Sunday, March 31, 2013

Prolegomena to an XML schema for pattern theory



A link to a working draft specification is here:




The pattern theory created by Ulf Grenander is based on mathematical definitions for a set of entities that are used to model and perceive the world: generator, bond, configuration, image, pattern, similarity transformation, deformation, among others.

Here is an example of what a configuration might look like (from Elements of Pattern Theory):

In the XML schema for PTML (Pattern-Theoretic Markup Language), this would be coded as follows:

<config>
<gen id="g1">
   <bond name="W" gref="#" bcxn="E"></bond>
   <bond name="E" gref="#g2" bcxn="W"></bond>
   <bond name="S" gref="#g3" bcxn="N"></bond>
</gen>
<gen id="g2">
   <bond name="W" gref="#g1" bcxn="E"></bond>
   <bond name="N" gref="#" bcxn="S"></bond>
   <bond name="S" gref="#g4" bcxn="N"></bond>
</gen>
<gen id="g3">
   <bond name="N" gref="#g1" bcxn="S"></bond>
   <bond name="E" gref="#g4" bcxn="W"></bond>
</gen>
<gen id="g4">
   <bond name="N" gref="#g2" bcxn="S"></bond>
   <bond name="W" gref="#g3" bcxn="E"></bond>
   <bond name="E" gref="#g5" bcxn="W"></bond>
   <bond name="S" gref="#g6" bcxn="N"></bond>
</gen>
<gen id="g5">
   <bond name="W" gref="#g4" bcxn="E"></bond>
   <bond name="E" gref="#" bcxn="W"></bond>
</gen>
<gen id="g6">
   <bond name="N" gref="#g4" bcxn="S"></bond>
</gen>
</config>


This includes elements config (configuration), gen (generator), bond (bond), a gen attribute id, bond attributes name, gref (generator being linked to), and bcxn (bond connection). (The bond names — or indices — N, S, E, W were chosen to suggest geographical directions.) A gref such as "#g4" is an internal link to a generator within the same configuration. bcxn specifies the bond (by name) within the generator being linked to. A gref="#" indicates an unconnected (external) bond. This is something of an "empty" configuration in that it currently holds no application-dependent content within the bond or gen elements.

Because the config element can have arbitrarily-connected internal links as shown in this example, any graph topology can be modeled, not just tree structures.

Further developments for PTML include:

0. Add syntax for bond domains (bset="set", where set is the name of a set of bond values), bond values (bval="val", where val is an element of bset), bond relations (brel="rel", where rel is the name of a two-argument function taking two bond values and returning TRUE or FALSE), and bond probability distributions (bprob="prob", where prob is the name of a one-argument function that takes the list of bond names from the generator and returns a list of random bond values. (prob is a multivariate probability distribution.)

Example:
<gen bset="MAPDIRECTION" brel="EQUALS" bprob="COINFLIP"
       id="g2">
   <bond name="W" gref="#g1" bcxn="E" bval="HEADS"></bond>
   <bond name="N" gref="#" bcxn="S" bval="TAILS"></bond>
   <bond name="S" gref="#g4" bcxn="N" bval="HEADS"></bond>
</gen>

Note: The probablities introduced by bprob induce a probability model over configrations known as a random field.

0.1. Add an attribute for the gen element, gtype="typeid" and a new element <gtype id="typeid" bset="set" brel="rel" bprob="prob" bsim="sim"> where sim is the name of a similarity group. The gtypes could be collected into another file defs.ptml and referenced by a link element:
<ptml>
<head>
    <link rel="definitions" href="defs.ptml">
</head>
<body>
   <config>
     ...
       <gen gtype="typeid" ...>
     ...
   ...
</body>
</ptml>
(See SVG <defs>, for example.)

1. Add a bdir=["in"|"out"] attribute to bond for where the underlying configuration graph is directed.

2. bcxn could list a set of prioritized options: bcxn="name1,name2,..."

3. Content to include <script>s.

4. Content to include analogs of SVG <filters>s, transforms, ...

5. XML transformation language to capture the other pattern theoretic definitions such as similarity, image, and deformation.
(Example: a PTML → SVG transform)

...

With PTML, one can publish pattern-theoretic objects or store them in XML databases.




Saturday, March 30, 2013

The Republicans' Trap


The Republican Party doesn't have a minority problem. It has an ideology problem: the combination of a fierce anti-government economic libertarianism (which serves to transfer wealth upwards to the richest) and a right-wing Christian legalism (which serves to attack gay rights and abortion rights). I would be surprised if it changed very much.

comment to The Republicans' Diversity Deserts, NYTimes.com, March 29, 2013


Wednesday, March 27, 2013

Polycodifism


There may not be a single primal code ("Theory Of Everything"), but a multiplicity of codes born in The Big Bang.


Tuesday, March 26, 2013

Philosophy, as easy as PIE


Pragmatism

Ironism

Existentialism

e.g., Charles Sanders Peirce, Richard Rorty, Jean-Paul Sartre


Monday, March 25, 2013

Wolfram in the T-fold


The language of mathematics has been the language of physics, but in practice the language of mathematics is about as flexible as any "natural" language, like English.

LaTeX:Math (the subset of \(\LaTeX\) used in inline and display math modes) is not exactly a candidate for a mathematical coding language since it could allow unwell-formed mathematical expressions, but it is the most used mathematical language that is used to write the physics articles published on arXiv. (I don't know if anyone writes MathML. I write LaTeX:Math and depend on MathJax's conversion into its internal MathML code.)

Stephen Wolfram has recently announced that the "language of Mathematica" (the language that is the core of the Mathematica system) will be called "the Wolfram Language".

This language hasn't quite been born yet, though. It's still germinating inside Mathematica. If it is, one could some day be making (packaged or online) HTML5 apps with Wolfram* as their program scripts just as can one make HTML5 apps that execute JavaScript or Dart.



Could the coding language of the universe turn out to be Wolfram?



A T-fold is a space that locally looks like a Riemannian manifold but is glued together from these not just by diffeomorphisms but also by T-duality transformations.
ncatlab.org/nlab/show/T-fold


* What do people call the English language? English.


Saturday, March 23, 2013

PC zombies


<irony>I assert that I am the only one who has phenomenal consciousness (PC). Gary Gutting and everyone else are zombies. They say they have PC, but I don't believe it. Even if I scan their heads with an fMRI machine and see that their brain processes appear to work very much like mine, I still assert they are zombies. How can they prove me wrong?</irony>


Friday, March 22, 2013

Brain codes


The human brain is a protoplasmic machine that generates new codes which it then uses to make programs to be run on itself.

Human brains biologically evolved to be able to generate new codes and therefore new culture.


Intelligence is the faculty of making artificial objects, especially tools to make tools.
~ Henri Bergson (@philo_quotes)



The universe is a machine running codes. Living things are machines running codes. We can create new codes.

Could 'consciousness' be brain code that is created to inspect other brain code (see code reflection)? It is something we can do, but perhaps not other animals.

The paper "Inner Sense" (faculty.philosophy.umd.edu/pcarruthers) talks about the "I-code" (introspective code) concept from the book "Simulating Minds" by Alvin Goldman (fas-philosophy.rutgers.edu/goldman).

Introspective code (I-code) - Inner sense involves a "transduction" process that takes first-order neural states and produces a second-order representation in a "proprietary" code.

Looking at brain I-code as a form of reflective computer code* could be the best approach to begin to simulate consciousness.

* "Procedural reflection in programming languages" Brian Cantwell Smith publications.csail.mit.edu/lcs/specpub.php?id=840


Thursday, March 21, 2013

Tractatus Logico-Codifist


The world is all that is the case.

The world is the totality of codes, not of things.

The world is determined by codes, and by their being all the codes.

For the totality of working code determines what is the case, and also whatever is not the case.

The codes in logical space run the world.

The world divides into codes.




(via Wittgenstein)


Wednesday, March 20, 2013

The Sarah Palin Code


Sarah Palin runs Tea Party codes.*

Are our brains coded (R) or (D) to love or hate Sarah Palin?

Or can we take new code out for a spin?

Then she reboots and reloads.




* CPAC 2013: Sarah Palin (video and transcript)


Tuesday, March 19, 2013

Codes vs. code


      Re: codifism


1. There are codes.

2. Associated with each code there is a coding language.

3. A "sentence" (document, program file, ...) in a coding language is called code (used as a mass noun).


Example:

   (1) chemistry → (2) CML <xml-cml.org> → (3) a CML document


Monday, March 18, 2013

Existentialism in an evolutionary universe


A recent article in The Chronicle Review contemplates the compatibility of existentialism with evolution.

Evolution and Existentialism, an Intellectual Odd Couple (by David P. Barash, March 11, 2013): For existentialists, there is no Platonic form of the person, no ideal self of which our corporeal reality is a pale instantiation. Rather, we define ourselves, give ourselves meaning, establish our essence only via our existence, by what we do, how we choose to live our individual lives. We have no "human nature," just our own intentions. For evolutionists, there is the idea that living things are a concatenation of genes, jousting with other, similar genes to get ahead.

What would be a codifist perspective?

We (humans) have biologically evolved — as evolutionists believe — but, however it happened, we have evolved to be code inventors (creators of new codes) whereas other animals are living within the codes that nature has dealt them. (Missing, of course, are our cousin and ancestral hominid species which went extinct, which could have been code inventors to some degree.)

There is this dictum cited by some: Biology is the hardware, culture is the software. Biological evolution may have occurred according to codes of nature (physics and chemistry), but, at least for us, it has produced brains that are machines that can produce new codes and new culture.

This ability to make new codes is what makes us free.


Wednesday, March 6, 2013

Was Wittgenstein a Rortian ironist?


(Interesting that Wittgenstein is experiencing a revival in NYTimes.com's The Stone.)

Could Wittgenstein be read as a Rortian ironist who thinks a philosopher should, as needed, make new "vocabularies" — codes (for either description or action) — but also thinks it wouldn't be "final"? Maybe so.


from The Stone:

Was Wittgenstein Right?

Of Flies and Philosophers: Wittgenstein and Philosophy


from the 33rd International Wittgenstein Symposium:

About Pictures which Held Us Captive – Richard Rorty Reads Wittgenstein (Was he a "philosophical satirist" or an "ironic propagandist"?)



Tuesday, March 5, 2013

When Ayn Rand married Jesus


Way back in Ronald Reagan's run
He said to Christian Right:
The government hurts God's One Son,
But tax cuts will ignite

The rich to make all dinghies rise.
That's what the Bible says!

And that's when they became allies,
And Reagan became prez.



Monday, March 4, 2013

Looping through the codiverse


I see coders as the new magicians, codifists as the new philosophers. They are coding and decoding the world.

I see the new generation endowed with digilectical electracy and widgets gone wild.

I see AI scientists programming machines with paraconsistent codes.

I see Dr. Phil Life Codes and Dan Brown Da Vinci Codes.

I see L-systems, QR codes, and semioticians codifying smiles.

I see tool makers under the spell of XML.

I see simulated brains and Tetris-made stains.

I see CSS and JavaScript making HTML be.

I see physicists coding in \(\LaTeX\):Math their next TOE.

I see a world that dances with codes.

...


Dances with Codes: A Loop Through the Codiverse is coming this summer from Cloudversed Publishing.


Sunday, March 3, 2013

Three paths to becoming a mathematical anti-platonist


It may be the case that "no good arguments exist either for or against mathematical platonism" (Platonism and Anti-Platonism in Mathematics by Mark Balaguer). Mathematical anti-platonists may come from a certain naturalistic belief that there's nothing outside nature, so if it's the case that there are no infinities in nature, how can one believe in platonist mathematical objects like infinite sets and the real number continuum?

The three paths below are not arguments against mathematical platonism. They are just ways mathematical anti-platonists can travel. (The first path is complete in the sense that it actually gets to a goal of a truly non-platonistic alternative to interpreting standard mathematics. The other two are incomplete in the sense that they result either with a somewhat restrictive or a non-standard mathematics.)


1. Finite mathematics (of indefinitely large size sets)*

In Understanding the Infinite, Shaughan Lavine describes the mathematics of Jan Mycielski ("The meaning of pure mathematics", "Locally finite theories"). In this approach, the quantifiers (∀, ∃) within the sentences of standard mathematics are replaced with indexed quantifiers (∀i, ∃j), and the interpretation of these quantifiers is that the variables they govern range over finite sets (Ωi, Ωj) with the same index. The key to this approach is that the finite sets can be of different sizes (unlike in the standard interpretation where the variables range over the same set). This indexing of quantifiers in sentences of a standard-mathematical theory T is done by process called relativization, and the result of applying this process to a sentence φ of standard mathematics is called a regular relativization φ' of φ. Beginning with a standard theory T, the result is the corresponding finitary theory Fin(T). The key theorem of this approach is:

"If φ is a sentence in the language of T and φ' is a regular relativization of φ, then φ is a theorem of T if and only if φ' is a theorem of Fin(T)."


Thus every theorem of T (interpreted with possibly infinite sets) has a corresponding theorem of Fin(T) (interpreted with only finite sets).

Note: Mycielski calls this interpretation intentionalism (which is different from intuitionism), in contrast with formalism and platonism. For some examples, see:

Mathematica materialis, or How not to be lured into Plato's cave
Persons without infinities
Plato's cave is closed
Transfinity

* or MIFS: Mathematics of Indefinitely-large Finite Sets


The other two paths I mention briefly.

2. Computable analysis

Can computable numbers be used instead of the reals?
Computable analysis
Constructive mathematics

E.g., only consider numbers and methods of analysis that can be represented by computer programs. It would interesting to link path 2 to path 1.


3. Paraconsistent mathematics (with finite models)

Inconsistent mathematics
Paraconsistent Logic

"One interesting implication of the existence of inconsistent models of arithmetic is that some of them are finite (unlike the classical non-standard models)."

Inconsistent models of arithmetic:
Part I: Finite models, Part II: The general case



Saturday, March 2, 2013

Digilectics


Digilectics is the set of principles and practices of codifism and digilectical materialism.

The world is observed as phenomena and coded in theories which model the phenomena:

P: P1|P2|P3| ... levels of phenomena (read by measuring devices)
T: T1|T2|T3| ... levels of theories (written in coding languages)

The lowest level could include, for example, the measurements made in the Large Hadron Collider (in P1) and the Standard Model (in T1). Higher levels could include chemistry, biology, psychology, politics, ...

Attention is paid to correlations (P), consistencies (T), and agreements (T with P).


Friday, March 1, 2013

coder, codifier, codist, code theorist, codifist


coder - A writer and tester of codes (e.g., a computer programmer).

codifier - An inventor of codes.

codist - A codifier.

code theorist - Someone who discovers and studies codes; a digilectical materialist; an armchair codifist.

codifist - A supporter and promoter of codifism.