Sunday, August 23, 2015

Yves Couder . Explains Wave/Particle Duality via Silicon Droplets [Through the Wormhole]

The modern double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena. This experiment was performed originally by Thomas Young in 1801 (well before quantum mechanics) simply to demonstrate the wave theory of light and is sometimes referred to as Young's experiment.[1] The experiment belongs to a general class of "double path" experiments, in which a wave is split into two separate waves that later combine into a single wave. Changes in the path lengths of both waves result in a phase shift, creating an interference pattern. Another version is the Mach–Zehnder interferometer, which splits the beam with a mirror.Double-slit experiment

To some researchers, the experiments suggest that quantum objects are as definite as droplets, and that they too are guided by pilot waves — in this case, fluid-like undulations in space and time. These arguments have injected new life into a deterministic (as opposed to probabilistic) theory of the microscopic world first proposed, and rejected, at the birth of quantum mechanics. See:
Have We Been Interpreting Quantum Mechanics Wrong This Whole Time?


The Binary Pulsar PSR 1913+16:

In youtube example video given, I must say if you have ever seen Taylor and Hulse's binary system, I couldn't help but see some relation. Such rotation, would cause gravitational wave that seems to hold the droplet in position for examination......but the gravitational wave production, is an affect of this rotation so I am puzzled by this.

Natalie Wolchover is pretty good at her job, and I think drew attention to the idea of a Bohemian mechanics/Pilot wave theory. This, as an alteration of choice of quantum mechanics it became clear, how interpretation was pervasive at the time between these two groups, as a point of view. Not saying this is the case, but as I read I see the division between the scientists as to how an interpretation arose between them, some choose one way and others, another. And still they did not discard the world of the two groups but leaned specifically to one side over another.

As de Broglie explained that day to Bohr, Albert Einstein, Erwin Schrödinger, Werner Heisenberg and two dozen other celebrated physicists, pilot-wave theory made all the same predictions as the probabilistic formulation of quantum mechanics (which wouldn’t be referred to as the “Copenhagen” interpretation until the 1950s), but without the ghostliness or mysterious collapse. -Have We Been Interpreting Quantum Mechanics Wrong This Whole Time?
I am looking at the experiment itself as illustrated in my link to youtube video of respective scientists given the relation and analogy used. This is to see the aspect of their relation to something current in our understanding "as observation," and something much more to it as particle and wave together. Still trying to understand the analogy. In the experiment, what leads the way, the wave, or the particle/droplet? The "wave function" guides the particle/droplet, yes? Why of course, it is called pilot-wave theory.

Before the experiment begins then, you know the particles state "as a wave function," and given that this is already known, "the particle" rides the wave function, is exemplary of the nature of the perspective in the first place, as to what is already known. Hmmmm....sounds a little confusing to me as I was seeing the waves in the experiment, but given that such state of coalesce exists when experiment is done, raises questions for me about the shaker as a necessity?

 So cosmological you are looking to the past? You look up at the night sky and when were all these messages received in the classical sense but to be an observer of what happened a long time ago. You recognize the pathway as a wave function already before the experimenter of the double slit even begins. It has a trajectory path already given as the wave function is known with regard to A to B. These are not probabilities then, if recognized as potential of the wave function as already defining a pathway.

The pathway expressed as the pattern, had to already been established as a causative event in the evolution in the recognition of a collision course regarding any synchronized event located in the quantum world, as a wave function pattern. You are dealing with a Bohemian interpretation here.


 On the flip side, I see spintronics, as a wave function giving consideration to the y direction. It is a analogy that comes to mind when I think of the fluid. Whether right or not, I see an association.

The idea, as a wave function is seen in regard to this chain as an illustration of the complexity of the fluid surface

To go further then,

Known as a major facet in the study of quantum hydrodynamics and macroscopic quantum phenomena, the superfluidity effect was discovered by Pyotr Kapitsa[1] and John F. Allen, and Don Misener[2] in 1937. It has since been described through phenomenological and microscopic theories. The formation of the superfluid is known to be related to the formation of a Bose–Einstein condensate. This is made obvious by the fact that superfluidity occurs in liquid helium-4 at far higher temperatures than it does in helium-3. Each atom of helium-4 is a boson particle, by virtue of its zero spin.
Bold and underline added for emphasis

A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero (that is, very near 0 K or −273.15 °C). Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point macroscopic quantum phenomena become apparent.
So fast forward to the idealistic perception of the analog by comparison in today's use against a backdrop of the theories and what do we see?

Nevertheless, they have proven useful in exploring a wide range of questions in fundamental physics, and the years since the initial discoveries by the JILA and MIT groups have seen an increase in experimental and theoretical activity. Examples include experiments that have demonstrated interference between condensates due to wave–particle duality,[25] the study of superfluidity and quantized vortices, the creation of bright matter wave solitons from Bose condensates confined to one dimension, and the slowing of light pulses to very low speeds using electromagnetically induced transparency.[26] Vortices in Bose–Einstein condensates are also currently the subject of analogue gravity research, studying the possibility of modeling black holes and their related phenomena in such environments in the laboratory. Experimenters have also realized "optical lattices", where the interference pattern from overlapping lasers provides a periodic potential. These have been used to explore the transition between a superfluid and a Mott insulator,[27] and may be useful in studying Bose–Einstein condensation in fewer than three dimensions, for example the Tonks–Girardeau gas. -

Shut Up and Calculate

I think its the Feynman approached the work of Dirac by using Feyman diagrams to illustrate a mapping of the interactions. Now to me the visualization techniques are much as Feynman puts it, where okay you are an alien, how would you approach the world and you see Feynman comes up with the method.....I think reiterating what his Father said to him.

Paul Dirac

When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.
link is evasive
So Feynman's series sort of helps you to set your self up in such a way in order to see that perception has to be ignited in such a way as to ask question in a the approach he discusses.

I always used these geometrical ideas for getting clear notions about relationships in relativity although I didn’t refer to them in my published works.Oral History Transcript — Dr. P. A. M. Dirac
So for Dirac to to help us understand anti-matter as symbol within the matrices, beauty in the analytical way, also needs as good way to visualize what he was doing. IN the same breathe Penrose uses Riemann sphere to elucidate the geometry as a sister approach to developing his thoughts regarding the universe. A geometrical underpinning.


"One particular thing that struck me... [LAUGHTER] the fact that he found it necessary to translate all the results that he had achieved with such methods into algebraic notation. It struck me particularly, because remember I am told of Newton, when he wrote up his work, it was always exactly the opposite, in that he obtained so much of his results, so many of his results using analytical techniques and because of the general way in which things at that time had to be explained to people, he found it necessary to translate his results into the language of geometry, so his contemporaries could understand him. Well, I guess geometry… [INAUDIBLE] not quite the same topic as to whether one thinks theoretically or analytically, algebraically perhaps. This rule is perhaps touched upon at the beginning of Professor Dirac's talk, and I think it is a very interesting topic."
So this is my suspicion and I am not sure many share it. It goes back to when Penrose's talks about cohomology and he illustrates, Penrose's triangle. How would he get anyone to see the way he does and point out the difficulties and say, maybe you have an answer, because I do not know? Your invited?

So you develop a model, and lets call it a virtual reality. Once you climb on board how will your world view have changed that the things you answer seem so different, had you not answer the question without such a bias? A alien really, I think this was quite suggestive of Feynman to help others see away into what he was doing.


‘Maxwell discussed … in terms of a model in which the vacuum was like an elastic … what counts are the equations themselves and not the model used to get them. We may only question whether the equations are true or false … If we take away the model he used to build it, Maxwell’s beautiful edifice stands…’ – Richard P. Feynman, Feynman Lectures on Physics, v3, c18, p2.
Shut Up and Calculate, you get what was meant.

Maybe, you will invoke different models with analytical functions in order to help you see differently, add perspectives that without considering Feynman's approach, this advancement in thinking would not take place. We get to these points and move the goal post(we get stuck), in order to see where the ole timers left off, and prepares for the next generation of thinkers? Feynman came to the realization on his own by correlating insights over a span of hundreds of years, by himself, not with others, so how did he do that? He is telling us. Like Penrose is telling us, requires visualization capabilities that have already been mapped and can be mapped to higher dimensions? What purpose to see Adinkras that will light the way toward.....???????

Beauty is understood then, when it came to pass, Dirac's equations lead the way, and Little did we know how Dirac actually used his perception. It propelled him forward, as it does for Penrose, but the beauty remains, and how far forward will somebody else with vision help us toward the next step?

 So cosmological you are looking to the past? You look up at the night sky and when were all these messages received in the classical sense but to be an observer of what happened a long time ago.


In his book Synchronicity (1952), Jung tells the following story as an example of a synchronistic event:

My example concerns a young woman patient who, in spite of efforts made on both sides, proved to be psychologically inaccessible. The difficulty lay in the fact that she always knew better about everything. Her excellent education had provided her with a weapon ideally suited to this purpose, namely a highly polished Cartesian rationalism with an impeccably “geometrical” idea of reality. After several fruitless attempts to sweeten her rationalism with a somewhat more human understanding, I had to confine myself to the hope that something unexpected and irrational would turn up, something that would burst the intellectual retort into which she had sealed herself. Well, I was sitting opposite her one day, with my back to the window, listening to her flow of rhetoric. She had an impressive dream the night before, in which someone had given her a golden scarab — a costly piece of jewellery. While she was still telling me this dream, I heard something behind me gently tapping on the window. I turned round and saw that it was a fairly large flying insect that was knocking against the window-pane from outside in the obvious effort to get into the dark room. This seemed to me very strange. I opened the window immediately and caught the insect in the air as it flew in. It was a scarabaeid beetle, or common rose-chafer (Cetonia aurata), whose gold-green colour most nearly resembles that of a golden scarab. I handed the beetle to my patient with the words, "Here is your scarab." This experience punctured the desired hole in her rationalism and broke the ice of her intellectual resistance. The treatment could now be continued with satisfactory results.[16]
and: are "meaningful coincidences" if they occur with no apparent causal relationship, yet seem to be meaningfully related.
Bold and underlined added by me for emphasis.

Yes you can see how the world of the woman by an event, knocked her out of her orbit? events given by deja Vu, this is a lining up of the information that exists in the mathematical/dream world to events as a classical description? The causal connection can seem totally unrelated, in the case that natural world described as the classical, can intercede with the mental realm of ones thought with such precision as to its timing.

I had an event, given that I was lost in the mental realm of deep thought, and the correlation of cognition as to an event, did happen and materialized in that same exact moment. You have to understand that you are aware of this deeper level of action going on underneath the existence of the material world.

Immanuel Kant, in the Critique of Pure Reason, described time as an a priori intuition that allows us (together with the other a priori intuition, space) to comprehend sense experience.[60] With Kant, neither space nor time are conceived as substances, but rather both are elements of a systematic mental framework that necessarily structures the experiences of any rational agent, or observing subject. Kant thought of time as a fundamental part of an abstract conceptual framework, together with space and number, within which we sequence events, quantify their duration, and compare the motions of objects. In this view, time does not refer to any kind of entity that "flows," that objects "move through," or that is a "container" for events. Spatial measurements are used to quantify the extent of and distances between objects, and temporal measurements are used to quantify the durations of and between events. Time was designated by Kant as the purest possible schema of a pure concept or category. Time
If we examined the nature of time in regards to what can exist in two places at one time what would relegated the experience so as to confirm a connection with nature's animal with one's internal experience?

So one perceives experience in life as lining up with other people blending with them, but the true value of the synchronize event is not really understood this way. What is the scarab's role "as a another group of people," following the same path way to merge with yours? Do we say the scarab and people, are the same thing?

 Now of course as I think deeper on this subject questions arise as to how one may see the world of dream time? This is so as to suggest that patterns are arising from a different world then the one we awaken too. So how do such patterns in seeing allow us to see and have precognitive events of what is to come? Just some thoughts then in regard to what happens in a irrational state so as to suggest that quantum cognition is operating in these areas where patterns are emerging?

Can such an allocation of the mathematical realm ensue into the world of the classical in such a way as to describe that the mathematical world and dream time are on the same plain? As consciousness is exploring what affects could contain the idea of a mathematical realm distant from the affect of emotions that hold consciousness close, and in such an inspiration state allow consciousness to move beyond the containment aspect of a negative emotion?

So elements of the expression of the physical world are being manipulated if I am to say, that would lead some to believe that there is no free will, yet we live lives that are not always synchronized with the pattern developed, so as having chosen a different Path?

Jung, in conjunction with the physicist Wolfgang Pauli, explored the possibility that his concepts of the archetype and synchronicity might be related to the unus mundus - the archetype being an expression of unus mundus; synchronicity, or "meaningful coincidence", being made possible by the fact that both the observer and connected phenomenon ultimately stem from the same source, the unus mundus.[2]

In 1952, he(Jung)published a paper "Synchronizität als ein Prinzip akausaler Zusammenhänge" (Synchronicity – An Acausal Connecting Principle)[4] in a volume which also contained a related study by the physicist and Nobel laureate Wolfgang Pauli.[5]
How is causality a connect in the case of the meaning of our experiences? The example given of the woman in OP and the scarab? Maybe, it could be explained away as coincidence? See also :


Feynman used his cognition skills to invent things that already happened in order to develop his skill as a scientist. He had to teach himself how discoveries were arrived at, without following the trajectory of the discoverers. This correlation of cognition sets up his confidence skills so as to pursue how he saw the world, and how he could simplify the interaction of such particles, as to say, these are feynman diagrams.

Regarding the quote of Einstein's reminded me of Dirac and what he had to say.

You can picture all the directions in Minkowski space as the points in a three-dimensional projective space. The relationships between vectors, null-vectors and so on - - and you get at once just the relationships between points in a three-dimensional vector space. I always used these geometrical ideas for getting clear notions about relationships in relativity although I didn’t refer to them in my published works.Oral History Transcript — Dr. P. A. M. Dirac -

Yes I was looking into Jim Gate's Adinkras. But regarding your observations I am looking.( ) What beauty emerges and you understand what a story does to helping to change perspective about a topic. That this is totally devoid of the materialistic notion that art can bring toward our understanding of what lies in the realm of ideas, all of a sudden blossoms on screen as color.

Such shifts in perspective have been understood with regard to sonification, as color. While it has a history this bend toward the mystical, it is a valid correlation when see light as a chaldni plate recording shape with sound. Such distinctions, in there own right serve to illustrate a collapse of the wave function?

"When I see equations, I see the letters in colors – I don't know why. As I'm talking, I see vague pictures of Bessel functions from Jahnke and Emde's book, with light-tan j's, slightly violet-bluish n's, and dark brown x's flying around. And I wonder what the hell it must look like to the students." Feynman, Richard. 1988. What Do You Care What Other People Think? New York: Norton. P. 59.
So what is needed to step outside the box figuratively?? What did Jim Gates and the crew do?

So, here are nice youtube interview videos of Feynmen that you might enjoy.

Feynman: Take the world from another point of view (1/4)

 The point(This is synesthesia-yes I know) is that when you look from different perspective and remain open to information you get insights as to the way in which the storyteller provides a new platform for you. Same as Jim Gates and the Adinkras. You do not have to believe its real or not but the ideas arise out of a place that we may call irrationality, but the beauty of information does now settle into the mind. Do you understand what I am saying....I am using synesthesia as an example. Its not a vase, but a face. A cube, can shift your perspective.

Cross wiring in the brain allows this attribute of synesthesia to bring a new perspective to the reality, yet, it is still a sensual example of our participation in the real world of senses. You have to be able to shift perspective, to be able to garner new points of view.

The quantum-like brain on the cognitive and subcognitive time scales Khrennikov, Andrei Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. Matematik. (Matematik) 2008 (Swedish)In: Journal of consciousness studies, ISSN 1355-8250, Vol. 15, no 7, 39-77Article in journal (Refereed) Published

This article takes as its point of departure the view that the discovery of the mathematical formalism of quantum mechanics (QM) was not merely a discovery of a new mathematical way of dealing with physical, and specifically quantum, processes in nature. It was also a discovery of a general mathematical formalism (in part discovered in mathematics itself earlier), which, supplemented by certain additional rules, consistently described the processing of incomplete information about certain events and contexts in which these events occur. This article proposes a quantum-like (QL) model of the functioning of the brain based on the (Hilbert-space) formalism of quantum mechanics, but now used as part of a QL mathematical model of neural processes in the brain, rather than for describing quantum physical processes. This model is, thus, fundamentally different from the (reductionist) quantum model of the brain and consciousness, according to which cognition arises by virtue of physical quantum processes in the brain. In the present view, the brain is an advanced biological system that developed the ability to create a QL representation of contexts, which, thus, allows one to describe a significant part of its functioning by the QM mathematical formalism. The possibility of such a description has nothing to do with the constitution and workings of the brain as a quantum system (composed of photons, electrons, protons, and so forth). The QL model offered here is based instead on conventional neurophysiological model of the functioning of the brain, even though the brain, the article suggests, does use the QL rule (given by von Neumann trace formula, used in QM) for the calculation of approximate averages for mental functions. The QL model developed in this article has a temporal basis, based on a (hypothetical) argument that cognitive processes are based on at least two time scales: a (very fine) subcognitive one and a (much coarser) cognitive one.
I see the Quantum Cognition community as being different then the one examining quantum mechanics in biology. Remember Quantum Robin? In this respect I may be mistaken, is where Penrose and Hameroff operate as to identifying an operation in the biology, yet, the neurological affect is an attribute of the erasure experiment in observation, versus not observing. The experiment is recording whether you are aware or not.

 If your animal is a scarab(not a drunk) or really a life's event is a "collision course with an animal" at the exact same time you are thinking about it? A collision course with the real world was inevitable given that you were unaware of the significance of the association between what happens in the mental realm and what is seen as irrationality given that we can see beyond the classical modern day experience. You are establishing patterns beyond ones everyday association with reality in the classical way. So, what came first?

The QL model developed in this article has a temporal basis, based on a (hypothetical) argument that cognitive processes are based on at least two time scales: a (very fine) subcognitive one and a (much coarser) cognitive one. -;jsessionid=qJt9jdFI-202NxWQUAnl3qzjYQAuLs7RROnBiNiU.diva2-search1?pid=diva2%3A203825&dswid=781
Jung had already referenced the Unus Mundus, and what value a archetype, as a messenger of what is created by you to help reveal such a pattern?

Tuesday, August 04, 2015

Quantum Cognition further explained?

Click the image to open in full size.
This paper reports a "delayed choice quantum eraser" experiment proposed by Scully and Drühl in 1982. The experimental results demonstrated the possibility of simultaneously observing both particle-like and wave-like behavior of a quantum via quantum entanglement. The which-path or both-path information of a quantum can be erased or marked by its entangled twin even after the registration of the quantum. -
Bold added by me for emphasis

So you keep this diagram in mind. We then go to looking at this other linked video.

The understanding of the word "erasure," needs to be clarified in relation too, diagrams.

Yes, since sub-atomic particles are actually 'probability distributions' prior to being measured - all possible positions and states are part of their potential until the 'collapse' of the wave function. -comment section of video
So consider this for example. Space time arises from a 5d world. Unification of quantum gravity and light, allow us to have a 4 dimensional understanding of the classical world. If you assume that a 2d screen is a 5D world, then what happens behind the screen?

Similarly, the laws of gravity and light seem totally dissimilar. They obey different physical assumptions and different mathematics. Attempts to splice these two forces have always failed. However, if we add one more dimension, a fifth dimension, to the previous four dimensions of space and time, then equations governing light and gravity appear to merge together like two pieces of a jigsaw puzzle. Light, in fact, can be explained in the fifth dimension. In this way, we see the laws of light and gravity become simpler in five dimensions.Kaku's preface of Hyperspace, page ix para 3
Is it a materialistic view you encounter, or perhaps a point of view you establish by your choice of perceptible qualities that exist for you now?? Given there is a potential for meaning, then, one "same" meaning could not have been encountered by all, for it leaves room for probability encounters, that reveal different views of the world.....yet, some will get the probable meaning, as to what exactly I am saying.

Quantum Theory, is not a materialistic point of view.


 The path of least resistance from a the path of probable outcomes?

What would this look like if we were to say such traveling paths through the cosmos were defined by the paths of least resistance versus a probability paths. Clumping, or interference. If you understand what I am writing then please comment. I would like my thinking to be destroyed by your reason and your science, or you can help clear up misconceptions that are forming wrongly as a Bad idea.

In non-relativistic physics, the principle of least action – or, more accurately, the principle of stationary action – is a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system by stating a system follows the path where the average difference between the kinetic energy and potential energy is minimized or maximized over any time period. It is called stable if minimized. In relativity, a different average must be minimized or maximized. The principle can be used to derive Newtonian, Lagrangian, and Hamiltonian equations of motion. It was historically called "least" because its solution requires finding the path that has the least change from nearby paths.[1] Its classical mechanics and electromagnetic expressions are a consequence of quantum mechanics, but the stationary action method helped in the development of quantum mechanics.-


Maybe I should insert here how we might look at gravitational lensing and gravitation field influences as to how that lensing can distort or divert the photon's path.......just another way to look at the way gravitational influences affect the photon's see that the least resistance could as a affect not deviate speed of light in one of those tunnels as a way in which to determine satellite travel? Should there be a correction here?

My assumptions are generalizations, so I needed to look further to understand this relationship in regards to abstractions and how one can see in different ways. I wanted to see as far as I could in correspondence with the physics, to understand what quantum theory may mean if and when united with gravity as to a correspondence to dimensional references.
Today, however, we do have the opportunity not only to observe phenomena in four and higher dimensions, but we can also interact with them. The medium for such interaction is computer graphics. Computer graphic devices produce images on two-dimensional screens. Each point on the screen has two real numbers as coordinates, and the computer stores the locations of points and lists of pairs of points which are to be connected by line segments or more complicated curves. In this way a diagram of great complexity can be developed on the screen and saved for later viewing or further manipulation From Flatland to Hypergraphics: Interacting with Higher Dimensions -
The simulation argument for me needed to be understood better as well, so the 2d screen needed for me to be further explained as pixels are used to highlight the depth of our abstractions. Banchoff demonstrations in terms of the geometry as an abstraction in geometry for instance. Topology.

Similarly, the laws of gravity and light seem totally dissimilar. They obey different physical assumptions and different mathematics. Attempts to splice these two forces have always failed. However, if we add one more dimension, a fifth dimension, to the previous four dimensions of space and time, then equations governing light and gravity appear to merge together like two pieces of a jigsaw puzzle. Light, in fact, can be explained in the fifth dimension. In this way, we see the laws of light and gravity become simpler in five dimensions.Kaku's preface of Hyperspace, page ix para 3
There is then this being incompatible with each other( gravity and Quantum Theory) that has been talked about that Einstein was after in explaining things in terms of materialism, and to find, that Quantum theory is not a materialist explanation. So I find Einsteins attempts and recognition in later life as a step toward the need for such unification.

As an example, your screen you are working on is a 2d example of a 5d reality. Can we indeed create mathematical reality of higher abstractions? What does that mean anyway? Thomas Banchoff demonstrates geometrical imaging on 2d screens?

Where would these other universes be in relation to ours? Is there a way to envision it? Well, we live in three spatial dimensions: We move back and forth, up and down, left to right. And then there's time, so that's our four-dimensional universe. Another universe might be essentially right next to ours by going in another direction that's not one of those four. We might call it "another kind of sideways." See: Riddles of the Multiverse
This screen has no depth other then the representations that we see are on this screen. You can call them pixels. What does a 5d world mean? In essence this is not about materialism anymore but a grasp for uniting space time with quantum theory? The 2d screen is derived from a 5d reality.

The understanding then sought for is that gravity and light are connected in a 5d world. Is a photon affected as it travels through a gravity field? What did Einstein mean as to a slide of light?

"Yet I exist in the hope that these memoirs, in some manner, I know not how, may find their way to the minds of humanity in Some Dimensionality, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality." from Flatland, by E. A. Abbott