[p2p-research] Building Alliances (limits of mathematical modeling)

Paul D. Fernhout pdfernhout at kurtz-fernhout.com
Sat Nov 7 22:35:58 CET 2009

J. Andrew Rogers wrote:
> On Sat, Nov 7, 2009 at 8:29 AM, Paul D. Fernhout
> <pdfernhout at kurtz-fernhout.com> wrote:
>> Another way to understand this might be to look at some of Marvin Minsky's
>> and other's work on multiple representations and artificial intelligence. I
>> was at a talk Minsky gave around 1999 where he outlined the idea that the
>> human brain simultaneously kept running several different models of the
>> world (semantic, 3D, 2D, and so on, don't remember for sure which ones he
>> discussed) and kept choosing solutions from one of the model as they were
>> most appropriate. So, there he was talking about building AIs with multiple
>> ways of knowing, all going on simultaneously. :-) Mathematical and abstract
>> enough for you? :-)
> You are misunderstanding what you are reading here.  The internal
> abstract representation of all those models is *identical*, it is the
> information that varies from model to model. Semantics and 3D are the
> same structure, you are just organizing the structures around
> different properties of the raw information. It is a local
> optimization with well-understood properties. This is a side-effect of
> ideal intelligence not being possible in this universe (it is
> non-computable).

Only in the sense that all Turing-complete systems are somehow equivalent. 
They may indeed have very different sets of information and representational 
structures associated with them. That's the point in having them -- each can 
get at different answers in different ways depending on what is most 
efficient (minimal energy use or minimal mass or maximum speed) for the 
current context.

If you talk about "ideal", everything biological we see in the universe is 
shaped, to the best of our knowledge, by evolutionary constraints like 
durability, power consumption, response time. Intelligence simply does not 
exist apart from evolutionary processes that shape it.

>> Only after the fact. Biofilms are theoretically not possible either,
> Nonsense. You are conflating theoretical possibility with empirical
> evidence.  This is a basic logic error.

I'm talking about the social processes of science. :-)

Theoretically, heavier than air flight was impossible too, or so said many 
people. Even when they saw birds and balloons.
Another example of his hubris is provided by his 1895 statement 
"heavier-than-air flying machines are impossible" (Australian Institute of 
Physics), followed by his 1896 statement, "I have not the smallest molecule 
of faith in aerial navigation other than ballooning...I would not care to be 
a member of the Aeronautical Society."

This is the sort of thing Michel is getting at. Lord Kelvin let his 
"certainty" about the theories he believed in at the time get the best of him.

>> Could the same be true for how you say other things, whether disordered
>> amorphous p2p volunteerism, or distributed search, are not theoretically
>> possible, or are certain to fail? :-)
> You are making some pretty severe category errors here, conflating
> completely unrelated constructs as though they are subject to
> equivalent analysis.

They are all about networks, right? What's the difference? A network of 
volunteer people or a network of volunteer search nodes? :-)

> Some things are provably impossible in a strong mathematical sense.
> Nothing proven mathematically has *ever* been invalidated by a fact of
> reality.  There are some things for which we have only proven partial
> properties i.e. we do not know what is potentially possible but we can
> prove that some things are impossible regardless of that fact.  And
> then there is science where nothing is ever proven at all.

You're talking math. I'm talking the history of science.

Besides, mathematical proofs have been found to have errors. Wiles first 
attempt at proving Fermat's conjecture was found to have a big error. 
Happens all the time, especially in complex things hardly anyone understands 
about stuff not easy to look at experimentally.

For another example, mainstream economists have all sorts of wonderful math 
to explain the economy and guide public policy, but it is almost all harmful 
and based on controversial or clueless assumptions. But, it's easy to 
intimidate people by saying things are "mathematical". So what? What are the 
assumptions? What are the values? What are the emotions? What in the 
rationale for a choice of reasoning tool or approach? What are the limits of 
the tool? And so on...

> There is no aspect of reality that does not obey strict mathematics as
> we understand it. 

Well, if mathematics is thought stuff, and can be anything with a little 
handwaving (simultaneously wave and particle, infinite quantum state 
constructs, whatever), then sure, it all is math. :-)

That's kind of like saying the universe is all carbon atoms (at least, the 
interesting parts).

But the relationships of the mathematical elements still matter, or the 
carbon atoms. Mentioned in here in passing by Carl Sagan: :-)
"YouTube - Symphony of Science - 'We Are All Connected' (ft. Sagan, Feynman, 
deGrasse Tyson & Bill Nye)"

> What is possible in the unknown areas of science is
> bounded by what is allowed in mathematics. 

And if something did not fit, we'd just invent some new math. What does that 

 > That leaves many
> unexplored possibilities, but it also means that we can say with a
> high degree of certainty that some ideas are strictly disallowed even
> without bothering to collect empirical evidence.

All based on assumptions.  Sometimes right. And sometimes wrong. That's why 
we are often surprised...

But I'd agree, one might argue that some areas of inquire are likely to be 
more fruitful than others. But overturning theory is so much fun if you can 
do it. :-) Look at the recent Nobel Prize about the theory of the commons 
economists have been pushing for so long was wrong based on empirical evidence.

There is always a continual interplay between theory and experiment/observation.

> Every time someone has pretended that mathematics doesn't apply to
> some aspect of reality, disaster has ensued.

And every time someone has pretended that reality doesn't apply to some 
aspect of something previously proved mathematically, disaster has ensued. 
:-) Well, I would not put it that strongly as you. Sometimes disaster has 
ensued. :-)

Mainstream economics is a prime example. Lots of math. No reality. :-) Like 
we already agreed. And disaster has ensued for millions of people. Although, 
even now, the mythology seems intact:
   "The Mythology of Wealth"
Old habits die hard. In fact, we still have a “leisure class”. As capitalism 
has grown so has the wealth and privilege of our leisure class. The old 
mythologies – gods, the “great chain of being” etc. – are no longer 
available to justify the existence and perpetuation of our leisure class, 
something our elites are definitely interested in perpetuating. What was 
needed was a new “rational” world-view that justified the existence of 
privileged elites.
   That rationalization came in the form of a brand new science known as 
economics, which included a brand new mythology.
   According to the new mythology, human beings are economic competitors. 
The “marketplace” is the new “Valhalla”, where “economic man” frolics. The 
“market” we are told, contains its own “rationality”. It rewards the 
efficient. It rewards that list of virtues George Will cites, like “thrift”, 
“delayed gratification” and of course, “hard work”. Free competition in the 
market place “rationally” selects the more “worthy” competitor. Thus, the 
wealthy are the superior competitors who have “earned” their elite status. 
If you haven’t succeeded it can only be because of your “inferiority”.
   Before debunking this whole ideology, a few observations are in order. ...

You might say, but the assumptions underlaying economics were wrong. Or the 
math was too simplistic. OK, but that's part of my point.  Which mathematics 
with which assumptions? To whose benefit? And who pays the costs?

Mathematics is a huge field, and classically does not even include 
individual based modeling, because if it does, mathematics is just 
computing. And as I see it, mathematics *is* essentially a subset of 
computing. (There may be some vague conceptual aspects of math we don't have 
a way to deal with in computing yet...)

Just about all computational models are made for some purpose. They are 
simplifications of reality to some end (economic models usually to make 
someone rich in ration units). So, they are not the same as reality. They 
are a reflection of part of it in some way, perhaps.

Besides, in general, the way your argument is leading, it is ignoring chaos 
theory. In practice, we don't have ideal information. We make 
approximations. That's real practical discrete mathematics. Any rounding 
error can magnify in chaotic ways unless we continuously sample and reset 
our models. Sure, in theory, that should not matter. But in practice, it 
matters. :-)

So, you're saying things are proven mathematically (and not even giving 
citations) and end of discussion. Where does that get us?

Sure, math is nice, as is the large framework of computation that math is a 
part of (I got that insight from discussions with math educators on the 
Python mailing list). But, like everything, math has its limits -- 
assumptions, emotions, choice of tool, rounding errors, logical errors, 
conceptual errors, and so on. And mathematical "proofs" are prone to all 
sorts of problems of these sorts.

Again, Michel is expressing the concern of how pride goes before a fall -- 
like when we find out our our assumptions are not as much in alignment with 
reality and survival as we had thought they were.

One problem is that "certainty" is heavily rewarded by social prestige in 
our economy. :-) So, even in your life, acting certain may have been heavily 

See, I live in a different (uncertain) world with my ventures. And it does 
harm them within this society, I know. People are so used to being bombarded 
with messages by people who are so certain, that when I come along and say, 
I'm working on this thing, and it has these problems, and all these 
uncertainties, and lots of limitations, and here is a long list of stuff 
that can go wrong, but I think it is a risk worth taking, well, then people 
then turn to someone else who sounds more certain. :-) Sometimes, 
commercially, we then get hired later to clean up the mess. :-) Usually 
people just bury the metaphorical bodies and move on to the next certain person.

Still, there are ideas like a cone of project uncertainty:

Anyway, I don't hear you talking much about the mathematics of statistics? 
There is a mathematical world where uncertainty is a big issue.
"Several statistical tools and methods are available to organize evidence, 
evaluate risks, and aid in decision making. The risks of Type I and type II 
errors can be quantified (estimated probability, cost, expected value, etc) 
and rational decision making is improved. ... A highly controversial issue 
is whether one can replace the use of probability in decision theory by 
other alternatives. The proponents of fuzzy logic, possibility theory, 
Dempster-Shafer theory and info-gap decision theory maintain that 
probability is only one of many alternatives and point to many examples 
where non-standard alternatives have been implemented with apparent success; 
notably, probabilistic decision theory is sensitive to assumptions about the 
probabilities of various events, while non-probabilistic rules such as 
minimax are robust, in that they do not make such assumptions. Work by 
Yousef and others advocate exotic probability theories using complex-valued 
functions based on the probability amplitudes developed and validated by 
Birkhoff and Von Neumann in quantum physics. ... A general criticism of 
decision theory based on a fixed universe of possibilities is that it 
considers the "known unknowns", not the "unknown unknowns": it focuses on 
expected variations, not on unforeseen events, which some argue (as in black 
swan theory) have outsized impact and must be considered – significant 
events may be "outside model". This line of argument, called the ludic 
fallacy, is that there are inevitable imperfections in modeling the real 
world by particular models, and that unquestioning reliance on models blinds 
one to their limits. For instance, a simple model of daily stock market 
returns may include extreme moves such as Black Monday (1987), but might not 
model the market breakdowns following the September 11 attacks."

So, lets say it turns out we are living in a simulation and someone changes 
the rules just now. What does math say about that? :-)

Anyway, you may well be a whiz at the kind of math you are working with to 
solve certain important problems you are interested in. I'm not disputing 
that. What both Michel and I are responding to what feels to me and 
presumably him that you are generalizing from that mastery of math to 
pronouncements on p2p issues and beyond, in ways aligned with mainstream 
economics, including without citing specifics.

As I see it, you are saying math is good, and I am saying math happens in a 
social context. :-) So, maybe we can agree on both those point? :-)

--Paul Fernhout

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