Discrete mathematics, also called finite mathematics or decision mathematics, is the study of mathematical structures that are fundamentally discrete in the sense of not supporting or requiring the notion of continuity. Objects studied in finite mathematics are largely countable sets such as integers, finite graphs, and formal languages.
Discrete mathematics has become popular in recent decades because of its applications to computer science. Concepts and notations from discrete mathematics are useful to study or describe objects or problems in computer algorithms and programming languages. In some mathematics curricula, finite mathematics courses cover discrete mathematical concepts for business, while discrete mathematics courses emphasize concepts for computer science majors.
For me this becomes the question that is highlighted in bold as to such a thing as discrete mathematics being suited to the nature of the Quark Gluon Plasma that we would say indeed that "all the discreteness is lost" when the energy becomes to great?
Systemically the process while measured in "computerization techniques" this process is one that I see entrenched at the PI Institute, as to holding "this principal" as to the nature of the PI's research status.
Derek B. Leinweber's Visual QCD* Three quarks indicated by red, green and blue spheres (lower left) are localized by the gluon field.
* A quark-antiquark pair created from the gluon field is illustrated by the green-antigreen (magenta) quark pair on the right. These quark pairs give rise to a meson cloud around the proton.
* The masses of the quarks illustrated in this diagram account for only 3% of the proton mass. The gluon field is responsible for the remaining 97% of the proton's mass and is the origin of mass in most everything around us.
* Experimentalists probe the structure of the proton by scattering electrons (white line) off quarks which interact by exchanging a quantum of light (wavy line) known as a photon.
Now indeed for me, thinking in relation to the 13th Sphere I would have to ask how and when we loose focus on that discreteness)a particle or a wave?). I now ask that what indeed is the fluidity of the Gluon plasma that we see we have lost the "discrete geometries" to the subject of "continuity?"
So the question for me then is that if such a case presents itself in these new theoretical definitions, as pointed out in E8, how are we ever to know that such a kaleidescope will have lost it's distinctive lines?
This would require a change in "math type" that we present such changes to consider the topologies in expression(this fluidity and continuity), in relation to how we see the QCD in developmental aspects.
In a metric space, it is equivalent to consider the neighbourhood system of open balls centered at x and f(x) instead of all neighborhoods. This leads to the standard ε-δ definition of a continuous function from real analysis, which says roughly that a function is continuous if all points close to x map to points close to f(x). This only really makes sense in a metric space, however, which has a notion of distance.
Note, however, that if the target space is Hausdorff, it is still true that f is continuous at a if and only if the limit of f as x approaches a is f(a). At an isolated point, every function is continuous.
Hi Plato,
ReplyDeleteIt’s been some time since I made comment and yet this note is more simply to acknowledge I have been following your most recent posts. What you attempt to piece together I find quite interesting and yet perhaps not as mysterious as you seem to find it to be. This is mainly due to the fact that unlike many who explore the question which hold to a singular ontological perspective while for me for some time it has been dual as it relates to the Bohmian view point. So then to find energy to be for the most part not localized to the particles yet spread out forms to be of no great surprise to me.
As for geometry and how it might fit into both a Riemannian and Einsteinian viewpoint I believe we too often focus on the simple solutions such as a sphere and forget possibilities such as pseudospheres which satisfy certain conditions as in sharing similar qualities yet lead to different realities that are both finite and infinite within the Euclidian frame of reference. I’m not saying this provides any answers, simply to point out that this forms to be just one alternative along with all those that are known or that remain to be discovered.
Best,
Phil
Phil:This is mainly due to the fact that unlike many who explore the question which hold to a singular ontological perspective while for me for some time it has been dual as it relates to the Bohmian view point.
ReplyDeleteThanks for continuing to follow. I do prize your opinion on these matters and like you, I maintain these interests in my life, without the support of my workmates, encouragement of those in the know, and hold to the same. It is a lonely road and one in which I need no motivation in which to continue with my want to understand.
This duality is on my mind.
Emergent processes from a condense matter theorist point of view, and, how such forms would contact the surface from a metal sheet perspective. The sound of billiard balls "is seeing" in a metric space.
Perhaps the mystery here for me is that while we dissect the energy, as to it's constituents, the glue that binds, is what I ask about. I see in these spaces.
What will be found of the Higg's field/partilce? Where do we go from here in our philosophical pursuance's? This is a experimental condition that people are now being predictive "for or against?"
We see where people lie in these positions and the outcome, will be the determination.
The "logic of nothing" is to talk about what does not exist. The logic dictates "that nothing is nothing," and to try and comment on nothing is like, to think that an opinion on theoretics, is somehow not as predictive as they are in opinion only. That is being safe, and not being bold.
Your point on geometrics is taken.
This is a underlying condition with which I see all advancements in materiality. These are needed as to be founded upon, as we transcribe our reality to the forms.
It is an observation I draw from in what I see in scientists are doing, whether is be by the mathematics, or, how they see in these spaces.
Clifford of Asymptotia has some Batman ontology that you might be interested in?:)The value of such predictive behaviors should be held to computerization techniques one way or another. If these are computationally transcribed then this leads our perspectives in how Thomas Banchoff sees.
There is a reason that I hold to methods whether psychological in nature or mathematical toward the geometrics,as to the foundation issues with which we ascertain our perspectives on reality.
I will reply to this more in the coming post.
Best,