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WEED IS LEGAL IN CANADA! Live 420chan Q&A and Site Merchandise Giveaways on Stream

Live 420chan Q&A, 420chan merchandise giveaways, Logitech hardware giveaways, partying on Twitch tonight!
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What's the biggest number? by Nathaniel Sacklespear - Fri, 23 Sep 2016 09:54:08 EST ID:XssdERJk No.15209 Ignore Report Quick Reply
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Assume we had all the possible methods of information storage in the universe and all the resources of the universe at our whimsical disposal.

What's the largest number we could put down in some kind of recording before we ran out of universe?

So I guess the core question I'm asking is what's the most compact way to write large numbers? Is there anything that beats out scientific notation? And what's the greatest extreme to which we could conceivably take this?
Edwin Gimbleforth - Fri, 23 Sep 2016 12:26:12 EST ID:ijd+nKqH No.15210 Ignore Report Quick Reply
So essentially you want, "what is the word size of the universe?". In compsci, word size is is the maximum size of the virtual address space, meaning all the available space in a system.

The number of atoms in the observable universe, is estimated to be between 4×10^79 and 4×10^81 so if the universe were a flat array of bits the size of atoms, and you used binary notation for each atom 0 or 1, you could by conservative estimate write out a positive number in full that equals 4 x 10^79 or write out positive and negative numbers in Two's Complement , by dividing that number in half and using 4 x 10^79 - 1 to be your 'flip bit' that indicates positive or negative.

As for greatest extreme, notice that a Googolplex is 10^Googol so 10^10^100 so develop a notation called Centillionplex that is 10^Centillion which is 10^10^303. Now develop a notation called Dollarillion which is 10^Centillionplex. Then a notation called Dollarillionplex which is 10^Dollarillion. The greatest extreme would be the notation for infinity I guess.
Edwin Gimbleforth - Fri, 23 Sep 2016 12:31:07 EST ID:ijd+nKqH No.15211 Ignore Report Quick Reply
>most compact way

Oops, just noticed that ques. Most compact is making up your own notation in different bases, Sci notation is base 10, Hex notation is base 16, so create something that is base Googolplex. You can also use Mod, to denote even or odd numbers. So in Mod2, you have 0, 1 only. 0 represents all even numbers, 1 represents all odd numbers. 1 + 1 = 0 (all even are 0), ect. nb
Clara Menderbury - Fri, 23 Sep 2016 16:16:17 EST ID:CvIq3Csd No.15212 Ignore Report Quick Reply
You can write down arbitrarily large numbers using arbitrarily few symbols.

Let f(x,y,1)=x+y, f(x,1,n)=x for any n>=2, and let f(x,y,n)=f(x,f(x,y-1,n),n-1). Then f(x,y,2)=x*y is multiplication, f(x,y,3)=x^y is exponentiation, and f(x,y,4) is tetration and so on. These operations grow faster and faster. Googolplex is tiny compared to f(2,3,10).
Reuben Sovingbatch - Sun, 25 Sep 2016 03:34:41 EST ID:XssdERJk No.15215 Ignore Report Quick Reply
1474788881043.webm [mp4] -(3334721B / 3.18MB, 640x352) Thumbnail displayed, click image for full size.

You dudes are like sorcerers, this shit is mad cool. Thank you very much for the explanations. Have my favorite .webm

And if anyone thinks they can go bigger, please do
Sidney Shittingstock - Wed, 28 Sep 2016 09:14:07 EST ID:bLacmKcV No.15222 Ignore Report Quick Reply
The function linked below grows faster than any function you can write down a formula for.

The study of ``how fast things get big'' in math and computer science is called time complexity.

The study of Ramsey theory in math typically leads to talking about some large numbers.

Also, you guys do know that there are different sizes of infinity and that there are people who are experts on classifying different kinds of infinities right?
Fucking Favingman - Wed, 28 Sep 2016 19:05:52 EST ID:FnqCMFm+ No.15224 Ignore Report Quick Reply
>Also, you guys do know that there are different sizes of infinity and that there are people who are experts on classifying different kinds of infinities right?
Yeah, but this guy is talking about cardinal values, not ordinal values. It's supposed to be a question about what the largest number we could theoretically record, meaning it'll be of finite value. I know you provided more info than just that, I was just clarifying.
Charlotte Chunnerpetch - Thu, 29 Sep 2016 17:30:02 EST ID:9fX9//hV No.15226 Ignore Report Quick Reply
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Wow... this is easy and common knowledge... the biggest number is 24. Thought everyone already knew that.
Frederick Siggletune - Thu, 29 Sep 2016 19:48:20 EST ID:eUbhXyVl No.15227 Ignore Report Quick Reply
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What about 25?
Isabella Hoggleshit - Thu, 29 Sep 2016 23:46:51 EST ID:sWygU/VW No.15228 Ignore Report Quick Reply
Most large numbers like 25 are just arbitrary groupings of smaller numbers. The real question is what is the largest prime number?
Charlotte Brezzlecheg - Fri, 30 Sep 2016 14:09:09 EST ID:ZD4TCLS2 No.15229 Ignore Report Quick Reply
I'll just leave this here.

Beatrice Subberbanks - Fri, 30 Sep 2016 16:49:46 EST ID:9fX9//hV No.15230 Ignore Report Quick Reply
I'll just leave this here.

William Wonnergold - Sat, 08 Oct 2016 04:08:38 EST ID:X69WEjIN No.15239 Ignore Report Quick Reply
For reference, this "largest storable number" would be a number with approximately 1,204,120,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00,000,000,000,000,000 digits in base-10.
Eugene Mudgenag - Sun, 16 Oct 2016 08:24:12 EST ID:b5LuzqFV No.15245 Ignore Report Quick Reply
What is that based on? The size of the observable universe?
Thomas Nickledale - Sun, 16 Oct 2016 22:21:09 EST ID:GRYB1TGG No.15246 Ignore Report Quick Reply
>The size of the observable universe?

What does that even mean? When our observations are constantly changing? The total number of atoms in the universe? What about the total number of quarks? What if we discover something even smaller and more numerous than that? Do you think we've already discovered the smallest thing? The largest storable number seems pretty meaningless, in that context.
Walter Grandgold - Sun, 16 Oct 2016 23:18:00 EST ID:v1Le0MKE No.15247 Ignore Report Quick Reply
Educate yourself please. You know how to search.
Thomas Nickledale - Mon, 17 Oct 2016 01:26:18 EST ID:GRYB1TGG No.15248 Ignore Report Quick Reply
That doesn't answer my question at all.
Esther Fazzlechire - Wed, 19 Oct 2016 14:27:29 EST ID:3FW0gDej No.15249 Ignore Report Quick Reply
The size of a representation space (e.g. number of bits in the universe) just gives us the number of different values that can be represented, not the greatest value that can be represented. Arbitrarily large values can be represented with single bit if the encoder and decoder share a common domain containing just that value.
Cyril Faddlehood - Sat, 22 Oct 2016 23:13:07 EST ID:FnqCMFm+ No.15251 Ignore Report Quick Reply
The observable universe is basically a round bubble, and it includes everything we are able to... observe. What that's saying is that it is the furthest distance that we can see light coming from, or that particles of light are able to interact with and be measured by some medium from our location on earth. Outside of that bubble, the universe we are able to see no longer interacts with or receives any information from any matter or particles that might lie outside.

If you can't grasp what observable light entails, then the concept is above you. It honestly shouldn't require explanation, but hopefully what I wrote helps. If it doesn't, sorry nigga, you just aren't gonna get it.
Esther Pebberworth - Wed, 21 Dec 2016 08:37:41 EST ID:XNyHHSTC No.15297 Ignore Report Quick Reply
A bunch of cajoles!
24 is the highest number and thats it!

Barnaby Brellyhick - Sat, 20 May 2017 21:51:19 EST ID:EJeHrwkJ No.15508 Ignore Report Quick Reply
Whatever you make it man.
Edward Smallbanks - Tue, 23 May 2017 02:05:16 EST ID:lub1zF0h No.15509 Ignore Report Quick Reply
Without doing something like "Base googleplex" the biggest numbers I have heard of people talking seriously about are the values of busy beaver function. The get very big.


But still even a countably infinite ordinal is bigger than these lames
Barnaby Wannersteck - Tue, 23 May 2017 09:34:33 EST ID:+WL4MNee No.15510 Ignore Report Quick Reply
There are lots of functions which grow faster than any computable function which people are interested in.

Charles Sennerstone - Sun, 28 May 2017 19:46:21 EST ID:lYjTKStM No.15514 Ignore Report Quick Reply
I think this is getting somewhere. The observable universe certainly is everything that we can currently have conceivably access to.

But, the amount of information the universe can store is much larger than you might expect.
It should be exactly equal to all possible arrangements of matter/energy inside the volume of the observable universe.
Of course that gets larger all the time because of cosmic inflation.

So you would have something like:
For each and every plank volume every possible subset of state of every possible subset of quantity of mass/energy.
Of course only a negligible fraction of those would be stable, but that's hardly the point.
The hard part is enumerating how many quantization states there are to arrive at an actual number.
Angus Grandfoot - Mon, 29 May 2017 04:50:28 EST ID:lub1zF0h No.15515 Ignore Report Quick Reply

Regardless of how much information could be stored in the observable universe by a method of your choice, the issue would be energy to store and access the information.

If there is information stored in a way that there is no physical way to access or decode it, is it really information for this purpose?
Nicholas Fonkinfot - Wed, 31 May 2017 17:07:34 EST ID:lYjTKStM No.15516 Ignore Report Quick Reply
Actually no. At least in the sense that TT has been posted in /math/

In a mathematical sense we are not interested how much of the universe has to be utilized to run the storage machine and how much is actual storage.
So I just assumed that the number OP is interested in is a theoretical upper bound of such mechanism in the sense that involved all matter/energy and space. Think of a omnipotent entity outside of the universe re-configuring it. Without actually adding or removing anything.

The number I described would be the number of ways such entity could possibly do that, which by the pigeonhole principle must be exactly the information storage capacity of the universe.
Jenny Hinkinridge - Thu, 01 Jun 2017 22:54:27 EST ID:sMHQkkFd No.15518 Ignore Report Quick Reply
In a mathematical sense we are not interested in the universe.
Graham Dartspear - Sun, 18 Jun 2017 10:13:26 EST ID:EJeHrwkJ No.15521 Ignore Report Quick Reply
Martin Surrywell - Thu, 29 Jun 2017 15:08:20 EST ID:h0vIir1X No.15532 Ignore Report Quick Reply
Wesley Feshham - Fri, 25 Aug 2017 23:59:07 EST ID:Kt7gF4g2 No.15551 Ignore Report Quick Reply
Infinity is the closest truthful answer you will get. It's incomprehensible. The lie you'd get is a guesstimation based off of a simulation which will undoubtedly have confounding variables, variables not considered, etc.
Molly Blimmerdock - Sat, 26 Aug 2017 19:59:57 EST ID:gFrVWF8h No.15553 Ignore Report Quick Reply

Given any infinite ordinal there is a larger one. Given any infinite value, you can construct a larger one.
Eliza Blackworth - Tue, 29 Aug 2017 19:44:00 EST ID:z6ik/LbC No.15555 Ignore Report Quick Reply
>It's incomprehensible.

For you maybe. Thousands of people have a solid understanding of infinity.
Matilda Clipperhood - Sat, 09 Sep 2017 10:23:22 EST ID:vnPM6s0z No.15558 Ignore Report Quick Reply
tree fiddy
Priscilla Fidgehed - Thu, 30 Nov 2017 22:42:13 EST ID:fjf6McJz No.15589 Ignore Report Quick Reply
Man, back when I was a Jehovahs Witness a kind hearted but pretty stupid priest there once said "A Googolplex is the biggest number of all." And if you tried to explain to him that it isn't he'd get mad.
Nell Bundleshaw - Wed, 06 Dec 2017 16:06:20 EST ID:F95jr/F4 No.15593 Ignore Report Quick Reply
There's no real boundary between "notation" and "formula". Arabic numbers might be conceived as a sort of formula which takes a vector of integers to a finite power series (a1, a2, a3, a4, ...) -> (...((a1 * 10 + a2)*10 + a3)*10 + ...))...). Likewise you can have formulas like Conway's chained arrows which express huge numbers, for which the chained arrows effectively take the place of notation because writing 3->3->3->3 in Arabic numerals is already far beyond impossible.
Cornelius Henningbanks - Tue, 12 Dec 2017 02:30:02 EST ID:BDm+BNlx No.15594 Ignore Report Quick Reply

I would think of it as a function rather than a formula. Interpreting the conway notation as a function, its domain is sequences of natural numbers and the codomain is natural numbers. It just happens to be a function that takes larger values, and of course there is always going to be a function that provides numbers larger than the ones you would obtain with the conway notation.

In fact, natural numbers and all other mathematical objects are functions in some sense. You could think of the number 5 as being a class function from the set theoretical universe V into 2, that takes the value 1 on 0,1,2,3,4 and is 0 everywhere else. The empty set would be the function that takes the value 0 everywhere.

This doesn't work depending on what theory you are trying to formalize math in. For instance in ZFC you can't talk about a function f from V into 2, or V at all for that matter. So, everything is a function and whenever we write something it is a description of the desired function. Even the text itself could be considered a function.

We can reason about an arbitrarily large numbers using symbols. I could say that n is the smallest number that can't be written out in arabic numerals using all of the resources of the universe, and then talk about 2^n. I couldn't do this in the theory of arithmetic, because there is no way to formalize the idea of the amount of data stored in the universe within the theory. If you moved to a more powerful theory, then another problem occurs.

We don't really know what the universe is, how big it is, or other things that we would need to know to get a real answer. So to answer OPs questions:

We don't know what the largest number we could write down is because we don't know enough about the universe, and it depends on the type of notation we use to write down the number. There is no most compact way to write large numbers. There are many ways that you can beat scientific notation. You can take it as extreme as you want.

The largest numbers we have ever talked about come about from sentences like "The smallest number than can't be expressed in 100 characters or less by a formula of set theory". You could change that to 1000, or a million, or however large you want. The point of that is to say that we can talk about fuckoff huge numbers without knowing specifically what its digits are, and know that it exists and is unique.
Samuel Pugglenire - Mon, 26 Feb 2018 18:49:49 EST ID:wktC+YFL No.15615 Ignore Report Quick Reply
Charles Mengerdack - Tue, 27 Feb 2018 18:26:26 EST ID:mqHT9rw/ No.15616 Ignore Report Quick Reply

that shit went over my head pretty quickly, lol
Nathaniel Fivingville - Mon, 05 Mar 2018 03:48:00 EST ID:Hv35haoR No.15617 Ignore Report Quick Reply
in the decimal system ten is the biggest individual number because its two characters
all numbers larger than ten are just combinations of components of the decimal system and not actual number in an of themselves. seven is the largest number by overall syllable count
Nigel Honeyson - Wed, 07 Mar 2018 19:53:03 EST ID:jv1Vx1Vn No.15619 Ignore Report Quick Reply
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This is absurd.
Henry Hunningstidging - Wed, 21 Mar 2018 03:37:51 EST ID:L0p96aSa No.15634 Ignore Report Quick Reply
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infinity lol
Charles Paffinghall - Thu, 22 Mar 2018 22:03:47 EST ID:5jiNtEAL No.15636 Ignore Report Quick Reply
Hugh Guffingfield - Wed, 09 May 2018 12:47:41 EST ID:NVr7Ludj No.15650 Ignore Report Quick Reply
If you wanted to be ethical, you wouldn't go about utilizing protons and neutrons needed to sustain life to save information for your 'Mirror Universal Computer." Of course you could take a torch to it all and set it all on fire. You'd need fine tweezers to configure those particles to suit your computation engine, and perhaps the holy grail of mathematics[: 'What configuration is needed to gain NP advantage...e.g.: how do I obtain energy out of a dying system;] EnEffZero)XQJZGueessTheLetterEtoanirshdlcwumfygpbvkxqjz
Hannah Dartham - Thu, 10 May 2018 13:56:37 EST ID:drSlH/C1 No.15651 Ignore Report Quick Reply
>>15636 aleph^infinity + 1 is larger
Doggo can Dance - Fri, 11 May 2018 00:01:14 EST ID:AQ7xCSUt No.15652 Ignore Report Quick Reply
wait... from zero to nine, the largest interger would be nime.
and if you go up to ten then the largest number would be nimety-nime.
Charles Paffinghall - Sun, 30 Sep 2018 20:11:06 EST ID:iKPdVfyo No.15691 Ignore Report Quick Reply
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the set aleph^infinty of uncountably uncountable number of numbers contains aleph^infinty+1, so try again friend.
Isabella Mirringchidging - Fri, 05 Oct 2018 04:28:50 EST ID:VP96Vn9X No.15694 Ignore Report Quick Reply
I always liked up arrow notation.
Isabella Mirringchidging - Fri, 05 Oct 2018 04:28:50 EST ID:VP96Vn9X No.15695 Ignore Report Quick Reply
I always liked up arrow notation.

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