The Toposense of Spacetime

Topo-Greek, from topos, place.

Basic Examples

In the early 1960s Grothendieck chose the Greek word topos (which means “place”) to denote a mathematical object that would provide a general framework for his theory of étale cohomology and other variants related to his philosophy of descent. Even
if you do not know what a topos is, you have surely come across some of them. Here are two examples:

See: What is a Topos? by Luc Illusie

Of course I am looking and trying to describe “Topo” in a different way. I do not want to diminish the significance of the mathematical intents. Just the realization of what we are doing with our perceptions, as we send them to extraordinary depth of of creation.

In 1952, in his book Relativity, in discussing Minkowski’s Space World interpretation of his theory of relativity, Einstein writes:

Since there exist in this four dimensional structure [space-time] no longer any sections which represent “now” objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence. Albert Einstein

Of course it was necessary to understand the evolution of Euclidean geometries to the non-euclidean, and the history associated with this. The word “Toposense” is one that becomes endearing when you realize that if your were to take to the meaning of “slide of light to heart” you would see the implications of what gravity could mean in the presence of the photon and it’s explanatory revolutionary ideas about how it can encourage “Gravities Rainbow” here within context of this blog.

“On the Effects of External Sensory Input on Time Dilation.” A. Einstein, Institute for Advanced Study, Princeton, N.J.

Conclusion: The state of mind of the observer plays a crucial role in the perception of time.

Unfortunately the link to the article below( now shows as Intuitively Excellent) has been removed from Scientific America’s data base or has changed, or, I may of copied it wrong in my search. Nevertheless, I do not have the link, but would like to conclude the remark above, in terms of those pointed out for further repercussions of that conclusiveness.

Einstein scholars disagree, but the pretty girl/hot stove experiment also may have led to another of his pithy remarks, namely: “If we knew what it was we were doing, it would not be called research, would it?” Then again, Einstein was a bit of a wag. Consider his explanation of wireless communication: “The wireless telegraph is not difficult to understand. The ordinary telegraph is like a very long cat. You pull the tail in New York, and it meows in Los Angeles. The wireless is the same, only without the cat.” This quote reportedly kept Schrödinger awake well past his bedtime.

Summing over Histories?

So how does all this come together into a physical theory? It turns out that the proper procedure is to construct every possible diagram allowed by the theory (for a given state of input and output particles and how they’re moving) and add up the corresponding complex numbers. The result is essentially the “wave function” for that specific input-output state combination, and by squaring that number you can determine the probability that the given input will result in the given output. Doing that is how theorists at particle accelerators earn their keep.

See: An Introduction to String Theory by Steuard Jensen

So you look at the basis of interactions that Feynman produced in his Toy models and having some insight to the elemental consideration of those same interactions, what comes out, if we were to see the world in such a way, that continuity of expression is “the Wave that was generated in the very beginning,” could have been reduce to some refractive expression of all life. The Spectrum, Hydrogen, or other wise.

Do we then know the nature of the source, that we are all derivatives of some coherent plan that manifests toward the “cyclical nature of being?” Some Shakespearean version of, “to E or not to E?”

Every known particle has an antiparticle; if they encounter one another, they will annihilate with the production of two gamma-rays. The quantum energies of the gamma rays is equal to the sum of the mass energies of the two particles (including their kinetic energies). It is also possible for a photon to give up its quantum energy to the formation of a particle-antiparticle pair in its interaction with matter.

No longer Reducible and Working from the Horizon?

How far can our perceptions be pushed? Can consciousness still remain as part of this “ability of creation,” that we are still “part and parcel” of it to consider it’s full scope?

So no geometrical idealizations in sight, other then to consider the significance of a place that is far removed from our looking to the cosmos, and while thinking about it, how far it has been reduce to a fuller picture of it’s reality?

See: Colour of Gravity

This entry was posted in Colour of Gravity, Heart, Hot Stove, Time Dilation and tagged , , , . Bookmark the permalink.

4 Responses to The Toposense of Spacetime

  1. Phil Warnell says:

    Hi Plato,“Since there exist in this four dimensional structure [space-time] no longer any sections which represent “now” objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated.”Each time you quote Einstein it causes me to not only to think yet also feel joy. That joy is in knowing that one of the most deep and sharpest minds of our species not only captured an idea yet transmits it clearly to those who care to look. When Einstein talks of the “now” in terms of the reality of space-time as being complicated I think of all those that believe that the “now” is but a fleeting illusion although “a stubborn one” as he would have insisted. When most talk of returning to a place in body they speak of those of only three dimensions, while when Einstein speaks of such, it is when time also is considered as an included yet indistinguishable part of the description. This is something then that cannot be accomplished solely in body.Yes, you can look upon a photograph, listen to a recording or gaze out into the heavens and say there lies that place. Yet when reasoned it is not the instrument of body alone that lets one do this, yet only possible when combined with the instrument of mind. For with the mind we truly can form the past while our body is confined to the now. What is even more astounding and also revealing, it is only with this combination of physicality and reason that we can not just only simply imagine the places that are said to reside in the future, yet often be correct in knowing what they are. This is Einstein’s gift of insight that many still fail to see.Best,Phil

  2. Phil Warnell says:

    Hi Plato,To serve as a comment to this post and as a follow up of my last one where I was expressing how I thought of extra dimensions and if they need to be limited to that just of the physical I quote here from the same 1952 Edition of Albert Einstein’s book entitled “Relativity”. It’s a preface called “Note to the fifteenth Edition”:“In this edition, as a fifth appendix, a presentation of my views on the problem of space in general and the gradual modifications of our ideas on space resulting from the influence of the relativistic view-point. I wished to show that space-time is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. In this way the concept of “empty space” loses its meaning”.A. Einstein (June 9th, 1952)This is simply to reinforce my position that “histories” that need to exist for events to occur have no space to be if considered physical in the Einstein concept of space-time. This would then infer that if this is correct, then such histories, although certainly necessary, must then exist in a region that is not physical as to exist within space or time as they have no place to be realized as physical to help compose all of what we consider real. Therefore, it is required to exist on a plane that transcends the physical to have this potential. This would be consistent with the thoughts of Plato, Einstein and Bohm.Regards,Phil

  3. Plato says:

    Phil:This would then infer that if this is correct, then such histories, although certainly necessary, must then exist in a region that is not physical as to exist within space or time as they have no place to be realized as physical to help compose all of what we consider real.IN my heart this does not seem complete to me, and not that I am not considering it, it just that I see it has much more potential to be realized.:) While you look at the body what else exists with the matters?Phil:Each time you quote Einstein it causes me to not only to think yet also feel joy. That joy is in knowing that one of the most deep and sharpest minds of our species not only captured an idea yet transmits it clearly to those who care to look. A sympathetic resonance perhaps, or an oscillation that “rings” true to you.:) These are some of my “strongest identifications” in regards to Einstein as well. I guess this is also the individuality speaking, that I cannot see the electromagnetic principal by itself, and not considered, “all together” in the complete model. That once joined with gravity, the fate of all things while we understand them as a “complex model” shall include a time when it came together( yin and yang). I am looking for where “things begin” and still we have relativity to consider at the very source of those QGP points of interest? So maybe I am not so different then then to realize the complexity of that space together with time, has much more meaning.:)Then ,our perceptions have to change again, and while we see the roads that lead our thinking through all that of what entanglement has to offer, there is another way, that while subjective and observer dependant does include the perceptions of everyday life. Is encompassed by what is really part of the whole reality picture. While we seemingly deal with the reality in the bodies around us and in the “manifestation of the matters” there is always a finer aspect to this that “reveals the condescension” as matter resulting. Bucky balls and the like, and what was seen in the crystalline structure(diamonds, carbon) that said, “hey, there is indeed a geometrical structure?” There has to be an architect for the manifestation(?), and while I do not attest these to God alone, I would think that such a choice to our determination would run much deeper then we currently understand.Relativity is about gravity. Relativity is seeing the Gaussian arcs as a “geometrical propensity of a much more dynamic process” that includes Maxwell’s equations?While dealing with the cosmologically large, relativity runs into trouble with the very small. But that is the work isn’t it? Such “discrete notions” having such fluidity all of a sudden brings up new thoughts for me about “the continuity” and the place where “relativity is born” to this world? That it is easily letting the “past slip through and manifest” from an earlier and previous existence(what is the universe’s motivations?)? Thus predictability of the future is indeed a deterministic valuation about our “place in mind” and about the possible futures.That what was considered as the before, can now manifest itself, and hold it’s motivations as a fuel for expression in a new universal way.Phil:When most talk of returning to a place in body they speak of those of only three dimensions, while when Einstein speaks of such, it is when time also is considered as an included yet indistinguishable part of the description. This is something then that cannot be accomplished solely in body.While you have moved to the mind, this does not escape the reality of the finer aspects and capabilities of our thinking, that is could also include a “heaviness of the emotive states” that holds a person to the ground(heavy heart) while there is an aspirational realization too, that there can be lightness to such thoughts too. This is a recognition for me about “the fog” and what shall transpire if we are to remain in the distinction of the “colours of gravity” without dealing with the “emotive struggling” for understanding. The weight of the atmosphere then becomes a determining factor on how our views dictate that future. Are we so lost then? The trick is then to become clear in mind(clear mind).Phil:For with the mind we truly can form the past while our body is confined to the now. What is even more astounding and also revealing, it is only with this combination of physicality and reason that we can not just only simply imagine the places that are said to reside in the future, yet often be correct in knowing what they are. This is Einstein’s gift of insight that many still fail to see.Such certainty in place of all that information? What is the thread that runs through it all. The HIgg’s?:)”Who is it” that is observing?

  4. PlatoHagel says:

    Phil:This would then infer that if this is correct, then such histories, although certainly necessary, must then exist in a region that is not physical as to exist within space or time as they have no place to be realized as physical to help compose all of what we consider real.IN my heart this does not seem complete to me, and not that I am not considering it, it just that I see it has much more potential to be realized.:) While you look at the body what else exists with the matters?Phil:Each time you quote Einstein it causes me to not only to think yet also feel joy. That joy is in knowing that one of the most deep and sharpest minds of our species not only captured an idea yet transmits it clearly to those who care to look. A sympathetic resonance perhaps, or an oscillation that \”rings\” true to you.:) These are some of my \”strongest identifications\” in regards to Einstein as well. I guess this is also the individuality speaking, that I cannot see the electromagnetic principal by itself, and not considered, \”all together\” in the complete model. That once joined with gravity, the fate of all things while we understand them as a \”complex model\” shall include a time when it came together( yin and yang). I am looking for where \”things begin\” and still we have relativity to consider at the very source of those QGP points of interest? So maybe I am not so different then then to realize the complexity of that space together with time, has much more meaning.:)Then ,our perceptions have to change again, and while we see the roads that lead our thinking through all that of what entanglement has to offer, there is another way, that while subjective and observer dependant does include the perceptions of everyday life. Is encompassed by what is really part of the whole reality picture. While we seemingly deal with the reality in the bodies around us and in the \”manifestation of the matters\” there is always a finer aspect to this that \”reveals the condescension\” as matter resulting. Bucky balls and the like, and what was seen in the crystalline structure(diamonds, carbon) that said, \”hey, there is indeed a geometrical structure?\” There has to be an architect for the manifestation(?), and while I do not attest these to God alone, I would think that such a choice to our determination would run much deeper then we currently understand.Relativity is about gravity. Relativity is seeing the Gaussian arcs as a \”geometrical propensity of a much more dynamic process\” that includes Maxwell\’s equations?While dealing with the cosmologically large, relativity runs into trouble with the very small. But that is the work isn\’t it? Such \”discrete notions\” having such fluidity all of a sudden brings up new thoughts for me about \”the continuity\” and the place where \”relativity is born\” to this world? That it is easily letting the \”past slip through and manifest\” from an earlier and previous existence(what is the universe\’s motivations?)? Thus predictability of the future is indeed a deterministic valuation about our \”place in mind\” and about the possible futures.That what was considered as the before, can now manifest itself, and hold it\’s motivations as a fuel for expression in a new universal way.Phil:When most talk of returning to a place in body they speak of those of only three dimensions, while when Einstein speaks of such, it is when time also is considered as an included yet indistinguishable part of the description. This is something then that cannot be accomplished solely in body.While you have moved to the mind, this does not escape the reality of the finer aspects and capabilities of our thinking, that is could also include a \”heaviness of the emotive states\” that holds a person to the ground(heavy heart) while there is an aspirational realization too, that there can be lightness to such thoughts too. This is a recognition for me about \”the fog\” and what shall transpire if we are to remain in the distinction of the \”colours of gravity\” without dealing with the \”emotive struggling\” for understanding. The weight of the atmosphere then becomes a determining factor on how our views dictate that future. Are we so lost then? The trick is then to become clear in mind(clear mind).Phil:For with the mind we truly can form the past while our body is confined to the now. What is even more astounding and also revealing, it is only with this combination of physicality and reason that we can not just only simply imagine the places that are said to reside in the future, yet often be correct in knowing what they are. This is Einstein’s gift of insight that many still fail to see.Such certainty in place of all that information? What is the thread that runs through it all. The HIgg\’s?:)\”Who is it\” that is observing?

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