Toss out the toss-up: Bias in heads-or-tails

W W W. S C I E N C E N E W S. O R G F E B R U A R Y 2 8 , 2 0 0 4 V O L . 1 6 5 1 3 1

CA

RN

EGIE

INST

ITU

TIO

N

Hard StuffCooked diamondsdon’t dent

Popping diamonds into a high-pressure ovenfor a few minutes can render the famouslyhard minerals even harder, researchers havefound. In particular, pressure-cooking arecently developed type of synthetic dia-mond has yielded the hardest single-crystaldiamond material ever tested, claims Russell J. Hemley of the Carnegie Institu-tion of Washington (D.C.). Single-crystaldiamond has a consistent geometric orderof atoms throughout, making it desirablefor uses ranging from jewelry to electronics.

The new material is so hard that toolsused to gauge hardness left no mark on sev-eral of the crystals, Hemley and otherresearchers say. In fact, the researchersbroke equipment worth about $10,000 intheir attempts at measurement.

Because the treated diamonds are alsohighly tough, or fracture-resistant, they mayprove superior for many uses, Hemley andother researchers say. They suggest the mate-rial may serve as anvils for high-pressureresearch, coatings for cutting tools and bio-medical implants, and wafers for electronicsthat must operate under extreme conditions.

Hemley and his colleagues at the CarnegieInstitution, Los Alamos (N.M.) NationalLaboratory, and Phoenix Crystal Corp. inAnn Arbor, Mich., present their findings inthe March Physica Status Solidi (a).

Some materials researchers are skepti-cal about the hardness measurements thatHemley’s team reports. Michael Popov ofthe Max-Planck Institute for Chemistry inMainz, Germany, and the Russian Acad-emy of Sciences in Moscow says that theteam should have used a different, also stan-dard, technique that some other recenthardness investigations have employed.

In the new data’s defense, Hemley notesthat he and his colleagues used their meas-urement method on a variety of types ofnatural and synthetic diamonds of knownhardness and obtained the expected values.

To create the diamonds that were so hardas to be unmeasurable, the group started

with a technique that Hemley and anotherteam, including some of the same Carnegiescientists, had previously developed (SN:9/14/02, p. 165). In a process known aschemical-vapor deposition (CVD), theresearchers rapidly deposited carbon atomsonto an ordinary diamond. They then cutthe new diamond free from the substrate.

However, extraordinary hardnessrequired another step: heating to 2,000°Cunder pressure like that found 150 kilome-ters or so beneath Earth’s surface. The newstudy indicates that natural diamonds ofone of the two types tested also show bigjumps in hardness when subjected to theheat-and-squeeze treatment.

The treatment is a type of annealing, awidely used process for modifying metals,metal alloys, and other materials. For dia-monds, annealing had previously been usedonly to change the mineral’s color.

Tetsuo Irifune of Ehime University inMatsuyama, Japan, calls the work a “signif-icant advance in synthesizing hard, single-crystal diamond.” He says he shares Popov’s

doubts about the accuracy of the new hard-ness measurements. Nevertheless, “it seemsclear that the new CVD diamond is harderthan normal natural and conventional syn-thetic diamonds,” Irifune says.

“The [hardening] mechanism is not wellunderstood and should be furtherexplored,” he adds.

Hemley says that his team has studiesunder way with that goal in mind. —P. WEISS

Toss Out the Toss-UpBias in heads-or-tails

If you want to decide which football teamtakes the ball first or who gets the largerpiece of cake, the fairest thing is to toss acoin, right? Not necessarily.

A new mathematical analysis suggeststhat coin tossing is inherently biased: A coinis more likely to land on the same face itstarted out on.

“I don’t care how vigorously you throw it,you can’t toss a coin fairly,” says Persi Diaconis, a statistician at Stanford Univer-sity who performed the study with SusanHolmes of Stanford and Richard Mont-gomery of the University of California,Santa Cruz.

In 1986, mathematician Joseph Keller,now an emeritus professor at Stanford,proved that one fair way to toss a coin is tothrow it so that it spins perfectly around ahorizontal axis through the coin’s center.

Such a perfect toss would require super-human precision. Every other possible tossis biased, according to an analysis describedon Feb. 14 in Seattle at the annual meetingof the American Association for theAdvancement of Science.

The researchers’ logic goes like this. Atthe opposite extreme from Keller’s perfecttoss is a completely biased toss, in whichthe coin stays flat while in the air. Since thecoin never actually flips, it is guaranteed toland on the same face that it started out on.

Between the perfectly spinning toss andthe flat toss lies a continuum of other pos-sibilities, in which the coin spins around atilted axis, precessing like an old-fashionedchildren’s top. Each of these possibilities isbiased, the team found. The bias is mostpronounced when the flip is close to beinga flat toss. For a wide range of possible spins,the coin never flips at all, the team proved.

In experiments, the researchers were sur-prised to find that it’s difficult to tell fromwatching a coin whether it has flipped. Acoin toss typically takes just half a second,with the circumference of the coin whizzingaround at 3 meters per second. What’smore, the coin’s spin makes it wobble, oftencreating the illusion that the coin hasflipped.

“Sometimes we had the complete impres-sion that the coin had turned over when itreally hadn’t,” Holmes says.

Magicians and charlatans may takeadvantage of this illusion. Keller observes,“Some people can throw the coin up so thatit just wobbles but looks to the observer asif it is turning over.”

To see whether the predicted bias showsup in actual coin tosses, the team mademovies of tossed coins and then calculatedthe axes of spin.

Their preliminary data suggest that acoin will land the same way it started about51 percent of the time. It would take about10,000 tosses before a casual observerwould become aware of such a small bias,Diaconis says. “Maybe that’s why societyhasn’t noticed this before,” he says.

This slight bias pales when comparedwith that of spinning a coin on its edge. A

HARD TO RESIST When exposed to highheat and pressure, single-crystal diamondslike this synthetic gem becomeextraordinarily hard, a new study shows.

SCIENCENEWSThis Week

FOBS.2-28 2/25/04 15:13 Page 131

REI

SS/N

ASA

,STS

CI

S C I E N C E N E W S

spinning penny will land as tails about 80 percent of the time, Diaconis says,because the extra material on the head sideshifts the center of mass slightly.

During World War II, South Africanmathematician John Kerrich carried out10,000 coin tosses while interned in a Ger-man prison camp. However, he didn’trecord which side the coin started on, sohe couldn’t have discovered the kind of biasthe new analysis brings out.

Says David Aldous, a statistician at theUniversity of California, Berkeley, “This isa good lesson that even in simple thingsthat people take for granted, there may beunexpected subtleties.” —E. KLARREICH

WrenchingFindingsHoming in on dark energy

Something is pulling the universe apart,causing galaxies to flee from each other atan ever-faster rate. Since 1998, whenastronomers discovered this bewilderingstate of affairs, theorists have been strug-gling to comprehend the mysterious sourcedriving the runaway expansion. Now,researchers have taken one of the first stepstoward identifying this bizarre influence,often known as dark energy.

In an analysis of a group of bright butdistant exploding stars called type 1a super-novas, researchers have found hints thatdark energy is distributed uniformlythroughout space and that its strength willremain constant throughout time. Thatwould make dark energy resemble the cos-mological constant, a term that Albert Ein-stein introduced into his general relativitytheory in 1917 and quickly abandoned, butwhich physicists have resurrected severaltimes since. The cosmological constantrefers to an unspecified property of spacethat could add to or oppose gravitationalattraction.

Adam G. Riess of the Space TelescopeScience Institute in Baltimore announcedthe new findings during a teleconferencelast week. He and his colleagues will alsodescribe their analysis in the June Astro-physical Journal.

In the study, Riess and his collaboratorsanalyzed the brightness and colors of 16type 1a supernovas, all of which the Hub-ble Space Telescope had discovered. The

group includes six of the seven most dis-tant supernovas known.

“These results are going to be an impor-tant foil for [testing] ideas about darkenergy,” says Robert R. Caldwell of Dart-mouth College in Hanover, N.H.

Because all type 1a supernovas haveabout the same intrinsic brightness, theyserve as cosmic markers, enabling research-ers to measure the size and expansion rateof the universe at different times in the past.From the expansion rate calculated fromthe new data, Riess’ team suggests that theuniverse experiences a constant push. Thisfinding is consistent with dark energy beingthe cosmological constant.

Because the cosmological constant wouldexist even in the absence of matter or radi-ation, dark energy might be an intrinsicproperty of space itself. Space on the sub-atomic scale isn’t empty but seething withelementary particles that pop in and out ofexistence on extremely short timescales.Dark energy might result from the activityof some of these particles.

The fate of the universe hinges onwhether the strength of dark energy variesover time, notes Paul J. Steinhardt ofPrinceton University. In the cosmological-constant scenario, the steady push pro-vided by dark energy causes space-time toexpand and the galaxies that lie within itto become ever more distant from oneanother, but they don’t fall apart. In sucha rarefied universe, a resident of the MilkyWay billions of years from now would notsee a single other galaxy in the sky.

In a competing theory known as quin-tessence, which Steinhardt and other the-orists have proposed, dark energy is not afundamental property of space. Instead, it’s

associated with some unidentified energyfield that has variable strength. If this fieldgrows stronger, it will not only expandspace-time but also shred every galaxy, star,and atom, ending the universe in what’scalled the Big Rip (SN: 3/8/03, p. 148). Ifthe energy field weakens sufficiently, thegravitational tug of matter will eventuallyoverwhelm it, and the universe will ulti-mately collapse, ending in a Big Crunch.

The new study of exploding stars dou-bles the precision of previous supernova-derived data on the character of darkenergy. At the same time, both Steinhardtand Riess agree, the new data don’t rule outmost versions of quintessence. —R. COWEN

Fox SelectionBottleneck survivors showsurprising variety

Foxes native to a California island—andfamous for having the least genetic diver-sity ever reported in a sexually reproduc-ing animal—have some variation after all.

The San Nicolas Island foxes (Urocyonlittoralis dickeyi) vary considerably in thegenes coding for immune system com-pounds known collectively as the major his-tocompatibility complex (MHC), reportAndres Aguilar of the University of Cali-fornia, Santa Cruz and his colleagues. Thesecompounds help the immune system rec-ognize intruders to the body.

The animals’ unusual pattern of carry-ing some uniform and some varying geneticmaterial may have arisen from two factors.They are a near die-off of the fox population

1 3 2 F E B R U A R Y 2 8 , 2 0 0 4 V O L . 1 6 5

SCIENCENEWSThis Week

UNIVERSAL FATE Dark energy can determine whether the cosmos will end in a Big Crunch,an indefinite expansion driven by the cosmological constant, or a Big Rip.

FOBS.2-28 2/25/04 15:13 Page 132