Resonance Magazine , 1st January 1996

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5RESONANCE January1996

different areas through a variety of contributions and features:

general articles, series devoted to different aspects of a chosen

subject, guest columns, question and answer and classroom pages

for teachers and students alike, book reviews, research and careernews, correspondence, to name a few. A conscious effort has been

made to work with teachers and students in determining the

contents and writing style ofResonance, and this will expand and

continue.

We welcome contributions, comments, suggestions and criticism

from our readers. Our constant endeavour will be to enhance the

attractiveness and accessibility of material to our readers, keeping

their needs in view. We hope to convey an understanding of con-

cepts, connections between different fields, the experimental methodand the art of rational thinking. We shall also attempt to bring out

an appreciation of science as a human activity, its relationship to

society, and as an important component of culture in todays world.

Not least we wish to make Resonancevisually pleasing.Many persons too numerous to mention have given us

academic and moral support: the President and Fellows of the

Academy, and a very large number of teachers, scientists and stu-

dents in institutions all over the country. We thank them all and

express the hope that they and our readers will continually keep intouch with us and support this effort.

Our constant

endeavour will be

to enhance the

attractiveness and

accessibility of

material to our

readers, keeping

their needs in

view. We hope to

convey an

understanding of

concepts,

connections

between different

fields, the

experimental

method and the

art of rational

thinking.


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SERIES I ARTICLE

Origin (?) of the Universe1.Historical Background

Jayant V.NarlikarThe first part ofthis.series covers the historical backgroundto the subject ofcosmology- the studyofthe structure andevolution of the whole universe. Ancient ideas, such asthose of the Greeks, already show the beginnings of at-tempts to account for observations by natural laws, and toprove ordisprove these byother observations. It needed theinvention of the telescope and studies by scientists likeHerschel and Hubble to reach the current understanding ofour place in our galaxy, and its place as only onemember ofa far larger collection of galaxies which fill the observableuniverse.Primitive Notions of the UniverseAn assessment ofour present understanding ofthe cosmosisbestcarried out with a historical perspective. The written historyavailable today covers a very tiny fraction of the time span ofhuman existence on eanh and an even smaller fraction of the ageof our planet estimated at some 4.6 billion years.Based even onsuch limited documentation we find that our ancient forefatherswereindeed ascurious about natureand the cosmosasweare today.It is against this background that weshould viewthe attempts ourancient forefathers made to understand the universe aroundthem. They added conjectures' and speculations to what theycould observe direcdy. They used fertile imagination to extrapo-late from the known to the unknown. Naturally the differingcultural traditions ledto different cosmicperspectives in differentparts of the world.I am always impressed by the depth of ideas in our Vedas andUpanishads. Those who wrote them had a questioning mind.

RESONANCEI January 1996

Jayant NarIikar,Director,Inter-University CentreforAstronomyand

. Astrophysics,worksonaction at adistance inphysics, new theories ofgravitation and newmodels of the universe.

He has made strong effortsto promote teaching andresearch in astronomy inthe universities and alsowrites extensively inEnglish and Marathi for awider audience on science

and other topics.

This six-part series willcover: 1. Historical Back-ground. 2. The ExpandingUniverse. 3. The Big Bang.4.The Arst Three'Minutes.S. Observational Cosmol-ogy and 6. Present Chal-lenges in Cosmology.

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SERIES I ARTICLE

Ourandentforefathers wereIndeed as curiousaboyt nature andthe cosmos as weare today. I am

always Impressedby the depth ofIdeas Inour

Vedas andUpanishads.Thosewhowrotethem had a

questioning mind.

Flguffl 1 A hlemrdllCtlI COI-lilt1$:One of our many 11n-dent spult1llDII$ In Indll1dll$Cl'/bed the eal'lh 11$f1Sf-Ing on elephants,_ndlngDn 11gll1nt frlrtrNse tht1t wasCtlrrled byl1$naltelHlflng H6own frill.We will come backfrI 1b/6P/duffl In the DnalI1rHdeIn 1b/6.rf..

They perceived the complexityofthe cosmologicalproblem. Thefollowing lines from the Nasadiya Sukta are quite eloquent:

"Then (in the beginning) there was neither existence nor non-existence.There was no space nor was there anything beyond. (In such a situation)what should encompass (what)? For whose benejitl Was there the denseand deep water?"

"Who will tell in detail how and from where canrethe expanse of theexisting? Who knows for sure?Even Gods canreaftercreation. So whowould know wherefrom the creationcanre?"These are fundamental questions which are being asked even bypresent day cosmologistS.Humans however are not satisfied byonly asking questions. One must have answers too - and if onecannot get them one tries to concoCtsome.Soout ofquestions likethese arose answers that werebelievedbymany tobe right. Therewere no scientific proofs for them but nevertheless they becamepart of the mythology and gained intelleetual acceptance.It was during the Greek civilization a fewcenturies beforeChrist,that such speculations began to be viewed somewhat scientifi-cally. The Pythagoreans - the followers of the Greek mathema-tician and philosopher Pythagoras - were worried about the sun-earth relationship. They refused to accept that the earth goesaround the sun (or evenviceversa!).Instead theybelieved that theearth goes around a central fire located elsewhere. The theorypredietably ran into difficulty because of the obvious question:"Why don't we see this fire?" To answer this question, thePythagoreans invented a 'counter-earth' that went around thecentral fire but in a smaller orbit. This orbit, they said, synchro-nized with the earth's orbit in such away that it alwaysmanagedto block the view of the central fire from anywhere on earth.The symptom of a wrong scientific theory is that to keep itSprediction intaCtadditional assumptions have tobemade. Subse-quently even these assumptions become untenable. The


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SERIES I ARTICLE

Pythagorean theory was of this type. First there was the diffi-culty of the central fire not being seen. Next came the problemof why the counter-earth is not seen...and so on. However inspite of our criticism of the theory from hindsight it had themerit that it was a disprovable hypothesis.Karl Popper, the philosopher of science, has laid down thiscriterion for a scientific theory: it should be testable and inprinciple disprovable. In other words weshould be ableto thinkofa testwhose outcome could rule out the theory. If the outcomedoes not disprove it the theory survives- until somebodycanthink of another more stringent test. PoppeJ;'s criterion pro-vides us with a way of distinguishing between philosophicalspeculation and a scientific theory.Aristotle's UniverseAristotle, another Greek philosopher, provided a seriesofprin-ciples that in today's parlance could be called aphysical theory.Hewas a pupil ofthe famous philosopher Plato and the teacherofAlexander the Great. Today Aristotle's ideas are known tobewrong.Yet we should look upon them as man's first attempt atquantifyingthe lawsthat governobservedphenomena.The keytoAristotle'sideasliesin his classificationofdifferenttypesofmotion.Aristotle distinguished two types of motion seen in the Uni-verse: naturalmotionwhich he supposed alwaysto be in circlesand oiolentmotionwhich was a departure from circular motionand implied the existence of a disturbing agency.Why circles?Because Aristotle was fascinated by a beautiful property ofcircles which no other curve seemed to possess. Take anyportion ofa circle(whatweusually calla 'circular arc') andmoveit anywhere along the circumference: that portion will coincideexaalywith thepartoftheciIcleundemeathiL(Thestraightlinealsohasthispropertybut it canbe considereda ciIcleofinfinireradius).In the jargon ofmodem theoretical physics the aboveproperty

Thesymptomof a wrongscientifictheory'Is that to keepIts predictionIntactadditionalassumptionshave to be made.Subsequentlyeven theseassumptionsbecomeuntenable.

F/gut82 Ep/t::ydtII:bJtImp/ilM ht1w, fDllMng Ar/$IotIs,the Greek tlstronomerPfDIIHIIYQlnsInJdtJd epl-qd_ to flXPltllnthe motionMtI p/tlnet PalfHlnd tI fixedfItIl1h EoThe pltlnet mt1fIeSon tI drde whose cenI1emotlllS on tlnothflf' dtdetllfHlndthefltll1h. Inspedf/eInslrJlIt:f1$tWfII'tIIlp/qd_fIfIfItIed.


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SERIES I ARTICLE

The key~Aristotle'sIdeaslies Inhis

dasslflcatlon ofdifferent typesof motion.

Figure 3 HtndIeI'$ tele-$tXIpI1:This malt' telescopeht1d II tube length 0148 frN1tIIndllnaperlutflo148/nt:hes.

is one of rotational symmetry. A one-dimensional creature mov-ing along the circumference ofa circlewill find all locations on itexactly similar, there being no privileged position. As we shallfind in the second part of this series, present-day cosmologistsemploy similar symmetry arguments about the large-scale struc-ture of the universe.Although the heavenly bodies, especiallyplanets, did not appearto move (naturally) in circles the Aristotelians brought in morecomplicated geometricalconstructions involving aseriesofcirclescalled epicycles.Thus a planet may move on one epicyclewhosecentre moves on another epicyclewhose centre moves on a thirdepicycleand so on leading ultimately to a fixed earth in the midstof all these moving real and imaginary points in space.The epicycle theory was thus no different from the kind ofparameter-fining exercise that goes on in modem times whenresolution of apparent conflicts between observations and afavoured theory is sought by introducing adjustable parametersinto the theoretical framework. Such an exercise tells us moreabout the freshly introduced parameters than it does about thebasic hypothesis of the original theory. In fact, aswith the Greekepicyclic theory a theory, requiring too much patchwork of thissort eventually has to be abandoned.While it is easy to deride Aristotle and welcome Copernicus,Kepler, Gali1eoand Newton wemust acknowledgethat the Greekphilosopher originated the notion that natural phenomena followcertain basic rules.Aristotle's perception ofsuch rules turned outtobeincorrect but the idea that theyexist wascarried overand hasbeen the guiding light of theoretical physicists to this day.The Advent of TelescopesThe major experimental input to astronomy as a science came inthe seventeenth century with the discoveryofthe telescope.It wasGalileowho first used the telescopefor astronomical purposes and


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SERIES I ARTICLEwho first appreciated its value in observing remote heavenlybodies. Today wewould not be discussing the subject of cosmol-ogyhad there been no telescopes to giveus aviewof the universe.No one appreciated the usefulness of the telescope more thanWilliam Herschel. A busy music master at Bath in England,Herschel wasknown for his organ recitals and his hugeorchestras.At the age of thirty-five he decided to become an astronomerlargely asa result ofnight-time reading ofbooks on mathematicsandastronomy. Herschel's interestwasinobservationalastronomyand starting with a small telescope he eventuallywent on tobuildthe great reflecting telescope of48-inch diameter.The telescopic investigations of William Herschel and his sonJohn led them to the first crude picture ofour galaxyasa disc-likesystem of stars encompassed by the white band known as theMilky way.By examining the distribution of stars awayfrom theSun in all directions the Herschels concluded that the sun was atthe centre of the galaxy. Thus although it was known in thenineteenth century that the sun is just a common star which .appears to be the brightest object in the sky only because it is thenearest, it still retained the special status ofbeing at the centre ofthe galaxy.Our GalaxyThis picture ofthe galaxysomethodically built upbytheHerschelsstill had two defectswhich were not corrected until much later atthe beginning of the present century. But even in the eighteenthand nineteenth centuries there were those who suspected thatsomething was wrong and whose perceptions came remarkably

ThetelescopicInvestigationsofWilliamHencheland his son Jf)hnled them to thefirst crude pictureof our galaxy as adisc likesystemof starsencompassed bythe white bandknownas theMilky way.

FIguffI 4 7h1lmt1p Df DurgtlltDty tIS pnJpt118d by W/I-IItlm HIJfXhe/ ht1dIhB$IIn St1f ". t:fIId1a


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SERIES I ARTICLEEvenas lateas 1920,astronomers

dung to thepicture of ourgalaxywith thesun not too farremovedfromthe centre.

close to the truth as we now know it. The mathematician J MLamben suggestedfor examplethat the stars in theMilkyWayarein motion around a common centre and that the sun along.withthe planets also moves around this galactic centre.Lamben alsosuggested that not all visible objects are confmed toour galaxy.In addition to stars and planets astronomers had alsofound diffuse nebulae whose nature was not clear.Were they far-awayclusters ofstars orwere they nearby cloudsofluminous gas?Lamben argued that the nebulaewere indeed very distant objectsfar beyond the galaxy.Even as late as 1910-20astronomers clung to the picture of ourgalaxyas developed by Herschel. For instance JCKapteyn usedthe new technique of photography which proved to be a boon toastronomy and arrived at a model of our galaxy as a flattenedspheroidal system about fivetimes larger along the galacticplanethan in the direction perpendicular to it. In this model commonlyknown as the Kapteyn Universe the sun was located slightly outofthe galacticplane ata distanceofsome2000light-years fromthecentre (one light-year is the distance travelled by light in one yearand this is approximately 1013kilometers). The Sunwas thus nottoo far from the galactic centre just as Herschel had proposed.When Kapteyn's work was published in 1920-22it was alreadybeing challenged by Harlow Shapley. In a series of papers pub-lished during 1915-19,Shapley studied the distribution oflargedense collections of stars called globular clusters. A globularcluster maycontain upto amillion stars and canbe identified froma distance because of its brightness and distinctive appearance.Shapley found that the num}>erofglobular clusters falls ofasonemoves perpendicularly awayfrom the galactic plane. Along theplane they seemed concentrated in the direction ofthe constella-tion of Sagittarius. Shapley therefore assumed that the galacticcentre lay in that direction well awayfrom the sun and estimatedthat the sun's distance from the centre was50000 light years.Themodem estimate of this distance is only about 60 percent of this


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SERIES I ARTICLE

Spe.culatlons

value but the sun does go around the galactic centre as guessedcorrectly by Lambert. The total diameterofthe galaxyisabout 100000light years and it contains some 100-200billion stars.While Shapleywasright in dethroning the sun from its presumedprivileged position at the centre of the galaxy his distance esti-mates were too large because he ignored the effects of interstellarabsorption. Nor did Shapley agreewith Lambert's viewthat mostof the diffuse nebulae layoutside the galaxy.But by the 1920stheobscuring role ofthe dust began tobeunder stood and the pictureofour galaxyunderwent a drastic change. Many stars which wereearlier believed to be far away because they looked faint werediscovered tobemuch nearer, their faintness being due to absorp-tion by the interstellar dust. Evenmore important wasthe conclu-sion that many ofthe diffuse nebulae layfaraway,well outside thegalaxy. Indeed it soon became apparent, thanks largely to thework ofEdwin Hubble, that these nebulae were galaxies in theirown right as large as our own which are moving away from ourgalaxyat very large speeds. It wasHubble who found an empiricallawgoverning their motion that wastobecomethe foundation formodem cosmology.

FlgUIfI S PtogIW$ t1f aI6-moIlIfIY: ThIs kH/dtIr-Illts fig-Uffl sIIOM how IdtJtJs DfI thet:t1$ITIt1$ffIaIirIed 1III1/Dr In-puI$. SlIme t1f IIH1mhtwebtJenmenIIonBd In the ffIJtI.In tlddllllln, AryrIbht1IrI...tIWfIlfI t1f the _"",. IpInabwf /1$.. whldl -cording to him explainedwhy fixed 6Ir1,. apptltlT toftrweI 1tWIMrnt-Kant andP1rN:IrN ht1d SII/1J18IBd tht1fWTgtllt11ty1s 'U8ftlllflanHlll/11III1ny.

Suggested'readingB Bondi.Cosmology.Cam.

bridgeUnivenity.I960.J V Narlikar. The LighterSide of Gravity. W BFreeman and Co. 1982.

F Boyle. Astronomy\ andCosmology -A ModemCourse. W B Freemanand Co. 1975.

Address for correspondenceJayant V NarlikarIUCAA, PBNo.4,

Ganeshkhlnd,Pune 411007, India


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SERIES I ARTICLE

Life: Complexity and Diversity1.AWorld in Flux

Madhav Gadgil is with theCentre forEcological

Sciences, Indian Instituteof Science and JawabarlalNehru Centre for

AdvancedScientificResearch, Banga1ore.His fascination for thediversity oflife bas

prompted him to study awhole range of life forms

frompaper wasps toaachovies, mynas to

elephants, goldenrods tobamboos.

Madhav GadgilEvolving patterns of matter and energy gave rise to thecosmos. Tbe earth, itself a dynamic entity, is inhabited byliving organisms that have a dialectical relationship withthe world around them.Cosmic DanceWelivein aworldin flux.In aworldofeverchangingpatterns. .Patterns that change with the time of the day, the season of theyear.Patterns that change fromplace toplace. Patterns that havebeen in flux ever since the cosmos originated with a big bangfifteen billion years ago. In the beginning was pure energy con-centrated in an infinitesimally small space. As the cosmos ex-panded, matter began to crystallize out of this cauldron. First astiny elementary particles, each on its own, each dancing sepa-rately. As things cooled down, the particles linked arms to formatoms. Initially smallerones, like hydrogen, helium, oxygen,laterlarger ones, such as iron or nickel. With time these atoms beganto formcomplexes,molecules like those ofwater, aswell aslargerentities like crystals and metals.Slowlymatter condensed to formheavenlybodies: nebulae, stars,planets, meteorites. All the while atoms werebumping into eachother, linking together toformbigger and biggermolecules.Ofallthe variety ofatoms, carbon and silicon are best at holding handswith each other, and with those of other kinds as well. LikeBrahma and Vishnu, our gods ofcreation and maintenance, theyhave four arms each. So not only can they form long carbon orsilicon chains, but avarietyofside chains, with hydrogen, oxygen,nitrogen, even iron or manganese.The chains soformed can twistand wrap around each other, forming balls with a multitude of


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SERIES I ARnCLEprojections and indentations. Thus isformed an incredible diver-sity of carbon-containing, or organic, molecules. Molecules pre-dominantly composed ofsilicon tend to form more regular sheetsand three dimensional structures, giving rise to particles of sandand crystals of quartz.But atoms can hold hands with each other only when the sur-roundings are cool enough. When things heat up too much theydelink, preferring to dance on their own.Atextreme temperatUresthey even lose their shells of electrons -the tiny particles thatwhirr around the nucleus of each atom. Asa result, a largevarietyof carbon containing molecules can only be formed at moderatetemperatUres, indeed just such temperatUres as we enjoy at thesurface ofthe earth. Not that the rest ofthe cosmoshas no organicmolecules; in fact there are some even in the wide open spacesbetween the stars. Somepretty largeorganic molecules alsooccuron meteorites called carbonaceous chondrites. But earth has inabundance one other substance that makes allthe difference.Thisis liquid water. This is because organic molecules move aroundwith the greatest ease when i~ersed in water. Then they cantwist and tUrn, taking on myriad shapes.And they can reallyplaywith each other, zipping and unzipping chains, chopping off apiece here, adding on a piece .there. Swimming in water, theorganic molecules have let themselves go, eventUally comingtogether to form the truly marvellous structUresthat living organ-isms are.Life thus owesits origin to the great goodfortUnethat onthe surfaceof the earth prevail temperatUres that permit water toremain for much of the time in its liquid form.Dynamic EarthThe earth onwhich this dance oforganic molecules is in progress,is itself a dynamic entity. On it the water is forever in flux;passingbetween its liquid and vapour forms; giving rise to clouds andrain, rivers and seas.More than two thirds ofthe earth's surface istoday covered by the seas; seas that have been there a long, longtime. An average cloud on the other hand survives no more than

RESONANCE I January 1996

Ufe owesitsorigin to thegreat goodfortune that onthe surfaceof theearth prevailtemperaturesthatpermit water toremain for muchof the time In itsliquid form.

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Uvlngorganismsmight be

thought of asco-operatlve

teams of complexorganicmoleculesthat

take Inmatterand energyfrom their

surroundings,anduse these ta keepthemselves Ingood repair aswell as ta makemore copies ofthemselves.

16

an hour or so; larger collections ofclouds persist for atmost a fewdays. But we now know that seas and islands, continents andmountains are alsosubject to change, albeit on amuch slowertimescale. For, the continual barrage of rain and wind on the surfacewears the land down; and the flux of hot molten rocks in theinterior ofthe earth raises it back again. Evenmore significandy,this flux of hot molten rocks in the bowels of the earth drivesaround whole plates ofland and ocean floor, sothat continents goon forming, splitting, reforming, albeit on a time scale of hun-dreds of millions ofyears.The rich kaleidoscope of patterns of natUre that we witness allaround us, every moment of our lives, is then a dance of organicmolecules, in a watery medium, set in a theatre that is itselfchanging slowlybut irrevocably, all the time. The dance patternshave been changing in all of the four and a half billion years that. the planet earth has been in existence.The pace of changequickened a litde when life first appeared on the scene three anda halfbillion years ago. It accelerated further when life invadedland four hundred million years ago.When tool-using ancestorsofhumans first appeared on the scene twomillion years ago,therewas litde reason to believe that the world was getting set for adramatic increase in the rateofchange in the manifold patterns ofnature. But that has come to pass, and today we humans are adominant force governing the variegated mosaicof nature.Molecules of Life

The most fascinating, the most complex, the most diverse ofpatterns ofnature are the handiwork of living organisms. Livingorganisms might be thought of as co-operative teams ofcomplexorganic molecules that take in matter and energy from theirsurroundings, and use these to keep themselves in good repair aswell as to make more copies of themselves. The set of complexmolecules constituting these co-operative teams is ultimatelyfashioned out of a small number, a few hundred basic buildingblocks. These include water, phosphate ions and four main types



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Building Blodesof UteH-O,c'l0H-'t-HIH-


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Table 1 d1emlcal composition of cells of livingorganismsConstituent Number of atoms

per moleculeEstimated number of vqrieties ofeach molecule

Proteins aremade up oftens If not hun-

dreds,of aminoadds, making

passlblemillionsupon millionsofdifferent

combinations.

18

two amino acids linked together there are 20x20or 400possibili-ties. With three, 400x 20or 8000,with four, 8000x20or one lakhsixty thousand. Proteins in fact are made up of tens, if nothundreds ofamino acids,making possiblemillions upon millionsofdifferent combinations. The chains ofproteins thus formed donot remain as long strings. They fold up, forming complexglobular, ovoidal bodies. The shapesofthese bodies are governedbythe sequenceofamino acids in the chain, sothat awholevarietyof intricate shapes can be generated by just varying the order inwhich the amino acids are linked one after another. And not onlydo these larger molecules come in many different, elaborateshapes, they b~ar on their surfaces intricate patterns of positiveand negative electrical charges. Like proteins, other buildingblocks oflife are alsolinked together in many different ways,but


Bacteria MammalsWater 3 1 1Inorganicions 1-5 20 20Sugarsand precursors 10-30 200 200Amino acidsand precursors 10-30 100 100Nucleotidesand precursors 30-50 200 200Upidsand precursors -50 50 50Othersmall molecules -100 200 200Polysaccharides > 1000 100 1000Proteins 1000-5000 4000 100000rRNA 3200- 96000 6 6tRNA -5000 20 20mRNA 2500-25000 1000 100000DNA 109-1012 1 20."'Thisnumber variesromspecies/0species.


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SERIES I ARTICLEeach in some precise order to form larger molecules. Thus manysugar molecules form polysaccharides, starches, cellulose, fattyacid molecules to constitute lipids, or along with sugars andphosphates glycolipids orphospholipids. Purine and pyrimidinebases are joined to sugar and phosphate to constitute nucleotidesand nucleotides are linked into long chains to constitute nucleicacids..Each of these molecules, large and small,playa particular role inthe co-operative team ofthemolecules to allowthe team to take inmatter and energy in appropriate forms, to keep the team in goodrepair and tomakemore copiesofthemselves. This isan elaborateexercisewhich requires the co-operation ofthousands ofdifferentmolecules. Table1 looks at the composition ofsuch teams for oneof the most ancient forms of life, bacteria, and one of the mostrecent, mammals. The diversity of simpler building blocks isessentially the same for bacteria and mammals. The larger mol-ecules however, are markedly more diverse,by one or two ordersof magnitude in the case of mammals.Once triggered off in the hoary old times three and a half billionyears ago,the dance oflife has become more and more elaborate,drawing in an ever larger number and variety of actors. And thestageoverwhich they havebeen dancing has alsogone on expand-ing, beginning with shallow seas,invading depths ofocean, land,air and finally outer space.

. Suggested ReadingBAlberts,DBray,JLewis,M~ KRoberts,J DWatson.Molecu1arBiologyof the CeILGarland Publishing, IDe.NewYorkand London. pp. 1146-1983.

R Cowen,History ofLife. BlackwellScientific Publications. pp. 470.1990.B0 WiIaoDlThe DiversityofLlfe. The BelknapPress ofHarvardUniversityPress, Cambridge, Massachusetts. pp. 424.1992.


Oncetriggeredoff In the hoaryold times threeand a half billionyears ago, thedance oflifehas becomemore and moreelaborate,drawing Inanever largernumber andvarietyof actors.

Address for correspondenceMadhavGadgil

Centrefor EcologicalScIences,ndianIns1IIute

of Science,Bangalore560012,India.

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Fascinating Organic Transformations:Rational Mechanistic Analysis1.The Wagner Meerwein Rearrangement and the Wandering Bonds

Afternearlya three-decade longinnings as aninspiring teacher and

researcher at llT Kanpur,S Ranganathan is now atRRL,Trivandrum. He andhis chemist wife,Darshan,plan to set up (withoutgovernment assistance)"Vidyanantha EducationCentre", to promote

education, art and culture.

R

R 1

Subramania RanganathanAcarbocation can stabilize itself by a series ofC-H and C-C shifts to reach the most stable form. Several examples areshown in which relatively strained systems upon such cat-ionic rearrangements p.-oducediamondoid systems.

The Ganges flows to neutralize the water potential, electricityflowsto compensate an electron gradient. Naturally therefore, anelectron deficiency in a carbon framework generates a "bondflow".This phenomenon, in its most simple representation (Fig-ure1), is the Wagner Meerwein rearrangement.A natural property of an electron deficient centre is to make thesystemdynamic, thus opening thepossibilities forcharge dissipa-tion. This can be illustrated with what is called the Grotusmechanism (Figure2). One can see how effectively the protonexcesson the left side is transmitted by the medium to the right.Similarly, charge deficiency created at a location can be evenly,and quite effectively,spread swiftly.The process that takes place

Figure 1 The WagnerMeerwelnffKll7f1ngemenf. Rgutrl2 TheGrtJtusmechanism.

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TheSerieson fascinating Organic Transformations: Rational Mechanistic AnalysisRational analysis of organic reaction mechanismswas initiated in the early decades of this century,when the now well-known 'arrow pushing' *,to de-scribe the flowofan electron pair, gained popularityamong chemists. Subsequently, In the 1930-1960period, the combined efforts ofseveral great organicchemists established mechanistic organic chemistryon a firm ground. Everyorganic transformation is,however, unique, in the sense that there is alwayssometwistwhen you carryouta new reaction (orelsemany ofuswould have been out ofbusiness II.Thus,in order to unde.rstand new transformations, onemust have a very good appreciation of the basicprinciples of mechanistic analysis.

Many of us feel that at the undergraduate level

- When organic chemists started using curved ar-rows a well-known chemist reportedly remarked:.Curved arrows never hitthe targer.

rational mechanistic analyses of exciting transfor-mations are seldom taught. Theexamples availableInmany textbooks tend tobe somewhat routine (andperhaps boring), and many good examples are leftout. S Ranganathan, one of the most popular or-ganic chemistry teachers at lIT,Kanpur for almostthree decades, has put together for Resonancereaders, six examples that demonstrate a step-by-step approach to rationalize fascinating organictransformations.

In this series of articles, he will cover Wagner-Meerwein rearrangement. molecular self- assem-bly, Woodward-Hoffmann rules, 'lone pairs', vonRichter reaction and synthesis vs biosynthesis ofIndigo. We are certain that students and teachersalike willenjoy the simple and classroom-type dis-cussions provided ineach ofthese examples.

Udoy Moitro

in the norbomyl cation system (1,Figure 3), leads to a total chargedissipation, as shown in Figure 4.Figures 3,4 permit the definition ofvery basic aspects associatedwith this type of bond migrations. By definition, whenever asigmabond (other than aC-Hbond) shifts, it iscalled theWagnerMeerwein shift [WM]. The hydrogen sigmabond migrations aredenoted as proximate [1,2] or through-bridge [1,3] shifts.The WM shift in substituted derivatives of 1 [1,2 ~ 2,1] takesplace with incredible speed*, of the order of ==1012ec-1at roomtemperature [RT]. This is an estimate, since no 'eye' can see thisbecause of the swiftness of the operation. We enjoy the videobecausewecannot 'see'it! The framesmoveatarate fasterthan the


1.2-alkyl shift ;: WM and1.2 H' shift ;: [3,211,3 H' shift ;: [6,2] if one usesnorbornane system.-The structure of the unsub-stituted 2-norbornyl cation ishighly controversial. Do1and 2rapidly interconvert or does theIon exist as an intermediate'non-classical' form? Spectro-scopic and theoretical studiesare currently Interpreted infavour of the latter proposal.However, tertiary derivativeshave classical structures andundergo fast WMshifts.

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Figulfl 5 A ptDflle of thediamond strudure. Notehow beauHfully the dlalrcydDhexa/ll1$alfl sIr1dtedIeadlngfoafhfJrtnlynami-cally sfrlble coMleilafion.

30

eye can discern [===16rames sec-I]; thus one frame merges intoanother creating an illusion of continuity. At one time the WM in1was called the windshield wiper [WW] effect. The WW of a caroperates (if at all!) at the rate of oneperseeond. So one can see howrapid the WM in 1 is.The [1,3] is slower [===OSsee -I],and the [1,2]even more so [===06see-I].The last two could be focused to the eyeof the NMR which can distinguish events that take place at l()4see-I. SO,cooling down the norbornyl Cation 1 can bring down therates to lie in the vision range of NMR and this has been done.Charge dissipation naturally opens avenues for equilibrationleading to stable systems from not so stable precursor cations.This is well documented in organic chemistry, and in this presen-tation is taken to esoteric heights leading to options forinakingdiamond!

A profile of diamond structure is shown in FigureS. Note howbeautifully the chair cyc10hexanesare stacked leading to a ther-modynamically stable constellation. This would imply that suchshuft1ing of bonds can lead to diamondoids from unrelated pre-cursors having the same carbon framework. This was dramati-callyillustratedwiththe transformationof2 -readilyformedbyhydrogenation of cyc10pentadienedimer -to adamantane (3) inexcellent yields, thus making a rather expensive compound verycommonplace!Like in a 'randomwalkjogging'wecanstart in


SERIESI ARTICLEWM Lh

+thWM & 7

hI

1.2 .d>(I) 7

1,2 th+ 63 -G- . 1,2 ih0= + IFigure 3.4

1.2 J>3 WM",.",." Rearrange-n the IIDtbDrny/

..

Ion .,.,.",. aIf-


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SERIES I ARTICLE

AIBr. [AI

W),I Wlot

several directions from 2 and teach 3. We have shown here onesuch pathway (Figure6). One can trace other pathways and doingso can be fun! To reinforce the notion ofequilibration leading todiamondoids, another example is given inFigure7,wherein theaesthetically pleasing C-lO triquinane (4) possessing a three foldaxis of symmetry, is transformed to adamantane (3).While adamantane (3) was known before the era of the under-standing of carbocation rearrangements, its logical homolog 5,notionally formed byplacement of additional chair cyclohexaneswas unknown. The fascination for this molecule was such that itwasthe motifforan international congress(IUPACConferencein1963) and the compound itself was named, before birth, asCongressane;dditionally,a rewardwasofferedfor anyonewhocould make it before the next congress, scheduled in two years.But no one could claim this reward! The facile synthesis ofadamantane(3) bywandering ofsigmabonds openedup possibili-ties, not only for congressane, but also for higher members ofthefamily. In the event, congressane, nowformallycalleddiamaQtane(5)wasmagicallymade, in excellent yields from6 and 7which areeasilyderived from the dimerization ofthe C-7bicycloheptadiene.Indeed, dimer 6 gave a 90%yield of 5 under equilibrating condi-tions! The transformation of 6 and 7 to diSlmsmtane(5)has beenrationalized in Figure8 and Figure9, respectively, by pathways


Flgul'fl 6 (fop left) Retlr-mngemenf of t:t1mpwnd :Jfo tJdt1mtJnIr1ne (3).

FIgure 7 (foprlghfJ 7hetJf1$-fhsflctJlly plstJslng C-l0trIqulntJne (4) frtJnsfrmnedfo tJdt1mtJnIr1ne (3).

5The fascinationfor the logicalhomolog 5 ofadamantane (3)was such that It\ws the motif foran Internationalcongress (lUPACConference In1963)

31


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SERIES I ARTICLE

FlguM 49 Ilet1I7f1I1f1111tN1111/lDp 1t1ff} tJf IXIfIIptHlnd f6}and ffop right} IXIfIIptHlnd 7to dk1mt1n1r1ns (S).

8Flt/UM 10 TrItImtlnIrIns f8}.

FlgUM n frlght}.!IenIIIrIepatt"rn ."arch fordltlmtlndold pnK:IIIWn onthe bt16I6tJf alYllto-t1l1t1/y616PfOIIIflm.

32

precisely similar to those discussed earlier. A recent addi-tion to this family is triamantane (8), which has a truetetrahedral carbon, attached to four other carbons as indiamond.Basedonthe aboveprinciples and illustrations, one could developa computer program to identify appropriate precursors for a

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specificdiamondoid. Even in the caseofC-l 0 adamantane (3),thenumber of possible C-I0 precursors would be huge. For highermembers of the series the options could be astronomical. Areasonable guess is that it would take 500-1000such rearrange-ments for substances that would have the propenies of diamond.Thus it is obvious ~at if the carbocation strategy is to be adoptedto make diamondoids, a listing of all possible precursors besecured using a computer and based on the three pathwaysinvolved. The task could be simplified by incorporating restric-tions in the program. Although using this strategy for diamondappears far fetched, it could lead to novel diamondoids andrelated precursors having desirable propenies. The iterativepattern is simple, and each generation produces three possibili-ties, as shown inFigure11(the three arrowshere represent, WM,[1,3] and [1,2]).Suggested ReadingP D Badett. Nonclassical Ions. Benjamin, New York. 1965.

Read this book for a historical account.N Anand, J S Bindra, S Ranganathan. Art in Organic Synthesis. 2nd edition.

1988. p.I48.P v R Schleyer. My Thirty Years in Hydrocarbon Cages: From Adamantaneto Dodecahedrane, from Cage Hydrocarbons, Ed. G A 0Iah, Chapter 1.Wiley. 1990.

One coulddevelopacomputerprogram toIdentifyappropriateprecursorsfor aspecificdlamondold.

Address for correspondence5 Ranganathan,

Senior Scientist (INSA)Biomolecular Research Unit.

Regional ResearchLaboratory,

Thiruvananthapuram695 019, India

Newton's Inheritance... After Newton's death on 20 March 1727, hisliquid assets, which totalled some 32,000 were to be divided equallyamong his eight nieces and nephews, but the estate at Woolsthorpe wasnow legally the property of the next surviving Newton. Heturned .outto beone John Newton, descendant of a brother to Newton's father, who wasdescribed as "a poor representative of so great a man". This assessmentproved to be accurate: John Newton gambled and drank his inheritanceaway, dying by accident when, after a round of drinking, he stumbled andfell with a pipe in his mouth, the broken stem lodging in his throat.

RESONANCE I January 1996 33


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SERIES I ARTICLE

Geometry1.The Beginnings

After spending about adecade at the School ofMathematics,TIFR, Bombay,

Kapil H Paranjape iscurrendy with IndianStatistical Institute,

Bangalore.

AnImportantmathematicalfeature of Eudld's

theory Isthatrules of deductionare verystrict

nathlng - noteven so-calledcommonsense orIntuition- can

be taken forgranted.

34

Kapil H ParanjapeMathematics is as much an art as a science. Thus tounderstand whywestudy the problems wedo todaywemustexamine the history of the subject. In this series of articleswewill try to examine how the geometric concepts that arein use today evolved.(Anote of warning: the 'history' hereis more a personal view than a historian's.) As in art,understanding is enhanced by doing. Readers are encour-aged to attempt the exercises scattered in the text.The Origin (s)Origin: the starting point of a flow or the centre of a coordinate system.

We are often told that geometry (=geo+metry) arose out of theattempt to measure land area. But this view ignores the develop-ment ofgeometry for navigation by travellerswho used stars, forthe design of buildings, in art and painting and so on. In factgeometry and geometrical thinking is one of the fundamentalactivities ofthe brain - the other being algebraic thinking (thesetwo modes are sometimes called the spatial and verbal functionsof the brain).The fIrst comprehensive treatment ofgeometrywhich wecancallmathematicalfroma modem perspective is that ofEuc1id. From afew basic concepts (point, line, angle etc.) and fewbasic state-ments (the fIve axioms) he wished to deduce aU the known(geometrical)phenomena using somelogicalprinciples (whichhecalled common notions). In other words he was constructing a'theory of everything'. At the same time he was aware that our'imperfect' world did not quite meet all the requirements - thetruly geometric world wasthe Platonic universe ofthe heavens; a



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Table 1.Rllbert'sAxIomsorEuclideanGeometry11 Inddence.Eachpairofdistinctpointsdeterminesa uniquelineand soon.2) Separation.Eachpointona linedividesthelineIntOworays;eachlinedividesthe plane Into1wohalf planesand soon.

3) Congruence.Alongany rayonecanmarka segmentcongruenttoagivenone;givenanyrayanda half plan~adlacentto It,for anyanglewe can find a congruentangle lying Inthe half plane based onthegivenray.The.slde-ongle-slde*postulateforcongruenceoftriangles.

4) Archlmedeanproperty.Givenanypairofsegmentsomemultipleofthe firstsegment Islonger than thesecondone.

5)' Parallelpostulate.Givena polnt'anda linenotcontainingItthereisaunique line through this pointparallel tothegivenline.

modem perspective would be that he had a 'model' for theuniverse.An important mathematical feature ofEuclid's theory isthat rulesof deduction are very strict; nothing - not even so-called com-mon sense,or intuition - can be taken for granted1.However,Euclid too fell into some traps set by common sense. One of themost (logically)circular parts ofhis theory ishis use ofthe circle!A number of corrected or alternate approaches to Euclideangeometry exist today but none has the all encompassing breadthofhis 'build-the-whole-thing-up-from-nothing' approach. Theclosest isHilbert's approach (see the box for a quick snrnrnRty)..Nowadays the real number system that comes up in Euclideanmeasurement is often constructed algebraically (via the decimalnumbers) and then imposedon geometry via the Ruler PlacementPostulate. However, the idea (embodied in the Ruler Placement,Postulate) that a line isthe setofitspoints would havebeen totallyunacceptable to the Greekmathematicians. In factone ofEuclid'sattempts was to give a geometric construction of the numbersystem. Each numberr isrepresentedbyapairofline segments (the


The study of realnumbers requireda whole newgeometric InsightduetoWeierstrass,Dedeklnd, Cantorand others. InEudld's time onlyEudoxus andArchimedes camedose to thisInsight.

1 It can never be over-emphasised that commonsense has a love-hate relation-ship with science.

35


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SERIES I ARTICLE

Figure' Addingnumbtn.

2 The fact that some line seg-ments give rise to Irrationalnumbers like 1'2 disturbed thecommon sense of Euclid andhis contemporaries but was no!in any way an Inconsistency inthe theory.

3A relatively 'unknown Indian'by the name of Madhavacharyaappears to have also comequite close.4 Unfortunately we mathemati-cians seem to fall Intothe 'gum-chewer' category; we can'tchew gum (verball and walk Ina straight line (spatlall at thesame time!

Figure2 MuHlp/ylng,anddividingnumbefS.

36

cIUnit a ba+b=c

first gives the 'unit' ofmeasurement and the secondgivesr whenmeasured in those units)2. Some simple constructions (see theFigures1,2,3) show how we can add, multiply, divide and takesquare roots of numbers represented asabove. (Exercise: Justifythese constructions using Hilbert's axioms,)However, not every number of geometrical interest arises bysuccessive application of the above constructions to the unitlength, Two important unsolved problems of Euclid's time were(1) 'unrolling' the circle (2) 'doubling' the cube, In fact, aswenowknow from the theory ofmeasure, 'most' real numbers cannotbeconstructed by means of straightedge (ruler) and compass; inGreek mathematics the only permissible entities were thoseconstructed in this way, The study of real numbers required awhole new geometric insight due to Weierstrass, Dedekind,Cantor and others, In Euclid's time onlyEudoxusandArchimedescame close to this insight3.Co-ordinating the Piane/Brain4Co-ordinates:A pair (triple) of numbersuniquelyidentifyingapoint on the plane (in space). .

By the time mathematics had wound its way via the Indian andArabic traditions, the algebraic and arithmetic aspects had seen

ab = c



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SERIES I ARTICLE

a

tremendous growth. With the use of negative numbers and (theall-imponant number) zero it became possible to talk of all thearithmetic operations on numbers. Decimal notation madearith-metic operations 'child's play'.In order to utilise this Descanes devisedthe following scheme.ByfIxing a point, the origin,on a line it becomes possible to talk of adirected distance as a positive or negative number depending onwhether the end point is to one or the other side of the origin.Similarly, he assigned a pair of numbers to every point of theEuclidean plane. First one chooses a pair of onhogonal linescalled the axes.The intersection point of these lines is called theorigin.The directed distance from the origin to the foot of theperpendicular from our given point to the fIrst axis is called theabscissa;he directeddistancefromthe originto the footof theperpendicular fromour given point to the secondaxisis calledtheordinateS(Figure4).(I havestated everything inwordshereto show


Figure3 Taldnga square1rH1f.

Much ofEudldeangeametrybecame absurdlvsimple Ifone usedcoordinates.

550 powerful Is this pairofnum-bers working together withsome (by now common) alge-bra and arithmetic that we usethe term 'coordinated' for well-organlsed activity!

Figure 4 The coordinateplane.

37

p

y

x


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SERIES I ARTICLE

Uke all gaadmathematics, the

Cartesiancoordinates alsoopened the doorto newer

geometricalIdeas.

38

how cumbersome this original - pre-algebraic methodofwriting things was; this continued in Europe for quite sometimein spite of the fact that the Indo-Arabic mathematicians hadalready introduced variables!)On the one hand, it followsfromEuclidean geometry that apointin the plane is uniquely determined by its Cartesian coordinates(Exercise: Prove this). On the other hand, much of Euclideangeometrybecameabsurdly simple ifoneused coordinates (at leastto those mathematicians who knew their arithmetic and algebra)- more importandy, the truth of various statements could bededuced by calculation (Exercise: Deduce all your favouritetheorems and riders in Euclidean geometryusing Cartesian coor-dinates). The tricky definition of a circle in Euclidean geometrygavewayto the much clearer point ofviewthat acircleis the locusspecifiedby an equation (x-a)2+ (y-b)2=r2where (a,b)are the co-ordinates of the centre and r the radius (Exercise: try to give thisdefinition without using symbols!). While common-sense andintuition seem to take a back seat and algebraic manipulationcomes to the fore, this is all to the good from ~e point of viewofEuclid's deductive method.This was not all. Like all goodmathematics, the Cartesian coor-dinates alsoopened the door to newer geometrical ideas. Firsdy,it became possible to talk about the locus associated with any(algebraic or functional) equation involving the twoco-ordinates,e.g.

In other words, the study ofplane curveswasbegun. Secondly, itwasno longer necessary to "construct" all the geometrical figuresthat were studied (Exercise: Try to find a sensible way of tracing.out the curvegivenby the equation above).The equations definedthe figures and then the mathematician could "analyse" them.This led to the term analyticgeometry ofDescartes asopposed tothesyntheticgeometryofEuclid. Cartesiancoordinates alsoopened

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SERIES I ARTICLE

up the possibility of studying geometrical relations between non-spatial entities-one can draw a graph showing a geometricalrelation between (say) the amount of gum chewed and the lineardistance traversed6. Finally, a most important consequence wasthat one could study geometry in dimensions other than two andthree. This idea flowered in the hands of Riemann.SummaryEuclidean geometry in its original form has only a marginal roletoplay inmodem mathematics. It isalmost totally supplanted byCartesian or analytic geometry. Why then dowestill learn it? Togive us a way of building our geometrical skills while we learnenough algebra and arithmetic to use coordinates.Moreover, it isprobably not easy to discOfJt1'ew results in-Euclidean geometrywhile thinking about it purely algebraically.A number of questions remained unanswered even with thesimplicity introduced by the coordinate approach.Will the circlebe squared?Will parallel lines meet? Can curvesbe straightened?Wait for the exciting next instalment!

.See earlier footnote 4 to seewhy this is Important.

EudldeangeometryIn Itsoriginal form hasonly a marginalrole to play inmodemmathematics.

Address for correspondenceKapil H paranjape,

Indian Statistical Institute,8th Mile, Mysore Road,

Bangalore 560 059,lndla.

RESONANCE I January 1996 39


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SERIES I ARTICLEKnow Your Chromosomes1. Nature's Way of Packing Genes

VaniBrahmachariis at the DevelopmentalBiologyand GeneticsDepartment at IndianInstitute of Science.She is interested in

understanding factorsother than DNA sequence

per se,that seem toinfluence geneticinheritance. Sheutilizeshuman genetic disordersand genetically weirdinsectsysteEnstounderstand thisphenomenon.

Figurel Fmmchmmosometo DNA..'f'1s telomere;theend of a chmmosome; ~'-longarm; 'Cen' Is centro-mere, whichaids In segre-gating chromosomes todaughter cells during celldivision; ))'- short arm; '11'-nudeosome, the unHof or-gan/zaf/onofchmmosomes;1/'- hlsfDnes,whicharepfD-IeInspresenflnnudfKJSDmBStIS odamers amund whichapproximately ISO basepairs of DNA are wmpped.Adenine, Guanine, Cytosineand Thymine are nitrogencontolnlng bases present InDNA.

40

Vani BrahmachariThe study of cellular structures including chromosomesbegan as early as the 17th century. The organization ofchromosomes, the structure and function of genes and therole of genetic mutations in diseases continue to be an areaof intense scientific investigation.The size of an average human cell is 20-40micrometers (um) ormicrons (u). One micrometer is one millionth of a meter i.e.,1~ meters). Deoxyribonucleic acid (DNA) the primary geneticmaterial is located in the nucleus which is 8-20/lm . The DNApresent in a single human cell if stretched out completely wouldhave a length of about 1.8meters (6 feet).That leavesus with thepuzzleof howcellspackup 1.8meters ofDNA inside atiny saclikethe nucleus which is 0.000020meters in diameter!! Nature hasdivided this DNA into 23piecesand compacted them severalfoldto accommodate them in the cell nucleus. These piecesof DNAwhich are clusters of several genes are called linkages groups orchromosomes. Therefore chromosomes are nothing but long



31/108

SERIES I ARTICLEstretches ofDNA compacted with the help ofproteins. Under anelectron microscope, chromarln appears asbeads on a string: thestring being DNA and the beads being the proteins (Figure1).

In the 17th century, the structure of various cell types wasanalysed by light microscopy using specific dyes or stains. Thecellular structures which readily took up the stain were thecomplexes ofDNA and protein. Since the chemical nature of thedarkly stained bodies was not known they were simply called'chromaticelements' - meaning colouredelements. The termchromosome was suggested byWWaldeyer in 1888.The numberofchromosomes in agiven species ischaracteristic ofthat species,and ismaintained constant from one generation to the next. Thechromosome numbers ofsomeplant and animal speciesare listedin Tabk 1. Most organisms are 'diploid' meaning that they havetwo copiesofeach chromosome, one receivedfrom the father andthe other from the mother. The sperm and the eggnuclei (whichfuse during fertilization to form the zygote, that grows anddevelops into a complete organism) contain only a single copyofeach chromosome. Therefore sperms and eggs are said to be'haploid'. For instance, the diploid number of chromosomes inhumans is 46 and therefore the haploid number is 23. The 46chromosomes in eachofour cellscarry all the genetic infomiationnecessary to build a human being, in the form of genes made upofDNA.Chromosomes: The Vehicles of HeredityThe number of chromsomes in humans has been known for only39 years, while Mendel formulated his laws of inheritance 130years ago and his workwas rediscovered almost 9Syearsago.Wehave been aware of the fact that children take after their parentsand that certain diseasesmn in families. Plant breeding has beensuccessfully practised by farmers who did not understand thegenetic basis for crop improvement. Gregor Mendel, regarded asthe father of genetics, sawa pattern in the inheritance ofdistinctcharacters in peaplants. The deliberate design ofcrossesbetween


Table 1Organism with Its

Chromosome numbe,.Man 46Chimpanzee 48Dog 78Donkey 62Mouse 40Frog 26Carp 104Silkworm 56Fruitfly(Drosophila) 8Rice 24Wheat 42Tomato 24Pea 14-rhenumberlndicotes/hediploid or 2n number ofchromosomes. One chro-mosome of each pair isreceived from the motherand /he other from the fa-ther..

Thenumber ofchromosomesInagiven species ischaracteristicofthat species,andis maintainedconstant fromone generation tothe next.

41


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SERIES I ARTICLE

The 46chromosomes Ineach of our cells

carryall thegenetic

Informationasgenes neoessary

to build ahuman being.

4Z

50X10-6m

20x10-6m

6 X 10-6 m

34 x 10-9m

3-5 X10-9

Cell: Is the building block of all plantsand animals. There are about 100trillioncells inthe human body.

Cell nucleus: is present within eachcell except red blood cells Inhumansand other mammals. this containsthe genetic material, DNAorganizedas chromosomes. Ineach ofour cellsthere Isabout 6 feet long DNApackedinto 46 units called chromosomes.Chromosome: Isa long thread of DNAwrapped around proteins. A specificblock of DNA represents a gene.

Gene: Isa unit of information usuallycontaining Information tomake a pro-teln. Thereare about 50,000-1.00,000genes in each human cell.

Proteins: are workhorses ofthe cellservingvariouspurpose liketransportof ions, antibodies to fightinfections, ~CI:and as catalystsinvariousbiochemi- :ical reactions. I

pea plants with distinct characters led him to formulate the lawsof inheritance. The first application ofMendel's 'gene' concept toa human trait was by the physician A Garrod. He described thegenetic disease alkaptonuria (Box 2) as an alteration in specificbiochemical reactions leading to the-excretion of homogentisicacid in urine. He introduced the concept of' chemical individual-ity' and observedthat an individual either doesbr'does not excretehomogentisic acid; no patient exhibits intermediate states. Inother words,the trait is a discreteone.This defectoccurred in



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SERIES I ARTICLE

AlkaptonuriaAminoacids are primarilyused as buildingblocksfor proteinsand as precursorsforotherblomoleculeslikehormones,purinesand pyrimidines.Whenan excess of protein is ingested, aminoacids derivedfromproteindegradation are used as a source ofenergy bya process calledoxidativedegradation.Inone such pathway phenylalanine Is converted into acetoacetylCOAthrough a series of enzymatic reactions.

One ofthe steps Inthis pathway Isthe conversion ofhomogentisicacid, an Intermediate in this pathway, to 4-malelyl acetoaceticacid by an enzyme called homogentisic acid l,2-dioxygenase.

Ifan Individualhas a defect Inthe gene codingforthis dloxygenaseit will lead to the production of a non-functional enzyme. This inturn results In the accumulation of homogentisic acid and itsexcretion in urine. This condition Is described as alkaptonuria.Defects at other steps in this pathway lead to genetic disorderslike phenylketonuria, tyrosinemia and albinism.

children of several first-cousin marriages but not all marriagesbetween relatives resulted in children with the disorder. Hereasoned that there may be some peculiarity in the parents ofchildren who inherited the disease. Garrod recognised thatMendel's lawsofheredity could provide a reasonablebasis for thephenomenon. In 1908, he published his monograph on inbornerrors of metabolism which was a reflection of his great insightinto the role ofgenetics in human physiology.Asisoften the casein the history ofscience, Garrod's contributions to human genet-ics remained unappreciated during his lifetime.Before the rediscovery of Mendel's work in 1900,the process of


ThefirstapplicationofMendel's'gene'concept to ahuman trait wasbythe physldan AGarrod.Hedescribed thegenetic diseasealkaptonuria asan alteration Inspecificbiochemicalreactions leadingto the excretionof homogentisicadd In urine.

43


34/108

SERIES I ARTICLEItwas found that

what wasdescribed as

Mongolismandlater as Down'sSyndromewasactually thepresence of three

copies ofchromosome21Instead of thenormal two.

Figure 2 Diagrammaticrepresenfaflon Df steps Innudear dMslon during celldMslon. 2n and n rep/'f1$tlnfthedlploldandhaploldslr:tleDf the nude/. In the givenexample 2n = 4. MeIosisfakes place during produc-Non Df the egg and thesperm.

44

cell division,meiosis and mitosis (Figure2)had been analysedandthe chromosomes were identified as entities that are evenlydistributed between daughter cells during cell division. Thesimilarity betweenMendelian segregation and chromosomal dis-tribution during meiosis was correlated and chromosomes wereidentified asbearers ofgenetic information. Soonafter the redis-covery of Mendel's work (1902 and 1903) chromosomes wererecognised as units of heredity by different scientists indepen-dently. Thus the discipline ofcytogenetics developedwith experi-ments in plants like Lilium and insects like the fruit fly, Dros-ophila. Although it was only in 1956that the correct number ofchromosomes in humans was established, the Mendelian mode ofinheritance was illustrated by the inheritance of the ABO bloodgroupsbyLandsteinerin 1900andbytwoGermanscientistsin 1911.

i .if.f~;Y'i,'4 ,.,\'~

'/~)';i(\..~ . '"" rI+t

"

h,


.......,:_" ,...-?' ,It. .'" y,> . ".;,,oft' I /-+;... , 'C ,>'.- i...." r "


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SERIES I ARTICLE

In the summer of 1955Albert Levan, a Swedish cytogeneticistvisited T C Hsu, who had developed a modified method forchromosome preparation and learned the method of preparingchromosomes from human cells. Later, Albert Levan with JoeHin Tijo discovered that by adding colchicine, an alkaloid de-rived from plants, the highly condensed state ofmetaphase chro-mosomes can be blocked from proceeding further (Figure3). Thetissue with which they worked was human embryonic liver. Outof the 261 metaphase cells they observed most had 46 chromo-somes.To this day a large number ofmetaphases are observedbycytogeneticists before reporting the diagnosis of the chromo-somal status of a patient. Following this discovery it was foundthat what was described as Mongolism and later as. Down'sSyndrome was actually the presence of three copies of chromo-some 21 in the patients instead of the normal two. Anomalies inchromosome number, in particular that ofthe sex chromosomes,were also reported in patients who had abnormal sexual develop-ment. All these were substantiated after the development of newmeth 1s for the analysis of human chromosomes. From thisperspective the revolution in the study of chromosomes referredto as cytogenetics seems to have arisen from methodologicalimprovements rather than the development ofanewconcept.Theadvantage was that inferences drawn from previous observationsdid not lose their value but got further supplemented and rein-forced. Thus human cytogenetics attained a new dimension. Inthe following years it was discovered that several human heredi-tary disorders are due to chromosomal defects.(0) (b)


Several humanheredity disordersare due tochromosomaldefects.

F/guffl3 ChrtH1lO$DITIIISISv/$uallssd bydiffflfflntmelh-ods (tl) SCtInnlng eledrt1nmlaogrtlph DfhumDn chro-mO$Dma (b) tl msIrIphasespfflt1d preptlred from Iym-phocyfss (WBC) tlf mef-tlpht1sB sft/ge Df cell dM-slon. The btlndBd pt1ftBm /$dUB to dlfferent/tll glBfTl$t1sft/lnlng. (c) tl mBlt1phllSBspfflt1d phologrtlphBd un-der the miCrtlSCtlpB; Indl-vldlHllchromO$Dml1$tlfflcufup tlnd tlf'rtlngBd In orderDffBr comptlrlson with tlsft/ndtlrd btlndlng pt1ffBrn.Th/$ /$ t:t1/1Bdtl karyotype.Th/$l1ryofypB (pirwldBd byDr SrldBvl Hegde, Sf John'sMBdIt:t11 CtHIBgB, Bt1"!Jt1lore)/$ thof of tl womtln.

(c)

frfri(-li,

II II

45


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SERIES I ARTICLE

Theprocedure ofpreparing apicture ofchromosomesof

an IndividualIs~lIed'karyotyplng'.

46

Chromosomal NomenclatureThe chromosome number in each cell was established but howwas the nomenclature arrived at? In 1968 it was realised thatcertain dyesstain chromosomes in a non-uniform fashion givingrise to lighter regions and darkly stained regions. This producesthe pattern shown inFigures3 h,c.There is also a variation in thelength of chromosomes and in the position of the centromerewhich helps in the segregation ofchromosomes to daughter cells,during cell division. Chromosomes areordered and numbered bytwo different conventions. Basedon their length they areordered1to 23. In the other system 23pairs are distributed into groups Ato G based on their length and the centromere position. Bothsystems are indicated inFigure3c, the pairs from 1to 22arecalledautosomes and the 23rd pair is called the sex chromosome,typically denoted by the letter X and Y. A female has 22pairs ofautosomes and twoX-chromosomes (44XX),whereas amale has22 pairs of autosomes, an X-chromosome and a Y-chromosome(44XY).Now you can appreciate the fact that by a chromosomalanalysis of an individual one can identify any change in number,length or staining pattern of chromosomes. This procedure ofpreparing a picture of chromosomes of an individual is called'karyotyping' .From Chromosome to GenesThe total amount of DNA in 23 chromosomes is estimated to bethree billion (3x 109)basepairs. Basepair means apair consistingof adenine and thymine (A-T) or guanine and cytosine (G-C) -the nitrogen containing bases in the building blocks of DNA.Therefore the total amount of DNA in our cell is six billion basepairs (in 46 chromosomes). The identification of any change inthe number of chromosomes is relatively easy,but any change orloss ofonlyone or a fewgenes froma chromosome will not lead toa change in the length that is detectable under a microscopenormally used for karyotyping. For instance, to find the causeofa hereditary disorder like haemophilia (a genetic disorder result-



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SERIES I ARTICLE

ing in defectiveblood clotting), the challengebefore the scientistswas to find a single base pair change out of six billion base pairs.It sounds almost impossible. But scientists haveworked out awayof narrowing down the region of the defect step by step. Some ofthe steps in this process are as follows: (a) to derive the pattern ofinheritance (autosomal or sex linked) by family history or pedi-gree analysis; (b) to find the linkage group or the chromosome onwhich the gene is likely to be located; (c) to find neighbouringmarkers or genes and (d) finally to find the defectivegene itself.With the advent of modem methods in biology, the order inwhich the steps are taken towards identifying a gene related to atrait can be different in different cases.But whatever the startingpoint one would like to derive all the information oudined in (a)-(d) to help in diagnosis, treatment or prevention of a geneticdisorder or in finding a gene.The total number of genes known in humans to date is reaching6,000.But this is only about 6 to 12%of the total number ofgenesestimated to bepresent in humans. Moreover eachgene doesnotfunction in isolation. It is like the words in a sentence; withdifferent meanings in different contexts. Similarly, a gene canbeapart ofdifferent complexprocessescontributing to different endproducts. Most often it is the defect in a gene which leads to theunderstanding of its normal function. In future articles, wewilllearn more about the structure and function of individual chro-mosomes along with the processes used to study them.

Tofind the causeof a hereditarydisorder IlIcehaemophllla thechallenge beforethe scientistswasto find a singlebase pair changeout of sixbillionbase pairs.

Address for correspondenceVanl Brahmacharl,

Developmental Biology andGenetics Laboratory, Indian

Institute of ScIence,Bangalore 560 012. India.

Suggested Reading ,A H Sturtevant. A History of Genetics. Harper International edition, Harper andRow, New York. Evanston and

London andJobn WeatherhiU Ine:.Tokyo. 1965.Bruce R VoeDer (Ed.). The Chromosome Theory of Inheritance. CJassicpapen in Development and Heredity.

Appleton-Centary-Crofts, New York. 1968.Monroe WStrickberger. Genetics. (lDrdedition). Macmillan PublishiDgCompany, New York. CoUiarAb m..n

Publishers, London. 1976.Adrian M Srb, Ray D Owan, Robert S Edgar (Comp.). Facets of Genetics. W H Freeman and Company,

SanFranc:isc:o.1970.Louis Levine (Ed.).Papen onGenetics. ABook ofReadiDp. TheCV MosbyCompany, St.Louis, USAandToppan

Company Limited, Tokyo, Japan. 1971.

RESONANCEI January 1996 47


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SERIES I ARTICLE

Know Your Personal Computer1. Introduction to Computers

- .~I.. f

Siddhartha KumarGhoshal workswithwhatever goes inside

paraDelcomputen. Thatincludes hardware, systemsoftware,algorithms andapplications. From hisearly childhood he hasdesigned and built

electronic gadgets.One ofthe most recent onesamong them is a shteen

processor paraDelcomputer withmM PCmotherboards.

FIgutrl , Computer-memDtywbsysfem.

0...B..

48

S K GhoshalThis article describes in brief the basics ofthe orgaqizationof the control and processing unit, memory subsystem andperipherals of a computer.IntroductionComputers are built using semiconductors and other electronicparts, magnetic media and electromechanical devices. Collec-tively these are calledthe hardwareofthe computer. Their organi-zation is subdivided into Control and Processing Unit (CPU),Memory subsystems and peripherals. They come in all sizes andcapabilities, ranging from supercomputers to pen-tops, but thereis a basic unity in their organization. We will first discuss theorganization ofcomputers andfollowwith adiscussion onperiph-erals and software.Computation and MemoryJust as humans use a base-IO arithmetic system because theyhave ten fingers on their two hands, computers use a base-2arithmetic as digital hardware computes and stores informationmost reliably in one of two stable states, called OFF and ON.Alternatively they are called 0 and 1.Bit is an abbreviation ofbinary digit.Usingpanerns ofbits, computers store integers, rational numberscalled floatingpoint numberswhich approximate real numbers,characters and many other data types.Figure 1 is a block diagram of a computer. It consist of a CPU andmemory.



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About the series Know Your Personal Computer

The advent of personal computers in the early

1980s revolutionized the applications of computers.

Computers which were expensive and somewhat

daunting to the common man suddenly became

affordable to many small organizations and indi-

viduals. An early decision by IBM (International

Business Machines Corporation) to publicize the

internal hardware structure and interface details

enabled many manufacturers to design IBM clones

and price them competitively. Concurrently soft-

ware companies, particularly Microsoft, designed

an operating system called MS-DOS (Microsoft

Disk Operating System) which allowed a novice to

start using the computer. A host of compilers for

popular programming languages (C, FORTRAN,

PASCAL, COBOL etc.) appeared. Application pro-

grams for word processing, database design,

accounting and numerous other areas were devel-

oped. These developments are of particular signifi-

cance to India as computers became affordable to

many colleges, schools and individuals. Almost all

colleges and many schools now have computer

centres with numerous personal computers. Stu-

dents routinely use them to write programs. As a

user one is usually curious to know what is inside

the personal computer and learn details not usu-

ally found in text books. The intention of this series

is to explain in some detail the hardware and

software of personal computers. It will include

articles on the CPU system, memory system, pe-

ripheral systems, PC interfacing, basic input-out-

put system, PC operating systems, PC networking,

multimedia and some recent developments re-

lated to PCs.

The topics are chosen such that a science graduate

will have a reasonably good knowledge of com-

puter basics, applications of computers and future

trends if she or he diligently reads the articles in the

series. It will assist the teacher in supplementing

information found in text books with issues of

practical consequence in using personal comput-

ers and may even be useful in troubleshooting

personal computers.

The series is written by S K Ghoshal who has many

years of experience in designing systems using

PCs. Readers are welcome to send suggestions on

the articles and queries about personal computers.

V Rajaramanresults specific to these types. The type of the operation performed

is called the op-code. An op-code combined together with the

addresses of the operand is called aninstruction.An instruction is also

represented as a bit pattern.

A collection of instructions is called a computer program, or code.They are kept in memory, which is a collection of memory cells

organized in a highly regular fashion. Eight bits are grouped to-

gether and called abyte. Each byte-wide memory cell has a unique

Just as humans

use a base-10

arithmetic system

because they

have ten fingers,computers use a

base-2 arithmetic.


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SERIES ARTICLE

RESONANCE January1996

50

address and its contents can be accessed by referring to it by the

address. The memory is connected to the CPU, using a large number

of data and address lines, called abus. There is anaddress bus whichis unidirectional and conveys the addresses generated by the CPU

to the memory. There is also a bidirectionaldata bus which allows

memory to exchange data with the CPU.

The width of the data bus is usually a multiple of eight. Memory is

thus often organized in bytes as a whole. Each byte has a unique

address. A byte is the minimum unit of information exchanged

between the CPU and the memory. Each data type needs an integral

number of bytes to be represented.

When data is brought inside the CPU for manipulation, it is kept

in memory cells which are located in the CPU and calledregisters.

Registers are also as wide as the integral multiple of bytes.

Each instruction also needs an integral number of bytes to be stored.

The CPU fetches, decodes and executes them one by one. The CPU

has an internal register called theprogram counter (PC)to index into

the code memory and point to the next instruction to be executed.

There is no way to distinguish between an instruction and a data-

type and this fundamental limitation of today's computer

organisation delays the development of correct programs.

The main memory of a computer can be read and written and data

which is to be manipulated is stored in it. The code that is translated

from highlevel language is also kept in the main memory. Code

memory should not be over written although some programs called

self modifying code do this.

When digital hardware is switched on, it is uninitialized. Each one-

bit memory cell of the system can be in a state 0 or 1, which is decided

randomly as it depends on so many physical parameters beyond the

analysis and control of the system designer. Thus before hardware

can be used, it must be initialized.

Self Modifying Code

This idea of interchange-

ability of instruction and

data was one of the most

important ideas of von

Neumann. In the early

days of computers this al-

lowed one to write self

modifying programs. So

the same instruction could

be executed repeatedly

each time modifying its bit

pattern to give it a differ-

ent meaning or to make it

access operands from dif-

ferent memory locations.

In those days memory was

scarce. So programs had

to manage with tiny

amounts of memory (com-

pared to todays stan-

dards) and do a lot of

work by the same stan-dards. Thus, without a

self-modifying code many

programs which later be-

came the first working

prototype of the many ap-

plication programs of to-

day, would never have

been written. However it

is difficult to make self

modifying programswork correctly and even

more difficult to document

them. So their use is dis-

couraged.


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That is done by executing the code from aread only memory (ROM)

which cannot be altered by the CPU and which retains the informa-

tion even when the computer is switched off. ROMs also containmany data objects that are needed to initialize the computer before

it can be used. Programs and data stored in a ROM are collectively

referred to as thefirmwareof the computer. In order to make the CPU

begin its execution by fetching code from the ROM, a signal called

RESET is applied to the CPU from outside. In most systems it is

generated when the system is switched on. Optionally there is a reset

button.

Main memory is made of two types of memory cells: static RAM

(SRAM) and dynamic RAM (DRAM). Static RAMs consume more

power per bit but are faster.

A given computer system has both of the above types of

memory. A small amount of SRAM and a large amount of

DRAM comprise the main memory system. Programs display a

phenomenon called coherence which can be used effectively to

design the memory systems of computers. There are two types

of coherence:

l Temporal Coherencewhich means that if a given memory location

is accessed now, there is a fair chance that it will be accessed soon

again.

l Spatial Coherencewhich means that if a given memory location

is accessed, it may well be that its neighboring locations will be

accessed next.

Thus it helps to keep frequently accessed blocks of memory in fast

SRAMs, which are backed up by slower but larger DRAMs. This

principle is calledcaching. The smaller, faster memory at the higher

level (i.e., closer to the CPU) is calledcache memory whereas the

larger and slower memory at the lower level, further away from the

CPU is calledmain memory.

Locality of Reference

There is a phenomenoncalled locality of reference

which programs display

when they are executed.

In fact 90%of the time they

access 10%of the total

memory locations they use

if one takes an average

over a large number of

programs. Both temporal

and spatial coherence areresponsible for this. Tem-

poral coherence occurs

because programs often

execute in tight loops,

waiting for an iteration to

converge or for some other

event to take place. Spa-

tial coherence arises be-

cause programmers of-

ten place data objects of

the same type (for ex-

ample the elements of a

matrix) in consecutive

memory addresses and

perform similar transfor-

mations on them, one by

one.

The memory is

connected to the

CPU, using a large

number of data

and address lines,

called a bus.


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SERIES ARTICLE


52

Note that this usage is relative as there are usually many levels in a

hierarchical organization of a memory system and what is cache

memory at a given level may itself be main memory at the next upperlevel. Caching is used at all levels in a memory subsystem design. The

aim is to provide a memory that appears as fast as the cells in the

highest level and as large as the capacity of the lowest level. For

programs that are coherent, this aim is realized to a large extent.

Between the SRAM and DRAMs of the memory system, the

caching functions are performedin hardware,that is, by designing

and physically implementing digital circuits using semiconductor

integrated circuits. These circuits are calledcache controllers.

Caching is transparent to the program that is running on the com-

puter or the programmer who wrote the program. The program does

not need to be written in a special way to accommodate caching. Nor

does the programmer even have to be aware of it. Whether at a given

point of time during the execution of the program (calledruntime)

a given data object or instruction is there in the main memory or the

cache memory is decided based on the behaviour of the program in

the immediate past and other ground realities prevailing at that

instant.

Secondary Memory

Main memory is too small to hold all the data and code that is

required. Sosecondary memory,which is magnetic in nature, is used

to supplement main memory. Secondary memory is slower, but is

cheaper per byte and is much larger in size, than the main memory.

It can be used in two ways:

l Virtual memorywhere the magnetic disk holds the code and data

objects which are not needed at the very moment of runtime.

However, the objects are placed in such an address space that

they can be addressed by the CPU (this address space is called the

virtual address space because it need not always be populated by

physical memory) directly at any time. They are kept in disks

and loaded into the main memory when needed. To make

What is a Cache?

The dictionary meaningfor cache is a hiding

place for food and stores

left behind (e.g. by ex-

plorers) for future use. In

computers however, it

denotes a small but fast

memory which acts as a

temporary storage or as

a buffer between two lev-

els of memory.

Caching is used at

all levels in a

memory

subsystem design.

The aim is to

provide a

memory that

appears as fast as

the cells in the

highest level andas large as the

capacity of the

lowest level.


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room for them, some other blocks of memory which have

not been used for sometime are stored in the disk.

l

Archival storage where objects are removed from the CPUsaddress space. They are brought back by a time consuming

process requiring human intervention.

For implementing virtual memory, random access magnetic stor-

age media, typically disks, are employed. This is because the CPU

may potentially require any item in its virtual address space at any

runtime. The physical location of the object referred in the virtual

address space should not affect its access time. So magnetic memory

devices such as floppy and hard disks, whose arms can seek any

desired track are used to implement virtual memory. Such devices

are calledswap devicesbecause they swap data objects and code pages

to and from the main memory. Of course floppies are much slower

as swap devices and in most cases it is impractical to use them due

to their small storage capacities. In a hard disk, the magnetic material

is coated on mechanically inflexible (hence the name) circular

aluminum platters which rotate at very high speeds and the read/

write heads float above them at a very small height. Hard disks can

record data at very high densities and access them very fast. In floppy

disks, a flexible substrate (hence the name) coated with a ferromag-

netic material is squeezed by a pair of heads. Floppy disks are cheap

and can be removed from the drives.

For archival storage and retrieval of data and programs, one can use

sequential storage devices. An example is magnetic tapes. They can

be accessed only from the beginning to the end and an object which

is placed deep inside the medium can be accessed only after all other

objects preceding it have been accessed and/or skipped. For back-

ing up and restoring contents of memory, this is adequate. Tapes

cost very little per bit of storage. Their capacities too are enormous.

Caching is employed between the swap device and main memory.

Frequently referred objects are retained in the main memory. Ob-

jects not in use are put back into the swap device. This is one of the

memory management chores that an operating system of the com-

puter performs routinely. Users and developers of computer pro-

What is a

Transparent

Mechanism?

We call something trans-

parent, if light passes

through it. Glass is trans-

parent. So one does not

see glass itself. One sees

what is behind the glass.

If the means of making

something happen is not

visible, that mechanism is

calledtransparentin com-

puter parlance.

In a hard disk, the

magnetic material

is coated on

mechanically

inflexible (hence the

name)

circular

aluminum

platters which

rotate at very high

speeds and the

read/write heads

float above them at

a very small height.

Hard disks can

record data at veryhigh densities and

access them very

fast.


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SERIES ARTICLE


54

SRAM CACHE (256 Kbytes, 40nS delay)

CPU REGISTER (128 bytes, 15nS delay)

DRAM MAIN MEMORY

(512 Mbytes, 150nS delay)

TAPE ARCHIVAL MEMORY

(256 Tbytes, 7days)

HARD DISK SECONDARY MEMORY

(8 Gbytes, 20mS delay)

SMALL

ER

FAST

ER

SLOW

ER

LARG

ER

grams need not be aware of these functions.

Thus objects go up and down the levels of memory hierarchy (seeFigure 2). An object which is frequently used will eventually find

itself in the CPU registers provided it is small enough to fit there. On

the other hand, objects not in use will go further and further away

from CPU until they are backed up in a tape and removed from the

computing system.

Peripherals

These are attached to the computers. They extend the computers

capabilities to function like printing on paper, exchanging informa-

tion with other computers, accepting input from human beings,

displaying text or graphic images and the like. Peripherals, by

themselves cannot do anything. They always need to be attached to

a computer, usually referred to as thehost computer. Peripherals too

can have their own memory, but that is beyond the virtual address

space of the host computer. Often they have their own built-in CPUs

which perform special functions within that peripheral device. In

such cases, the microcontroller chip containing the CPU is called an

Figure 2 Levels of memory

hierarchy, typical site and

speed at each level is given

as of 1995. These typical

numbers change every year.

There is no way to

distinguish

between aninstruction and a

data-type and this

fundamental

limitation of

today's computer

organisation

delays the

development of

correct programs.


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SERIES ARTICLE


embedded controller.

Software

The set of programs that run on a computer is collectively called its

software. There are two types of software:

l System software which manage resources like the CPU and the

main memory, extend the capabilities of the hardware and

otherwise help users and application programs use the com-

puter.

l Application software which run on the computer and have some

end use.

Examples of system software are operating systems, different utili-

ties and high-level language compilers.

There are many types of applications of computers. Numeric graphic,

database and symbolic computing applications are some of them.

Certain computers are specially suited for certain applications, and

they keep

Documents

Resonance Magazine , 1st January 1996