RE: Principle of Least Power

This principle looks less useful with every message. 
We seem to be unclear about how to apply it and 
even less clear about how to explain its application 
to a non-information theory specialist.

My eyes don't glaze over when I see "Kolmogorov 
complexity" except where the description says 
'complexity' I substitute 'cost' because a 
string's length can be arbitrarily long without 
being arbitrarily complex given any function 
that produces it, yet to the consumer, it can 
be expensive to process and not necessarily 
equally expensive for any given run. Cost of 
applying a language is good; information reuse 
or discovery is a characteristic that contributes 
to lower cost.

This may be one of those principles that has 
a disclaimer on it saying 'don't apply this at home' 
or like the 'division by zero' prohibition which
everyone learns but is seldom explained.

If this were operational, I would explain it in 
terms of the old story from a sci-fi story about 
strategy, tactics and probability:  strategy says pick a 
sensitive system.  Tactics say pick the point 
of highest sensitivity such that the lowest cost 
or lowest force or least risk action is applied 
to get the most effect by taking advantage of the 
complexity (density of interconnection over affective 
message rate) of the system itself; sometimes known 
as 'wasping' because of the example where the 
probability of changing the vector of a two-ton 
object moving at a given velocity by impacting 
it with a one gram object is low until you 
consider the effect of hitting a speeding car 
with a wasp in the driver's eye.

Again, if this is about data typing, this is 
oblique.  The fact of a number being stored as 
an integer is not necessarily informative with 
it being a person's age. 

HTML is a pretty bad example too.  As soon as it 
became widely available, it was customized and 
extended to the point that it is now a collection 
of languages ready to bifurcate (Say HTML, CSS, 
Forms, XHTML, microformats, XML data islands, 
namespaces, and so on).  Less power or incomplete 
with respect to reapplication to new problems?


-----Original Message-----
From: Harry Halpin []
Sent: Sunday, February 12, 2006 2:44 PM
To: Bullard, Claude L (Len)
Subject: Re: Principle of Least Power

More power does not always equal less information. For example, both
Haskell and C++ are Turing-complete, but you can argue pretty well that
Haskell via its type system/monads/etc. gives you *more information*
even though they are on the same level of the Chomksy Hierarchy. The
Chomksy Hierarchy is the ranking of languages from regular languages to
Turing-complete and recursive languages.

    It goes more confusing if you have something of a *lower rank*
(DTDs?) in the Chomksy Hierarchy that you want to argue provides *less
information* than something of a *higher rank* (XML Schemas?). What I am
saying is that in general knowing Turing-completeness gives you some
information - whether the program will halt or not given the halting
problem. But the space of all possible informations may not be
objectively measurable - although I do think Kolmogorov
complexity/information theory has something to say about that. However,
what we could argue is that knowing some technologies place in the
Chomksy Hierarchy only gives you some information, but that is far from
the only metric. We can argue XML Schemas give more information by
saying that their typing information and annotations (not present in
DTDS) allow them to express more information even though they may be 
higher in the Chomksy hierarchy.

Bullard, Claude L (Len) wrote:
> That confuses me, Harry.  Are you saying that XML Schemas being more powerful 
> and more expressive than DTDs (they are) also provide more information?
> Wouldn't that contradict the principle?
> I get the halting example.  The language can't be used to determine 
> if an answer will return.  In that sense of information (the 
> probability of halting), it is undecidable.   An analog to this 
> discussion occurred recently on the CG list concerning the 
> "reality or intuition" of infinities.  Practical applications 
> don't care but schools of mathematics bifurcate around that debate 
> (platonism vs intuitionism vs constructivism and so on).  All 
> computer systems are finite if they work; they may use concepts 
> of infinities but these are functional (eg. limits, or the empty 
> set is a member of all sets).
> Let me try another example:
> If a language automatically casts data types, thus hiding from the 
> user what it is doing, it exposes in the syntax less information 
> but has more power in the implementation.  So in the sense that it 
> hides that under the covers, it is more *powerful*.  In what it 
> documents in the syntax of the program, it is hiding information. 
> One of the original principles used to sell object-orientation 
> was 'information hiding'.
> I'm looking for an example I can explain to the pointy-haired guy 
> without him rolling his eyes.  "Trust me" isn't good enough.  If 
> we have to explain the halting problem, he will say "you are making 
> my head hurt".  That is not a good thing.
> len
> From: Harry Halpin []
>    Point was that it seems to me the "power" in this note isn't
> Turing-completeness only, but that often less powerful languages give
> you *more information* than more powerful ones. So I'm not sure if
> ranking a bunch of things according to Turing-completeness is really all
> that useful, although it helps!
> So an XML Schema gives you more information (i.e. it has more types,
> substitution groups, numeric ranges etc.) than a DTD, and you should use
> XML Schemas instead of DTDs even if both can be implemented as regular
> languages  (Now the RELAX NG question is a whole other post...). Same
> with programming in Haskell versus C - although both languages are
> Turing complete, Haskell would give you more information via its typing
> system and pure functional architecture about itself, and is so more 
> amendable to analysis without looking at the code or running the
> program. I think this way of thinking about it help connects sections 2
> and 3 to each other.
> One example of this idea of information is Turing-completeness - if you
> know a language  is Turing-complete, then you know whether it halts or
> not, while for Turing complete languages "you don't and can't know" -
> which translates into *less information* even if the formalism is *more
> powerful.*
> Ditto for traditional complexity computer science re Henry - if I tell
> you a problem is of class L (solvable in logarithmic time), than if I
> tell you it's solvable in P (polynomial), and even more than if I told
> you if it was solvable in NP (non-deterministic polynomial time) , since
> we don't know if P=NP, but we do have a pretty good idea what L is :)
> I don't think this requires any major amendments to said document, maybe
> a sentence or two about this as suggested earlier might help clarify
> Henry's issues, which confused me as well when I first read it, as I
> thought it was talking about only Turing-completeness - and so the
> Haskell bit  seemed a bit weird, but in retrospect it makes sense.

Received on Monday, 13 February 2006 19:58:15 UTC