uncool

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Everything posted by uncool

  1. My argument against the Riemann hypothesis

    The linked paper is...very bad. The first thing I'd require correction for is the statement about why the Riemann zeta function is interesting. It's not interesting "because we can’t be sure if it is the correct analytical form of the continuation". It's interesting because of its properties. Second, you never define "nontrivial zero". What are the trivial zeroes? Third, your notation should use a backslash, not a forward slash, to denote "Remove these". The forward slash denotes "Take these things as equal". Fourth, the domain of zeta includes points with theta = pi. Most famously, zeta(-1) = -1/12. Fifth, the extended complex plane is (as you say) equivalent to the sphere (though I have no idea what you mean by "up to a complex phase factor"), so it is not the union of the sphere with "i". Sixth, the Riemann sphere is not the extended complex plane minus a ray. I haven't left the first page and I've caught 6 things that each indicate some basic misunderstanding of the Riemann hypothesis. I rather heavily doubt you have disproven it.
  2. functions

    In terms of set theory, a function is a set of ordered pairs (x, y) such that for each x, there is a some unique y such that (x, y) is in the set.
  3. The magic i

    Um. No? cos^2(90 deg/pi) = cos^2(1/2) ~.77 is not 4/5 = (2/sqrt(5))^2.
  4. Dark matter is Negative mass!

    I have, too, although I'm not spelling it out here in case swansont was trying to get more information from icarus2. Suffice to say: any algebraic mechanical equation satisfied for arbitrary positive masses remains true when one or more masses are negative. This is a mathematical fact about real numbers (from algebraic geometry). Conservation of kinetic plus potential energy is such an equation. It has some unexpected consequences that are likely to be unphysical, but I repeat that the math does work.
  5. Dark matter is Negative mass!

    I a honestly uncertain here as to whether you are making a deliberate error here to test icarus2, but you have made an error. There is nothing wrong with the idea of negative mass on a purely mathematical level, and conservation of energy in a situation like the one you posed can be expressed purely mathematically. There may be physical problems (and I think there are), but purely theoretically negative mass does not contradict any mechanical conservation laws.
  6. Dark matter is Negative mass!

    The forces may be the same, but wouldn't the accelerations be reversed?
  7. Square Through Squares

    Strange - it doesn't mean max. It means number of lattice points in a rectangle with the two given dimensions. This gives the formula "(Ath Sq. on X-Axis) * (Bth Sq. on Y-Axis)" = (A+1)*(B+1). For example, mathspassion, am I correct in saying that (2nd Sq. on X-Axis)*(4th Sq. on Y-Axis) = 15? I don't know what you mean by "how this formula came into existence"; I have provided a geometric proof (or at least, the summary of one), which is what you asked for.
  8. Square Through Squares

    To see it more geometrically, you can see the (N - 2)^2 as a square in the center of the N^2 square. Then you can divide up the "border" into 4 parts. Each will have N - 1 points.
  9. Square Through Squares

    The idea was that the * the OP was using denoted the largest number gotten when labeling the vertices of a lattice inside a rectangle of the two given side lengths. So the 3rd square *3rd square denotes the largest number gotten when labelling the vertices of a lattice inside a 3 by 3 rectangle, as shown in the picture. But once we have that, it's not hard to see that that is equal to (A + 1)(B +1), where A and B are the "number of squares". So, translating the formula, we get N^2 = (N-1)(4) + (N-2)(N-2).
  10. Square Through Squares

    If I'm not mistaken, this is a rather long assertion of the fact that for any N, 4 (N - 1) + (N - 2)^2 = N^2.
  11. Taking GR as a classical (non-quantum) theory: The answer to the question should be: what do you mean by "the same path"? The assumption in that principle is that the "path" doesn't care about time. Which is fine in a classical (non-curved spacetime) world, but breaks down in GR.
  12. Zero Element Equivalency

    Heh. I thought it was suspiciously similar, but forgot conway had been banned.
  13. Zero Element Equivalency

    You're providing more equations, but not answering the ones I have. If you dispute my equations, which of these is wrong? Does 1 = n/n? Does n/n = (-0)*n/n? Does (-0)*n/n = (-0)?
  14. Zero Element Equivalency

    We can then divide by n: 1 = n/n = (-0)*n/n = (-0) where the first and last equalities are from the fact that division is supposed to "undo" multiplication, and you've already agreed to the middle one. But I just noticed something I'd consider worse: you have the equation 1*(-0) = 1. The main reason 1 is important is that it is the multiplicative identity, that it multiplied by anything is that thing. Breaking this pretty much breaks multiplication, and makes inverses all but useless.
  15. Zero Element Equivalency

    The statement that inverses are unique is not a postulate, but a theorem. You have to break more than that statement to get things to work. For the proof that 1 = (-0): n = (-0) * n/(-0) = (-0) * n, right?
  16. Zero Element Equivalency

    The term "unique" in mathematics means only one. If you can't use the normal rules of equality, why use that version of equality at all? Do you agree that (-0) * n/(-0) = n?
  17. Zero Element Equivalency

    Actually, the fact that multiplicative inverses are unique is a basic fact. If n/(-0) = n, then under the usual rules of equality, we can multiply both sides by (-0): (-0) n/(-0) = n (-0). The usual definition of division then tell us that (-0) n/(-0) = n. We therefore have that n = n(-0). Finally, we can divide by n, and get 1 = (-0). So for what you are saying to make sense, you have to deny either: the ability to multiply both sides of an equation by the same number, the definition of division, the ability to divide both sides of an equation by a nonzero number, or transitivity of equality.
  18. Zero Element Equivalency

    If 0 + 0 is not equal to 0, then 0 doesn't have the property of being an additive identity (with respect to that equivalence relation). 1 already has a multiplicative inverse: 1. If n/(-0) = n, then it's not hard to deduce that (-0) = 1, unless you are assuming that = has very few properties in common with what we usually think of as equality. In short, your idea takes away many of the things that make fields useful in the first place.
  19. General topology

    I'm guessing they mean the product in the infinite product of the real line. Have you tried applying the definitions of the two topologies?
  20. Size & Gravity - Is General Relativity Incorrect?

    No. Newton's laws are still accurate for liquids and gases; the only difference is that they have to be analyzed through densities (note: not necessarily mass densities). The laws are still accurate. Because the sun is much, much, much, much closer than anything else in the galaxy. It's not because the Sun is more dense. It's that everything else is really, really, stupendously far away - so Newton's law of gravitation says that the corresponding force is tiny compared to that of the Sun.
  21. Size & Gravity - Is General Relativity Incorrect?

    The forces are, by Newton's third law, equal (and opposite). The accelerations are inversely proportional to the mass, by Newton's second law - so, as an interstellar cloud will generally be more massive than a planet, the planet's movement will be more affected. If you believe otherwise, then you are rejecting Newton's laws. Let's take interstellar gas out of the picture for a moment (as that runs into definition issues - interstellar literally means "between stars"). Instead, let' focus on galaxies. Yes, I have heard of stars orbiting galaxies (or, more precisely, orbiting as part of a galaxy). The closest thing to your statement is that, say, the acceleration of the Earth is more affected by the Sun than by the galaxy. Is that what you are trying to talk about?
  22. Size & Gravity - Is General Relativity Incorrect?

    What, precisely, do you mean by this? I think this is central to your claims.
  23. Size & Gravity - Is General Relativity Incorrect?

    Two things. 1) There is no part that says that; it isn't even true in general. More specifically: there are systems of objects where one object is not attracted towards the center of mass, but instead towards a nearby mass. This is clearest, for example, in the Sun-Earth-Moon system; the moon is attracted to the Earth, not to the center of mass of the Earth and Sun. 2) In the case of an object being attracted to a massive (that is, having mass) sphere, that in't separate from Newtonian gravity. It's a direct consequence (via the shell theorem, as Mordred says). As such, do you reject Newtonian gravity?
  24. Size & Gravity - Is General Relativity Incorrect?

    My apologies - I mistook your enthusiasm for that of the newly-"initiated". Good on you for keeping up that enthusiasm! I would say that even in the OP, the thread should clearly have been at the level of Newton's laws, and simple integration. I think that there already as a problem just with intrinsic vs extrinsic properties, as I plan to explain.
  25. Size & Gravity - Is General Relativity Incorrect?

    Unified Field: how much of standard physics do you accept? Do you accept Newton's laws? Newtonian gravity (as a nonrelativistic approximation)?