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Hamilton, Irlannin Suurin Luonnontieteilijä Hamilton, Irlannin suurin luonnontieteilijä Osmo Pekonen Irlannissa on vietetty Kansainvälistä fysiikan vuotta 2005 kansallista teemaa käyttäen. Ein- steinin lisäksi on voitu muistella maan omaa suurta poikaa Sir William Rowan Hamilto- nia (1805–1865), jonka syntymästä on sopivas- ti 200 vuotta. William Rowan Hamilton syntyi Dublinissa keskiyöllä 3./4. elokuuta 1805, joten hänen syn- tymäpäivästään on kirjallisuudessa kahdenlai- sia tietoja. Kotiosoite oli 36, Dominick Street. Isä U T U H Archibald oli asianajaja ja setä James pappi. He herätti huomiota ilmoittamalla asiasta Irlannin A P A kannustivat pikku Williamia opintielle omape- kuninkaalliselle astronomille John Brinkleyl- T räisillä menetelmillä: pojan isovarpaaseen kiin- le. Tämä totesi nuoren Hamiltonin olevan suuri Ä 17 S S nitettiin naru, josta nykäisemällä hänet saatiin matemaattinen henki ja kehotti häntä tulemaan E E T E I takaisin läksyjen pariin. William oli ihmelapsi, aamuteelle milloin vain hän haluaisi. Kahdek- T jonka lahjakkuus ilmeni aluksi kielellisesti. Jo santoistavuotiaana Hamilton kirjoittautui Dub- ennen kouluikää hän oppi heprean, kreikan ja linin Trinity Collegeen, vuonna 1592 perustet- latinan alkeet. Myöhemmin seurasivat arabia, tuun kunnianarvoisaan opinahjoon, josta mo- bengali, hindi, kaldea, malaiji, persia, sanskrit net Irlannin suurmiehet ovat valmistuneet. Ha- ja syyria. Pojalle ajateltiin uraa Itä-Intian kaup- milton sai parhaat arvosanat niin humanistissa pakomppanian palveluksessa, mutta ennen pit- kuin luonnontieteellisissä aineissa. kää selvisi, että hänestä tulisi tiedemies. Kaksitoistavuotiaana William näki amerik- kalaisen päässälaskijaihmeen Zerah Colburnin Matematiikkaa vai runoutta? esityksen, joka sytytti hänessä matematiikan ki- pinän. Epänormaalin hyvät päässälaskijat ovat Hamiltonin ensimmäinen, John Brinkleyn oh- usein autisteja, ja varmaan siitä oli kysymys jaama matemaattinen tutkielma On Caustics Colburninkin tapauksessa. Myös Williamilla oli valmistui 1824. Sitä ei kuitenkaan vielä julkais- ilmiömäisen hyvä laskupää, mutta hän ei sen- tu, vaan Irlannin Kuninkaallinen Tiedeakatemia tään pärjännyt Colburnille. Nuori Hamilton kehotti tekijää pyrkimään kyseisen ongelman kohtasi ehkäpä ensimmäistä kertaa itseään suu- ratkaisussa pitemmälle. Tämä olikin hyväksi, remman mentaalisen kyvyn, mikä lienee jäänyt sillä vuonna 1826 Hamilton esitti merkittäväs- harmittamaan häntä. sä artikkelissaan Theory of Systems of Rays hyvin Kolmetoistavuotiaana Hamilton alkoi lukea yleisen karakteristisen funktion, joka mahdol- ranskalaisen ihmelapsen – aikoinaan muuten listaa monien optiikan perinteisten ongelmien Maupertuis’n mukana Lapissakin käyneen – matematisoimisen. Tulos oli suuri sensaatio. Alexis Clairaut’n kirjoittamaa algebran oppikir- Vuonna 1827 Hamilton jo valittiin sillä vä- jaa. Viidentoista vuoden iässä olivat lukulistal- lin Cloynen piispaksi nimitetyn opettajansa la Lagrange, Laplace ja Newton. Hän löysi Lap- Brinkleyn seuraajaksi Irlannin kuninkaallisena lacen taivaanmekaniikasta erään virheenkin ja astronomina. Tähän juhlavaan titteliin kuului TIETEESSÄ TAPAHTUU 8/2005 myös Trinity Collegen tähtitieteen Andrewsin säteen tunkeutuessa sopivasta suunnasta opti- oppituoli sekä virka-asunto Dunsinkin tähtitor- sesti kaksiakseliseen kiteeseen, esimerkiksi ara- nissa – ei hassumpaa kaksikymmentäyksivuo- goniittiin. Tällöin säde taittuu ontoksi valokar- tiaalle opiskelijalle, jonka lopputyö oli vielä te- tioksi. Hamilton ennusti kartiotaittumisen ma- kemättä! Näin nuoren henkilön nimitys herätti temaattisesti, ja kaksi kuukautta myöhemmin tietenkin myös arvostelua, ja totta puhuen Ha- Trinity Collegen fysiikan professori Humphrey miltonista ei kovin hyvää tähtitieteen havain- Lloyd todisti sen kokeellisesti, mikä teki Hamil- noijaa koskaan tullutkaan. Tähtitiede sai jää- tonista maailmankuulun. Koejärjestelyssä valo- dä sivuseikaksi, sillä Hamiltonin aika kului pi- kartio näkyy kirkkaana ohuena renkaana valo- kemminkin matematiikan parissa. Trinity Col- kartiota leikkaavalla tasolla. lege suhtautui kuitenkin asiaan suvaitsevaises- Vuonna 1839 Poggendorff havaitsi, että ky- ti: pääasia, että jokin pysyvä virka lahjakkaalle seinen valorengas itse asiassa muodostuu kah- nuorelle miehelle saatiin. desta renkaasta, joiden väliin jää pimeä alue. Kielellisesti lahjakas Hamilton askarteli pal- Vuonna 1905 Voigt selitti tämän ilmiön teoreet- jon myös runouden parissa. Hän osasi pitää ko- tisesti. Vuonna 1941 Raman havaitsi, että pitkil- meita juhlapuheita, joissa kernaasti siteerasi ai- lä etäisyyksillä valokartio supistuu pisteeksi. kakauden suuria runoilijoita ja lisäsi jatkoksi Belsky ja Khapalyuk mallinsivat vuonna 1978 omiakin säkeitään. Hän runoili mielellään täh- valokartion hienorakenteen matemaattisesti, titaivaasta. mutta vasta 1997 Warnick ja Arnold kehittivät Kun Hamilton teki opintomatkan Englan- numeerisen menetelmän, jolla Belskyn-Khapa- tiin, hän ystävystyi William Wordsworthin lyukin yhtälöt voidaan ratkaista. Tällöin löytyi kanssa. Tietenkin hän näytti mestarille runo- sisemmästä Poggendorffi n renkaasta vielä oma jaan ja kertoi suunnittelevansa myös kirjailijan matemaattisesti ilmenevä hienorakenteensa. uraa. Wordsworth kuitenkin totesi pelkäävän- Ei kuitenkaan ole pystytty valmistamaan niin T I sä, että kaunokirjallinen puuhastelu vieroittaisi säännöllisiä kiteitä, että tämäkin hienorakenne E T E E nuoren professorin tieteestä. Hän suositteli Ha- saataisiin kokeellisesti näkyväksi. S S Ä miltonille keskittymistä matematiikkaan, jossa Kartiotaittumista on tutkittu kohta kaksisa- 18 T tämä voisi saada aikaan suurempia asioita ih- taa vuotta, mutta kumma kyllä sille ei ole keksit- A P A miskunnan hyväksi kuin runoilijana. ty merkittävää käyttöä optisissa laitteissa. Han- H T U U Kaunosielu Hamilton ei kuitenkaan koko- noverissa toimiva yhtiö Vision Crystal Techno- naan malttanut luopua runoudesta. Hänellä oli logy AG tarjoaa Hamiltonin juhlavuoden kun- lukuisia nuoruuden ihastuksia, joille hän syy- niaksi 10 000 euron palkinnon sille, joka keksii ti sonettejaan, eivätkä ne olleet vallan huonoja. parhaan kartiotaittumisen sovelluksen. Elämänsä loppuun asti Hamilton kävi epätoi- Vuonna 1834 tutkimuksessaan On a General voista runokirjeenvaihtoa erään Catherine Dis- Method in Dynamics Hamilton esitti sittemmin neyn kanssa, johon hän oli rakastunut, vaikka Hamiltonin funktiona tunnetun suureen, jol- tästä oli tullut erään papin vaimo. la on erittäin keskeinen merkitys mekaniikas- Hamilton päätyi kuitenkin avioliittoon tähti- sa. Hän päätyi dynamiikan uuteen teoriaan so- torninsa naapurissa asuneen Helen Maria Bay- veltamalla samantapaisia metodeja, jotka aikai- lyn kanssa. He saivat kolme lasta. Hamilton ei semmin olivat johtaneet karakteristiseen funk- kuitenkaan pitänyt vaimoaan tarpeeksi älyk- tioon optiikassa. käänä. Kun Hamiltonin salarakkaansa kanssa Matemaattisiin yksityiskohtiin on tässä tur- käymä kirjeenvaihto paljastui, papinrouva Cat- ha mennä. Riittäköön todeta, että Hamiltonin herine joutui asumuseroon miehestään ja yrit- mekaniikka on monissa tilanteissa käyttökel- ti itsemurhaa, ja myös Helenin elämä synkistyi. poinen vaihtoehto aikaisemmin tunnetulle La- Hamilton teki siis runoilullaan kaksi naista on- grangen mekaniikalle. (Hamiltonin funktio on nettomiksi. itse asiassa Lagrangen funktiosta muodostettu Legendren muunnos.) Vuonna 1835 Dublinissa pidetyssä British Optiikka ja dynamiikka Association for the Advancement of Science’n kokouksessa Hamilton puhui aiheesta Algebra Optiikan ja dynamiikan töillään Hamilton saa- as the Science of Pure Time. Irlannin varakuningas vutti kansainvälisen maineen jo alle 30-vuotiaa- (”Lord Lieutenant”) aateloi hänet valtiomiekal- na. Vuonna 1832 hän julkaisi teoriansa kartio- la Trinity Collegen kirjastossa, kuuluisassa Long taittumisesta. Merkillinen ilmiö esiintyy valon- Hallissa, pidetyssä seremoniassa. Vuonna 1837 TIETEESSÄ TAPAHTUU 8/2005 i2 = j2 = k2 = ijk = -1 Hän kirjoitti kaavan heti muistikirjaansa, joka on säilynyt, ja varmemmaksi vakuudeksi kaiversi sen veitsellä myös Broughamin sillan kupeeseen. Kvaternioilla tarkoitetaan lukuja q = a + bi + cj + dk, missä a,b,c,d ovat tavallisia reaalilukuja ja kirjaimet i,j,k ”imaginaariyksikköjä”, jotka nou- dattavat em. kvaternioalgebraa. Kvaterniot an- tavat tavan muodostaa neliulotteiseen avaruu- teen kertolasku, jossa ei ole nollanjakajia. Toi- sin sanoen, jos kahden kvaternion tulo on nol- la, niin ainakin toinen tulontekijöistä on nollak- vaternio. Nollanjakajattomia kertolaskuja on olemassa vain ulottuvuuksissa 1 (reaaliluvut), 2 (kompleksiluvut), 4 (kvaterniot) ja 8 (oktoni- ot), joten kysymyksessä oli hyvin harvinaislaa- tuisen uuden algebrallisen rakenteen löytymi- nen. Kvaterniokertolasku ei ole vaihdannainen, mikä aikanaan tuntui merkilliseltä. Algebralli- sesti kyseessä on ns. vinokunta (skew fi eld). Ni- U T U H men ’kvaternio’ Hamilton keksi Apostolien te- A P A kojen jakeesta 12:4, jossa kerrotaan neljän ne- T limiehisen roomalaisen sotilasvartioston (four Ä 19 S S Hamilton valittiin Irlannin Kuninkaallisen Tie- quaternions of soldiers, Kuningas Jaakon Raama- E E T E I deakatemian puheenjohtajaksi. Hän oli myös tun käännöksen mukaan) vartioineen Herodek- T Berliinin, Pariisin, Torinon ja Yhdysvaltain tie- sen vangitsemaa Pyhää Pietaria. deakatemioiden jäsen. Aivan erityisesti Hamil- ton arvosti Pietarin keisarillisen tiedeakatemian hänelle myöntämää kirjeenvaihtajajäsenyyttä – Bloomsday ja Broomsday ottaen huomioon, että hänen maansa oli silloin sodassa Venäjää vastaan! (Siihen aikaan totises- Broughamin
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