44*44=1936.
45*45=2025. This year!
46*46= 2116.
Since my fake birthday is Oct 1, 1960 (I do not reveal my real birthday to try to prevent ID theft), which is past 1936, and I won't live to 2116 unless Quantum-AI finds a way to put my brain in a a vat, I will not see two square years in my life :-(
Since I keep a list of celebrities (defined as people I know who have some fame - so its subjective) who are over 80, I have a LIST of celebrities who were born in 1936 or earlier. I was going to list them in this post but there are to many. So I list those that I think my readers care about, and point to the full list.
Here are people who have lived through two squares who I think you care about. I leave out how old they are or what year they were born. They are in alphabetical order by their first names. I put a * next to the people who, in 1936, were AWARE that it was a square year. So the starred names are those who truly ENJOYED living through 2 square years.
NAME KNOWN TO US FOR
Andrzej Ehrenfeucht Math. EF-games (he is the E)
Anil Nerode Math- Recursive Math
Aviezri Fraenkel Math-Combinatorial Games
Buzz Aldrin Walked on the moon
Charles Duke Walked on the moon.
Dana Scott Math-CS. Prog Langs. Turing Award
David Scott Walked on the moon
Dirk Van Dalen Math- Logic
Eric Hirsch Jr American Educator *
Harrison Schmidt Walked on the Moon.
Harry Furstenberg Math-Ergodic methods in Ramsey Theory.
Heisuka Hironik Math-Algebraic Geom-Fields Medal
Herman Chernoff Math-Probability *
Jack Edmonds CS. Theorist.
James Watson Biologist-The Double Helix. Nobel Prize with Crick.*
Jane Goodall Zoologist and Activist
Jean-Pierre Serre Math. Algebraic X. Fields Medal.*
John Thompson Math. Group Theory. Fields Medal, Abel Prize
Micahel Rabin CS/ Math. Theorsit. Turing Award.
Noam Chomsky Linguistics. Did work on Grammars
Richard Friedberg Physicist. Also invented Priority method in Rec Theory.
Richard Karp CS. Theorist. Turing Award. .
Richard Stearns CS. Theorist. Turing Award.
Stephen Smale Math-Lots of Stuff
Tom Baker Actor-Dr. Who.
Tom Lehrer Math/Novelty songs..*
Tony Hoare CS. PL. Turing Award.
Volker Strassen Math-CS.
Walter Koenig Actor. Star Trek
William Shatner Actor- Star Trek
For my complete list see here
It is currently impossible for someone to live through three square years (again, unless they get their brain in a vat, or some other not-yet-invented mechanism). In a much earlier era it was possible:
20*20=400
21*21=441
22*22=484
So if you were born in 400 and lived to be 84 years old, three squares! While MOST people didn't live that long back then, SOME did.
10*10=100
11*11=121
12*12=144
Born in the year 100, live to be 44 years old. Was the calendar well established by then?
(ADDED LATER: a colleague emailed me about the calendar. Dionysius Exiguus is credited with inventing the AD/BC calendar (not to be confused with the band AC/DC). He was born in 470 so lets say that the modern calendar was in known from 500 on. (I am not dealing with the times its changed a bit.). SO
23*23=529
24*24=576
25*25=625
To live through three squares you would need to live to 96.
To be aware that you lived through three squares you would need to ive to 104.
To enjoy the 3-squareness you would need to be a healthy 104 year old.
Did someone who was born in 529 live to 625. I would doubt it. See here for an article about how long people lived in Middle Ages. Or, more accurately, how short they lived.
)
Reminds me of a great line from A Funny Think Happened on the Way to the Forum, a musical that takes place in the early AD's. The character Pseudolus says:
(Looking at a bottle of wine) Was 1 a good year?
Someone born in France in 1764 would have lived through four square years when reaching the age of 36: 1764 = 42 * 42, and the years 1791, 1795 and 1800 are the years I, IV and IX of the French Revolutionary Calendar which was in effect those years. The calendar was abolished before reaching year XVI. But if said person lived to be 85, he/she could add a fifth square year: 1849 = 43 * 43.
ReplyDelete1) Did not know that! Thanks!
Delete2) Was IV a good year for wine?
It is Andrzej Ehrenfeucht
ReplyDeletefixed, thanks
DeleteIf you consider the classical Roman calendar, somebody in the 3rd century BC Roman republic could've lived through 3 'square years' without it being an artifact of a novel (less than 200 years old) or short-lived calendar.
ReplyDeleteThat calendar was "From the founding of the city", or the acronym "EUR" in Latin, with the traditional founding date of Rome to be 753 BC = 0 EUR. So if you lived from 484-576 EUR (269-177 BC), you would've lived through 3 square years by age 93. Hard but not totally impossible for an upper class priestly or official type to pull off in that time & place, even with the additional requirement that you be aware of it. Such a person could've known both the relevant math & calendar, and we know some of them reached their 80s due to surviving records (e.g. Roman senators). Similar logic would apply to contemporaries in Ptolemy's Egypt, except the locals there wouldn't have been using the Roman calendar yet.
There are really 4 different factors here:
1) Time Gap: Once you get to the years 26^2 - 24^2 = 676-576 =100, the gap becomes too big for anybody to live through in most times & places. But it's not really an achievement in the 1st 100-200 years either.
2) Population size: Having more than a handful of lucky people reach 90-100 years old is a matter of population statistics more than anything else. Only a small fraction of people live that long, even now, so you need a very large population to draw from. The kind of population sizes most places didn't have before 1500AD.
3) Calendar adoption: Major calendar changes usually only occur when entire societies rise and fall. And the year 0 is often retroactively selected in such a way that few living in "Year 100" would themselves that the date. In fact the AD/BC calendar wasn't widely adopted until after 500 AD (Britain didn't until the 700s with the Venerable Bede).
4) Math knowledge: Even if the first 3 are checked off, our potential centenarian needs to know he's pulling this off. And before about 300 BC, that math was limited to a few pockets of civilization like India and the Med. Until relatively modern times only a small # of people anywhere would've learned it.
1) Great! Enlightening!
ReplyDelete2) From a 21st century prospective i think (unfairly) `Gee, SQUARES are not a hard concept. Surely even in those days people had an awareness of squares.'' Rather than say I am right or wrong, it would be an interesting (though likely impossible) question to answer: When did various civiliazation have basic math concepts like squares, primes, quaternions, etc.