Hacking Lojban

Those familiar with Godel's incompleteness theorems would recall that certain formal systems that are sufficiently complex contain paradoxes. Two particular paradoxes are of concern, namely:

1. Such systems that are complete are also inconsistent (Godel's first theorem)


2. Such systems that are consistent cannot be complete as such a system cannot prove its own consistency (Godel's second theorem).

Predicate logic, how pretty delicate thou art

Natural language is not a formal system. Partially due to this reason, ambiguities arise which renders natural language somewhat inadequate for formal expression, but rather appropriate for planting memes in the impressionable. Ask Roman Polanski.

In an attempt to rid ourselves of the ambiguities of language, projects arose to establish language based on the principles of first order logic. That is, these projects aimed at formalising natural language by injecting a set of formal rules into a mixture of natural languages. Two of these projects are:

1. Loglan, which is one of the first of its kind and copyrighted.


2. Lojban, which is similar to the open source nemesis of Loglan because what good is a language if you can't speak it with anyone?

In my previous post on nerd bands, I lamented the fact that I couldn't find any bands who sang in Lojban. I went through a few Lojban lessons and noticed the following:

Lojban nouns

In Lojban, there is a class of word called cmene. Cmene is the Lojban term for name. This is similar to the existential quantifier in predicate logic. In other words, without the jargon or the batty symbols:

There exists one something with one particular name. The name for this name is cmene

All cmene follow the format of CCVCV, or five letters consisting of Consonant Consonant Vowel Consonant Vowel. Even cmene, so that's pretty sweet as this barber shaves himself.

Edit: this is incorrect. All gismu (root words) follow the format of CCVCV or CCVCV. Cmene is the gismu that refers to proper nouns in Lojban. All cmene that are first names are preceded by a full-stop if they start with a vowel and end in a consonant.

Lojban verbs, or what functions as verbs

Words that function as verbs in Lojban are called selbri. In the lesson on selbri, the authors explain that a selbri and a verb are not the same thing, as a selbri merely functions like a verb does. A selbri is usually a root word from a class called gismu. Gismu is a type of word that indicates a root word in a similar way that verbs have roots, though a gismu is not necessarily a selbri, or vica versa.

All gismu have one of two forms: CVCCV or CCVCV. This means that all cmene are gismu, or that all names are root words. Right?

Edit: Since I was mistaken and cmene do not have the form of CVCCV or CCVCV if they are first names, all cmene are not gismu.

What is the hax?

Cmene (name) is a gismu (root word) because cmene is a root word that indicates a name for a group of words that indicates names.

Gismu (root word) is the cmene (name) for root words in Lojban. It has the form CVCCV. Yet all cmene are meant to have the form CCVCV. This barber does not shave himself. Maybe it's a bit of a long shot as all cmene are gismu but all gismu don't have to be cmene? Fine.

Edit: I was wrong here so the above hacks does not apply.

Selbri (connective that acts like a verb) is the cmene (name) that refers to a group of words that function like verbs in Lojban. Thus, selbri is a cmene that has more than five letters. Selbri also breaks the rule that all cmene have the format CCVCV, as it has the format CVCCCV. This barber does not shave himself either. Hello, Russel's paradox.

Edit: Selbri is not a cmene in the first name sense, but a cmene for connectives that act like verbs. This means the only cmene rule for selbri is that it has to end on a vowel, which it does.

Is Katie the cmene of Katie Price or Katherine Jenkins?

Well, this is not so much a paradox as a set on its own. A couple of nice sets within the set, though.


Katie Price Jordan. I wish she'd make up her mind about her cmene.



Katherine Jenkins. Too classy for this blog.

I can just imagine the kind of selbri you have in mind for these two ladies, but please let me imagine it's an empty set, thank you.

The Demon of Morton

South African author Joan De La Haye offers Demon Friday. Surprisingly, it's each Friday and it involves a demon from one grimoire or another. She also greets us as 'freaky darlings', similar to Vampira. Top class!

This is my own take on Demon Friday, except it's not always on Fridays and it doesn't feature real demons or pictures of real demons. Sorry.

These are all my posts on demons:

1. The demon of Laplace, regarding probability.


2. The demon of Maxwell, regarding thermodynamics.


3. The demon of Descartes, designed to invoke skepticism.


4. The demon of Morton, designed to make one aware of confirmation bias.

"I knew I had a problem, and I couldn't admit it." - Lindsay Lohan, showing possession by Morton's demon.

Morton's Demon

This demon is similar to Descartes's demon in that it is a demon intent on fooling you. Except, instead of fooling you that the world is real and that you are wrong for not conforming to the world, Morton's demon convinces you that you are right and the world is wrong for not conforming to your ideals. To put it succinctly, Morton's demon is a personification of confirmation bias.


Paris Hilton. She knows all about critical thinking.

How to combat Morton's Demon

Naturally, combating Morton's demon involves admitting that you are wrong. This is not as easy as it seems, especially since you're already convinced that you aren't wrong. In other words, you rely on faith instead of on reason. It is deceivingly simple to substitute reason with faith, as is evident by the success of the law of attraction and the common misconceptions regarding the incompleteness theorems of Kurt Godel. A good way to combat Morton's demon is with critical thinking.

Filchers: A field guide to critical thinking

Filchers stands for Falsifiability, Logic, Comprehensiveness, Honesty, Replicability [sic] and Sufficiency. You may read all about Filchers in James Latt's excellent post on critical thinking. I shall only give a brief description of each aspect here:

1. Falsifiability: Falsifiability means that the assertion is testable. In order for an assertion to be considered scientific, conditions have to exist that would render the assertion false. It is not always applicable to Morton's demon, especially since different degrees of belief are under scrutiny.


2. Logic: Arguments presented to support a claim must be sound. This means that your assertions should necessarily follow upon each other. To paraphrase John Reed, everyone is entitled to their own opinions but everyone is not entitled to their own facts and logic. To paraphrase Paris Hilton, see you at the debates, bitches!


3. Comprehensiveness: All the available evidence must be considered. This is where Morton's demon meets his match.


4. Honesty: Evaluate evidence objectively. This means that all the evidence is evaluated without self-deception. Honesty means you come to a rational conclusion after evaluating all the evidence. Honesty is essential and complements all the other components of Filchers.


5. Replicability: If the assertion is based on an experiment, then the experiment must be repeatable. Repeatability means that accurate predictions about future results may be made.


6. Sufficiency: The evidence has to be sufficient to justify the assertion. Ordinary claims are supported by ordinary evidence, whereas extraordinary claims require extraordinary evidence.

In addition, it is helpful to keep some common logical fallacies in mind when evaluating evidence or when doing some soul searching to cast Morton's demon out of your own house. Marilyn vos Savant, one of the people with the highest recorded IQ, has a great article on logical fallacies for the layman.

Suggested reading

• Morton's demon discussed with regards to creation science.


• Morton's demon showing how beliefs alter reality.


• Panda's thumb cartoon on Morton's demon. "You reach a conclusion to a theory first, then just ignore all evidence that proves you're wrong".

Anamorph DVD Review

Conclusion

This is a gem of a find - an independent film (which means the stars lived in a greasy motel instead of in their own personalised trailers) that stars Willem Dafoe and Scott Speedman (of Underworld fame) in an engaging psychological thriller. Like The Silence of the Lambs, it features a team of special agents taxed and taunted by their perpetrator. Also like The Silence of the Lambs and Manhunter, the focus is on the characters of those doing the hunting instead of on the character of the hunted. But this is not a Robert Harris rip-off. It's more of an Umberto Ecco rip-off.

Plot

The serial killer in this film takes the anamorphosis technique as employed by Julian Beever to an entirely new level. By employing camera obscura, tattoos, finger painting (in a somewhate literal sense) and an elaborate pantograph, he anoints himself as the MacGuyver of the macabre. The blood and guts are almost as vile as agent Stan Aubrey's (Willem Dafoe) fascination with antique chairs.

There are some valuable life lessons to be learnt from the macabre staging of the murders. Of course I shall bore you with them now. You're welcome.

Thinking outside the box

Think outside the box has to be one of the most flogged of dead horses out there. Usually, when life coaches expect this quantum leap of faith from their victims, it results in us unsuspecting victims focusing on boxes. After focusing on boxes, we focus on the inside of the box, then we try to wrap our minds around the box to the outside.

This is usually followed by a blunt sense of irrelevancy to daily commuting, the numbing buzz of fluorescent lights, the flat-line sound of deadlines as they fly by, cafeteria food and the perpetual catharsis resulting from arriving at the water cooler only to find the coffee pot empty, filthy and surrounded by the optical illusion of cattle carcasses complete with hovering vultures and a tumble weed. Thinking about boxes or thinking differently about boxes has somehow failed to deter us lost souls from turning to debauchery for a paradigm shift. Perhaps there is something more fundamentally wrong with our thinking than boxes?

General Semantics and the Death of Some Square Boxes

General semantics is a mental hygiene regimen invented and endorsed by Korzybski. In our usual modes of thinking, logic is based on certain infallible axioms. These axioms are largely derived from Aristotle's laws of thought:

• The law of identity: Also noted as A is A. This means you are what you is.


• The law of non-contradiction: This means A can't be something other than A.


• The law of the excluded middle: This means either A is A, or A is not A. A can't be both A and not A at the same time. Thus, there is no middle way between being A and not being A.

General semantics reminds us that things are not necessarily so three dimensional as we are lead to believe by our dogmatic clinging to Aristotle's legacy. General semantics should not be interpreted as contradicting Aristotle's laws of thought. Instead, they remind us that some things are just unknown, ineffable and inexplicable. As an augmentation to Aristotle, here are the laws of general semantics:

• The law of null-A: Boolean logic, with only true and false categories for all its elements, cannot accurately map the full expressions of our universe. The law of null-A reminds us that some things fall in the murky areas between true and false. Much like Justin Bieber's gender, there are things that are best described in terms of probabilities, instead of with absolutes like A or not A.


• The law of null-I: The law of non-identity reminds us that no two events, no matter how similar, may be considered exactly the same. This actually echoes the law of identity of Aristotle, because it classifies two similar events as two separate events, each with its own identity.


• The law of null-E: The law of non-Euclidean geometry reminds us that Euclidean geometry is insufficient to describe our entire universe. Take a look at hyperbolic geometry and Gödel's (or Godel's) incompleteness theorems.

A hyperbolic triangle. These angles don't add up to 180 degrees.

How does this relate to Anamorph?

Anamorph will remind you that there are many ways to look at a situation. Sometimes, the tools you employ may be the problem. Different tools may give different results. And you don't have to think about boxes.

Director

Henry S. Miller

Cast

Willem Dafoe and Scott Speedman and some other people I don't care to google now.

Rating

Yeah it's aright.

Gödel's Incompleteness Theorems: Background

Background to Gödel's Incompleteness Theorems

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