Talk:2

Conway joke
The bit I removed... Guy and Conway wrote: "Two is celebrated as the only even prime, which in some sense makes it the oddest prime of all." This is a joke, because of the incongruousness of applying the ordinary meaning of "odd" to an even number. This does not mean that the number 2 is ever actually referred to using the expression "the oddest prime". Of course JHC and RKG are as impeccable a source as you could have for a maths article, but I do not think this adds anything in an elementary exposition of the properties of 2. Imaginatorium (talk) 04:24, 22 September 2023 (UTC)


 * Humor can aid the learning process. People are capable of differentiating terms, especially when described appropriately. Memory improves drastically when information is diversified properly, without lending to confusion, and when the information is tied to things not directly related to what is being presented at hand that others might find meaningful. I would prefer to re-include this in a note, since it is a historically valuable quotation from a reliable source, however I see your point and it is valid, though I believe it can still be incorporated in a more indirect way. Radlrb (talk) 17:03, 25 September 2023 (UTC)
 * Yes, but Wikipedia is supposed to be an encyclopedia. It is supposed to give an overview of a topic to the general reader (at least as far as this is possible within the constraints of necessary technical background). It is not supposed to include everything anyone can find in a Wreliable source that might have some connection with the topic. As I said at 5 I do not think that the huge amounts of sometimes extremely technical content that you have been adding to these articles is an improvement. Absolutely nothing personal, but I will start an RFC somewhere to see if everyone disagrees with me. Imaginatorium (talk) 18:07, 25 September 2023 (UTC)
 * Alright. Please move forward with it. This quote relates entirely, which is why it has lasted so long, relevant to your point. I'd like to point out that you are not being constructive in seeking amendments, and are firing away immediately toward an Rfc. Inclusive, of me writing in your talk page a while back, yet you chose to not give a response, whatever it may mean . Radlrb (talk) 21:11, 25 September 2023 (UTC)
 * Writing as a great admirer of the late Professor Conway, I must sadly agree that his comment is unsuited to this page. It might be used in his own article as an example of his humour, but it's not helpful in explaining the properties of the number 2. Certes (talk) 22:43, 25 September 2023 (UTC)
 * Its actually useful in amplifying the property of it being the singular even prime number, if one can get accustomed to the idea of being presented both a true statement and a humorous juxtaposition at once, and generate a stronger first impression. That's deeper philosophy of psychology of learning, here being a great example of this; of course it can backfire, but I rather tend on the end of generating an article suitable for all audiences on an elementary property, that might bring to light some joy, even if it is a challenge to bring together if not ready. Again, a note is actually harmless, and it being a note too would let the reader understand the nuance; esp. when including explicitly a statement about the infinitude of odd numbers. Radlrb (talk) 23:39, 25 September 2023 (UTC)

The pool ball 2
"2" is the notable number of the second pool ball. Its color is blue.

191.255.194.29 (talk) 10:01, 30 October 2023 (UTC)


 * Please see related discussion at Talk:15 (number). Certes (talk) 12:42, 30 October 2023 (UTC)


 * For any n from 1 to 15(?), the nth pool ball is marked n. The colour is not notable, and any generic n statement is not notable. Therefore these should not go in. Imaginatorium (talk) 13:47, 30 October 2023 (UTC)
 * I am asking myself: would the typical reader look for this information in 2, or in Pool (cue sports)? However, without a good source, I'm not sure it belongs even in the latter. Certes (talk) 14:46, 30 October 2023 (UTC)
 * It belongs in the latter, with a source. Polyamorph (talk) 14:56, 30 October 2023 (UTC)

Semi-protected edit request on 22 February 2024
2 is the second number in the number line 74.142.90.6 (talk) 16:39, 22 February 2024 (UTC)
 * Red information icon with gradient background.svg Not done: There are numerous number lines. It is not the second number in the real number line, the integer number line, or even the natural number line if you include zero (which is often the case). This would also be self-referential and so not helpful to a reader. Tollens (talk) 17:38, 22 February 2024 (UTC)

Why is this page semi protected?
and 3 is not 120.21.89.235 (talk) 22:38, 21 April 2024 (UTC)
 * Some Wikipedia articles, such as those for political leaders, are routinely permanently protected because they would otherwise be frequent targets for vandalism. Others are protected temporarily when the level of vandalism becomes too high. That's the case here. It's perhaps time to lift the protection here. HiLo48 (talk) 02:25, 22 April 2024 (UTC)

Transcendental numbers
In this section you added the following paragraph - I have removed the reference clutter, and included the "efn" bits in the text, to attempt to make it readable. The problem is that despite being a native speaker of English and holder of a maths degree I can make no sense of it at all...

"In decimal representation, after the first two, three, four and five digits in the approximation of $\pi (\approx 3.14159)$ the number 2 is the only digit greater than zero not yet represented (overall, up to the largest appearing digit). [Where also, operations of strings $1 \times 2^{2} = 4$ and $ 5 - 3 = 2$ are collectively satisfied.]"

Is the "efn" supposed to be a qualifying clause on the end of the preceding sentence? I understand "after the first n digits", for some n, but your sentence baffles me. Can you explain? Imaginatorium (talk) 07:37, 14 June 2024 (UTC)


 * The note is not a qualifying clause for the sentence. Just, 5 - 3 = 2 and one times the square of two as four (or conversely) in between, as an addendum (both operations on strings can only be true when inputting 2). There could be a simpler way to write this. Radlrb (talk) 12:22, 14 June 2024 (UTC)


 * Thanks for replying. First an English problem: "where" is a relative pronoun, so it cannot normally start a sentence, particularly followed by a comma. Perhaps it could be "Here, ..." -- but I still have no idea of the relevance of the trivial numerical identities. I really do not understand at all what you are trying to say. Is one example of the facts implied by the sentence that "after after the first three digits of $$\pi$$ there are representations of the digits 1, 3, 4, 5, 6, 7, 8, and 9"? Is that right? What does "representation" mean? (I looked at the various linked topics, and wondered if the relevant one was "strings" in computer science, which I am familiar with, but I have no idea how that could be relevant.) Imaginatorium (talk) 13:55, 14 June 2024 (UTC)


 * Followup: just made an edit summary: "This is not true. 6,7, and 8 are all also numbers greater then 0 that aren't represented in the first 6 digits." I assumed that anyone would see that, and that somehow there was some other meaning conveyed by "represent" other than simply "these digits appear in the decimal representation." Hoping for some clarification eventually. Imaginatorium (talk) 16:21, 14 June 2024 (UTC)
 * I removed the part that I meant to remove in the first place, until it can be clarified, if needed. Dhrm77 (talk) 16:35, 14 June 2024 (UTC)
 * No, the point was, if you read carefully, up the the highest digit represented, or appearing from that base. I.e., and I guess it is not obvious: first in up to the first two digits, in 3.1 only 2 is not yet represented in the set covering set of what would be {1,2,3}; in 3.14 2 is not represented in (1,2,3,4), and at both 3.141 also 2 is not represented in {1,2,3,4}, as with at 3.1415; the only digit in {1,2,3,4,5} not yet represented is 2. Then, comes 9, in 3.14159... (which is the sum of the second prime and composite), which is where you two are referring to, and what I was not referring to, which is why I added the specific wording alluding to this (up to the "LARGEST"-yet appearing digit). Radlrb (talk) 18:16, 14 June 2024 (UTC) Then after these comes 2, at the seventh position. Radlrb (talk) 18:33, 14 June 2024 (UTC)
 * So if I understand correctly, we are comparing the digits of pi to the list of integers at each step. This is a very arbitrary thing to do, and what is the point? Is there a purpose to it? Will the reader actually learn something useful from that? Dhrm77 (talk) 18:52, 14 June 2024 (UTC)
 * Yes, that in base ten (i.e. with digits 0;1,2,3,4,5,6,7,8,9), the number 2 is the only digit missing up to these points. Then followed by 2,6,7,8 which add to 23 (the ninth prime, at this location, ALSO the sum of the digits "3.1415"!!; come on). Then followed by two. It's cool, more than just cool...incredibly interesting and telling if you have the sensitivity to understand how immensely useful and absolute most unlikely to be trivial, if you don't think its meaningful then you don't think so, but if you have any hope for something in mathematics that makes sense, instead of fronting the same arguments over and over, over "trivialities" that I am adding (meaning you are not really clicking with what is going on here), then you will noot want it removed. I don't, we can vote on it. Then let it to history to see if these sort of things were worthwhile, when our world is dying and we need so many things to save us from absolute asynchronous boredom and shitdom. Radlrb (talk) 19:19, 14 June 2024 (UTC)
 * PI is interesting, no matter what base it is expressed in. When you look at PI in a specific base, play with its digits, and try to find meaning in that, it borders on numerology. I would also point out that it is unsourced, and can be considered original research. See OR. Dhrm77 (talk) 19:44, 14 June 2024 (UTC)
 * Yes, the first mathematicians were numerologists by modern standards, in deep thought and in practice. That's how you have modern mathematics (see most brilliant mathematicians reference God at some point as the highest ideal, or the Self; and how it is pure mathematics). People trying to find symmetry when er'yone else said "no". Today is just a more technical re-manifestation of the same prejudice that mathematics "cannot have true and complete meaning" in all manifestations of existence (i.e., lower the power of mathematics onto the real world, because it seems too "chaotic", or in other words, too complicated for simple minds to see the enormous and extensive symmetry that does NOT necessarily easily appear in minute scales of approximation, large or small). That will pass like it has each and every time there is a full and complete revolution in knowledge, which we are currently going through (for the first time in many Millennia). Radlrb (talk) 19:48, 14 June 2024 (UTC)
 * And yes, people don't play around enough, that's exactly what the problem is here, everything is still so stagnant (and stoic) in society, that it has putrefied the keys to understanding how to dig into truth *(and suffer through it openly as it undoes misunderstandings, unafraid Radlrb (talk) 01:14, 15 June 2024 (UTC))*, which requires exploring paths of novelty. Like a l w a y s. Never has doing nothing new led to new information, except in the emanation of nothingness itself that generates All. Radlrb (talk) 19:54, 14 June 2024 (UTC)
 * Recreational mathematics can be fun and stimulate interest in the subject, but Wikipedia isn't the place to play. This looks like original research to me.  Even if it were supported by a reliable source, I don't see how it would enhance even a relevant section like Pi, let alone an article about the number 2. Certes (talk) 16:47, 15 June 2024 (UTC)
 * Well I can’t help you on any of that Certes, to me Wikipedia is an extremely fun place, but that’s because I enjoy knowledge and find life like a game of love. I guess when you take away the element of joy in Wikipedia, you can’t see how it stimulates the game of learning. But that’s because in the West we don’t understand what gaming really even is, since it’s rooted in notions of “winning” and “losing”. I’ll take it out then, glad it was shown here, as it is a key to understanding pi, and connections with the circle as being defined with two points (for a circular diameter and as a digon), very naturally (so pi better have something to do with 2 very directly at the fundamental numeric level - here one a base-ten rep. with 9 as a largest digit - and, with the unit, aside from being a direct expression of pure space and zero; this is an extremely useful elementary connection). Radlrb (talk) 19:13, 15 June 2024 (UTC)
 * Any property that only works in base 10 raises a small red flag for me, because there's nothing mathematically special about the number of fingers our species typically has. Pi has one 2 in its first ten decimal places, and one 2 in the next ten: exactly the expected number, which is unremarkable. Certes (talk) 20:12, 15 June 2024 (UTC)
 * How is that the expected number? If anything, the fact that it hits 23 at the first six digits with an end in 9, links the prime index with the base itself (where 9 IS THE SUM of the second prime and composite, where nine is the largest numeral represented in base ten). That is remarkable. I’m going to check and see in which of the first 100 bases this happens in. Again, linking digits, with prime indices, in two different ways (sum of digits at the sixth decimal place, and sum of digits absent, coincide). Actually, there are three notions being tied at once: digit sum, appearing digits, and absence of digits. Not trivial, no matter how one looks at it. In fact, at that point, you’d have to define triviality and a measure of triviality, before throwing that word around without care (meaning, preventing a revelation of something deeper, simply because of being used to ignore the possibility). Again, opening doors rather than closing them. The first 0 in pi occurs at the 33rd decimal place, and the next two at the 165th and 168th place, indices that add to 333 and have a difference of 3. Unremarkable, huh, when the first digit is also 3? Seems like nothing will ever be enough (0 then violates your “expectation” in this example for pi, yet likely still not worth your interest). Radlrb (talk) 21:36, 15 June 2024 (UTC)
 * I mean "expected" in the sense that the expected value of the number of 2s in ten random digits is 1, so finding precisely one 2 in a ten-digit sequence is no surprise. Of course, the digits of pi are not random, but they follow no obvious pattern and pass most statistical tests of randomness. Certes (talk) 21:49, 15 June 2024 (UTC)
 * You cannot claim an “expected value” on the decimal expansion of a transcendental number, since a formula for it will naturally yield a value whose strings of digits have a variation that is not ordered in any way (since it is not a quotient of rational numbers, and more deeply, not the root of a non-zero polynomial of finite degree with rational coefficients). However, patterns inside could come in other forms, such as partial sums of strings, and other arithmetic properties deeper inside. That’s yet to be really studied, however. We can’t claim anything on it. Your last sentence was not logical, it is self-contradicting. (Not random, but yet random?) Radlrb (talk) 21:58, 15 June 2024 (UTC)
 * I think you are showing you are out of your depth here. The probability of finding the entire text of the King James translation of the Old Testament in pairwise decimal digits read as decimal ASCII in the digits of pi is surely 1. Anyway, that's enough really. Imaginatorium (talk) 03:22, 16 June 2024 (UTC)
 * Ah? Surely you don’t expect the 33rd location string of pi to be the first zero string right? Yet it is. What nonsense are you uttering right now? (Yes, the probability of finding the entire spatial metrics - in whichever measure - of the multiverse inside digits of pi will also be very likely be 1, if those metrics are coordinates fixed on a two-dimensional complex plane; but why bring this up?) Because I said nothing on the probability of finding two twos in the first 20 digits of pi, as Certes pointed. No, while you can “mathematize” a “probability”, that will only give you a mean average of what to expect, which is different than what you will actually see in given ranges; moreover, look at the placement of zeroes or any other digit and your “probability” function will actually tell you nothing of whether that does pan out in a given range, and with what population of other digits. In some ranges it will be much closer, and some far out. Of course, when mathematicians today are so inclined to rely on probability rather than true mathematical behavior, you will confuse the two, or even worse, forget about looking for the latter. Radlrb (talk) 04:13, 16 June 2024 (UTC)
 * Let me add here one thing: pi is not yet proven a normal number... expected (pun intended), but not proven; this is also not a singular value, but a range of 10 numbers, so by expected value I meant something far stronger than just a mere "average of averages". Radlrb (talk) 07:31, 16 June 2024 (UTC) And, even then, the idea that all possible strings of numbers exist within pi (or that any digit appears an infinite amount of times) is still not proven to be absolutely true. Radlrb (talk) 07:41, 16 June 2024 (UTC)
 * Have you ever added new material to number articles? Or did you just join the Numbers Project so that you can frustrate the hard work that others make, where you can’t seem capable of adding material yourself. Radlrb (talk) 04:20, 16 June 2024 (UTC)
 * But yes, enough, actions speak louder than words. Radlrb (talk) 06:10, 16 June 2024 (UTC)