Tetraphobia: the number the world builds around

The floor that isn't there

In elevators across much of East Asia, the buttons run 1, 2, 3, 5. At the Wynn in Las Vegas, the omissions run further still: no fourth floor, and nothing at all between the thirty-ninth and the fiftieth. Vancouver has residential towers that skip every number with a four in it.¹ Across the English-speaking world, you’ll find buildings where the twelfth floor is followed by the fourteenth.

Now count the landings. For sure, whoever lives above the third floor opens their door onto the same view they’d have had if the button said 4. Nothing was built or demolished. Eradicating a floor is just a matter of labelling; this particular instance of number-superstition costs nobody anything.

That this phenomenon exists doesn’t, in and of itself, prove that large swathes of the world’s population believe in superstition. But these buildings do tell you that somebody decided it was cheaper to skip a level than to argue about it.

Why four is unlucky in China, Japan and Korea — and what travelled without the sound

Say the Mandarin word for four out loud: 四, sì. Now say the word for death: 死, sǐ. What separates them is a tone, a small shift in pitch across a syllable that’s otherwise the same syllable.² In Japanese and in Korean, even that much is gone. Four is shi and death is shi; four is sa and death is sa.

That’s the engine. Four is the unlucky number across much of East and Southeast Asia — in China, in Japan, in Korea — because you can’t say it without very nearly saying death. Nothing about four itself is at issue: not its evenness, not its squareness, not the four directions or the four seasons or the four humours that so occupied the Greeks. A sound collided with another sound and morphed into a cultural association.

Japanese has a way around it. The language runs two sets of number words, one borrowed from Chinese and one native, so four can be said as shi or as yon. It’s yon you’ll usually hear when someone counts out loud.

But the avoidance runs further than conversation. When Saskatchewan, Canada, ran short of telephone numbers, the committee planning its second area code had 474 available and asked the regulator for 639 instead.

That was SaskTel’s spokesperson. The reporter supplied what she was pointing at: four is considered bad luck in Chinese culture.

The pun can tell you where the superstition began, but how far has it spread? This one crossed an ocean into cities where the words for four and death have never once been confused, and was incorporated into buildings raised by developers who couldn’t tell you what 死 sounds like.

So the sound of these words — the foundation of this superstition in China, Japan and Korea — didn’t travel into English, but a slice of culture did: the expectation that some buyer, some tenant, some guest will mind. What the taboo’s strength seems to follow is where the communities that hold it have settled, rather than any feature of the local language.

There’s a word for all of this, assembled out of Greek: tetraphobia, from tetra, four, and phobos, fear. It belongs to a family of such coinages, most of them built by lexicographers rather than clinicians.

Eight, the lucky number — and the question everyone actually asks

Four has a counterpart. Eight is the lucky number, and it sprang from the same machinery in reverse: 八, bā, sits a shade away from 发, fā: to prosper, to make a fortune.¹ The same accident of sound, the same absence of any reason belonging to the number itself, and the opposite verdict.

China put it on display at the largest scale available. The Beijing Olympics opened at eight minutes and eight seconds past eight in the evening, on the eighth day of the eighth month of 2008 — a run of eights assembled for a ceremony in which nothing else had been left to chance, either.¹

There’s no word for this one. The lexicographers who assembled tetraphobia out of Greek never got round to its opposite: there’s no coinage, in any dictionary you can check, for the person who wants the eight. The fear was named. The preference — the half that leaves receipts — was not.

Set the elevator panels and the ceremonies aside. The question that gets typed into search boxes is blunter than any of it: does the number eight attract money?

As far as we know, nothing about the number 8 reaches out into the world and tilts a fortune toward whoever picks it, much like we don’t expect the number 4 to bring you bad luck. In fact, according to economists, eight doesn’t attract money — it costs money.

Where enough people want the number, the number itself becomes expensive — a licence plate with an eight in it, a house with an eight in the address.

What the number is worth

Let’s start where the market is cleanest. Hong Kong auctions its licence plates in public and publishes what they sell for, which is how a superstition ends up being measured. Ng, Chong and Du, three economists at the Chinese University of Hong Kong, worked through 41,069 plates sold across 292 auctions between 1997 and 2009.

Houses are slower and messier than plates, and the effect shrinks to match. Fortin, Hill and Huang, economists at the University of British Columbia, took in about 117,000 Greater Vancouver sales between 2000 and 2005. An address ending in eight sold for 2.5% more, one ending in four for 2.2% less — but only in neighbourhoods where more than 18% of residents were Chinese.¹ Region-wide there’s nothing to find. The premium sits precisely where the people who carry the convention sit.

The oldest study is still the tidiest. Steven Bourassa and Vincent Peng, working from the University of Louisville in Kentucky, took 2,164 detached-house sales across two adjacent Auckland suburbs between 1989 and 1996: under five square kilometres, similar houses, similar households, which leaves very little besides the number on the door to explain a gap in price. Houses whose address ended in 3, 6, 8 or 9 sold for about 2.4% more: some NZ$7,100 against a mean price of NZ$293,200.⁵

Then they ran the same test on a comparable patch nearby — same city, same sort of houses, same distance from town — where few Chinese residents lived. If the premium were really coming from something else, from wider streets or larger sections or any of the hundred things a house number might quietly stand in for, it should have shown up there too. It didn’t. The only thing that had changed was who lived there.

The ladder has nine rungs, not two

Every article on the subject teaches the same two facts: four is bad, eight is good. But the auction data has all ten digits in it, and the ladder runs a good deal longer than anyone reports.

Eight sits alone at the top. Then a tight band of three, one, two and six; then nine, then zero, then seven. At the bottom, four — and five.

Five is the surprise. It’s discounted about as heavily as four is: roughly 12% against four’s 11% on the four-digit plates, and on the three-digit plates the two swap places. It sits in the same table, drawn from the same auctions, significant in every column the authors ran — and they never mention it. The word five does not appear anywhere in their paper.⁴

One caution before carrying that anywhere. This is Hong Kong. The Auckland study counted five among its lucky digits in combination — the opposite verdict, in a different market, and nobody has reconciled the two.⁵

Meanwhile, in the West

The West has its own missing floor, its own unlucky number, and its own Greek coinage for it — triskaidekaphobia, built the same way and no more clinical. Thirteen is older than the four, and its origins are harder to pin down.

Tok Thompson, an anthropologist at USC, went looking for where it came from and found the same association in traditions with no obvious route between them: early Europe, the Aztec world, several Native North American peoples, pre-Buddhist Tibet. His explanation is a calendar. A year holds about 12.41 lunar months — more than twelve, fewer than thirteen — so any culture keeping time by both the sun and the moon is left with an awkward, irregular thirteenth month to dispose of. Thirteen is the leftover. He offers this as a hypothesis rather than a finding.⁶

If he’s right, the two taboos on this page were built by opposite methods. Four is an accident of sound that then travelled with the people who made it. Thirteen was stumbled upon separately, several times over, by people looking at the same sky. Neither has anything to do with the numbers.

And like any convention, it drifts. In Greece, Spain and Mexico the unlucky day is Tuesday the thirteenth rather than Friday.⁷ In Italy the unlucky number is a different one altogether — seventeen, and the date to be wary of is Friday the seventeenth.⁸

In 2007, Gallup asked a thousand Americans how much it would bother them to be given a hotel room on the thirteenth floor. Eighty-seven per cent said it wouldn’t. Thirteen per cent said it would, a figure Gallup reported with some visible pleasure. And of those, nearly three-quarters said they would ask to be moved — nine per cent of everyone asked, willing to trouble a stranger at a front desk over a number.¹¹

What thirteen is worth: nothing

So somebody went and looked. James Larsen, a finance professor at Wright State University in Dayton, took 3,701 single-family house sales in his own Montgomery County, Ohio, and asked what a thirteen in the address was worth.⁷

Nothing at all. Not a small effect, not a suggestive one — nothing. He widened it to more than eighty thousand sales, counting a thirteen anywhere in the house number, and got the same nothing.

Then he did the thing that makes the paper worth reading. He ran the identical test on every other house number — ninety-eight more times. Seven came back with a price effect: 7, 25, 27, 34, 40, 54 and 59. Nobody has ever thought 27 lucky. Nobody crosses the street to avoid 54. Larsen’s own conclusion is that all seven are coincidence — roughly the crop you would expect from running the same test a hundred times over.

The same thing happened to the stock market, more slowly. Kolb and Rodriguez, at the University of Miami, reported in 1987 that returns on Friday the thirteenth ran below other Fridays, and the finding has been famous ever since.¹² Nobody has managed to reproduce it. When Brian Lucey, a finance economist at Trinity College Dublin, went back over nineteen national indices, he found no support for it anywhere — and something stranger in its place: on Friday the thirteenth, returns tended to run higher, in eleven of the nineteen by enough to count.¹³ Nobody has explained that either.

The claim that fell apart

The strongest version of this idea ever published says that the number 4 can kill you.

In 2001, the BMJ carried a study of US death certificates by David Phillips, a sociologist at the University of California, San Diego, reporting that cardiac deaths among Chinese and Japanese Americans peaked on the fourth of the month: the date that sounds like death in both languages. The authors named it the Hound of the Baskervilles effect, after the Conan Doyle story in which a man is frightened to death. The mechanism they proposed was stress: the dreaded date finishing off the already ill.¹⁴

This finding has come apart in three separate places.

The heart-disease category was assembled from five of the thirty-six available codes, where the same author had used all of them in earlier work. The peak was measured against the average of the surrounding days rather than against the days on either side of it.¹⁵ And when Panesar and colleagues, at the Chinese University of Hong Kong, repeated the test in their own city — more than ninety-five per cent Cantonese-speaking — using those same five codes, checking the fourth, the fourteenth and the twenty-fourth against both the Western and the lunar calendar, none of those days stood out from any other.¹⁶

The effect is missing from the population that holds the taboo the hardest. That’s close to fatal.

It also points at something the clinical pages have wrong. Search for tetraphobia and you’ll be offered treatment — exposure therapy, coping strategies, a way to be rid of it. But the thing this study went looking for was never a disorder. Almost nobody who avoids a fourth floor is frightened. They’re observing a convention, the way you say bless you to a stranger’s sneeze without holding any theory about the soul. A phobia is a distressing, disabling fear, and it is rare. This is a manner, and it is everywhere.

Where the cost actually goes

So why does four impact a price and thirteen doesn’t?

Look at what each number is attached to. A Hong Kong licence plate is a number and nothing else. You cannot relabel it, cannot renumber it. If you want the plate, you bid for the number. The taboo has nowhere to go but into the price, and the auction records it to the dollar.

A house isn’t like that. Neither is a floor.

Larsen noticed this on his way out of the paper, and declined to chase it. American streets run the odd numbers down one side, which makes 11, 13 and 15 interchangeable for any given lot — whichever house number the developer picks, it’s the same house on the same ground. His sample holds seventy-one sales at number 11, and a hundred and three at number 15. At number 13 it holds twenty-nine. He suggests developers in the area “have avoided the use of 13 as an address, but no formal analysis of the possibility has been conducted here,” files it as an interesting extension of the research, and stops.⁷

Here’s what we think that adds up to, and this is our reading rather than anyone’s finding. The taboo always leaves a mark. What changes is whether the mark is a price. Where the number can be avoided at no cost — a floor renamed, a lot numbered 15 instead of 13 — the mark is the label itself, and the market never sees a bill. Where the number can’t be separated from the thing it names, there’s nowhere for it to go, and it turns up in the price.

Thirteen is not the weaker superstition. It is the cheaper one to obey.

And when it can’t be settled in advance with a pen, somebody absorbs it later. Somewhere tonight a hotel guest is being moved to another floor, and a front desk is paying for a convention in minutes.

Nobody had to believe it

The economists who put a price on all this don’t believe any of it, and they say so in the middle of their own paper.

They measured it anyway. What somebody pays is a fact whatever the reason behind it — and the interesting part is how many of the payers would have agreed with them.

Go back to Auckland, to the oldest study on this page. Bourassa and Peng cite a survey of the city’s buyers taken a few years before their own data ran out. Buyers who said they didn’t believe in feng shui still preferred lucky house numbers and still avoided unlucky ones, “because they are concerned about resale prospects.”⁵

That’s the whole mechanism, printed in 1999. You don’t have to believe in the superstition yourself. You just have to think the next buyer might.

Fortin, Hill and Huang met the same thing from another direction in Vancouver. The price effects turned up in repeat sales in neighbourhoods where hardly anyone holds the belief — not like seeking a fortune, but like buying an address in order to sell it on.¹

If what these studies price is agreement rather than belief, it ought to be less durable than a superstition sounds. Two findings point that way, and we have both at one remove — reported in a survey of the literature rather than read in the original. Chinese companies that listed under lucky code numbers traded at a premium that was gone inside three years. On the Tokyo exchange, returns ran low on the fourth of the month for decades, then faded from the mid-1980s as foreign money arrived with no opinion about the fourth.¹⁷

When the unlucky number is the product

Everything so far has treated an unlucky number as something to dodge or to outbid. There’s a trade that sells it.

Whenever a Friday falls on the thirteenth — which happens once, twice, or three times a year — tattoo shops put out a sheet of small ready-made designs at thirteen dollars apiece and a queue forms on the pavement outside. The convention is to add a seven-dollar tip, for luck. Oliver Peck, of a shop on Elm Street in Dallas, is credited with turning the date into an event in 1995; by one reporter’s account, his shop expects something like twelve hundred customers in the twenty-four hours.¹⁸

A number that costs a Hong Kong bidder a fortune is, on this one day, the entire product, and it costs thirteen dollars.

There’s even a little experimental support for the digit doing the work. Swee Hoon Ang, a marketing professor at the National University of Singapore, put lucky and unlucky alphanumeric brand names in front of Chinese consumers and found the lucky ones judged better made and likelier to succeed.¹⁹ That’s perception measured in a study, not sales in a shop. Nobody has shown a company losing money by shipping a 4.

New Mexico went the other way, and left better paperwork. In 2003 the state asked to be rid of a number. US Route 666 ran up through Gallup and Shiprock, and the legislature resolved that people “refuse to travel the road … because of the fear that the devil controls events” on it, and that the infamy of the name “will only make development in the area more difficult.” No one measured any of that; the legislature asserted it and acted on it. Highway officials from three states applied, and on the last day of May 2003, the road became US 491.²⁰

What it turns out to be

The elevator, one last time. The landing above the third is exactly where it always was; the button beside it says 5. Somebody made that call on your behalf, at no cost to anyone. If you asked them, most would tell you the number means nothing to them at all.

That’s what most of this turns out to be — not a fear but a courtesy, performed by people who don’t hold the belief for the benefit of people who might. Now and then the courtesy runs out of places to hide, and it surfaces in the price of a plate, or a house, or in a road sign three states wanted rid of.

The economists who totted up the receipts end their paper like this: