Re: Continuing the story - another stab at an IETF mission statement
Sorry to have disturbed you Robert;-(... But, I have to wonder what this URL is about, given your comment about geometry being not spherical. http://www.google.com/search?q=spherical+geometrysourceid=operanum=10 Google only found [Results 1 - 10 of about 221,000. Search took 0.24 seconds.] Maybe we need to reverse our views of things. If geometry is not spherical, then maybe it is spheres that are geometrical. Anyway;-)...\You might find some interesting theorems among those 221,000 web cites. Or, maybe this one asking about [spherical geometry + manifolds] will be of even more interest. [Results 1 - 10 of about 563. Search took 0.08 second] http://www.google.com/search?hl=enlr=ie=ISO-8859-1q=%22spherical+geometry%22++%2B+manifoldsbtnG=Google+Search In any case, I was claiming that the Internet is a Manifold in terms of spherical Geometry, (or as you like it) Geomety of Spheres; and clearly there are manifolds in the concepts of spherical geometry, and I see no difficulty in mapping your network onto my manifold. It is a set of pipes all connected together somehow such that a packet can enter via one pipe and flow through the manifold to arrive at the exit (given the correct address) of any other pipe in the manifold. This seems to me to describe exactly what you say about the internet, so I believe we no longer have any disagreement. Cheers;-)...\Stef On Tue, 9 Mar 2004, Einar Stefferud wrote: It might be interesting to view the Internet through the contextual lens of spherical geometry concepts which I think fit as well as anything, contrary to some of our historical internautical terminology. For example, in spherical Geometry, a manifold has no edges, and has no center, while IETF folk insist that the Internet has an edge somewhere (just one) but I have not heard any claims that it has a surface, or that it has a center. Not to be picky, but the geometry isn't spherical. In fact, the geometry of the Internet is a network -- a network IS a geometry consisting of nodes (locations) connected by links. The mathematics of a network is called graph theory. The network geometry of the Internet isn't horribly well ordered or simple and is highly dynamic. It certainly isn't (hyper)spherical in any dimensionality -- spherical geometries have certain properties that the network lacks, although of course there exists a projection of the physical network onto the physical sphere (the globe) that provides some useful information. Less than one might think, of course. The network isn't necessarily simply connected, for example, as I could go upstairs and unplug my router and create a network fragment disconnected (transiently) from the rest of the Internet. The metrics are not obviously connected to real space geometry on any but a very local scale. For example, I am LESS than two physical miles away from my office at Duke as I type this. However, I'm 17 network hops away from my desktop there, and traceroute reveals that the packets go through Atlanta and Raleigh (it can be worse depending on congestion and dynamic routing -- I've seen as many as 30 hops). The network geometry is multidimensional and nodal. One can define a surface (of a simply connected nodal set) -- the union of all nodes with a single entry/exit route (link). Similarly, it has an interior (all nodes with multiple links). It has a norm that permits a discrete measure of distance to be constructed -- the hop from one node to another (the information revealed by traceroute measures a normed distance between nodes, albeit quite possibly a transient one and one where physical distance is nearly irrelevant). It even has a center -- one could usefully define it to be the union of all interior nodes that are a weighted MINIMUM distance, on average, from the entire surface -- the so called backbone -- although this isn't a sharp concept and may not even be all of that useful because of details of the network. For example, one can generate a variety of renormalized views of the Internet where nodes are THEMSELVES networks (or the routers/gateways that isolate them) -- rgb.private.net (my home LAN might be one) -- and the relevant network links are ones that connect routers, ignoring the edge nodes served by the routers. Then there are aggregations of LANs (such as duke.edu) which may have multiple links as well as LAN aggregations that have just a single link. Nowadays although one can still talk about a network backbone people also speak of clouds and use other metaphors to more accurately describe the core connectivity. A lot of this topology is built into both the internet addressing scheme and the underlying routing schema. Usually a surface node has a single IP number and is part of a IP LAN that is at least reasonably spatially contiguous. Usually interior nodes have multiple IP numbers. Usually routing attempts to dynamically solve a problem in the topology such as how to
Re: Continuing the story - another stab at an IETF mission statement
On Thu, 11 Mar 2004, Einar Stefferud wrote: Sorry to have disturbed you Robert;-(... You didn't disturb me. I love this stuff:-) But, I have to wonder what this URL is about, given your comment about geometry being not spherical. OK, I will explain a bit of history and mathematics. Briefly, since this is way off topic. Geometry is the study of objects in a space of a given number of dimensions and a given type. Historically it of course began with (actually somewhat before) Euclid's famous Elements and plane geometry as the first axiomatically developed branch of mathematics. This was so cool that it was damn near turned into a religion for close to 2000 years. Axioms are unprovable assumptions upon which the mathematics is based. They are NOT (as is often asserted) obvious truths -- one can choose the axioms, and different choices (as was discovered by Gauss and Riemann only a couple hundred years ago) lead to different geometries (note well the plural) in particular to non-planar geometries. Euclid's was planar, and plane geometry is one of the few really standard and universal exposures to mathematics even non-math/science oriented students are subjected to. Formally, geometry is distinguished from other forms of axiomatically developed algebra (as yes, there is an algebra associated with each geometry, including one called geometric algebra which contains things like Quaternions, Grassmann and Clifford algebras) by virtue of having a) a manifold (the space mentioned above) and a metric (named a Riemannian metric in honor of Gauss's protege, Riemann, who nominally discovered non-Euclidean differential geometry although it seems historically likely that Gauss was already aware of it and supported Riemann BECAUSE he was on what Gauss already knew to be a fruitful track). The metric of a geometry on the manifold typically defines its properties. There are many ways to vary the manifold, the metric, the axioms. One can make the manifold 1, 2, 3...N dimensional (where N can be infinite, and in some branches of mathematics is). The metric is what we would call the measure of distance -- given two points in the manifold, how can we compute the distance between them. Note that this isn't precisely true but I don't want to get into differential geometry and local/differential definitions of the metric here. A spherical geometry is the study of figures on a spherical manifold and is certainly of interest -- it is the geometry we live in on the planet, after all. It differs from Euclidean plane geometry in that triangles have = \pi radians in the sum of its angles (instead of = \pi radians), two points define TWO line segments, one short, one long, on a so-called great circle, and certain special pairs of points (antipodal points) define and infinite number of line segments and the possibility of drawing a biangle. Two distinct lines always intersect twice. And more. NONE of this resembles a useful mathematical description of the Internet except to the (nearly irrelevant) extent that of course the physical network is physically wrapped around the roughly spherical globe and that spatial distance and the speed of light create temporal delays in packet propagation in a predictable manner (note that this describes the USE of the network, not its geometry per se and certainly not its connectivity or routing characteristics). As far as your other remarks about the Internet being a manifold of some sort, well, it is and it isn't. A physical information network is a kind of graph, a directed multigraph or pseudograph. To be completely honest, I don't know that graph theory is, properly speaking, a geometry, although I went along with the metaphor in my previous reply. It is generally considered a branch of discrete mathematics. One often VISUALIZES graphs as being EMBEDDED in a geometry, e.g. drawn figures consisting of nodes and links on a plane or other surface, but in many cases the metric is discrete and completely distinct from the underlying manifold metric. In others it isn't. The travelling salesman problem is one where there is a correspondance between a spatial metric and the graph metric (a cost function or distance assocated with each link). The famous Bridges problem also required a 2d manifold (the city of Konigsburg) and a rule that links could not cross in that manifold. A network where physical propagation and distance-related delays are not being considered is an example of a graph metric that is divorced from the underlying visualization manifold (each link is a discrete hop and counts the same in the total distance). The dimension of a network or graph is also an issue. Graphs are nearly always drawn on a 2d planar manifold for visualization purposes, but one could argue that they are actually very high dimensional objects where links open out new dimensions, or where links are permitted to cross because in a higher dimensional manifold they can go over and
Re: Continuing the story - another stab at an IETF mission statement
--On 18. februar 2004 18:06 + Tom Petch [EMAIL PROTECTED] wrote: I find your definition of the Internet delightfully ambiguous. I was taught that the Internet (as opposed to an internet or the internet) was the public network accessible through public IPv4 addresses (this predates IPv6) ie the Internet ceased at a firewall or other such IP level gateway. Reading your definition, I cannot tell where you stand; are firewalls and networks behind them included in IETF mission or not? Tom, reviewing, I cannot tell whether I answered this one or not I was definitely intending to include them, since IMHO they are connected to the internet (see both core and edge networks, host to host). If you can suggest words to make this clearer, I'd appreciate it! Harald
Re: Continuing the story - another stab at an IETF mission statement
At 19:25 -0800 3/9/04, Harald Tveit Alvestrand wrote: --On 18. februar 2004 18:06 + Tom Petch [EMAIL PROTECTED] wrote: I find your definition of the Internet delightfully ambiguous. I was taught that the Internet (as opposed to an internet or the internet) was the public network accessible through public IPv4 addresses (this predates IPv6) ie the Internet ceased at a firewall or other such IP level gateway. Reading your definition, I cannot tell where you stand; are firewalls and networks behind them included in IETF mission or not? Tom, reviewing, I cannot tell whether I answered this one or not I was definitely intending to include them, since IMHO they are connected to the internet (see both core and edge networks, host to host). If you can suggest words to make this clearer, I'd appreciate it! Harald Just to throw a wrench into your discussion, The Internet just happens to be a Manifold (which literally means a bunch of pipes all connected together, such that entering at the end of any pipe, you can traverse the manifold and get to the open end of every other connected pipe in the manifold. Every manifold pipe can be extended, so it is not possible to define the ends in any rigid way. Extension can be with PPP over dial-up, or a NAT router, or even a printer or word of mouth, or CD/DVD/TAPE/Postal-Service/etc/et al, ad nauseum. It might be interesting to view the Internet through the contextual lens of spherical geometry concepts which I think fit as well as anything, contrary to some of our historical internautical terminology. For example, in spherical Geometry, a manifold has no edges, and has no center, while IETF folk insist that the Internet has an edge somewhere (just one) but I have not heard any claims that it has a surface, or that it has a center. Apparently, what people call the edge of the Internet consists of an imaginary canvas stretched over the ends of all those manifold pipes with an imaginary elastic sheet of imaginary fabric. But this only forms an edge if the Internet exists only in a two dimensional plane. And even then, I have problems imagining all those spokes as making an edge. Actually, they are referring to all those ends of all the manifold pipes, in that when attached to an end, the attachment is said to be made at the edge. I have big problems trying to imagine this as an edge (or a surface). So, I have tried to stop using those terms as they get in the way of thinking about various aspects of the Internet. Not that I really understand much more than this about spherical geometry. I just wanted to toss this into the mix while all y'all are trying to decide what this thing called the Internet actually is. I notice that all y'all have not settled on much of any agreement. Reminds me of the 8 blind wise men trying to discover what an elephant is by each exploring a different part with their hands. So far, I do not know anyone who claims to have touched its edge with their hands. So, I just want to suggest that some of you out there who do understand spherical geometry might discover some things from looking it the net with spherical geometry glasses. I only know that certain aspects seem to fit better than might be expected. For one thing, a manifold has no center, and indeed, an internet has no center. From my management consultant background, this has been an important realization, because, without the existence of a center, there is no logical place to put a control center to enable central control. We like to say that the internet is controlled from its edges, by which I expect they mean it is controlled from its manifold pipe endpoints. Also, I note that from any endpoint a user can, and generally does, create a personal private network of (sometimes) collegial correspondents that is controlled by it owner. Those networks are centrally controlled with address lists in address books and routing tables, and such. Surely, some of you will be quite upset about my observations, but I ask you to stay cool and just ponder it all for a while to see of things don't start to look different from this point of view, hopefully yielding some useful new insights. Enjoy;-)...\Stef
Re: Continuing the story - another stab at an IETF mission statement
I find your definition of the Internet delightfully ambiguous. I was taught that the Internet (as opposed to an internet or the internet) was the public network accessible through public IPv4 addresses (this predates IPv6) ie the Internet ceased at a firewall or other such IP level gateway. Reading your definition, I cannot tell where you stand; are firewalls and networks behind them included in IETF mission or not? Tom Petch -Original Message- From: Harald Tveit Alvestrand [EMAIL PROTECTED] To: [EMAIL PROTECTED] [EMAIL PROTECTED] Date: 11 February 2004 01:59 Subject: Continuing the story - another stab at an IETF mission statement Apologies to those who are already tired of this debate, and those think that we have enough of a clear idea of what the IETF mission is, and that discussing more is harmful to the community, but I attempted to incorporate the latest discussions into an internet-draft, which I managed to get out just before the deadline draft-alvestrand-ietf-mission-00.txt The core of the draft: The goal of the IETF is to make the Internet work. The mission of the IETF is to produce high quality, relevant technical and engineering documents that influence the way people design, use and manage the Internet in such a way as to make the Internet work better. These documents include protocol standards, best current practices and informational documents of various kinds. The IETF will pursue this mission in adherence to the following cardinal principles: Open process - that any interested participant can in fact participate in the work, know what is being decided, and make his or her voice heard on the issue. Part of this principle is our commitment to making our documents, our WG mailing lists, our attendance lists and our meeting minutes publicly available on the Net. Technical competence - that the issues on which the IETF produces its documents are issues where the IETF has the competence needed to speak to them, and that the IETF is willing to listen to technically competent input from any source. Technical competence also means that we expect IETF output to be designed to sound network engineering principles - this is also often referred to as engineering quality. Volunteer Core - that our members and our leadership are people who come to the IETF because they want to work for the IETF's purposes. Rough consensus and running code - We make standards based on the combined engineering judgement of our participants and our real- world experience in implementing and deploying our specifications. The rest of the document is trying to define the terms and explain the issues faced in formulating the mission statement. An appendix (to be deleted before publication) lists some other attempts at formulating a mission statement - the purpose of including this is to give honor to those who worked on them, and to allow those who debate the issue to see what other attempts to formulate the mission could look like. Comments are welcome, of course! Harald
Re: Continuing the story - another stab at an IETF mission statement
--On 18. februar 2004 18:06 + Tom Petch [EMAIL PROTECTED] wrote: I find your definition of the Internet delightfully ambiguous. I was taught that the Internet (as opposed to an internet or the internet) was the public network accessible through public IPv4 addresses (this predates IPv6) ie the Internet ceased at a firewall or other such IP level gateway. I certainly agree on the ambiguous, but not with the delightful :-) Reading your definition, I cannot tell where you stand; are firewalls and networks behind them included in IETF mission or not? Here, I feel that I stand firmly on the quicksand left by those who have gone before... if you read Dave Crocker's 1995 RFC 'To be on the Internet' (RFC 1775), you will see that the problem is not a new one. Luckily for us, mediated access and messaging access are mostly things of the past - but in my opinion, the Internet extends to the applications run by the people who have client access to the Internet. After all, the Internet model is an end-to-end service; if the Internet stopped at the gateway/NAT box/firewall, it would be an end-to-firewall service for 90% of today's Internet traffic - and that doesn't make sense to me. So in my opinion, firewalls and the networks behind them are part of the Internet, because we have to design for the Internet that is there, even as we labor to make it more like the Internet we want to have. (now, is that sufficient straddling of the NAT debate? :-) Harald
Re: Continuing the story - another stab at an IETF mission statement
On 18 Feb 2004, at 13:06, Tom Petch wrote: I find your definition of the Internet delightfully ambiguous. I was taught that the Internet (as opposed to an internet or the internet) was the public network accessible through public IPv4 addresses (this predates IPv6) ie the Internet ceased at a firewall or other such IP level gateway. I'm not sure who teaches that, but that's an extremely weak definition. Define public network. Define accessible. Define public IPv4 addresses. Note that even with definitions, the resulting Internet is subjective in the sense that the shape of the network changes according to the perspective gained from local connectivity (so one host's Internet is different to another host's Internet). The idea that the Internet is properly partitioned between devices which block packets would these days mean that in reality today it rarely extends beyond a single autonomous system, and often not beyond a single router. This is not, to my knowledge, a common definition (and even if it was common, it hardly seems very useful). Lots of people seem to enjoy being needlessly pedantic about the Internet vs. the internet vs. an internet, regardless of the fact they are unable to cite a reason for the distinction. So that's at least a common distinction, albeit arguably a fairly pointless one. Q: But what *IS* the Internet? A: It's the largest equivalence class in the reflexive transitive symmetric closure of the relationship 'can be reached by an IP packet from'. - Seth Breidbart Joe
Re: Continuing the story - another stab at an IETF mission statement
On 14-feb-04, at 1:28, Harald Tveit Alvestrand wrote: Good point. At least to make the point that the IETF sees the Internet as a global phenomenon, and that its standards-setting therefore must be global too - with English chosen for its utility, not its affiliation. Suggestions on which sections to put it in? 4.1 The Scope of the Internet seems appropriate although this deals with other issues. Or maybe make it a separate item under 4.
Re: Continuing the story - another stab at an IETF mission statement
On 10-feb-04, at 22:43, Harald Tveit Alvestrand wrote: I attempted to incorporate the latest discussions into an internet-draft, which I managed to get out just before the deadline draft-alvestrand-ietf-mission-00.txt Good stuff. But wouldn't it be useful to say something about the global nature of the internet and the IETF body of participants, and how this influences both the IETF's goals and the way it carries out its activities? More specifically, the fact that the IETF exclusively uses English for its standards and internal processes creates a non-level participation field, but at the same time the use of a single, widely-spoken language allows for much lower costs and higher efficiency than any alternative.
Re: Continuing the story - another stab at an IETF mission statement
--On 13. februar 2004 11:38 +0100 Iljitsch van Beijnum [EMAIL PROTECTED] wrote: On 10-feb-04, at 22:43, Harald Tveit Alvestrand wrote: I attempted to incorporate the latest discussions into an internet-draft, which I managed to get out just before the deadline draft-alvestrand-ietf-mission-00.txt Good stuff. But wouldn't it be useful to say something about the global nature of the internet and the IETF body of participants, and how this influences both the IETF's goals and the way it carries out its activities? More specifically, the fact that the IETF exclusively uses English for its standards and internal processes creates a non-level participation field, but at the same time the use of a single, widely-spoken language allows for much lower costs and higher efficiency than any alternative. Good point. At least to make the point that the IETF sees the Internet as a global phenomenon, and that its standards-setting therefore must be global too - with English chosen for its utility, not its affiliation. Suggestions on which sections to put it in?
