pozorvlak: (Default)
Monday, June 20th, 2011 11:30 pm
You've probably already heard of Rule 34 of the Internet:
If it exists, there is porn of it on the Internet. No exceptions.
Now, as any mathematician can tell you, the statement "if X then Y" is equivalent to its contrapositive, "if not-Y then not-X". For instance, "if Socrates is human, then he is mortal" is equivalent to "if Socrates is not mortal, then he is not human".

[Pause to digest that for a second if you haven't thought about contrapositives before.]

Hence, Rule 34 is equivalent to its contrapositive:
If there is no porn of it on the Internet, it doesn't exist. No exceptions.
At DrMathochist's suggestion, I'm going to refer to this equivalent statement as Contrapositive 34, though we could just think of it as a re-statement of Rule 34: it's true if and only if the original Rule 34 is true.

Note that Rule 34 is not equivalent to its converse, which states "If there is porn of it on the Internet, it exists". That one's probably false. Links NSFW, obviously. This means that we can't, for instance, construct existence proofs by writing pornography featuring the thing whose existence we wish to prove ("'Come here, you sexy thing,' said the set whose cardinality was greater than that of the integers but less than that of the real numbers"). Bummer. However, Contrapositive 34 does have some interesting consequences:
  • While the amount of pornography on the Internet is mindbogglingly large, it's still finite; hence, there are only finitely many things in existence.
  • Since all Internet pornography, when you get right down to it¹, consists of finite strings of bits, the set of all possible Internet pornography is countable. Hence, there are only countably many possible things.
Edit: Conor McBride points out that this is a sexed-up version of Richard's Paradox. Which makes me wonder about the extent to which pornography could be reduced to a formal symbolic language - but that way lies madness.

Will Strinz suggested that you could build an accurate database of all things by searching for Internet pornography ("mining pornspace", as he called it). Unfortunately this doesn't quite work, since the converse of Rule 34 is false; you could, however, build an accurate database of things that might exist. If your search engine were powerful enough, you could try building a database of things that are believed with high confidence not to exist - generate search queries somehow (taking sets of dictionary words and adding "porn" would be a good starting point), and anything that returns no hits probably doesn't exist.

You might have a hard time explaining your multi-petabyte porn collection to your grant committee, though.

¹ *snigger*
pozorvlak: (Default)
Thursday, March 24th, 2011 10:01 am
In Clackmannanshire, where [livejournal.com profile] wormwood_pearl grew up, the word "minky" means filthy, messy, disgusting; there's a heavy connotation of shame. "Ugh, this kitchen's minky!" An approximate synonym is "clatty".

My friend [livejournal.com profile] buffalo_gill, who is from... somewhere in England, uses "minky" to mean great, excellent, cool: "that party was minky".

In the teenage fiction of Joanna Nadin, "minky" is a noun meaning "vagina": "According to Sad Ed, it is the law to have been sick on Strongbow and have seen several willies (or minkies in his case) by the end of Year Ten."

So I was delighted to see this at the shops yesterday:

Half-price Minky ironing board
pozorvlak: (Default)
Tuesday, March 22nd, 2011 12:24 pm
A couple of days ago I saw a tweet from @TomCadwallader, claiming that
1 sperm has 37.5MB of DNA information in it. That means a normal ejaculation represents a data transfer of 1587GB in about 3 seconds.
That's cute, but there's a more interesting question lurking here: it may represent 1.5TB of data, but how much information is transferred? In other words, how many bits would be required to convey the same "message" if we compressed it as cleverly as possible?

[Also, three seconds? Either Tom's ignoring the time required for the initial protocol handshake, or he's doing it very, very wrong.]

First off, some Wikipedia-reading (it may surprise you to learn that I actually research these posts) brings Tom's figures into question. The raw information content of the human haploid genome is actually more like 770MB, of which 38.7MB is the X chromosome and 14.4MB is the Y chromosome. So a single sperm contains roughly 755MB if X, or 730MB if Y. Sperm density and volume of semen varies wildly, but the adult average is apparently 3.5ml and 300 million sperm per ml. That's around a billion sperm per ejaculation, rather higher than the (1.5TB/37.5MB) =~ 420,000 sperm in Tom's figures! This gives us a total raw information transfer of about 750 petabytes, and a bandwidth of 250PB/sec - comfortably exceeding the bandwidth of a fully-laden 747, let alone Andrew Tanenbaum's speeding truck full of videotapes.

[The relationship between karyotype and apparent sex is more complicated than that, of course: Tom might have Klinefelter's syndrome (XXY) or XYY syndrome, which would make the numbers come out differently. But let's assume he's XY for the sake of simplicity.]

But this data is actually highly redundant, and thus extremely compressible. To see why, we'll need to review some high-school biology. Most human cells are diploid, meaning that they have two copies of each chromosome (one from your mother and one from your father), giving 46 chromosomes in all. Sperm cells, on the other hand, are haploid, meaning that they only have one copy of each chromosome. Sperm cells are formed by meiosis: for each type of chromosome, the new sperm cell is randomly assigned either the mother's copy of that chromosome or the father's copy.

This immediately gives us a huge data reduction. Once we've got a full copy of Tom's genome, all we need to store about each sperm is which chromosomes it's got. That's one bit (mother/father) per chromosome, or 23 bits per sperm. Using our estimate from above, that means we need 23 billion bits, or 2.9 gigabytes. We can also compress our representation of Tom's genome using standard compression algorithms: the entropy of the human genome is apparently 1.7 bits per base pair, as opposed to the 2 bits per base pair we used for our naive encoding, so we can fit his genome into a bit under 1.3GB. Our total information transfer is thus 4.2GB.

... but that would be too easy, wouldn't it?

It turns out that meiosis is more complicated than that: as part of the process, paired chromosomes exchange data - sorry, sections of DNA - in a process known as homologous recombination. I've been unable to determine how frequent this is - any biologists able to help me out here? - but apparently it's vastly more common at recombination hotspots, of which there are known to be over 25,000 in the human genome. If recombination's relatively rare then we could use a space-efficient sparse representation - "exchanges occurred at positions 12, 94, 509, 1337, 2424,...", but if it's common then we're going to have to store one bit per hotspot, to indicate whether or not a recombination occurred there. That's 25,000 bits per sperm, or just over 3kB each: scale it up by a billion, and we're storing 3TB of recombination data.

So, as it turns out, the total bandwidth of Tom's, er, "uploads" is around twice what he thought it was. I suggest that he not use that as a chat-up line, though.
pozorvlak: (Default)
Saturday, June 26th, 2010 02:39 pm
Last night I was re-watching The IT Crowd S3E4. It was one of my favourite episodes, and I still think it's beautifully constructed, but I found it a bit... squirmier this time round. For those who haven't seen it, one of the main characters meets a woman, invites her to dinner, then asks her to go to bed with him. She tells him that she's trans ("I used to be a man - I wish there were an easy way to say that, but believe me, there isn't.") and he says "I don't care. Takes all sorts to make a world." Cue romantic courtship montage: they get drunk, eat pizza and watch the darts, she beats him at arm-wrestling, she astonishes him with her prowess in bed and detailed understanding of the male anatomy, she teaches him to shoot pool, she beats him in a lager-drinking contest, they go to the football together, and so on. Then one night they're in bed together, tell each other that they love each other for the first time, and he says "And to think you were worried about telling me you were from Iran!" Turns out he misheard, they break up, they get into a fist-fight in a chemistry lab, throw each other through walls and into racks of glassware, and end up destroying the Internet and causing the collapse of society... but that's another story.

A beautiful relationship ruined by transphobia and prejudice. How sad.

Thing is, though, she was really apologetic when she first told him, and was worried that he'd feel deceived. Half-way through their first date, remember. It seems to me that, while she's probably sensible to worry about a potential adverse reaction, (a) she has no need to apologise for having done something difficult, expensive and brave, (b) she could hardly have told him much earlier.

And then I log on this morning, check my friends page, and discover that one of those godawful LJ Writer's Block suggestions recently was
Regardless of your sexual identity/orientation, would you be upset if a long-term romantic partner neglected to tell you that s/he'd had a sex change operation before you met, and why?
Funny how these coincidences happen.

[You can't see the question any more: they wimped out and changed it to one about partners who'd committed serious crimes in the past.]

Anyway, there are a couple of transfolk who read this blog, and plenty of people who are more clued-up about trans culture and trans rights than me, so I'd like to ask: at what stage (if ever) do you tell potential romantic or sexual partners about your trans status? What do you say, and what kind of reactions have you had? If you weren't to tell them (and I guess I'm directing this at the postops) would they be able to tell? Please feel free to comment anonymously if you'd rather.

For the record: if I discovered that someone I was sleeping with was trans, it would probably freak me out a little bit, but that would be my problem, not hers, and I'd work to get past it. I'd really like to have kids some day, which could be an issue.
pozorvlak: (Default)
Saturday, July 25th, 2009 09:18 pm
At the bouldering wall this afternoon...

[livejournal.com profile] wormwood_pearl: God, why am I so tired? I'm pretty sure I'm not pregnant.
[livejournal.com profile] pozorvlak: Yeah, I'm pretty sure you're not pregnant too. But if you are, I shall endeavour to love it as if it were my own.
[livejournal.com profile] wormwood_pearl: *glares*
*glares some more*
*glares a bit more for good measure*
I haven't been going down Alien 2 and seducing all the hunky boulderers! But, imagine if I did - the baby would come out all triangular. And you'd be there at the birth, shouting "Go on! Send it!"
[livejournal.com profile] pozorvlak: *boggles*
[livejournal.com profile] wormwood_pearl: Though it would have the umbilical cord, so technically it would be a roped climb...¹
[livejournal.com profile] pozorvlak: *boggles some more, goes off to do more climbing*
[livejournal.com profile] wormwood_pearl: [pursuing him] And I'd be shouting "Oi! No wirebrushing!"

¹ As she remarked later, the placenta wouldn't be up to much as a belayer. Though it might be OK as a bouldering mat...
pozorvlak: (gasmask)
Friday, December 12th, 2008 08:26 am
Dear Facebook,

You know I'm not single. If you track IP addresses, which I'm sure you do, then you also know that I share a computer with my girlfriend, and thus even if I were inclined to stray, I wouldn't do so from here.

So could you please stop showing me adverts for hot singles I could meet in my area?
pozorvlak: (babylon)
Monday, November 24th, 2008 09:16 pm
Over on qntm.org, the always-entertaining Sam Hughes presents us with an essay on gay marriage: the database engineering perspective. It's a discussion of the real obstacle to legalising gay marriage, namely migrating the schemas of all the government databases so that they can accommodate the idea. Worth a read, perhaps especially if you don't know much about how databases work.

As Sam progressively broadens the allowable definition of marriage, he quickly ends up with the problem of representing an arbitrary undirected graph in a relational database. Recall that a graph is something like a half-filled-in join-the-dots puzzle: more formally, it's a collection of vertices and a collection of edges between pairs of vertices (or if you prefer, some dots, and lines connecting some of the dots), and that a graph is directed if the edges have a direction associated with them, and undirected otherwise. Here, the vertices are people, and the edges are marriages between people. It shouldn't come as too much of a surprise that graphs show up in this problem: graphs arise all over the place in mathematics and computing (another obvious one: the machines on your network, and the cables connecting them). And so Sam runs into one of the classic problems: how do you represent something fundamentally unordered (the endpoints of an edge, here the spouses in a binary marriage) using something that's fundamentally ordered (the memory of a computer)? More concretely, how do you decide who gets put in the spouse1 column of your marriages table and who gets put in spouse2?

Sam's solution is expedient if inelegant: since every person in his database has a unique identifying number (good DB design practice, but still, shudder), he can simply make spouse1 the partner with the lower CitizenNumber. But there's a more common solution which I'd like to talk about. Since it's easy to represent directed edges ("A is married to B"), we represent an undirected edge by two directed edges going in opposite directions ("A is married to B, and B is married to A"). When I first encountered this trick, I thought it was an ugly hack, but it turns out that it actually makes more sense than you might think. )

TL;DR version: Very often in mathematics, we have a pair of operations, one of which forgets about extra structure on some object and one of which adds that structure in simple-mindedly. We capture this notion using adjunctions. Applying this framework to undirected and directed graphs, we discover that the well-known trick for representing an undirected graph as an invertible directed graph actually behaves more like forgetting structure than adding it back in. Thus undirected graphs "really are" invertible directed graphs.
pozorvlak: (Default)
Sunday, August 3rd, 2008 01:02 pm
I like knots.

I was always terrible at them as a Cub Scout: in my pack, knotting was taught via a series of "rabbit goes out of the hole"-style mnemonics, which I could never remember or apply. I suspect this was one of the reasons why I never went further in the Scouting movement. However, a couple of years ago I picked up Geoffrey Budworth's excellent The Knot Book, which takes an entirely different tack. He dispenses with mnemonics in favour of clear diagrams and (where possible) a breakdown of the knot into simpler components. I think very visually, and learn best by connecting new ideas to things I already understand, so this approach works very well for me. Just as good is the organisation of the book: each knot is accompanied by a discussion of its pros and cons, and cross-references to related knots. Knots are largely collected together by function, allowing for easier comparison. For a couple of weeks, I spent most of my spare time tying knots in things, and festooning my flat with knotwork. I was particularly proud of the barrel sling arrangement for hanging a cup of tea off a doorknob.

When choosing knots, the two most interesting factors are usually
  • The breaking strain - knots (which are essentially twists and kinks in rope on which pressure is exerted unduly) all weaken the rope, often substantially. Different knots weaken the rope to different extents. This tendency is usually expressed as a percentage of the breaking strain of the unknotted rope - a simple overhand knot, for instance, has a breaking strain of 40%, which means that a rope with an overhand knot tied in it can be broken with 40% of the force that would usually be required. A reef knot (US: square knot) has a breaking strain of around 45%, whereas sheet bends and double fisherman's knots have breaking strains nearer 65% - this is one of the reasons why the reef knot is not recommended for joining two lines together.
  • The security - the tendency of the knot to come undone, particularly when subject to random, inconstant loads. Knots with the same breaking strain might have wildly different securities - for instance, the left-handed bowline is as strong as the right-handed version, but much less secure. Security's harder to measure than breaking strain, but UIAA bounce tests give some idea.
Different groups prioritise these differently - anglers, for instance, work with very thin line and comparatively high forces, so have evolved elaborate knots with breaking strains close to 100%, whereas climbers will often choose a more secure knot with substantially lower breaking strain - modern climbing rope has such absurdly high breaking strain that your rope, however knotted, will probably still be the strongest part of your belay or abseil (US: rappel) system. See this discussion of the best bend¹ for joining two abseil ropes together for some idea of the considerations used. Other factors come into play too, of course: climbers value knots which are visibly correct from some distance away, such as the Figure of Eight Loop, and sailors prefer knots that can be tied one-handed (so you can use your other hand to hang onto something). The nature of the rope to be used matters, too: many knots which were secure in hemp or gut had to be abandoned after the switch to synthetic ropes after the Second World War.

Budworth devotes specific chapters to discussing the knots used by three groups: sailors (of which he is one), anglers and climbers (including cavers). Which is all very interesting, but there's an important (and growing) group of rope-users he leaves out, namely BDSM enthusiasts. While I'm not interested in BDSM per se², I am interested in their approach to knotting: what, I wondered, are the criteria that they use for selecting the knots that they use? Which ones do they select? (And are BDSMers welcome at knotting conventions?)

I tried to work it out from first principles. A human being would be very unlikely to exert enough force to snap a modern rope, so breaking strain probably wouldn't be a consideration. Security, on the other hand, probably would. But there, I got stuck.

I was forgetting something, of course. Now we have an Internet, we don't need to wonder about things any more: we can simply go and find out. A quick search turned up this page, which answered many of my questions. Many of the usual suspects turned up: the reef knot, the lark's foot, the bowline, etc. No bends - I suppose BDSMniks have little occasion to join ropes together. I was rather surprised to see the Prusik knot (used by climbers to ascend a rope) - the author advocates using it as an adjustable loop. I'd have used a Tarbuck knot for that, but I suppose the Prusik is easier to check visually. I hadn't come across the French bowline before, but it turned out that that was the key to the mystery, for I had failed to spot the two key factors at play. When your hitching post is a human limb, it's vitally important to (a) minimise the pressure (force/area) on the skin - this means using lots of turns or loops to maximise the area of rope in contact, and (b) choose a knot that doesn't tighten under load, or you could constrict blood vessels. The lashings (knots used to hold two struts, or in this case, limbs, together) used follow a similar pattern - many loops of rope where only a couple would usually do. I imagine this improves the security of the lashing, too.

Googling for "bondage site:igkt.net" suggests that the International Guild of Knot Tyers (whose Vice President, mathematicians may be interested to learn, is the Fields Medallist and famous knot theorist Vaughan Jones) is well aware of the use of knots in bondage, but somewhat divided about whether or not to discuss bondage ropework on their main forum :-) It also appears that the analysis of breaking strain above is too simplistic - the precise geometry of each instance of a knot matters too.

1 A bend is a knot used for joining two ropes together. A hitch is a knot used for attaching a rope to a solid point. Annoyingly, the Fisherman's Knot is a bend, and the Fisherman's Bend is actually a hitch.
2 Though judging from my friends page, quite a few of you are: perhaps you'd care to comment? This is a public post, but feel free to comment anonymously if you'd rather.
pozorvlak: (babylon)
Thursday, October 25th, 2007 10:41 am
This point came up in a conversation over on [livejournal.com profile] steerpikelet's LJ, and I thought it bore repeating here. Partly because it's important, but mostly because it allows me to talk about one of my favourite bits of maths, namely probability theory.

The failure rates of contraceptives are invariably quoted per year, rather than per use. So when people say that condoms have a breakage rate of 3%, this does not mean that for every 100 condoms you use, you can expect 3 to split: it means that for every 100 couples who have been using condoms for a year, 3 couples will have had at least one condom split on them. The difference is dramatic; let's see what would have happened if 3% of condoms split. In that case, every time you use a condom, it has a 97% chance of not splitting. So if you use, say, 100 condoms, the chance you won't experience any breaks at all is the product of the probabilities of each condom not breaking, i.e. 0.97 x 0.97 x ... x 0.97 = 0.97^100 = 0.047... . Which is to say that if 3% of condoms split, and you had sex 100 times in a year, you'd have only a 5% chance of not experiencing at least one broken "condom". And you'd have more than an 80% chance of experiencing two or more condom breakages in that year: the probability of exactly one condom breaking is 0.03 (for the broken condom) x 0.97^99 (for the 99 unbroken ones) x 100 (choices for which condom is the broken one) = 0.147, so the probability of two or more breaking is 1 - P(none break) - P(exactly one breaks) = 1 - 0.047 - 0.147 =~ 0.806. Such a "contraceptive" would be effectively useless.

"Blimey, guv'nor," I hear you say, "100 times a year? Are you avin' a laugh? It's all right for you layabout students with your peace marches and your LSD, but some of us have got to work for a livin'." Well, OK, suppose you have sex 20 times a year and use special fundie condoms that break in 3% of uses. Your chance of not experiencing any breaks would be 1 - 0.97^20 = 0.456..., which is to say that you've only got a bit better than a 45% chance of not seeing a broken "condom". Like I said, effectively useless.

Let's return to reality, and try to work out the actual per-use failure rate of real condoms. Suppose, again, that the couples in the studies had sex on average 100 times a year (adjust up or down as you prefer). Then the probability of a given condom not breaking is the 100th root of 0.97, which is 0.999695. So the chance of it breaking is actually 0.03%. If the couples had sex on average 200 times a year, we'd get 1 - (0.97^(1/200)) = 0.015%.

This is important to know about, because the less-scrupulous opponents of contraception will frequently quote per-year failure rates as if they were per-use rates (when they don't just lie outright, that is). And they're right: if condoms did fail on 3% of occasions, there wouldn't be much point in bothering with them. But they're actually much, much better than that. So if anyone ever says "condoms are useless, they fail 3% of the time", now you know what to say to them.

[Beware also the difference between breakage rate (interesting for STD protection) and conception rate (interesting for, well, contraception). Also, according to the site linked above, about half of breakages occur when you're putting the condom on, and are therefore harmless. Assuming you don't do something stupid like say "oh bugger, that was the last one, we'll just have to carry on without one." Mathematics is powerless against such stupidity.]
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pozorvlak: (gasmask)
Monday, June 25th, 2007 11:43 am
One evening in Carvoeiro last week, I was telling one of the other grad students (an American girl called Emily, who's just finished Part III at Cambridge) about a memorable logic exercise I'd done in my first year as an undergraduate. The story goes that lesbianism was never made illegal in Britain (unlike homosexuality between males), because Queen Victoria refused to believe it happened. "Only men admire only women," she apparently declared, and refused to sign the bill.

But here's the thing: she almost certainly didn't mean that. )
pozorvlak: (Default)
Monday, May 21st, 2007 10:21 am
Back in 1998, I had a job at JET, the Joint European Torus, one of the world centres of research into nuclear fusion. The complex sprawled over most of the former RAF base at Culham, but the heart was the Machine: a huge torus of metal, machined to precisions of thousandths of an inch, which during experiments contained a few milligrammes of heavy hydrogen at a temperature ten times that of the Sun's core.

This machine pumped out what was at the time a daft amount of data: all the instrument readings and all the analyses of those readings came to around 120MB per run of the Machine (or "shot", as they were called). This was then fed into a wonderfully crockish home-brewed database system running on an IBM 390 mainframe. The system pre-dated the current ubiquity of relational databases, so it was actually a hierarchical database, something that most modern geeks haven't even heard of. The system operated in layers: recently requested data was held in RAM, data that hadn't been requested for a while lived on hard drives, data that hadn't been requested for longer than that lived on tape drives, and data that hadn't been requested for long enough was exiled to the Stygian depths of the tape store: your request for, say, deuterium-band emission spectra from May of 1983 would cause a small, red-eyed robot to trundle off into the tape store, fetch the tape with your data series, trundle back, and physically load it into the mainframe. I used to get lifts to work from the database administrator, and he hated the little robot: it was apparently always breaking down, and he'd then have to crawl in and fix it. "And the red eyes are really sinister! It looks like it's plotting against you."


An integral part of the JET database architecture. Possibly.

The JET Joint Undertaking had been founded in 1978, and had been collecting data for most of the time since. This all added up to a lot of data. My friend apparently used to go to conferences for administrators of large databases just to laugh at what everyone else considered "large".

By performing a simple calculation ) we get an estimate of 900 GB (which is to say nine hundred thousand megabytes) for the total amount of data collected by the JET project in twenty years.

As it happens, 900GB is only slightly larger than [livejournal.com profile] dreamstothesky's porn collection, which currently stands at around 880GB...


The JET Machine: red-hot nucleus-on-nucleus action
pozorvlak: (kittin)
Sunday, April 29th, 2007 12:03 am
From the mighty Wikipedia, in the article on Henry VIII:

Technically, Henry was married only twice. Four of his marriages were annulled, which technically means they never happened at all.

In other words, four of his marriages were retconned out of existence, like the original Supergirl :-)

By the way, the links from the Henry article provide yet further evidence of Wikipedia's insane greatness. There are articles on Henry's chief mistresses, almost all of his children (illegitimate or legitimate), including a couple who only lived for a day, and even his court jester.

Edit: yet more exciting historical trivia! It seems that Camilla, Duchess of Cornwall (mistress and then wife of Prince Charles), is not only descended from Alice Keppel, the mistress of Edward VII (which I knew), but also from Arnold Joost van Keppel, catamite of William III!1 It's a wonder the Keppel clan still get invited to Royal garden parties, really...

1 Whom some of you may remember from Quicksilver...
pozorvlak: (Default)
Monday, January 29th, 2007 10:40 am
The two or three of you who don't already read xkcd may like this:

http://syndicated.livejournal.com/xkcd_rss/49065.html?view=1775529#t1775529

I do like [livejournal.com profile] cambler's comment (currently third from the top).
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pozorvlak: (babylon)
Tuesday, November 21st, 2006 04:02 pm
Interesting article from LiveScience.com, about some researchers who investigated networks of sex and relationships at US high schools, and discovered that they're fascinatingly different from adult networks.

But there's something else they don't mention - if I'm reading that diagram right, then out of over 800 students over 18 months, there was only one gay relationship! Whether it's due to under-reporting or active repression, I think that's worth mentioning - statistically, you'd expect about 80 students to be gay/bi/whatever, IIRC...

[Edit: I wasn't reading it correctly - there were actually three. Still, that's still rather less than I'd expect... And I note that one of the guys who's connected to another guy is also connected to six girls - in denial, or just rapacious, I wonder? And the two connected girls share a boyfriend :-)]
pozorvlak: (Default)
Tuesday, August 8th, 2006 03:25 pm
Perhaps not entirely SFW - contains Rude Words )

See the thread here for some idea why. I especially like [livejournal.com profile] citizen905's comment.

This photo, naturally, comes courtesy of [livejournal.com profile] jwz. What, you mean you haven't subscribed to his blog yet?
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