Caribbean Stories

The Day Time Machines Went Kaput

6. The Arrow of Entropy

SEEING THE PROFESSOR PRESIDING OUR ORIENTATION JUMP from the stage to go after his colleagues made me wonder if physicists are regular people like the rest of us. Picture the frizzle-haired, absent-minded Einstein and you’ll catch my drift: “Professor, your wife called to see if you ate your lunch.” “My vife?” When they invite you to participate in cutting-edge research on the very fundamentals of their discipline and you’re just a history major, you seriously question the soundness of their common sense. In any event, might as well take advantage of this opportunity to check out my messages. Time was when civilizations left their mark with monumental works of engineering. Everyone would see their magnificent works and laud them for their advancement of humankind. But we, I’m afraid, will go down in history for our gadgets. Imagine an extraterrestrial archaeologist finding a corroded smartphone or a tablet computer at her dig. She would probably conclude it was a fetish of some sort, a teknogeek talisman used to channel primitive urges. An artifact of cultural significance, undeniably, yet of minor consequence in the broader scheme of things. The foibles of a self-indulgent generation, she might proclaim, spoiled by an insouciance born of material plenty. Ah! Message from Julia, my roomie:
    «Gretchen, dorm girls going out for dinner, celebrt bck-in-BU, TGIF, whtevr. Grendel’s Den eatery, then stroll Hvd Sq, windw shop, hang around, whtevr. Lv @ 5 & catch ½$ menu. okwu? JS :) »
    Boston girls trekking to Cambridge. Oh my gosh! The Bostonians are coming! By land, Paul; one lantern. No ‘sea’ business, please. Actually, the ‘sea’ reference is due to Henry Wadsworth Longfellow, who used the word for rhyming purposes in his celebrated mythical poem. Revere* had stated, correctly, ‘by water’, explicitly referring to ‘the Charles River’. And it was William Dawes the patriot who did the midnight riding through Cambridge. Missed Grendel’s Den entirely. It was dark, you know. What. The people at Grendel’s aver it was established in 1271. Check out their sign. Everything you find here is kosher. At any rate, unbeknownst to the average American —Average? What, they slice, dice, and Osterize® the poor fellow and then apportion him into standardized containers? For all intents and purposes, you betcha! [live audience cheers] That’s what makes this country great: ideological uniformity! E pluribus unum? Bah! Pro plebis una doctrina! All citizens are at liberty to think as they wish as long as it doesn’t contravene the received mythos. For that would be un-American. Gotta give that beaut a name for handy reference. How about… The Big Gotcha! Yes! Pop quiz: Was Tricky Dick a member of HUAC? “Mister Dick, are you now or have you ever been a member of the House Un-American Activities Committee?” You betcha! Ah, America! We’ll be right back— Madison Avenue was alive and well in Boston way back then. Get outta here. America’s contribution to the world: industrial-strength Make Believe! Best darn Tinker Bell fairyland this side Giza, ma’am. But not the only one, mind you: “L’État, c’est moi!” What a jerk! Failed to see the revolution and ensuant terror incubating under his nose. Дa! Aбcoлютно! Let him eat cake. Which one? All three kings. To Bozo’s credit, he was not a crook. That depends upon what the meaning of the word ‘was’ was. American exceptionalism at its finest, folks. Don’t see that anywhere else. Estos americanos, son un poco locos, no? ¿Un poco? Hey, Poco Loco is back! Squawk! This version of Six Flags Over Fairyland comes courtesy of John Broadus (Burrhus?) Watson, Mr Mad Ave himself. Set back the science of psychology half a century. That’s one small step for a publicist (and cashiered academic), a great leap forward for propaganda. Great moments in American mind control, brought to you by Skinner’s Own Operant Conditioning™: fair and balanced. Hey, what about Jerzy Konorski? Hush! These behaviorists, no better than your garden-variety, unconsciously repressed, ultra-neurotic Viennese. Achtung! Omigosh‼ Wo ist Herr Doktor Freud, Fräulein? Chill out, goose-stepper. What are you, a Bibi wannabe? Here, take Woody. Please! Better yet, do a Rasta. It’s the real thing. Ah-ah! No Coke, Pepsi. Okay, okay. Tell ’em, Bob.  ♫ One love… ♪  (Keep these bastards away from the Achterhuis. You hang in there, sweetheart.) Yoo-hoo, Mr Watson, come here, we want to see you! (← BU Prof!) Or should it be: “Elementary, my dear Watson”? Wait, Tinseltown fake! Doyle never wrote that. That’s the way things work here in Fairyland, ma’am. Work for whom? Besides, Holmes’ a Brit. Zero lanterns.
    Remind me one day to tell you about exceptional chutzpah: the doling out of Congressional Medals of Honor to Tinseltowners who never served in the military. Blasted ’Publicans almost pulled that one off. Bronx cheers just won’t do with these sleazy, flag-enwrapped opportunists. You want fries with that? Must throw the bums out! And straight into Boston Harbor, the history of this town prescribes to a T. Tarring and feathering, anyone?
    See the downside of majoring in history: you tug on a thread and the whole schmear unravels. «okwm! Catered affair here after biz. Can’t pass it up. If I tarry, I’ll txt u. GT :o ». Tarry? Gretchen, hon, you is educated. LOL Boston! Yay!
    College days are the best time of your life.
    Indeed. Here come the physicists. Quick hop. “Alright, people, I leave you with Professor Stauffenberg, who will tell you all there is to know about why time flows only forward.” Down hop. Must be his exercise regimen.
    This prof prefers the side stairsteps, I see. Prudent behaviors tend to accompany the onset of middle age, along with the suggestive, more ample girth. “Hello, eferyone. I vould like to talk to you a leetel about time. Since vee don’t haf much time —who does, eh?— leetel joke, zere —I am not zis korny in my natif language, by zee vay— I vill try to keep zee talk schort. Go gif a talk in German und see how much fun it vill be.”
    Oh, I love this guy.
    “Zee problem vis time, vat makes it different from ordinary shpace, is zat it gifs zee impression of somehow being in motion, a uniform motion zat is unidirektional, shtriktly one-vay: you are here now und you go zere zen. Zat’s it. You haf no say on zee matter und you kan nefer kome bak here from zere or from anyvere else. Vell, as long as anyvere else is not in zee past of here-now. In zee past und visinn zee light kone, I schould add. Vell, if it is in zee past, zen it has to be in zee light kone. But vee kannot trafel bakvards in zee light kone from zee here-now to zee zere-zen to begin vis. So I schould not add anysing to zat.”
    This man must have suffered tremendously the torments of freshman physics.
    “But vee kould trafel forvard in zee future light kone, tilting zee kone kontinuously vis zee help of a vell-chosen blak hole’s kolossal grafitational field, such zat zee kone vould zirkel bak in shpacetime und approach zee anterior zere-zen from behind, zat is, from an efen more remote past. Zis vay vee kan easily return to zee here-now from zee zere-zen, verefer-venefer zat zere-zen may happen to be. But let’s not get into zat now-here.”
    I stand corrected. I think.
    “Zee question is zen: Vye is it zat time, quote unquote, flows, only forvard, forvard being from zee present into zee future. Vye kan’t time flow bakvards into zee past? Leafing sermodynamiks aside for zee moment, zere is nossing in zee fundamental laws of physiks zat requires time to flow only forvard. Vee vill get to sermodynamiks schortly. At zee mikroskopik lefel of reality, zee atomik und subatomik realms, zee laws vork equally vell going bakvards. Time kould, in principle, flow bakvards und eferysing vould be just fine. But makroskopikally, at our lefel of perceifed reality, it nefer does. Vee nefer see sings going bakvards like a moofie running in referse. Time is, mikroskopikally, funktionally refersible, but makroskopikally it is definitely not. Temporal irrefersibility is infiolable at zee makro skale. But zen, how is it possible for such an irrefersibility to arise from an underlying infinitude of refersibility? Vee must determine vye zis glaring kontradiktion exists.”
    Now, there’s a stumper. Will physics save the day? Of course.
    “Zere are ozer questions vee kould ask, more komplikated questions, such as: Vye kan’t time flow sidevays or up und down? In ozer vords, vye does time haf only one dimension —und a one-vay dimension at zat— vile shpace has sree dimensions? Kan time, or shpace for zat matter, haf more zan sree dimensions? If zat vere so, how many more dimensions kould each haf? If shpacetime vere to haf extra dimensions, vould vee four-dimensional beings be able to detekt zem? Vee are sree-dimensional at any given point in time, zat is, seen from a shtatik perspekteefeh. But dynamikally, vee are like eferysing else: four-dimensional. Does failing to detekt further dimensions proof zat zey do not exist? Kould it be possible to haf infinite dimensions? Und vat vould such a vorld be like? Kould zee higher dimensions of such a hypershpace harbor life? If so, kould zose beings be able to vatch us, much like vee shpy on mikrobes from aboff vis our mikroskopes? Zees questions kan be numerous und utterly mind-boggling. But let us restrikt ourselfs to zee simplest question, vich fortunately for us has a relatifely simple ansver.”
    Whew! Glad to hear that.
    “Zee reason vee know zat time passes is bekause sings change. «Zee sun also arises, und zee sun goes down, und hastens to zee place vere it arose.» It has alvays been known zat zee sun changes its position vis zee passage of time. Vell, pretty much alvays, since a fery long time ago. Zee time-honored vay of keeping time is by keeping trak of zee position of zee sun in zee celestial shphere. (At night vee kan trak zee shtars.) Zis, vee all know, is how vee perceif Erde’s rotation, how it appears to us, but zat is fine; it serfs to illustrate zee point. Und zee point is zat an extended amount of time elapses between sunrise und sunset. Zee two diurnal efents do not okkur simultaneously, alzough simultaneity is a shpecial-relatifistik kan of vorms vee schould afoid for now. A blok of time —a duration— separates zee two efents of sunrise und sunset. Zat is goot; ozervise zee entire history of zee kosmos vould flash by in an instant. More korrektly, one kould not haf any history in a timeless uniferse bekause zere vould be no temporally manifest efents for history to rekord. Nor vould zere be any time in vich to do zee rekording, to say nossing of a reasonable time interfal in vich zee kronikler kould fleetingly exist. Zis schows zat visout time —a temporal dimension— physikal reality as we know it kould not be possible.”
    Whoever designed this universe knew darn well what she was doing. Cool it, atheists. ‘She’ is Mother Nature. Doggone scientism fanatics.
    “So vee kan tell zat time passes bekause vee kan see zat sings change. But it is not only zee perception of change zat matters, a phenomenologikal impression planted in your head. Perception und memory are necessary but not sufficient. Zee change vee perceif is objektifely real. It exists ‘out zere’ independently of us, our percepts, und our beliefs. Zus, keeping und telling time requires matter und energy —physikal objekts und motion, specifikally, periodik cyklikal motion— real physikal shtuff. Since sings keep changing all zee time —a kafalkade of perpetual motion, ironikally— time just keeps on flowing. Zat is zee vay zat nature is built. If sings vere not to change at all, zen time vould not pass. I schould explain zis more klearly: If all sings in zee uniferse vere frozen shtiff —frozen to absolute zero, vere one might sink zat zee motion of molekules und atoms shtops— time vould also be frozen shtiff; it vouldn’t flow anyvere. Time as vee know it vould simply cease to exist.”
    Hmm… an untimely end for time, one might say.
    “But it is not possible to freeze zee material kontents of zee uniferse to absolute zero bekause of zee kosmik mikrovafe bakground radiation left ofer from zee Big Bang, zee afterglow of zee birs of zee uniferse. Und efen if it vere possible to eliminate zis festigial sermal radiation, zere remain tiny pokkets of energy at efery point in shpace sroughout zee uniferse, vat vee in zee business kall quantum fakuum zero-point energy. It is not possible to do avay vis zees two energy reserfoirs zat are intrinsik to zee fabrik of shpace. So, since zere is alvays some residual energy around, zere is alvays some jiggling here und zere und time zerefore just keeps on ticking.”
    Ah! Eternity. Sounds good to me.
    “Seen from a different perspekteefeh, a philosophikal one, a uniferse visout time kannot efer be bekause visout time zere is no motion und visout motion physikal processes kannot possibly okkur. I am now subsuming all of kemistry visinn physiks. Vis no physikal processes, nossing kan bekome existent. In partikular, no DNA kan emerge. But Deskartes demonstrated zat zere is indeed at least one sing in zee vorld zat assuredly attained existence, namely, «I», zee sinking self, who happened to get shtukk here in zis plane for some reason. Konsequently, since zere are certain physikal sings in zee vorld —kognitif supershtruktures requiring zee preexistence of biophysikal infrashtruktures to sushtain zem— time must exist und alvays haf flowed in our uniferse. Time simply kannot shtand shtill und disappear.”
    I never realized that physics was philosophy in disguise. Interesting.
    “Zat all makes sense, but does it akkurately deskribe physikal reality? Vat I mean by zat is, kan zee essence of zee kosmologikal und ontologikal arguments zat I haf presented be expressed in terms of konfentional physikal framevorks? In physiks, vee like to keep sings physikal bekause zat is vat vee know about. So let’s get physikal. Is zere a korresponding argument in physiks zat proofs zat time exists, zat it flows, und zat it flows only forvard? Here is zee goot news: Ja, zere is!”
    Make a note of that: «The Good News according to physics must be expressible in conventional physical terms. No vishy-vashy stuff.»
    “To see zee physikal argument, vee must probe into zee fundamentals. Let’s take zose molekules vee vere talking about und assume zey’re perfume molekules of identikal makeup. Fery fragrant. Let’s open zee leetel bottel of perfume in a room zat is perfektly sealed off from its enfironment und leaf it zere for a few days. Vat vill happen to zee perfume?”
    Gotta take a shot at this while the questions are such that I can answer them. Wave that hand high, Gretch!
    “Ja, zee shtudent ofer here!”
    “The perfume will evaporate and saturate the air in the room. But it will take more than a few days.”
    “Zat is korrekt! Fery goot! A big applause for zee Fräulein, please? Sank you. Sank you fery much. You haf experience vis zee perfume, ja?”
    “Goot, goot. Und vat is your name?”
    “Gretchen. Gretchen Trent.”
    “Fräulein Trent kan teach us all a sing or two: Zee only vay to know sings for sure is to kondukt an experiment. Sank you, Fräulein Trent. I haf learnt somesing important today, zat I schould test my anekdotes before I use zem in publik.”
    Aw geez, made me blush. Smile and wave genially, Gretch. Attagirl!
    “Fräulein Gretchen Trent! sehr geehrte Damen und Herren!
    Oh my God‼ He’s brought the house down!
    “Danke. Danke. Herzlichen Dank! Danke.
    Boy, does he ever know how to win over an audience! Move over, Watson and Junior. Gestalt rules!
    “Danke fery much. Now, vee know zat as time passes zee perfume molekules, vich initially vere koncentrated in zee leetel bottel, vill tend to vaft into zee room, efentually saturating zee air of zee room, just as Fräulein Trent explained. In zee bottel, vee kan konceif of zee perfume as a physikal system in a somevat organized shtate, namely, a kohesif liquid zat kan easily be used by zee person, applying it to her body und garments. But ven zee perfume efaporates, it is no longer in an organized shtate. It has bekome a gas, an agglomeration of free molekules randomly skattered sroughout zee room. Und alzough zee number of molekules of zee fluid remains zee same, ignoring kemikal dekomposition reaktions, zee person kan no longer make use of zem as before bekause zee system is now in a disorganized shtate. Zee original liquid system has transformed into a gaseous system vich, from zee point of fiew of zee person, renders zee perfume unusable.”
    Valid point. Go on.
    “But zis process of system disorganization —transformation is perhaps a better term, less subjektif— happens not only vis matter but also vis energy. In fakt, it vas vis energy zat zis process vas first analyzed und undershtood. Keep in mind zat zee only sings known to exist in shpacetime are matter und energy. Vell, und forces und fields. But zees sings go hand in hand vis matter und energy in zee zeoretikal framevorks of partikel physiks und of klassikal und quantum field zeories. So vee’ll  shtik to matter und energy. Vee vill not go into zee physiks of information in zis diskussion.”
    Umm, do these people really know what they’re up against? Might they not be abstracting richly textured actuality to the point of dismantling it into a flat collage of purely symbolic, intellectual formalisms that stultifies the immediacy and tangible vibrancy of sovereign existential reality?
    “Vis energy vee haf an analogous situation to zee issue of usable und unusable perfume: usable und unusable energy. Ven energy is used to do vork or ven it is transformed from one form of energy into anozer, part of zee energy input is dissipated und bekomes unusable. Vye is zat? Bekause ven energy is used by, say, a machine, some of it is lost to friktion of zee moofing parts; to noise, vich are sound vafes; to machine fibrations; und so on. Zees dissipations are irrefersible; you kannot undo zem to rekofer zee lost energy. Zee dissipated energy defolfes into vaste heat, vich bekause of its low temperatur, has fery leetel kapacity to do vork. Maybe you kan use it to help heat your haus or badin vater but zat’s about it, downshtream tasks. You kannot kollekt all zee vaste heat und add it to zee vork produced by zee machine to pover zat machine, zee same zat produced zee vork und vaste heat in zee first place. Zat vould be a perpetual motion machine, vich kannot be bekause zee vaste heat is shpent insofern als its kapacity for povering zee machine is koncerned. Zee energy is shtill around in zee form of ambient heat, for energy kannot be kreated or destroyed, but it kan no longer be used to do upshtream vork. In time, zee heat vill radiate avay into shpace und zen truly bekome lost forefer. For us.”
    Ominous sign. If all energy is destined to go that route, it spells the death of the universe. Aha! The infamous heat death of the universe!
    “Zis transformation of usable energy into unusable energy is at zee heart of zee koncept of entropy. Teknikally, in sermodynamiks, entropy is a measure of zee amount of sermal energy in a system zat is not afailable for doing mekanikal vork. Informally, zee term is interpreted as zee amount of disorder in a system und, by extension, as zee process of gradual dekline into disorder itself, zee ill-fated deterioration of any system. In a klosed system, such as our sealed room, entropy vill inkrease until it reaches its maximum possible lefel, vich okkurs ven zee kombined machine-und-room übersystem attains sermal equilibrium, ven zee temperatur bekomes zee same eferyvere. Of kourse, by zen zee machine has long shtopped.”
    Maschinenstopp. Yes! Hey, goosh-shtepper: Shtoppit, shtuppit!
    “Zere are ozer possible equilibria: mekanikal, kemikal, radiatif, for instance, depending on zee type of system. In zee kase of zee efaporating perfume, vich is a mekanikal system, maximum entropy is reached ven zee perfume gas kompletely saturates zee air of zee room und its molekules are most randomly dispersed. Zee perfume is zen maximally useless, except for zee lingering fragrance of zee room, vich vill in due kourse also cease being fragrant bekause of molekular dekomposition, a form of kemikal entropy.”
    Zere goes mein Parfüm. Kerplunk! (Beware.)
    “Entropy is alvays present in physikal systems, vezer zey konsist of matter or energy or efen information. It is a fundamental property of nature: sings efentually fall apart. If zee system is a klosed system, vis no exchange of matter or energy vis its enfironment, entropy vill alyays inkrease to zee max, vere equilibrium is reached und zee system bekomes uniformly inert. Vat zis means is zat eferysing in zee uniferse is gradually going kaputt.”
    Oh, dear. There goes eternity.
    “Assuming zat zee uniferse is a klosed system. It may or may not be, no one knows.”
    A glimmer of light at the end of the tunnel, perhaps?
    “But it looks pretty bad.”
    Dang! Who got us into this mess, anyway?
    “Nefertheless, on zee flip side, efer-inkreasing entropy turns out to be useful, for it signals zee direktion of zee passage of time. Since all sings are alvays running down due to entropy —ineskapably in klosed systems; open systems by und large haf a leetel more leevay for a leetel more time und kan dekrease entropy in zee schort term by partly exporting their entropy to zee enfironment— zen zee future must lie in zat same direktion. Entropy results from zee existence of asymmetrik irrefersible processes, und irrefersibility marks an arrow of time. It is zis irrefersibility und its konkomitant entropy —vich is vat vee kan aktually measure, alzough at times only in principle— vat prefents time from flowing bakvards or bekoming shtagnant or going up und down or sidevays or getting shtukk in an infinite loop or vatefer. Time has to go vis zee flow. Zat’s zee law.”
    Eureka! Got it! Sort of. Slippery little thing. Wait. Ooh! Lost it. Darn.
    “Time flows down zee gorge wrought by entropy deep in zee fabrik of nature.”
    Dazzling allegory! Metaphorically speaking. Ergo, entropy works like the Colorado River. But if that is the case… time is not at all like space.
    “So you see, time is not at all like shpace.”
    Yes‼ A born physicist, Gretch. Danke, Damen und Herren! Danke! Please, you are too kind. Danke sehr. Okay, okay, sit down already.
    “Does zis mean zat time is Zee Great Destroyer?”
    Shades of Shiva! Boy, you could hear a pin drop in here.
    “No. Entropy is.”
    Now Entropy is become Death, the destroyer of worlds.
    We need a dash of Vishnu here.
    “Fery vell, zere is one sing zat remains to be explained: Vye is it zat irrefersibility prefails at zee makro-lefel ven zee underlying mekaniks at zee mikro-lefel are perfektly refersible? How kan one rekoncile zees diametrik opposites at different hierarkikal lefels of zee selfsame physikal reality?”
    Sure beats me. Instruct us, Professor, with thine erudition.
    “Shtatistikally. Remember: Ven all else fails, try shtatistiks.”
    Mark Twain’s Disraeli attribution puts it best: «There are lies, damned lies, and statistics.»
    “Konsider matter: Inside zee leetel bottel of perfume, zere is a limited number of possible konfigurations zat zee molekules kan assume. Zee bottel is, after all, quite small und zee limited afailable konfigurations force a low entropy kondition, zee liquid. But ven zee molekules vaft out into zee much larger room, zere are many more possibilities, far exceeding vat our intellekt kan eshtimate visout zee use of masematikal komputations. Most of zees gazillion, mikro-lefel konfigurations korrespond to zee makro-lefel shtate zat vee kall high entropy. Zus, it is far more likely for randomly distributed molekules to be in one of zee gazillion konfigurations zat korrespond to zee high entropy kondition zan in one of zee few konfigurations korresponding to zee low entropy kondition. Zerefore, it is astronomikally far more likely to haf high entropy zan low entropy in a large klosed system. Irrefersibility arises not bekause it is physikally impossible for zee molekules to arrange zemselfs into orderly, low entropy patterns but bekause it is highly unlikely for orderly patterns to happen by chance. Vezer vee like it or not, zee game is rigged in fafor of kaotik disorder und shtatistikally preordained system degradation at zee makroskopik lefel. Zose are zee rules of zee game.”
    I hate this game! Who’s responsible for this infernal Skinnerian box?
    “Analogous arguments hold for energy und for information. Vee kan now see zat irrefersibility und inkreasing entropy are only shtatistikal laws, not hard-und-fast deterministik laws. Zis leafs open zee possibility of seeing an extremely unlikely efent efery now und zen — a mirakel, if you vill. But mirakels do happen, so zee zeory is on a sound empirikal footing.
    “Properly, vee schould say probabilistik laws instead of shtatistikal, for likelihood is synonymous with probability, not shtatistiks. Alas, zee term has already been koined, if erroneously.”
    There are errors, damned errors, and statistics.
    “Fräulein Trent, did zee talk lif up to expektations?”
    “Yes, sir, it most certainly did! Danke sehr, Herr Professor.
    And there’s the standing ovation. Rightfully earned, Prof! Bravo!

Posted:   21 Jan 2015
Revised:   1 May 2015

The Real McCoy • Web Lectures on Entropy & Time

Entropy • Bozeman Science • Paul Andersen, Bozeman High School • 7:04

Entropy • MIT OpenCourseWare • John Lienhard, MIT • 13:32

A New Theory of Time • Lee Smolin • 23:43
Perimeter Institute for Theoretical Physics,
University of Waterloo, University of Toronto

Why Is Time a One-Way Street • Santa Fe Institute
Leonard Susskind, Stanford University • 1:13:38

The Origin of the Universe and the Arrow of Time • Google Tech Talks
Sean Carroll, Caltech, University of Chicago • 1:17:34

No Coke, Pepsi! • "The Olympia Restaurant" • SNL 28 Jan 1978

Image credits:

Rudolf Clausius, originator of the concept of entropy. Public domain. Zeitschrift für Physikalische Chemie, Band 21, von 1896. Picture taken by Theo Schafgans (1859–1907), Bonn; heliogravüre by Meisenbach, Riffarth & Co. Berlin. Image scanned, processed and uploaded by Kuebi = Armin Kübelbeck. Punjabi Wikipedia.

Ludwig Boltzmann, developer of the statistical-mechanical conceptualization of entropy. Pictured, Boltzmann's grave on Zentralfriedhof (Central Cemetery), Vienna, Austria, May 2005. Original work by work by Daderot, licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license via Wikimedia.


* David Hackett Fischer quotes Paul Revere's 1798 account of the midnight ride as follows:
Later Paul Revere recalled, "I agreed with a Colonel Conant and some other gentlemen, that if the British went out by water, we would shew two lanthorns in the North Chuch steeple, and if by land, one, as a signal, for we were apprehensive it would be difficult to cross the Charles River, or git over Boston neck."
— David Hackett Fischer, Paul Revere's Ride, Oxford University Press, 1994, p 99

I am indebted to Barry Gian James for his excellent instructable, "How to Type and Talk with a German Accent". Danke vielmals, Gian!

German language support provided by the LEO online translation dictionary from Leo GmbH. Danke für die gute Zusammenarbeit.

Further reading:

Wikipedia: Rudolf Clausius

Wikipedia: Ludwig Boltzmann

Wikiepdia: History of Entropy

• Paul Davies, About Time: Einstein's Unfinished Revolution. Simon & Schuster, 1996 - Google Books Preview

• Sean Carroll, From Eternity to Here: The Quest for the Ultimate Theory of Time. Dutton, 2010 - Google Books Preview

• Lee Smolin, Time Reborn: From the Crisis in Physics to the Future of the Universe. Houghton Mifflin Harcourt, 2013 - Google Books Preview