism is a form of fatalism.MondoR
    Nope; there's a clear difference.

    Fatalism:

    Nostradamus predicts he and his host will eat the black pig. The host then orders his chef to prepare the white pig. As the chef begins to prep the kitchen, a wolf sneaks in and steals the white pig. The chef, left with only a black pig, prepares that.

    Nostradamus can say what happens and it must be true, because things are fated.

    Determinism:
    #!/bin/bash
    while true; do
       echo "Which letter will I pick, b or w?"
       read -rsn1 PROPHECY
       case $PROPHECY in
          B|b) echo "I pick W.  You lose." ;;
          W|w) echo "I pick B.  You lose." ;;
          *) echo "Neither?  I still pick B.  You lose." ;;
       esac
    done
    

    The outcome depends on the input. Nostradamus cannot win.
  • The paradox of Gabriel's horn.
    Are you saying that the paint on the outside is a cylinder of radius 1/3000 and infinite length and asking why that infinite amount of paint doesn't agree with the finite amount of paint needed to fill needle?Ryan O'Connor
    Almost; I'm talking about arbitrarily large but finite amounts of paint. And the only point here is that it's not really surprising this "outside" can be indefinitely long with a layer while the inside is limited.
  • Free will
    Just another form of fatalism.MondoR
    Determinism and fatalism aren't the same thing. An event that is fated will happen regardless of what occurs. An event that is determined happens because of what occurs. A classic example is that you're sick. If your future health is fated, it doesn't matter if you go to the doctor or not. If it's determined, it does matter.
  • The paradox of Gabriel's horn.
    Let's remove this necessity of a "real number", maybe that's what's misleading you. Is there any limit to how small the value can be?Metaphysician Undercover
    You seem to be imagining a hypothetical number "so big that" 1/x dips below 0. This sounds like speculative fantasy to me. Your reasoning that it dips below 0 could equally be applied to an imagined consequence that it levels off at and stays at 0, or that it rises again. There's basically no meaning to this.
    Perhaps you cannot claim that 1 ft3 can only paint 3000 ft2 of wall.Ryan O'Connor
    Those are loosely based on real numbers. A gallon of paint can paint approximately 400 square feet . A gallon is about 1/7.5 square feet.

    But thinking like an engineer, our really long Gabriel's horn is "mostly" "essentially" a negligible sized needle... the first portion that's much bigger is essentially a fixed amount of error. If our paint is 1/3000 feet thick (as the volume to area-covered ratio implies), then most of our paint on the outside is a cylinder with radius 1/3000. We could imagine this as if we're squeezing paint out of a tiny hole like a roll of toothpaste; in that sense, there's no limit to the amount of "paste" we can squeeze out of the tube.
    Consider the Stern-Brocot tree.Ryan O'Connor
    Already had that thread with MU.
  • Free will
    It's a series of meaningless, pre-determined outcomesMondoR
    Why does an outcome being determined make it meaningless?
  • Free will
    Your life is totally meaningless.MondoR
    Why?
  • The paradox of Gabriel's horn.
    This is not really what I'm saying.Metaphysician Undercover
    But that is really what's going on at 6:20; the ∞ there is the ∞ symbol of the upper limit of the integral, and it is a sentinel; a placeholder meaning unlimited. There's a notation here that requires filling in a spot for the lower limit and a spot for the upper limit. "Usually" you would fill that in with something like 1 and 2. To show you're doing this same kind of thing, but there is no upper limit, you put ∞ there. The 1/x comes from that integral.
    By saying that the one is infinite you say that there is no limit to how small the value of the other can be, and zero is an incorrect representation.Metaphysician Undercover
    You told me that infinite just means unlimited. Try taking that seriously for a moment. Don't say it's infinite, just say it's unlimited.
    By saying that the one is infinite you say that there is no limit to how small the value of the other can be, and zero is an incorrect representation.Metaphysician Undercover
    But there is a limit to how small the value can be; for any real number > 1, 1/x cannot be less than 0, whereas it can be less than any other positive real number. The limit is saying something similar... that the farther out you go, the closer you get to 0 (and that you can get arbitrarily close). The limit in its definitive form can be used to show that this is only true for 0; it is not true to say that the farther out you go, the closer you get to 1 billionth. It is only true to say that the farther out you go, the closer you get to 0 (arbitrarily so).
    What I think is that there is a fundamental incommensurability between two distinct dimensions of spaceMetaphysician Undercover
    Again, pi and square root of 2 are real numbers. So the spaces involved have those as coordinates.
    So if we look at the difference between a straight line and a curved lineMetaphysician Undercover
    From here down you're pontificating about physical space, which is not the space being used here.
  • The paradox of Gabriel's horn.
    Correct me if I am mistaken, but it appears you have tossed in AG to impress the readers of this thread.jgill
    This is a standard example from freshman calculus.fishfry
    I'm open to suggestions, but all I'm after here is a description of the space and the object. This is related to the conversation. This came up several times:
    Saying that 1/infinity equals zero is obviously an instance of rounding off.Metaphysician Undercover
    ...referring to 6:20 in the video. So MU thinks the process is to substitute infinity in, as one would do in a proper integral. The point being made here is that in contrast to the proper integral limit, the ∞ in the improper integral with infinite limit isn't even a coordinate in the space.
  • The paradox of Gabriel's horn.
    I don't see the paradoxRyan O'Connor
    I don't see the original paradox; a square foot of area has no meaningful volume.

    But the same exact questions arise in the finite scenarios. "If it's holding about 3.15 cubic feet of paint, isn't that already painting the inside? If so how come it takes 1000 cubic feet then to paint the outside?"
  • The paradox of Gabriel's horn.
    (all of which have a finite volume - and so there is nothing paradoxical about any of these horns).Ryan O'Connor
    ...is there? Back to "intuitive paint" based on real paint, 1 cubic foot of paint can paint 3000 square feet of wall. With that in mind, we can construct a Gabriel's horn with units of feet, chopped off at a finite length, such that it holds less than 3.15 cubic feet of paint, but takes over 1000 cubic feet to paint the outside.
  • The paradox of Gabriel's horn.
    Whereas one can describe the collection of points in 3-space comprising GH with the zeros of jgill
    And the lazier definition of it typically given, such as the one in the video, is that we start with the curve 1/x starting at x=1 and rotate it about the x axis. Then the resulting object we call GH (with the same "starting at x=1" specification). But that is precisely this object. And we're talking about this object, so it's relevant for that reason.

    So what are you on about jgill? And I mean that question literally; I have no idea what you're actually objecting to. Incidentally, no, calculus doesn't give us the GH paradox... broken intuitions do. I also find it a bit strange to claim that calculus is used to define the object; rather, it's used to analyze the object (surface area/volume in this case).
  • The paradox of Gabriel's horn.
    This is where your mistaken.Metaphysician Undercover
    Nothing you described justifies a concern about the length of tasks.
    The paradox assumes a spatial form, created from mathematical principles, and names this form Gabriel's horn.Metaphysician Undercover
    The spatial form is given by Cartesian coordinates with three axes at right angles; that defines a space where the set of all points are (x, y, z) coordinates with x, y, z being reals.

    Formatting for brevity.

    "You want to use the same numbers which create the form, to measure the form." If it works.

    "But when infinity is induced, this represents a failing in the capacity of the numbering system, so it is impossible to measure the form produced with the same numbers which produce it." That does not follow.

    "That's what happens with the square root of two, and pi." The square root of two and pi are real numbers. See above. Also, square root of 2 is not infinite; it's between 1.4 and 1.5. Pi is not infinite; it's between 3.1 and 3.2.

    This is your false presumption, which is misleading you, that "the quantity of volume 'on the inside' is finite". If you would approach the problem with an open mind, rather than with what I see as a false presumption, we could probably make better progress in this discussion.Metaphysician Undercover
    It's not a presumption; it's the result of a calculation. The fundamental issue here is that you're critiquing the methods without understanding what they are or why they are employed. Take your critique of Tom at 6:20 in the video for example. There, Tom is calculating the results of an integral. Tom has an improper integral, and this describes the method for its evaluation:
    — Paul's online notes
    When Tom says: "Well one over infinity, that's zero", that's okay, so long as we know it's a shortcut for:

    ...which is exactly 0, as shown previously by definition of that limit. You have confused this with saying that 1/infinity=0. That's baseless; infinity is not a real number; the domain of the integral is the same domain as the x axis, and infinity isn't even in that domain. The method isn't "plug in infinity", and there's a reason it isn't.
    I see that the spatial form which we are talking about, Gabriel's horn, is infinitely long. Therefore it is impossible, in theory, to precisely figure its volume.Metaphysician Undercover
    That does not follow.
    Will you justify your presumption that the volume is finite?Metaphysician Undercover
    That was already shown, and you're mischaracterizing the problem. The most fundamental problem here is that you're objecting to the efficacy of these methods without understanding what the methods are being employed or why they are employed. The other big problem is the obvious bias portrayed in objecting to the efficacy of the method before understanding these things.
    A spatial form which has an unlimited (infinite) extension in one of its dimensions, will have an unlimited (infinite) volume accordinglyMetaphysician Undercover
    That does not follow.
  • The paradox of Gabriel's horn.
    This has nothing to do with algebraic geometry.jgill
    What do you mean this has nothing to do with algebraic geometry?:
    Algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of polynomials, and the geometry is the set of zeros of polynomials, called an algebraic variety. For instance, the unit circle is the set of zeros of and is an algebraic variety, as are all of the conic sections. — Wolfram
    Gabriel's horn is the algebraic variety defined by the polynomial z^2+y^2=(1/x)^2 starting at x=1.
    G's Horn is elementary calculus.jgill
    Sure, you use calculus to analyze the surface area of and volume surrounded by this object, as they did in the video. But that doesn't preclude the fact that you're studying geometric properties of an algebraic variety.
  • The paradox of Gabriel's horn.
    A phrase is a bag?Metaphysician Undercover
    Yes.
    Come on Pitzotl, you're reaching for straws. Get back to the subject.Metaphysician Undercover
    But the subject is the paradox of Gabriel's horn; it's literally the title of this thread. Gabriel's horn is an object defined using algebraic geometry. Algebraic geometry defines points in a space using coordinates using number lines. Number lines are defined with real numbers.

    And that's what this bag is; it's the real numbers.

    Ironically, your accusation and your imperative to me to get back to the subject is itself an avoidance of discussing this subject.
    You cannot paint an infinite area regardless of how much paint you have, because no matter how much painting you do there is always more to be painted. ... Suppose you conclude it's 3.1 gallons,. You pour that in, but you haven't filled the horn because it hasn't reached the bottom.Metaphysician Undercover
    These are non-issues. In the paradox that is the subject of this thread, we're concerned primarily with the quantities not the length of the tasks. These are mathematical spaces; in the span of 30 seconds we define the entire infinite horn in an algebraic geometry space... doing infinite things is certainly not a problem here. Your imagined alleged problem has a lot more problems than you're letting on... the 3.1 gallons not going to the bottom is child's play. How are you upturning the horn in a gravitational field, and where do you put the planet? How does that planet manage to exert a field on the top of the horn anyway? But the biggest and most relevant question of all here is... do these really sound like mathematical questions?
    We're discussing Gabriel's horn not snowflakes. How my answer relates to a snowflake is irrelevant.Metaphysician Undercover
    We're discussing the presumed paradox of Gabriel's horn. The presumptions that appear to introduce the conflicts is the point of the thread. Those presumptions are based on the fact that the quantity of the surface are "on the outside" is infinite while the quantity of volume "on the inside" is finite... the "outside-ness" of the surface of which is really an irrelevant detail that is part of the intuitive distraction of using paint to compare areas to volume. You are presuming that the paradox is solved by questioning the volume, but you haven't even shown a good reason to doubt the volume much less the flaw in the presumptions leading to the paradox.
  • The paradox of Gabriel's horn.
    Yes, apply a limit to what is stipulated by the premise, as without limit. That is the mistake. Can't you see that it is stipulated that there is no limit to the length of the horn, therefore to apply a limit is to contradict the premise?Metaphysician Undercover
    I can see that you're equivocating. You're confusing "limit" as a method with "limit" as a point beyond which you don't go.
    You cannot put all the finite numbers in a bag, because there is an infinite quantity of them.Metaphysician Undercover
    The phrase "all the finite numbers" is itself such a bag.
    This example provides nothing of relevance.Metaphysician Undercover
    Of course it's relevant. The 1/∞ that you're whining about is the 1/∞ in the video at 6:20. Right? That 1/∞ is 1/x with ∞ substituted in it. That 1/x is the 1/x from . And that is from . And that is a Riemann integral; it's applied over the range where we want to take this volume. For Gabriel's horn, the lower limit here is 1, and there is no upper limit. To simply plug in infinity here as if it's a number is to say something different than what you yourself said in the prior post... that "infinite" simply means unlimited.

    According to the rules of the method being applied, this is an improper integral. For improper integrals of this type, the calculation for the infinite portion is performed using a limit, whose definition I gave earlier.
    It is stipulated in the Gabriel's horn example, that there is no lower limit.Metaphysician Undercover
    If there's no lower limit, then what's up with this big giant yellow arrow pointing to the lower limit during the segment where Gabriel's horn is defined?:
    https://youtu.be/yZOi9HH5ueU?t=56
    ...not to mention Tom saying straight up, "and what we do first of all, is we're going to chop it here at 1"?
    I did addressed this. If the horn can go infinitely thin, then so can the paint. They must play by the same rules.Metaphysician Undercover
    No, you didn't address this, because if this were indeed the case... if you could paint infinitely thin, then you can paint an infinite area with a finite amount of paint. And if you can do that, then there's no paradox. And you can do that, and there is no real paradox. But such infinitely thin paint simply becomes an empty metaphor... it's equivalent to what I was saying here. But you replied to that post saying that it wasn't the "real answer", and as recently as here you were peddling this one:
    The "real answer" is that the horn is, stipulated by the stated premise, as infinitely longMetaphysician Undercover
    But your proposed "real answer" doesn't address the extruded Koch snowflake, because that isn't infinitely long. The thing you're proposing isn't the real answer does address the Koch snowflake, because the infinite area on its perimeter is not a volume.
    Again, we're not talking about an infinite number of points within a confined space...This seems to be where your misunderstanding lies. You want to make this into an issue of a confined, "limited" space, but it is clearly stipulated that the horn is infinitely long, therefore there is no such confined space.Metaphysician Undercover
    You're reasoning by equivocation; "the extent is infinite, therefore the volume is infinite" simply doesn't follow.
  • Free will
    I'm not doing that - where have I done that?Bartricks
    Relax Bartricks... I'm not refuting you; you've been quoted as an example of someone who agrees with me. (At least wrt choice).
  • Free will
    I suppose my terms are that no decision is random ergo, no decision is truly free because it is the direct consequence of something that happened before.Barondan
    My personal view differs from the conventional in that I don't believe that free will should be concerned with the possibility of non-determinism, be it material or otherwise. It should be concerned with human agency.simeonz
    But there is no good argument for hard determinism. Here's the main argument:Bartricks
    So to Barondan, I'm quoting these other people for emphasis. There's a generic tendency to equate predictability of choice to lack of choice; but there's something mightily suspicious about this tendency.
    One common modern "scientific" argument against Freewill in general (not specifically religious choice) is the findings of Benjamin Libet's experiments on voluntary acts. A common interpretation of those results was to conclude that the body had already chosen to act before the mind became conscious of its own intention to act. Hence, "freewill is an illusion".Gnomon
    When you extend your notion of self to the very surface of your being, beyond the little homunculus we often pretend is there, you’ll find that the “outer forces” are often your own.NOS4A2
    To Gnomon (and Barondan), I think Libet's veto hypothesis is naive; there's a much more fundamental flaw in the will skeptic analysis based on the underlying presumptions. The general underlying assumption is that there's a "decision making" part of us, and that that "decision making" part must be the "conscious part" (this is what NOS4A2 I believe is talking about and calls the homunculus). But that violates even our own subjective experiences of how choices work. When I type a long sentence I generally type exactly what I mean to type, for example, but it doesn't subjectively appear to me as if I deliberate on the entire sentence. Rather, I'm only consciously aware vaguely of the intent, and of chunks of phrases coming to me as I type them. Somehow once the entire sentence comes out, it winds up following all of the rules of grammar and also winds up being what I meant to type. In other words, there are some problems with the generic presumption that the "consciousness" part of our mind is the "us" part. NOS4A2 I think is touching on this very thing.

    Barondan: I'm both sketching an argument and quoting others here who have their own thoughts to demonstrate that my views here aren't simply some pet theory I've come up with... there seems to be problems in the general free will debate with the underlying presumptions we make about the nature of choice and the nature of the self. The real point here isn't to convince you that free will works that way, but rather to convince you that you should be looking very carefully at the fundamental assumptions people tend to make by default and make sure those are actually valid.