Page 3 of 10 FirstFirst 12345 ... LastLast
Results 61 to 90 of 287

Thread: New Math Function Redux

  1. #61
    Join Date
    Feb 2003
    Location
    Depew, NY
    Posts
    11,801
    Quote Originally Posted by steveupson View Post
    I don't understand the question. My computer is running XP and the software doesn't work with XP. I have downloaded the program to other computers, though, and it does make things easier to view. Much easier. The slider can be moved manually, and the view can be rotated. I don't know what you're asking.
    Let me be blunt. You or someone else has uploaded a file to an anonymous server and labeled it as a .cdf file.

    At face value, assuming that the file is exactly what it is labeled and the uploader didn't have some sort of virus and the uploader wrote an intelligible .cdf code, and the audience is willing to download the Person's Wolfram Alpha interface, you are asking someone to decompile it and ascertain what that file contains and report that back here. That isn't a "normal" requirement of knowing a fact or detail.

    Worst case scenario is someone clicks on that file, that you cannot read because you don't know how, and kills their computer. Best case scenario is they provide you with the information you desire, which is not incumbent on anyone but you. The middle ground is someone negatively impacts their computer because they dove into something that was ill advised. I absolutely reject that risk... for others. Simply put, DO NOT risk your equipment.

    Having mention that I am slightly crazy, I have created a "burner" install of Linux on a burner computer (burner meaning, I don't care if I have to throw it away. Most people don't have this option, so it is profoundly poor form to ask someone to do this.) and downloaded the file and decrypted it. It is more 1000 lines long and more than half of it is hash. I am not troubling myself to decrypt the hash. None of my business what it says. Besides that hash, there is html style code that describes the animation but I cannot see anything to indicate how or why such an animation was created. There is a description of the size of the sphere and the shading of such, plus a tiny bit that references the code that controls the slider, but all and all it is a paint by number description of what the little app does with no reasoning at all.

    There is no formula or anything else to indicate that someone "designed" or used any math to construct the tool.

    Let me say this again for the gentle reader at home. DO NOT download files like this. It is profoundly unwise. And it isn't all that interesting.

    Besides, it is preambled with this text:

    (************************************************* ************************)
    (* *)
    (* The Mathematica License under which this file was created prohibits *)
    (* restricting third parties in receipt of this file from republishing *)
    (* or redistributing it by any means, including but not limited to *)
    (* rights management or terms of use, without the express consent of *)
    (* Wolfram Research, Inc. For additional information concerning CDF *)
    (* licensing and redistribution see: *)
    (* *)
    (* http://www.wolfram.com/cdf/adopting-...g-options.html *)
    (* *)
    (************************************************* ************************)

    Which pretty much means no one should be distributing it.
    Solfe

  2. #62
    Join Date
    Aug 2008
    Location
    Wellington, New Zealand
    Posts
    4,214
    Quote Originally Posted by steveupson View Post
    I don't understand precisely what you're claiming, then.
    I am pointing out English: A description of a plane and 2 cones does not contain a function. I did not write one. You did not write one.

    So there are now: Three orthogonal planes that look like a Cartesian coordinate system. A plane? A cone (on that plane?) and a "similar" cone (an identical cone but tilted so tat its axis is along the surface) . A vague, complex description of various kinds of angles. A guess on your part. Orthogonal means the right angles in plane geometry - 3 orthogonal planes are at right angles to each other.

    Sorry, steveupson, but the "guess on my part" is a description that is too vague to be anything useful. What I see you doing is using the standard definition of angles to derive other ordinary angles. Your "original" angle is an ordinary angle, etc.
    Last edited by Reality Check; 2016-Jul-04 at 05:34 AM.

  3. #63
    Join Date
    May 2016
    Posts
    238
    Quote Originally Posted by Solfe View Post
    Which pretty much means no one should be distributing it.
    I'm not a third party. The author and I collaborated for weeks in order to produce the model, and he has also given me permission to publish with proper credit to him. I would provide a link to the online discussion where we collaborated, but it's since been deleted, together with any internet archive that I've searched.

    http://community.wolfram.com/groups/..._auth=xWI25qyy

    Let me be blunt. You or someone else has uploaded a file to an anonymous server and labeled it as a .cdf file.

    At face value, assuming that the file is exactly what it is labeled and the uploader didn't have some sort of virus and the uploader wrote an intelligible .cdf code, and the audience is willing to download the Person's Wolfram Alpha interface, you are asking someone to decompile it and ascertain what that file contains and report that back here. That isn't a "normal" requirement of knowing a fact or detail.
    I have never made such a request. As a matter of fact, I have tried my best to explain to you why that won't work. There's nothing to "decompile." The critical bit of arithmetic that we're searching for cannot be found there, unless you want to try and figure out how Mathematica works, which would be a gargantuan task, to say the very least, what with it using its own proprietary language and everything.

    Worst case scenario is someone clicks on that file, that you cannot read because you don't know how, and kills their computer. Best case scenario is they provide you with the information you desire, which is not incumbent on anyone but you. The middle ground is someone negatively impacts their computer because they dove into something that was ill advised. I absolutely reject that risk... for others. Simply put, DO NOT risk your equipment.
    I've tried to attach it as a text file here, on this site, but I cannot attach text files. If anyone here has any recommendations on how to upload it here, then please speak up, and I'll do it if I can.

    And in case anyone thinks that this is some sort of shady internet software scam, the standard Mathematica package for individuals sells for $2,745.00. (The viewer is free.)

    Having mention that I am slightly crazy, I have created a "burner" install of Linux on a burner computer (burner meaning, I don't care if I have to throw it away. Most people don't have this option, so it is profoundly poor form to ask someone to do this.) ...
    I was joking with you.

    and downloaded the file and decrypted it. It is more 1000 lines long and more than half of it is hash. I am not troubling myself to decrypt the hash. None of my business what it says. Besides that hash, there is html style code that describes the animation but I cannot see anything to indicate how or why such an animation was created. There is a description of the size of the sphere and the shading of such, plus a tiny bit that references the code that controls the slider, but all and all it is a paint by number description of what the little app does with no reasoning at all.
    If you change the .cdf extension to .txt it can be read as a text file.

    I wasn't suggesting that anyone should look at how the actual model is programmed. I wanted you (and anyone else who might be interested) to simply download and "run" the program. This would entail installing the viewer, if you don't already have it on your computer.

    There is no formula or anything else to indicate that someone "designed" or used any math to construct the tool.

    Let me say this again for the gentle reader at home. DO NOT download files like this. It is profoundly unwise. And it isn't all that interesting.
    I didn't intend for you to try and read the program, I meant that you should run it because it gives a much better visual understanding of the function than the .gif illustrates.

    Sorry if you misunderstood, but I don't know what I should have said to make it more clear to you. There is no formula in the program because there is no formula. No one has yet been skillful enough to compose it. It's not a necessity that the equation exist in order to make the computer model. That's the whole reason why a computer model was made in the first place, because there was no other way to proceed. No one has figured out the proper expression.

    We've developed computer models to the point where they can surpass the current ability of humans. No doubt someone will eventually come up with the formula, but it was done first by a computer model. This shouldn't surprise anyone.




    From the wiki entry on the Kepler conjecture:

    "Hales' proof[edit]
    Following the approach suggested by Fejes Tóth (1953), Thomas Hales, then at the University of Michigan, determined that the maximum density of all arrangements could be found by minimizing a function with 150 variables. In 1992, assisted by his graduate student Samuel Ferguson, he embarked on a research program to systematically apply linear programming methods to find a lower bound on the value of this function for each one of a set of over 5,000 different configurations of spheres. If a lower bound (for the function value) could be found for every one of these configurations that was greater than the value of the function for the cubic close packing arrangement, then the Kepler conjecture would be proved. To find lower bounds for all cases involved solving around 100,000 linear programming problems.

    "When presenting the progress of his project in 1996, Hales said that the end was in sight, but it might take "a year or two" to complete. In August 1998 Hales announced that the proof was complete. At that stage it consisted of 250 pages of notes and 3 gigabytes of computer programs, data and results.

    "Despite the unusual nature of the proof, the editors of the Annals of Mathematics agreed to publish it, provided it was accepted by a panel of twelve referees. In 2003, after four years of work, the head of the referee's panel, Gábor Fejes Tóth, reported that the panel were "99% certain" of the correctness of the proof, but they could not certify the correctness of all of the computer calculations.

    "Hales (2005) published a 100-page paper describing the non-computer part of his proof in detail. Hales & Ferguson (2006) and several subsequent papers described the computational portions. Hales and Ferguson received the Fulkerson Prize for outstanding papers in the area of discrete mathematics for 2009.

    "A formal proof[edit]
    In January 2003, Hales announced the start of a collaborative project to produce a complete formal proof of the Kepler conjecture. The aim was to remove any remaining uncertainty about the validity of the proof by creating a formal proof that can be verified by automated proof checking software such as HOL Light and Isabelle. This project is called Flyspeck – the F, P and K standing for Formal Proof of Kepler. Hales estimated that producing a complete formal proof would take around 20 years of work. The project was announced completed on August 10, 2014.[3] In January 2015 Hales and 21 collaborators published "A formal proof of the Kepler conjecture".[4]"

    https://en.wikipedia.org/wiki/Kepler...Hales.27_proof

  4. #64
    Join Date
    Aug 2002
    Posts
    9,259
    Quote Originally Posted by steveupson View Post
    The graph of the function shows this relationship clearly. Here the result for a cone having an aperture of is shown (blue trace) together with a sin curve (red trace).

    The curve will be different for every different aperture of cone. Mathematically, we can substitute the half angle of the cone and view the function as a representation of an angle in three dimensional space.
    wow. a plot with two curves and no labels on the axes, colour me not amazed
    All comments made in red are moderator comments. Please, read the rules of the forum here and read the additional rules for ATM, and for conspiracy theories. If you think a post is inappropriate, don't comment on it in thread but report it using the /!\ button in the lower left corner of each message. But most of all, have fun!

    Catch me on twitter: @tusenfem
    Catch Rosetta Plasma Consortium on twitter: @Rosetta_RPC

  5. #65
    Join Date
    May 2016
    Posts
    238
    Quote Originally Posted by Reality Check View Post
    I am pointing out English: A description of a plane and 2 cones does not contain a function. I did not write one. You did not write one.

    So there are now: Three orthogonal planes that look like a Cartesian coordinate system. A plane? A cone (on that plane?) and a "similar" cone (an identical cone but tilted so tat its axis is along the surface) . A vague, complex description of various kinds of angles. A guess on your part. Orthogonal means the right angles in plane geometry - 3 orthogonal planes are at right angles to each other.

    Sorry, steveupson, but the "guess on my part" is a description that is too vague to be anything useful. What I see you doing is using the standard definition of angles to derive other ordinary angles. Your "original" angle is an ordinary angle, etc.

    What is the blue curve in the graph?

    Can you explain, mathematically, what the curve represents? I now know that you believe it to be something other than a function. What is it?

  6. #66
    Join Date
    May 2016
    Posts
    238
    Quote Originally Posted by tusenfem View Post
    wow. a plot with two curves and no labels on the axes, colour me not amazed
    You don't know what's on the axes of a sine curve?

    Color me amazed!

  7. #67
    Join Date
    Aug 2002
    Posts
    9,259
    Quote Originally Posted by steveupson View Post
    I'm not a third party. The author and I collaborated for weeks in order to produce the model, and he has also given me permission to publish with proper credit to him. I would provide a link to the online discussion where we collaborated, but it's since been deleted, together with any internet archive that I've searched.
    Okay, if you "collaborated" for weeks, than you can actually tell us what you have done in detail.
    That mathematica images is nothing, it shows a rotation and nothing else.
    The attachment in post #55 clearly shows that this is a 3D rotation:
    • but clearly fails to identify what exactly cos(pg) or better yet what pg is and so we can also not check why the second =-sign for x' or z' is anyway correct, apart from deducing that cos(pg) = z tan(pi/2 - theta) + x
    • Then going to x'' is just a rotation around the z' axis with angular speed omega and dependent on time t
    • Then going to x''' is a rotation around the x'' axis over an "angle" E

    So basically the whole image is showing the combination of a few rotations, and nothing whatsoever about cones and planes and what-have-you-nots.
    Strange that YOU cannot explain that to us, the goniometry guys are here all the time, but unless you give us some specifics, we cannot do anything. Now we see what you and your mathematica collaborator have done, and look, it's just a rotation that can be split into three separate rotations, something you get to learn at high school level (at lease in Europe).
    WOW I am amazed (not)
    All comments made in red are moderator comments. Please, read the rules of the forum here and read the additional rules for ATM, and for conspiracy theories. If you think a post is inappropriate, don't comment on it in thread but report it using the /!\ button in the lower left corner of each message. But most of all, have fun!

    Catch me on twitter: @tusenfem
    Catch Rosetta Plasma Consortium on twitter: @Rosetta_RPC

  8. #68
    Join Date
    Aug 2002
    Posts
    9,259
    Quote Originally Posted by steveupson View Post
    You don't know what's on the axes of a sine curve?

    Color me amazed!
    where does it say it is a sine curve? what is plotted on x-ases, what is on the y-axis. Labels are everything if you want to explain something.
    Also, I have seen many sine curves and none of them looked like this, but usually like this: http://betterexplained.com/wp-conten.../sine-plot.gif
    All comments made in red are moderator comments. Please, read the rules of the forum here and read the additional rules for ATM, and for conspiracy theories. If you think a post is inappropriate, don't comment on it in thread but report it using the /!\ button in the lower left corner of each message. But most of all, have fun!

    Catch me on twitter: @tusenfem
    Catch Rosetta Plasma Consortium on twitter: @Rosetta_RPC

  9. #69
    Join Date
    May 2016
    Posts
    238
    Quote Originally Posted by tusenfem View Post
    where does it say it is a sine curve?
    You quoted me in post #64. Read the second sentence in the quoted text.

    But sure, you're right, and in a perfect world the graph would have labels on the axes, sure. My bad. If anyone wishes to add the labels and repost the graph, please do so. I think it would help, and anything that simplifies this subject is a welcome improvement.

  10. #70
    Join Date
    May 2016
    Posts
    238
    Quote Originally Posted by tusenfem View Post
    Okay, if you "collaborated" for weeks, than you can actually tell us what you have done in detail.
    I've created (or caused to be created) a verbal description of the function, a computer model of the function, and a graph of the function.

    How much more detail would you like me to provide? I have pretty much reached the limits of my abilities, which is why I'm here. I cannot provide any more hand-holding than what I've already provided. All I can do is continue to answer people's questions. But I don't know the answer to the main question that everyone is asking; it's why I'm here, to ask the exact same question that everyone else seem to be asking. We really need an expression of the equation. Not having one is grinding everything to a standstill. I'm sorry that I cannot solve the problem myself. Very sorry, but I have held nothing back when asked. I can't do more than that, can I?

    If you're asking for a more detailed version of the history of how we got here, then look at this post in the ATM thread:

    http://cosmoquest.org/forum/showthre...33#post2358133


    That mathematica images is nothing, it shows a rotation and nothing else.
    Nope, I disagree on both counts. It's not nothing, and it doesn't show a rotation.

    The attachment in post #55 clearly shows that this is a 3D rotation:
    • but clearly fails to identify what exactly cos(pg) or better yet what pg is and so we can also not check why the second =-sign for x' or z' is anyway correct, apart from deducing that cos(pg) = z tan(pi/2 - theta) + x
    • Then going to x'' is just a rotation around the z' axis with angular speed omega and dependent on time t
    • Then going to x''' is a rotation around the x'' axis over an "angle" E
    This requires a lot more clarification. As you may already know, spherical trigonometry uses great circles (or more specifically, arc segments of great circles) to mathematically solve right triangles on the surface of a sphere. There is no method for using spherical trigonometry to solve anything dealing with small circles, and more specifically, the slope of a tangent of a small circle on the surface of a sphere.

    The function in question defines the relationship between two angles. One of these angles (the angle of the tangent plane) is derived from the slope of the tangent of a small circle on a sphere (or at least that's one way to derive it, and I seriously doubt that the Mathematica model does it this way). The three rotations orient the frame such that this slope can be determined. The rotation only finds one of the two angles that are related to one another, and it does nothing to express the relationship between the two, which is what the new function does.

    So basically the whole image is showing the combination of a few rotations, and nothing whatsoever about cones and planes and what-have-you-nots.
    Strange that YOU cannot explain that to us, the goniometry guys are here all the time, but unless you give us some specifics, we cannot do anything.
    What is it that I haven't explained?

    Now we see what you and your mathematica collaborator have done, and look, it's just a rotation that can be split into three separate rotations, something you get to learn at high school level (at lease in Europe).
    WOW I am amazed (not)
    You don't see, and I'm not amazed at that, either. Do you understand, completely understand, what the blue curve is in the graph?

    I don't believe you understand it all. As a matter of fact, I know you don't. I think that you'd readily admit that you don't fully understand the math that creates the curve.

    I generally continue asking questions whenever I don't understand something. It confounds me a great deal that no one here can explain the curve, at all, but everyone seems to somehow know, without really knowing, that it isn't what I'm telling you it is. And no one seems to understand that they owe me an explanation of why they think they can comment on the math without actually doing the math or understanding the math.

    All this makes me respond to snarky comments with equally disruptive snarky comments.

    Obviously you didn't understand that one of the curves was a sine, and that's completely my fault. I should have just corrected my graph and moved on. There is nothing to be gained by my being rude to you over such a simple thing.
    Last edited by steveupson; 2016-Jul-04 at 07:36 AM. Reason: syntax

  11. #71
    Join Date
    Aug 2002
    Posts
    9,259
    Quote Originally Posted by steveupson View Post
    If you're asking for a more detailed version of the history of how we got here, then look at this post in the ATM thread:
    ATM has no place outside of ATM.

    Quote Originally Posted by steveupson View Post
    Nope, I disagree on both counts. It's not nothing, and it doesn't show a rotation.
    You could have fooled me, I see a point and its vector move in a clear rotational fashion, so it is a rotation.

    Quote Originally Posted by steveupson View Post
    This requires a lot more clarification. As you may already know, spherical trigonometry uses great circles (or more specifically, arc segments of great circles) to mathematically solve right triangles on the surface of a sphere. There is no method for using spherical trigonometry to solve anything dealing with small circles, and more specifically, the slope of a tangent of a small circle on the surface of a sphere.
    This is no clarification. If you want to discuss this you need to give us INFORMATION. What on Earth is "solve right triangles".
    And of course, if you would just write down the equations, you can determine the "slope of a tangent TO a small circle on the surface of a sphere. The idea that you cannot do that is ludicrous, how could we then have a coordinate system on the Earth which uses "small circles"?

    Quote Originally Posted by steveupson View Post
    The function in question defines the relationship between two angles. One of these angles (the angle of the tangent plane) is derived from the slope of the tangent of a small circle on a sphere (or at least that's one way to derive it, and I seriously doubt that the Mathematica model does it this way). The three rotations orient the frame such that this slope can be determined. The rotation only finds one of the two angles that are related to one another, and it does nothing to express the relationship between the two, which is what the new function does.
    Then what IS mathematica doing? Keeping us in the dark does not help this discussion.

    Quote Originally Posted by steveupson View Post
    What is it that I haven't explained?
    Better question is what HAVE you explained? Nothing. You come with walls of text and a mathematica image showing something and a plot showing "a sine curve" and we are supposed to understand what it all means? Now you say that you calculate something about "a tangent to a small circle on a sphere" but the mathematica model is probably not calculating that.

    Quote Originally Posted by steveupson View Post
    You don't see, and I'm not amazed at that, either. Do you understand, completely understand, what the blue curve is in the graph?
    The blue curve in which graph, do you mean your "sine wave" (which is not a sine wave, because that is not what a sine wave looks like), I don't thinik there is a blue curve in the animation. So no I do not know what the blue curve is, as you have never ever explained it, I also do not know what the red curve is and I also do not agree that it is a sine wave.

    Quote Originally Posted by steveupson View Post
    I don't believe you understand it all. As a matter of fact, I know you don't. I think that you'd readily admit that you don't fully understand the math that creates the curve.
    I fully understand the math that is in the attachment that you showed. there is nothing spectacular about it and apart from not defining what "pg" is it is just three rotations in a row around three different axes in different coordinate systems and in the end glued together to get one formula.

    Quote Originally Posted by steveupson View Post
    I generally continue asking questions whenever I don't understand something. It confounds me a great deal that no one here can explain the curve, at all, but everyone seems to somehow know, without really knowing, that it isn't what I'm telling you it is. And no one seems to understand that they owe me an explanation of why they think they can comment on the math without actually doing the math or understanding the math.
    Wait YOU are presenting this stuff here and WE are supposed to explain whatever curve that you are showing us? Well that's the world upside down.
    And you have not told us what it is. You tell us nothing.
    All this makes me respond to snarky comments with equally disruptive snarky comments.

    Quote Originally Posted by steveupson View Post
    Obviously you didn't understand that one of the curves was a sine, and that's completely my fault. I should have just corrected my graph and moved on. There is nothing to be gained by my being rude to you over such a simple thing.
    It is NOT a sine, that is NOT what a sine looks like, you show something that for some reason goes from 90 on the y-axis to 90 on the x-axis.
    So you are probably showing two angles plotted against each other.
    All comments made in red are moderator comments. Please, read the rules of the forum here and read the additional rules for ATM, and for conspiracy theories. If you think a post is inappropriate, don't comment on it in thread but report it using the /!\ button in the lower left corner of each message. But most of all, have fun!

    Catch me on twitter: @tusenfem
    Catch Rosetta Plasma Consortium on twitter: @Rosetta_RPC

  12. #72
    Join Date
    May 2016
    Posts
    238
    Quote Originally Posted by tusenfem View Post
    You could have fooled me, I see a point and its vector move in a clear rotational fashion, so it is a rotation.
    We need to be a lot more precise than you are trying to be. It’s really two rotations, of two different structures, which occur simultaneously in the same frame. The two simultaneous rotations, of two separated structures, are what establish the two separate derived angles, which have the relationship where one of the angles is a function of the other angle.

    These derived angles are different, and have a different relationship to one another, for every unique value of original given angle.

    This means that a different curve will result for every unique value of the original given angle.


    This is no clarification. If you want to discuss this you need to give us INFORMATION. What on Earth is "solve right triangles".
    And of course, if you would just write down the equations, you can determine the "slope of a tangent TO a small circle on the surface of a sphere. The idea that you cannot do that is ludicrous, how could we then have a coordinate system on the Earth which uses "small circles"?
    It’s not within the scope of this discussion to teach anyone spherical trigonometry, which is based solely on great circles. The latitude lines on the earth are not used for trigonometry. They are for map making.

    The idea that anything other than great circles can be used in spherical trigonometry is – not to put too fine a point on it – ludicrous.

    Then what IS mathematica doing? Keeping us in the dark does not help this discussion.
    How am I keeping anyone in the dark? I’m in the dark along with everyone else, wrt how Mathematica solves this. If I could enlighten us all somehow, then I would.

    Mathematica is simply performing its intended purpose. It is modeling a math function, which is exactly why the software was designed in the first place.

    Better question is what HAVE you explained? Nothing. You come with walls of text and a mathematica image showing something and a plot showing "a sine curve" and we are supposed to understand what it all means? Now you say that you calculate something about "a tangent to a small circle on a sphere" but the mathematica model is probably not calculating that.
    The walls of text are the only way forward at this point. What other options are available? I am open to any reasonable suggestions.

    These references to spherical trig won’t make any sense to anyone unless they have at least a superficial understanding of how, and why, it works the way it does. Although the principles underlying spherical geometry may be relevant to the function in a tangential (pun intended) fashion, ignoring these nuances should not make any difference in understanding the function mathematically or conceptually.

    The blue curve in which graph, do you mean your "sine wave" (which is not a sine wave, because that is not what a sine wave looks like), I don't thinik there is a blue curve in the animation. So no I do not know what the blue curve is, as you have never ever explained it, I also do not know what the red curve is and I also do not agree that it is a sine wave.
    I understand the confusion. The red trace (a curve in the shape of a quarter sine wave) has been added alongside the curve of the function (blue trace.) This was done for comparison, in order to show that the blue curve is not a sine curve. It does have the visual appearance of having the shape of a sine curve when viewed by itself, that is, until a curve in the shape of an actual sine quarter wave is presented along side it for comparison purposes. I hope that this explanation resolves any confusion about this. It should have been presented this way to begin with. Again, I apologize for unintentionally muddying some already murky stuff. My bad.

    I fully understand the math that is in the attachment that you showed. there is nothing spectacular about it and apart from not defining what "pg" is it is just three rotations in a row around three different axes in different coordinate systems and in the end glued together to get one formula.
    Once again, the relationships in the function are not part of that attachment. The attachment explains one method for solving part of the math involved. It wouldn’t even be necessary to do it this way if a method that uses spherical trigonometry were available.

    Wait YOU are presenting this stuff here and WE are supposed to explain whatever curve that you are showing us? Well that's the world upside down.
    Yes, because I think it’s the best way for us to understand each other. I can’t tell what it is that you’re not hearing if you don’t tell me what you think I am saying. We’ll simply continue to talk past one another.

    All this makes me respond to snarky comments with equally disruptive snarky comments.
    I'm beginning to really appreciate the snark a lot more. It livens up what would otherwise be a painfully dull conversation.

    It is NOT a sine, that is NOT what a sine looks like, you show something that for some reason goes from 90 on the y-axis to 90 on the x-axis.
    So you are probably showing two angles plotted against each other.
    Yes, exactly! Now, can you tell me which two angles? (For the win!)

  13. #73
    Join Date
    Oct 2009
    Location
    a long way away
    Posts
    10,660
    Quote Originally Posted by tusenfem View Post
    wow. a plot with two curves and no labels on the axes, colour me not amazed
    I created that graph! (And it isn't annotated because I didn't really know what the two sets of numbers represented.) I just took the changing numbers from the animation and plotted the curve. I thought it might be as simple as a (scaled) sine curve so I also tried plotting that. But it is obvious it is not that simple.

    I have tried to understand how to derive the "function" (set of equations) that steveupson is looking for. I think it is a fairly simple problem in geometry but it is too poorly defined for me to get to grips with - there are terms like "the angle between the two planes" that I don't know how to interpret.

    This is made unnecessarily complicated by the OP's inability to provide any better definition than the animation, his lack of mathematical knowledge and his repeated sidetracks about this being special or previously unknown.

  14. #74
    Join Date
    Oct 2009
    Location
    a long way away
    Posts
    10,660
    Quote Originally Posted by steveupson View Post
    There is no method for using spherical trigonometry to solve anything dealing with small circles, and more specifically, the slope of a tangent of a small circle on the surface of a sphere.
    I find that hard to believe. I have seen very simple calculations regarding (non great) circles on the surface of a sphere. Spherical geometry is just one example of more general geometry that includes Euclidean and other non-Euclidean geometries.

    OK. I see you said "trigonometry". So, I guess you are right. But my feeling is, "so what".

    This still looks like it should be a fairly straightforward problem. It just needs to be defined more precisely than your animation can do.
    Last edited by Strange; 2016-Jul-04 at 06:33 PM.

  15. #75
    Join Date
    Mar 2004
    Posts
    15,801
    Quote Originally Posted by strange View Post
    This is made unnecessarily complicated by the op's inability to provide any better definition than the animation, his lack of mathematical knowledge and his repeated sidetracks about this being special or previously unknown.
    Truth
    0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...
    Skepticism enables us to distinguish fancy from fact, to test our speculations. --Carl Sagan

  16. #76
    Join Date
    Mar 2004
    Posts
    15,801
    Quote Originally Posted by Strange View Post
    This still looks like it should be a fairly straightforward problem. It just needs to be defined more precisely than your animation can do.
    More truth
    0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...
    Skepticism enables us to distinguish fancy from fact, to test our speculations. --Carl Sagan

  17. #77
    Join Date
    Mar 2004
    Posts
    15,801
    We can guess what the function is, based on the illustrations, but it will be a guess, and then run the risk of our effort being rejected because it doesn't capture exactly what is insuffciently described.

    Why should anyone bother?
    0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...
    Skepticism enables us to distinguish fancy from fact, to test our speculations. --Carl Sagan

  18. #78
    Join Date
    Oct 2009
    Location
    a long way away
    Posts
    10,660
    Quote Originally Posted by 01101001 View Post
    Why should anyone bother?
    And, on that, I guess I should say that it was me who suggested that steveupson should pay someone to work on this problem with him...

  19. #79
    Join Date
    Aug 2008
    Location
    Wellington, New Zealand
    Posts
    4,214
    Quote Originally Posted by steveupson View Post
    What is the blue curve in the graph?
    The blue curve is s curve. Mathematically it is a curve. It is wrong that I believe that the blue curve anything but a curve. Like all curves generated by an unknown function we can fit the curve with a function. This is known as curve fitting as used extensively in experimental science. That is all we can do with the graph.
    Curve fitting
    Curve fitting[1][2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points,[3] possibly subject to constraints.[4][5] Curve fitting can involve either interpolation,[6][7] where an exact fit to the data is required, or smoothing,[8][9] in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis,[10][11] which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization,[12][13] to infer values of a function where no data are available,[14] and to summarize the relationships among two or more variables.[15] Extrapolation refers to the use of a fitted curve beyond the range of the observed data,[16] and is subject to a degree of uncertainty[17] since it may reflect the method used to construct the curve as much as it reflects the observed data.
    The rest of the "new math" is old math - a confusing set of rotations.
    Last edited by Reality Check; 2016-Jul-04 at 09:13 PM.

  20. #80
    Join Date
    Mar 2007
    Location
    Falls Church, VA (near Washington, DC)
    Posts
    8,654
    I would not be surprised if mathematicians in the past have diddled with whatever it is that steveupson is envisioning or something similar, decided that it was a curiosity that did not amount to a breakthrough, and just set it aside unpublished.

  21. #81
    Join Date
    Jun 2009
    Posts
    1,840
    Let's see if we can agree on what the animation http://community.wolfram.com//c/port...f&userId=93385 shows.

    I'll assume the x-axis is the one roughly toward the right and horizontal, the y-axis is "away" from us and the z-axis is "up". There is apparently a sphere. For simplicity, I'll assume it is the unit sphere. There is a circle C that apparently lies on the sphere. One of its diameters is a line segment between "the north pole" (0,0,1) and and a point on the xy plane. That point might be (0,-1,0). ( The circle lies in some plane. That plane contains the center of the circle.) There is a point P on the perimeter of the circle that the animation moves. There is dark green plane G that is normal to the XY plane contains the points (0,0,0) and P. There is a yellow or light green plane Y that is normal to the plane G and contains the points (0,0,0) and P. There is a blue plane B that contains (0,0,0) and also the tangent line to the circle drawn though P, which lies in the plane that contains the circle.

    The angle E could be the angle between two radii of the circle with one radius from the center of the circle to the point (0,-1,0) (or wherever the circle is tangent to the xy plane). The other radius is from the center of the circle to P.

    The "angle between the longitude and tangent planes" could be the acute angle between the plane Y and the plane B. Is the "new functIon" the function that expresses this angle as a function of angle E ?

  22. #82
    Join Date
    Jun 2006
    Posts
    4,758
    Quote Originally Posted by Hornblower View Post
    I would not be surprised if mathematicians in the past have diddled with whatever it is that steveupson is envisioning or something similar, decided that it was a curiosity that did not amount to a breakthrough, and just set it aside unpublished.
    The most relevant thing I could find on Mathematica was here:

    https://en.wikipedia.org/wiki/A_New_...ural_selection

    I think we need somebody from Mathematica to explain this mess. Preferably Steven Wolfram himself.
    I'm not a hardnosed mainstreamer; I just like the observations, theories, predictions, and results to match.

    "Mainstream isn’t a faith system. It is a verified body of work that must be taken into account if you wish to add to that body of work, or if you want to change the conclusions of that body of work." - korjik

  23. #83
    Join Date
    Oct 2009
    Location
    a long way away
    Posts
    10,660
    Quote Originally Posted by tashirosgt View Post
    Let's see if we can agree on what the animation http://community.wolfram.com//c/port...f&userId=93385 shows.

    I'll assume the x-axis is the one roughly toward the right and horizontal, the y-axis is "away" from us and the z-axis is "up". There is apparently a sphere. For simplicity, I'll assume it is the unit sphere. There is a circle C that apparently lies on the sphere. One of its diameters is a line segment between "the north pole" (0,0,1) and and a point on the xy plane. That point might be (0,-1,0). ( The circle lies in some plane. That plane contains the center of the circle.) There is a point P on the perimeter of the circle that the animation moves. There is dark green plane G that is normal to the XY plane contains the points (0,0,0) and P. There is a yellow or light green plane Y that is normal to the plane G and contains the points (0,0,0) and P. There is a blue plane B that contains (0,0,0) and also the tangent line to the circle drawn though P, which lies in the plane that contains the circle.

    The angle E could be the angle between two radii of the circle with one radius from the center of the circle to the point (0,-1,0) (or wherever the circle is tangent to the xy plane). The other radius is from the center of the circle to P.
    That seems like an accurate summary. The blue plane can also be thought of as being tangential to a cone with its apex at the centre of the sphere and which forms the circle on the surface of the sphere. (There was some talk of a second cone, but I can't visualise where that would be.)

    The "angle between the longitude and tangent planes" could be the acute angle between the plane Y and the plane B.
    I think that the "angle between the longitude and tangent planes" is the acute angle between the plane G and the plane B.

    Is the "new functIon" the function that expresses this angle as a function of angle E ?
    That is my understanding.

  24. #84
    Join Date
    May 2016
    Posts
    238
    Thank you, tashirosgt, for responding to my request. I had no idea on how to proceed.

    Quote Originally Posted by tashirosgt View Post
    The "angle between the longitude and tangent planes" could be the acute angle between the plane Y and the plane B. Is the "new functIon" the function that expresses this angle as a function of angle E ?
    edited to make a correction>>>

    This is correct.

    Strange is correct in #83 above, it's the acute angle between G and B.

    (I got a little too excited there for a minute, and didn't look closely enough. I'm still awarding the win to you, though.)

    >>>

    The angle E could be the angle between two radii of the circle with one radius from the center of the circle to the point (0,-1,0) (or wherever the circle is tangent to the xy plane). The other radius is from the center of the circle to P.
    Now I have another confession/correction to make. There was an error in the original video snippet that showed angle E. This error was corrected after it was discovered in the draft version of the model. I simply forgot to mention this. The public discussion about producing the model has been deleted and I no longer have access to that material. I am working from memory (rather poor memory at that) on much of this. Sorry for the confusion.

    Angle E is smallest angle that can be formed by a line in the xy plane and a line that contains (0,0,0) and P.

    I'll assume the x-axis is the one roughly toward the right and horizontal, the y-axis is "away" from us and the z-axis is "up". There is apparently a sphere. For simplicity, I'll assume it is the unit sphere. There is a circle C that apparently lies on the sphere. One of its diameters is a line segment between "the north pole" (0,0,1) and and a point on the xy plane. That point might be (0,-1,0). ( The circle lies in some plane. That plane contains the center of the circle.) There is a point P on the perimeter of the circle that the animation moves. There is dark green plane G that is normal to the XY plane contains the points (0,0,0) and P. There is a yellow or light green plane Y that is normal to the plane G and contains the points (0,0,0) and P. There is a blue plane B that contains (0,0,0) and also the tangent line to the circle drawn though P, which lies in the plane that contains the circle.
    This is perfect, afaict.
    Last edited by steveupson; 2016-Jul-06 at 05:16 AM. Reason: correction

  25. #85
    Join Date
    May 2016
    Posts
    238
    Quote Originally Posted by Strange View Post
    I created that graph!
    Thank you again for doing this.

    I think it is a fairly simple problem...
    Not so.

    This is made unnecessarily complicated by the OP's inability to provide any better definition than the animation, his lack of mathematical knowledge and his repeated sidetracks about this being special or previously unknown.
    Yes, yes and yes (especially the last part about it being new, because if that were not the case then we would just look it up somewhere, wouldn't we?)
    Last edited by steveupson; 2016-Jul-06 at 12:00 AM. Reason: syntax

  26. #86
    Join Date
    May 2016
    Posts
    238
    Quote Originally Posted by Strange View Post
    I find that hard to believe. I have seen very simple calculations regarding (non great) circles on the surface of a sphere. Spherical geometry is just one example of more general geometry that includes Euclidean and other non-Euclidean geometries.

    OK. I see you said "trigonometry". So, I guess you are right. But my feeling is, "so what".
    The "so what" is that this function is a result of solving for the tangent of a small circle on a sphere using trig.

  27. #87
    Join Date
    May 2016
    Posts
    238
    Quote Originally Posted by 01101001 View Post
    Why should anyone bother?
    Some of us see this as an "interesting math problem" and we are more bothered by not knowing how to solve it than by expending the effort that it takes to solve it.

  28. #88
    Join Date
    May 2016
    Posts
    238
    Quote Originally Posted by Reality Check View Post
    The rest of the "new math" is old math - a confusing set of rotations.
    We've been over this. Can you produce any evidence to support your assertion? Without evidence doesn't your criticism simply amount to so much hand waiving?

  29. #89
    Join Date
    May 2016
    Posts
    238
    Quote Originally Posted by Hornblower View Post
    I would not be surprised if mathematicians in the past have diddled with whatever it is that steveupson is envisioning or something similar, decided that it was a curiosity that did not amount to a breakthrough, and just set it aside unpublished.
    I have no doubt at all that mathematicians have grappled with this in the past, for several hundred years. Much better minds than mine have probably given it a shot. Napier worked out the spherical case for the Law of Sines a few hundred years ago. No doubt he gave this problem of solving for tangents of small circles some consideration.

    I think that the computer model is what makes this puzzle solvable now. I know that it has never been solved before this computer model was constructed.

    Somewhere around a century ago mathematicians adopted another method (involving calculus instead of trigonometry) for determining angles on curved manifolds. That other method ignores the gross position of the manifold in 3space and concentrates on the surface. This new trigonometric technique re-establishes that connection of how the surface is grossly positioned in space.

    Or, I'm making all this up.

  30. #90
    Join Date
    May 2016
    Posts
    238
    Quote Originally Posted by John Mendenhall View Post
    The most relevant thing I could find on Mathematica was here:

    https://en.wikipedia.org/wiki/A_New_...ural_selection

    I think we need somebody from Mathematica to explain this mess. Preferably Steven Wolfram himself.

    Really, because this quote from the wiki entry on Mathematica seems a lot more relevant to me:

    "Mathematica is a symbolic mathematical computation program, sometimes called a computer algebra program, used in many scientific, engineering, mathematical, and computing fields."

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •