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## [ontolog-forum] Fw: Presentism etc

 To: "sean barker" Mon, 7 Feb 2011 19:44:58 -0000
 ``` In my mathematics degree, dimension simply was the number of elements of a tuple. The dimensionality of a vector space is the same as the number of basis vectors needed to get to any point in the space. For example, in 3D space, one might use a basis (1,0,0), (0,1,0) and (0,0,1) and if these correspond to the unit vectors in the x, y and z directions the any point (a,b,c) corresponds to the vector sum a.(1,0,0) + b.(0,1,0) + c.(0,0,1). Note that a set of basis vectors must be linearly independent, that is, for a set of vectors V1,...,VN, there does not exist a set of constants c1,...,ci-1,c1+1,...cn such that Vi = c1.V1 + c2.V2 +... + ci-1.Vi-1 + ci+1.Vi+1 +...cnVn; All very dull and mathematical.    (01) Among the odd consequences of this definion is that I have a couple of 5-dimensional objects in my pockets. When I use a finger to point, it takes three dimensions to locate my hand and another two to define the direction in which I'm pointing. Or 6-D if you want to model the time when the pointing is measured. The extrusion of it through time might make it into a gallery of modern art, though I don't know whether it should make it into an ontology.    (02) I suspect that calling an ontology "4D" is one of those language games where a family resemblance is noted to 3D and other not-quite-similar things. Thomas Aquinas, commenting I think on Avicenna, describes a column of marching men, each of which sees the person in front and behind, but God, sitting on the mountain sees the whole column - this was an analogy for eternity. Perhaps rather than 3D+1 or 4D we could use terms like "on the road" and "up the mountain" to describe the differing ontologies.    (03) Sean Barker Bristol, UK > -----Original Message----- > From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx > [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Mike > Bennett > Sent: 05 February 2011 16:13 > To: doug@xxxxxxxxxx; [ontolog-forum] > Subject: Re: [ontolog-forum] Presentism etc > > > *** WARNING *** > > This message has originated outside your organisation, > either from an external partner or the Global Internet. > Keep this in mind if you answer this message. > > > I think you've hit on why I for one find 4D approaches a little > disquieting, even though I personally see the world in 4+ dimensions > (hence Hypercube). > > I hope it's safe to say that we are all thinking about differences in > how to represent the world rather than how the world is. In which > case... > > Dimensions (I submit) are that along which we choose to measure > properties which are orthogonal to any other properties we have thus far > so measured. > > Spatial lengths and distances are measures which can be applied three > times before they can't be applied again orthogonally. > > Time is orthogonal to these, and this is usually the one we choose to > apply fourth. However in most domains of discourse it presents us with > the unique feature of causality. This itself presents the problem you > describe. > > In some ways in which we may wish to model the world (though not as yet > in banking ;-) ), time and space can be treated as a single space of > interchangeable dimensions, giving us 4D space-time. Though I can't help > noticing that even black holes have a time before they existed. > > Mass remains orthogonal to these (except, again, under certain > descrptive frameworks which one may wish to ontologize). So that > requires another dimension along which to measure it. So does electrical > charge. And so on. Unlike time, there is no consensus about what order > to label these in. Like time, the question is not whether they are "new" > dimensions, but whether on certain scales the properties we usually > measure along them can be regarded as interchangeable within a single 4 > or 5 or 6 dimensional hyperspace. > > The 11 dimensional (or is it 7 dimensional?) Calibi-Yau surface > described in string theory looks to this naive onlooker like something > other than a bunch of orthogonal directions along which some properties > are measured, so I'm curious to find out whether this framework formally > defines the concept of "dimension" in the same way I have done here. But > if not, that would not present a challenge for semantically modeling it, > it just means that this is a different descriptive framework using a > different definition of "dimension". It seems to me that dimensions are > sometimes described as actual things rather than measurement constructs, > when one could as easily say "here is some actual property which is > orthogonal to the rest" and give the property a name. If we are clear > about what we mean by "dimension", and in what problem domains we are > applying that definition, this might be more helpful than all this 3D +1 > minus the square root of whatever. > Then we have properties of a thing, and dimensions as a property of > those properties. And interesting constraints or properties about what > we can measure in some of those dimensions in our domain of discourse. > > Coming back to the more immediate space of business problems and > semantic modeling of them, can't we simply recognise that here are some > things that have an extent in space and time, along with optionally a > mass, a charge and so on, and that these properties each present > particular differences as to how a given property, which occupies a > given kind of dimension, are modeled. Including for example the unique > challenges of causality, which means that historical facts can be nailed > down in a simple space of spatial and temporal facts, while the "future" > presents unique modeling requirements based on for example how and by > whom it is predicted. These become problems of provenance. > > My favourite practical example about dealing with the future is the > floating rate note (FRN). This is a bond which pays a rate of interest > that is pegged to some variable interest rate (say, the London Interbank > Offer Rate). Suppose this is reset at the end of each month. Then the > current value of the bond is based on the value of its future cashflows, > which are a known unknown. Each day, my best guess about the present > value is based on the future rate of this bond. This is a calculation of > what the next reset rate would be if it were calculated according to > today's interest rate, this being the most up to date information I > have. > > Now, for risk management and compliance purposes, I may need to have a > record of what I perceived the current value of a bond to be at the > moment I purchased it. If I purchased a FRN a week ago, then I now know > what it's projected future interest rate (and so current value) is > today, but I also know what I thought that future value was a week ago. > These two valuations (past and > present) are based on the two estimates of the future value of the same > variable. > > That is, there is a time series, in the past, of projected future values > of the same quantity - the reset rate at the end of this month, along > with the full set of bond analytics based on current value, that depend > on this. And these past values matter because they were the basis on > which investment decisions were made. So there will be data in a system > somewhere whose meaning we would rather like to ontologize. > > If we fail to account for the unique challenges presented by the arrow > of time, I'm not sure we would be able to properly model these sorts of > scenarios. Time is not just a dimension, it's a dimension along which > every point in the past possesses an infinite number of unknowns about > its future. We have a future, but every past has a future of its own. > > Mike >    (04) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (05) ```
 Current Thread [ontolog-forum] Fw: Presentism etc, sean barker <= Re: [ontolog-forum] Fw: Presentism etc, Rich Cooper Re: [ontolog-forum] Fw: Presentism etc, Ian Bailey Re: [ontolog-forum] Fw: Presentism etc, John F. Sowa Re: [ontolog-forum] Fw: Presentism etc, Rich Cooper Re: [ontolog-forum] Fw: Presentism etc, Ian Bailey Re: [ontolog-forum] Fw: Presentism etc, Rich Cooper Re: [ontolog-forum] Presentism etc, Conklin, Don Re: [ontolog-forum] Presentism etc, Rich Cooper Re: [ontolog-forum] Presentism etc, Ian Bailey