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Related to this question, except I do not believe (and have not claimed) that I have solved an open problem, famous or otherwise.

I came up with an idea (specifically, how to pronounce numbers in bases that are a power of two) that I think is useful for the research community, for educators, and in recreational math.

I have seen it mostly ignored and poorly understood. Occasionally it has been ridiculed and called 'pure crankery', 'Doctor Seuss names', 'pure bullsh*t' without the asterisk, downvoted, and even in a some rare cases deleted on internet answers sites. But about three (out of about a hundred) maths and computer professors have said it is 'valid', 'very clever, or 'works to some extent' (all on Quora).

How do I interpret this? How to find out whether I am a crank? I am not aiming to convince others that I am not a crank because only others can judge whether I am a crank or not. I don't want to convince people that I am not a crank if I actually am one, because that would mean I would be more likely to stay deluded, if I am deluded.

How should I respond to those that refuse to discuss the idea on the ground that it is crankery? What are they thinking?

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    I removed a number of obsolete comments and moved the others to chat. Please read the post notice and this FAQ before posting another comment; we can only move comments to chat once.
    – Massimo Ortolano
    Mar 29 at 17:21
  • The move to comments led to some meta discussion, which has been moved to a separate chat. Please note the FAQ above; any comments below this one should suggest improvements or request clarifications to the post.
    – cag51
    Mar 31 at 2:29
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    I removed some arguments in the comments; please note our code of conduct. I also rolled this question back to an earlier version -- the question has already gone through being closed and reopened, so let us not wildly deviate from the version that the community voted to accept.
    – cag51
    Mar 31 at 19:42
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+100

A lukewarm response would mean that either the idea is not interesting or useful to the intended audience. You should try to judge whether the idea is intrinsically interesting (the question certainly indicates that you feel so) and whether you are approaching an appropriate audience using an appropriate medium.

It certainly seems that you are pushing the idea too hard when you face a lot of indifference and still continue to reach out to individual professors. It is evident that they aren't interested in discussing it, and you should respect that. Maybe the proposed method has value in a different setting. Not every tool that is/could be useful to a researcher is published in scientific literature or discussed on academic fora. Seek out other media, gauge interest and try to identify if there is a group that is interested in/benefits from the idea as you envisage them to.

If you don't find such a group, record the method somewhere, preferably on an open platform and simply leave it until somebody that finds it useful comes along. If the idea is ahead of its time, then you should wait for somebody visionary enough to come across it. If you feel that the idea can do with more refinement, keep working at it and then try exhibiting it once you find significant improvement. Or if you feel it can be monetized and are interested in that, explore intellectual property options.

The bottomline is, irrespective of the true worth of an idea, it is counter-productive to force people to take note of it.


EDIT: Since articles related to the idea/tool have recently been shared by the OP, I am adding a few thoughts specific to the present situation. I hope that these will help clarify the difference between a research submission and an invention.

At the outset, the idea is (to me) clever, of possible interest to hobbyists and recreational number crunchers, and may have some potential contributions to specific fields (linguistics). There is no indication of crankery. As such, a case may be made that this idea (once established as novel) could be converted into a research submission. To make this case, the following crucial points would need to be addressed:

  1. Identification of a target group/domain which would be benefitted by this work.
  2. A clear and emphatic justification of why there is a need to undertake this effort. Presently, this is lacking. There must be a concrete use-case or demonstration of value, beyond a general statement of it being interesting or 'worth exploring'. Without this, the academic reader would conclude that insufficient background study and thought has gone into this idea. The onus of establishing worth through objective arguments lies on the author of the idea, not on the reader.
  3. A discussion of why this has not been addressed so far (i.e. did nobody think of it or was it not worth the effort), and the related work that has already been done in the field. This may indeed require access to some academic literature, but is necessary. Hopefully OP has found some useful references in the linked answers.
  4. A clear statement of what benefit the proposed tool gives. Is it to make teaching easy (in that case, look for a pedagogical audience)? Is it to enhance linguistic/numerical abilities (look for a linguistic audience)? It is going to make some computational process more efficient or unambiguous (go to computer scientists)? Is it going to add to how we deal with number systems (seek out mathematicians)?
  5. Related to 4., demonstrate (ideally quantitatively) that the tool achieves this objective in comparison to the existing procedure, and therefore is worth consideration.

If these can be addressed, the response from academicians may be warmer. Personally, I think the blog format is well-suited and is quite engaging for these ideas.

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  • Could you provide some examples to illustrate your points? I'm wondering what sort of size document you are envisaging for example and just how formal the language would have to be. Apr 5 at 8:25
  • @MatthewChristopherBartsh : The primary form of scientific communication in many fields is a scientific journal. Each journal has its own style guide that specifies these points (they can vary significantly). As example, see this guide (selected because of its reputation and because you won't be blocked by paywalls): nature.com/nature/for-authors/formatting-guide Apr 5 at 13:30
  • @MatthewChristopherBartsh I should also mention that there are some journals which cater specifically to recreational math. You'll be able to find them quite easily on Google. Apr 5 at 13:31
  • Should I send a link to an article on my blog to the journal? Apr 6 at 12:10
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    1. No. Ideas are plentiful and incredibly cheap, this is often hard to swallow. For an idea to stand out, it's context and presentation very much matter. This is true in most spheres of human activity. 2. I mean that I found the blog articles quite engaging and interesting. I'm not sure that converting them to a journal article is worth the effort, but that's only my opinion. Apr 6 at 13:02
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If I draw a drawing on a piece of paper and show it to some friends, that won’t make me a crank despite the fact that I have zero talent in drawing. But if I start claiming my drawing is an important work and should be published or sold or talked about, then I am a crank. The difference is in having a realistic view of the significance of what you’ve done.

Your idea is “valid” and can be reasonably described as “clever”. It is a cute idea, in the same way that I thought it was cute one day many years ago when I discovered I can count all the way to 1023 using my fingers instead of 10 if I make use of binary representations. But your idea is not an idea in math — maybe in math education or in the general area (that doesn’t have a proper name because there is little need for one) of math terminology/notation. And, like my idea at the time, it solves a problem that I don’t think is a real problem anybody has: there just aren’t enough people with a need to extensively communicate numbers in base two by reading them out loud.

What does it mean when on the Internet most academics ignore your idea, and a few say you are a crank and a few say your idea is valid?

It means your idea is technically valid but not as interesting as you think it is.

How do should I respond to those that refuse to discuss the idea on the ground that it is crankery?

You should not respond in any way but leave those people in peace. People have no obligation to discuss your idea, and if they don’t want to discuss it then it means they don’t think it is interesting enough to discuss. Find someone else who does, or find a better idea that people will be more impressed by.

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    I was once told that in some cultures the fingers have an ordinal, not cardinal sense. So, if you want to signal the barman to bring you one beer, hold up your pinky. But if you hold up your index finger you get four. I told this to a group of students once and was asked by a wise--guy "How do you ask for three?". Not my proudest moment as a professor, but I did demonstrate.
    – Buffy
    Mar 27 at 19:33
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    This answer and Stephen McKean's answer combined would be a very good answer. +1
    – justhalf
    Mar 29 at 11:48
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    @nick012000 Using binary numbers in general does solve a real problem that people have. Using your fingers as binary digits, not so much. There is not often a reason to indicate several hundred things by holding up two hands and nothing more. Mar 29 at 14:46
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    @nick012000 there’s a reason why humans count in base 10, after all.
    – Dan Romik
    Mar 29 at 15:17
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    +1 OP solved a problem which is simply not a problem for virtually all people, and has a hard time accepting it. That's all there is to it. People don't need to care about anyones ideas.
    – cheersmate
    Mar 31 at 7:19
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In my opinion, "Dr. Seuss names" and other epithets you get don't contradict statements like "it's valid" or "clever". If I understand your idea correctly, you basically propose to introduce alternative number names, such as "shi" for what I'd pronounce as "sixty-four", which provides some potential benefits.

Academics would ignore this proposal because it's simply outside the domain of academic research. For me, introducing "shi" as an alternative for "sixty-four" is like proposing Dvorak (or other alternative) keyboard layout instead of the usual QWERTY.

You can do it, and you can argue why it is superior in your opinion, but what kind of response do you expect? Some people would like your idea, others would not. I personally can't force myself to use "kibibytes" and "mebibytes" even though they are kind of established.

Even if you manage to prove that your method is "better" according to some well-defined criterion, I think it is still mostly a political and cultural matter, and should be treated as such, rather than a part of an academic discourse.

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    +1 but what on earth is a kibibyte?!
    – astronat
    Mar 27 at 14:54
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    This box is too small, sorry. "Pedagogical & psychological research" is too general to talk about. If you write a scientific paper, it will be reviewed, and you'll receive more specific feedback rather than "bullsh*t". It's political/cultural matter because I am not switching to Dvorak regardless of it's benefits, and I can both recognize it's efficient and call enforcing it 'crankery' due to other (non-scienific) reasons I might have. Likewise, I might recognize ingenuity of your system and oppose its adoption for this or that reason. Mar 27 at 17:07
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    When we discuss 'research', we usually don't discuss 'research in general', we analyze a specific work (paper). Your proposal is not 'research' because it doesn't provide experimental evidence proving anything. It isn't bad, it just isn't research (in terms of genre). It is enough to submit your paper in order to get feedback, even if it is rejected. If you say that you aren't pushing eforcement, then what is your goal? You published your proposal, and anyone interested can follow it. Some criticize it, but you can't please everybody, really. Mar 27 at 17:31
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    Right, in math you don't usually experiment, but then you solve some problem and provide proofs. And here are no problems/solutions/proofs here. (For starters, the issue you are tackling might not be considered a 'scientific problem') You can submit your idea, but the odds are it will be considered out of scope for most journals since it is not 'research', and they do publish 'research'. I can only speculate why people tend to comment harshly on your proposal, but I think no 'scientific' issues are involved here (and hence I called it 'political/cultural'). Mar 28 at 3:05
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    @astronat: See here: en.wikipedia.org/wiki/Byte#Multiple-byte_units Mar 28 at 4:24
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The main question to ask is: why should anyone care?

Naming conventions are a dime a dozen. It's not like they need to be nonsense, not at all. Every computer library developed from scratch comes up with naming conventions, usage conventions, interface conventions, etc. But precisely because such conventions are quite freely choosable, it creates a cost to use them consistently and this will not happen if there is not a very tangible benefit.

If I have a software library with very extensive, say, parallelization support, then it may make sense to learn the conventions that it imposes on the user. Maybe it even finds a way of expressing things more cleverly than existing models and if that happens, it may ultimately take on. Still, this can take a very long time. Many clever programming paradigms from languages such as Lisp or Haskell took decades to seep into the mainstream. Mind you, these are operational advantages that they confer and yet it was not easily accepted.

Introducing a notation/expressive language that does not fill an obvious niche or confer a distinct advantage is mostly a futile exercise and rarely takes off, independent of its rationality. Perhaps the most interesting such experiment is Esperanto, which is, comparatively spoken, a modest success.

So, your idea may be rational (I cannot judge if it is), it may be even modestly useful (I have no opinion on that), but to get many people to adopt it or even just take it seriously, it needs to provide very tangible and substantial benefits and even then its success may still be decades off.

Unlike a mathematical theorem where there may be few people able to judge its merits or proof, but where there is at least a kind of "objective" importance to the question and reality check to the proof, naming jugglery is often close to crankery in the sense that many self-styled physics "revolutionaries" simply clothe either trivialities or non-committal vague statements with verbal jiu-jitsu which makes them capable of "proving anything" and impossible to falsify. I guess that your idea is also a name game is what may induce some of your critics to consider your idea close to crankery.

Again, I personally do not have an opinion about that, but it's clearly not an idea many people consider important to discuss or advances their own understanding of things.

The fact that 3 out of a hundred profs have stated something positive about your idea, may give some indication that you are trying to cram the idea into a hundred people's throats. Is it really such an important idea? I mean, it's not solving world hunger, cancer or even just determining the nature of Dark Matter or the Hubble constant.

It begins and ends with the one question I mentioned at the beginning: Why should anyone care?

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    The main question to ask is: why should anyone care? --- It seems likely that I've spent more time reading all the comments (including those in chat) and answers here than I've spent over my entire life actually writing and/or speaking numbers in different bases, and I'm in math. For me this only seems to be when working non-trivially with the ternary representation of elements in the Cantor middle thirds set. Mar 30 at 13:14
  • Naming conventions are a dime a dozen. Reminds me of this xkcd.
    – Dan Romik
    Mar 31 at 2:21
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    Good answer. Why should anyone prefer to pronounce 10,120 (base eight) as "one tin one shi two mi (base eight)", instead of "ten thousand one hundred twenty (base eight)"? It just replaces the widely known names of the ones/tens/hundreds/etc places with unfamiliar names. It seems this just reduces the number of syllables needed, but that's not a problem most people need or want solved. I haven't seen any argument of why the proposed method is in any way superior to the usual "non-zip code" way of pronouncing numbers. This seems similar to renaming the digits 0-9, which no one wants. Mar 31 at 17:00
  • @NuclearHoagie Did you click on the phrase 'an idea' in the question? It's a link to an article explaining and justifying the idea. Your complaints are all addressed in it. Including how renaming the digits could help prevent confusion among young students learning/acquiring additional/foreign spoken bases. Apr 5 at 3:19
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    @MatthewChristopherBartsh I think you'd need some way to show that adding a language element has any pedagogical benefit, and isn't just additional overhead that makes the problem worse. You also have the problems that you can only count up to 2^9 with this system, and you need to remember about twice as many place names (every power is completely unique, unlike ten thousand/hundred thousand/ten million/hundred million, which only introduces a new term every third power). Apr 5 at 12:37
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Terry Tao might suggest that you be skeptical of your own work. In order to produce great ideas, you need to put bad, average, and good ideas through many phases of refinement. If you do not view your own work critically, you might not identify necessary changes.

It is my personal opinion that your idea is not a mathematical idea (or at least, not an interesting one); based on the responses you have received from others, it seems like I am not alone in this opinion. It may be an idea about a topic relevant to math, but it does not provide any insight into the sort of questions that math aims to study. If you view your work skeptically, you may come to the same conclusion as me.

However, this is not to say that your idea is not interesting whatsoever. Suppose I were reading a science fiction book with a civilization that used binary as their customary number system. If one of these creatures said the word "tinmirlish" for 2^123456, I would be intrigued. If I then went and read your naming system, I would be floored by how creative and interesting it is -- changing vowels to express negation and inversion?? Awesome!

Upshot: Maybe the real issue you are facing is how to categorize your idea. I don't think your idea is interesting mathematically, but I think it is very interesting as a world-building concept. Perhaps other people find it interesting in some scopes and uninteresting in others. If you want to convince someone that your idea is interesting, try presenting it in a context that best fits the idea.

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  • 1. Upvoted. 2. Did you mean 'world-building' or 'word-building'? 3. I think my idea is mathematical and linguistic. It's in the overlap of the two areas. 4. The idea of using it a science fiction story had crossed my mind. It could even be a way to get people to experiment with seriously, kind of like what happened with Klingon, although that was unplanned as far as I know. 5. Besides negation and inversion, I considered 'imaginaryness' and asked in Mathematics Chat what else could be added to the list but I was unable to grasp the suggested idea of quaternions. Mar 28 at 21:24
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    I mean world-building, but word-building is a part of that. If you've read anything by Tolkein, you'll know that good word-building is a huge boon to world-building. Mar 28 at 21:31
  • I'm not a linguist, so I can't speak to whether your idea is linguistic or not (it seems to be more in the realm of con-langs to me). But making up new words for numbers isn't mathematical, because it doesn't answer any questions that you couldn't have answered with pre-existing names or symbols. If I start using "#" for addition and "@" for multiplication, rewriting pre-existing equations isn't math. Mar 28 at 21:33
  • 1. Yes, of course word-building helps enormously with world-building. Lord of the Rings would not have been the same without all those languages :-) 2. I always thought conlanging was a part of linguistics. 3. My system helps you to answer the question of what are the differences between the bases in practical use. If that isn't a mathematical question, does that mean the invention of Arabic numerals was not mathematical? Was it not a mathematical question once what is better, Roman numerals or Arabic ones? Mar 28 at 21:44
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    I can already distinguish 1010_4 and 1010_8 from their notation. As for your last questions, I think Captain Emacs's excellent answer gives a better response than I could. Mar 28 at 21:48
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In answer to the 'How to find out whether I am a crank?' sub-question, you could try surveying the (especially peer-reviewed) literature in the same area to see whether there are any easily-discoverable objections to your ideas, or alternatives to your proposal, with which your articles have failed to engage. For example, given the IEC definition of "kibi", isn't it rather unfortunate that your proposal uses "ki" for $2^7$, rather than reserving it for $2^{10}$? And what makes your proposal better than that of Stern (1958, Science 128(3324):594-596), or that of McFeely (1959, Math. Teach. 52(5):356-357)?

You could also check the text of your articles for potentially-controversial assertions that are presented without a citation or other supporting evidence (For example, 'In schools and universities around the world, students are often invited or required to do arithmetic in base two, and/or in base eight. The students are often explicitly asked to compare base two or base eight with base ten' sounds far from obviously-true to me.)

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    @MatthewChristopherBartsh 'How can I read about those proposals from the 1950's?' If you're on the campus or logged in to the library web services of an institution whose library subscribes to the relevant journals, you should be able to get the papers here and here; if your library doesn't subscribe to the relevant journals, then you can make inter-library loan requests; and if you don't have a library, you may have to hand over some money to the publishers. Mar 27 at 22:14
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    @MatthewChristopherBartsh "Perhaps I should substitute 'are sometimes explicitly asked...' or 'are often implicitly asked to...'" Even those weakened forms of the claims remain potentially controversial, and shouldn't be asserted without a citation or some other form of supporting evidence. Mar 27 at 22:26
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    @MatthewChristopherBartsh I'm currently in the "don't have a library" category, so I'm flying somewhat blind, but from a subsequent letter in Science, I'm fairly sure Stern would pronounce 111111 binary as "aponedagcidbruapone". Mar 28 at 20:27
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    @MatthewChristopherBartsh You might well be able to make a case that your formulation is superior (at least in some ways) to Stern's, but to avoid the suspicion of crankery, you'll need to present that case in a more analytical, more temperate, and more balanced (can you really not spot any advantage that Stern's formulation has over yours?) way than you did in your comment above. Mar 29 at 14:19
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    "If my idea is good, intelligent people should be able to see that." If enough intelligent people do not think your idea is good, then you need to honestly ask yourself whether your idea is good. Mar 30 at 21:37
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First of all, find out if you are not even wrong. From your description of your proposal, it does not seem to be a falsifiable statement.

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    My idea is a precise procedure, an algorithm more or less, and is not a theory, and so it is of course not falsifiable. So it is not even wrong, but wrong and right don't apply to a procedure. The question is whether it works. In my humble opinion. Mar 27 at 14:01
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    Define "works". "This method of counting makes it easier to understand the binary system"? That's a falsifiable claim. Mar 27 at 14:09
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    Upvoted F Poloni. I hadn't thought of that. I guess in that sense my idea is falsifiable, as long as an operational definition of 'easier' and 'understand' is found. Mar 27 at 14:14
  • To newbies: of course, by 'falsifiable' we mean 'in principle capable of being falsified', and not that it can actually be proved to be false in actual fact. It's a term from the philosophy of science. Don't imagine that I conceded that my idea is false. Mar 27 at 15:15
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    @MatthewChristopherBartsh "Easier to understand" is a well established, testable notion. People have been performing randomized studies to settle such questions for a long time. Take a few hundred students of appropriate age, teach a random half your method and the other half a normal curriculum about binary numbers, then give both halves the same test on the topic and perform some statistical analysis on the results. Doing that would be proper science. Arguing about your idea with people on the internet is not.
    – mlk
    Mar 29 at 12:27

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