[p2p-research] Limits of mathematical modelling (was Re: Building Alliances )

[Smári McCarthy]

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[For some reason it seems like my messages to this list rarely make it
through... can somebody debug?]

Re the axiom of choice, it is still controversial and not commonly
assumed to be true, but the majority of mathematicians believe it to be
true. The difference here is that belief does not validate assumption,
and thus in any case where you make an assumption based on your belief
you must state that that is the case. So any (respectable) paper in
mathematical logic which assumes the axiom of choice will say so very
near the beginning. Axioms are exactly that: Unproven theorems that are
assumed to be true.

Assumption of a statement, regardless of it's truth value, can lead to
the successful proof of many other theorems, however, if the statement
that led to their proof is found to be false, the theorems themselves
may also be false.

The axiom of choice is equivalent to Zorn's lemma and the well-ordering
theorem, which state, respectively, that every poset in which each chain
has an upper bound contains at least one maximal element, and that any
set, given an ordering relation, has exactly one correct order.

Both of these statements, and many other equivalences of the axiom of
choice are very hard to refute, but still a bit controversial.

Anyway, it seems a bit silly to bring up the Axiom of choice in this
discussion. As an example to illustrate a point it's a bit obscure and a
lot irrelevant.

  - Smári



Paul D. Fernhout wrote:
> J. Andrew Rogers wrote:
>> On Sun, Nov 8, 2009 at 3:52 PM, Paul D. Fernhout
>> <pdfernhout at kurtz-fernhout.com> wrote:
>>> You seem to be using the term mathematics below like it was one unified
>>> whole, inclusive also of physics, and one where all the conclusions
> flowed
>>> from a few basic unarguable assumptions (like, do parallel lines
> touch at
>>> infinity? :-)
>>
>> On the contrary, I was fairly explicit that the axioms of mathematics
>> are arbitrary, selected for simplicity and power rather than any
>> universal truth. See, for example, the Axiom of Choice which was
>> controversial at first but which has become generally accepted because
>> it could be used to prove a large number of important theorems that we
>> could not prove without it.
> 
> The "Axiom of Choice" seems to boil down to saying if you have a numeric
> interval you can pick a number from it. Almost a definitional argument.
> Like aspects of this conversation. :-)
> 
> Which also has become a digression from you squirming away from the main
> point, which is that there are alternative ways to put together
> resources to solve big problems. There's been a deafening silence in
> regard to the post I made about GNU/Linux's cost being in the billions
> of dollars to do by a centralized financial system. So, you're ignoring
> the existence proof, and putting up side issues.
> 
> Exhibit A:
> http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-November/005630.html
> 
> "Concentrations of wealth are extraordinarily useful for real progress.
> It is how most really great ideas get funded."
> 
> Exhibit B:
> http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-November/005635.html
> 
> "It would be a death sentence for the development of many, many
> innovations if one had to aggregate funds from a large number of
> parties."
> 
> Now, you've qualified those with "most", and "many, many", but the
> subject of this  list is mostly peer production as exemplified by
> GNU/Linux and Wikipedia (or even the web itself seen as a totality) and
> things that flow around that (alternative economics, envisioning a
> better society).
> 
> So, you made the points above. Then you said:
> Exhibit C:
> http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-November/005652.html
> 
> "This planet is desperately short of people capable of usefully
> contributing to non-trivial R&D efforts. A million average people with
> no particular expertise cannot replace one extremely brilliant person
> with deep expertise. If this was not true, "design by committee" would
> not be pejorative."
> 
> And have proceeded to go on and say fairly derogatory things about
> people on this list (including myself) as well as this community in
> general. While ignoring that an essential aspect of p2p is how
> understanding emerges out of the community through a stigmergic and
> interactive process.
> 
> You also said, responding to what I wrote:
> Exhibit D:
> http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-November/005665.html
> 
> """
>> But, one could imagine that the people who started Google had just
>> published their idea, and further, that someway was found to adapt it,
>> in a "Folding at Home" distributed computer way to use idle CPU cycles
>> and a p2p meshwork. We might not need Google server farms at all to
>> do fast searches. But, there is not much incentive for people to spend
>> millions or billions developing that idea, even if it was better and
>> more secure and more democratic, because, in a captilist society,
>> where is the profit?
> There are well-understood theoretical reasons why that won't work.
> Centralization was required, not a design choice. No need to look for
> the profit bogeyman when simple mathematics will do.
> """
> 
> So, there you are justifying the current social order based on "simple
> mathematics" and "theoretical reasons" even when given a plausible
> alternative. Which is all starting to sound a lot like this:
>   "The Mythology of Wealth"
>   http://www.conceptualguerilla.com/?q=node/402
> "Justifications for elites and social hierarchy goes all the way back to
> the pharaohs. ..."
> 
> 
> Then you said this:
> Exhibit E:
> http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-November/005676.html
> 
> """
> I did research a few years ago on the mathematics of optimally
> efficient and pervasively decentralized networks. This theoretical
> area is very important because it is used to prove all sorts of things
> about cooperative systems of independent agents. It is literally the
> mathematics of dynamics of P2P systems in the abstract and very
> challenging theoretically with many unanswered questions. One thing
> that has surprised me is that it is never discussed here even though
> it is very relevant.
>   One of the critical theoretical problems of such systems is that there
> are only two known strategies -- from two different theoretical
> derivations -- for P2P system design that do not decay into
> pathologically suboptimal equilibria. If you have a system that
> necessarily cannot be constrained to those strategies, the system is
> not stable in a well-functioning configuration.  The reason I was
> researching it at all was because there was an interesting real-world
> political policy problem that could not use either known strategy; I
> never found a satisfactory solution, but I suspect one might not even
> exist for that case.
>   The problem is that the two robust strategies in literature (someone
> may have come up with a new one in the last couple years, probably
> not) are both effectively based on adaptive market-like pricing
> mechanisms. You can solve the problem with strong centralization, but
> that has its own problems in real systems e.g. single point of
> failure/corruption.
>   I don't have answers, but designing theoretically stable, strongly
> decentralized P2P systems that do not have major provable pathologies
> is very, very hard outside of some fairly narrow cases. I am very fond
> of the idea of strongly decentralized P2P economies but I haven't seen
> much in the way of a rigorous formulation of such a system here that
> would be both robust and without significant pathologies.
> """
> 
> Once again, you say there are reasons, or there is a literature, and do
> not explain them, and do not cite anything specific, and then proceed to
> make a broad sweeping claim that, essentially, everything people are
> doing in P2P, like Wikipedia, Debian GNU/Linux, Apache,  and the rest of
> the web, and so on, can't possibly work on theoretical grounds. Well,
> you use wors like "decay into pathologically suboptimal equilibria" but
> that seems to me what you are trying to say, that it won't work. Even
> when it does. And then proceed to tell us we should be studying math to
> prove they work. Well, math is nice. Math may be useful. But, I don't
> see the connection between math and your points about how P2P will never
> fly, like Lord Kelvin said heavier than air vehicles will never fly,
> even when there were birds flying all around him.
> 
> Or, maybe I truly just don't understand what you are trying to
> accomplish here?
> 
>>> There was a time when all that was not understood about geometrical
>>> possibilities. What mathematical issues now are the same? We may
> think we
>>> understand them only because we do not see the other possibilities, as
>>> you suggested elsewhere, some assumption made decades ago that gets
>>> propagated through the mainstream thought on some subject.
>>
>> You are conflating deductive axiomatic systems with inductive
>> non-axiomatic systems; algorithm design is an engineering discipline
>> even though you can (sometimes) prove the properties of a particular
>> design.  In mathematics, a theorem is strictly proven from a set of
>> axioms.  There is no "think we understand", it is either proven
>> absolutely or not. There is plenty of mathematics that is not
>> well-understood in a formal sense. The job of a mathematician is
>> nominally to fill in those holes so that mathematics can move on to
>> the next hypothesis.
>>
>> While new patterns and relationships may be found, they do not and
>> cannot invalidate anything that has already been proven.  We may get
>> new knowledge, but it never destroys or invalidates old knowledge in
>> this context.  Math is not science.
> 
> This is a beautiful sentiment. But, it is not true. :-) Or rather, it is
> only true when you define science differently than math. If math and
> science are considered as their historic literatures and a bunch of
> people working together to build on that literature as a social process,
> then there is no difference. Both involve an accumulation of facts and
> ideas and examples. You hand wave away mistakes in proofs, or
> unproductive unpublished explorations in math as not important, but they
> happen all the time. So, is math as a human endeavor really than
> different than science in that sense?
> 
> The fact that people think heavier than air aircraft can fly now, and
> have theories about it, does not invalidate that the literature exists
> relating to statements with rationales for why they could never fly.
> Some things about flying still remain controversial arguments, like
> which is more important, the kite effect or the Bernoulli effect;
> otherwise, some ask, how could aircraft fly upside down?
> 
> You have made statements about math and P2P, as in the exhibits above.
> You offer no evidence to back them up. You don't even say what "the
> problem" is. I don't see that as making a solid point. I'm happy to read
> and listen to what you have to say about this -- if you said it. :-)
> Rather than just saying, we don't understand your handwaving.
> Mathematics is not the same as bullying with confident sounding
> terminology. If you have a truly deep love of mathematics you wished to
> share with us on the list, then by all means, we could all benefit from
> that.
> 
> Maybe being financially rewarded for doing math has destroyed your love
> of the subject? :-(
> 
> In which case, please don't blame the people who are trying to help fix
> the larger social situation if you are becoming alienated from that
> which you have obviously long cared about:
>   "Studies Find Reward Often No Motivator: Creativity and intrinsic
> interest diminish if task is done for gain"
>   http://www.gnu.org/philosophy/motivation.html
> 
>>> You seem to be doing a standard mathematicians trick here. :-) That
>>> trick is to take any messy and interesting part of the problem and
>>> define it as outside the scope of the area of study. Or, alternatively,
>>> the trick is doing some handwaving that because we have some guesses
>>> about quantum wave functions, the simulation of large universes are
>>> left as an exercise to the reader, but are proof that mathematics we
>>> now know covers everything going on in the universe. :-)
>>
>> You have some very strange ideas about what mathematics is and how it
>> functions.
> 
> True. Probably one reason I did not do so well in a PhD program in
> Operations Research and Statistics at Princeton. :-)
> 
> In the end, I did learn to have more appreciation for networks and
> centralization (and now cite Manuel de Landa as penance. :-)
>   http://en.wikipedia.org/wiki/Penance
> 
> On the other hand, I was right that their mathematical models, with all
> sorts of proofs and lots of fancy handwaving, focusing on "optimizing"
> to maximize short-term profits were extremely risky to our civilization,
> and now, twenty years later, many trillions of dollars have been forked
> over to the bankers to paper that over, and tens of millions of people
> are without income, we face all sorts of other instabilities from wars
> over oil profits and such, and many other aspects of our society are
> failing, and you can thank people like at Princeton University for all
> that. "Picking up nickels in front of a steamroller", indeed:
> http://www.google.com/search?hl=en&q="Picking+up+nickels+in+front+of+a+steamroller"
> 
> 
> No hard feelings though: :-)
>   "Post-Scarcity Princeton, or, Reading between the lines of PAW for
> prospective Princeton students, or, the Health Risks of Heart Disease "
>   http://www.pdfernhout.net/reading-between-the-lines.html
> 
> Even though everyone else got the decades of health insurance, nice
> offices, students learning from then, pensions, nice walkable
> surroundings full of happy people, and so on. All while they were
> helping set up one of the biggest swindles in history and potentially
> setting the stage for even more huge wars. All based on "math" and
> "certainty", using language much like you have been using.
> 
> Again, "math" is really a meaningless term. It's almost like saying you
> solve problems with chalk on a chalkboard. What are the assumptions?
> What are the values? What tools have been chosen and what are their
> limits and areas of applicability? What things are uncertain? What are
> the unknown unknowns?
> 
> Now, you yourself may understand that. But the language you use here
> does not seem to reflect that. Again, the exhibits above.
> 
>>> So, we have books on, as you say, "the eerily robust correctness of
>>> mathematics as it applies to the real world", but the fact is, even
>>> with our best supercomputers, it is my understanding (from a few years
>>> back) we still can't 100% accurately model how a few molecules of water
>>> interact at the quantum level. How are those two statements
>>> reconcileable, other than to state that people who like math are often
>>> willing to look the other way? :-)
>>
>> Your example above, modeling molecular interactions, has nothing to do
>> with mathematics nor does it say anything about mathematics. Your
>> assumptions about these things are sufficiently wrong that you are not
>> making much sense. The validity of mathematics is not dependent on
>> better measuring tools or the next CPU upgrade.
> 
> Again, it shows the limits of people trying to build what might seem
> like the simplest of mathematical models -- some water molecules
> interacting.
> 
> What do you mean by "validity of mathematics"? Again, from what I've
> been reading here, it seems like you are defining "valid" and
> "mathematics" as essentially the same thing. If it's invalid, it can't
> be mathematical. If it's valid, it is or will be part of mathematics.
> 
> Maybe the issue is that I read an ellipsed "the" in front of mathematics?
> So, I read "The validity of *the* mathematics is not dependent on better
> measuring tools or the next CPU upgrade." Because, as I see it, that's
> what one can talk about. If you want to talk about "mathematics" then we
> have to talk about a social enterprise. If you talk about "the
> mathematics" than we need to talk about assumptions, values, choice of
> tools, and so on.
> 
> Anyway, that's another reason we are talking at cross-purposes here.
> It's almost like you had said "The science of p2p is flawed, as I know
> from studying it" and we said, "Where is the evidence? Can you cite
> anything? What specifically do you object to?" and then you start
> talking about how wonderful the scientific method is for arriving
> eventually at some truths. Well, sure, math and science are nice
> (although, not the only ways to relate to the universe or other people).
> But, moving right along, where is the math about what specific problem
> that you are saying invalidates what specific aspect of what we are
> talking about here?
> 
> I'm not saying math is not important. It is. You're right to make the
> point that not much math is discussed here and we may all benefit from
> some of that. I'd agree with that. But that seems to be the starting
> point for contributions by you or others, not the ending point of some
> argument about P2P like you make above.
> 
> What are the P2P questions you think math could help solve? And can you
> give real life examples of the problems? You point in the above Exhibit
> E above to "pathologically suboptimal equilibria". Can you give a real
> life example of that? Does Debian GNU/Linux exhibit that somehow?
> 
>>> And that's even ignoring the more profound social statement by Muriel
>>> Rukeyser, poet that: "The universe is made of stories, not atoms." :-)
>>
>>
>> Meh. The universe is made of information, which includes both stories
>> *and* atoms.
> 
> Good point. If you have a computational view of the universe, which I am
> inclined to myself. Still, they do represent different paradigms.
> Different types of models.
> 
> Just because you can model chemistry as physics does not meant that
> chemistry is physics. They use different models for various practical
> reasons.
> 
> A joke on this I worked out on this a while back. :-)
> 
> All philosophy is sociology.
> All sociology is psychology.
> All psychology is biology.
> All biology is chemistry.
> All chemistry is physics.
> All physics is mathematics.
> All mathematics is philosophy.
> (See the first point. :-)
> 
>>> Or, another trick is to say, math can't be wrong, because if
> something is
>>> wrong, it isn't math. Well, it's hard to argue with that.
>>
>> Again, you are betraying a deep misunderstanding of the basics of what
>> mathematics is.  Math isn't "wrong" within the context of the accepted
>> axioms, it simply "is".
> 
> There is so much talkie-talk at the edge of math that yes, it can be
> "wrong" even within the bounds of math. Again, Andrew Wiles' first proof
> of Fermat's conjecture was wrong. I'm even suspicious of the current
> one, because it is so long and convoluted. :-)
> 
> Still, right or wrong, Andrew Wiles was doing math when he worked on
> that proof. Glorious, courageous math (even hiding away in his attic for
> seven years because he knew all the other mathematicians would laugh at
> him, call him crazy, and maybe lock him up in an attic somewhere. :-)
> 
> And, from another angle, if Andrew Wiles had to hide his work for almost
> a decade, was he not, at least in a social sense, doing "wrong" math?
> 
> The same thing happens in science. Some breakthrough Nobel-prize winning
> "high temperature" superconductor work at IBM Research was done on the
> sly because the higher ups did not think it worthwhile. They don't
> mention that here though:
>   "IBM's Zurich Research Lab celebrates its 50th anniversary "
>    http://www.zurich.ibm.com/news/06/anniversary.html
> "Also in 1986, ZRL scientists K. Alex Müller and J. Georg Bednorz
> discovered high-temperature superconductivity, for which they received
> the physics Nobel prize for following year."
> 
> Really, they risked their jobs messing with that stuff. It was not what
> they were supposed to be working on. Had they been found out before
> repeatable success -- most likely fired for insubordination, I think.
> 
> Chalk on a blackboard is not wrong. It simply is. :-) But, what you can
> write on a blackboard in your office is socially constructed and
> socially controlled.
> 
>> Applications of mathematics can be wrong, but
>> you don't invalidate mathematics just because someone forgets to carry
>> the one when balancing their checkbook.
> 
> Good point.
> 
> On the other hand, you've also defined away most of the interesting
> issue about math. Because, much of how mathematical models are used is
> exactly like balancing a checkbook. You have assumption (initial
> balance, accuracy of inclusion of all the right deposits and
> deductions), values (what you decide to spend money on), and choice of
> logical reasoning tool (double entry method? Single entry? Paper?
> Spreadsheet? Online?). Big questions like "cash flow" may never enter
> your mind, staring at a checkbook. After all, it's money, and you're
> tracking it. What else could there be to know about cash? Also, things
> just out of the blue, like hyperinflation, can render the whole activity
> meaningless.
> 
>> If you don't like mathematics,
>> you don't have to use it.
> 
> Well, if computation underlies the universe, and math is a subset of
> computation, I can't avoid using it as long as I'm in this universe. :-)
> 
>> Invent your own mathematics if you wish, it
>> is certainly allowed.
> 
> And people do that all the time, in the sense of creating both new ways
> to model things, and using old ways to build models about new things.
> 
> Again, you're trying to make this an issue of "mathematics" while I'm
> sticking a "the" in there, to talk about "the mathematics" of something.
> 
> It seems like we've got at least there mathematics running around here:
> * "mathematics" as you want to use it, which is the dross of everything
> that is self-consistently valid.
> * "the mathematics" relating to a specific thing people want to model
> * "mathematics as a social enterprise" which actually is a stigmergic
> P2P thing, as I reflect on it just now, like all academic things
> involving publishing and indirect collaboration through a literature.
> 
> In that sense, I guess, if I were to be accept your earlier point on the
> impossibility of p2p, especially considering most early famous
> mathematicians did math as a hobby or for spiritual or aesthetic reasons
> (not for a paycheck), then mathematics can not exist, because the p2p
> social processes surrounding it for the last few millennia long ago
> should "decay into pathologically suboptimal equilibria".
> 
> So, as a proof, working together, we've just proved mathematics does not
> exist. :-) Wow. We make a great team. :-)
> 
> But, mathematics does seem to exist. A contradiction!
> 
> So, with a contradiction in hand, we can prove anything:
>  http://www.phy.duke.edu/~rgb/Philosophy/axioms/axioms/node30.html
> "If you ring a contradiction into a theory (however subtly) you can
> prove anything you like symbolically."
> 
> So, this means, we've just proved by formal logic that P2P works! :-)
> 
>> What it boils down is that you don't like the fundamental processes of
>> mathematics.
> 
> I don't know about that. You seem to be the one who is not willing to
> acknowledge the social and iterative dimensions of the activity?
> 
>> It seems you are looking for a way to falsify a theorem
>> that does not comport with a preconceived notion,
> 
> No need for that now. I've got a contradiction. Now I can prove anything
> I like, and there is nothing anyone can do mathematically to stop me. :-)
> 
> Hmmm. Maybe I should use that contradiction to prove I have a million US
> dollars? :-)
> 
> Step one: One of: "I have a Million dollars" and "I don't have a million
> dollars" is true.
> 
> Now, how does the rest of all that go again? :-) Ah, it would be too
> easy to make money that way. Not enough fun. :-)
> 
>> but the only way to
>> do that is to discard conventional mathematics *entirely* and start
>> with a new set of axioms of your choosing.  That seems like too much
>> work (true) so you are trying to find a way to selectively edit
>> mathematics to your liking.
> 
> Again, we're talking past each other here. I'm making very specific
> points about mathematics as a social enterprise and mathematical models
> used by people for specific purposes. You keep shifting this to be a
> referendum on whether chalk works on chalkboards. Sure, it works. Now
> what are we going to draw on the chalk board and what will it prove?
> 
>>> Another way to look at this is the term "emergent properties".
>>
>> The term "emergent properties" is used in the *application* of
>> mathematics for systems where the properties of the system have not
>> been formally proven because it would require too much work or because
>> no one built a proper non-statistical model.  It isn't all laziness,
>> sometimes the proof would be intractable and we can measure the
>> properties of the system inductively to a high degree of certainty in
>> any case many times.  Inductive tests aren't "proof" in the absolute
>> sense, but they are much, much cheaper. Just look at the amount of
>> work required to formally prove a small piece of software and you'd
>> know why.
> 
> Ah, see, here comes magic words. "Intractable". "High degree of
> certainty in any case many times". "Cheaper".
> 
> Or, in other words:
>   "How To Speak Hedgie: What hedge-fund managers mean when they talk
> about challenges."
>   http://www.slate.com/id/2172224/
> "In these days of market volatility, hedge-fund managers and executives
> at all types of money management firms have been forced to explain why
> their funds are shutting down, losing money hand over fist, and freezing
> investors' funds. When they do so, however, they frequently lapse into a
> strange euphemistic dialect. And so we thought it would be helpful to
> provide a handy Hedgie-English glossary."
> 
> A translation table:
> 
> "Intractible" == "Mathematics can't solve it in practice, even it can in
> theory if we have complete control over all matter and energy in an
> infinite number of universes."
> 
> "High degree of certainty in any case many times" == "Wrong a lot"
> 
> "Cheaper" == "We only do what we can do easily, and leave the hard bits
> for others."
> 
> Or, in other words, that's all why chemistry is not physics, and biology
> is not chemistry, and so on. And why mathematics only gets you so far,
> given incorrect assumptions, disagreements over moral values, and the
> limitations of various tools.
> 
>> A lot of laypersons think "emergent systems" or "emergent properties"
>> is a codeword for "magic", but it really isn't.  In fact, computer
>> science has mostly stopped using the term "emergent" to describe
>> systems because it gave too many people the wrong idea.
> 
> True.
> 
>>> So, we can't even model a couple of water molecules interacting at
>>> the quantum level, but we fudge it instead and move on.
>>
>> That is science, not math. Completely unrelated things.
> 
> Completely *interrelated* things. Along with the rest of human knowledge.
> 
>>> Science is not "inductive"...
>>
>>
>> Huh?  At its core, that is all science is.
> 
> http://en.wikipedia.org/wiki/Inductive_reasoning
> "Induction, also known as inductive reasoning or inductive logic, is a
> type of reasoning that involves moving from a set of specific facts to a
> general conclusion. ... Criticism of inductive reasoning Inductive
> reasoning has been attacked several times. Historically, David Hume
> denied its logical admissibility. Sextus Empiricus questioned how the
> truth of the Universals can be established by examining some of the
> particulars. Examining all the particulars is difficult as they are
> infinite in number.[2] During the twentieth century, thinkers such as
> Karl Popper and David Miller have disputed the existence, necessity and
> validity of any inductive reasoning, including probabilistic (Bayesian)
> reasoning.[3]"
> 
> But in any case, you clipped that point. Here it is again in its
> rhetorical entirety: "Science is not "inductive"; science is a social
> enterprise, and many scientists spend a lot of time thinking inductively."
> 
> And I stand by that. Again, you're trying to make this IMHO a referendum
> on whether validity (math) is valid. :-)
> 
> This particular choice of quote bothers me a lot, because it's like
> you're intentionally avoiding thinking about my point of math and
> science as social enterprises (and fairly p2p ones at that).
> 
> Normally, I might not care much. But in this case, it ties in
> understanding the whole p2p issue which is also itself a social
> enterprise issue. So, your choice here to miss my point, fits in with
> trying to skip around the bigger issue of peers sharing socially and
> using handwaving and mathematical jargon to denigrate p2p and the people
> on this list.
> 
> So, it seems to me at this point like you are being willfully evasive on
> this issue of the functioning of social networks in general. But, that's
> what this list is about in a deep sense (at least, social networks doing
> peer production in a not strictly hierarchical way).
> 
>>> So, when you, earlier make sweeping statements about the "stability" of
>>> p2p networks and so on, by the way not citing any specific literature,
>>> well, that's why I take them with a grain of salt.
>>
>> This email was routed using a protocol proven using the mathematics you
>> are taking "with a grain of salt".
> 
> Oh, come on. People probably hacked the code together and some
> mathematicians came around later and started talking about it. :-)
> 
> But that is a pereniall issue with engineering vs. science/math.
> Engineers do the impossible. Then scientists using math or whatever deny
> it, and then eventually grudgingly explain it, and likely figure out
> some generalities. The engineers then take those generalities and make
> even more amazing stuff instead of flying by the seat of their pants.
> And somewhere along the line, the engineers do the impossible again, and
> the whole thing starts over. :-)
> 
> And sometimes, the cycle goes the other way. A theoretician says, I
> think this new thing should be theoretically possible (antimatter?
> lasers?) and engineers set out to make it.
> 
>> That's fine, it is not as though you are qualified to make such
>> determinations anyway.
> 
> Seriously, you probably know little about me. Why say that? What does it
> accomplish? Even let's say everything I've said is stupid. Maybe I'm
> having a bad day. Or a bad week. Or bad year. Why make such a sweeping
> generalization?
> 
>> It is telling that you choose to ignore the
>> math instead of working on the open questions in math related to P2P
>> that could help make it robust and viable.
> 
> Ah, at least here we have a "the". :-) "The math". :-) That's good.
> 
> Still, let me translate that without the "the": "P2P is fragile and
> non-viable, unless you do lots of math first".
> 
> OK, let's assume that was true. Then how do you explain Wikipedia?
> Debian? Apache? The Web? Email? Twitter? Facebook? Science? Math? :-)
> And so on?
> 
> You're sounding here, to me, like a mathematics faculty person berating
> a grad student. :-( But, maybe, admittedly, that's just projection from
> my own psychological baggage. :-)
> 
> Another way to look at this is, if you, say, define "good thinking" as
> "math", then whenever people think in some productive way it is "math".
> 
> Still, sometimes it seems to me like there really is some sort of "cult
> of math" that has dominated much of engineering and science in academia.
> It's understandable because people get good at some branch or twig on
> the mathematics tree, learning to use some mathematical tools really
> well, and they like to use it and tell others about it. It's only human.
> But it's also convenient, because if engineers and scientists were
> encouraged (or even just allowed) to think about assumptions, values,
> and the limits of their tools, the world might be a much nicer place --
> though likely less profitable in the short-term for a very few.
> 
> Again though, you make a sweeping claim with no specifics. No list of
> open questions. No literature references. No web references. Just
> blanket condemnation at this point. And no attempt to help people who
> have been willing to spend a significant amount of their time reading
> what you wrote and replying to it.
> 
> I'm not writing this to disagree with you, so much as to help you (and
> others) see some of these issues more clearly (at least, clearly from my
> own hazy point of view. :-)
> 
>> Really, if I have one complaint it is this. When faced with hard facts
>> that contradict preferences,
> 
> Have you introduced even one citeable (linked to any literature) hard
> fact into this discussion?
> 
> Oh, there's probably one somewhere. Maybe even a few. But not as regards
> your main points, at least that I recall.
> 
>> the reaction here seems to be knee-jerk denial of reality.
> 
> Well, reality is a slippery topic. :-) Especially if it is a simulation.
> :-)
>   http://www.simulation-argument.com/
> 
> But, as I see it, we are raising questions about assumptions, values,
> and tools, including in regard to what you write here, and you are
> ignoring all that.
> 
>> Instead of doing something constructive like
>> understanding the limitations well enough to work around them, we'll
>> pretend the limitations don't even exist.
> 
> Well, what are the limitations of mathematical inquiry as a social
> process? :-)
> 
> And how has P2P influenced the development of mathematics?
> 
> Example:
>   http://en.wikipedia.org/wiki/Nicolas_Bourbaki
> """
> Nicolas Bourbaki is the collective pseudonym under which a group of
> (mainly French) 20th-century mathematicians wrote a series of books
> presenting an exposition of modern advanced mathematics, beginning in
> 1935. With the goal of founding all of mathematics on set theory, the
> group strove for rigour and generality. Their work led to the discovery
> of several concepts and terminologies still discussed.
>   While Nicolas Bourbaki is an invented personage, the Bourbaki group is
> officially known as the Association des collaborateurs de Nicolas
> Bourbaki (Association of Collaborators of Nicolas Bourbaki), which has
> an office at the École Normale Supérieure in Paris.
> """
> 
> Sounds P2P-ish to me, involving peer production to build a mathematical
> commons. :-)
> 
> What really happened there?
> 
> I'm not saying it's a great example of modern P2P, but it's a starting
> point for thinking about it as far as P2P and mathematics as a social
> process.
> 
> --Paul Fernhout
> http://www.pdfernhout.net/
> http://www.beyondajoblessrecovery.org/
> 
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