27 February 2010

Acts of God by Architecture of Aggression Review


The friendly beardos of Architecture of Aggression were not content with Christian blasphemies alone. Nay, nay, they decided to take a stab at all the desert peasant religions on this ambitious concept album. Regardless of your opinion on Islam, Christianity or Judaism, if you like technical death metal with a solid groove, you'd be content with this album.


Lyrically, this album borrows from the Bible, the Quran and Richard Dawkins plenty. I shall not venture on this too long because the concept of memes and how religion is a destructive one is quite popular of late. Read The Selfish Gene if you are interested in the topic.

Richard Dawkins Selfish Gene
Richard Dawkins, who wants to eat your young, apparently.

By the time of their previous release, the band had just completed their stable touring lineup. One of the tracks that resulted from this unholy union is Systems of Control. That track more or less sets the tone of the new album. It also happens to be one of my favourite A.O.A tracks, so this album heads in exactly the right direction for me. They self-released it and practically gave it away for a mere R50 at the launch gig.

Some highlights of this album are the closing track, Requiem for a Meme, with its chanting and horn section (yes, you read that right), the middle tracks, Designer Religion and Immaculate Deception, and House of War. It's also fun to hear the Boere accents bashing religion.

My favourite section is the last section, which focuses on the atrocities of Islam. These tracks have a Middle Eastern feel to them, with their exotic rhythms and scales used to personify the region and its religion.

Overall, this album represents a transitional album for the band, moving from a comfortable duo to a slightly more dynamic power trio. Sometimes the results are amazing and sometimes the results are a little rough around the edges. I feel this represents a positive change, as the band members are not staying in their comfort zone.

Individually, the tracks take some time to get going and to get locked into a groove. Some fans rate their previous releases higher, though I disagree. I think this new album is their best yet and deserves a couple of listens. To me, it is always good when a new album makes you feel uncomfortable at first and then comes back to haunt you over time.

Track listing

  1. Sol Invictus

  2. Memetaphage

  3. Brutal Belief

  4. Covenant

  5. Peadophage

  6. Religion of Love

  7. Designer Religion

  8. Immaculate Deception

  9. Verses of the Sword

  10. Slaves of God

  11. House of War

  12. Deus Ex Memetica

  13. Requiem for a Meme


  • Van666 Alberts: guitars and vocals.

  • Anton 'Belial' Alberts: drums, percussion and vocals.

  • William Tempest Bishop: bass, trombone, keyboard and vocals.


Buy it, listen to it and give me your rating for a change.

20 February 2010

Gödel's Incompleteness Theorems: Underground

This post is part of a series on Gödel's incompleteness theorem. You may find all of them here:
  1. Gödel's incompleteness theorem: Background.

  2. Gödel's incompleteness theorem: Foreground.

  3. Gödel's incompleteness theorem: Underground.

Gödel's second incompleteness theorem

The consistency of the axioms cannot be proven within the system.

This means that you cannot prove meta-statements from within the system. A meta-statement here is defined as a statement about the system. This causes a strange loop.

M.C. Escher Drawing Hands

What's more is if you have a system with meta-statements that are consistent, the system is inconsistent.

The weird and wonderful metaphysical wine rack

It should be noted that Gödel's incompleteness theorems only apply when:
  • Your system is expressive enough to model arithmetic.

  • Your system can determine what is an axiom in the system and what is not. That is, your system has to be recursive.

Suggest then that we have a wine rack that can only take red wine. Like my wine rack. We have a cellar filled with wine - both red and white - and I'd like to fill my wine rack with nothing but the finest red wine. Only there is a problem.

Red, red wine

I'd like to know if my wine rack can fit all the red wine in this particular cellar. My wine rack knows to only accept red wine, so this makes my wine rack consistent. But my wine rack will only be complete if my wine rack contains all the red wine in the cellar. My wine rack has a counter that can add wine and subtract wine, as I put bottles inside and as I remove bottles respectively. This means my wine rack can model arithmetic. In addition, this wine rack is incredibly smart and can determine whether I put red wine or any other kind of wine in it. If you want to put white wine or fortified wine in it, the wine rack shoots you with lasers. In a sense, the wine rack is recursive because it knows when a wine is red (and thus fit for the rack, or an axiom of the system), and when it is another (and thus unfit for the rack, or not an axiom of the system).

What Gödel's incompleteness theorems teaches us about metaphysical wine racks

From Gödel's first incompleteness theorem, we know that if a system is consistent, it cannot be complete. Thus we know that if my wine rack consistently accepts only red wine until it is full, it cannot be said to contain all the red wine in the cellar.

This means that when I pick a red wine with deep colour, rich palate, exquisite nose, tantalising body and of magnificent development, open it, let it breathe and take a sip, I have no way of proving whether it is from the cellar in general or from my incredibly fancy metaphysical wine rack. Especially not after a couple of glasses.

It does not mean that this red wine is either from the cellar or from my wine rack. Knowing me, I probably hid it in my coat. It also does not make the wine inside my wine rack or from the cellar any less red. Similarly, proven statements of determined truth value do not become untrue just because there are other statements in a system that are true but unprovable to be true. Likewise, it does not suddenly make any statement of indeterminable truth value necessarily true.

This is a grave mistake made by religious people who claim a syllogism as follows:
  • From Gödel's first incompleteness theorem, we know that if a formal system is incomplete, then statements exist within the system which can never be proven true or false within the system.

  • We cannot prove that God exists from within our system.

  • Therefore, God exists.

Firstly, religion is not a formal system. Like the Law of Attraction, it's not advanced enough to model arithmetic, so Gödel doesn't apply. Secondly, we also know that religious systems are inconsistent, even though some claim to be both complete and consistent. If Gödel did apply, we already know a system that can claim itself consistent is not. Lastly, even if we assume that a religious system is both formal and incomplete and consistent, the only conclusion is that statements exist of which we cannot determine the truth value. If 'God exists' is such a statement, then our conclusion is that 'God exists' is an indeterminable statement in our system. But we knew this already, so even if Gödel's theorems did apply to religions, they're not really advancing the debate.

Ford says Ford makes the best cars, so Ford makes the best cars

Clearly, this doesn't help us at all. It's like my metaphysical wine rack claiming that it contains all the red wine in our cellar. How does it know? It can only tally the wine coming into the rack or going out, but it hasn't counted all the wine in the cellar. If we want to determine whether all the red wine in the cellar is contained in the wine rack, we have to step outside the wine rack and tally the wine in the cellar. But if we climb out of the wine rack, the wine rack is no longer complete because it couldn't determine whether it contained all the wine in the cellar by itself.

Suggested reading on Gödel's Incompleteness Theorems

If you are interested, follow these helpful hints:

19 February 2010

Gödel's Incompleteness Theorems: Foreground

Enter Gödel, exit certainty

This post is part of a series on Gödel's incompleteness theorem. You may find all of them here:
  1. Gödel's incompleteness theorem: Background.

  2. Gödel's incompleteness theorem: Foreground.

  3. Gödel's incompleteness theorem: Underground.

Kurt Gödel accepted Hilbert's challenge. Sort of.

Gödel's first incompleteness theorem

If the system is consistent, it cannot be complete.

This means that if there are no contradictions in your system, the system cannot be complete. A contradiction occurs when a statement has no definite truth value. That is, when you cannot determine whether a statement is true or false. An example of such a statement in our ordinary system of language is the liar's paradox ("This sentence is false").

This sentence is false

If this is true, then the sentence is false. But if the sentence is false, it cannot be true. Now all the white rabbits go tumbling down the rabbit hole and Alice comes tumbling after into Blunderland.

For the record, it doesn't mean that if there are contradictions in your system that your system is complete. It works like this:
  • A cause leads to an effect.

  • We determine the cause, therefore we know that it would lead to the effect. We thus know the effect. This is called modus ponens.

  • We determine the effect, but we cannot determine the cause, all things being equal. To assert the cause from the effect is called the converse error.

This actually makes perfect sense. From modus ponens, we know that Chuck Norris causes broken legs without fail. We see Chuck Norris working on someone's legs. We can therefore be certain that Chuck Norris broke both their legs.

But the converse isn't true - we can't be certain that everyone with broken legs had a tussle with Chuck Norris (though I wouldn't take that bet) because this is the converse error.

Chuck Norris Wikipedia image

Chuck Norris proves modus ponens. And he doesn't even know it.

Similarly, from Gödel's first incompleteness theorem, we know that a system being consistent implies that it is incomplete (we have the cause, so we know the effect). But to claim that a system being incomplete implies that it is consistent is to commit the converse error (we have the effect, so we cannot determine the cause).

Many religious people state that the wonderful universe we live in was caused by god. Therefore, the wonderful universe we live in proves the existence of god. See the resemblance to the converse error?

Another fan favourite is irreducible complexity. Irreducible complexity - however defined - is an effect. An effect does not imply a cause, and to claim so is to commit the converse error, as we have seen.

18 February 2010

Gödel's Incompleteness Theorems: Background

Background to Gödel's Incompleteness Theorems

This post is part of a series on Gödel's incompleteness theorem. You may find all of them here:
  1. Gödel's incompleteness theorem: Background.

  2. Gödel's incompleteness theorem: Foreground.

  3. Gödel's incompleteness theorem: Underground.

One of my hobbies is to throw myself in at the deep end somewhere exotic and to see if I can swim, metaphorically speaking. It turns out that doggy paddling makes up for a lack of flamboyance with efficacy in buoyancy. Recently, I wondered how we can know that something is true?

Ayn Rand, who believed that something is true when it obeyed Aristotle's laws of thought. That is, the law of identity, the law of noncontradiction and the law of excluded middle.

Something is true because you can prove that it is true

Being a Randroid, the short and sweet answer is of course that something is true because it is proved to be true. We prove that something is true with reason. Reason rests on logic. Logic rests on axioms. This is all good and well, but how do we know that axioms are true? That is, what proves axioms true?

The trouble with axioms

An axiom is a self-evident statement. Naturally, it has to be self-evident to someone who'd like to make use of the axiom. But if it relies on someone to recognise it as self-evident, then it's not all that self-evident after all. Thus we get more people involved and the truth value of an axiom is determined by some kind of democracy whereby:
  • An axiom is true if it is self-evident to enough people.

  • An axiom is false if it is not self-evident to enough people.

  • All axioms are equally true, but some axioms are more true than others.

This is dangerously close to faith, which would make axioms true because we believe them to be true. Faith alone inevitably leads to a dangerous mindfield of paradoxes and inconsistencies because it is a curiosity stopper. Faith alone was certainly not enough for David Hilbert, who wanted at the very least to have maths axioms that are more true than others.

Hilbert's program

Hilbert suggested that maths axioms could show itself to be more true than other axioms by showing that:
  • There is a finite number of mathematical axioms, which would make maths complete.

  • Each axiom has a definite true or false answer, which would make maths consistent.

The purpose of Hilbert's program is to formalise all of mathematics. That is, it would give mathematicians the language they need to express anything with the knowledge that it is either true or false, but at least it is not wronger than wrong.

Google sucks piles I'm moving to Steemit

Short and sweet, Google isn't allowing me to post ads on my blogs here on blogspot any longer. Not that I provide my angry nerd rants fo...