Recursion Tattoo Ideas

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Malconstant
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Recursion Tattoo Ideas

Postby Malconstant » Wed Aug 24, 2011 2:10 am UTC

(Hopefully this is an appropriate place for this thread, let me know if not, I'm a bit new to these forums. But I figure it's a safe bet that Mathematicians on an xkcd forum wouldn't mind a recursion thread. And also I figure if ever there was an internet forum that Douglas Hofstadter checks out, it's probably xkcd)

I'd like to get a tattoo involving recursion and I'm trying to think of clever ways of doing this. Preferably using the closed geometry of an arm (or fingers/torso/whatever if need be) to loop in on itself. So far I've come up with the following:

- A time vs. recursion graph on the arm that's tilted 45 degrees clockwise so that the actual line for the graph is just a straight band around the arm, thus making a graph which embeds itself inside itself indefinitely as the recursion axis increases.

- A time vs. r (standing for either recursion or space for a Minkowski diagram) that's not tilted on the arm with a 45 degree line (speed of light for Minkowski diagram). In order to make the line wrap in on itself, I'd make it a Fourier series expansion to some finite order so you can see some good sine wave components in there, and then it's defined to be periodic at a period of the arm circumference, naturally.

- For a text-based tattoo, I've got (sic): The following is a fine example of the liar's paradox, "

- And finally, it's harder to describe, but a back-and-forth sequence of -i d/dx((1/i) d/dx(-i d/dx((1/i) d/dx (-i d/dx( back and forth making an arm band. This can come to represent two mutually recursive sets of numbers which define Cosine and - i Sine respectively, spelling out Euler's identity (this last one I used to define two mutually-recursive rings in group theory to propose with, the wife having Euler's identity as a tramp stamp).

So yeah, any ideas for other clever recursion-based tattoos?

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Re: Recursion Tattoo Ideas

Postby doogly » Wed Aug 24, 2011 5:52 am UTC

There's also a thread over here to poke at, if'n ya like pokin:
viewtopic.php?f=2&t=9770

But yeah, your sine cosine thing seems good, apart from my having no idea how that is supposed to work.
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Re: Recursion Tattoo Ideas

Postby LaserGuy » Wed Aug 24, 2011 2:34 pm UTC

Wouldn't the obvious recursion tattoo be to have one that shows a picture of the place on your body that includes that tattoo?

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Re: Recursion Tattoo Ideas

Postby Malconstant » Wed Aug 24, 2011 3:38 pm UTC

Damn, that tattoo thread is massive, but they didn't seem to get into recursion so I'll re-post over there. If the good people want to take this down that'd be alright, I don't know how these things work here (does "merging" copy future thread posts, in which case this one can stand alone and also contribute to the greater thread?).

LaserGuy wrote:Wouldn't the obvious recursion tattoo be to have one that shows a picture of the place on your body that includes that tattoo?


Yeah, that's definitely an option. Though it ends up being more "implied" recursion than actual (for infinite recursion at any rate, go hard or go home). The best of this idea that I've heard was a tattoo on my chest of me ripping off my shirt, embedded a couple times for good measure.

doogly wrote:But yeah, your sine cosine thing seems good, apart from my having no idea how that is supposed to work.


It's a pretty ridiculous way of describing sin and cos. But just take a Taylor series expansion of i sin[x] and cos[x] around x=0, and define two sets (C = the elements of the cos[x] expansion, and S = the elements of the i sin[x] expansion). From there it's possible to re-write the definitions of C and S by mutually-recursively defining them, because their elements naturally build up in very similar ways. So you have something like

C = {1, -x^2/2!, x^4/4!,-x^6/6!,x^8/8!, ...}
S = {i x, -i x^3/3!, i x^5/5!, -i x^7/7!, i x^9/9!, ...}

Now for C, you can define C_n (the nth element of C) as C_n = (1/i) d(S_n)/dx , and you can likewise define S_n as S_n = -i d(C_(n+1))/dx.

There are other ways you can describe the sets, but those work. And from there, you can just reiterate the process:
C_n = (1/i) d(S_n)/dx = (1/i) d(-i d(C_(n+1))/dx)/dx = (1/i) d(-i d((1/i)d(S_(n+1))/dx)/dx)/dx = (1/i) d(-i d((1/i)d(-i d(C_(n+2))/dx)/dx)/dx)/dx etc.

So for the arm band idea: -i d/dx((1/i) d/dx(-i d/dx((1/i) d/dx (-i d/dx( I really meant the above line, but with this kind of representation which is something that's a lot easier to write down on paper. Here, lemme try out this fancy Math button thing.

[imath]-i \frac{d}{dx}\left(\frac{1}{i} \frac{d}{dx}\left( - i \frac{d}{dx} \left( \frac{1}{i} \frac{d}{dx} \left( - i\frac{d}{dx}\left( \frac{1}{i} \frac{d}{dx} \left( - i\frac{d}{dx}\left( \frac{1}{i} \frac{d}{dx} \left( - i\frac{d}{dx}\left( \frac{}{} \right. \right. \right. \right. \right. \right. \right. \right. \right.[/imath]

That's better. And that'll look the same for S as for C, they only differ in which operation you begin with, so that's a nice symmetry. Here, while making this post all fancy, here's an image of what I meant with the Fourier series time vs. r graph, except probably with only one iteration on an actual tattoo:

Image

And here are two other representations of Fourier series expansions of lines constructing a basic Minkowski diagram of two reference frames, which is just barely recursive enough (cyclic really, due to Fourier expansion) and compelling enough to be willing to include:

Image
This is just a normal Minkowski diagram for two reference frames with additional lines drawn in to point out time dilation (nothing labeled)

Image
This is a stylized version of the above Minkowski diagram.

Image
Same graph as above, but the cyclic nature is drawn out, which has the consequence of making the graph totally unrecognizable as relating to a Minkowski diagram (that makes it artistic right?).
Attachments
FT Minkowski1.pdf
Same graph as above, but emphasizing the periodicity.
(49.63 KiB) Downloaded 102 times
FT Minkowski2.pdf
Stylized version of the Minkowski diagram
(25.32 KiB) Downloaded 99 times
FT Minkowski3.pdf
This is the normal Minkowski diagram situation of two reference frames that the other graphs play off of with Fourier series approximation.
(3.61 KiB) Downloaded 96 times
FT c.pdf
Fourier series expansion of a 45 degree line (c in a Minkowski diagram)
(17.28 KiB) Downloaded 123 times
Last edited by Malconstant on Wed Aug 24, 2011 4:00 pm UTC, edited 2 times in total.
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Re: Recursion Tattoo Ideas

Postby doogly » Wed Aug 24, 2011 3:48 pm UTC

Malconstant wrote:Yeah, that's definitely an option. Though it ends up being more "implied" recursion than actual (for infinite recursion at any rate, go hard or go home). The best of this idea that I've heard was a tattoo on my chest of me ripping off my shirt, embedded a couple times for good measure.

Yeah, that is a great idea.
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Re: Recursion Tattoo Ideas

Postby Tirian » Wed Aug 24, 2011 4:02 pm UTC

I'm not grabbed by these ideas, but it's not going on my arm so that's okay.

I suppose the logician in me would be mildly amused by "-- the preceding yields falsehood when infinitely repeated" wrapped around the arm if recursion is what you're after.

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Re: Recursion Tattoo Ideas

Postby Giallo » Wed Aug 24, 2011 6:44 pm UTC

You could write something like "get a life to get a girlfriend to" with "to" ending just before the beginning of "get". It would read "get a life to get a girlfriend to get a life to get a girlfriend to get a life to get a girlfriend to...".

Or the more classical dictionary entry: "Recursion: see Recursion."
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Re: Recursion Tattoo Ideas

Postby Talith » Wed Aug 24, 2011 6:52 pm UTC

There's always the infamous hand drawing a hand drawing a.....

Image

replace the pencil with a tattoo needle and you're set.

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Re: Recursion Tattoo Ideas

Postby Malconstant » Wed Aug 24, 2011 7:24 pm UTC

Giallo wrote: "get a life to get a girlfriend to get a life to get a girlfriend to get a life to get a girlfriend to...".


Ooo, That's a sad one. I feel that may be rule number 2 in avoiding long-term tattoo regret. Rule number 1 being irony.

Another idea for an arm/leg/finger band:

++++++++++++++++++++++++++++++++++++

tilt your head to the side and it becomes x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x... which is a kind of fun function to think about, along with its derivative. Probably not compelling enough for a tattoo, but oh well.

I tried to think of a way to work in a Klein bottle (because I guess mobius strips are too cliche for me, but one more dimension must be a ok), but I haven't been able to come up with an elegant way of doing it.

Talith wrote:There's always the infamous hand drawing a hand drawing a.....

Image


That's not a bad idea. I was trying to think of ways of drawing in hands that are "drawing" my actual hands. Or maybe draw in a tiny Escher on my forearm, where we share my right hand (so a perspective shot I guess), and then with his left hand he could be "drawing in" our mutual right hand, though I feel that's also destined for regret. I'd definitely be down for a good (simple/elegant) Escher-style optical illusion though, but that may diverge too strongly from mathematics to be worth getting into here.
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Re: Recursion Tattoo Ideas

Postby doogly » Wed Aug 24, 2011 8:21 pm UTC

Yeah, hand on hand with tattoo needles sounds pretty dope. I would not actually tattoo the wrist and hand though.
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Re: Recursion Tattoo Ideas

Postby Giallo » Thu Aug 25, 2011 9:45 am UTC

Clearly my sad sentence was only an example. I used that sentence because I couldn't come up with anything better :(
"Ich bin ein Teil von jener Kraft, die stets das Böse will und stets das Gute schafft."

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Re: Recursion Tattoo Ideas

Postby AvatarIII » Thu Aug 25, 2011 10:26 am UTC

Giallo wrote:You could write something like "get a life to get a girlfriend to" with "to" ending just before the beginning of "get". It would read "get a life to get a girlfriend to get a life to get a girlfriend to get a life to get a girlfriend to...".

Or the more classical dictionary entry: "Recursion: see Recursion."


better would be "work a job to earn some money to live a life to"

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Re: Recursion Tattoo Ideas

Postby Malconstant » Thu Aug 25, 2011 1:55 pm UTC

AvatarIII wrote:better would be "work a job to earn some money to live a life to"


live a life to work a job? Your employers must love you.

How about a positive event chain one? something like "make someone else smile, brighten their day, now that person will want to"

Or use the Zach Weiner joke as an implicit premise: "Did you know that the word "recursion" contains the word "recursion" in itself?" with the actual tattoo being

Spoiler:
Image

Source: http://www.smbc-comics.com/?id=2325

That'd be a fun one to turn into an arm/leg/finger band. I can appreciate the lack of subtlety.
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Re: Recursion Tattoo Ideas

Postby AvatarIII » Thu Aug 25, 2011 2:09 pm UTC

Malconstant wrote:
AvatarIII wrote:better would be "work a job to earn some money to live a life to"


live a life to work a job? Your employers must love you.

How about a positive event chain one? something like "make someone else smile, brighten their day, now that person will want to"

Or use the Zach Weiner joke as an implicit premise: "Did you know that the word "recursion" contains the word "recursion" in itself?" with the actual tattoo being

Image

That'd be a fun one to turn into an arm/leg/finger band. I can appreciate the lack of subtlety.


yeah i had a feeling there was something off about it,
maybe better would be "get paid to work to live to get paid"

also if anyone is interested in where the recursion thing mal mentioned comes from
http://www.smbc-comics.com/index.php?db=comics&id=2325
Image

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Re: Recursion Tattoo Ideas

Postby Malconstant » Thu Aug 25, 2011 2:26 pm UTC

AvatarIII wrote:maybe better would be "get paid to work to live to get paid"


Maybe, though I think the trap lies with "to work" I'm not sure it's possible to put that in an implicitly depressing message in a way that's like "yeah, that's why I'm doing it, my partial end game is the work itself."

Also I included the smbc link in the spoiler. The forum won't let me embed URL's (is that a threshold number of posts thing?) so I was trying to be discreet about posting to another webcomic while I'm still new to these forums. But of course you're quite right.
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Re: Recursion Tattoo Ideas

Postby AvatarIII » Thu Aug 25, 2011 2:36 pm UTC

Malconstant wrote:
AvatarIII wrote:maybe better would be "get paid to work to live to get paid"


Maybe, though I think the trap lies with "to work" I'm not sure it's possible to put that in an implicitly depressing message in a way that's like "yeah, that's why I'm doing it, my partial end game is the work itself."

Also I included the smbc link in the spoiler. The forum won't let me embed URL's (is that a threshold number of posts thing?) so I was trying to be discreet about posting to another webcomic while I'm still new to these forums. But of course you're quite right.


i guess, but i was going for "getting paid to work" as in "getting paid for the work" like "i got paid to mow the lawn"

and i quoted you before you edited in the reference, or the spoiler tag, and since i only read 2 web comics, xkcd and smbc, i knew what you were talking about, but i thought i'd link to smbc for you, and for the people that might not read it.

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Re: Recursion Tattoo Ideas

Postby Giallo » Fri Aug 26, 2011 10:59 pm UTC

Malconstant wrote: "make someone else smile, brighten their day, now that person will want to"


Nice :D

What about:
"...your eyes reflecting my eyes reflecting..."?
"Ich bin ein Teil von jener Kraft, die stets das Böse will und stets das Gute schafft."

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Re: Recursion Tattoo Ideas

Postby 4=5 » Tue Aug 30, 2011 4:02 pm UTC

You could try jethro tull; "watching me watching you watching him".

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Re: Recursion Tattoo Ideas

Postby PM 2Ring » Wed Aug 31, 2011 9:43 am UTC

How about some kind of variation on Escher's "Drawing Hands", eg with the hands holding tattoo guns instead of pencils?

http://farm1.static.flickr.com/223/476543243_2eed08e3fc.jpg

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Re: Recursion Tattoo Ideas

Postby AvatarIII » Wed Aug 31, 2011 1:24 pm UTC

you mean exactly what Talith said earlier in the thread?

Talith wrote:There's always the infamous hand drawing a hand drawing a.....

Image

replace the pencil with a tattoo needle and you're set.


i guess you were just posting a recursion of that post :D

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Re: Recursion Tattoo Ideas

Postby GOD_Over_Djinn » Wed Aug 31, 2011 9:08 pm UTC

Get a tattoo that contains all the tattoos that contain themselves.

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Re: Recursion Tattoo Ideas

Postby Malconstant » Wed Aug 31, 2011 11:53 pm UTC

GOD_Over_Djinn wrote:Get a tattoo that contains all the tattoos that contain themselves.

Hahahaha. I loved this. Although I read it as "get a tattoo that contains all the tattoos", and that's the one I actually want.
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Re: Recursion Tattoo Ideas

Postby PM 2Ring » Thu Sep 01, 2011 10:03 am UTC

AvatarIII wrote:you mean exactly what Talith said earlier in the thread?

Oops. * blush *

How about http://mathworld.wolfram.com/TuppersSelf-ReferentialFormula.html, then?

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Re: Recursion Tattoo Ideas

Postby Malconstant » Thu Sep 01, 2011 3:47 pm UTC


Also delightful. I'll need to look over some GEB sometime, I recall there was a program written very much like that idea.
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Re: Recursion Tattoo Ideas

Postby PM 2Ring » Thu Sep 01, 2011 5:10 pm UTC

Malconstant wrote:

Also delightful. I'll need to look over some GEB sometime, I recall there was a program written very much like that idea.


On a similar note, you could have the source code of a program that outputs its own source code. Here's one in C which is also a palindrome:

Code: Select all

/**/char q='"',*a="*//**/char q='%c',*a=%c%s%c*/};)b(stup;]d[b=]d-472[b)--d(elihw;)q,a,q,q,2+a,b(ftnirps;)b(stup{)(niam;731=d tni;]572[b,",b[275];int d=137;main(){puts(b);sprintf(b,a+2,q,q,a,q);while(d--)b[274-d]=b[d];puts(b);}/*c%s%c%=a*,'c%'=q rahc/**//*"=a*,'"'=q rahc/**/

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Re: Recursion Tattoo Ideas

Postby MHD » Thu Sep 01, 2011 6:50 pm UTC

If you are into that sort of thing you could go with a fixed point combinator.

Y f =
f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f ( f (...
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Re: Recursion Tattoo Ideas

Postby dumbzebra » Sat Sep 10, 2011 2:37 pm UTC

Re|cur|sion; noun,f,(lat.):
Recursion
As the great philosopher Socrates once said: "No."

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Re: Recursion Tattoo Ideas

Postby undecim » Sat Sep 10, 2011 10:56 pm UTC

Ever since I read the GOD (GOD Over Djinn) narrative from GEB, I've thought that an illustration of the genies exactly halfway through the "moment" it takes for the genie to ask the infinite chain of meta-genies (i.e., when there is an infinite number of genies summoned) with each genie a fraction the size of the last would make a pretty cool illustration. Wouldn't make a bad tattoo, either, I would suppose.
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