Numbers and words [entries|reading|network|archive]
simont

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Mon 2012-05-28 15:46
Numbers and words

This morning I tried to return a phone call. I managed to dial the wrong number three times at widely separated intervals, and (I later worked out) on all three occasions I transposed the same pair of adjacent digits. And despite carefully cross-checking between the number shown on the display of my phone, the number on the email (my employer's voicemail system works by sending you an email containing the caller ID and a sound file) and the number read out by the caller, I managed not to spot the error for most of the morning.

I'm actually quite worried by that. I've always prided myself on my ability to remember long strings of digits, and found it repeatedly useful. I've known for a while that I was prone to occasionally transpose adjacent digits in a number I'd only just seen, but I usually notice on the second attempt. This is the first time I've spent hours completely blind to the difference between the right and wrong versions and I don't like the feeling. :-(

My best guess for how it might have happened is that the transposition turned a trailing 245 into a trailing 425, and my brain might have found the latter more plausible because it's common to see round-ish numbers ending in 25, so perhaps it unilaterally 'corrected a typo'. But even that's not a very good explanation.

In other news, I visited my niece at the weekend, and she's just learned to say my name. (She's one and a half.) I'm not usually all that susceptible to the cuteness of toddlers, but when they repeatedly look at me and say ‘Si-mo’ I have been forced to make an exception.

[xpost |http://simont.livejournal.com/236962.html]

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[identity profile] feanelwa.livejournal.comMon 2012-05-28 15:14
I have done that for ages. Especially when they are both even and have multiple similar properties! I cope with this by writing the number on a piece of paper with the digits separated into groups. E.g. I will do this to the Anglian Windows phone number since it's a public post and I vaguely associate double glazing with cold calling though they don't necessarily do it:
0800 because it's free, 9 ach nein, 541 5=4+1 203 twins - oh wait - triplets

If I didn't do this I would never phone a right number again except that my phone remembers them for me!
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[identity profile] tigerfort.livejournal.comMon 2012-05-28 16:41
Is Si-mo related to El-mo? Si-mo like numbers, but get confused sometimes. El-mo also like numbers, but get confused lots. Si-mo not furry, but that OK, because El-mo not prejudiced.

Separately, the thing that really puzzles me is the way that after a couple of years of regular typing, I started writing typos by hand. Looking down at a page of notes and realising that you've written both "teh" and "adn" out in longhand leaves you (well, me, at any rate) wondering precisely which parts of my brain are now being controlled by skynetchanged in ways I might not expect.
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[personal profile] gerald_duckMon 2012-05-28 16:49
Drat. Now you've got me wondering something not entirely related.

My first thought was that maybe your subconscious was rearranging digits to make the number prime — which would be a feat of Ramanujan proportions. Though clearly both the real number and your transposition ending in 5 militated against this possibility.

But now I'm pondering collections of digits that form a prime number however they are arranged. For example, (1,1,3) where 113 131 and 311 are all prime. It feels displeasing to have repeated digits in the collection, but with that constraint it soon becomes clear no examples of more than two digits exist in base ten. Without the constraint, repunit primes like (1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1) become especially degenerate examples.

Considering other bases, binary is especially unedifying since Mersenne primes are the only examples. Being a curious sort, I wondered if larger collections of distinct digits worked in other bases. Having written a quick program, I find that all permutations of the digits (1,3,9) and (3,6,A) in base 11 are prime; plenty more in higher bases.

I have a proof that no collections of four digits exist in any base such that all permutations of those digits are prime. But this comment is too small to contain it. And I don't for a moment believe that's actually true, but it's certainly true up to base 100 and a brute force search is O(n4).
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[personal profile] simontMon 2012-05-28 18:16
I note that the Wikipedia page you cite links to a page describing just those things. It appears to be quite hard to think of natural questions in recreational maths that haven't been investigated yet :-)
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[personal profile] gerald_duckMon 2012-05-28 19:49
Humph!

In my defence, the Wikipedia article on prime numbers does not link to that page. Guess where I went looking. )-8

At least my conclusions seem to have been correct. And, especially, at least I didn't waste time looking for any more base-ten permutable primes after I'd found the three-digit ones.

That Wikipedia article doesn't touch on [livejournal.com profile] gerald_duck's hopefully-far-from-last theorem, though.
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[identity profile] hilarityallen.livejournal.comMon 2012-05-28 17:36
One can occasionally make quite uncharateristic errors. I'm sure Drswirly's told you about his A-levels, where he persistently misread numbers in an equation *for the entirety of the exam*, despite normally being very resistant to those sort of mistakes (in a way that I'm really not).
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[identity profile] twigletzone.livejournal.comMon 2012-05-28 19:13
I had no idea Sophie had a kid! Congratulations to her :)

Also my oldest friend's little boy visited me a while back and kept calling me Pelix. There is something about them isn't there :)
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[personal profile] simontMon 2012-05-28 19:23
It's a bit mean to do this, but yes you did ;-)
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[identity profile] arundelo.livejournal.comMon 2012-05-28 21:41
"[Time] is a hell of a drug." (http://www.youtube.com/watch?v=udNHsk57f24)
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[identity profile] hairyears.livejournal.comMon 2012-05-28 21:24
As someone who works at the soft end of software, I have an interest in this kind of thing: I am fairly sure that there are number combinations which are consistently mistyped, and I should probably go looking for published research.
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[identity profile] feanelwa.livejournal.comTue 2012-05-29 13:31
the soft end of software
The end you don't wear.
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[identity profile] hairyears.livejournal.comTue 2012-05-29 18:38
No, it's soft because it's all a bit GUI.
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