Math Quirks:...Anybody (else) experienced strange Date coincidences ?

[RJSV]

Of course, many many folks experience coincidences, in personal affairs, but I'm thinking, what are some interesting, unexpected, and, Engineering being a 'MATH' driven occupation, what's your cute story.
(Please refraining from offensive material, right now).

   #1.). I'll start with business address intrique, although seemingly harmless irrelevance:
    A first job, the headquarters was at '1440 Fourth Street', charming Berkeley industrial shop.
    Couple years later, (20 years), I've obtained a new job, address at:
    '1444 Market St.'  an actual play on words, a bit, if you say both addresss fast.
     Maybe not so spectacular, or dramatic, but I like the word play!

   #2.).  A certain date and number, let's just call it a 'recuring 1230', that's woven itself into several, unrelated events, including one girlfriend's birthday, and also a place I worked at, several years.
Again, perhaps more interesting to myself, than as a publicly shared 'irony'...I think it was an old friend had, also, passed on that date.

Anybody else, with a mathematical or career / business related story ?

[helius]

Do you consider it a strange coincidence that thousands of stoners celebrate by lighting up on 4/20, unaware of the corporal from Austria whose birthday is that day?

[tggzzz]

Do you consider it a strange coincidence that thousands of stoners celebrate by lighting up on 4/20, unaware of the corporal from Austria whose birthday is that day?

Strictly speaking it is the anniversary of his birthday

I suggest the OP searches the number pi, to find his date and time of birth.

Don't you find it a strange coincidence that the people who find coincidence between unrelated numbers often lived in the pre-scientific era or are astrologers/new-agers/"healers" etc?

[HighVoltage]

If you start interpreting coincidence numbers and go down that rabbit hole, it will never end.
I know some wacky people who have done that.

But on the other side you can also not avoid real coincidences.

I had to move out of a business building once and found a new place in the adjacent city and got the same street name and the house number was almost the same, just had a letter behind the number.

What I find more interesting is that test instrument companies like to use the same number combination.

For instance:
Datron 1281 is considered one of the best multimeters of all times.
I just bought a Burster calibration resistor, model number 1281

And there are plenty more examples in the lab.
One has to wonder, how that happened.







 

[Sredni]

Well, it feels like every time I pick up my phone to look at the time, it's xx:17.
 I noticed because where I live the number is considered bad luck. Of course I notice because all the other times I pick up the phone and did not get xx:17 I did not register the event. But then, out of fun, I tried to find the number 17 in combination of numbers of the clock and or date and... sure enough, a disproportionate number of times I can get 17 by either summing up the single digits, or groups of digits, or subtracting them. Like, for example, 14:21 -> 14+2+1 = 17, or 19:34 -> 9+1+3+4 = 17, 19:02 -> 19 - 2 = 17 and so on.

Since I am "almost always" able to extract 17 out of the time (sometimes with the help of the date to make it) I wonder if 17 for hours is like 7 for dices: does it have a higher probability of coming up than other numbers? Or is there a number with higher probability?

If we only consider summing all the single digits, the probability distribution function is bell shaped and spans all numbers between 0 and 24 both for the 24h and 12h formats. So, the number with the highest relative probability of coming up is 12, in both cases. Whoops, no. It's 12 in the 24h format and 11 in the 12h format.
Here are the number of occurrences for the 24h format

{{0, 1}, {1, 4}, {2, 10}, {3, 19}, {4, 31},  {5, 46}, {6, 62}, {7, 78}, {8, 93}, {9, 107},  {10, 118}, {11, 124}, {12, 125}, {13, 121},  {14, 112}, {15, 98}, {16, 82}, {17, 66}, {18, 51},  {19, 37}, {20, 25}, {21, 16}, {22, 9}, {23, 4},  {24, 1}}

and here are those for the 12h format

{{0, 1}, {1, 4}, {2, 9}, {3, 16}, {4, 24}, {5, 33},  {6, 42}, {7, 50}, {8, 57}, {9, 63}, {10, 67},  {11, 68}, {12, 66}, {13, 61}, {14, 54}, {15, 45},  {16, 36}, {17, 28}, {18, 21}, {19, 15}, {20, 10},  {21, 6}, {22, 3}, {23, 1}, {24, 0}}

But this just one of the ways of combining the digits to get a number. I could sum the first two digit and then subtract the sum of the last two, or summing the first, third and fourth and subtracting the second. How to get all the possible combinations?

[jpanhalt]

Most people are aware of the Boeing 7x7 series of aircraft:  https://simpleflying.com/boeing-7x7-series-line-up/

A "lucky number" or just a number that easily rolls off the tongue?

Now to add further intrigue, check out the author(s) of the above link and this thread?  Related in the stars?   

[igendel]

This warrants the great scene from the film Pi - excellent monologue and, towards the end, on-topic:

[ebastler]

But this just one of the ways of combining the digits to get a number. I could sum the first two digit and then subtract the sum of the last two, or summing the first, third and fourth and subtracting the second. How to get all the possible combinations?

That seems straightforward enough to answer via a little brute-force program. There are 24*60 = 1440 different hour:minute combinations. For each of these times there is a manageable number of sums you can test, if you allow yourself to either look at single digits or to combine the hours and/or minutes into two-digit numbers, and then count each of the units either as positive or negative:

2^4 = 16 single-digit sums
2^3 = 8 sums which use the hours as a two-digit number
2^3 = 8 sums which use the minutes as a two-digit number
2^2 = 4 sums which use both hours and minutes as two-digit numbers,
hence 36 combinations (which will not always produce 36 different sums).

You could easily write a program which loops through these combinations for each of the 1440 time values, to see for how many of them you can obtain 17 (or -17) as the sum. And likewise for other target sums, to see whether 17 is indeed "special".

I would be surprised if 17 happens to be the most frequently achievable sum; I think it is just your personal bias in looking at these numbers. (I assume you have not tried the other target sums when you did this manually?)

[TimFox]

Many years ago, some debated if the CDC 7600 mainframes were four times better than the ICL 1900 computers.

[Circlotron]

About 6 months ago I started seeing candy apple red Mazda 6's everywhere I went. it's like they were after me. Was at a shopping centre sitting down having a coffee with a friend and was telling him about this phenomena. After we had finished and came outside to the parking lot there was one either side of my car and a third one right behind it. 

[Sredni]

Many years ago, some debated if the CDC 7600 mainframes were four times better than the ICL 1900 computers.

I took me three re-readings to get it.
 

[Circlotron]

Many years ago, some debated if the CDC 7600 mainframes were four times better than the ICL 1900 computers.

Three times better.
Four times as good.
My pet peeve!

[TimFox]

Many years ago, some debated if the CDC 7600 mainframes were four times better than the ICL 1900 computers.

Three times better.
Four times as good.
My pet peeve!

A quick look for grammar sources indicates that "four times as good" is better usage, but "four times better" is still grammatically correct for A/B = 4:1.

[AVGresponding]

And is the equivalent of 300% better, which media sources consistently get wrong (would likely be stated to be 400% better). Yes, this annoys me as well.

[tggzzz]

And is the equivalent of 300% better, which media sources consistently get wrong (would likely be stated to be 400% better). Yes, this annoys me as well.

Worse: 2 is "10 times less" than 20.
<insert muffled sound of screaming while holding a pillow over my mouth>

[TimFox]

My standard reference book, B A Garner Garner's Modern American Usage 3rd edition, Oxford University Press 2009, discusses these usages in his entry "Illogic".
On p 440, he points out the difference between logic and grammar:  "No serious student believes anymore that grammatical distinctions necessarily reflect logical ones.", for example "burn up" vs. "burn down", or "fat chance" vs. "slim chance".
Case H on p 441 discusses "times more than", and that the common understanding is that if X = 2 and Y = 1 then X is two times more than Y.  He prefers "X is two times as much as Y", and advises against the opposite wording "Y is two times less than X", but allows "two times more than".
In my opinion, "times more than" implies a ratio.
If A = 8 watts, and B = 2 watts, then
A is 6 watts more than B.
A is four times as much as B.
A is four times more than B.
A is 6 dB more than B, parallel to the above.

In my joke, where the comparison is goodness, rather than quantity, this would read "X is two times as good as Y", which is awkward compared with "X is two times better than Y",

[helius]

On p 440, he points out the difference between logic and grammar:  "No serious student believes anymore that grammatical distinctions necessarily reflect logical ones.", for example "burn up" vs. "burn down", or "fat chance" vs. "slim chance".

If those are the examples cited, they aren't especially useful. A slim chance is a low probability, but "fat chance" is a sarcastic expression (you can tell by the vocal stress). The author seems to be blinkered by an approach to grammar that ignores the purpose and freight of the speech act itself. Expressions of sarcasm emanate from a personality and emotional state that sees the world through a gimlet eye, and can't be understood by simply reading the words' denotations or applying grammar rules. The other example is also more complicated when you include the phrases' connotations. When something burns up, we mean that it deflagrates in a more or less spontaneous way. Burning up is intransitive. Burning down, on the other hand, is mostly transitive—we impute a conscious intent to destroy or allow to be destroyed. Even when habitable structures burn down accidentally, there is a moral weight to that destruction that we don't assign with movable objects burning up (that is why fire departments were created to protect structures and not just to put out all fires). The Talking Heads song isn't called "Burning Up The House". On an over-literal level, it's true that this distinction has nothing to do with the common up-down dichotomy in terms of space, but expecting it should can only appear reasonable if the words are shorn of all their context.

Based on the quoted analysis, I think you would get more illumination from "How To Do Things With Words" by J.L. Austin.

In my opinion, "times more than" implies a ratio.
If A = 8 watts, and B = 2 watts, then
A is 6 watts more than B.
A is four times as much as B.
A is four times more than B.
A is 6 dB more than B, parallel to the above.

The inconsistencies come in when you want to substitute "four" by "one half".

[TimFox]

Garner contends that "four times less" is better avoided in English.

The discussion of "burn up" vs "burn down" is only the introduction to the discussion of logic and grammar;  point "H" in that section is directly relevant to "four times" usages and does not involve sarcasm.
"Four times more" or its variation are worth discussing since we are discussing quantities.
"Four times better" is not really mathematical:  comparing the two computers' goodness was a joke.

However, when googling "four times better", the results from periodicals such as the Guardian and the Economist have used it to compare, for example, lines of resolution in HDTV.
(I didn't link them due to paywalls.)

I seriously recommend his book, which shares my preference for discussing "standard English" and careful usage, while admitting the usefulness of non-standard English and slang for other purposes.
He found that permissive authors who encourage slang, etc. always discuss their ideas using standard English.

With respect to logic, mathematics, and grammar:  an example is the "double negative", such as "I have not done nothing."
In standard English, that is not good usage, but would mean the positive "I have done something", following Aristotle and Boole.
My Russian co-workers told me that in grammatical Russian, the equivalent sentence would be a strong negative, rather than a logical positive.

[RJSV]

   Red Mazda Conspiracy is OK, but, good thing we ARE NOT involving any meth users (Mr. White!).
That crew, for whatever reason, diagnostic 'paranoia' or psychosis maybe underlying, but those heavy meth users get the 'manic' high, combined with way, way whacky imaginative creativity and results...from a safe observing distance, results can be incredulous.  Witness that effect, in the show, Breaking Bad, making 'drama' out of simple hole digging.
"You know why,..." The shovel weilding actor addresses the (digging) action dismissively.

   (Part of my point, about coincidence tracking, is that the meth using crowd often approaches the topic from a hyper self-defensive angle, and can be dangerous and unpredictable!)

   At any rate, look;  good ole' 1440 showing up in one of the reply posts, lol.
Although my experience, involved street names also, like '4th' street.  Almost as a 'PUN', form.

[RJSV]

Sredni:
   Nice to see you've gone a bit deeper than most would...one comment I could make about frequency and statistics related.  That is, many street addresses (likely) have, statistically more numbers similar to '3569' due to simple counting, that is, some address like 9412 won't be encountered so often, as street blocks don't always go very high.  That means house address less than, say, 3000 or 4000, as the higher address values aren't there, in the city map.
Probably similar bias in any 5-digit numbers, such as 19248, which perhaps some town planners or zoning dept. know about...meaning that you maybe won't see something like 89124 as that higher number isn't seen, in the community.

[vk6zgo]

About 6 months ago I started seeing candy apple red Mazda 6's everywhere I went. it's like they were after me. Was at a shopping centre sitting down having a coffee with a friend and was telling him about this phenomena. After we had finished and came outside to the parking lot there was one either side of my car and a third one right behind it. 

Where did they find a space with all the late 1990s/early 2000s silver Toyota Camrys using them up?

[Circlotron]

About 6 months ago I started seeing candy apple red Mazda 6's everywhere I went. it's like they were after me. Was at a shopping centre sitting down having a coffee with a friend and was telling him about this phenomena. After we had finished and came outside to the parking lot there was one either side of my car and a third one right behind it. 

Where did they find a space with all the late 1990s/early 2000s silver Toyota Camrys using them up?

LOL You are so on the money.  except for the fact that my 1999 Camry is white, not silver.

[MIS42N]

The first 3 digits of my mobile and my bank account are the same. I know it's not a date coincidence. But this is:

I have four daughters (this is true, not a joke - although sometimes I wonder).
First born 30 Jan (xxxx-1-30). The second born 7 Oct (-10-7). sum the days and the months 11-37.
So what?
The third was born -7-25 and the fourth was -4-12. sum the days and the months 11-37.

My favourite is “Why do programmers always mix up Halloween and Christmas?”
“Because Oct 31 = Dec 25.”
[ Credit to the person that saw this first - Octal 31 = Decimal 25 ]

And how about this weird little calculation. I found it many years before Y2K was a thing.
Good from 1st March 1900 to 2099 if for 1900 Y=0 and for 2099 Y=199:
'
' Get date, reduce to number of days in P [1/1/1900 = 1]
'
  INPUT "Date D,M,Y"; D, M, Y: IF M < 3 THEN M = M + 12: Y = Y - 1
  P = D + INT((M+1) * 153 / 5) + INT(Y * 1461 / 4) - 63

[Nominal Animal]

For a 24-hour clock, taking either the hours or minutes as-is, and then adding or subtracting the other, or one or both digits of the other, 24.3% of the time you can end up with +17 or -17.

Bash+awk:

Code: [Select]

for H1 in 0 1 2 ; do \
  for H2 in 0 1 2 3 4 5 6 7 8 9 ; do \
    H=$[10*H1+H2] ; [ $H -ge 24 ] && continue ;\
      for M1 in 0 1 2 3 4 5 ; do \
        for M2 in 0 1 2 3 4 5 6 7 8 9 ; do \
          M=$[10*M1+M2] ;\
          printf "%d $[H*60+M]\n" $[H+M] $[H-M] $[H+M1] $[H+M2] $[H+M1+M2] $[H-M1] $[H-M2] $[H-M] $[H-M1-M2] $[H+M1-M2] $[H-M1+M2] ;\
        done ;\
      done ;\
    done ;\
  done | awk '{
                r = $1; if (r < 0) r = -r
                result[r]=r
                seen[r][$2]=1
              }
              END {
                possible=24*60
                for (r in result) {
                  n=0; for (s in seen[r]) n+=seen[r][s];
                  printf "Result %d: %d/%d = %.1f%%\n", r, n, possible, 100*n/possible
                }
              }'Even though it is brute force calculation using Bash and awk, it is still basically instantaneous.  You can paste that in any Bash shell with any variant of awk available as-is, and it will print out each possible result (in random order; append | sort -n -k 2 to the command to sort the output by the possible results), and how large a fraction of all 24-hour clocks, HH:MM, can be evaluated to that particular result.

[helius]

And how about this weird little calculation. I found it many years before Y2K was a thing.
Good from 1st March 1900 to 2099 if for 1900 Y=0 and for 2099 Y=199:

The regular cycle of days to days-of-the-week begins on March 1 because the "Ides of March" was the original start of the year.
The Julian calendar, instituted by Julius Caesar, was a revision of that earlier calendar. You can still see the traces of the ancient calendar by translating the names of months from Latin: September, October, November, December mean 7th, 8th, 9th, 10th: so the year originally began in March, with leap days inserted at the end of the year (as is done today with leap seconds).

[TimFox]

The Ides of March is actually March 15.
The Ides of March, May, July, and October are on the 15th, the other months have Ides on the 13th, in the old Roman calendar.
The Nones of each month are 8 days earlier than the Ides.
The Kalends of each month are the 1st of the following month, just to confuse people.

[helius]

Thanks for the correction!
In addition, the Romans considered each day to begin and end at noon instead of at midnight.

[TimFox]

Noon is much easier to determine than midnight.

[RJSV]

I love it when one of these number quirks / anomalies contain a partial language component, like the conversion of October to mean octal code, and of December to the decimal mode identifier.   Somewhat classified in the 'PUN' catagory.   (Seen a few posts back.)

   Of course, I should have anticipated that many of the responses here are calendar related.

[Nominal Animal]

Noon is much easier to determine than midnight.

Icelandic vikings at least seem to have used "sunstones", cordierite or iceland spar, to detect the direction (azimuth) of the sun even in overcast weather.  Not just on sea voyages, but in everyday life, to check the time of day.

Many of the daily aspects of even Roman life have been forgotten.  For example, why did they carry those dodecahedra around in second to fourth century CE?

[TimFox]

The noon start persists in modern language:  AM and PM abbreviations mean "before noon" and "after noon" (not midnight) in Latin.
Latin:  "ante meridiem" and "post meridiem"  ("antemeridian", a rare word sometimes misused, means "of or belonging to the morning")

[RJSV]

   Actually, (thanks Helius),  the slang term '420' had it's origins in the police radio code chatter, which, if I'm to believe the common folk-story, the '420' was the code number for
   'Cannabis smoking taking place', as the illegal activity to respond to.

   However, I'm not sure what is the term to use, for some social assumption, commonly believed, or non-scientific fact being stated.  Those type statements are difficult to track or verify directly...(maybe I should start by checking out what Wikipedia says.)
Now, if you read, someplace, that Marijuana was discovered by Bob Marley, THEN I'd be assuming that's just an old rumour.

[TimFox]

One possibility for "the term to use, for some social assumption, commonly believed, or non-scientific fact being stated" is "urban legend", originally applied to lurid stories heard from a "friend of a friend".
https://www.dictionary.com/browse/urban-legend

[RJSV]

Yes, thanks Tim:
   It's a small diversion from topic, but I noticed I had difficulty fumbling for the appropriate terms, when discussing non-scientific labels, but you have similar approach:
   Wiki, and other sources use phrases like 'Some say...' or 'Common belief is....' without delving into rigorous proof.  Of course that creates a lot of wiggle room for creative manipulations, but that can happen also with 'Urban Myth' types of Meta-descriptors.
   Did I just create a novel word combo ?

[TimFox]

You might be interested in G Flaubert's  Dictionary of Accepted Ideas  https://archive.org/details/gustave-flaubert-dictionary-of-accepted-ideas-barzun
Many of those ideas are actually true.

[helius]

Phrases like "some say" are known as weasel words because they are irrefutable.
The idea put forth may still be true, but it provides no basis for believing it so.

[RJSV]

...Yes but WEASLE words accurately describes the setting, that is of a sort of 'common understood' to the degree that, for example, you could state:
   "All my cousin's friends keep saying they think my singing is professional."

   This the WEASLE word is, ironically, a definite term, (while describing an indefinite situation).

At the end of the day, there's got to be some technical language term or word for this.

Like, anachronism or some such wordy word.  Some non-science conclusion about meaning of some word, or term, that's more by (social) consensus.

[RJSV]

   At any rate, back to more MATH
or calendar  related coincidences, one date I've seen is Jan. 25.
If you take that date it's 1-25 or simply 125.  Now, that's a perfect CUBE, of 5.  I'm not going into the personal history of that, right now, but it's been 'a presence', such as a business street address.
Even better, that address is actually '25125'  and thats a massively ironic number!
I mean; you've got 5 squared, 5 cubed, and a little bonus in that the '125' portion has the cube value containing the squared value....That would be similar to something like:
   '1664' where you have 4 squared and 4 cubed...but notice, however, THIS time we don't get that '64' as containing a '16', like the '125' contains (contains 25).

   Seems maybe obsessive, but have to admit that 5 in this process has the special quality that using '4' doesn't, which brings up the question, of Where the specials are?...or is this self referenced only for when using integer '5' to square and cube.
By themselves these effects are merely interesting, but when living and working under such 'magic' numbers can be interesting to greater effect....a louder Wow factor, (I suppose).
Enjoy

[RJSV]

...oh yeah, I also forgot to mention........wait for it......
   Office number is 'Suite #5', there, (or actually distantly associated but close enough to notice)

Also, (at the moment expense of possibly boring the reader, lol,),
   Notice the '125' is very close to saying 1/2 of 25 is 12.5   So readers can see how fluid the process is, of associating seemingly random bits of random English into the numbers.

[RJSV]

   So, round and round this quirky process goes!  It can get to be a vanity, with all the self-attention from Numerology.
   Now that I'm on a roll, might as well get into some additional 'Squares', in the form of 12 squared, '144'.
Notice, that seems to be sneaking up on my original '1440' address mentioned at thread start.
Then, #169....that's 13 squared (this is getting easy).  But that storage unit number shows itself, to the degree where I had started to look;  Where is (my) 14 squared, then ?  Haven't seen it, but that comes to 196.  When I have some more time, or see another route to coincidence, I can tackle decode that one.

   Maybe I should post a contest, Lol.

[RJSV]

   First 100 digits of PI:
   Interesting, this contains '1971'  and a couple, '2089' and one other '20xx',  (plus I don't have time of birth).  Must go to 1000 digits, to get more relevant results.

[helius]

At the end of the day, there's got to be some technical language term or word for this.

Like, anachronism or some such wordy word.  Some non-science conclusion about meaning of some word, or term, that's more by (social) consensus.

A term or phrase used outside of its consensual meaning is called a solecism. All you need is an antonym of that.

edit: "relevant results"? You do realize that the expansion of pi contains every possible subsequence?

[RJSV]

No, I hadn't realized the fuller aspect, of finding literally anything, any sequence of digits.
   Which brings up a question about books, do you know of a good book or two that has focus on PI and some historical stuff ?   Of course, I'll have to do web search on books, thanks.

[RJSV]

   I forgot to put in reply, that how much of this thread involves language, and even edging into ironic 'puns'.  That is treating numbers, in singular isolation, and in subgroups.  BTW one of my favorite things is to regard digit sequences backwards or forwards.  Thus an area code, like (494) can be instantly considered to contain '49' twice; meaning once left-to-right and once right-to-left (looks like '94').

That '49' by the way, is (effortlessly) an old, established reference, to Grass Valley, CA and Nevada City from the GOLD RUSH era around 1850's !

[helius]

Not a book about π specifically, but I do have some interesting math (history) books.

Prime Obsession by John Derbyshire, ISBN 0-309-08549-7
Gamma by Julian Havil, ISBN 0-691-09983-9
The Monty Hall Problem by Jason Rosenhouse, ISBN 978-0-19-536789-8
The Annotated Turing by Charles Petzold
What is Mathematics? by Herbert Robbins (credited to his boss, Richard Courant)
(can't find the latter two so no ISBN)

I was given Fermat's Enigma but found it disappointing. Barely any mathematical content at all, on the level of "A Beautiful Mind".

[TimFox]

A wonderful interesting recent novel about nothing, words, logic, and mathematics:  "Dr No" by Percival Everett (without so much Ursula Andress)  https://www.influxpress.com/dr-no

[RJSV]

   I glanced at that book review, 'Dr. NO', thanks.
Not sure your drift, if it's subtle, but yes, this thread about seemingly unrelated numerical structures can have a feel of being, maybe frivolous.   That so because (we are) maybe chasing some aspects that have no apparent, clear goal or outcome, aside from some immediate little 'aha' moment when a couple of items match up.
    Humans have long history of 'pondering' things and processes that contain clues of mysterious relation.  Maybe a couple of relatives had died, on the same day of the month, or same holiday.  But where (those) little 'drama' paths lead isn't clear, besides having a good grasp of coincidences in the statistical sense.  In fact, a little investigation may prove that, for example, a person should not, rationally be nervous when a third occurrence of a 'friday 13th' comes along, and recognition that coincidence won't 'cause' yet another relative to pass.  I get that.

   But, I'm saying we could still look at things, maybe just for frivolous entertainment, then, as various combinations of addresses, dates and times, and even quirky word play pass by, as world turns under our noses.  Next, here is my latest example (fictional):

   Is there a radio talk code for 'NO VISABILITY' sky or cloud conditions ?  Like "We got a '409' going on along the coast".  (A totally made up example).
Then, there is a blind fellow, 'Hector',  who has been living in a cottage there, at '409 Jackson St.'

Coincidence ??    Probably, 99.9 %

[RJSV]

LOL, I looked up some various radio (police) codes and, right away there are verbal codes for 'weather conditions', I think it said '10 - 25' or similar.  The code '10 - 4' means acknowledgement, msg received.

   BUT THEN, further down the list was '10 - 20', one of my (all-time) favorite numbers!  THAT was my first office address, as a 'professional' inventor, and overall unemployed 'dead-beat', having no tangible success to show, other than interesting stories to relate....

   Meaning of radio code '10 - 20' is 'LOCATION'...as in, in my case;

   "My, uh, '10 - 20' is 1020.".         That had been '1020 D St. Hayward, CA'

Post Script:    that's 17 X 6,  X 10,  for anyone interested in '17' action.

[Circlotron]

https://bluewatercredit.com/random-event-generators-predict-911-attacks-world-events-tune-princetons-global-consciousness-project-find/

[DavidAlfa]

I very often have a peek at the clock and catch 12:12, it must be a Final Destiny thing.

[SiliconWizard]

I very often have a peek at the clock and catch 12:12, it must be a Final Destiny thing.

That, or OCD.

[DavidAlfa]

Absolutely not, i'm doing my stuff at work, when I finish something... Hmm how many time did it take?
10:45... 2hours - note down in the repair form.

Start  with the next one,  initial test / diagnose / repair / more tests...
Huh, I might take a break, I'm dead! Time for coffee!
What time is... 12:12 ...it...?

Else than that I rarely watch the clock. Except when the hunger comes in at the last hour or so, then it's way worse than OCD! (But that's about 14h/2pm).

[MIS42N]

edit: "relevant results"? You do realize that the expansion of pi contains every possible subsequence?

Are you sure?
Take pi to any arbitrary length. Change one digit. A subsequence that does not occur in that expansion.

The problem with infinity. Pi may have an infinitely long string of digits, but there will be a bigger infinity of substrings that are not in that string.

Aaaargh (disappearing up own ***)

[Andrew LB]

I very often have a peek at the clock and catch 12:12, it must be a Final Destiny thing.

I always look at the clock when it says 11:34. It's really annoying.

And no, it's not OCD. It always happens when i haven't looked at a clock in hours.

[MIS42N]

I very often have a peek at the clock and catch 12:12, it must be a Final Destiny thing.

I always look at the clock when it says 11:34. It's really annoying.

And no, it's not OCD. It always happens when i haven't looked at a clock in hours.

Maybe it's not the clock you are looking at. 1134 (kHz) is the frequency of the local radio in Armidale NSW. The car radio shows the time when the radio is not on, and the frequency when it is on. Caught me a couple of times.

[helius]

Are you sure?
Take pi to any arbitrary length. Change one digit. A subsequence that does not occur in that expansion.

I don't think so. You have to be careful when reasoning about "infinity", since it is not something that actually exists. It's a concept that serves as a shorthand for "behavior under limit condition(s)". When we speak of "infinitely many" of something, i.e. an infinite set, we have a criterion for how the members of the set are generated, and the limiting condition is what the criterion generates when allowed to proceed without end.

In particular when you say "bigger infinity" there is only one plausible meaning for that phrase, and it's not what you think it is. The cardinality of an infinite set is a "number" that specifies how the members of that set can be mapped onto any other set. So even though intuitively there are "more" rationals than integers—since between every two integers there are infinitely many fractions—the set of all rationals and the set of all integers have the same cardinality: there are "equally many" of them, because we can devise a method of mapping one set onto the other. In Cantor's language, they both have the same cardinality, \$ \aleph_0 \$. Any infinite set that can be mapped onto the integers is enumerable: there is a way to order the set such that you can cover all of the elements by counting them.

In particular, note that the infinite set of all decimal substrings is enumerable. Proof:
I. Assemble all of the strings of length 1 in lexicographic order and count them.
0 1 2 3 4 5 6 7 8 9
II. Then append all of the strings of length 2 in lexicographic order.
00 01 02 ... 10 11 12 13 14 ... 96 97 98 99
III. Then append all of the length 3 strings, etc up to length N strings as the limit of N goes to ∞. This sequence includes all decimal substrings of any length whatsoever.
Therefore the set of all decimal substrings is enumerable and its cardinality is aleph-null.

The problem with infinity. Pi may have an infinitely long string of digits, but there will be a bigger infinity of substrings that are not in that string.

As I have shown, the set of all substrings cannot be a "bigger infinity" than the sequence of digits in pi's expansion.

∞+1 is not "bigger" than ∞. Neither is ∞+∞. To keep things clear, better to use \$ \aleph_0 \$ instead.

Take pi to any arbitrary length. Change one digit. A subsequence that does not occur in that expansion.

This is a mutilation of Cantor's diagonal proof. Cantor proved that the cardinality of the reals, which he called the continuum or c, must be greater than the cardinality of the integers, aleph-null. This amounted to a proof that the reals cannot be enumerable:

I. Consider only the reals between 0 and 1, exclusive. They have the form ".XXXXXXX"... where each X is some decimal digit. If the number is a fraction, then the expansion will be all 0 or some periodic pattern after some point, but the reals also include transcendental numbers which never repeat.

II. Suppose we have enumerated all these numbers in an (infinitely long) list. So we have a kind of grid of digits. The first row of the grid is the first number in the list, the second row is the second number, and so forth. The first column in the grid is the tenths digit of all of the numbers; the second column is the hundredths digit, and so forth.

III. So making a diagonal from the upper left, take the tenths digit of the first row, the hundredths digit of the second row, etc., to construct a number b with infinitely many digits.

IV. Now change every digit of b to produce d (for example by adding 1 modulo 10), each digit of which differs from the corresponding digit in the grid. Because d differs at at least one digit from every number in the entire grid, it cannot be in the list. But d is between 0 and 1, since it has the form ".XXXXXXX", so it should have been in the list. Therefore the assumption in (II) that we had an enumerated list of reals between 0 and 1 is false. So the reals are not enumerable and c > aleph-null.

Note that the only way this argument works is if the grid is infinitely long in both directions: both infinitely many numbers in the list, and infinitely many digits. Otherwise it can't prove anything, since there could be some position at which d does not differ from an element of the list and might indeed be in it.

Cantor also famously hypothesized that there is no other cardinality between aleph-null and c, so that c represents the next set larger than the integers, or \$ \aleph_1 \$. This is called the continuum hypothesis. While most everyone believes it to be true, it has so far not been proved.

Take pi to any arbitrary length. Change one digit. A subsequence that does not occur in that expansion.

One thing you have to be careful of is arguments that prove more than intended, in other words overgeneral arguments. Since you invited me to, I take "arbitrary length" to be 1.

I. Pi to 1 digit is 3.

II. "Change one digit": okay, now I have 4.

III. "A subsequence that does not occur in that expansion": while it's true that the first digit of pi does not contain 4, it is irrelevant to the topic because 4 is contained someplace else within the expansion, which is all that I claimed (in fact, infinitely many places). And the same is true for substrings of any length, not just 1.

The property of containing every possible sequence is called normality: the uniform distribution of digits. It has been known for a long time that nearly all real numbers are normal, but proving that specific numbers are normal is difficult. The known decimal digits of pi are very uniform, and those digits are known to around 10 trillion places, but uniformity of all digits is unproven. We can, however, easily construct normal irrational numbers, such as Champerowne's constant.

[MIS42N]

Take pi to any arbitrary length. Change one digit. A subsequence that does not occur in that expansion.

One thing you have to be careful of is arguments that prove more than intended, in other words overgeneral arguments. Since you invited me to, I take "arbitrary length" to be 1.

I. Pi to 1 digit is 3.

II. "Change one digit": okay, now I have 4.

III. "A subsequence that does not occur in that expansion": while it's true that the first digit of pi does not contain 4, it is irrelevant to the topic because 4 is contained someplace else within the expansion, which is all that I claimed (in fact, infinitely many places). And the same is true for substrings of any length, not just 1.

The property of containing every possible sequence is called normality: the uniform distribution of digits. It has been known for a long time that nearly all real numbers are normal, but proving that specific numbers are normal is difficult. The known decimal digits of pi are very uniform, and those digits are known to around 10 trillion places, but uniformity of all digits is unproven. We can, however, easily construct normal irrational numbers, such as Champerowne's constant.

I think I was not clear. I was arguing that take pi with x digits. Change the first digit to create a different number with x digits. Those x digits are not contained in the original x digits. There was no intent to extend pi to more digits (in which case I alter the first digit of the more digits and the argument still holds). However, I was assuming a finite string of arbitrary length. Bad assumption. A finite string of arbitrary length is not an infinite string. Different beast.

I agree with your original statement. A persuasive argument. It relies on pi being a truly random sequence of digits and I assume there is a proof of that somewhere.

[TimFox]

I believe the correct statement is that the sequence of digits in the decimal expansion of pi passes all the tests for randomness.
I don't know if randomness can be "proven" past that statement.

[helius]

The number theoreticians just speak of uniform distributions of digits (not "randomness") because it has nothing to do with random probabilities. Every digit of pi is calculable from simple formulas: it has zero entropy.

There are some numbers that are called "uncomputable" because there is no simple formula for finding their approximants. An example is Chaitin's constant.

There are, of course, other ways to represent numbers such as pi which are totally regular: that must be the case since it is computable. An example is
$$ \frac 4 \pi = 1 + \cfrac {1^2} { 2 + \cfrac {3^2} { 2 + \cfrac {5^2} { 2 + \cfrac {7^2} { 2 + \dots } } } } $$

[TimFox]

From my early math studies (ca. 1965), I remember an example where the reader could group the digits in the decimal expansion of pi into discrete groups of 5 digits and compare the probabilities to poker hands played with a corresponding deck of only 10 cards.

[SiliconWizard]

The number theoreticians just speak of uniform distributions of digits (not "randomness") because it has nothing to do with random probabilities. Every digit of pi is calculable from simple formulas: it has zero entropy.

Yes, that's an interesting question actually.
Yes, all decimals of pi are calculable iteratively. So in that regard, they are not "random".
Does the sequence of decimals of pi provide a reasonable pseudo-random generator though?

More generally speaking, if we admit that everything in the universe is a succession of causes and consequences, then "randomness" is just a fiction anyway.
But then comes the trickery of quantum physics and you don't really understand what a cause is anymore. Or randomness. Or just about anything, actually.
Small digression maybe.

Fun exercise: can you find irrational numbers that do not have a uniform distribution of their decimals?

[helius]

Fun exercise: can you find irrational numbers that do not have a uniform distribution of their decimals?

We could construct a number that didn't use all 10 digits in its expansion.
For example, along the lines of Champerowne's constant, suppose we have a decimal sequence
1.101001000100001000001...
It's easy to see that this is irrational. Whether such numbers arise in other contexts, I do not know.

[Nominal Animal]

Interestingly, binary (and quaternary, octal, hexadecimal, etc.) digits of Pi can be calculated directly using Bailey–Borwein–Plouffe (discovered in 1995) and Bellard's (discovered in 1997) formulae.

[helius]

Interestingly, binary (and quaternary, octal, hexadecimal, etc.) digits of Pi can be calculated directly

It's always interesting when there is a "closed form" for a function that is usually defined iteratively or recursively.
The Fibonacci function is a favorite of mine, which is always taught in programming textbooks, but never as a closed form.
Yes, it is possible.

[Nominal Animal]

Yup:
$$F_n = \frac{\varphi^n - \psi^n}{\sqrt{5}}, \quad \text{where} \quad \varphi = \frac{1 + \sqrt{5}}{2} \quad \text{and} \quad \psi = \frac{1 - \sqrt{5}}{2}$$
and \$\varphi \approx 1.61803\$ is the golden ratio, and \$\psi = 1 - \varphi = \frac{-1}{\varphi} \approx -0.61803\$ is its conjugate.  Funky!

[helius]

It's even possible using just integers
In fact that's true for any function defined as a recurrence formula, because it has a generating polynomial encompassing all of the terms of the sequence. The Fibonacci sequence just happens to be the most primitive recurrence.

[SiliconWizard]

Proof there: http://mathonline.wikidot.com/a-closed-form-of-the-fibonacci-sequence

It's even possible using just integers

By that, I suppose you mean a closed form not involving any radicals, or any irrational numbers? Just integers, do you even mean no (non-integer) rational number either?
Would you care to share such a closed form?

[helius]

$$ \DeclareMathOperator{\fibonacci}{fibonacci} \fibonacci(n) = \cases{ n & \text{if } n\lt 2\cr \left\lfloor \frac {2^{n(n+1)}}{(2^{2n} - 2^n - 1)} \right\rfloor \bmod 2^n & \text{otherwise}} $$

By the way, there's nothing special about base 2. It will work in any base, because as I said it's derived from the generating polynomial for the recurrence which is \$ \frac {1}{1 - x - x^2} \$. In some sense this polynomial is equal to the entire Fibonacci sequence.

[SiliconWizard]

Sorry about the delay - yes the closed form above appears to be correct. It's rarely shown! The form with the golden ratio is much more common.

Interestingly (or is it?), from the generating function \$\displaystyle s(z) = \sum_{k = 0}^{\infty} F_k z^k = \frac{z}{1-z-z^2}\$ , with \$z = \frac{1}{2}\$, we get : \$\displaystyle \sum_{k = 0}^{\infty} \frac{F_k}{2^{k+1}} = 1\$ , while \$\displaystyle \sum_{k = 0}^{\infty} \frac{1}{2^{k+1}}\$ also converges to 1.

[Circlotron]

Yup:
$$F_n = \frac{\varphi^n - \psi^n}{\sqrt{5}}, \quad \text{where} \quad \varphi = \frac{1 + \sqrt{5}}{2} \quad \text{and} \quad \psi = \frac{1 - \sqrt{5}}{2}$$
and \$\varphi \approx 1.61803\$ is the golden ratio, and \$\psi = 1 - \varphi = \frac{-1}{\varphi} \approx -0.61803\$ is its conjugate.  Funky!

And of course 1/phi = phi - 1 and phi^2 = phi + 1.
What is there not to like about phi? 

[SiliconWizard]

What is there not to like about phi? 

I find it too irrational.

[RJSV]

Thanks DavidAlfa!   Of the '1212' mentions.   My (beloved CAT pet died on that date.
   I'm pretty sure, something ELSE happened that dark day...(try looking up December 12,2000.)

   This only goes to show, the incredible and coincidental links, with some of the non-mathmatical world.

   And thanks, folks, for the detailed coverage of phi.

[RJSV]

   Another example, of the linking to supposedly non-mathmatical things is '49' appearing in (various) family members phone numbers;  My family history has the Grass Valley, CA  / Nevada City Gold Rush, (i.e. '49'ers) derived from the 1849 Discovery of gold, that cemented the future fate of California, as a kind of wild ride experience.

   Oh and I'm not very experienced in the formal mechanisms, of numerology, but often will 'test' out things, sequences backwards.  So that has connotation that a number like 948 would STILL be a qualified march, (to 49).
Thus I've recognized (phone area code) '494' as a 'double' hit.

   A friend's birth date, 4-25, seemed an ironic match, almost '420', and that's a good match, for him.
Dividing that, by five, and you've got '85', divide again, to '17'.  So what, but that's in his address, and if you think about it, I actually just had divided (the 425) by '25', actually. 
This game, for that friend, goes on and on, a relatively harmless but also maybe useless fact... But I'd have to say that, the coincidences in that particular person, the birth, and residence numbers have so many coincidental matches with that it's 'hilarious'
   Much of it with a '711' slant.   His house at '1711' Blackbourne St.

[RJSV]

   It can get a bit silly, I know, but as long as I'm doing study just for curiosity / entertainment.
So...also tried that little process, with 4-20 even though that's not his month-day of birth, but
   420/5 = '84'.   A bit comical, as that person was born 1984...
   Of course here, I'm not really sure why I've been dividing by five...

[babysitter]

How can you discuss this without hitting

https://de.wikipedia.org/wiki/Cornelis_de_Jager#Radosophie

This guy found the numbers for some physical/astronomical constants in the size of his bike!

BR
Hendi