To: |
doug@xxxxxxxxxx, "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx> |
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From: |
Mike Bennett <mbennett@xxxxxxxxxxxxxxx> |

Date: |
Sat, 05 Feb 2011 16:12:45 +0000 |

Message-id: |
<4D4D76FD.6010902@xxxxxxxxxxxxxxx> |

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). (01) 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... (02) 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. (03) Spatial lengths and distances are measures which can be applied three times before they can't be applied again orthogonally. (04) 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. (05) 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. (06) 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. (07) 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. (08) 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. (09) 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. (010) 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. (011) 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. (012) 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. (013) Mike (014) On 05/02/2011 08:09, doug foxvog wrote: > |

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