6 ms·

The Ramsey number R(m,n) is the minimum size of a fully connected graph with edges colored red or blue such that there is either an m-sized blue clique or an n-

by sn41 6y ago

The Ramsey number R(m,n) is the minimum size of a fully connected graph with edges colored red or blue such that there is either an m-sized blue clique or an n-sized red clique. R(3,3) is 6, which is stated as every group of 6 having 3 mutual friends or 3 mutual strangers. Ramsey showed that these exist for every m and n, I think. But they grow very rapidly. Ramsey theory has usually the biggest constants found in mathematical papers.[1] There is a famous quote by Erdos: "Suppose aliens invade the earth and threaten to obliterate it in a year's time unless human beings can find the Ramsey number for red five and blue five. We could marshal the world's best minds and fastest computers, and within a year we could probably calculate the value. If the aliens demanded the Ramsey number for red six and blue six, however, we would have no choice but to launch a preemptive attack." [1]https://en.m.wikipedia.org/wiki/Graham%27s_number https://en.m.wikipedia.org/wiki/Graham%27s_number

zimpenfish 6y ago
What always gets me about Graham's Number is that you can't even write down how many digits it has using the entire observable universe ... but "the last 12 digits are ...262464195387". I swear mathematicians are witches.
- signa11 6y ago
  if you have not seen this before: https://waitbutwhy.com/2014/11/1000000-grahams-number.html https://waitbutwhy.com/2014/11/1000000-grahams-number.html and it's companion https://waitbutwhy.com/2014/11/from-1-to-1000000.html https://waitbutwhy.com/2014/11/from-1-to-1000000.html are pretty cool.
- bonoboTP 6y ago
  It's so big that going from the number itself to the number of digits (i.e. taking its logarithm) is not even something worth talking about. It's like blowing a kiss to an exploding nuclear bomb. You just get dizzy even thinking about it. The observable universe is just not really that big when talking about this stuff, there are not even 100 orders of magnitude in the universe from smallest to biggest. Anything that you can have a conception of (even stuff like the number of possible lottery tickets or possible books that could ever be written etc) is just indistinguishable from mundane everyday sizes when dealing with googology. You're trying to roar but it comes out as a whisper. You have to explicitly design these. Most of the time if you think "but wouldn't it be comparable if we counted the XYZ) the answer is no. It's like an adult equivalent of a kid saying "I get that galaxies are big, but are they also bigger than really big houses? How about a house with its own swimming pool? Really really big mansion of a big movie star?" Edit: Tone is difficult in writing, I don't mean to be condescending, I'm getting dizzy myself when thinking of this and remember my frustration and amazement when first hearing about these.
  - ppod 6y ago
    >going from the number itself to the number of digits (i.e. taking its logarithm) Why did nobody ever tell me to think of logs like this before!!?
    - deleted 6y ago
      [deleted]
    - tonyarkles 6y ago
      Another fun property of this is that you can use it across bases. For example, how many bits would I need to represent 34812923 in binary? log2(34812923) = 25.05 -> round up to 26 bits.
    - SummerlyMars 6y ago
      Thank you for posting this. The significance of this statement was lost on me until you pointed it out. Going by MathOverflow, it's slightly more complicated than that, but it's pretty close. https://math.stackexchange.com/questions/1384917/relation-between-number-of-digits-of-a-number-and-its-logarithm https://math.stackexchange.com/questions/1384917/relation-be...
  - jonahx 6y ago
    > I don't mean to be condescending Fwiw, I did't read it that way at all. I thought the child's question was a great analogy.
  - frogpelt 6y ago
    Numbers get big really fast. They quickly grow to proportions that practically mean nothing to us. A million seconds is 11.5 days from now. A billion seconds is 31 years, 8 months, and 15 days from now. A trillion seconds is 31,709 years from now.
  - dunefox 6y ago
    That was an excellent and entertaining comment.
  - marcosdumay 6y ago
schr0dinger 6y ago
How would Graham’s number compare to, say, Aleph Null? https://en.m.wikipedia.org/wiki/Aleph_number https://en.m.wikipedia.org/wiki/Aleph_number
- hansvm 6y ago
  It basically rounds down to 0, like every finite number.

by sn41 6y ago

zimpenfish 6y ago

What always gets me about Graham's Number is that you can't even write down how many digits it has using the entire observable universe ... but "the last 12 digits are ...262464195387". I swear mathematicians are witches.

signa11 6y ago
if you have not seen this before: https://waitbutwhy.com/2014/11/1000000-grahams-number.html https://waitbutwhy.com/2014/11/1000000-grahams-number.html and it's companion https://waitbutwhy.com/2014/11/from-1-to-1000000.html https://waitbutwhy.com/2014/11/from-1-to-1000000.html are pretty cool.
bonoboTP 6y ago
It's so big that going from the number itself to the number of digits (i.e. taking its logarithm) is not even something worth talking about. It's like blowing a kiss to an exploding nuclear bomb. You just get dizzy even thinking about it. The observable universe is just not really that big when talking about this stuff, there are not even 100 orders of magnitude in the universe from smallest to biggest. Anything that you can have a conception of (even stuff like the number of possible lottery tickets or possible books that could ever be written etc) is just indistinguishable from mundane everyday sizes when dealing with googology. You're trying to roar but it comes out as a whisper. You have to explicitly design these. Most of the time if you think "but wouldn't it be comparable if we counted the XYZ) the answer is no. It's like an adult equivalent of a kid saying "I get that galaxies are big, but are they also bigger than really big houses? How about a house with its own swimming pool? Really really big mansion of a big movie star?" Edit: Tone is difficult in writing, I don't mean to be condescending, I'm getting dizzy myself when thinking of this and remember my frustration and amazement when first hearing about these.
- ppod 6y ago
  >going from the number itself to the number of digits (i.e. taking its logarithm) Why did nobody ever tell me to think of logs like this before!!?
  - deleted 6y ago
    [deleted]
  - tonyarkles 6y ago
    Another fun property of this is that you can use it across bases. For example, how many bits would I need to represent 34812923 in binary? log2(34812923) = 25.05 -> round up to 26 bits.
  - SummerlyMars 6y ago
    Thank you for posting this. The significance of this statement was lost on me until you pointed it out. Going by MathOverflow, it's slightly more complicated than that, but it's pretty close. https://math.stackexchange.com/questions/1384917/relation-between-number-of-digits-of-a-number-and-its-logarithm https://math.stackexchange.com/questions/1384917/relation-be...
- jonahx 6y ago
  > I don't mean to be condescending Fwiw, I did't read it that way at all. I thought the child's question was a great analogy.
- frogpelt 6y ago
  Numbers get big really fast. They quickly grow to proportions that practically mean nothing to us. A million seconds is 11.5 days from now. A billion seconds is 31 years, 8 months, and 15 days from now. A trillion seconds is 31,709 years from now.
- dunefox 6y ago
  That was an excellent and entertaining comment.
- marcosdumay 6y ago

schr0dinger 6y ago

How would Graham’s number compare to, say, Aleph Null? https://en.m.wikipedia.org/wiki/Aleph_number https://en.m.wikipedia.org/wiki/Aleph_number

hansvm 6y ago
It basically rounds down to 0, like every finite number.