As I have probably mentioned at some point, some of the bands I like include Behemoth and Belphegor. Both came with new albums recently. Behemoth’s new album ‘Evangelion’ is definately different from ‘The Apostasy’, but it definately kicks at least as much ass (which is quite a lot!). Since ‘Walpurgis Rites – Hexenwahn’ from Belphegor is far more recent, I havn’t really listened to it enough to form an opinion, but there are definately things that I like here

Also, a few weeks ago someone mentioned something math-related. As you may know, x⁰ (x being any number except 0) is 1. I was told once why that was, though I couldn’t remember it and it bugged me for weeks. But I found it again (and it seems that very few people know this), so if you’re interested:

Basic rules when working with powers include that x^a · x^b can also be written as x^a+b. For division, a similar rule exists which says that x^a / by x^b equals x^a-b. Now if we take the second rule, and assume that a and b are equal, we find that x^a / x^a = x^a-a, which is the same as 1 = x⁰ (which is valid as long as x does not equal zero, in which case it is undefined).

Yay!

As we all know, CD-ROM discs are used for endless numbers of applications. They can contain pretty much anything – as long as it fits on them – music, videos, backups, games, applications, instructions to build a nuclear warhead accompanied with a guide title ‘World Domination for Dummies’, the secret collection of private pictures from your neighbor, and so on.

The amount of data that a CD can hold, however, is limited, and each byte can only have a limited number of values. This automatically means that there is a limited number of possible combinations of that data. From that results my, purely hypothetical question:

What if you had enormous amounts of storage space (and too much time on your hands), and wrote a program that generates every possible combination of bits that can fit on a standard 700 MB CD-ROM?

(any other size or medium will do, but for the purposes of this article, I’m going with CD’s).

It would mean you had everything, if you can filter out the garbage. You would have every piece of music that can possibly exist, every videogame, every movie, every application, every version of every operating system Microsoft is ever going to create, every book, every last top secret government document, all the deepest secrets of mathematics and physics, and so on – and in every possible data format mankind could ever come up with. And if any of those things won’t fit on a single CD-ROM, then you’ll have multiple discs over which it is split or it’s compressed in one way or another. You’d even find the program that generated the files on many different copies, as well as the contents of your ‘My Documents’ folder. You’d find all the work you’re ever gonna need to do on one of the discs. Yes, if possessing information equals power, you’d be the most powerful person in the galaxy.

There’s one problem though. Or two, actually. First, the number of possible combinations is huge, which leads to number two: you’d need to filter out everything that’s just garbage, incorrect (there’d probably a copy of the United States constitution proclaiming  that all humans who do not think like microwave ovens are to be drowned in solid rock, for instance), or otherwise useless.

A standard CD-ROM holds 700 megabytes of data. That is 71680 kilobytes, 73400320 bytes, or 75161927680 bits. Each bit can have two different value (1 or 0, or any combination of those if you start taking quantum computing into account). That leads to the following number of possible options (there are 2270 digits here):

41560048263861436654475508679796312052029218009913182562367006418669795133738677325303829283902099461683768394190770980283679635078751063822618386805812838838303804835247879766315166734455333535683358814434813663349102246666424981806460601928318569109854576954786119818448542312867993682137144435507290928098755647875003380853428300895596305593559299463478439540154542790952888179033834007520623513696748661147784926411675672345265415386421907369222580620580057964638871826899236684237846333319010115476041297070325851814982604002774773195585007201934813928941921904876472888434797815496460083517021451032132295669827602759661947035120120846618273540692805492960805094224448593026845599970027471939253922696047034668721591021344726827328131712537809367433079518384287605426291625425313041643768023912646929874041007720315988047687254633130795234177820761430309126055836770489514373931510971271792353296548877968241515974272875989782334657937031437501105704222162508125649071619599383296535137824001280615579884391211228601106105314564462541137989320753754255409337080898983919658187473289919882724301755391103464565652949062361680312937710052112856600316200094257405362631948684541214867146409424988250903963596233902404930669255343019463762208367648031571737057549700712046659157023806395507915616404070200018132701062721506830784625613311912694266673404330491387200073314684893248919524749048959153777871149991948500487185581730754185937873866203878251168734737587231326488641050598094861683470605896398593085319761830045089436004138466391521325214416958909455885921153196657959245081430996240154174079623421680565937289117542211340227166129132811906252486650841319323086523661297193645306243775007007485050498324647562243944659365996157620321456643217817600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Let’s say that at least, the CD should have a correct structure. I don’t know the exact specifications of the CDFS file system, but I’ll presume that the first two bytes are ‘CD’. At that point, we’re down to the following number (still 2270 digits, but at least the number got a whole lot smaller):

41560019273882484721350366560533047580828429594256717527864863052271508084842596992950908379448089285142417669909616427292121947211555590165431463671900568144138997203812069279949973107406716032251730399281413324702860191957409234442734041280086708423684325442504979677019087941286897320973599686657670655098282295781732036010808800532769077252570412047411348234670231942044243795186594340164899748720953936465695617000314878647766056113239640983974671445912647758548162275659893980045917669035850682325483732657717339710098587418717576870866662655604822817431160764683043737585385867502107884498713945018997191265874967478747209642473729268451187893433221656171314211009627035218024646034095772795903048201166276142097522590829427103680190235947930980554967958567417965789988678435183111300305779237598205610810957895777257155022262701137726446304182142443697383720882330271742296308558472662166485159144135393856709949427038847026856924016221048757489940746263741899303393311349867922331686721150913967220524065404198861547866344304500665210897615356980528516508894133435871481519430135098893031451954262440861157361929671519651166721454073599914465149412625713249597893086209783150594388008469457177837953416991616705826231056399956938405253947784331106471956937753167217860677792536721429817137834582298283848391328989169191363102004971487142281952406179263495704582339189610726486197473357284778084563848670175545858631197146422363532953483639551087292336803161147327499601731014172535101598730700528251674278631424499440653386736447992504293420544979557813680448657739822089086852051675335465310825717015262488711808177973767459617767248675892989823345041908355108643311355628768188101882677515614248647618611631799563873060304086856011242045518722531483835603758008209329214600308575455009307287668229066165792067103881536904235290976894148521128308730756190301866381682454034763721563103249035460309040579155810247706901992390584624513409777632212755149760150803817076772939092313735123383574578468067313279614617052152562259545374712492378678130559714927615995623637983197197885945530177234651495726317453122988274137393085827767335064774149790169707884128961444470947322453114444647353687182873888418942684934210427902987294845892877825580776702245520682254336

A CD is 1.2 millimeters thick, so if you would actually create all those discs and stack them up, the height of the stack needs to be measured in parsecs (which is over 3 lightyears) at the lack of a bigger unit of measurement. The stack would go to the edge of the visible universe and back, probably millions of times over (that is 92×10^26 light years per trip). Unfortunately there are some practical issues involved with building such a stack, not to mention that it’d be a real bummer if it toppled over when you’re almost done building it, but you get the idea. It’s a lot.

Obviously, 700 MB would be a bit much. Let’s use a different subject: a 100 kilobyte bitmap image. Bitmaps are very simple in terms of file structure and very predictable when it comes to the relation between file size and picture size. The header for each file would be the same except for the image dimensions, which means that the value of 46 out of 102400 bytes are already known, leaving 102354 for image data. As a result, the number of possible 100kb bitmap images is (1283 digits this time):

38621915839819383776156980391709084941306067905143183265687961723080821305959590283401753598149727655197260685817493781836969325569604238581869156726602582950591384531818001345164220862260151747139603901744837097758576456302408942470762097063662706223836899801655007423182729973906008437261806550861923880433213326410624122666374422645631842424830712955324974618930377986368719271695955930216205502621029530051031074336241029308510873363146995803614386296599126309651274804630620379142113354752832984747473807269286033400590488478235440819467647773905724739497484798460906196419869672879762636210764794461958544247051445638670685323456393171623453281428476884841064799493452728311545224032434346174947095287625574547402827389736516533868114375804758906699820893083624953883705124160618575740530335787016139854614684706089327960579462214730514550399804309799011615108890763596994973149176222389617422254313574524607629907964248596999780882071628151782363938411426973124973565685960396785160836599828592474298355586905321031050981271098976722213717998766600992378789562291893869070678567964811385084928768960998832087321001816188802048207700599654878194647595770156826363500059354296838325190350669647834306755266222657031034230439413380266682086613584051011187524325029691123874922496

Burn each of those on a CD, and the stack will span the diameter of the Milky Way 46×10^1260 times. And I’m talking about the galaxy, not the candy.

Obviously, doing such a thing wouldn’t be very practical. But just imagine what you would have…

For many of us, the Ultimate Question has something to do with the reason of life/why do we exist/etcetera etcetera blahdiblahdiblah. If you ask me why do we exist I can answer that question: there is no reason. Everything that happens, has happened and will ever happened is nothing but the combination of the laws of physics and a complicated playback of events that were recorded at the time of the Big Bang, or possibly even earlier. Now hold on: the science bit is coming up.

According to Newtonian physics, the future is predetermined. Every particle in the universe is at one particular location and is moving at some speed in a direction. If you know where it is and where it’s going, you can predict when and how that particule will interact with another, which may or may not cause something significant to happen. This is a very significant thing, since this means that everything that happens is the result of some action (and in any case the indirect result of the big bang), and every action causes something else to happen. And no, there is nothing you could ever do about it, since every thought we have is nothing but the product of a complex electrochemical device known to and possessed by many, but used by few, that is known as a brain.

In fact, that you are now reading this is the direct result of some electrical pulses in your brain that made you decide it was a good idea to go to www.damnleet.com and read this article. That you are still reading here, is the result of you reading it in the first place, since that caused more electrical pulses to make you decide it is interesting enough to keep reading.

I know that some people (including Samantha Carter in one particular Stargate SG-1 episode, but I’m too lazy to review all episodes to find which one it was, thank you) will now start whining about the Heisenberg uncertainty principle. For those of you not familiar with it, quamtum physics has a funny little thing called the Heisenberg uncertainty principle, which basically states that the more certain you are about a particle’s location, the less certain you are about it’s speed, and vice versa. The point is, this only means that it would be impossible to create a device to predict the future, not that it isn’t predetermined. And it would be impossible either way since you would need to know the speed, direction and location of every particle that exists, because no matter how far away, they might accidently have a significant effect that completely throws your little time machine off course.

Okay, and now back to the science and fiction thing. As you may have noticed I just explained that everything is predetermined. I will now explain why the Ultimate Question and Ultimate Answer indeed can’t exist at the same time, knowing that the answer is 42.

Let’s say we know the Ultimate Question: what is the reason of our existence? It’s easy here: because there is no reason to existence, the question cannot be answered, and therefore given the question the answer can’t exist as well.

Let’s say we know the Ultimate Answer: 42. It is simply impossible to come up with a question that is important enough to be considered the ultimate question, and to which the answer is 42, thus confirming that the question and answer can’t exist at the same time.

And for those who are now complaining that ‘What is the reason of our existence? 42.’ is not logical: I would like to refer you to the scene where Arthur and Ford are stuck on prehistoric Earth, and Arthur utters the words “I always thought there was something fundamentally wrong with the universe.”

And as final thing, for those of you who claim that the above is way too much philosophic to be science: consider this:

science + fiction = philosophy

Doesn’t seem at all that crazy, eh?