Re: Bureaucracy and identity

On Thu, 17 Mar 2005, Alessio Guglielmi wrote:

> The same thing in other words: every time a `problem' (like `getting rid of 
> bureaucracy') is not formally defined, there is a strong temptation to define 
> it *after* one has found a technical solution. I think we should resist the 
> temptation and set the bar (2) *before* making the jump (1). (In computer 
> `science', where formalised problems don't abound as much as in mathematics, 
> many people don't set the bar or set it after, and this of course is 
> ridiculous, in my opinion.)
>
> Enough said. Do we agree on this?

OK. we agree on that. This more or less was my concern.

> > > Do we agree that the *very first* source of bureaucracy in *all deductive 
> > > systems* in *all formalisms* is associativity and commutativity (when 
> > > present) in formulae?
> >
> > no.
> > It certainly is bureaucracy. But not necessarily the "very first". You 
> > simply lose importaint aspects if you take that for granted.
>
> Which aspects? I might very slightly agree about associativity, but I feel I 
> will never agree about commutativity. Give examples!

If you per se identify A*(B*C) and C*(A*B) you lose the information in 
which order the three guys are associated. Of course, you can consider 
this a pure act of bureaucracy, and probably you are right in most cases. 
But sometimes you need the information about this additional structure.

You came up yourself with the best example I can think of. Before I have 
seen it I wasn't sure whether the problem was real or just a gut feeling.

> > In principle yes. But I have my objections to putting this on a higher 
> > level than "type A" or "type B" bureaucracy.
>
> The plot thickens... Which objections?

Right now, they are only of the "moral" kind. The first is that I think it 
should be possible to deal with A and B independently from associativity 
and commutativity.
And the second is that I guess that it is easier to deal with A and B 
without having to take care of associativity and commutativity. So, I'd 
propose to do that first. Once we have done that, i.e., we have formalisms 
A and B, we can think about the associativity-and-commutativity-problem 
from a much better starting point.

> > > Do we agree that *every* war to bureaucracy should start from this 
> > > realisation?
> >
> > no.
>
> So, what's the alternative? Suppose I have to write an introduction to the 
> subject, what would you suggest?

Explain the different types of bureaucracy, and say that they are 
*orthogonal* to each other, i.e., can be dealt with independently.

> > > Consider
> > >
> > >        E   C
> > >     [  |   | ]
> > >      [A B] A
> > >   * ---------- .
> > >       A [B A]
> > >     [ |   |  ]
> > >       D   F
> > >
> > > This is a derivation in formalism B in which two derivations are 
> > > vertically composed by *, and we work under commutativity and 
> > > associativity. The problem is that this is the only way I have in 
> > > formalism B for representing (what I could graphically and imprecisely 
> > > represent as)
> > >
> > >        E    C
> > >     [  |    | ]
> > >      [A B]  A
> > >       |  \  |   .
> > >       A  [B A]
> > >     [ |    |  ]
> > >       D    F
> > >
> > > However, the same derivation above could also stand for
> > >
> > >        E   C
> > >        |   |
> > >     [[A B] A ] ,
> > >        |   |
> > >        F   D
> > >
> > > and this of course is *morally different*!
> > >
> > > What can I do? Well, I could stop working under commutativity and 
> > > associativity: this way I could easily distinguish between the two cases. 
> > > However, if I drop commutativity and associativity, I get back all the 
> > > bureaucracy in formulae, with a vengeance, because now this bureaucracy 
> > > scales up to proof composition.
> >
> > I think the problem only appears because you put the 
> > commutativity-and-associativity-bureaucracy on a higher level than the 
> > type-A-bureaucracy and the type-B-bureaucracy. The problem would disappear 
> > if you consider commutativity-and-associativity-bureaucracy as a special 
> > case of type-B-bureaucracy.
>
> Example, please.

Hmm. Now I realize that what I said in that paragraph is not only unclear 
but also wrong. The problem is more subtle. Your example clearly 
shows that the commutativity-and-associativity-bureaucracy is 
*independent* from type-A-bureaucracy and the type-B-bureaucracy.

And sometimes commutativity and associativity is not purely bureaucratic, 
but is needed to keep track of what comes from what. This is my 
interpretation of the example.

Of course I do not have the patent solution in my pockets, but my 
suggestion would be to try to solve the two bureaucracy-problems 
seperately, and not at the same time.

-Lutz