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Showing posts from February, 2010

Acts of God by Architecture of Aggression Review

Conclusion
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.

Review
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, 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 th…

Gödel's Incompleteness Theorems: Underground

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



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. …

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:
Gödel's incompleteness theorem: Background.
Gödel's incompleteness theorem: Foreground.
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…

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:
Gödel's incompleteness theorem: Background.
Gödel's incompleteness theorem: Foreground.
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…