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[ontolog-forum] Fw: Presentism etc

To: <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "sean barker" <sean.barker@xxxxxxxxxxxxx>
Date: Mon, 7 Feb 2011 19:44:58 -0000
Message-id: <D1B1A5D1AA1F4103955279B08BFB4BC2@SMB>
 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
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> 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)

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