Talk:1234 (number)

Mock rational

Is the "first member of sequence to have a repeated digit in the first five after the decimal" property really interesting? The probability that a random decimal would have this property is more than 1/3, and it appears unrelated to the non-random repetitions in the sequence ${\sqrt {1}},{\sqrt {12}},{\sqrt {123}},{\sqrt {1234}},{\sqrt {12345}}$ as those only appear in alternating positions. —David Eppstein (talk) 05:41, 12 July 2024 (UTC)

That property looks more like clutter than a feature of interest, and the given source doesn't make a case for it. XOR'easter (talk) 19:19, 12 July 2024 (UTC)

I found it interesting within its class of numbers. Do what you want you with it, I'm done fighting irrationally over things here. Radlrb (talk) 01:16, 13 July 2024 (UTC)

The reason I kept it is, because the first two strings are 33 and 00 that repeat in base ten. While yes, this property in these numbers happen to be of more import for odd-numbered square of digits, nonetheless this is the earliest appearance within this class of numbers, regardless of whether the chance is more than 1/3 for any number (i.e., within its class it is the first, and therefore the first within its class to fall under the greater probability within all classes of numbers). Inverting the question of "probability", then "what is the probability that any of these classes of numbers will not be inline with the tendency to have repdigits in the fractional part, within fractional powers of a number" and then move on to ask, "if it is outside the boundary of expectation, how many of these are also outside the line of expectation", and if it continues to fall out of line, then there is likely interesting mathematical behavior that can be outlined in formulaic fashion (if not, the converse is likely true, unless behavior is seen much later on in the sequence). Radlrb (talk) 02:47, 13 July 2024 (UTC)

"Out of line" would be on when these digits appear, and if their appearance follows some sort of behavior (as well as on how many repeat, which is already known to show increments), and so forth. In other words, appearing earlier on or further out for the first time in the square root of a mock-rational number, has significance if these are to be taken together as a group, and tell a story-line. Radlrb (talk) 02:51, 13 July 2024 (UTC)

This being said, you both already know this, so this is half-trolling or something : ). (55:38:25) Radlrb (talk) 02:56, 13 July 2024 (UTC)

And if we are going to be entirely clear, how this: "Because it is not divisible by 4, 1234 is the first number in these sequences that is not divisible by its final digit" is any more a "relevant property" with your same reasoning (other than "substantiated by a source"), then there is not enough fair critical reasoning going on (the amount of integers not divisible by their final digit in a given base is enormous, right? *base ten if it ends in 0, 2, 4, 6, 8, or 5 aside from 5 will be divisible by 2 or 5 alone or one of its multiples; etc. Radlrb (talk)* 04:29, 13 July 2024 (UTC)) I.e., a type of WP:Cherrypicking. My point (if it isn't clear) is that your contribution, and mine, are both worthwhile. (talk) Radlrb 04:14, 13 July 2024 (UTC)

Base 10 divisibility: (no divisibility by 0, all ending in 1 are divisible by 1, all in ending in 2 are divisible by 2); 3 if the sum of all digits of that number is divisible by 3, 4 if its last two digits are divisible by 4, 8 if its last three digits are divisible by 8, etc; divisible by 5 if ending in 0 or 5, 6 if it is divisible already by 2 or 3, and therefore if the digit sum of the number is a multiple of 3; for 7 taking twice the unit digit of the given number and subtracting the remaining part of the given number needs to be 7 or a multiple of 7 (or 0). 9 is the simplest, in some senses: if the digit sum of the number is divisible by 9, then the number is divisible by 9. So, divisibility of a number by its final digit is for the most part "predictable" and not exceptional, relative to base-specific divisibility rules, and aside from enormous numbers whose very digit computations becomes difficult for, and of course, for numbers that happen to be prime (and therefore, odd-looking), which can "appear" to make more sense digit-wise relative to given ranges in different bases (and, therefore an important clue in describing them). Radlrb (talk) 04:57, 13 July 2024 (UTC)

Radlrb please stop edit-warring to add your junk WP:SYNTH non-interesting property to this article. It should be removed. Despite most of this conversation being dominated by your walls of text replying to yourself I see no other supporters of this content. —David Eppstein (talk) 23:27, 13 July 2024 (UTC)

I'm not replying to myself, I am adding context to my own points (that is extremely rude of you to even say; so why even bother collaborating with you when you lack respectful scholarship here). The support I have comes in the form of all the number pages I have written and published on where all of the editors watching and vetting the information have let it stand. It's called silent support, something you are not aware of it seems. I don't blame hold anything against them for not speaking up (they don't necessarily need to), usually people who push interesting points are deemed uninteresting by those whose time has long passed, and stick to old dysfunctional archaic ideas. Radlrb (talk) 00:12, 14 July 2024 (UTC)

Interesting would be to see you respond to some of my points, rather than ignore them. It could give validity to your perspective, however you do not want to engage. In the light of true intellectual pursuit, you come heavily short, and all from substantial prejudice you still hold against me, and people of the like, who are willing to cross bludgeoned barriers of destruction that continue to exist today. But you're not the type to fight such heavy things. Radlrb (talk) 00:16, 14 July 2024 (UTC)

@David Eppstein, @Radlrb. I don't want to interfere your conversation here, but I think asking in WT:WPM is another option to give more perspective about this mock property. Dedhert.Jr (talk) 02:28, 15 July 2024 (UTC)

Actual real world application of the interesting number paradox with respect to WP:UNDUE.

No, we do not need random facts about the number 1234 that just emerge from the fact it is a number. No matter how interesting the underlying concepts are, these facts are trivial, see the Interesting number paradox for a good explanation why. Yes, I could say that 1234 is the LCM of 2 and 617, I could list the groups of group order 1234, but does anybody really care (unless it's sporadic or something), no! Allan Nonymous (talk) 16:06, 5 August 2024 (UTC)

Article instability

I was trying to merge some footnotes (in the long version) into the main body text, but the article content keeps flipping back and forth between short and long versions. I have no opinion on which version is best, but we need to have discussion replace instability in order to make collaboration possible.

Wikipedia:WikiProject Numbers already has guidelines as to what should and shouldn't be included in number articles. @Davey2116 and Polyamorph: It might be helpful to resolving this dispute if you could identify which disputed passages should be retained under these guidelines. If you feel these guidelines are missing important facts, perhaps it would be best to start a discussion on Wikipedia talk:WikiProject Numbers specifically listing some of the most important properties across all numbers you think should be included that editors might be able to agree on, or at least accept as interesting to others. That way the guidelines could be changed to reflect consensus and the many number articles could simply follow the new guidelines. -- Beland (talk) 19:10, 7 August 2024 (UTC)

I don't have a stake in this article. specifically listing some of the most important properties across all numbers you think should be included that editors might be able to agree on, or at least accept as interesting to others. We actually already have this, but it needs updating and needs agreement. I've mentioned this previously at the wikiproject and in the current "cruft" thread there.Polyamorph (talk) 19:15, 7 August 2024 (UTC)

Following up at Wikipedia talk:WikiProject Numbers#Help remove WP:CRUFT on number articles!. -- Beland (talk) 19:26, 7 August 2024 (UTC)

AFD

This article was previously nominated for deletion, earlier this year (Wikipedia:Articles for deletion/1234 (number)). It was closed as Keep by @OwenX: this is the version that was kept. It includes much of the same material which is now being deleted. There was consensus to keep the [article so it is not correct to delete a large portion of the article without first getting consensus. These deletions are contested and there is a small edit war over the deletions. Polyamorph (talk) 15:06, 11 August 2024 (UTC)

Deciding at AfD to keep an article is not a reason to preserve that article in that state like a cryogenically frozen head. Plenty of articles are kept and then cleaned up. XOR'easter (talk) 20:07, 11 August 2024 (UTC)

Yes, of course. But the change is quite drastic and is contested. Really this is just to say there was consensus to keep the previous version, so discussion on the merits of deleting or keeping certain sections is surely preferable to continuing the edit war. Polyamorph (talk) 20:46, 11 August 2024 (UTC)

I don't find that persuasive at all; to me, holding onto junk like It is the 363rd indexed semiprime and 1234 has a prime composite index of 1031 and It is the number of partitions of 33² = 1089 into exactly four prime numbers, etc., etc. as a matter of some grand principle is just silly. If an article about a company were full of promotional language and COI drivel at the time it was kept at AfD, would we have a discussion thread for each worthless LinkedIn-ism before removing it? XOR'easter (talk) 21:04, 11 August 2024 (UTC)

No, probably not. Edit war away. Polyamorph (talk) 21:14, 11 August 2024 (UTC)

I would like to remove the claims that are not about 1234 itself (e.g., how 1031 is also the index of some other number in some other sequence); and claims sourced to OEIS entries that the OEIS itself does not mark as interesting in any way (like OEIS: A243940, which has no special keywords). The position of 1234 on the list of semiprimes is ... well, I can't think of a reason why it would be interesting, and the only sources for that are OEIS lists that don't go far enough to include 1234 explicitly. The source for the claim Because it is not divisible by 4, 1234 is the first number in these sequences that is not divisible by its final digit does not use it to argue that 1234 is interesting. The answer to the puzzle there is 381,654,729. So, that claim should go. XOR'easter (talk) 21:35, 11 August 2024 (UTC)

Some of the points mentioned in the long version might be worth including. OEIS: A006506 is tagged as a "nice" and "hard" sequence, so it's above the general indiscriminate mishmash, and 1234 is only the fifth item in that sequence, rather than being so far down the list it doesn't even show up. But the most we need say is one sentence ("There are 1234 4-by-4 binary matrices with no two adjacent entries equal to 1"), rather than a whole paragraph. Generally, anything that doesn't need to be cut completely needs to be rewritten for clarity and concision. To me, the simplest course of action would be to cut way back and then potentially re-add, carefully, so that the dead weight of overdone prose isn't in the way. XOR'easter (talk) 21:56, 11 August 2024 (UTC)

I'm perfectly fine with these edits. Radlrb (talk) 22:45, 11 August 2024 (UTC)

Thank you! Good to see this is now on a more productive, cooperative path. Owen× ☎ 22:55, 11 August 2024 (UTC)

Polyamorph and Radlrb: I didn't review the details of this edit war. All I know is that XOR'easter and David Eppstein are two of the most experienced and knowledgeable editors when it comes to WP policy and guidelines, particularly with regards to math topics. If the two of them agree that the content is unencyclopedic fluff, I'm willing to risk my reputation that this is indeed the case. Don't trigger WP:3RR by continuing this edit war. If the issue cannot be resolved here on the Talk page, take the matter to WP:DRN or to the relevant topic portal page. The decision to keep the page at AfD was based on the notability of the topic, and does not reflect an endorsement of the page content at the time, or of any content for that matter. Owen× ☎ 21:29, 11 August 2024 (UTC)

However, reverting back when two other editors chose to not just remove everything, is not with policy. I'm willing to remove some information too, I'm just surprised they were okay with mashing away with their own additions, or opinions of entries they deemed worthwhile. Radlrb (talk) 22:34, 11 August 2024 (UTC)

I'm confused by the edit summary on Special:diff/1239791869. Were you asserting this content complies with Wikipedia:WikiProject Numbers/Guidelines as it currently stands, intending to argue for changing the proposed guidelines to allow for this content, intentionally putting this article out of compliance with the expectation someone will bring it back into compliance later, or something else? -- Beland (talk) 06:52, 12 August 2024 (UTC)

I don't understand, please clarify. You also should reference the following revert I made for clarificatin needed. I.e.: You are right, I used the wrong wording. I meant, many of the properties listed here that were kept after the discussion to keep this article are points whose admission on a number article are actively being discussed, and therefore should not be used as criteria yet (for/against inclusion). Also, two other people returned the information by reverting two other editors that attempted to remove it; clearly there is no consensus to delete. Radlrb (talk) 13:51, 12 August 2024 (UTC)

Thanks for pointing out the later history...I'm not sure I understand your second edit summary either, but this is a little moot since later edits removed some of this same material but kept some of the material you were restoring. So let me ask this freshly: Given the current state of the article, is there anything you feel is missing that satisfies the current state of Wikipedia:WikiProject Numbers/Guidelines? Also, is there anything you feel is missing that would justify an amendment of those guidelines so it could be included? -- Beland (talk) 21:17, 12 August 2024 (UTC)

My pleasure. It's quite simple: 1: Why remove content here alone en-mass without a discussion as other editors asking for other pages? Small removals that are non-controversial are much more "workable" for review, however so much at once is not as tenable to go over by one or multiple editors necessarily (here it's less difficult than say at 1 or 5. And 2: Two other editors also reverted mass deletions on this page, so that's another sign that there was no true consensus to take it all out at once. Then that consensus changed, leading to the present state of the article.

On your fresh second set of questions, I personally would include the sequence on binary that was here before, I don't think 22 is too far down the line, infinity is quite a large incalculable number, so 22 is quite small in comparison. Aside from that, this would be the only sequence that would be admissible from what existed prior, given the guidelines as they existed then and maybe now. Maybe the "triangle of the gods" sequence is also admissible from the perspective that it is a well-known sequence that asks an interesting question: which is the first prime entry? (My extension would be, in all relatively small bases, which is the first such prime entry? I digress, though). However, that's not relevant to 1234. Because it has been covered with weight by secondary sources, I think this entry is worthwhile. Radlrb (talk) 01:04, 13 August 2024 (UTC)

Binary sequence and triangle of the gods

@Radlrb: OK, if I'm understanding correctly, these are the passages in dispute:

1234 is the number of "straight" binary strings of length 22 (i.e., the simplest way of representing quantities with binary numbers), equivalently the number of finite Sturmian words of length 22.

and:

The sum of the base-ten digits of 1234 forms the fourth triangular number (10). 1234 is more specifically the fourth member of the "Triangle of the gods" sequence, obtained by concatenating decimal representations of positive integers.

References

It looks like the binary passage fails NUM/OEIS, because it doesn't cite any citations outside of OEIS that establish this sequence is important enough to mention.

It looks like the "triangle of the gods" passage fails NUM/NOPAGE, because there is no Wikipedia article Triangle of the gods, which is an indication that it is not important. The first cited source for this passage is OEIS, which is discounted. What do Pickover and Guy say about 1234 and the triangle of the gods? (By which I mean, could you give us a direct quote from these books that supports the idea this fact is important enough to mention?)

If other editors have arguments on the merits for or against inclusion, I'm curious to read your thoughts as well. -- Beland (talk) 01:53, 13 August 2024 (UTC)

The first point could be substantiated with a reference cited in OEIS, L. Dorst and A. W. M. Smeulders, Discrete straight line segments: parameters, primitives and properties. Vision geometry (Hoboken, NJ, 1989), 45-62, Contemp. Math., 119, Amer. Math. Soc., Providence, RI, 1991, though I haven't read into it (it comes from OEIS, maybe therein could be found some other sources, one would have to check).

The "triangle of the gods" sequence is trickier, because it's referencing does not cite uses, however, it is a well-known sequence that has attracted attention of number-theorists over time, and that's really why I would include it; it's more or less a significant curiosity. But, maybe this is not enough, admittingly. It, not having a Wikipage as our outlines say, is not necessarily a determiner of inclusion, yet it is a strong indicator. Radlrb (talk) 02:04, 13 August 2024 (UTC)

OK, not having a strong opinion myself, how would other editors evaluate these passages against the proposed guidelines, given these sources? -- Beland (talk) 02:16, 13 August 2024 (UTC)

The "straight" binary strings line is incomprehensibly written. Is it supposed to be talking about strings of bits, i.e., where binary string redirects to? That is certainly how many readers would interpret the phrase binary strings of length 22, i.e., sequences of 22 characters, each of which is either 0 or 1. But then what is a "straight" binary string? (Is there a Kinsey scale for bit sequences?) The parenthetical about the simplest way of representing quantities with binary numbers clarifies nothing. The last part of the sentence mentions finite Sturmian words and links to an article that says a Sturmian word is infinitely long. So, a reader trying to learn what a finite Sturmian word might be is completely lost. I looked up the Dorst references cited by the OEIS entry and figured out what the rather cryptic comment there was trying to say (it's talking about rasterizations of straight line segments), but since we don't have articles on Farey fans or any of the other related concepts, it's hard to argue that the property is interesting enough to include here.

The statement The sum of the base-ten digits of 1234 forms the fourth triangular number (10) is a roundabout way of saying $1+2+3+4=10$. The triangular numbers just are the sums $1+\cdots +n$, so the text isn't saying anything special; indeed, it's making a mundane observation sound more special than it is. Inserting more specifically into the next sentence confuses the logic; the second sentence isn't narrowing down the statement in the first to a special case or anything like that.

It's bleeding obvious that "1234" is the concatenation of "1", "2", "3", and "4". So, is there anything to say about that? Not really. The book by Richard K. Guy briefly mentions the sequence made by concatenating base-10 natural numbers, but it doesn't say anything in particular about 1234. Pickover talks about a different sequence, made by appending successive digits. The two sequences agree up through 123456789, but Pickover follows that with 1234567890 whereas the next number by Guy's definition is 12345678910. There's some interest in concatenation sequences as a whole, but nobody picks out the number 1234 and says that it has a special position in any such sequence. XOR'easter (talk) 01:05, 14 August 2024 (UTC)

1234 is the smallest whole number that contains the digits 1 through 4 in decimal

Why is this an important property? What is the justification for excluding 0? The smallest number that includes the first four digits in decimal (or any four distinct digits) is 1023 [1]. And maybe more importantly, where is the source for this being a significant property? —David Eppstein (talk) 02:12, 13 August 2024 (UTC)

I have removed it and restructure the article. For some reason, I think this should be merged to 1000 (number) per WP:BLAR. I do not think 1234 has its own article. Dedhert.Jr (talk) 12:34, 13 August 2024 (UTC)

Lets see if we can save it with two more math properties, it might be possible. Radlrb (talk) 17:16, 13 August 2024 (UTC)