phys2094@waikato.ac.nz (08/09/90)
In article <WEX.90Aug6124507@dali.pws.bull.com>, wex@dali.pws.bull.com (Buckaroo Banzai) writes: > It would be easy in this framework to have, for example, a quantum dimension > which represented the energy states of electrons. In such a dimension > objects could occupy only specific points along the dimension, and not be in > between. This quantum dimension is not clear. The possible energy states of electrons lie on the positive portion of the real number line. Only when the potential for the system is specified does the energy spectrum become a subset of the positive portion of the real number line. To suggest that points will occupy only specific points and *not those in between* would only apply to a discrete energy spectrum which applies to a special subset of potentials. In fact even the discrete spectrum can vary continuously with a continuous variation of some parameter in the potential. Looks to me like a set of discrete points would not be the best way to represent the energy spectrum for general systems of electrons. > ... despite the blatherings of a certain idiot in this newsgroup. Let's make a deal. I won't blather and you don't discuss concepts in physics that you are not knowledgeable about. Are we friends now? -- Barry (the watchful physicist)
wex@dali.pws.bull.com (Buckaroo Banzai) (08/11/90)
In article <9008082218.AA27737@milton.u.washington.edu>
phys2094@waikato.ac.nz demonstrates that he knows a *hell* of a lot more
about physics than I do. Good enough. I was just trying to give an example
of a space that would be naturally represented as non-continuous.
Of course, now that it's days later I can think of other examples. Perhaps
the best example is the Boolean space. Values of this type are either true
or false. Some multi-valued logics may allow another value (e.g. unknown),
but if we are going to represent truly Boolean properties our dimension will
have two values and no more.*
[*OK, maybe three. There is an argument for including a value in every
dimension to represent the state this-property-not-present-on-this-object.
Call this value <Alpha>.
For example, you may have properties that simply don't make sense for an
object or that are not or can not be measured on a given object.
Now in theory you don't need this value, you can describe objects by the
property tuple:
<P0, P1, ... , Pm> where m<=N, N being the number of properties in
the union of all Pm in your cyberspace.
Adding Alpha gives you:
<P0, P1, ... , PN> with the not-m properties filled in by Alphas.
The reason for doing this is that it allows more generality in constructing
the actual displays. In particular, it allows you to construct displays
where one dimension represents a measured property and another dimension
does not. It is *very* hard to show a screen where an object has a position
on the Y axis and *no* position on the X axis :-)
]
--
--Alan Wexelblat phone: (508)294-7485
Bull Worldwide Information Systems internet: wex@pws.bull.com
"Politics is Comedy plus Pretense."brucec%phoebus.phoebus.labs.tek.com@RELAY.CS.NET (08/16/90)
In article <WEX.90Aug10135005@dali.pws.bull.com> wex@dali.pws.bull.com (Buckaroo Banzai) writes: > ... > > In particular, it allows you to construct displays > where one dimension represents a measured property and another dimension > does not. Is this really what you mean to say? I thought the definition of a dimension included some notion of measurement, whether it's continuous or not is another story. > It is *very* hard to show a screen where an object has a position > on the Y axis and *no* position on the X axis :-) > ] > It's hard if your display space is of topological dimension larger than 3, but then most *everything* is hard to display. As I mentioned in a previous article, humans seemed to have evolved in 3D space, and have trouble visualizing higher spaces. On the other hand, it's not so hard to display 3D objects and 2D objects together, when the intention is that the 2D objects don't have a well-defined position along the third axis (I like that terminology better than "no position"). There are two choices: the kludgier one is to pick a plane transverse to the third axis to put the 2D object in, that is, identify ill-defined positions with a unique position. The cleaner way is simply to place all the 2D objects in a plane transverse to the 3D axis, and then extrude them parallel to it. Having done that, it's easy to see where the true 3D objects intersect with the extrusions. --------------------------------------------------------------------------- NOTE: USE THIS ADDRESS TO REPLY, REPLY-TO IN HEADER MAY BE BROKEN! Bruce Cohen, Computer Research Lab email: brucec@tekcrl.labs.tek.com Tektronix Laboratories, Tektronix, Inc. phone: (503)627-5241 M/S 50-662, P.O. Box 500, Beaverton, OR 97077 -- --------------------------------------------------------------------------- NOTE: USE THIS ADDRESS TO REPLY, REPLY-TO IN HEADER MAY BE BROKEN! Bruce Cohen, Computer Research Lab email: brucec@tekcrl.labs.tek.com Tektronix Laboratories, Tektronix, Inc. phone: (503)627-5241 M/S 50-662, P.O. Box 500, Beaverton, OR 97077
wex@dali.pws.bull.com (Buckaroo Banzai) (08/18/90)
[I said:] In particular, it allows you to construct displays where one dimension represents a measured property and another dimension does not. [Bruce Cohen replied:] Is this really what you mean to say? I thought the definition of a dimension included some notion of measurement, whether it's continuous or not is another story. Yes, that's really what I meant. Remember that our data comes from the "real world" even if it is somewhat abstract. The real world can be very recalcitrant. The desired property may simply never exist on the object in question, or it may exist but not be recorded in the system, or it may have become corrupted, or the person viewing is not authorized to see it, or... Of course the property must be, in theory, measurable, but that doesn't say much. It's hard if your display space is of topological dimension larger than 3, but then most *everything* is hard to display. As I mentioned in a previous article, humans seemed to have evolved in 3D space, and have trouble visualizing higher spaces. True, true. That's why you do a lot of selecting out of groups of dimensions. It's also why you have to go to automatic icons fairly quickly. There are two choices: the kludgier one is to pick a plane transverse to the third axis to put the 2D object in, that is, identify ill-defined positions with a unique position. The cleaner way is simply to place all the 2D objects in a plane transverse to the 3D axis, and then extrude them parallel to it. Having done that, it's easy to see where the true 3D objects intersect with the extrusions. What about a 1D object? (I also don't see why one method is "kludgier" than another. Yours, it would seem, would obscure a lot more of the display. Also, if you're trying to convey additional information with the objects (auto-icons again), extrusion may cause things to mean more than they ought. Shapes are important, too :-) -- --Alan Wexelblat phone: (508)294-7485 Bull Worldwide Information Systems internet: wex@pws.bull.com "Politics is Comedy plus Pretense."
brucec%phoebus.phoebus.labs.tek.com@RELAY.CS.NET (Bruce Cohen) (08/19/90)
In article <WEX.90Aug17185842@dali.pws.bull.com> wex@dali.pws.bull.com (Buckaroo Banzai) writes: [I wrote:] > There are two choices: the kludgier one is to pick a > plane transverse to the third axis to put the 2D object in, that is, > identify ill-defined positions with a unique position. The cleaner way is > simply to place all the 2D objects in a plane transverse to the 3D axis, > and then extrude them parallel to it. Having done that, it's easy to see > where the true 3D objects intersect with the extrusions. [and Alan Wexelblat replied:] > What about a 1D object? (I also don't see why one method is "kludgier" than > another. Yours, it would seem, would obscure a lot more of the display. > Also, if you're trying to convey additional information with the objects > (auto-icons again), extrusion may cause things to mean more than they ought. > Shapes are important, too :-) > Yes, extrusion has its problems too, though they can be ameliorated with clever graphic solutions like translucent volumes, etc. (I'll try to say more about this in a later posting when I have more time). I guess I feel that selecting an arbitrary position for something which ereally has no position does damage to the underlying data you are trying to show, probably a remnant of my time in "scientific visualization". Both solutions will have their uses. -- --------------------------------------------------------------------------- NOTE: USE THIS ADDRESS TO REPLY, REPLY-TO IN HEADER MAY BE BROKEN! Bruce Cohen, Computer Research Lab email: brucec@tekcrl.labs.tek.com Tektronix Laboratories, Tektronix, Inc. phone: (503)627-5241 M/S 50-662, P.O. Box 500, Beaverton, OR 97077