# Infinity Antonyms?April 28, 2010 5:11 PM   Subscribe

What is a symbolic antonym for infinity?

I have an infinity symbol tattoo, and I'm thinking of getting a opposing symbol as well. Only problem is, I don't know what symbol to use!

Dictionary antonyms are things like "end" and "termination" don't really capture what I'm going for. To me, infinity represents cycles and recursiveness, and what I'm looking for is something that represents breaking out of those cycles. So not a symbol of ending, but a symbol of a new beginning.

I know of the delta sign for change, but I'm looking for other options!
posted by yellowbinder to Grab Bag (45 answers total) 3 users marked this as a favorite

The word I'd look for is "finite," perhaps? I'm not sure if I can think of a symbol that represents finite.

Perhaps a complete circle?
posted by SNWidget at 5:14 PM on April 28, 2010

Goose egg.
posted by LonnieK at 5:16 PM on April 28, 2010

.
posted by unknowncommand at 5:17 PM on April 28, 2010 [3 favorites]

A line with a point at each end, perhaps.
posted by The World Famous at 5:17 PM on April 28, 2010

Or maybe an arrow?
posted by unknowncommand at 5:18 PM on April 28, 2010

Goose egg because you could say the opposite of infinity is zero. Symbol: Goose egg. There aren't that many symbols for zero, are there? Also like SNWidget's answer -- nice coincidental relationship to mine, no?
posted by LonnieK at 5:18 PM on April 28, 2010 [1 favorite]

So you don't want Null (Null set) or Omega?
posted by miasma at 5:20 PM on April 28, 2010

How about a broken infinity sign, trailing off into something new?
posted by iamkimiam at 5:20 PM on April 28, 2010

Null? No value vs. Infinite value?
posted by blue_beetle at 5:21 PM on April 28, 2010 [2 favorites]

Anything Satanic.

Why? Because, God is infinite, according to the theory. And only God is infinite, otherwise He's not really . . . you know. Satan, God's opposite, must perforce be finite. Otherwise . . . you know.

But is Satan the only finite quantity? It gets tricky. But as the perfect opposite of the only true Infinite, i.e. God, he certainly takes pride of place.
posted by LonnieK at 5:23 PM on April 28, 2010

What about an end and then a new start? A little literal, but...

----->| o---->
posted by miasma at 5:23 PM on April 28, 2010

Perpendicular symbol? If you take "infinity" as "infinitely in one dimension," i.e., an infinite line, then "perpendicular" could represent breaking out of that single dimension.
posted by DevilsAdvocate at 5:23 PM on April 28, 2010 [1 favorite]

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posted by sanko at 5:24 PM on April 28, 2010

The ΑΩ or αω symbols might be a fairly good fit, if you're religious that way.
posted by Fiasco da Gama at 5:26 PM on April 28, 2010

For the opposite of infinity: ∅ (empty set).

Zero is quite closely related to infinity. `lim x/0` goes to ±∞. The empty set, however, is non-operable. That is, there's nothing you can do to it that doesn't either yield itself or leave the other operand untouched, and it's inherent in all other sets.

But, if you want a mathematical symbol that symbolizes a new beginning, how about an orthonormal basis? This could be pleasingly formatted as the ℜ3 identity matrix:
|1, 0, 0|
|0, 1, 0|
|0, 0, 1|

The orthonormal basis is a beginning. It defines a complete space in which all arithmetic operations are possible. If your basis is not orthogonal, you get weird* results and some areas of the space you would expect to exist are unreachable. If they're not normal, then things act differently on different axes. An orthonormal basis is the beginning of all things you and I recognize as reality.

*Please note, a non-orthogonal basis can be useful. It's just weird.
posted by Netzapper at 5:34 PM on April 28, 2010 [7 favorites]

I like '0'.
posted by spinifex23 at 5:39 PM on April 28, 2010

my math teacher wife agrees with the "null set" symbol, but wants to think about it some more...
posted by HuronBob at 5:39 PM on April 28, 2010

If you don't like 0, the letter epsilon (ε) is used to represent an arbitrarily small number. ("For all ε > 0, ...")

To continue the science theme: electrical ground symbols. (The third one, labeled "Earth ground," is most familiar.)
posted by k. at 5:40 PM on April 28, 2010 [1 favorite]

Φ (capital Phi)

It looks somewhat like a null set and could be a visual pun.

Simple as a symbol it is circularity crossed by a strong line, somewhat opposite of endless flow of ∞.

Most common meaning of Φ is for the golden ratio, which is not infinity but rather correct proportion, measurement, static balance.
posted by fleacircus at 5:43 PM on April 28, 2010

Response by poster: I love the orthogonal basis, where as the symbol for infinity shows a closed path, the orthogonal basis allows infinite paths.

I understand that my interpretation of the infinity may not jive with the mathematical definition, but the idea of null or zero is not really what I'm looking for.

Further interpretations are welcome, I'm enjoying figuring out the possibilities!
posted by yellowbinder at 5:44 PM on April 28, 2010

Response by poster: orthonormal, rather. Got to get that straight if I'd have it put on my skin!
posted by yellowbinder at 5:46 PM on April 28, 2010

Yeah, empty set.

That or lowercase epsilon, usual notation for an arbitrarily small number. However small a number you can think of, even a squillionth, epsilon is weensier than that.
posted by ROU_Xenophobe at 5:46 PM on April 28, 2010 [1 favorite]

To me, infinity represents cycles and recursiveness, and what I'm looking for is something that represents breaking out of those cycles.

It's a cliche, but it really sounds like a phoenix represents this sentiment perfectly.
posted by PhoBWanKenobi at 6:14 PM on April 28, 2010

How about a delta function?
posted by pombe at 6:16 PM on April 28, 2010 [2 favorites]

Logarithmic spiral?
posted by leahwrenn at 7:09 PM on April 28, 2010

If your basis is not orthogonal, you get weird* results and some areas of the space you would expect to exist are unreachable.

The null space of a full rank matrix is always trivial. The basis
|1,1,0|
|0,1,0|
|0,0,1|
still spans ℜ3 even though it's not orthogonal... or did you mean something else by "unreachable"?
posted by tss at 7:20 PM on April 28, 2010

How about a circle with a point at the north pole removed, and two dots at the end to signify finiteness? This corresponds to the real numbers under the following correspondence:
Place a circle on the real line with the south pole intersecting at 0. For every point on the circle a line from the north pole through that point hits the real line at a unique point. The north pole corresponds with infinity.

I'm picturing it like one of those body piercing rings, or a bent barbell.
posted by monkeymadness at 7:31 PM on April 28, 2010

still spans ℜ3 even though it's not orthogonal... or did you mean something else by "unreachable"?

No, you're right. I absolutely did mean span; and I was absolutely wrong. My relationship with linear algebra is limited to use of algebraic and computational geometry these days--the natural basis is pretty much implicit in my datasets. My apologies.

Nonetheless, I still think that an orthonormal basis is a good mathematical symbol for what the OP's trying to convey.
posted by Netzapper at 7:47 PM on April 28, 2010

(a continuation from my above---in which I argue against the identity matrix, but bear in mind that this is a statement reflecting my own personal aesthetics, etc.)

More to the point, is the following matrix still tattoo-beautiful to you

|1,0,0|
|0,1,0|
|0,0,1|

if you know that to more than a few technical audiences, the following matrix is essentially the same thing?
```|0.36, 0.48, -0.8|
|-0.8,  0.6,    0|
|0.48, 0.64,  0.6|```
And in fact, there are an infinity of equivalent matrices. Why is this so? One way to interpret both of these orthonormal matrices is as the three orthogonal arrows showing the directions of the x, y, and z axes in a 3-D plot. The first row shows the direction of the x axis, the second row shows the direction of the y axis, and so on.

As anyone who's visited the space station knows, there's nothing special about any particular orientation of those three arrows. If you need an "up", just pick one that's convenient for you and rotate the coordinate arrows to match.

TL;DR. Here is my suggestion

I tend to agree with k. in that if you want a fitting counterpart to ∞, you should go with an infinitesimal, a quantity that is impossibly small and yet is still not zero. If you want to imply "finite" without implying "nothing", then an infinitesimal is (to me) as far away from infinity as you are going to get. Yet at the same time, it's a similarly mindbending concept that (like infinity) mathematicians have taken centuries to formalize, and one that (with its conceptualization) gave us new and revolutionary analytical powers (calculus!).

Finally, and most importantly, it can be made to look cool. You can certainly go with k.'s ε, but this can also connote error in statistics. Personally, I would use the ubiquitous dx given to us by Leibniz, connoting an infinitesimally small step along x. Here are dx and ∞ rendered together in Computer Modern, the font used in so many modern textbooks and technical papers, but you have more choices too---go to a university library, find old math books, and copy/blow up an even sweeter dx from there!

To me, dx and ∞ seem quite complementary. In the yin and yang sense, not the set theory sense!
posted by tss at 7:58 PM on April 28, 2010

This, or this.
posted by WCityMike at 7:59 PM on April 28, 2010

If you like the differential concept, but want something more fancy than a "d" you can use the symbol for partial differentiation:
𝜕x/𝜕t or maybe just 𝜕x or even just 𝜕
posted by forforf at 8:16 PM on April 28, 2010

not so mathy, but an open beginning parenthesis or bracket, maybe?
posted by so_gracefully at 9:16 PM on April 28, 2010

Presuming it could be rendered effectively as a tattoo, how 'bout a Mobius Strip? It offers visual symmetry and, thanks to it's one-sided-ness, meaningful antonym-etry.
posted by carmicha at 9:27 PM on April 28, 2010

Here I go again. Careful rereading of your post makes me realize that dx doesn't readily connote this notion of "escape" or "breaking out" that you seem to want. Sorry about that---I got too wrapped up in my own idea.

Unless...

...

In probability theory and statistics, there is the notion of the probability density function or PDF, which reflects the likelihood of outcomes within a continuous range. PDFs you may know include the normal distribution's bell-shaped PDF, which matches well with so many seemingly unrelated things---the ranges of human height, test scores, etc. etc.

The normal distribution PDF says that the probability of seeing an outcome between real numbers x1 and x2 is the total area underneath the PDF starting at x1 and ending at x2. There are more distributions besides normal distributions, of course, but let us stick with that one for illustration. Speaking of illustration, there are some pictures of this concept here.

Now, what of the probability of a specific outcome? You are the only person in the world who is exactly the height you are. Your height x occupies an infinitesimal interval on the real number line, stretching from x to x + dx. Accordingly, the area under the PDF over human heights within this interval is also infinitesimal. In other words, the chances of anyone being the height that you are are impossibly, impossibly small. It is weird, but sensible in a way.

In general, if we imagine an even bigger and badder PDF reflecting the entire range of human characteristics, not just height but weight, eye color, degree of allergy to bee stings, tendency to make apple pies, fondness for eighties music, etc., then the probability associated with any specific instance---any one person---is still vanishing, and yet, here you are, an infinitesimal portion of this wide range actually and improbably realized, the dx that escaped. In this sense, dx might also characterize some sense of individuality.

Fun question; I'll stop now. Good luck choosing.
posted by tss at 9:37 PM on April 28, 2010

Here's a version of the new moon. Here's another: "In astronomy and calendars [the filled-in circle] is used to denote the new moon, i.e. the conjunction of the sun and the moon that takes place once every 28 days."

That said, the new moon is not a discontinuity; it is part of a cycle. For discontinuities, I turn to geology. There are also a lot of geography symbols for fault lines, where one terrain ends and another begins. These vary slightly based on how the two sides relate to one another. Here is more structural geography, and if any of those concepts works for you, there are map symbols to go with it. Another one you might like is the strike and dip whose symbol is basically a line with another line parallel to it. Or what about the eruption of a volcano? Something new emerging.

Another form of fresh start, what about this or a new paragraph sign?
posted by salvia at 10:39 PM on April 28, 2010 [1 favorite]

-∞
posted by TheophileEscargot at 2:25 AM on April 29, 2010

Expanding on pombe's idea for the dirac delta function and how that might relate. The symbol δ(x) is used for this function, but any delta symbol could work (Δ or δ).
If you want something that is "anti-infinity" and symbolizes "breaking out" and that still has a firm basis in math, then this is probably the ideal.
The dirac delta is a special function, it's also called the impulse function. It reaches to infinity for an infinitesimal duration. In other words, it symbolizes the most powerful immediate impulse that is there and then gone. However, the effects of that impulse may have repercussions. For example, if you had a function that integrated over a flat constant infinitely long (see what I did there?) the result would be the exact same constant.
However if you inserted a dirac delta, then the integration will look very different. At the instant of the impulse of the dirac delta, the integral will have made an instantaneous jump to a new level (i.e., a step function), and that new level would then be the new constant value of the integrated function.

The dirac delta can be looked at as the mathematical basis for representing instantaneous change.

Oh, if greek letters aren't you're thing, then it can also be represented by a upward arrow from a line, like this: ↥; which may provide a better base for stylistic interpretations if you want to make it a bit more fancy.
posted by forforf at 7:42 AM on April 29, 2010

The empty/null set isn't a direct counterpart to infinity, as infinity isn't (generally considered as) a set , Principia Mathematica aside. The counterpart to the empty set is the universal set U, but there is no "one" U - it is dependent on the situation you are dealing with.

My vote for the counterpart to infinity is zero, for reasons stated above but also because it is diametrically opposite on the Riemann Sphere (look it up, it's cool).
posted by Earl the Polliwog at 12:12 PM on April 29, 2010

How about a snake eating its own tail, but this one isn't eating its own tail -- it's eating a veggie burger! and it's saying "veggie burgers eh?"
posted by Vic Morrow's Personal Vietnam at 1:40 PM on April 29, 2010 [1 favorite]

How about a geometric series? It starts as something infinite and repetitive, but sums to something finite.

Or non-math, you could have an egg and an apple (from eggs to apples--from beginning to end).
posted by anaelith at 6:08 AM on May 1, 2010

Response by poster: Ok, I think I got it. This is sure to make some mathematical heads spin, but you've already seen I play fast and loose with the rules. I'm sure it will piss off the author of at least one deleted comment I saw whose point was essentially stop getting tattoos.

I do like the idea of the orthonormal basis, and the symbol is pretty and tattoo worthy, but there's some debate as to its accuracy in here which is going over my head. I'd like to have a justification, no matter how mathematically inaccurate, solidly locked down in my head.

So I love my infinity symbol, butas I've described here, to me it's a symbol of recursion, or at least fate, the idea that any path you can think of has already been walked and accounted for, even if just the idea of it, within this symbol. So here's what I've come up with:

∞+1

I love it, mathmatically impossible, it allows for something new outside that which is known, experienced and catalogued. It also calls back ideas of schoolyard debates, what tops "You are so times ∞!" other than "I am not ∞+1!!!"

Thoughts?
posted by yellowbinder at 9:52 AM on May 2, 2010

Have you heard of transfinite numbers?
posted by anaelith at 5:51 PM on May 2, 2010

I'd wait for more people here to comment on your idea, given this new information. Transfinite numbers might be a good topic to delve into. But tattoo-making by arranging symbols together that have rich and precise meanings to the community that uses them the most, whilst not being quite too clear on those meanings, particularly if you choose a new and unorthodox arrangement, well, it's risky business.

I'm not a mathematician, and I wouldn't trust myself to make a mathematical symbol tattoo for anyone. That said, ∞+1 would make me wonder if you also routinely try to give 110%! Both statements seem about as sophisticated to me, to be frank.

The orthonormal basis is valid for all of the aesthetic reasons that Netzapper gave, except for a technical bobble that I pointed out, which doesn't have much to do with what I think you're trying to express. It's not my cup of tea as a counterpoint to infinity, but whatever. If I saw someone with the 3x3 identity matrix (another term for Netzapper's suggestion) for a tattoo, I'd think it was interesting and unusual, as well as highly nerdy. I'd probably ask them a MATLAB question for fun.

Here is a PDF containing the 3x3 identity matrix in the Computer Modern font I mentioned earlier.
posted by tss at 8:25 PM on May 2, 2010

I wouldn't trust myself to make a mathematical symbol tattoo for anyone

On reflection, this is a pretty silly thing to say given all of my posting. I guess this is just the usual Random Internet Guy disclaimer.
posted by tss at 8:27 PM on May 2, 2010

Infinity plus one isn't mathematically impossible. If you're actually using infinities (rather than merely approaching them), you're not in the real numbers proper anymore, and in the extended reals etc. you can do infinity plus one. It's just infinity again.

As a math guy, it's not really something I'd do unless you really want to emphasize that if you try to exceed infinity by mere addition, you just get infinity yet again.

Now if you want to talk about bigger infinities, check out the Cardinality of the Continuum and the Aleph Numbers.
posted by Earl the Polliwog at 1:51 AM on May 24, 2010

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