Quasiperfect Numbers with Eric Lander - Numberphile
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- เผยแพร่เมื่อ 17 ม.ค. 2021
- Eric Lander discusses how quasiperfect numbers gave him a start...
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This interview was filmed in 2015 but remained unedited and unpublished until now... The other main interview from that day (about "Basic Research") can be found here: • Why Basic Research is ...
The Westinghouse Science Talent Search has since become the Regeneron Science Talent Search: en.wikipedia.org/wiki/Regener...
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This interview was filmed in 2015 but remained unedited and unpublished until now... The other main interview from that day (about "Basic Research") can be found here: th-cam.com/video/6gnsQjPCC78/w-d-xo.html
Hello
This man is going to make me rich with his passion for genomics sitting in the cabinet
Why was it not published till now?
i thought this looked quite familiar. :D even back than i wondered if he had some german or austrian ancestors, due to the nice way of proper pronunciation.
His new job has nothing to do with that
A bit of trivia: since Eric Lander has an Erdős number of 2, and has published very widely in genetics and biology, most working biologists have relatively low Erdős numbers, even if they don't themselves collaborate with full-time mathematicians.
wtf is an erdos number?
The Erdős number is the number of "hops" needed to connect the author of a paper with the prolific late mathematician Paul Erdős. An author's Erdős number is 1 if he has co-authored a paper with Erdős, 2 if he has co-authored a paper with someone who has co-authored a paper with Erdős, etc.
@@honorarymancunian7433 Excellent answer! And now the 'heisenmountain B' will probably ask next, ''who tf'' is Erdos?
And just as an aside, how did you manage to get that accent over the letter e?
@@bazsnell3178 First ¨ then e does the trick: ë.
@@bazsnell3178 and on an iPad I press ‘e’ and hold on. Ė ę ē ê è é ë
I've watched some of his biology lectures, I didin't even know he was also a mathematician! He's such a great educator.
this course changed my life
Same. I loved his lectures
Go for his lecture " 7.00x, the secret of life" on EdX. He's superb👌
Same! I took his “Intro to Biology, the secret of life” MOOC on edX several years ago and it changed my life. I learned about a whole new field of human knowledge that I knew absolutely nothing about previously. Prof. Lander is a fantastic educator and researcher.
??
OEIS list of quasiperfect numbers: [ ]
Odd perfect numbers: We can relate.
"People meeting at 8 O'clock in the morning - when I was in highschool - coming in an hour before classes."
9 am. They started high school 9 am. I had to be there by 7. I wouldn't even dare to come in at 6.
My high school started at 8:30. I usually came at 8:50
What time feels like too early heaviely depends on your sleep schedule.
Some people wake up 4AM everyday, they just fall asleep earlier too (or just sleep less)
@@heisenmountainb6854 yeah and the vast majority of teenagers not only sleep more, but sleep later.
Mothers were home all day then to tend the home fires. Today’s society relies on public schools for their day care.
The beauty of the “if” statement. You can prove things about things that don’t exist
How do you know they don't exist?
Lander was my biology professor last semester. Great guy with super engaging lectures
Even though I'm American, just because I'm so used to non-Americans on numberphile it sounds like he has a heavy accent 😂
He has a Brooklyn accent.
@@Sam_on_TH-cam Not heavy at all though
@@brandonwalker5011 No. I'm from New York and I notice it easily. But it isn't a heavy accent.
I agree, I took a double take to check that I was still on Numberphile
Bruh, I'm an American living in South Africa. He definitely sounds like he has an accent to me :😂
First US cabinet member on Numberphile... Brady has grown too powerful.
That's in a couple days. Also, this was filmed 5 years ago.
@@PeterNjeim Back to the Future ...
Filmed 5 years ago and re-edited this last week.
Watch out for the new channel Bidenphile
@@trueriver1950 Why not? There's an entire Trump network.
How many years untill we get a Numberphile president??
Wow, the lighting and exposure in this video is really old school Numberphile! I never noticed how much it has changed over the years, but a throwback to 2015 makes it clear!
Can you explain the difference? They all look the same to me
He’s just trolling.
This guy's so cool, his commitment is inspiring. It seems that he found his home from that math club. That sounds like something you see in an anime or a movie. That moment you realize you're truly at home, and that you feel that neverending connection with your passion, to which you're able to experience it alongside other people too. And from then on that's where you'll expand alongside your family. I wish I could experience that someday too.
Can we please get an in-depth video on Sierpiński? Guy was a genius, but since his works span at least 3 different languages - it is hardly accessible.
Pretty please?
nah
@@heisenmountainb6854 Trolling again? You must be a Trump supporter.
@@bazsnell3178 no one cares about american politics
I'm a current student at hampshire College. I don't think we still have that program, but it sounds sooo hampshire-y, just like "yeah go out and figure some stuff out it'll be cool". we don't have any majors or grades or tests or a core curriculum, every student chooses exactly what they want to study. one of my favorite professors is David Kelly, this real old grandpa guy who sounds like aemon targaryen, I took a class called "puzzles and paradoxes" where we just learned how to solve puzzles and riddles it was incredible
He was referring to HCSSIM which is still very much a thing. It's a math camp for high school kids
@@nyferox5637 i stand corrected then!! I dont know much of what goes on on campus the past year haha
David Kelly still runs/teaches in the program! I took part in it a few years ago, and my younger brother was a part of the remote program last summer. I credit the program as one of the reasons I’m a math major nowadays
Eric is such a great communicator and lecturer. I knew very little about biology but ended up watching his entire lecture on the free education resource edX. It was his enthusiasm while teaching that kept me coming back and watching the whole course.
This guy is very insightful ! I'd like to show the video to every student sickened or scared about mathematics. And I love the triplett "find patterns/make conjectures/prove them".
Very interesting and worthwhile video. And quasi-perfect numbers are interesting.
Which genius framed that shot at 0:48, making out like the interviewee was talking to a disembodied pair of legs?
The guy in the chair is likely the cameraman rather than the interviewer. Note the echo on the voice.
Cartoon Network Reference: Cow and Chicken ... we now know what Dad does ...
Matt Parker
as a math hobbyist with biotechnology background, i find this interview really motivating🙏🏼
The most amazing thing he said was that 8am was an hour before high-school. I used to start school at 7:30.
Lot of stuff I’ve scene points to school moving from 9-4 or so to these days, much closer to 7 or 7:30 to 2 or 2:30.
And...terrible idea. No idea why it’s common
I’m not mathematically inclined, but I am inspired by the passion of mathematical geniuses. I get a glimpse into the gorgeous world of math. Thank you.
Same :)
Beautiful interview!!!! I'm very inspired.
Congrats on the new job, Eric.
Quasiperfect number is a positive integer equals the sum of its "non-trivial" divisors (i.e. trivial divisors of N are 1 and N).
Thank you. I really enjoyed this one. ☺️
When numberphile video comes out after numberphile2's
"UNO Reverse Card"
I've completed his genetics course on edx by MIT. This is a great professor!
Eric Landers is awesome...
5:40 Yay for the Stuyvesant shoutout! I too am on the math team and have loved getting to interact with so many people who also love math like me. It’s been great.
This guy is a great pick for Biden’s Cabinet.
@@jessehammer123 But can he play the saxophone, though?
@@sisyphus645 Hmmm, the [WHAT APPEARS TO BE AN INSIDE JOKE] eludes me.
Awesome! I too was on the math team, class of 2011. Enjoy your time at Stuy!
Congrats Dr Secretary Lander!
if you changed the definition for a quasi-perfect number to be one more than the sum of ALL its factors, every prime would be quasi-perfect🙃
No, because right off he said that the number itself is not a proper divisor.
jursamaj thats why i said if you changed the definition:)
@@david10erdz if you changed the definition of primes to something reasonable, 1 would be a prime.
pluto would be a planet if you would change some definitions about planets.
2^n factors add up to n-1, including 1. So we just need to find something on the other side.
Throwback to 7.012
This might be the only circumstance that finding imperfect things is harder than finding perfect ones
Wow! I wasn’t expecting this crossover from by TH-cam Biology content into my math content.
Still rocking that 'tache!!
It's nice when you can find something like that early.
Everyone:first
Me:Actually classical mechanics forbid this
Novel technique; featuring only the interviewer's lower legs.
Great video! The last question asked of Dr. Lander was "Do you think there's one out there? What's your gut tell you?" and he answered like a truely honest person would. But it led me to a second question:
How common are QuasiQuasiPerfect numbers? Quasi^3Perfect numbers?
If it turns out there's some neat ratio between those, or just a deluge of Q^2P numbers, it might spur some interest :)
so were not gonna talk about the problem, like at all?
maybe thats why he didn't wanna upload it at first
The title is a bit misleading, but I think the real reason this was uploaded is to see a bit more on Eric, since he was just nominated to head a new White House department.
Eric Lander is one of the most exciting educators to listen to. Every time he appears in a documentary about the Genome Project, I'm all ears. Props for having him on!
Stuyvesant had a great Ultimate Frisbee team when I was in high school in the 1990s. Not quire as good as Bronx Science or Brooklyn Tech, but a solid number 3 in New York.
My school had the worst Ultimate Frisbee team. But at least we had one. There were only about a dozen schools in the city that did.
Funny thing... I knew his name was familiar but had forgotten why until you revealed it near the end!
2:42 - Is that Glenn Seaborg?! Nice!
Sorry if it's a silly question, but I want to ask: is there any group or set where we can define a quasiperfect element (and actually find it)?
This guy seems really cool
I thought exactly that. The kind of guy I would like to have a coffee and a chat with.
Very nice mini-biography.
Now, about the robotic legs...
Pls show more videos of Dr. Lander's other math-related discoveries. I know he's a geneticist, but are there any other math things he did?
no
@@heisenmountainb6854Troll Warning!!!
I love math because of all the "magic" with numbers.
awesome 🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻
What is application of such number in mathematics (to solve anything) if found ???
Seems obvious why there aren't any, divisors are smaller than 1/2 Q and amount of divisors grow slowly therefore you would need a lot of divisors to add together to add up to the number much less the number +1
I did one of those NFS summer programs. Mine was in Computer Science, 1977. I did not know there were others.....
Does anyone know where to find his paper? I've only done some basic, surface level research, but I can't find anything
Wow. He's a biologist and a mathematician ?? So cool !!
Is Dr Lander being interviewed by Dr Claw?
Missed ya Brady
I think this guy is about to become director of the Office of Science and Technology Policy for the United States
Yea! Do you think he had any idea of that when this was filmed?
I actually know the background music LOL it is used in an android app about the night sky
I had a terrible teacher and the classes I am forced to take in uni for astronomy and physics are not helpful at all, I have been forced into a situation where I no longer enjoy mathematics in any form and it means I don't enjoy numberphile anymore. As an entertaining entertainment channel I beg you to please try to do more to change the way we learn mathematics because me and hundreds of thousands of others who are forced into these classes are having our thoughts about mathematics destroyed and make it impossible to enjoy maths, you understand how to make mathematics enjoyable to learn about in a way that everyone can handle wheras I am just told "boohoo do better" whenever I fail.
This guys attitude towards math is so based
Is there a name for a number that is a number Q where the sum of its factors is Q-1, because 8.
yes, they're called "almost perfect numbers" and all the powers of two are such numbers
When being perfect is not enough...
hmmm if M is the number checking and f1 is the smallest proper factor other than 1 then the sum of all of the other factors bigger then f1 must be equal to (M-f1) (if 1 is included)
Are there any quasi quasi perfect numbers?
Or sub quasi perfect numbers there the factors add up to N-1?
Numbers where factors are N-1 are: 2,4,8,16,32,64... etc
An equivalent definition of a quasi perfect number is that it is the sum of its sublimely perfect divisors, where a sublimely perfect divisor excludes unity as well as the number itself.
Note that this is not a generally used term, but it always seems strange to me to include 1 as a proper divisor as that fact is totally general. I tried to get some results using that definition but didn't get as far as this guy...
Are the three arrows in "More links & stuff in full description below ↓↓↓
" related to Graham's Number?
On Wikipedia 1 isn't included as a proper divisor. Makes sense because the number itself isn't a proper divisor. So did you make a mistske or did someone on Wikipedia make a mistake?
Sir Is there any quasi perfect number ? If it is plz mention it .Thanks .DrRahul Rohtak Haryana India
Are there any perfectquasi numbers (where instead of +1 it's -1)
2,4,8,16,32,64.... etc
Damn , I am early
and this video is pretty old
Whaaaaat daaa
what do you mean my geophilic friend?
As we ignored 6 in fctrs of 6 ignore 2 in fctr of 2 we get 1 Nd add 1
Wait, 8 o clock in the morning was an hour *before* high school started for you???
A quasi Parker square?
Perfect Parker Number
what's the name of numbers that is the sum of it's divisors -1 then?
Just what I was thinking. In a way more significant because every number has divisor of 1 (as it does of itself)?
A mathematician who is also eloquent in speech, a rare combo.
Is it? I think all the NumberPhile presenters are eloquent.
wow
Qué grande Caszely
Can someone find me the paper?
How could there possibly be quasit perfect numbers?, I would liked an example of any "sum of factorials (except itself)" that is bigger then the number factored?
Can anyone give me an example?
Well 24 1+2+4+6+12, what am i missing, another one that is square? Well apparently 3 and 8 but more examples preferably squares?
lets try with 30. lets take all without the number itself (though if 1 is a factor, so should the number itself always be one). : 1, 2, 3, 5, 6, 10, 15 = 42 > 30
what's the word for a number like 4 whose proper divisors sum to 1 fewer than the number?
"Power of two". It may not be obvious to you, but in fact we can prove that "sum of proper divisors is one less than itself" only ever happens for numbers of the form 2^k (and all 2^k with k ∈ ℕ do have this property).
@@theadamabrams binary expansion is a fun surprisingly powerful tool.
@@antanis True. My phrase "it might not be obvious to you" basically meant "you might not be used to working in binary" 😂
wow neat! thanks Adam 😀
World’s best biologist on Numberphile? Glorious
Why is it that when defining a perfect number they included 1 in the list of divisors? They excluded the # itself in the list (so 6 wasn't included in the list of divisors for 6) which makes sense, but typically 1 and the # itself are included or excluded together, like with primes. Just wondering, because in this case if they did exclude 1 then it would have switched the definition of perfect and quasi perfect numbers. We'd know of a bunch of quasi perfect numbers (the ones that add up to one less the the number itself) but no perfect numbers.
Which means we would be currently saying that we have never found a perfect number, but are constantly searching for it. Which just sounds so much more epic!! Lol.
So does it exist?
It was never the question
I made a program that leads a tree like 3n + 1 but with these quasi numbers
But no one else has ever found any.
Will be nice having qualified people in the Biden administration.
makes up for the braindead president
@@heisenmountainb6854 it's fine. People expect the president to be some sort of genius that does everything.
It should be the opposite. The president should be a humble honest selfless person that assembles the best team and is not too concerned with the spotlight.
@@heisenmountainb6854 It's far easier to be effectively a genius on everything by outsourcing it to the actual geniuses than by being a genius-level intelect at every field (it's almost certain people will be able to demolish buildings in a single punch before that happens).
At 2:49 in the upper left corner. Is that Tom Holland? Is Tom Holland a time traveler???
Yes
Doesn't really look like him.
Tom Holland is indeed a time traveler though
All humans are hard-wired to search for patterns. Mathematicians find and codify the ones that are real.
I take issue with your last sentence.
Yes, mathematicians try to codify, to formalise, but what patterns are real depends on the axioms of your choice, so one cannot say in general which patterns are real or not (and anyway, finding patterns in the real world is the job of physicists).
@@xCorvus7x "I take issue with your last sentence."
It's the youtube comments, of course you do.
@@jansenart0
What? Why?
I'm certain I would have pointed this out on any other forum, too (possibly phrased differently; maybe I should have tried to sound more casual).
@@xCorvus7x Oh look, a pattern is emerging.
What a sympathic man, he is...
that 2nd camera angle throws me off
It's a quasi perfect camera angle.
These seem to be secondary cameras, the primary ones must have turned out not to work
@Andrea D. N. wins the internet today! :)
Whenever I hear about "Perfect Numbers", I tend to think that the definition is somewhat arbitrary. Why do we not count the number itsellf (presumably because the number itself is an obvious divisor), but include 1 (which is just as obvious)? I suppose actually finding so called "Perfect Numbers" is more satisfying than having a definition that doesn't yield any definitive results (as quasiperfect numbers do). In any case, I'm happy to find that there is some research into that topic, even if we haven't found any yet.
Would that not just make the pattern look for n where divisors sum to 2n?
Bah! If 1 is a proper divisor of a number, the number itself must be as well! The two go together. How many 1s make 6?
7:03 Biden named him (Jan2021) as PSAC: "Geneticist Eric Lander will be the presidential science advisor and is nominated to serve as director of the White House Office of Science and Technology Policy." Cool
Isn't the definition of quasi perfect numbers wrong here? Isn't it twice the original number plus one?
I was never more than a high school“C” grade math guy so I’m not sure why I watch these but here is my question: Now that computers are everywhere and unbelievably powerful, can (or has) the search for the proof been programmed and then tested out to 10 million places? It seems that the test could be done and if none occur after all that, we could call it, if not proof, at least astronomically unlikely.
But there are infinitely more numbers with more than 10 million digits, so in that case, computers have only checked 0% of numbers.
I wonder if anyone has ever studied or conjectured about "Antiquasiperfect numbers" (I don't even know if that's an official term), i.e. numbers whose proper divisors, when added up, give one less than the number itself
2^n is antiquasiperfect for any n, I think that's the only ones
"Nut out"
Ooo err missus.
1:08 why so many shots of this guy talking to a pair of legs
bc the numberphile dude was shy 5 years ago
If they're "almost" perfect, why can't we consider numbers whose factors sum to Q-1?
There r many of Q-1, eg: 8, has divisors 1,2 and 4.. Adds to 7.. Something that abundant, is not almost perfect, but trivially imperfect for mathematicians
You definitely can consider those. (People are already using the word "quasiperfect" to mean sum is Q+1, but that's just a name.) However, it turns out that all the Q numbers for which the sum of proper divisors is Q-1 are exactly the *powers of two.* So we already know everything about when the Q-1 case can occur.
Also 1 is diviser of any number, so you could even exclude it and... See?
Eric L Andre?
a video on numbers that don't even exist yet
They either exist or they don’t, what doesn’t exist isn’t yet is knowledge by humankind whether there are any.