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Post by little j ᵛᵉʳᶦᶠᶦᵉᵈ ✔ on Feb 15, 2017 8:35:55 GMT -5
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Post by Waveon on Feb 15, 2017 16:01:07 GMT -5
So 196 is special because it's possibly not a palindrome, yet it's not the only number that's possibly not a palindrome.
196 is also a candidate for being a lychrel number, yet there are other numbers that are also candidates for being one.
196 appears to be the smallest lychrel number, yet there's no proof or certainty.
Speaking of which, he also mentions how there are no definite lychrel numbers yet, only candidates.
Then he goes on listing the candidates, but fails to mention a glaring pattern... most have an interval of 99. Now apparently this is just coincidence, there are candidates between the numbers he listed. But it still makes me more interested why there's an exact interval of 99. And yes, even the noted 689 has this pattern, though it's by 2x99 since 787 is already an palindrome.
"A rough, but not quite anagram" Really? That just seems like grasping at straws.
And in the end, even if my above complains didn't apply, why 196? Why not it's partner, 691? What makes 196 more special than 691? After all, both are are required to get to a possible palindrome, and thus to prove his point.
Yeah, I might be over analyzing this, but there are just so many issues with his reasoning of why 196 is "special". Nothing special about 196 has been shown in that vid.
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Post by little j ᵛᵉʳᶦᶠᶦᵉᵈ ✔ on Feb 15, 2017 18:40:21 GMT -5
Maybe you could shoot the guy an email and start corresponding with him about the problem.
Also note that the 99 pattern quickly falls apart after 689. May not be enough to go by.
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Post by Waveon on Feb 15, 2017 18:51:24 GMT -5
Nah, I'm not a mathematician. And he's probably just another youtuber trying to get views like any other youtuber.
It just triggers me how people set up a whole premise and story that just has so many holes. It triggers me even more that people fall for these things and often don't even think about what they've read/watched/heard/whatever.
Also, the 99 pattern fails even earlier at 97 (196 - 99), which has a fast palindrome of 44044. As I said, probably just coincidence, still interesting there's even such pattern.
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Post by little j ᵛᵉʳᶦᶠᶦᵉᵈ ✔ on Feb 15, 2017 19:27:07 GMT -5
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Post by Waveon on Feb 15, 2017 19:42:13 GMT -5
Clearly not in marketing or sales pitches though.
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Post by little j ᵛᵉʳᶦᶠᶦᵉᵈ ✔ on Feb 15, 2017 19:50:21 GMT -5
Nerds rarely are.
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Post by Mastery on Feb 16, 2017 8:20:19 GMT -5
why's this gotta be waveo exclusive
Numbers is my jam
PALINDROMES IS DEFINITELY MY JAM
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Post by Mastery on Feb 16, 2017 8:23:16 GMT -5
the reason 196 is special compared to 691 is because it's the "smallest" candidate
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Post by little j ᵛᵉʳᶦᶠᶦᵉᵈ ✔ on Feb 16, 2017 11:53:26 GMT -5
why's this gotta be waveo exclusive It's the number involved. PALINDROMES IS DEFINITELY MY JAM And yet, not a single palindrome in that post. You're a disgrace. |
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Post by Waveon on Feb 16, 2017 15:49:40 GMT -5
But it's because they're nerds that their reasoning tend to be more logical. This video didn't have logic, just assumptions. because it's the "smallest" candidate He said 196 appears to be the smallest candidate, but he immediately admits that there's no proof or certainty at all. So there might be a smaller candidate. Maybe 196 is a palindrome after all. Maybe it's neither. Maybe there's more to either system. We just don't know and only have assumptions. I say assumptions because he literally said there's no proof, meaning 196 could be anything right now. Hell, it theoretically could be the biggest Lychrel number. Unlikely, but still a possibility with all the uncertainty he's been saying. |
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Post by little j ᵛᵉʳᶦᶠᶦᵉᵈ ✔ on Feb 16, 2017 16:22:35 GMT -5
He said 196 appears to be the smallest candidate, but he immediately admits that there's no proof or certainty at all. So there might be a smaller candidate. I'm fairly certain that numbers 1 through 195 have been empirically tested to show that they end in a palindrome, thus the focus on 196. The purpose of the video isn't to prove anything, but to introduce the viewer to something new and interesting that they have never seen before. It's someone saying, Hey, let me show you some stupid thing that's pretty cool. And by exposing a large number of people to the concept via Youtube, they may get the attention of a viewer who just might have some insight to offer. So just say, Huh, that's neat, and maybe work the problem out. : ) SPEAKING OF WORKING THE PROBLEM OUT The thing I think that makes problems like this so tricky to work out is that it's dealing not with the number itself, but with how it's displayed and written out. Such a thing would be of greatest interest to a computer scientist, who may have to convert numbers between different bases. So, to be able to work on the problem, I'd have to ask: Is there a way to rigorously define one number as being another flipped around that is independent of said numbers base? I know the wording is a little weird, but saying, 691 is 196 flipped around, isn't mathematically rigorous. I guess what I'm saying is, is there an algorithm that lets you take a number a, and write out its palindrome in any chosen base b? I would imagine such a thing does exist, and would involves a but of logarithms, modulos, and summation series. So, correct me if I'm wrong, but the number of digits a natural number a would have in base b would be, floor( log b a ) +1, correct? |
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Post by Waveon on Feb 16, 2017 17:49:14 GMT -5
He said 196 appears to be the smallest candidate, but he immediately admits that there's no proof or certainty at all. So there might be a smaller candidate. I'm fairly certain that numbers 1 through 195 have been empirically tested to show that they end in a palindrome, thus the focus on 196. The purpose of the video isn't to prove anything, but to introduce the viewer to something new and interesting that they have never seen before. It's someone saying, Hey, let me show you some stupid thing that's pretty cool. And by exposing a large number of people to the concept via Youtube, they may get the attention of a viewer who just might have some insight to offer. So just say, Huh, that's neat, and maybe work the problem out. : ) Even then it's a very vague and baseless explanation. He just goes on and on about "196 is amazing because we don't know, oh and also these other numbers and systems that we don't know". No, I don't find it neat. I find it too assumption-based. "There's no proof, so we don't know, but we'll assume on these uncertainties" yeah no thanks. We have a Dutch saying, "Aannamens doen je de das om." Not sure about the English translation, but it basically means that assuming things will mostly create more issues than not. The thing I think that makes problems like this so tricky to work out is that it's dealing not with the number itself, but with how it's displayed and written out. Such a thing would be of greatest interest to a computer scientist, who may have to convert numbers between different bases. So, to be able to work on the problem, I'd have to ask: Is there a way to rigorously define one number as being another flipped around that is independent of said numbers base? I know the wording is a little weird, but saying, 691 is 196 flipped around, isn't mathematically rigorous. I guess what I'm saying is, is there an algorithm that lets you take a number a, and write out its palindrome in any chosen base b? I would imagine such a thing does exist, and would involves a but of logarithms, modulos, and summation series. So, correct me if I'm wrong, but the number of digits a natural number a would have in base b would be, floor( log b a ) +1, correct? I'm not sure if the last one is correct, so I'm not even going to try to be a smartass there.  However, I do agree that the display is an issue that's probably a major factor. Humans tend to be visually orientated, after all, so these math magic will give our brains a BSOD. Hence the whole log() and and number a notation, there's a lot of logic and magic behind it that's tough for the average person to comprehend. So is there some magical algorithm for palindromes or anything? Maybe, but I think it doesn't necessarily have to stop at being an algorithm. There's highly likely some other magical math thingy that would defy algorithms and other known calculations, and yet actually solve these problems. If there isn't.... Why haven't we gone to space and populated Mars already? |
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Post by little j ᵛᵉʳᶦᶠᶦᵉᵈ ✔ on Feb 16, 2017 22:05:31 GMT -5
So investigate the assumption.
So, yeah, this got me thinking about getting developing this algorithm. Some poking around shows that, yes, floor( logb a ) +1 is how you represent the number of digits a has in base b. I guess we could call this the d value.
So, let's start with a number in a base we are familiar with. I choose the year I was born, 1986.
Divide by 1000, round down to nearest integer. Save it. That give us 1.
Divide by 100, round down, mod by 10, multiply by 10. That gives us 90.
Divide by 10, round down, mod by 10, multiply by 100. Gives us 800.
Divide by 1 (to keep the pattern), round down, mod by 10, multiply by 1000. 6000.
Add them together, you get 6891.
That sounds like a summation series. Let me see if I can Sigma notate this, and generalize for other bases. We'll call this the flip function.
flip(a) =
d
Σ bd-n(floor( a/bn-1 ) mod b)
n=1
Where b is the base you wish to work in, and d = floor( logb a ) + 1.
Does this look ok to anyone?
Now, of course, a would be a palindrome if a = flip(a), but I don't know where to start with that. Simple for computers, not so simple with pure maths...
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Post by Mastery on Feb 16, 2017 23:34:27 GMT -5
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