While unqualified to critique either Russell or Cantor on set theory, I don't hesitate to recommend they both make the leap beyond barber-as-character-in-a-paradox and actually visit one and get rid of that hideous growth!
By Mark Fenton
Published November 13, 2013
this article has been updated
Bottom: I must to the barber's, monsieur, for methinks I am marvelous hairy about the face. And I am such a tender ass, if my hair do but tickle me, I must scratch.
Edwin Landseer - Scene from A Midsummer Night's Dream, Titania and Bottom, 1851.
Captain Torres walks into the barber shop and hangs up a bullet studded belt complete with holstered firearm. Then he hangs up his cap. (The brimmed pillbox favoured by Castro or the more European beret modeled by Che? You decide.)
The barber trembles. No kidding. Captain Torres trains his soldiers to shoot by hanging rebels upside down and designating body parts for target practice. (Yes, the Captain is that kind of mid-20th century martial autocrat.)
As I write it's October 31st and if I thought I could carry it off I'd consider dressing as a Colombian Guerrilla leader and I'd use this description as a starting point.
Here's where things get conflicted. The barber isn't just a barber. He's a rebel sympathizer.
El Capitan has come in for a shave. Nothing more. The barber runs his razor back and forth against the strop as one imagines barbers perpetually do between customers.
Captain Torres settles himself in the chair. The barber lathers his customer. Casual barbershop banter ensues. Torres recounts how a dozen or so rebels hidden deep in the woods were captured earlier that day.
The barber probes politely about whether any might be left. 'Yes,' Torres responds. 'There are still a few, but rest assured they'll be rounded up. It's just a matter of time.' In another country and another era, the new football stadium or the possibility of light rail would be discussed in the same tone of relaxed semi-engagement.
We are in the barber's mind. It is clear he is an artist with a razor. He understands the nuances of the face and has mastered the angle of the blade and the optimum tension against the stubble. He's even perfected how to adjust for thicker clumps of hair.
Above all, he walks the tightrope of getting as close to the skin as possible without tearing it or aggravating the pores.
How hard would it be for a barber this skilled to adjust the angle, increase PSI an iota, and liberate the carotid artery into a crimson fountain, spattering the cape and ceiling and wall calendar.
(I've always imagined a calendar from a supplier, each month illustrated with a specialized shaving product. I don't see our dedicated barber hanging up images of a smiling and swimsuited Miss Bogotá. But this is my embellishment. No words are wasted on décor in this urgent tale.)
While executing the perfect shave the barber considers his options. There is the question of cleanliness (there will be a big mess to clean up if he slaughters the Captain.) And there's the time-honoured eye-for-an-eye argument. If one kills the killer, and then someone kills the killer of the killer, and so on, where does it end?
Is the barber really torn between professionalism (a slaughtered customer, could, one imagines, affect business down the road) and an assassination window that allows the target no chance of escape and retaliation? The gun may only be a few feet away, but the captain would never make it.
Is the barber simply a coward?
The barber finishes the job. His narrow window of opportunity is closed forever. The Captain pays up. He straps on his belt. He puts his cap back on.
He turns to the barber and says that 'they' told him the barber would cut his throat. So he came to find out for himself. "But," Captain Torres concludes. "It's hard to kill. Trust me. I know."
The above is a synopsis of "Just Lather, That's All" (1950) a short story by Colombian author Hernando Téllez.
I don't know when the safety razor arrived in Colombia, or at what point it made economic sense to purchase one rather than continuing to visit the town barber. I do know that in 2013 in Hamilton, few men use a straight razor to shave, and fewer still pay a barber to do it for them.
In a certain town there is a barber, and this barber is a resident of this town. (I've always imagined that the barber walks to work, or failing that that the barber takes some form of public transit. We all have, do we not, an environmentally idyllic picture of the world before our birth?) This barber shaves all the men in the town who do not shave themselves.
Problem: Who shaves the barber? According to the rules of this scenario if the barber shaves himself he doesn't. And if he doesn't shave himself he does.
While Bertrand Russell
does not take credit for the Barber Paradox, he uses it as an example of a flaw he finds in the "naïve" set theory of Georg Cantor.
(Obviously one's CV has to be as jaw-dropping as Russell's to get away with referring to something Cantor proposed as 'naïve.' While unqualified to critique either Russell or Cantor on set theory, I don't hesitate to recommend they both make the leap beyond barber-as-character-in-a-paradox and actually visit one and get rid of that hideous growth!)
Here's how Wikipedia expresses Russell's Paradox and notates it symbolically and I'm so far out of my depth here that I'm just going quote Wikipedia and you're welcome to visit the page on Russell's Paradox and pursue the problem deep into cyberspace:
Let R be the set of all sets that are not members of themselves. If R is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set of all sets that are not members of themselves. This contradiction is Russell's paradox. Symbolically:
I am unsurprised that the conversation in "Just Lather, That's All" avoids set theory completely. When your comrades are being stripped and hung upside down for target practice I don't think these questions are as urgent as they would be to an analytic philosophy professor at Oxford in the early 1900s.
I just can't see it going down like this.
Captain Torres: (idly) ...but we'll soon have every last one of the rebels. They can't hold out much longer.
Barber: Tough line of work. Don't envy you. (And after a silence befitting the description of an atrocity.) Here's something that might take your mind off-Ugh! Those diabolical ingrown hairs! Might I ask that you remain particularly still as I just carefully-there-it's out-What was I saying? Oh, right. Here's a puzzler. A certain town has a barber. A barber much like myself. A barber who shaves all men who do not shave themselves. Who then shaves the barber? It's an irresolvable paradox. If he shaves himself he doesn't and if--
Captain Torres: What frivolity is this? Only an imperialist pig would fret over propositions of logical atomism-problems that in no way benefit the emancipation of the proletariat! I will take my grooming requirements elsewhere, even if it means travelling to another town and-AUUGHHH!!!!
(For in his ideological disgust Captain Torres has thrown off the cape, and lurched forward with such outrage and vehemence he has forced the tender skin of his neck into the edge of the blade. The epidermal veil of mortality gives way. The carotid has become an unstoppable purple cascade over the razor and hands of the barber, and a fine spray crimsons the wall calendar whose April image advertises a foam so lubricious the blade skates effortlessly along the neck and leaves the skin smooth as glass. The very life of Captain Torres is an evaporating mist in the room. Weighed against countless victims his fate is just. The barber is blameless. The assassin is a brave new world of academic free thought.)
No. It doesn't happen. The Barber Paradox belongs in the set of "first world problems."
It is 2013 and I am in Hamilton, Ontario. A place more 'first world' even than Russell's Oxford, where people at least had to deal with stuff like air raids and war rationing. (Films and novels of the era portray the shortage of razorblades as particularly gripeworthy).
Russell would have lived though the period during which the straightrazor was all but replaced by the safety razor. Perhaps you remember the iconic blade.
A thin rectangular thing. Sharp on both sides. It was what I used when I first started shaving and you laid it flat onto a bed that lay perpendicular to the handle, and when you twisted the bottom of the handle two pieces of metal converged and held the blade in place. Any brand fit.
It seemed to me to do a good job. Among other things it solved the problem of subjecting your throat to a person with unknown political convictions who wields a blade that could kill you in a microsecond.
But at some point in the 1990s these razors became difficult to find. I noted their complete disappearance after 9/11/01.
Here is a picture of what I have going right now in the way of razors.
I am out of fresh blades for them.
I am out of fresh blades for every single f*ing one of them.
Such is my current state of unshavenness that if I wanted to be Bottom as metamorphosed by Puck, all I'd need is a pair of big novelty ears which I know I've seen at Fortinos.
It is a filthy rainy day this October 31st and I am not in the spirit befitting the costumed day that brings gently creepy joy to small children.
As usual our neighbours have installed their ghost Ku Klux Klansman blow-up doll.
For what is more chilling to the tots than wandering spirits of an ethnic terrorist organization. The crazed Klansman frightens and depresses me at my very core. Members of our species chasing fellow members deep into the woods and annihilating them. When will it end?
I put Halloween out of my thoughts and return to my quest for razorblades. Nothing is simple. One size that fits all devices is pure 20th century nostalgia. All I'm able to buy now are long strips of blade embedded in plastic. It's a stretch to call these things razorblades. And no two are the same.
For a start there's the quantitative phenomenon of how two blades became better than one. And then three became better than two. And then four became better than three, etc... Where, where is this supposed to end?
The barber shaved Captain Torres with a single blade, not five stacked blades in dexterous parallel motion. (I think you'll agree this would have set off serious alarm bells in the already suspicious Captain.)
And despite the fact that these multiple blades are so thin, and embedded in such a way that you couldn't possibly extricate them from the plastic and wield them as a weapon, you still can't get them through security in a carry-on.
As usual I end up having to visit several stores. This photograph is typical of what I find. Most rows are empty. They almost don't sell refills. It's usually a whole new system they want to stiff you for.
For once I'm not simply taking photos in a store to get retailers into a lather.
For once I actually need to get a photo of the attachment process so I can compare it to the action on one of the six razors I've accumulated at home. Because I am not going to fall into the trap of buying the wrong kind of three, four or five blade refill and then - having kept them, as I always do, for so long that I have forfeited my return option - going out to buy the razor handle that I'm almost certain these blades fit so that I will at least have another handle/blade option and not waste the erroneously purchased blades.
But when I get home I will discover that this razor handle fits neither the blades I erroneously purchased, nor any other refills I erroneously purchased in past weeks, months and even years and which refills are gathering dust in a closet.
I will not do that anymore. I will now go out and do photo-recon on purchasable blades and return home and examine the photos against my existing razor handles, most of which, I know full well, are by now obsolete.
But in order to get these photos I have to pull open a transparent thermoplastic flap that every time I do deploys a sound somewhere between the siren of a European police vehicle and a dental drill. A sound alerting staff to likely shoplifters of small merchandise, or at the very least alerting them to a guy taking photos of merchandise and, trust me, they don't like you doing that.
But even that's not where it ends. Because there's a further selection of refills behind the checkout counter which I'm not allowed to just browse.
There are still more blades hanging behind the clerk alongside batteries and other easily pocketable and in some cases not-quite-G-rated items like cigarette lighters depicting scantily clad women and what appear to be niche market condoms that I've never asked to examine and that are sold in twos and that I suspect you might have to show ID for if the clerk deems you sufficiently youthful and unjaded.
Why certain razorblades are behind the counter and others aren't I couldn't possibly say, but I now have to ask to be allowed to handle each of these others to determine from the back illustration whether they might possibly fit one of my six on-the-go razors, and don't even ask if you can photograph the backs of the packaging.
If photos are grudgingly tolerated in the aisle, up at checkout the photographer is pegged as a collector of debit card PINs or of lottery ticket numbers as though the photographer could do something diabolical with that information at home.
The lineup behind me lengthens. Customers stare at me as if to say, 'This stuff isn't that complicated.'
And my daggerlike and justified stare says back to them, 'And how often do I stand serenely as you decide which lottery ticket to buy. Even knowing that the fortune, should you blindly have chosen the winning number, won't liberate you from your true chains, I nevertheless wait patiently as you vacillate over the cards as though your very salvation depended on it. I, on the other hand pursue no grail beyond that most humble of men's' desires: the near post-coital satisfaction of a half-decent shave. So suck it up.'
While I don't have Bertrand Russell's irreconcilable problem of accounting for sets that are members of themselves, I do have the irreconcilable problem that the set of all the razor handles I have at home refuse to overlap with the set of all refills I can buy at a store.
It doesn't seem mathematically possible that today, this October 31st, the stores are stocked with blades that don't match the razor handles I have at home, and in fact, don't match any of the razor handles that they are selling. It doesn't seem possible, but that's how it is.
(And, yes, I'd be the first to agree that the courageous and doomed men and women in the Colombian woods would love to have my problem with razorblades as they instead await the arrival Captain Torres's death squad.)
I returned home empty and despondent. I wished I had a straightrazor to wield against the ghost Klansman and make him my helpless, groveling slave. But someone had beaten me to it, leaving him bowed like a spent prophylactic.
After the emotional exhaustion of writing Section 3.1 I took a break and checked my Yahoo mail. The ad-tag at the top of the homepage read, "Why Are The Big Razor Companies Afraid of This Man?"
As I want the big razor companies to be afraid, and as I can't really afford to ignore any razor options if I ever hope to be freed of my Bottomlike donkey-visage. I followed the link to dollarshaveclub.com.
He introduces himself simply as Mike. Already warning bells go off. How exactly do I find this guy if I order from him and am unsatisfied with the product? "Dollarshaveclub how may I direct your call?" "I'd like to speak with Mike." "Sir, we have 17 Mikes. Do you have a last name?"
He is so clean and close shaven he might well put the barber of "Just Lather, That's All" to some kind of shame. But I don't see him shaving. In fact I don't see a razor, or anything that manufactures razors, other than this illustrated detail when he tells us that even a toddler could use his product, it's so smooth.
This, incidentally, is the image from the video that interests me the most. (Question: Would even the seemingly fearless Captain Torres have the cojones to get in the chair if he walked in and found a three-year-old wielding the blade?)
The female toddler provides a compelling loophole to the Barber Paradox and I'm tickled that clean-shaven Mike took a logic class back in the day and is choosing to riff on it.
See, if you simply phrase the problem as "In a certain town there is a barber who shaves every man who does not shave himself..." but don't specify age or sex of the barber, you can make it work. Because not being a man, the barber neither shaving herself nor being shaved by the barber is irrelevant.
She isn't in the set of "all men in the town" (and on a more basic level, I'm guessing she doesn't actually, um, shave). So self-referentiality is gone.
I'll admit this loophole is sneaky and not what Russell's Paradox is set on untangling. Probably some smart-ass philosophy undergrad used this loophole on an exam and had to be given full marks and subsequently the wordy-to-the-point-of-sounding-legalistic qualification "who is an adult male" always gets added into the scenario.
I don't see any machinery, so I'm guessing Mike doesn't actually manufacture the razorblades, he just buy's them wholesale from China and ships them. All I see are boxes and now that I think about it, they aren't a size I imagine razors being shipped in.
In fact the whole production of this video impresses me as a maverick theatre troop with a Nikon who found an open loading dock and walked onto the warehouse floor and shot the ad in a single take.
I admit it. I'm as out of my safe zone here as the barber was with Captain Torres.
Concert pianist Alfred Brendel stated in an interview I read years ago that he possesses thick fingers that slip dangerously on the surface of the piano keys when he begins to sweat. (How his pores would tolerate the blade of a straightrazor I don't even want to imagine.)
In the decades during which he was practicing and performing daily, he solved the problem by applying to each finger a brand of adhesive bandage called Hansaplast. When asked what he would do if Hansaplast were to go out of business, he replied that he'd already purchased a lifetime supply.
(Questions like this are geared to readers who idly pick up the Gramophone in their physician's waiting room and don't really care how many repeats Brendel takes in late Schubert piano sonatas. For surely all magazine readers are amused by weird stuff wrapped around the fingers of a man wearing a tux. NOTE TO SELF: Great costume idea if I am ever invited to a Halloween party in which all other guests are concert pianists.)
So. I'll first consult my GP for an estimate of how many years I have left to live. Then I'll do the math and order the correct number of boxes to supply me with shaves till I die.
I can probably get a bulk deal. And not having to shop for razors will open up a lot of time in my ever-diminishing days. Maybe Mike at dollarshaveclub.com is the man for this. I'll order a sample and get back to you on how it goes, probably as a digression in a future essay about something entire unrelated to shaving.
Then it hit me. What if any adhesive bandage would work. What if Brendel's insistence on Hansaplast was simply product placement? What if Brendel got a kickback in the form of free Hansaplast? Till death do Brendel and Hansaplast part.
The cynic in me is behind the wheel. I Google Alfred Brendel+Hansoplast to determine if the man is indeed Hansaplast's posterboy.
But I come up with nothing. It appears Herr Brendel has too much integrity to promote anything but classics of European concert music.
And Hansaplast has had to settle for professional models to advertise its product-line.
In that spirit you'll note that I've avoided brand names. I don't want any 'big razor company' to gain a single additional hit from to this essay when its name goes into Google.
Editor's Update: RTH received the following email from Dollar Shave Club:
Hey Raise The Hammer,
This is Cassie Jasso, the community manager for Dollar Shave Club. I am reaching out because of this article written by Mark Fenton: http://raisethehammer.org/article/2010
Thank you for writing about our video, and we hope you really think it was F****** [sic] Great! For the record, a young female toddler really did shave a man's head for the video. However, the reason I'm writing to you is this: we would really appreciate if you could insert a link to DollarShaveClub.com when you mention us in the article. We are so happy you wrote about us already, and would love if you could include the link.
Thank you, and please let me know if this will be possible.
I asked Mark how he felt about this and he replied:
Yes, definitely accept. I may have been unclear here because I'm really on dollarshaveclub's side, i.e. we're both fighting the BIG companies who charge 20.00 per package. Was actually hoping to somehow connect through Twitter and pretty tickled they found ME!
As such, I made the reference to dollarshaveclub.com into a clickable hyperlink.
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