Wow Andrew, as usual you knocked it outta the park, but this post... POOF! goes my brain. Just staggering and I've read it a couple times and still can't wrap my pea brain around it. You pick such good topics!!
There's this book I read and love (ok -technically, I'm only 2/3rds of the way through it... it's in my TBF pile and I do intend to finish it): "Fantastic Numbers and Where to Find Them: A Cosmic Quest From Zero to Infinity" by Antonio Padilla.
In it, one of the numbers he writes about is Graham's number. As described on wikipedia: "Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes's number and Moser's number, both of which are in turn much larger than a googolplex."
Now here's where it's gonna REALLY hurt everyone's head.
Graham's number is SOOO large, it's impossible to represent it in our universe.
There are about 10^80 atoms in the observable universe. Even a *small fraction* of Graham's number has more digits than the number of atoms... If each digit of Graham's number were written in the smallest possible font, it would still take more space than the entire universe to write down.
Mind-bending post, Andrew. I had a similar mental gymnastics routine yesterday while thinking about timescales on Earth. Something that happened 15 million years ago seems insane to think about when you really try and picture it. But then the Earth is 4.5 billion years old…. Several orders of magnitude longer. I tried to contemplate that and failed miserably. Fun exercise, but those huge numbers are truly problematic for us!
Thanks, Jacob! We are on the same page, always wrestling with this concept and trying to compare it to things we think we understand. One step at a time, we get just a tiny bit smarter every day.
I guess I'm asking what you visualize when you compare those numbers. Can you really grasp what's going on when 10 times as much of something happens when one of those zeros moves? It's like the best we can do, but I wonder how cognizant we really are in those moments.
I should maybe also add that I got pretty far in math early in life, but quit academic study 30 years ago, give or take, so I don't do math with gargantuan numbers on the regs or anything.
I "visualize" relative magnitudes. Like our senses do, with logarithmic response, i.e., it takes ten times as much power to double the perception, e.g., hearing. I was taught engineering notation, which uses powers of three, so everything was in that notations, and I could compare exponents to "see" ratios. Science is full of ratios and logarithmic ways of looking at things. "Orders of magnitude" comes up quite a it.
No. I do not use these really huge numbers, but I have used numbers like the number of atoms in the universe to compare in algorithmic analysis. Like worst case analyses. I guess I'm just used to theoretically extending systems to see how they scale. I read an entire book about scale! :-)
I do not know if this helps, but I gave it a try. Hee! In math I don't really visualize unless there is geometric component, which it does many times, but analysis with symbols is my game.
I've read a lot of books about scale through the lens of business ("scaling up" is a really hot catchphrase, but also a really important concept). I think about physics every day, too! I guess I'm not surprised at you wanting to read a whole book on scale, honestly. I think that's really cool!
I read a lot! My boss and some collaborators over time were physicists. I really do like the approach they (usually) have of not sacrificing the good for the perfect.
I’ve only strayed into business systems as a consultant so I could get out quickly when the project shows signs of completion. :-)
I feel like you are just trying to hurt my brain with this post.
Wow Andrew, as usual you knocked it outta the park, but this post... POOF! goes my brain. Just staggering and I've read it a couple times and still can't wrap my pea brain around it. You pick such good topics!!
Thanks so much! And, thanks for helping me think about this stuff. Simply having a place to have these sorts of fun conversations is everything to me.
"Hello, Bank, Andrew told me I have a few zeros extra on my account, can you check?"
- Daniel, who has as little grasp of the concept of hypothetical scenarios as he has of the googolplex.
Tell them I said to double check!
They say it's illegal to issue more than a single check at a time.
Did you tell them you're leaving Prague soon, so you shouldn't count as a Czech?
#dadding
Checkmate!
Czechmate?
There's this book I read and love (ok -technically, I'm only 2/3rds of the way through it... it's in my TBF pile and I do intend to finish it): "Fantastic Numbers and Where to Find Them: A Cosmic Quest From Zero to Infinity" by Antonio Padilla.
In it, one of the numbers he writes about is Graham's number. As described on wikipedia: "Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes's number and Moser's number, both of which are in turn much larger than a googolplex."
Now here's where it's gonna REALLY hurt everyone's head.
Graham's number is SOOO large, it's impossible to represent it in our universe.
There are about 10^80 atoms in the observable universe. Even a *small fraction* of Graham's number has more digits than the number of atoms... If each digit of Graham's number were written in the smallest possible font, it would still take more space than the entire universe to write down.
:)
Graham's number pretty much defines what I think of as a kajillion-jillion in my mind. It's literally unimaginably large.
Mind-bending post, Andrew. I had a similar mental gymnastics routine yesterday while thinking about timescales on Earth. Something that happened 15 million years ago seems insane to think about when you really try and picture it. But then the Earth is 4.5 billion years old…. Several orders of magnitude longer. I tried to contemplate that and failed miserably. Fun exercise, but those huge numbers are truly problematic for us!
Thanks, Jacob! We are on the same page, always wrestling with this concept and trying to compare it to things we think we understand. One step at a time, we get just a tiny bit smarter every day.
I’m not sure or if I get smarter or dumber… the more I learn, the more I figure out I don’t know. So I guess, does that make me smarter or dumber?
Smarter. You just didn't realize how dumb you used to be! Same with me, every single day.
Smarter! Woohoo!
Moar smarterer!
Scientific (or engineering) notation did it for me.
What did it do?
Got rid of the zeroes so I could compare better.
I guess I'm asking what you visualize when you compare those numbers. Can you really grasp what's going on when 10 times as much of something happens when one of those zeros moves? It's like the best we can do, but I wonder how cognizant we really are in those moments.
I should maybe also add that I got pretty far in math early in life, but quit academic study 30 years ago, give or take, so I don't do math with gargantuan numbers on the regs or anything.
I "visualize" relative magnitudes. Like our senses do, with logarithmic response, i.e., it takes ten times as much power to double the perception, e.g., hearing. I was taught engineering notation, which uses powers of three, so everything was in that notations, and I could compare exponents to "see" ratios. Science is full of ratios and logarithmic ways of looking at things. "Orders of magnitude" comes up quite a it.
No. I do not use these really huge numbers, but I have used numbers like the number of atoms in the universe to compare in algorithmic analysis. Like worst case analyses. I guess I'm just used to theoretically extending systems to see how they scale. I read an entire book about scale! :-)
https://www.abebooks.com/Scale-Universal-Laws-Growth-Innovation-Sustainability/31231031510/bd
I do not know if this helps, but I gave it a try. Hee! In math I don't really visualize unless there is geometric component, which it does many times, but analysis with symbols is my game.
I've read a lot of books about scale through the lens of business ("scaling up" is a really hot catchphrase, but also a really important concept). I think about physics every day, too! I guess I'm not surprised at you wanting to read a whole book on scale, honestly. I think that's really cool!
I read a lot! My boss and some collaborators over time were physicists. I really do like the approach they (usually) have of not sacrificing the good for the perfect.
I’ve only strayed into business systems as a consultant so I could get out quickly when the project shows signs of completion. :-)