"do you sometimes feel sad that, in all probability, you will die?" - brady
sngfrx
Chaitin’s constant has actually been proven to be normal. Congrats, Matt! You lived to see one!
AngryArmadillo
"Each halting probability [Chaitin's constant] is a normal and transcendental real number that is not computable"
- Wikipedia, page on Chaitin's Constant
"Every Chaitin's constant Ω is a normal number (Calude, 1994)."
- Wikipedia, page on normal numbers
Seb-ei
Matt Parker has one of the most interesting repertoire of facial expressions I’ve ever seen.
TIOS
1:35 I would like to add it to Matt's words is that not only the people of the future will get to be excited about the discoveries
But also, the progress of the future depends on today's progress, so the future mathematicians won't be able to discover what we're looking for today without current day mathematicians making progress today
avi
Please make these kind of videos longer.
Sometimes I feel like listening a little longer to a video than the standard youtube length.
Cheers!
ericbell
This is by far the most fascinating numberphile video and artifact I have encountered in mathematics.
JamesSpeiser
I love Brady's existential question on the eternal ignorance that comes with death. That is one of my greatest fears in facing my own mortality... That I will never know the answer to some of life's greatest mysteries. Pondering such matters has quite literally kept me up many a night.
tomharner
This just took an unexpectedly deep turn _real fast_
pedroscoponi
The fact that the most common numbers are the ones we can't find is not a coincidence. Any reasonable way to randomly sample from all possible numbers must encode an infinite amount of random information in it, which is both the reason they're normal and can't be computed. And it's very hard to specify a number without directly giving the algorithm to compute it.
MrCheeze
So all math up till now has been the equivalent of searching for your keys under the streetlight.
HebaruSan
Woah numberphile getting all existential on us.
torlumnitor
This, and the accompanying standard numberphile channel video really, really made me think, and that is the best feeling in the world.
Thank you!!
fishandchips
Also for people who want a number that can be easily understood as an uncomputable: The halting number.
Turing machines are countable because they consist of a finite ruleset, so we can list them all. Machine number 1, machine number 2 and so on. Define h such that the nth decimal place is a 1 if machine number n halts and 0 if it doesn't. h is uncomputable because computing h would solve the halting problem which is impossible.
Supremebubble
The set of all normal uncomputable numbers be like: I have an infinite amount of numbers in me, but you can't name a single one
zionfultz
Improving on Tim Anderson's question, are there any transcendental numbers proved to NOT be normal?
donach
That existential question reminds me of the interview Brady did with the great John Conway a number of years ago, which is split into several smaller videos with the most relevant one hauntingly titled "Life, Death, and the Monster."
alecbader
I wonder if there are other sorts of categories or nested categories to be discovered out in the normals. Like what if the computables aren't the only major subset?
eragonawesome
"Do you sometimes feel sad"
Yes I do
MonzennCarloMallari
I personally get great joy from our human race’s ability to collectively know so much which no one person could ever get to know alone in one lifespan. In contrast to those who choose to dwell on our collective faux pas and make statements like they have no faith in humanity. Each human is imperfect and makes mistakes; therefore the collective will as well. It’s the overall trajectory while not paying too much attention to the inevitable standard deviations that matters.
