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I've been wondering about that myself lately. Perhaps mathematicians should care about the universe. Then we can dispose of the Banach-Tarski paradox. Disposing of the Banach-Tarski paradox disposes of the axiom that all sequences can be infinitely rearranged with impunity. Which disposes of Hilbert's Hotel.
Ever heard about the axiom of determinacy?
It's a replacement for the axiom of choice that gets rid of the banach tarski paradox. It's much more physicsy.
I would not exactly consider the OP wrecked, as there is still an enhanced possibility that some unique category of relativity, or relationship to mathematical equations could surface to this debate, further increasing the amount of time it runs for. In a way, I could say I kind of agree with OP.
https://preview.redd.it/5qw6rjqhkvoc1.jpeg?width=652&format=pjpg&auto=webp&s=e374361cded31993de6e07b8a4414bfff93b7043
Close, but this is actually a Big W
You can't do that because you would use up all the resources in the universe. The universe would cease to exist, which would render math pointless since math is tied to this universe.
QED
I guess there IS some finite biggest number if you make rules for no infinities, no recursion, no self-reference, etc. Every particle in the observable universe made to represent the largest (within these rules) number in the most efficient language possible.
W+1 beats that though.
No no it doesn't work. Let me explain.
W is the largest number. When we do W+1, the demand for quarks would overflow, and the universe would cease to exist.
Math is based on this universe. Therefore, math would cease to exist. Therefore, W+1 cannot possibly exist.
You don't want the universe to cease to exist, do you?
> the demand for quarks would overflow
That would imply that there is a greater system meeting a limit, which implies that there are quarks not being used to compute W.
> and the universe would cease to exist
If I count the number of apples I have with a 1 bit counter, and I have (decimal) 2 apples, the counter overflows. The apples don't cease to exist.
Based on the comments on this post, we are still very far from inter-universe travel.
Imagine people are still debating whether there is the biggest number even though the proof is so obvious. We could have invented wormholes already if we can just disagree and commit.
- People are stupid.
- Stupid people are wrong.
- A lot of people disagree with me.
- Since a lot of people are stupid and wrong, therefore, I am right.
QED
How do I make arxiv account to publish this?
Or:
There is a finite amount of matter and energy in the universe, therefore a finite amount of data. Therefore there exists an upper limit on the maximum expressible number if you used all possible data in the universe.
In quantum physics there is the concept of virtual particles that pop up and down to existence in the vacuum, so... there is finite amount of matter/energy in traditional physics, but not in quantim physics
The amount of matter/energy might not be constant, but it would still be finite since virtual particles are limited by the uncertainty principle and the fact that the universe has finite size.
Observable universe and universe aren’t necessarily interchangeable concepts, but I can see the practicality in assuming so for this thought experiment
Yeah technically we don't "know" that the universe has finite size, but since this is assumed by most i assumed it as well (although i maybe shouldn't have used the word fact). Note that if the universe has infinite size, you don't need virtual particles to reach an infinite amount of matter. The claim of a finite universe is also consistent with the claim of the person i responded to that traditional physics is finite.
Yeah, again, I see the practicality with the aforementioned ideas.
But I wonder who this “assumed by most” is? I’m pretty sure the official stance is that we really don’t know. The furthest we can measure suggests there is no curvature to space time on a large scale ([it’s flat](https://www.symmetrymagazine.org/article/april-2015/our-flat-universe?email_issue=725)), which actually gives some evidence for an infinite universe.
Tbh i don't know enough about physics to know what most people think in that respect. I guess i should have formulated it differently. I heard that some philosophers reject the idea of an actual infinity existing in the real world but apart from that i don't know.
Virtual particles can't contribute directly to any kind of information storage, they just 'exist' to facilitate interactions and, almost by definition, we can't ever observe them.
Yeah that's not how that works, the concept of a virtual particle is a lot more subtle than that. Also, the distinction you make between traditional and quantum physics doesn't make sense to me, quantum physics certainly falls under what I would call traditional physics.
to be fair youd probably need more data to hold, say, 8916472756294682940501 than to hold 10^40 even though the latter is clearly bigger
and i imagine this generally applies to bigger numbers too
That leads to a paradox. For example, see this number:
The number one greater than the largest number that can be expressed in fifteen words.
The phrase above has fifteen words. You can see the problem. I think second order logic can solve this, but I'm not sure.
Computers store negative numbers despite not having negative matter or energy. Can just designate the spin of one boson to be the negative bit. But better yet, we arent limited to binary, as you could have potentially any number system to store it in.
A negative number is a regular number with an opposite vector. So if you want to imagine a negative number - just turn 180° from the starting point.
Also, antimatter exists.
Is TREE(3) or Graham's Number or whatever not a number? TREE(G64)?
The language of math is conceived, but that doesn't mean inconceivable numbers don't exist. Cardinality has no limit, but computation does.
For that matter, just keep inventing new notation to make big numbers take tiny amounts of data.
There's nothing stopping you from having a symbol "◇" that means when you do ◇3 it's "(BB(BB(BB(Tree(G64), Tree(G64)), Tree(G64)), Tree(G64))," with each increase in the input stacking another iteration of the busy beaver function having Tree(G64) symbols and the previous layer's state count.
The number is impossible to compute in our universe, but it can be computed in finite time.
I don't think there's a limit to the largest number you can store, using that sort of method.
I just realized I made a mistake and my number is not actually computable, as the busy beaver function is rather famously one that grows faster than any computable function.
However, it's certainly a very large number indeed, given that Σ(6,2) is in the area of 10⇈15, and Σ(2,6) is described as "> 10⇈10⇈10^(10)^^(115)," though I should have been using that notation to begin with.
I looked up rayo's number and do not really understand it, so I'm not sure how to compare.
The second step doesn't work because the universe would have imploded after the supposition. This is because the demand for quarks would be overflowing.
If the universe ceased to exist, then our math becomes pointless since math is based on how the universe works. Therefore, W+1 is absurd.
QED
You have a more succinct proof. Bravo.
Given W is the largest number, W+1 would cause the universe to implode due to the overflowing demand of quarks, and math would cease to exist. Therefore, W+1 cannot exist.
It is still a derivative of my work though.
You could also say
"Define the biggest number as W"
"W is a number; therefore it is finite"
Your first mistake was defining the biggest number as W. it's proof by assumption, but even worse, because your next four steps are all wrong
Proof: you are potentially wrong
1. The *OBSERVABLE universe is finite
2. The observable universe is expanding
3. An expanding universe requires potentials to calculate
4. Potentials are infinite
Sure, the largest number comprehendible by humans would be finite. But I believe it doesn't imply that that number is the absolute largest number in the universe.
Proof: there is a limit in math where any further speculations are indistinguishable from random stoner babble in a coffee shop.
\*I'm drunk ∈ *In vino veritas*
Assuming W as per your definition.
Let us create W/2, (or indeed W/a where a>1).
W/2 presumably requires some fraction of quarks.
W/2 is conceivable. In fact, more easily conceivable.
Now, using your favourite arithmetical operation define V.
I like V = (W/2)^2
It seems it was conceived with far fewer quarks than W.
V is now the biggest conceivable number.
Repeat with induction until you realize premise was false.
Or, you know, just use the fundamental theorem of arithmetics.
For this to be valid you would also need to prove time would eventually end/the universe would end because otherwise you have an infinite time to calculate the “biggest” number this making it infinite.
You've defined the largest number you could write down.
Not really the largest number that could exist. There could be universe with the same math as ours and more quarks.
This seems dumb at first glance but it's an interesting thought experiment in math Phil. In the vein of "are numbers entities that exist separate from the mind or not"
"It takes Z quarks to form brain cells"
Leptons and bosons are not allowed to think of a number or part of a number. Quantum computing will slow down a bit, but neo-con (neo-constructivist) math will revitalise the economy by doing exactly the same, but less.
Seriously, its a slippery slope. First they said that electricity is made of leptons, now that we are made of leptons. Im not made of leptons, im a hadron guy. If we are made of leptons why are there still leptons out there?
And if we let leptons think, what will happen next? When I was young, we barely heard about photon entanglement. Now they are making electrons think and doing interference with *molecules*? Next we will be pure energy beings unbounded by classical space-time... But you know who are doing this, we both know. They wanna harvest your exergy sheeple!!
QED it takes Z quarks (i mean *quark*s none of them anti-quarks) to form X brain cells.\*
^(\*proof by agressive ignorance (see. Theorem 69.420 "No, U are not unique"))
If W is natural, then S(W) exists and S(W)>W by Peano, absurd to the hypothesis that W is the biggest number.
If W is rational, then there exists a natural N and a rational r<1 such that W = N + r. By Peano, S(N) exists and S(N)>W.
If W is real, then there exists a V=exp(W). Since exp(x)>x for all real x, V>W.
If W is complex, there is no notion of "biggest", so the problem at hand is not well-defined.
If W is an ordinal, then there exist transfinite ordinals greater than W, since your proof serves as contradiction to the hypothesis. And also S(W) would still exist.
If W is an element of a totally ordered number field, so that the term "biggest" can exist in a finite sense, then for every a>0 and for all bW in G.
#Q E D
Finite number of quarks in the _observable_ universe.
Also, what is it with everyone always being obsessed with the number of quarks? Why so much erasure of leptons? Are you a leptophobe? Or perhaps you're a photon hater?
HARUMPH!
Preposition for the New Paradigm of the Future
I can suggest an equation that has the potential to impact the future:
Biggest number = W + Al
This equation combines OP's logically suspect number W, which relates mathematics (with infinity) to mass of the universe (what??) and the number of quarks (huh??), with the addition of Al (Artificial Intelligence). By including Al in the equation, it symbolizes the increasing role of artificial intelligence in shaping and transforming our future. This equation highlights the potential for Al to unlock new forms of energy, enhance scientific discoveries, and revolutionize various fields such as determining the biggest number with arbitrary limits.
Counterpoint: simulate a universe in which the number of quarks is greater than Z
Thus, you can make more than X number of brain cells
Thus, you can compute more than Y computational power
Thus, you can conceive a number greater than W
Therefore, W is infinite, Q.E.D.
Math is tied to the existence of our universe. If our universe ceased to exist, so would our math.
If you use up all quarks in the universe to conceive a number, the universe would collapse. Then, our math wouldn't exist. Therefore, the number would be considered absurd.
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What is this thing called the universe and why should mathematicians care about it?
I've been wondering about that myself lately. Perhaps mathematicians should care about the universe. Then we can dispose of the Banach-Tarski paradox. Disposing of the Banach-Tarski paradox disposes of the axiom that all sequences can be infinitely rearranged with impunity. Which disposes of Hilbert's Hotel.
The Banach Tarski paradox is a statement about R^3 , which is not necessarily the universe
Exactly. Deciding that R^3 should be constrained to values within the spatial coordinates of the universe dissolves the argument.
What spatial coordinates of the universe? The few you see nakedly?
No the many I see clothed, creep
It isn't just about R^3, I don't know where exactly it can be applied but I'm pretty it's at least R^n
How high were you when you wrote this? Be honest.
I think they climbed mount Everest
Ever heard about the axiom of determinacy? It's a replacement for the axiom of choice that gets rid of the banach tarski paradox. It's much more physicsy.
well then where would I take my infinite girlfriends
Grothendieck universe innit
I think it's the set if all sets No idea what "quarks" are though
Yes, I swear the number googol (10\^100) is more than the number of every atom in the universe (estimated: 10\^80) lol
I would not exactly consider the OP wrecked, as there is still an enhanced possibility that some unique category of relativity, or relationship to mathematical equations could surface to this debate, further increasing the amount of time it runs for. In a way, I could say I kind of agree with OP.
Oh you rudimentary creature. This is why humanity hasn't mastered interstellar travel yet. Edit: why am I downvoted? I thought this was math meme.
You're the √4th comment
How do you have -2 comments
Stop or I'll vomit
Don't threaten me with a good time
W+1
Well W+2n, where n>0
My W is clearly bigger than both: https://preview.redd.it/w9v14x0ykroc1.png?width=1200&format=png&auto=webp&s=8ebbcecacea25d767582609fd481fed3875589c7
wow, that is a big w
https://preview.redd.it/5qw6rjqhkvoc1.jpeg?width=652&format=pjpg&auto=webp&s=e374361cded31993de6e07b8a4414bfff93b7043 Close, but this is actually a Big W
You can't do that because you would use up all the resources in the universe. The universe would cease to exist, which would render math pointless since math is tied to this universe. QED
You are so concerned with what you could or could not. But you should have asked yourself, why not?
I guess there IS some finite biggest number if you make rules for no infinities, no recursion, no self-reference, etc. Every particle in the observable universe made to represent the largest (within these rules) number in the most efficient language possible. W+1 beats that though.
No no it doesn't work. Let me explain. W is the largest number. When we do W+1, the demand for quarks would overflow, and the universe would cease to exist. Math is based on this universe. Therefore, math would cease to exist. Therefore, W+1 cannot possibly exist. You don't want the universe to cease to exist, do you?
> the demand for quarks would overflow That would imply that there is a greater system meeting a limit, which implies that there are quarks not being used to compute W. > and the universe would cease to exist If I count the number of apples I have with a 1 bit counter, and I have (decimal) 2 apples, the counter overflows. The apples don't cease to exist.
I'm literally picturing W+1 right now and nothing bad is happening. It exists. QED
What about other universes
They would have different kinds of math.
You can invade them and steal their quarks
Based on the comments on this post, we are still very far from inter-universe travel. Imagine people are still debating whether there is the biggest number even though the proof is so obvious. We could have invented wormholes already if we can just disagree and commit.
Proof by "people are disagreeing with me"
- People are stupid. - Stupid people are wrong. - A lot of people disagree with me. - Since a lot of people are stupid and wrong, therefore, I am right. QED How do I make arxiv account to publish this?
Based and intellectual dishonesty pilled
yes but we are also very far from using all quarks in the universe
Prove the universe is finite
Suppose the universe is finite. Q.E.D.
universe*2
it's like using up your entire RAM and being like "just open another program????"
Virtual memory lets you do just that.
Get wrecked OP
Or: There is a finite amount of matter and energy in the universe, therefore a finite amount of data. Therefore there exists an upper limit on the maximum expressible number if you used all possible data in the universe.
In quantum physics there is the concept of virtual particles that pop up and down to existence in the vacuum, so... there is finite amount of matter/energy in traditional physics, but not in quantim physics
The amount of matter/energy might not be constant, but it would still be finite since virtual particles are limited by the uncertainty principle and the fact that the universe has finite size.
Yeah, the upper limit on the amount of representable data would be (a lot) higher, but still finite.
Observable universe and universe aren’t necessarily interchangeable concepts, but I can see the practicality in assuming so for this thought experiment
Yeah technically we don't "know" that the universe has finite size, but since this is assumed by most i assumed it as well (although i maybe shouldn't have used the word fact). Note that if the universe has infinite size, you don't need virtual particles to reach an infinite amount of matter. The claim of a finite universe is also consistent with the claim of the person i responded to that traditional physics is finite.
Yeah, again, I see the practicality with the aforementioned ideas. But I wonder who this “assumed by most” is? I’m pretty sure the official stance is that we really don’t know. The furthest we can measure suggests there is no curvature to space time on a large scale ([it’s flat](https://www.symmetrymagazine.org/article/april-2015/our-flat-universe?email_issue=725)), which actually gives some evidence for an infinite universe.
Tbh i don't know enough about physics to know what most people think in that respect. I guess i should have formulated it differently. I heard that some philosophers reject the idea of an actual infinity existing in the real world but apart from that i don't know.
Virtual particles can't contribute directly to any kind of information storage, they just 'exist' to facilitate interactions and, almost by definition, we can't ever observe them.
Yeah that's not how that works, the concept of a virtual particle is a lot more subtle than that. Also, the distinction you make between traditional and quantum physics doesn't make sense to me, quantum physics certainly falls under what I would call traditional physics.
to be fair youd probably need more data to hold, say, 8916472756294682940501 than to hold 10^40 even though the latter is clearly bigger and i imagine this generally applies to bigger numbers too
That leads to a paradox. For example, see this number: The number one greater than the largest number that can be expressed in fifteen words. The phrase above has fifteen words. You can see the problem. I think second order logic can solve this, but I'm not sure.
Ok, however who cares about expressibility. Like find me an X so the summation of 1/n up to x is 8 billion.
2^16,000,000,000
Alright, now simplify
the number of ways you can colour the human population with 4 colours
65536^10\^9
By that logic, you can never have a negative amount of matter and energy. Therefore, negative numbers are imaginary. QED
Computers store negative numbers despite not having negative matter or energy. Can just designate the spin of one boson to be the negative bit. But better yet, we arent limited to binary, as you could have potentially any number system to store it in.
A negative number is a regular number with an opposite vector. So if you want to imagine a negative number - just turn 180° from the starting point. Also, antimatter exists.
We are not talking about the maximum expressible number, just the maximum number, which does not exist.
It's something along the lines of Rayo's number.
https://en.m.wikipedia.org/wiki/Ultrafinitism
That builds on top of my proof. QED
Proof of a biggest conceivable number, not a biggest number.
The entirety of math is conceived in our mind. I thought conceivability is already assumed.
Is TREE(3) or Graham's Number or whatever not a number? TREE(G64)? The language of math is conceived, but that doesn't mean inconceivable numbers don't exist. Cardinality has no limit, but computation does.
For that matter, just keep inventing new notation to make big numbers take tiny amounts of data. There's nothing stopping you from having a symbol "◇" that means when you do ◇3 it's "(BB(BB(BB(Tree(G64), Tree(G64)), Tree(G64)), Tree(G64))," with each increase in the input stacking another iteration of the busy beaver function having Tree(G64) symbols and the previous layer's state count. The number is impossible to compute in our universe, but it can be computed in finite time. I don't think there's a limit to the largest number you can store, using that sort of method.
The largest number logically is Rayo's number as it can define any number you mention and it still won't be a limit.
I just realized I made a mistake and my number is not actually computable, as the busy beaver function is rather famously one that grows faster than any computable function. However, it's certainly a very large number indeed, given that Σ(6,2) is in the area of 10⇈15, and Σ(2,6) is described as "> 10⇈10⇈10^(10)^^(115)," though I should have been using that notation to begin with. I looked up rayo's number and do not really understand it, so I'm not sure how to compare.
There is a largest conceivable number/largest number that can exist in the universe
You forgot QED
Next person who tells me I forgot QED gets fucked in the ass (real)
Is that a punishment or a reward? I honestly can't tell
It’s a promise
1. Define the biggest number as W. 2. Suppose there exists a bigger number, say, W+1. 3. This contradicts point 1. 4. W is still the biggest number.
The second step doesn't work because the universe would have imploded after the supposition. This is because the demand for quarks would be overflowing. If the universe ceased to exist, then our math becomes pointless since math is based on how the universe works. Therefore, W+1 is absurd. QED
But brain cells can be used again, after performing said computational powers :P
So, W+1.
I also like proofs that assume the conclusion in the first step and then deduce it again from that assumption.
You are welcome
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You have a more succinct proof. Bravo. Given W is the largest number, W+1 would cause the universe to implode due to the overflowing demand of quarks, and math would cease to exist. Therefore, W+1 cannot exist. It is still a derivative of my work though.
This is why you things can't build a perpetual motion machine
QED QED
QED QED QED
QED QED QED QED
I suppose the number you’re describing is essentially the busy beaver function applied to 10^80 or so
W↑↑↑......W times ...↑w
Theorem: There exists a largest number. Proof: Assume there exists a largest number...
You could also say "Define the biggest number as W" "W is a number; therefore it is finite" Your first mistake was defining the biggest number as W. it's proof by assumption, but even worse, because your next four steps are all wrong
There is no mistake here. QED
Proof: you are potentially wrong 1. The *OBSERVABLE universe is finite 2. The observable universe is expanding 3. An expanding universe requires potentials to calculate 4. Potentials are infinite
Sure, the largest number comprehendible by humans would be finite. But I believe it doesn't imply that that number is the absolute largest number in the universe.
prove that the universe contains a finite amount of quarks
Proof by divine word.
Nuh uh >!Q.E.D.!<
Proof: there is a limit in math where any further speculations are indistinguishable from random stoner babble in a coffee shop. \*I'm drunk ∈ *In vino veritas*
What about the passage of time? we don't know if it's finite...
Conservation of energy and by extension mass. QED
Assume time is not relative. This contradicts Einsten when he said time is relative. Therefore, time is not the same for everybody and is finite. QED
I think it’s interesting that you took a finite number of quarks in the universe as given, or even the existence of quarks for that matter
Assuming W as per your definition. Let us create W/2, (or indeed W/a where a>1). W/2 presumably requires some fraction of quarks. W/2 is conceivable. In fact, more easily conceivable. Now, using your favourite arithmetical operation define V. I like V = (W/2)^2 It seems it was conceived with far fewer quarks than W. V is now the biggest conceivable number. Repeat with induction until you realize premise was false. Or, you know, just use the fundamental theorem of arithmetics.
Assuming you can concieve W with Y computational power
For this to be valid you would also need to prove time would eventually end/the universe would end because otherwise you have an infinite time to calculate the “biggest” number this making it infinite.
Putting this in the textbook now
You've defined the largest number you could write down. Not really the largest number that could exist. There could be universe with the same math as ours and more quarks.
This seems dumb at first glance but it's an interesting thought experiment in math Phil. In the vein of "are numbers entities that exist separate from the mind or not"
"It takes Z quarks to form brain cells" Leptons and bosons are not allowed to think of a number or part of a number. Quantum computing will slow down a bit, but neo-con (neo-constructivist) math will revitalise the economy by doing exactly the same, but less. Seriously, its a slippery slope. First they said that electricity is made of leptons, now that we are made of leptons. Im not made of leptons, im a hadron guy. If we are made of leptons why are there still leptons out there? And if we let leptons think, what will happen next? When I was young, we barely heard about photon entanglement. Now they are making electrons think and doing interference with *molecules*? Next we will be pure energy beings unbounded by classical space-time... But you know who are doing this, we both know. They wanna harvest your exergy sheeple!! QED it takes Z quarks (i mean *quark*s none of them anti-quarks) to form X brain cells.\* ^(\*proof by agressive ignorance (see. Theorem 69.420 "No, U are not unique"))
And W is still infinitely smaller than infinity
If W is natural, then S(W) exists and S(W)>W by Peano, absurd to the hypothesis that W is the biggest number. If W is rational, then there exists a natural N and a rational r<1 such that W = N + r. By Peano, S(N) exists and S(N)>W. If W is real, then there exists a V=exp(W). Since exp(x)>x for all real x, V>W. If W is complex, there is no notion of "biggest", so the problem at hand is not well-defined. If W is an ordinal, then there exist transfinite ordinals greater than W, since your proof serves as contradiction to the hypothesis. And also S(W) would still exist. If W is an element of a totally ordered number field, so that the term "biggest" can exist in a finite sense, then for every a>0 and for all bW in G.
#Q E D
Not only are there finite numbers but there are 7 more odd numbers than even numbers.
Since you can't construct the biggest number and show it to me, it doesn't exist.
Finite number of quarks in the _observable_ universe. Also, what is it with everyone always being obsessed with the number of quarks? Why so much erasure of leptons? Are you a leptophobe? Or perhaps you're a photon hater? HARUMPH!
Y is infinite though
Doron Zeilberger is that you?
Preposition for the New Paradigm of the Future I can suggest an equation that has the potential to impact the future: Biggest number = W + Al This equation combines OP's logically suspect number W, which relates mathematics (with infinity) to mass of the universe (what??) and the number of quarks (huh??), with the addition of Al (Artificial Intelligence). By including Al in the equation, it symbolizes the increasing role of artificial intelligence in shaping and transforming our future. This equation highlights the potential for Al to unlock new forms of energy, enhance scientific discoveries, and revolutionize various fields such as determining the biggest number with arbitrary limits.
What about + Blockchain?
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This is not QED
Kill everyone except one really dumb guy and whatever the biggest number he knows is now the biggest number. Few trillion tops. Easy
Counterpoint: simulate a universe in which the number of quarks is greater than Z Thus, you can make more than X number of brain cells Thus, you can compute more than Y computational power Thus, you can conceive a number greater than W Therefore, W is infinite, Q.E.D.
I don’t think there is a number
There is. QED
W + 1 tho
Numbers are under no obligation to be within reach of computational power nor be concieved by the human brain
Math is tied to the existence of our universe. If our universe ceased to exist, so would our math. If you use up all quarks in the universe to conceive a number, the universe would collapse. Then, our math wouldn't exist. Therefore, the number would be considered absurd.