bytor2112 Posted February 7, 2015 Report Share Posted February 7, 2015 Enjoy!! https://www.facebook.com/video.php?v=593521430803116&pnref=story JimmiGerman and Vort 2 Quote Link to comment Share on other sites More sharing options...
Vort Posted February 8, 2015 Report Share Posted February 8, 2015 Hint: The digits in any number evenly divisible by 9 will sum to 9 (or will sum to a number whose digits sum to 9, and so forth). Let's make up a self-referential way to say this: Any number evenly divisible by 9 is a sum-9 number, where a sum-9 number is defined as follows: A sum-9 number is a number whose digits sum to 9 or to a sum-9 number. Note that this is not a circular definition; it is a self-referential definition, and is perfectly valid. Quote Link to comment Share on other sites More sharing options...
Vort Posted February 8, 2015 Report Share Posted February 8, 2015 Note that this is a property of a number system of any base. For example, in base 8, (dec) 49 is 61, and 6+1=7. For any number system of base n, the numeral n-1 will have the property that any number evenly divisible by it will be a sum-n number, as defined above for sum-9. mordorbund 1 Quote Link to comment Share on other sites More sharing options...
yoyoteacher Posted February 8, 2015 Report Share Posted February 8, 2015 Oh, be still my math loving heart! I recently taught these divisibility rules to my students this year. The number 3 is pretty similar too, in base 10. The difference being that the sum of the digits is a multiple of 3. Litzy 1 Quote Link to comment Share on other sites More sharing options...
JimmiGerman Posted February 8, 2015 Report Share Posted February 8, 2015 (edited) It depends on the base, as Vort says. And why does a circle have 360 degrees? It results from the Babylonians with their arithmetic system based on 60. So it's pure chance, and nine is not a mysterious number, purely appearing accidentally by some algorithms shown by the "circle mystery" here in this thread. Like the so-called "Bible code" (leave me alone with that!). There is no mystery or supernatural power behind any number. It may sound ignorantly, but the nine, as any other number, is only a result of assumptions and abstractions based on human thinking, and mathematics don't substitute the cognitive knowledge. Maybe the zero is an exception: but if there is zero money in your pockets, even the zero won't tell you where your money has gone, and, as it happens so often, the answer is blowin' in the wind. PS... However, maybe I'm only jealous of those people who are good at mathematics, since I'm a rivet on this field. Edited February 8, 2015 by JimmiGerman Litzy 1 Quote Link to comment Share on other sites More sharing options...
bytor2112 Posted February 8, 2015 Author Report Share Posted February 8, 2015 (edited) And let us not forget that any number multiplied by zero is zero. Edited February 8, 2015 by bytor2112 Quote Link to comment Share on other sites More sharing options...
JimmiGerman Posted February 8, 2015 Report Share Posted February 8, 2015 And let us not forget that any number multiplied by zero is zero. It's the most mightyful number, I guess. I forgot... the Babylonians didn't know a "zero" in their arithmetic system. It's maybe that why their tower fell to pieces... due to incorrect calculations...? Vort and bytor2112 2 Quote Link to comment Share on other sites More sharing options...
classylady Posted February 9, 2015 Report Share Posted February 9, 2015 42: The answer to life, the universe and everything. The computer when asked what 6 by 9 was, answered 42, in "The Hitchhiker's Guide to the Galaxy". Obviously incorrect. But 613 × 913 = 4213 (using base 13.) lol Vort 1 Quote Link to comment Share on other sites More sharing options...
JimmiGerman Posted February 9, 2015 Report Share Posted February 9, 2015 (edited) 42: The answer to life, the universe and everything. The computer when asked what 6 by 9 was, answered 42, in "The Hitchhiker's Guide to the Galaxy". Obviously incorrect. But 613 × 913 = 4213 (using base 13.) lol One could believe there is some kind of higher and revealing knowledge behind mathematics. I'm not the right person to judge about it. The String Theory and comparable concepts according to an all-embracing theory of the nature are certainly based on mathematical eqations. It's not difficult to represent some higher dimensions only by increasing the exponent to get a five- or even ten-dimensional "space" instantly, in an abstract way. But our mind wouldn't find an adequate word for that... something (or singularity), and we would be far beyond our abilities to describe or even to imagine what it was. Mathematics and abstract concepts apparently are miles and miles ahead of our cognitive understanding and ability of transforming that knowledge into words. Thus, we are very often unable really to see or imagine what all those equations might tell us. Maybe we've been made for understanding words, not numbers. But we don't always even understand those words. Edited February 9, 2015 by JimmiGerman Quote Link to comment Share on other sites More sharing options...
PolarVortex Posted February 9, 2015 Report Share Posted February 9, 2015 Maybe we've been made for understanding words, not numbers. But we don't always even understand those words. Possibly, but I'm still amazed at what mathematicians can prove these days. There is something called Graham's Number, which for a while was listed in the Guiness Book of World Records as the largest known number of interest to mathematicians. If you could write digits as small as electrons, just writing Graham's Number would fill up the known universe. Actually, if you could write digits as small as a Planck Volume, Graham's Number would still fill up the known universe, according to Wikipedia. The last 500 or digits of Graham's Number are known, but the first digit will probably never be known. There's a YouTube video out there where someone asks Professor Graham himself what the first digit of his famous number is, and he laughed, "Well, in binary it would be a 1." ROFL Vort and classylady 2 Quote Link to comment Share on other sites More sharing options...
JimmiGerman Posted February 9, 2015 Report Share Posted February 9, 2015 (edited) Possibly, but I'm still amazed at what mathematicians can prove these days. There is something called Graham's Number, which for a while was listed in the Guiness Book of World Records as the largest known number of interest to mathematicians. If you could write digits as small as electrons, just writing Graham's Number would fill up the known universe. Actually, if you could write digits as small as a Planck Volume, Graham's Number would still fill up the known universe, according to Wikipedia. The last 500 or digits of Graham's Number are known, but the first digit will probably never be known. There's a YouTube video out there where someone asks Professor Graham himself what the first digit of his famous number is, and he laughed, "Well, in binary it would be a 1." ROFL Oh, you certainly mean this (let me, to make it more understandable for you, use Donald Knuth's up-arrow notation): Wait... ...wait a minute... just calculating it, and it seems to me to be a really large number, and I'm not at the end yet... puuuh, even greater than... than... ...it fills out the... how can I describe it... can you still hear me?... much greater than the number of all popcorn sub-particles in the XXL bag that Jimmi Popcorn is holding in his hands... ...and be sure he won't share even a single popcorn with you, 'cause he wants to eat all sub-particles alone! Edited February 9, 2015 by JimmiGerman Vort 1 Quote Link to comment Share on other sites More sharing options...
Vort Posted February 9, 2015 Report Share Posted February 9, 2015 Possibly, but I'm still amazed at what mathematicians can prove these days. There is something called Graham's Number, which for a while was listed in the Guiness Book of World Records as the largest known number of interest to mathematicians. If you could write digits as small as electrons, just writing Graham's Number would fill up the known universe. Actually, if you could write digits as small as a Planck Volume, Graham's Number would still fill up the known universe, according to Wikipedia. The last 500 or digits of Graham's Number are known, but the first digit will probably never be known. There's a YouTube video out there where someone asks Professor Graham himself what the first digit of his famous number is, and he laughed, "Well, in binary it would be a 1." ROFL The number of Planck volumes in the known universe is a rather small number -- something under 10200 -- compared to Graham's Number. If every Planck volume were the number 9 and you put them all in ascending exponential order (like 33³ etc., except with 9s), it would still be smaller than Graham's Number. If each Planck's volume held a googol (10100) and you lined those up in ascending exponential order...that would still be invisibly microscopic compared to Graham's Number. What is Graham's Number, anyway? By the way, numbers far, far larger than Graham's Number have since been devised. (And of course, the very largest of these unthinkably large numbers is itself a very tiny number when compared with all numbers possible.) Quote Link to comment Share on other sites More sharing options...
JimmiGerman Posted February 9, 2015 Report Share Posted February 9, 2015 (edited) So the example with the cube shows that at the 13th dimension the constellations that are mentioned were unavoidable, and that would be the point at which Graham's number appears, and, under his restrictions, no bigger number was thinkable, then. Impressing. By the way, numbers far, far larger than Graham's Number have since been devised. (And of course, the very largest of these unthinkably large numbers is itself a very tiny number when compared with all numbers possible.) But you mean that those possible numbers have not been proven? So it's only a hypothetical assumpton that there were larger numbers than Graham's or others' proven numbers by their mathematical models? Maybe, somehow and somewhere, there is a limitation, an end, and mathematical equations resulting in eternity end in singularities. But singularities are worthless for us, unimaginable, uncalculable, undescribable, beyond the frame of experimental or even theoretical physics and science. I've often asked myself why we can't imagine eternity. Maybe our mind works correctly and there is no eternity, only in our wishes and imagination...? However, we can't imagine our own death, in the meaning of total non-existence, and maybe, therefore, there is no death, if our mind doesn't deceive us, and this, on the other hand, makes us strongly believe in eternity. In this case, I would say, it ends in a draw between mathematics and religion for the moment. Edited February 9, 2015 by JimmiGerman Quote Link to comment Share on other sites More sharing options...
PolarVortex Posted February 9, 2015 Report Share Posted February 9, 2015 Maybe our mind works correctly and there is no eternity, only in our wishes and imagination...? However, we can't imagine our own death, in the meaning of total non-existence, and maybe, therefore, there is no death, if our mind doesn't deceive us, and this, on the other hand, makes us strongly believe in eternity. In this case, I would say, it ends in a draw between mathematics and religion for the moment. I find it very difficult to imagine the nonexistence of the universe. I can try to picture the universe as a large darkened sphere seeded with zillions of galaxies, and then I imagine that this sphere disappears like Samantha on Bewitched. I simply cannot comprehend what is left: no time, no space, no energy, no matter, no π, nothing. Jimmi, you earn bonus points for mentioning my hero, Donald Knuth. He came up with one of the greatest proverbs ever. He once warned a correspondent, "Beware of bugs in the above code; I have only proved it correct, not tried it." Quote Link to comment Share on other sites More sharing options...
Vort Posted February 9, 2015 Report Share Posted February 9, 2015 Jimmi, you earn bonus points for mentioning my hero, Donald Knuth. He came up with one of the greatest proverbs ever. He once warned a correspondent, "Beware of bugs in the above code; I have only proved it correct, not tried it." A few years ago in a discussion thread on another site, I used an inductive proof (proof, mind you) to show the solution to the Blue Forehead Room problem. Question settled, right? Wrong. People said, in essence, "That's a very nice proof, but in the real world, it's not that simple." "Proof" <-- Somewhere around here, I have a set of Stanford lectures by Don Knuth where he talks about his religious background (Lutheran) and how he combines his religion with mathematics. Really fascinating stuff. My favorite Donald Knuth comic: JimmiGerman 1 Quote Link to comment Share on other sites More sharing options...
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