## My googol rank

According to my usage statistics, of the people who come to scottaaronson.com via a search engine, about 5% do so by typing in one of the following queries:

biggest number in the world

the biggest number in the world

what is the largest number

largest number in the world

what is the biggest number

These people are then led to my big numbers essay, which presumably befuddles them even more.

So, let me satisfy the public’s curiosity once and for all: the biggest number in the world is a million billion gazillion. But stay tuned: even as I write, Space Shuttle astronauts are combing the galaxy for an even bigger number!

Comment #1 October 31st, 2006 at 5:34 am

I thought that the biggest number was 45,000,000,000?

http://www.youtube.com/watch?v=MiMWJ1xBo8w

Comment #2 October 31st, 2006 at 5:50 am

Dude, that clip was from the eighties. Numbers have gotten bigger since then. Sheesh, get with times man.

Comment #3 October 31st, 2006 at 5:57 am

Everyone talks about the largest known prime number. Why doesn’t anyone talk about the largest known number?

In either case, there is a straightforward way of going from one to the next largest one.

Comment #4 October 31st, 2006 at 6:06 am

Obviouslythe reason people talk about the largest known prime (generally a Mersenne) is the application to locally decodable codes…(Incidentally, if you don’t assume GRH, then I

don’tthink there’s a polynomial-time algorithm for passing from a given prime to next largest one.)Comment #5 October 31st, 2006 at 10:57 am

I’ve never read this before, I’m really enjoying it.

So in theory if one can design a Turing machine with 4 rules, which can also check every even number for being a sum of two primes, then he can prove Goldbach’s conjecture.

Curious of what would be the lower limit on the number of rules needed to test the assertion.

Comment #6 October 31st, 2006 at 2:17 pm

I was reading today, and the following passage jumped out at me, for a reason that will be immediately apparent to anyone who regularly reads the comments on this blog:

“The desktop protein microscope would be a device combining the atomic resolution of the atomic force microscope with the penetration of a magnetic resonance imager. The conceptual design of such a device was published by John Sidles a few years ago. Sidles is a theoretical physicist working in the orthopedics department of the University of Washington medical school. He deals with human patients every day and invents imaginative tools in the evenings. Several groups of inventors at other places are attempting to develop other versions of high-resolution magnetic resonance imaging. If Sidles’ dream of a magnetic resonance imaging microscope with atomic resolution could be made to work, it could precisely locate every nitrogen and hydrogen atom in a protein molecule or in a virus. Precise structures of all kinds could be determined cheaply and rapidly.”

John Sidles, congratulations! You’ve been namechecked by one of the great ones: none other than Freeman Dyson in his book “The Sun, the Genome, and the Internet”

Comment #7 October 31st, 2006 at 5:12 pm

Dear Scottie,

I am in fourth grade. This is the first article of your bloggie that I read. Loved it! Before that, I read Quantum Pontiff’s article about the quantum percent. Loved that too! Fourth graders often wonder about the largest number and quantum percents too! My doggie’s name is Tucker.

Annie

Comment #8 October 31st, 2006 at 7:46 pm

Yes … Dyson invited me to the ISA to speak at his retirement festschrift (sp?). Of which my vivid memories include:

(1) The bronze statue of Einstein in the IAS library does NOT have a shiny nose. How do those giant brains keep their hands off it?

(2) Ed Witten told me the hardest problems he had ever worked on, were when his wife served on the Princeton School Board.

Which made me feel pretty good, because MY wife served on the Seattle School Board. In consequence of which, she and I had the pleasure of being personally sued for $200 million dollars. Ed and I agreed, political problems are tough.

Seriously, it was a huge honor and a big thrill to be asked to speak at Dyson’s retirement.

Now, after fourteen years of work on quantum microscope technology, and three device generations, we have reached the milestones of year eight of our original ten-year plan. Not great, but could be worse.

Nowadays, the main missing link in the quantum microscopy technology “stack” is not the biology or the nanotechnology (those are in pretty good shape); it is quantum MOR algorithms that need a major upgrade

This is why I am so focussed on MOR—my interest is purely driven by quantum system engineering needs, not by any personal love of complex geometry.

Comment #9 October 31st, 2006 at 8:27 pm

John,

Thank God, while talking to Dyson and Witten, you didn’t get started on agnatology…or did you? Please tell me you didn’t.

Comment #10 October 31st, 2006 at 8:56 pm

Anonymous sez:

Thank God, while talking to Dyson and Witten, you didn’t get started on agnatology…or did you?Back then, the term “agnotology” hadn’t been invented. But next time I see them, I surely will bring it up!

Because, what other new-born scientific discipline so compellingly — and self-referentially too! — unites information theory, evolutionary biology, moral philosophy, system engineering, cognitive science, economics, and practical politics?

Greatest … discipline … ever !!! 🙂

Comment #11 October 31st, 2006 at 11:57 pm

(Incidentally, if you don’t assume GRH, then I don’t think there’s a polynomial-time algorithm for passing from a given prime to next largest one.)Scott,

James meant numbers, not primes. Heavens man, why do you make everything so complicated.

Comment #12 November 1st, 2006 at 2:49 am

So, not assuming anything, there’s no polynomial time algorithm for finding a prime between n and 2n, right?

Comment #13 November 1st, 2006 at 12:08 pm

James meant numbers, not primes. Heavens man, why do you make everything so complicated.No. No. No. No. No. Read what he wrote again:

In either case [primes or numbers],there is a straightforward way of going from one to the next largest one.Again:

In either case [primes or numbers],there is a straightforward way of going from one to the next largest one.Again:

In either case [primes or numbers],there is a straightforward way of going from one to the next largest one.Sometimes I wonder why I bother…

Comment #14 November 1st, 2006 at 1:09 pm

What is this way of getting to the next prime number, assuming GRH?

Comment #15 November 1st, 2006 at 2:11 pm

In response to Douglas Knight’s question .. I think Scott is referring to the consequence of RH/GRH which says that if p is a prime, then the next prime is at most O(log^2 p) larger. So, since primality-testing is

doable, you get a polytime alg. to get to the next prime. -Aravind Srinivasan

Comment #16 November 1st, 2006 at 2:22 pm

anonymous:

So, not assuming anything, there’s no polynomial time algorithm for finding a prime between n and 2n, right?Well, there’s no known deterministic one. (Picking numbers at random until you find a prime will work w.h.p.)

Comment #17 November 1st, 2006 at 2:22 pm

Aravind: Right.

Comment #18 November 1st, 2006 at 6:20 pm

So I don’t know what the biggest number is (I leave that to Scott). The biggest prime is obviously about nlogn for n = the largest number. OK, so nlogn is bigger than n. I’m not responsible for the biggest number, remember?

The smallest number, on the other hand, is 1, at least if recent polls amongst my students are correct.

And to think I walked those people through Zeno’s paradoxes. . . I’m still fighting the idea that number=natural number. “Pick a number between 1 and 10.”

Comment #19 November 1st, 2006 at 6:48 pm

A Little Night Musing, I must protest against your posting. The smallest number is definitely known to be 0.999 … . Please refrain from disseminating incorrect information.

Comment #20 November 1st, 2006 at 10:02 pm

I pictured David Deutsch undergoing open-heart surgery with the bypass operation being controlled by a quantum computer. Instead of knowing where to cut, with certainty, the computer was making decisions in accordance with probability. Under anaesthesia, he was dreaming about the difference between theory and practice.

Comment #21 November 1st, 2006 at 10:34 pm

@Herb Ivorous:

Point taken. FWIW I offer into evidence the following conversation

verbatim:Dennis Sullivan: What is the next number in this sequence? [Writes on blackboard] 4, 14, 14, 42, ?

Sylvan Cappell: Unfortunately, the next number is Columbus Circle.

Comment #22 November 1st, 2006 at 10:35 pm

Left off 34. ARGHH

Comment #23 November 2nd, 2006 at 4:37 am

Sometimes I wonder why I bother…Oh!

My bad. Never read between words.

Comment #24 November 2nd, 2006 at 11:20 am

Aravind Srinivasan,

thanks!

I had poked around on wikipedia, but it only mentioned weaker results (maybe the consequence of merely RH).