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Political corruption lambda calculus

Who watches those who watch those who watch...the watchers of the watched?
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Quis custodiet ipsos custodes? - Who watches the watchers?

Zerothly, there are the watched. These can be defined as those to whom the function "watches" can be applied, returning the value "the watched". That is, they are self- aware and may have lives which they themselves examine.

Firstly, there are the watchers, for example the police, intelligence services, professional bodies, OFSTED or the CRB - in general, certain quangos, the government, local government and various other things such as security firms. They are people or organisations to which the function "watches" returns a different value than its original. The watchers watch the watched rather than themselves. Their function is to "surveill" the activities of the watched.

Secondly, there are organisations or people who are concerned about "who watches the watchmen". These people include pressure groups, charities, concerned individuals, possibly also certain MPs and so on. These watch the watchmen, so the function "watches" returns a different value again, but that value can again return a different value when the function "watches" is applied to it. Specific examples would be the NSPCC, Greenpeace, TICL (back when it existed) and umbrella professional associations such as exist in the EU.

Thirdly, there are more people who are concerned about the activities of such organisations and people. For instance, there are those who feel that Greenpeace or the NSPCC have reached a stage where they promote their existence by interpreting what goes on on the level below them in a certain manner. Once again, the function "watches" returns a different value, which in turn returns another until we finally reach "the watched".

Fourthly, there are at least people if not organisations who observe the behaviour of those who are suspicious of such organisations and become concerned about their paranoia. These people constitute a group to whom the function "watch" can be applied yet again.

I'm not sure how many times this process can be iterated, but looking at it this way it becomes rather familiar. These are very similar to Church numerals. At the bottom there are the rather appropriately named "zeroes" - those who don't matter, have no value in the system and are simply watched. They don't watch anything, except maybe television. Above them are a series of cardinal numerals which behave in a more Orwellian or "Report On Probability A" manner. These have value in the system. Hence the Lambda Calculus can be applied to this system.

That means, moreover, that arithmetic can be done within this system. Peano's axioms apply. Any organisation or person within this system has the same value as itself, and derives its value from how many levels of watching are going on. That's a reflexive property. If it has the same value, i.e. is on the same level, as another organisation, it is equal to it and the other is equal to it too. If it's equal to another organisation in that respect, and that organisation is equal to a third, the first organisation is also equal to the third - transitivity. Any organisation or person which is equal to something is a member of this system. Therefore, this is a system in which addition and multiplication can be done. Effectively, there is an arithmetic, within limits, which can be performed in the system of organised suspicion of others.

This also means there are theoretical entities within this system. For instance, there are infinitely suspicious organisations or individuals who watch everything, even themselves. Maybe there are even uncountably infinitely suspicious such entities.

Questions:

Are there organisations who watch themselves? Is there an organisation which only watches organisations which do not watch themselves? Does that organisation watch itself? Does there need to be another way of describing the calculus of suspicion which can avoid this paradox?

Could there be organisations with negative or non-integral levels of suspicion?

Is there a way of dividing or subtracting levels of suspicion?

Should we establish a series of organisations which are so unwatching that even watching them doesn't lead to them actually being watched? Is it possible that such organisations already exist in an undiscovered and maybe even undiscoverable form? Should we be suspicious of these organisations, or would that be dangerous because they would absorb all our suspicions and lead to us not being suspicious enough and thereby susceptible to the likes of spam or being accused of crimes we not only have not committed but cannot commit? On the other hand, could we perhaps bribe such organisations to do things for us by having them pay us?

What should we do about these dangerously non-suspicious entities? They are unfindable. I find that thought very frightening indeed, if indeed it is a thought.

nineteenthly, May 30 2011

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       Surely the "watches" relation is not a function; rather, it is many-to-many.
pertinax, May 30 2011
  

       No, don't think so. Take a spy. Their job is to spy on others, so to simplify it the function of watching is applied simply to at least one object outside the set of spies of which that spy is a member, and probably to another set of spies too. That applies to the set of spies in, for example, MI6 or the CIA too. They may also spy on their own spies, but in that case there is a set which includes spies who spy on other spies, who are in the set of spies who do not spy on their own spies. You can count members of those sets separately as separate sets because they are "CIA spies considered in their role as spies on other spies who are not members of the CIA" or "CIA spies considered in their role as spies on other spies which are members of the CIA". However, that does mean that the roles are what are being counted rather than either organisations or individuals. Thanks for helping me to get to that realisation.   

       That means you could watch yourself a la 'A Scanner Darkly' and still be counted as a spy to whom the concept "Custodeo custodem" applies - "I watch a watchman" - but you are also both a watched person and a simple, first-order custodian. So you have three personas.
nineteenthly, May 30 2011
  

       Why stop at three ... ?   

       // umbrella professional associations //   

       Tell us more about these putative "professional umbrellas". Are they the special big umbrellas that commissionaires and golf caddies carry ?   

       // dangerously non-suspicious entities? They are unfindable //   

       That's what makes them so dangerous, and that's what MKULTRA and MKSEARCH were investigating. But of course, the findings were kept secret.   

       These "entities" are actually just single secretive individual conspiracy theorists, who need watching very closely because they may suspect someone is spying on them.
8th of 7, May 30 2011
  

       It isn't necessarily the case that this recurses to infinity, there are for example, only 5 platonic solids - and there may well be be some deep limiting analogy between the number of faces and vertices that an object can be constructed from that also applies to the network of watched/watcher/ suspicion/suspect that you describe.
zen_tom, May 30 2011
  

       Have you considered this question-   

       Since we ourselves are 'In' an 'Organisation' (The Halfbakery), what value would the function return from the argument 'The group of us who have read this and have now become intrigued, thereby having become concerned about entities who watch other organisations who watch the zerothly watched'?   

       And is there therefore a possibility that those who read this actual annotation, as written by me, return a recursive value?
bhumphrys, May 30 2011
  

       What truly makes us human is our ability to learn behavior from others' craft. Paranoia (fear without memes) is another uniquely human functionality arising, as a matter of course, in response to conspiracies of secrecy. Governments have power according to value derived from caches of secrets. All sort of conspiratorial edginess occurs across the continuum from originality to awe; so, why not quantify it? Vicis verto buns.
reensure, May 30 2011
  

       This cannot regress to infinity except in the case of infinite loops of people watching each-other.
Voice, May 30 2011
  

       That could happen easily and i suspect it often does. It might even happen inside the same person.
nineteenthly, May 30 2011
  

       Social control of the inner man is labeled "acceptance", it is the only external locus of control that is considered status quo. That's why narcissists, on par with borderlines, are the most tumultuous among disordered personality types, and nihilists the least popular.   

       An interesting conjecture that the absence of watchfulness places one outside suspicion, unfindable. That may or may not be true of a nihilist; and, might be achieved by way of the 'false positive' atmosphere around some antisocial types wherein they'd find a place to be calm amid the chaos.
reensure, May 30 2011
  

       Combining lambda calculus with _Report from Probability A_ is certainly my cup of tea, but does the idea really hold water? Specifically, recursion seems the wrong concept here; the branch of math(s) that seems most applicable would be graph theory. And applying graph theory to social networks is kind of old hat.   

       The fact that you *can* use recursion to describe cyclic graphs doesn't mean it's the natural way to do it. After all, tail recursion does the work of iteration, and, more generally, lambda calculus can do anything a Turing machine can.   

       The new element here might be that the nodes in the graph (or network) are sets, and that some node/sets may, as you point out, be nondisjoint with each other.
mouseposture, May 30 2011
  

       So... the domain of this "watches" function is a set of person-role pairs? Or is it just a set of roles?   

       Also, sp. "Custodio custodem".
pertinax, May 30 2011
  

       Yes, i thought i'd probably got that wrong.   

       It could be a set of asymmetrical functions "watches(x,y)", where x is a role and y is a perceived person, i.e. x is the adoption of the role of the watcher, effectively a reduction of one's full identity, and y is the person watched, but that person is a similar reduction as constructed in the mind of the watcher. So it's sort of existentialist: both arguments are reductions of the real blurring buzzing confusion of the manifold to a couple of apparently concrete objects. However, just because we're trying to force them to become concrete doesn't mean we succeed. I recognise that right this second, this annotation is more a string than something which refers successfully.   

       [Mouseposture], i suppose i see that as a question of whether this is pure or applied. I'll just have to go away and think about what you've said because right now i can't answer that. A brief and possibly futile flight of fancy there is, since lambda calculus is another way of looking at a Turing machine, can there be hypercomputers which apply to hierarchies of suspicion? And would it get anyone anywhere if there could?
nineteenthly, May 31 2011
  

       rather dull pointless musing. I wish we could delete this category. Get out and enjoy some fresh air, 19th.
RayfordSteele, May 31 2011
  

       I have no problem with the pointlessness of the musing; it's the relative incoherence (by [nineteenthly]'s normally high standards) which troubles me. Indoors or out, I hope you're all right, [nineteenthly]. Maybe you could prescribe yourself some sort of herbal pick-me-up.
pertinax, Jun 01 2011
  

       No, it's fine. I think the problem is i've spent too long on here recently and need to do other stuff for a bit. Currently trying to get my head round functional programming for [eleventeenthly]'s benefit and this is a kind of kick- around with the notion to see how much sense i can make. I've forgotten a lot of stuff about the lambda calculus and i'm trying to see if i can say something coherent with it.
nineteenthly, Jun 01 2011
  

       I'm sure you can but <sotto voce>this idea is not that something</sv>.
pertinax, Jun 01 2011
  

       But knowing that it's not is itself enlightening.
nineteenthly, Jun 01 2011
  
      
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