I have been wondering for a while.There dozens of topics which prove the earth is round. But they all heavily rely on the vision of the person you proof it to. Is there any way, not at all relying on vision, to proof the earth is round?
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Assume you've come in contact with a tribe of people cut off from the rest of the world, or you've gone back in time several thousand years, or (more likely) you've got a numbskull cousin.  How would you prove that the Earth is, in fact, round?
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I've always hit two big stumbling blocks in conceiving of the proof or disproof of  as being even valid idea, let alone an answerable question... I feel I must be misunderstanding some very fundamental things.   Quantum mechanics is deterministic, ignoring the bit where we take our complex number and fudge it into a probability. We use computers to make calculations to provide the predictions of quantum mechanics - how is this not itself a hidden variable theory?   From what I understand the famous Bell theorem and work around it doesn't disprove hidden variable theories, just one specific flavour of them, and even then I am not convinced. I feel like I must be missing something again, because this result seems to me in no way profound... although it certainly fits into the picture of the EPR 'paradox' and is a good demonstration of the validity of QM.  I guess the crux of my problem is that this 'area' really addresses wave function collapse and the problems it causes, but I don't see the need for some collapse mechanism to begin with... again I feel like I am missing something really fundamental.  Apologies if this is a bad question. I have had a look around and there are similar questions, but I don't feel that either of my points are addressed...
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In my graph theory book exercise, I found a problem that:     Prove that the World is not flat using Mathematics     This picture is used in the exercise, but no idea of applying it.  I would have used the angles don't add to $180^\circ$, but the author is using a fourth city.
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When I composed my     I would have liked to have the camera pitch up enough to show the horizon, except I didn't have enough geometry to extend the cobblestone street and the sidewalk all the way to infinity (mostly because that would require infinite stuff).  Even in that shot it is clear that I need to widen the "sidewalk" to cover up the "sky"box.    Contrast with     where the ray tracer can use the procedurally replicated geometry.   is a failed attempt at faking out the horizon, even with low detail.  It fails because lighting's interaction with the geometry gives it away.  Some techniques that prevent you from having to deal with infinity include   put the scene in a box (usually a room) put the scene in a canyon (which is just a box without a top so you can see the relatively featureless sky) route the road into a tunnel, or around a corner and hide the horizon with other geometry (which is really just a variant on the canyon). have no detail on the ground at all (flat color or gradient)   Those are all dodging the question of interest to me:  What techniques have people used in blender to fake various kinds of detail repeating into the distance (instead of just obstructing the view of infinity)?
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The belief that everything is relative is obviously self-refuting, because it holds to an absolute.  However, in my experience, people who believe this (or some form of it) such as some Buddhists and atheistic materialists, or people who have an even more radical belief that permits no knowledge at all, such as nihilists, still actively resist those who suggest that there are at least some absolutes. In their discussing what reality is like and whether one idea corresponds to reality better than another idea, aren't they admitting that reality itself is an absolute and that at least one thing is absolutely knowable (a way in which reality is or is not, to which certain ideas correspond more or less closely)?  To put it another way, this very desire to show others that "some-absolute-truths-exist" is wrong seems to destroy their own "all is relative" or "nothing is knowable" positions. By taking a stance against any truth claim at all, they are making an ontological claim about what reality is not like and that this should apply globally—thus making a truth claim, admitting to at least one absolute. That seems ridiculously inconsistent, like someone going around and yelling at random passersby, "I'm not yelling at you!" and "You can't hear me yelling!"  I think that someone who believes in absolutely comprehensive global relativism (to me an impossible bit of nonsense, like square circles) has no business arguing with anyone at all. Any discussion they engage in cannot be intended to find truth together with their discussion partners, because they're either insane, lying, or the discussion was undertaken solely for their own pleasure—why else would someone who doesn't believe anything is true argue with you about whether something you think is true actually is? And pleasuring oneself in public at the expense of other people's comfort and in violation of basic human propriety (I don't know how to put this more delicately, it honestly seems like a very apt analogy) seems like a pretty reprehensible thing to do.  What kind of basis do relativists and their more extreme nihilist friends have for arguing against anything at all? And why do they seem to never, ever admit that when they do argue with others about the truth of any claim, that this is mistreatment solely in pursuit of their own offensive pleasure and amusement (since it can't be an attempt to discover truth, and their argument with the other person can't be an attempt to discredit an incorrect idea, since neither correct nor incorrect ideas exist)?
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If there are 5 points on the surface of a sphere, then there is a closed half sphere, containing at least 4 of them.  It's in a pigeonhole list of problems. But, I think I have to use rotations in more than 1 dimension.  Regards
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The origin of spin is some what a puzzle to me, everything spin from galaxies to planets to weather to electrons.  Where has all the angular momentum come from? Why is it so natural?  I was also thinking do photons spin? we always think of the wave as a standard 2d sin wave but could this rotate in 3d? What implications would this have?   And what about spacetime how does all the spinning effect?  This has always been avoided in all lectures and classes I ever went to.
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Someone posted a question on the notice board at my University's library. I've been thinking about it for a while, but fail to see how it is possible. Could someone verify that this is a valid question and point me in the right direction?  'Given an infinite set of points in a plane, if the distance between any two points is an integer, prove that all these points lie on a straight line.'
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As human beings, we observe the world in which we live in three dimensions. However, it is certainly theoretically possible that more dimensions exist.  Is there any direct or indirect evidence supporting a fourth dimension?
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I understand that you can (in principle) measure whether "free particles" (no forces) experience accelerations in order to tell whether a frame is inertial. But fundamentally, what determines which frames are inertial (i.e. what principle selects in which frames free particles will not appear to accelerate)? I've been told that the cosmic microwaves determine the ultimate rest frame of the universe, but that doesn't make sense to me, since one can still ask why that frame is an inertial frame.  Also, I understand that there are no real inertial frames in general relativity, but it seems like there certainly exists approximate inertial frames and we can ask why those frames are approximately inertial and not others. For example, in the frame of a person riding a merry go round, free particles appear to greatly accelerate; while in the frame of someone standing next to the merry go round there are no such great accelerations. Why does the guy (or gal) on the merry go round see free particles accelerating while the other guy doesn't.   And if you're gonna tell me that it's "the rest of the stuff in the universe" that determines whether the person on the merry go round sees free particles accelerate, I'll ask how you know that all that stuff is not spinning.  I hope this question sort of makes sense, it's been bothering me for a while and my study of relativity (most of special relativity and just the outline of general relativity) hasn't really clarified it for me much.
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In the following link () the authors are basically arguing that there are statements that we cannot deny without contradicting ourselves. Is it possible to prove that?   The initial reason that led me to ask this question is the following: Let us suppose someone asks you if you think it is possible for you to know something. If you reply "no", you contradict yourself. Is it possible to prove that it is impossible to deny such a statement without contradicting yourself? If not, what does it mean for the statement itself? Do we just suppose the statement is true until we find an example that falsifies it?
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The earth is not a sphere, because it bulges at the equator.   I tried fiddling with centripetal force equations and gravity, but I couldn't derive why this bulge occurs.    Is there   (a) a mathematical explanation using forces (not energies) and   (b) a simple intuitive explanation to explain to others why the bulge occurs?
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Question: Can you provide an example of a claim where the base case holds but there is a subtle flaw in the inductive step that leads to a fake proof of a clearly erroneous result? [Note: Please do not answer with the very common  example.]  Comment: Sometimes inductive arguments can lead to controversial conclusions, such as the ,  and a host of other paradoxes. However, I am interested in examples of a more mathematical nature (as opposed to linguistic) where the inductive argument is subtly flawed and leads to erroneous conclusions.   Note: If you provide an answer, please do so in a way similar to how current answers are displayed (gray out the flaw so people can be challenged to discover it).
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I was just wondering whether or not there have been mistakes in mathematics. Not a conjecture that ended up being false, but a theorem which had a proof that was accepted for a nontrivial amount of time before someone found a hole in the argument. Does this happen anymore now that we have computers? I imagine not. But it seems totally possible that this could have happened back in the Enlightenment.   Feel free to interpret this how you wish!
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My statistic professor says so, all the books that I look at state it:  is unscientific. You must derive a hypothesis from theory first, and then collect data and analyse it.  But I really don't understand what the problem is.  Suppose, I see sales figures for different car colors and form the hypothesis that from numbers of different-colored cars sold the largest group of cars on the street shoud be white. So I sit at some street one day and note all the colors of all the cars that pass me. Then I do some tests and find whatever.  Now, suppose I was bored and sat at some street one day and noted all the colors of all the cars that passed me. Since I love graphs, I plot a pretty histogram and find that white cars form the largest group. So I think that maybe most cars on the street are white and perform some tests.  How and why do the results or the interpretation of the results of the post-hoc test differ from those of the theory-driven* hypothesis test?  *&nbsp;What's the name for the opposite of a post-hoc test, anyway?    I would like to add that most of our knowledge about the universe (the Earth moves around the Sun) is deduced post hoc from observation.  It seems to me that in physics it is perfectly okay to assume that it is not coincidence that the sun has been rising in the East for the last thousand years.
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According to General Relativity I am being accelerated upwards by planet earth while writing this question. But a curious person on the the other side of the planet relative to me would have the same experience. That means we are accelerated in opposite directions, although earths diameter do not seem to increase. How can this be?
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I recently watched  by Veritasium where he talks about the One Way Speed of Light and talks about the limiting case where in one direction the speed of light is $c/2$ while it's instantaneous in the other. He also says this is perfectly fine according to our Physics theories. He also points at Einstein's assumption in his famous 1905 paper where he assumes that the speed of light is same in all directions. This made me ask this question is taking the speed of light same in all directions an axiom of some sort? As I've often read no information can be sent at more than the speed of light but here one-way taking the speed to infinite makes no difference. So are all of our physics theories based on the assumption and what would happen if light turns out to be moving at different speeds in different direction? Will that enable transfer of information faster than the speed of light and is there any way for us knowing that the transfer happens faster than the speed of light? The video takes a Earth Mars case where he says it isn't possible for us to every realize this discrepancy but is there a more general proof which says it isn't possible