Tuesday, November 18, 2008

No-Point Zen of Artificial Intelligence

The goal of Artificial Intelligence is utterly pointless. After careful consideration, I have come to this conclusion. It is perhaps fitting that I should announce this on the 71st birthday of the Universal Turing Machine. Or perhaps it is merely felicitous happenstance. In any event, it is my considered view that:
  1. Without Openness, there is no point;
  2. Without Debate, there is no point;
  3. Without Freedom, there is no point; and
  4. Without Habeas Corpus, there is no point.

In turn, my reasoning for such pronouncement goes as follows:
  1. An AI developed in secret is like a Doomsday Device developed in secret (see: Dr. Strangelove for amplification)
  2. Open debate is necessary to explore all possible risks and to divert from unintended and unanticipated consequences
  3. Neither should we be free from examining what is possible nor from engaging in valid scientific pursuit (while being tempered by moralistic circumspection), and
  4. We should place organic, sentient life and its needs at the base of any such exploration; we do not wish to be "disappeared" by an uncaring mechanistic intelligence

Such thinking has been the product of single-minded focus on both the goal and the possibility of Artificial Intelligence. As a Buddhist, I am happy to relinquish the focus of my attention when I realise that it is empty of any essential merit. We inhabitants of this planet have too many problems without compounding them with chasing after ill-advised ephemera such as AI.

Friday, September 26, 2008

Five Varieties of Truth

After considerable introspection and examination of my omphalos it has become apparent that there are but five possible strata of logical truth. These are enumerated below:

  1. existential (unitary/"there exists"/"a-priori")
  2. dualistic (TRUE|FALSE)
  3. quantised ternary (TRUE|FALSE|UNDECIDED or TRUE|FALSE|UNKNOWN or TRUE|FALSE|MAYBE)
  4. spectral ternary (TRUE|FALSE|SOMEWHAT_TRUE, ie "fuzzy" truth variables)
  5. quaternary (BOTH_TRUE_AND_FALSE| NEITHER_TRUE_NOR_FALSE|ONLY_TRUE|ONLY_FALSE, ie "relativistic" truth)

In what will be probably my enduring legacy to the field of non-standard logics, I would like to present a synthesis of all five of these logical possibilities:


This summation should, of course, come as no surprise to any tree-dwelling Buddhist, but I am sure that the more mathematically-inclined among my readers will be screaming "Gödel's Incompleteness Theorem!" at the top of their lungs. Indeed. This is not a complete theory without invocation of Humberto Maturana and Francisco Varela's concept of Autopoiesis. Forewith, we can see that all truth rests on shaky (nay, even swaying) foundations, and all that is possible is, by necessity, subject to the vagaries of this ground realisation. Such relativism, as Burroughs points out, is not a licence to immorality (which would be a minor affair, which would run its course), but rather more like an invocation of Lazlo's Axiom of Relativity: your Truth is not Universal. As a Buddhist, I would hope that this revelation would ultimately lead to the liberation of all sentient beings, but unfortunately given the negative reactions I have received for such views, I am not so sure the world is ready for such wisdom.

Saturday, July 12, 2008

A failed paean to 3-4-3

I came across this humorous version of the Lord's Prayer a while back (click the link for the translation):
0ǔr $¥$@dM!n, \/\/|-|0 ©|-|!££$ !n |-|34\/3|\|
ph34r3d β3 7|-|¥ |\|@m3
†|-|ÿ p\/\/n@g3 ©0|\/|3, †|-|ÿ $©r!p7$ b3 d0|\|3 !n /earth @$ i7 !$ i|\| /heaven.
$33|) u$ 7h!5 |)@ÿ oǔR d@!£ÿ R0|\/|$.
f0rG!\/3 u$ 0ǔr n00b 3xP£017$ @$ \/\/3 f0rG!\/3 $©r!P7 | R3\/34£ t0 u$ |\|07 Ζ3R0 |)@ÿ \/u£|\|$, βu7 $A\/3 u$ fR0|\/| t3h RIAA.
f0r 7|-|!|\|3 i$ t3h |\|37\/\/0R|<, @|\|d t3h rm -rf*, @|\|d @££ 0ǔR β@$3 @r3 β3£0|\|G t0 j00, f0R3\/3R @|\|d 3\/3R.
4|\/|3|\|.

I can see several mentions of "343" in the text, which got me thinking that perhaps the author had heard of my website and my exhortation to "reference project 343" and had decided to write this in response? It's a little vain of me, I know, to imagine such a thing. But if it were intended as a tribute to my site, I'd give it a "fail" grade. I'm sorry to bore my readers with nit-picking over an obvious piece of fluff, but since it gives me a chance to explain myself and my "church" a little more, I hope you will indulge me a little...

I would describe myself as "agnostically athiest". That is, even though I don't believe in a God, neither do I believe that we can prove God exists (or, indeed, that He doesn't). To put it in the language of mathematics, I believe that while the existence of God is not necessarily true, it's certainly true that he is sufficient for believers (in the sense that belief in Him fulfills a basic human spiritual need). I want my church to be not taken so seriously, and not to cause unintentional offense to any other person's faith. So, while I appreciate the playful humour in the verse, I'm aware that others would not see it that way. The verse simply sails too close to the wind, in my estimation.

A second problem with interpreting the verse as a tribute to my site is that it would appear to elevate the church to some exalted level. I am but a man, and I do not seek or desire such exaltation. Exultation, on the other hand, is something we could all do with finding in our lives.

Wednesday, June 18, 2008

What is 3-4-3?



Four-sprung duck technique.

Sunday, June 15, 2008

ARN chart dote (a mailbag entry)

>
>
> Is glas iad na chnoic i bhfad uainn.
>
> I palindrome I,
> Lala Glosso

Tuesday, June 10, 2008

Constructing the spiral honeycomb mosaic

There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry.
Martin Gardner, "The Mathematical Magic Show"


This site is partly inspired by (and takes its name from) the geometry of the Spiral Honeycomb Mosaic. I will now show how the spiral honeycomb mosaic with 343 tiles is constructed. There is really nothing to it. First, we take a generator:



From the inside out, we have a brown hexagon, which is the SHM of order 0. Then there is a blue flag which has one point fixed at the centre, around which it is free to move. This is the key linkage in understanding how points from the centre of the SHM are projected towards more outwards points, and the key to efficient triangulation of points outside the central hexagon. Outside this again is the boundary of the SHM of order 1. Benoit Mandlebrot gave this boundary the nomenclature "Gosper Island". I will come back to talking about fractal construction of this "limit cycle" later. But back to the generator... the final shape is a larger hexagon, which is a copy of the original hexagon which has been rotated by arctan sqrt(3)/2 and scaled by sqrt(7).

Given this generator, we can construct all points in the spiral hexagonal lattice. The flag shape includes 5 points:

  • the centre
  • two point on the boundary of the SHM of order 0
  • one point in the centre of a hexagon neighbouring the central hexagon (this is inside the SHM of order 1, but outside the SHM of order 0)
  • one point on the boundary of that same hexagon (this is on the boundary of the SHM of order 1)

By repeated rotation of the flag by 60 degrees we can address the centres of all hexagons neighbouring the central hexagons (or, more generally, as you shall see, we can replace "hexagon" with "spiral honeycomb mosaic"). We can also address some of the points of the boundary. The remainder of the points on the boundary are constructible from a simple fractal construction method, or, alternatively, by translation or central symmetry of fractional parts of the original SHM boundary.

Construction of the SHM of order 2 proceeds by first constructing two similar copies of the original flag:



The red flag has been rotated by 30 degrees and scaled by sqrt(3), while the green flag has been rotated by arctan(sqrt(3)/2) and scaled by sqrt(7). We should note:

  • the green flag will have similar properties to the original blue flag, with the point in the centre staying at the centre, points on centres mapping to other centres, and points on boundaries mapping to points on other boundaries
  • if a generator of order n is extended in this manner, the green flag will map out points in the SHM of order n+1, so
  • the green flag finds points in the centre and on the boundary of the surrounding SHM, while
  • the red flag finds a hexagon neighbouring the current SHM
  • the green flag measures distances in terms of powers of sqrt(7)
  • the red flag measures distances in terms of powers of sqrt(3)

While the red flag is not necessary for constructing the boundary of the shape, it is necessary if you plan on constructing a set of hexagons interconnected into an SHM shape. If you're using a compass and ruler construction, you will be thankful of the red flag since it allows you to propagate the more useful metric of sqrt(3) rather than straining to reconstruct numbers in terms of sqrt(7).

The construction can be shown via induction to tile the plane. Here is a partial construction of the SHM of order 3 (343 cells) using some short-cuts for generating some points:



I haven't completed the boundary, but it should be clear from the foregoing how it should go. This was down to laziness on my part, as all the images were created by hand using the excellent Dr. Geo software.

This description wouldn't be complete without defining the fractal corresponding to the SHM boundary, or "Gosper Island". It is most easily specified as an L-System with the following parameters:

  • Start String: F+F+F+F+F+F+
  • Production Rule: F → F-F+F

As a final note, there are similar constructions possible with triangular and square tiles. I intend to write a follow-up article on the shapes and numbers arising from examining the three tilings together.

Wednesday, April 23, 2008

Rules of 3-4-3

The rules of 3-4-3 are as follows:
  • You will reference project 343.
  • You will reference project 343.
  • We are not anonymous. We are Everymen (and -women).
  • We got grounds.
  • 3-4-3 is indistinguishable from magic.
  • 3-4-3 works in your area.
  • There are no real rules about posting.
  • There are no real rules about moderation either—enjoy your ban.
These are reworkings of the Rules of the Internet. 3-4-3 represents a chapter of the Internet, though Your Internet May Vary. Yes, and ninthly: