[HN Gopher] 6174
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6174
Author : gone35
Score : 164 points
Date : 2024-01-16 20:35 UTC (2 hours ago)
(HTM) web link (en.wikipedia.org)
(TXT) w3m dump (en.wikipedia.org)
| playingalong wrote:
| That's surprising. Any informal thoughts why would even a single
| 4-digit constant exist with this property? The intuition would be
| there are multiple cycles in this graph.
| Arnavion wrote:
| The first reference in the article has the working out.
|
| https://plus.maths.org/content/mysterious-number-6174
| dcow wrote:
| The conclusion is that we don't know and therefore it might
| be coincidental. Hardly satisfying.
|
| It does appear there are cycles for other lengths.
| t-3 wrote:
| Check out https://en.wikipedia.org/wiki/Kaprekar%27s_routine
|
| At a glance, there seem to be some patterns, like how for those
| bases with a 2-digit Kaprekar number the sum of the digits is
| base-1. There must be some number theory explanation for it.
| codeflo wrote:
| There's so much numerology in the world, even among smart people,
| that I think this is worth being pedantic about:
|
| There's no such thing as a "four-digit number", only a four-digit
| _base-10 numeral_. And facts about base-10 numerals aren't facts
| about numbers.
| recursive wrote:
| A lot of numbers have representations in base-10. A fact about
| the base-10 digits is a fact about the base-10 representation
| of the number, which is also a fact about the number.
|
| You might be able to satisfy yourself by replacing "the digits
| of" with "the decimal digits in the base-10 representation of".
| codeflo wrote:
| The point is that most of the time when digits are mentioned,
| it's only a coincidental fact about one inelegant
| representation of the number -- and often people are
| insufficiently aware of that.
| bee_rider wrote:
| Base-10 isn't _in_ elegant, is it? I mean there are good
| arguments for 12 being better but it isn't like 10 is prime
| or anything.
|
| Happened across a neat comment yesterday that presents a
| defense of ten. Not 100% convinced but it is interesting to
| see pushback.
|
| https://news.ycombinator.com/item?id=39000882
| dr_dshiv wrote:
| 1+2+3+4=10
|
| And you can swear by that, if you know what I mean.
| * * * * * * * * * *
| kelnos wrote:
| It's only a coincidence if you ignore the fact that "digit"
| first and foremost refers to the things sticking out of
| your hands, and so was repurposed to talk about numbers
| because we have 10 digits on our hands.
| shermantanktop wrote:
| In some cases, the fact in base-10 has analogous facts in
| other bases. A trivial example that adding N-1 to any base-N
| number yields a value with the same digit sum. That makes it
| a bit more interesting. But I can't think of an example that
| doesn't pivot on the representation rather than something
| more fundamental.
| toxik wrote:
| 1+9=10
| semiquaver wrote:
| 1 = 1+0
| ChainOfFools wrote:
| i'm not sure what you are demonstrating?
|
| 1 sums digitwise to 1
|
| 1 + (10-1) = 10 which also sums to 1 in the same way
| shermantanktop wrote:
| Right, the digit sum of 10 is 1...perhaps I should have
| said "final digit sum." Same for 10000, or 1 with any
| number of zeroes after it.
|
| The point of this trickery is that N-1 added to any
| number is really adding N (which adds 1 to the second
| position, by definition) and adding -1 (which subtracts 1
| from the first position).
|
| In base 10, this is the adding 9 trick. It can be
| extended by using any multiple of 9. That applies to the
| N-1 version, so that adding M*(N-1) to a base N number
| yields the same digit sum.
|
| 1+9 = 10 = 1
|
| 1 + 27 = 28 = 10 = 1
|
| In hex:
|
| 1 + F = 10 = 1
|
| 1 + 2D = 2E = 10 = 1
| dbrueck wrote:
| Eh, I don't know - it doesn't really add much value most of the
| time, because these days more or less everyone uses base 10 by
| default, so it's entirely reasonable to assume base 10 unless
| stated otherwise.
|
| An argument _against_ being overly pedantic in this case is
| that this is a neat and accessible example of something quirky
| about numbers, and so even people who don 't know much about
| numbering systems can approach it. If you instead emphasize
| that it's base 10 or that there is "no such thing as a 4 digit
| number", the main thing you'll probably do is cause disinterest
| in anyone who is sometimes overwhelmed by math. :)
|
| Randomly, one of my sons told me about 6174 just a week ago,
| and it turned into an interesting conversation following by a
| little programming to find more of these numbers. After we went
| down that rabbit hole for awhile, _then_ the conversation
| shifted to how these numbers might look in e.g. hexadecimal,
| and that seemed about the right time for that topic to come up.
| selcuka wrote:
| > it's entirely reasonable to assume base 10 unless stated
| otherwise
|
| The point of the parent comment is that this is not a
| property of numbers in general. It's just a coincidence that
| only works in base-10.
|
| For example, a prime number is prime in every base. An
| irrational number is irrational in every base. Collatz
| conjecture is valid in every base. This one is not.
| ksenzee wrote:
| Is there no similar phenomenon for four-digit numerals in, say,
| base 8, or base 13?
| majewsky wrote:
| If you follow the link in the second paragraph to
| https://en.wikipedia.org/wiki/Kaprekar%27s_routine, there are
| some statements on how this routine plays out in different
| bases. For base 8, there is no fixed point with 4 digits
| (i.e. any number that immediately loops back to itself), but
| apparently there are some cycles (e.g. 3065 - 6152 - 5243 -
| 3065).
| joehx2 wrote:
| > There's no such thing as a "four-digit number", only a four-
| digit base-10 numeral
|
| Being further pedantic - aren't all digits base ten? I thought
| that was part of the definition of digit.
|
| Other bases would have different words for their numbers - bit
| in binary, for example (which, yeah, I know, it a combination
| of the words "binary" and "digit").
| Anon84 wrote:
| If you _really_ want to be pedantic, you say that every base
| is base 10 :) (in its own representation)
| selcuka wrote:
| > Other bases would have different words for their numbers -
| bit in binary, for example
|
| Do we have another example? I don't think there are special
| terms for "octal digits" or "hexadecimal digits".
| SkyBelow wrote:
| While I do personally find tricks involving numbers only in a
| specific representation to be worth a bit less, often the
| underlying pattern of the trick generalizes into a more
| interesting problem.
|
| For example, per another's link in these comments, this 'trick'
| works for 3 digits, but hits 1 of 3 possible loops for 5
| digits. From this, interesting but likely useless questions can
| arise, such as finding an easy way to test for these loops,
| seeing if there is a way to calculate the loop without brute
| forcing it, and understanding the problem enough to know how
| much of this holds true when swapping to a new base.
|
| In general, most of this is just for fun and doesn't lead to
| anything serious. But sometimes a fun problem can be hard to
| solve, possibly leading to discovering something new, which
| ends up being applicable to more serious mathematics. Other
| times it can become a trap that just seems to waste time
| without ever leading anywhere, like the 3n+1 problem.
|
| I don't think this should be considered numerology, though I do
| think sometimes people treat tricks as if they have some more
| serious meaning that they don't deserve, at least not based on
| how they are presented. 3 Blue 1 Brown goes into the spiral
| pattern of the primes as something that appears to be deep, but
| ends up being an unique way to present an otherwise boring
| tidbit about prime numbers.
| kelnos wrote:
| The word "digit" is defined as 0-9, and specifically refers to
| base-10. This meaning of the word comes from one of its other
| definitions, referring to fingers and thumbs. We have 10 of
| those (usually), hence its use as as a reference to the symbols
| used in base-10 numbers.
|
| ("Binary digit" and "hexadecimal digit" are weird terms that
| abuse the language a bit.)
| Lendal wrote:
| It's not really numerology though. Yes it's a dumb trick with
| base-10 math but that doesn't make it numerology. It's not
| trying to draw any connections between otherwise unrelated
| things. I think of numerology as trying to use stupid-glue to
| connect things that aren't connected. Like, I was born on the
| 8th day of the 2nd month, 8 - 2 is 6, the sixth planet is
| Saturn which also has 6 letters, and Jeffrey Epstein's first
| pet fish was named Saturn! OMG! That's numerology.
|
| Numerology is far stupider than this admittedly useless
| arithmetic game.
| ChainOfFools wrote:
| > Like, I was born on the 8th day of the 2nd month, 8 - 2 is
| 6, the sixth planet is Saturn which also has 6 letters, and
| Jeffrey Epstein's first pet fish was named Saturn! OMG!
| That's numerology
|
| no that's highly opinionated compressionn in the domain of
| crazy
| epcoa wrote:
| Overly specifying a nerdy arithmetic trick will reduce
| superstition? If only it were that easy. And properties in a
| specific base representation are still properties of the
| number. You haven't foiled the numerologist.
| dang wrote:
| Related:
|
| _Mysterious number 6174_ -
| https://news.ycombinator.com/item?id=2625832 - June 2011 (64
| comments)
|
| _6174_ - https://news.ycombinator.com/item?id=1625606 - Aug 2010
| (1 comment)
|
| _Mysterious number 6174_ -
| https://news.ycombinator.com/item?id=480200 - Feb 2009 (41
| comments)
| Ontol wrote:
| it is y combinator
| clktmr wrote:
| Article says it does work for all numbers except repdigits, but I
| think it fails for all palindromic numbers?
| mysterydip wrote:
| 1221 would become 2211, which avoids the difference becoming
| zero.
| chasing wrote:
| A rabbit hole into poking around a whole mess of Wikipedia pages
| about specific numbers, which was pretty entertaining.
|
| That said, https://en.wikipedia.org/wiki/List_of_numbers is
| woefully incomplete.
| prvc wrote:
| Why do you find this to be significant?
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