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by WarDaft
Fri Feb 20, 2015 5:12 pm UTC
Forum: Mathematics
Topic: Permutation 'logarithm'
Replies: 4
Views: 2123

Re: Permutation 'logarithm'

Thanks! That was actually much simpler than I was expecting it to be.
by WarDaft
Fri Feb 20, 2015 2:02 pm UTC
Forum: Mathematics
Topic: Permutation 'logarithm'
Replies: 4
Views: 2123

Permutation 'logarithm'

I'm sure this can't be a new topic seeing how old group theory is, but my Google-fu has failed to turn up any relevant articles.

Suppose you have permutations p and k, and you know that k = pn for some n, how do you find n without manually applying p n times?
by WarDaft
Wed Feb 18, 2015 9:02 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Anyway, this is indeed the crossover I was waiting for to re-vamp things. < > are the repeater operator, such that <X> means the string X repeated n times ( ) denote an array, which is to be evaluated lazily, rather than immediately. [;] is an advanced delimiter. : and ; will not work the same, so I...
by WarDaft
Mon Feb 16, 2015 11:07 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Yes, that comes through. I'll be posting the revised notation later today or early tomorrow, once I have drummed up a good list of example values.
by WarDaft
Mon Feb 16, 2015 8:48 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

I see only boxes.
by WarDaft
Mon Feb 16, 2015 8:33 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

U sure about that? If x^1 = x and x^4 * x = x^5 and x=w^w where am i misapplying the math here? Exponentiation is not associative. (x^x)^5 is not the same as x^(x^5) (x^x)^5 is x^(x*5) Also, Vytron, what ordinal is 𝛝? It's not rendering for me... I just get a box. Typically after φ, one uses ordina...
by WarDaft
Mon Feb 16, 2015 4:49 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

That's how ordinals work. Like, with my system, literally all of the size right now is coming from the colons, literally nothing else is doing anything anymore, and could be discarded.

Which is exactly what I am doing. But all shadowy like.
by WarDaft
Mon Feb 16, 2015 7:53 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Uh, no, sorry, I'm afraid that's not right either. {ω^ω^4}*{ω} = {ω^(ω^4+1)} yes {ω^ω^4}*{ω2} = {ω^(ω^4+2)} no, it's {ω^ω^4}*{ω2} = {ω^(ω^4 + 1)}*2 {ω^ω^4}*{ω^2} = {ω^(ω^4+ω)} no, it's {ω^ω^4}*{ω^2} = {ω^(ω^4 + 2)} {ω^ω^4}*{ω^ω} = {ω^(ω^4+ω^2)} no, it's {ω^ω^4}*{ω^ω} = {ω^(ω^4+ω)} In general, ω a *ω...
by WarDaft
Thu Feb 12, 2015 4:15 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

I didn't actually want to go that far, was just trying to concisely define the base form. This helps because it has revealed an incongruity in what I thought you were doing.
by WarDaft
Wed Feb 11, 2015 7:18 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Hmm, I think I have discovered a very concise way of expressing your base rule: (0,X)-- = X (a,X)-- = (<a-->,a,X--) (a)-- = (<a-->) (X,()) = X Though I believe this is reversed left-right. With the first rule: 0,0,1,0 -> 0,1,0 -> 1,0 With the second rule, we have 1,0 -> <1-->,1,(0)-- = 0,0,0,0,0,1,(...
by WarDaft
Wed Feb 11, 2015 4:04 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Excellent! Let the rampant 1-upmanship continue unabated.

[2|0[ :[ : :0[]]:0[]]] for f{φ(1,φ(1,0,0),0)}(2)
by WarDaft
Tue Feb 10, 2015 11:28 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

It actually can be done, because there is an ordinal representation for what he wanted to do but was having trouble expressing with illusory space. This may or may not be exactly what he wanted, but on the face of it, there's nothing wrong. I haven't done a precise analysis to ensure there's no erro...
by WarDaft
Tue Feb 10, 2015 7:25 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Yes, we extend Veblen's φ function to multiple arguments. Thus, φ(1,0,a) = Γ a , φ(a+1,0,b) is the b'th fixed point of c -> φ(a,c,0) φ(a,b+1,c) is the c'th fixed point of d -> φ(a,b,d) And some other bookkeeping needed to deal with limit ordinals, but this is the general idea. So my latest entry is ...
by WarDaft
Mon Feb 09, 2015 6:26 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Alright, I'll accept that.

In return, I challenge thee with [2|0[1:0[]:0[]]], being the ωth fixed point of the gamma function.
by WarDaft
Mon Feb 09, 2015 2:29 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

That's not how ordinals work. It's a fixed point, the point where δ = Γδ. So Γδ is still just δ. If your notation works so that you can truly substitute ordinals like that, then that should be equivalent to 5[0-0,0-0].
by WarDaft
Sun Feb 08, 2015 7:29 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

If X is less than ζ_1, no. The supremum (least ordinal greater than all of the elements) of the sequence ζ_0 + 7, ε_(ζ_0+7), ε_ε_(ζ_0+7), ε_ε_ε_(ζ_0+7)... is also ζ_1. The reason for this is because for every ordinal δ less than ζ_1, there is an ordinal in that sequence that is greater than δ, yet e...
by WarDaft
Sun Feb 08, 2015 6:30 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Yes.
by WarDaft
Sun Feb 08, 2015 4:49 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Ah yes, making sub sections act like substitutable ordinals is an excellent way forward. On that note, I feel I must leap to [2|0[ :0[]:0[]]]. This operates at the first fixed point of a -> Γ a . I'm developing a made general extension from colons, part of that is making a repetition operator, < >. ...
by WarDaft
Fri Feb 06, 2015 3:52 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

That was quick, clearly I am not being sufficiently evil challenging.

[2|0[0[][][0[]]: :0[]] for f{Γζ_1}(2)

If you folks want the progressions for these, by the way, the progression for [2|0[X: :0[]]] = f{Γδ}(2) looks like the progression for [2|X] = f{δ}(2)
by WarDaft
Fri Feb 06, 2015 2:02 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Well then, I simply must see how you respond to:

[2|0[0[][0[]]: :0[]], for f{Γ_(ε_1)}(2)
by WarDaft
Thu Feb 05, 2015 4:17 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

It seems like gamma subindexes aren't too hard for your notations, so I'm skipping up to [2|0[0[0[]]: :0[]] for f{Γω^ω}(2)

EDIT: I keep accidentally typing 1 instead of 0[], which really matters in some places.
by WarDaft
Thu Feb 05, 2015 6:09 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Aha, a leap ahead!

[2|0[2: :0[]]] for f_{Γω2}(2)
by WarDaft
Tue Feb 03, 2015 3:30 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Well, then it appears I have no choice but to go to [2|0[0[]0[]: :0[]] for f_{Γ2}(2)
by WarDaft
Sun Feb 01, 2015 9:19 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

The think limit of the single-colon-per-bracket notation is actually Γ 0 . Anyway, the obvious next step is a second colon [n|0[W:X:Y]Z] for non-empty W,X reduces to [n+1|n[W:dec n X:Y][dec n W:X:Y]Z] [n|0[W:X:Y]Z] for empty W,X, reduces to [n+1|n[||f(n,0:[)||0:0:dec n Y||f(n,]:dec n Y)||]Z] [n|0[W:...
by WarDaft
Tue Jan 27, 2015 5:45 am UTC
Forum: Forum Games
Topic: My number is bigger! (competitive version) 115679 points
Replies: 52
Views: 6727

Re: My number is bigger! (Slow version)

1/(xkcd-2)
by WarDaft
Mon Jan 26, 2015 5:11 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

GoogologyMaster wrote:The limit of φ(α, Γ0+1) as α→Γ0 is φ(Γ0, 1), I think. I know that Γ0 = φ(Γ0, 0).

Hmm.

The fundamental sequence for φ(b,a+1) is φ(b[n],φ(b,a)+1). So yes, you're right, it's φ(Γ0, 1). Which puts you are even further from Γ1.
by WarDaft
Mon Jan 26, 2015 5:54 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

>snip< [1 [1 [1 [1 [1 [1 [1 [1 [1 [2 ¬ 2] 2] 2 ¬ 2] 2] 2 ¬ 2] 2] 2 ¬ 2] 2] 2 ¬ 2] 2 [1 \ 2 ¬ 2] 2] = φ(φ(φ(φ(φ(ω, 0), 0), 0), 0), Γ 0 +1) Are we at Γ 1 yet? No, we're not, and you aren't going to get there very fast that way. The limit of your sequence looks like φ(Γ 0 ,Γ 0 +1) which is a weird lim...
by WarDaft
Sat Jan 24, 2015 7:34 am UTC
Forum: Forum Games
Topic: My number is bigger! (competitive version) 115679 points
Replies: 52
Views: 6727

Re: My number is bigger! (Slow version)

Tree(4)

Yep.
Because everything is made up and the points don't matter!
by WarDaft
Sat Jan 24, 2015 6:03 am UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Ah, I have been challenged.

If I recall my notation correctly (it's been like, 3 months, at least) I believe I have to go with [2|2[2[2]:2]] (or it might be [2|2[2:2[2]2]], possibly) This should be f_{phi_omega^omega+omega}(n) or something like that.
by WarDaft
Thu Jan 22, 2015 3:43 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Unfortunately, the y axis of the graph will have to be a function for generating large numbers, so it will effectively be an entry in the thread and then people will try to beat it.
by WarDaft
Sun Jan 18, 2015 10:59 pm UTC
Forum: Forum Games
Topic: Your number is, in fact, not bigger!
Replies: 1240
Views: 150343

Re: Your number is, in fact, not bigger!

Vytron wrote:Ohh, good job by GoogologyMaster to become the thread champion with a post that didn't appear until much later, so it sneakily took over the thread

How so? His number is less than the [2|2[1:1]] I posted many pages back.
by WarDaft
Sun Jan 18, 2015 7:18 pm UTC
Forum: Forum Games
Topic: largest programmed number
Replies: 10
Views: 2146

Re: largest programmed number

But given the rules that for numbers of a similar size, the one produced by less code is preferred, you'd be better off with:

Code: Select all

a = 10 ** 10 ** 10 ** 10 ** 1.1 * 14
b = 9
for x in range(a):
     b = b ** b


It is only 2% percent smaller (irellevant at this scale) but uses 8 fewer characters.
by WarDaft
Sat Jan 17, 2015 10:50 pm UTC
Forum: Forum Games
Topic: largest programmed number
Replies: 10
Views: 2146

Re: largest programmed number

Code: Select all

 a = 9 ** 9 ** 9 ** 9 ** 1.13
b = 9
for x in range(0,a)
     b = b ** b


I'm pretty sure, if I understand the given rules, that this is the biggest number we can reach for close to the least code.
by WarDaft
Sat Jan 17, 2015 3:26 pm UTC
Forum: Forum Games
Topic: My number is bigger!
Replies: 1590
Views: 412288

Re: My number is bigger!

And, doing all the job again from zeta_0 gets you to zeta_0*2, so you can specify a function that recurses on that, up to zeta_0*omega, and begin the process again at this level until reaching zeta_0*epsilon_0, and so on. Once you increase the recursions levels up to zeta_0*zeta_0 you reach zeta_0^...
by WarDaft
Sat Jan 17, 2015 1:25 am UTC
Forum: Forum Games
Topic: Chaotic Nomic
Replies: 28
Views: 4271

Re: Chaotic Nomic

1. In your post, you may delete one rule, and then you may create one new rule. Your post is not affected by the rule you deleted, as the deletion is considered to happen before the posting itself. It is not possible to alter, delete, or avoid this rule in any way, shape, or form. 6. Any post in th...
by WarDaft
Sat Jan 17, 2015 12:32 am UTC
Forum: Forum Games
Topic: Chaotic Nomic
Replies: 28
Views: 4271

Re: Chaotic Nomic

I delete rule 27. I remove the 100 points Reecer6 gave themselves. I create rule 28: Within the context of the game, any and all actions players take have no meaning, consequences, or results, unless specifically given meaning, consequences, or results, by one or more rules. 1. In your post, you may...
by WarDaft
Fri Jan 16, 2015 11:26 pm UTC
Forum: Forum Games
Topic: Chaotic Nomic
Replies: 28
Views: 4271

Re: Chaotic Nomic

The reinstatement of deleted rules as a delete action rule and adding additional rules for points rule contradict the first rule, they have to go. New rule: 26. Players may make up to 3 suggestions per post that last from that point until the end of the current page, and they then reset. Every post ...
by WarDaft
Sun Jan 04, 2015 6:19 pm UTC
Forum: Forum Games
Topic: Chaotic Nomic
Replies: 28
Views: 4271

Chaotic Nomic

1. In your post, you may delete one rule, and then you may create one new rule. Your post is not affected by the rule you deleted, as the deletion is considered to happen before the posting itself. It is not possible to alter, delete, or avoid this rule in any way, shape, or form.
by WarDaft
Fri Dec 26, 2014 5:07 am UTC
Forum: Computer Science
Topic: how to communicate under heavy targeted surveillance
Replies: 13
Views: 8343

Re: how to communicate under heavy targeted surveillance

I don't think there is. Assuming that, for some reason, they haven't simply thrown you in a small room, they are certainly watching everything you do. If you can visually see what you are doing, they will almost certainly also see what you are doing. So you need an encryption/decrytion you can perfo...

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