I thought I saw a little bit of Shakespeare in there.
Naah. It’s just monkeys typing on turtles. All the way down.
Try 5, 12, 17 or 8, 15, 17 or 9, 40, 41 or infinitely many other Pythagorean triplets. The general principle is take two integers m > n, one even and the other odd with no common divisor and look at 2mn, m^2 - n^2, m^2 + n^2. It’s easy to see that always gives a triplet. It is not that much harder to see that gives all primitive (no common divisor) triplets.
As for 1 + 1 = 2, it all depends on the definitions you use. If you define addition starting with n +1 is the successor of n and define 2 as the successor of 1, then it is immediate. My late colleague liked to define 2 and the cardinality of a pair of platinum-iridium balls held in a vault in a suburb of Paris.
Explain what, exactly? There are millions of possible rare coincidences between any two people. The fact that some happen to pan out isn’t unusual. In fact, if you couldn’t find any at all that would be remarkable. Finding random chance coincidences without establishing a data set and predictive result isn’t really very interesting.
There are infinitely many rare events (specifically, coincidences in this discussion) that could happen, that it can’t be surprising that some (indeed, many) do happen.
Now, if you try to specify in advance exactly which coincidences you bet will happen, then that’s a real long shot. Yet there will still be some coincidences that are bound to happen, and after the fact you will marvel at them. (Like, that encyclopedia of parallels people keep finding between Lincoln and Kennedy and their respective assassinations.)
An analogy: It’s understood that in any gathering of 35-or-so people, there is a better-than-50% chance that some two of them will have the same birthday. But if you pick a particular day of the year and look for two people with that particular birthday, it’s not likely at all. Thus, if you are one of the people in that room and you look for another person with the same birthday as yourself, that isn’t likely to happen. (Says the guy who was in a class of 35-or-so people in 8th grade and the teacher noted THREE people, myself included, with the same birthday!)
Of course coincidences on the order of 500 million to 1 happen. Nearly every day when someone wins the lottery. Name ONE with those odds that happened to you in your entire life, that you know of. I can name TWO. That’s the point of this post. To hear more of them. Since you say they exist. And it’s not so special or rare.
A related topic from another post, combined with this one. Here I mentioned a few numbers outside of the tropical year. 3,4,5 and e. This happened hours ago. I couldn’t possible predict the future right? The other post focused on 5 and some really long numbers. Nothing else short. How many more did I type here outside of the year formula?
=3* 4* 5+e-SIN(SQRT(5))
My new friends phone number all 9 digits.
There are 635,013,559,600 possible bridge hands. The chance of any one of them coming up is the same. Having 13 spades is just as likely as getting a random mix of suits. I’ve had all sorts of numerical coincidences show up in a bridge hand depending on how you look at the cards; birthdays, phone numbers, addresses, PINs, etc. I’ve had my own phone number show up in my randomly generated SecureID key fob frequently.
Human brains are fine tuned to look for patterns, and will find them in just about any collection of numbers. That isn’t surprising. If you look for them you will find them anywhere. Without setting some parameters beforehand on what you count as a coincidence you really don’t have much of anything.
Perfect example. Now find your phone number within 10-20 digits the FIRST time you look at a long string of digits. This is what I’m talking about.
But I’m not looking for my phone number. I’m looking for any coincidence.
That’s much easier. Find ANY 10 or more digit coincidence the FIRST time you look at any source of a long string of numbers.
3,4,5 and e is in advance. Sorta. Ham radio call signs are the only identifier we had as a child. We didn’t know our parents employee ID or SSN or DL. There were no other numbers to match up. Can you think of any besides age birth and phone? We mostly shared the same 3 digit exchange. Nobody I knew had the same Bday beyond the first 4 digits. I only knew 6 ham operators in person at the time. The first 2 I met were in the group of 3 matches. Sure I wasn’t looking for that. It’s like meeting someone with the same phone number in Czech, being from the USA. I only know 2 people there. It doesn’t matter if I’m looking for that or not. You notice it either way. Assuming you don’t search the internet to find that one person.
I wonder how someone would feel if they were born on March Fourteenth five and a halfish years ago, twenty six minutes after the ninth hour of the day.
I don’t really get excited or anything, but I do note when a total comes to the current or a notable year.
All Norwegians are assigned a national identification number at birth (or immigration). It’s 11 digits, with the first 6 being your birth date in DDMMYY-format and the last five a unique additional identifier. In 1993 Norway eliminated area codes and adopted nation wide 8-digit phone numbers. The first five digits of our adjusted phone number were the five non-date digits of my national identification number.
That event, by itself, has a probability of 1e6, if no other events could possibly happen in your life. Those happen often to me and my friends, maybe because of so many opportunities in these modern times full of numbers. Try to find a 1e8 event.
But the thing is, life is so full of numbers, and there are so many potential patterns in numbers, that every person has billions or more of chances to get one of those “one in a billion” coincidences.
Would be an interesting exercise to calculate the odds or how many billion events we get to watch in a lifetime. First you have to define what it means. You wouldn’t count meeting your childhood friend in Latvia on New Years day. That’s too hard to quantify. And it happened to me. The odds of sitting next to someone on a plane from your neighborhood when the flight originated in another state not going home. Again you can’t count it. How many times do we compare or view long strings of random numbers or letters? When one side is a phone number or Bday. How many digits do we view in a lifetime more than 12 digits? This could tell us the probability of a 1 in a billion match. Any estimates?
This happens more than it should. It can be proven statistically.
Can you show us the proof, please?
I am searching for the math I had read.
bit.ly/361PZdT