What I do is create diagrams that try to capture my thoughts.
You can see my diagrams in some of my Quora answers, this one [Thinking: Why are we so quick to judge and choose sides? ] shows the relation to between the kinds of knowledge in Aristotle and the phases of Plato’s divided line. The diagram is totally adapted to the structure of the ideas being represented.

Concepts are non-representables. But we indicate them with verbal and prose descriptions and their relations can be shown diagrammatically. Creating these representations that are completely adapted to the structure of the ideas used to indicate relations between concepts is difficult but rewarding, because once you get it right then you can remember it easily. It gives the context of the ideas which point toward the concepts

I think the answer is in these words that come before the shell:

“But man himself only is hard to bear! The reason thereof is that he carrieth too many extraneous things on his shoulders. Like the camel kneeleth he down, and letteth himself be well laden.”
“Especially the strong load-bearing man in whom reverence resideth. Too many EXTRANEOUS heavy words and worths loadeth he upon himself–then seemeth life to him a desert!”
“And verily! Many a thing also that is OUR OWN is hard to bear! And many internal things in man are like the oyster–repulsive and slippery and hard to grasp.”

He is talking about the camel that is burdened by heavy words like Good and Evil to others which are extraneous injunctions.

But then he says that it is man who is hardest to bear for himself. Then he says that the internal things in man are slippery like the inside of the shell of the oyster.

So the metaphor is the oyster and he is saying that the shell of the oyster is what is hardest to bear, even harder than extraneous injunctions of others. But basically I think he is saying we have to come to find our own Good and Our own Evil and learn to say I and not be dependent on others to give us their Good and Evil but to express our own tastes, and this hardness of the shell which is difficult to bear then becomes the basis of our own will to power, i.e. to good to evil we ourselves have developed and chosen and acted upon.

It is a difficult but interesting passage. Thanks for bringing it to our attention.

The exact answer to this question I do not know, but would like to know as well. But what I do know is that hyperspheres get larger and then smaller again as you go up the ladder of dimensions. They peak out between five and seven dimensions in terms of surface area and size. Then they get smaller and smaller the higher you go. Right now M theory is 11 dimensional. F Theory is 12 and 14 dimensional. To my mind we could interpret this fall of in the size of hyperspheres as gathering things in the universe closer together because each higher hypersphere contains the lower hyperspheres. And one speculation is that the nth degree of dimension, i.e. the highest whatever that is or perhaps even infinite degree occurred at the Big Bang. Under that assumption we could see what is happening as the Universe cools as producing lower and lower dimensional asymmetries. It seems to be if that were true then it could be that at the highest dimension that the universe could be at the Big Bang still gathers the entire universe in a very compact space in that dimension, and expansion in some sense comes from the unraveling of dimensionality down to the place where it widens out below the level of M theory. Not sure whether physus take this expansion of the size of hyperspheres as we come from an arbitrarily high dimensions down to a lower dimension into account. I think they are assuming that the universe has a set dimension. But it seems the truth of unification of theory and perhaps the multiverse theory as well might be something like this:

In the Multivese which is a very high dimensional plasma and thus with hyper sphere radii that are very small and thus it is very compact, probably less than Planck length by a lot, some asymmetry occurs which causes the dimensionalities within these high dimensional hyperspheres to start to unravel, and perhaps it is at the barrier of Planck length that the actual big bang occurs, but regardless during the Big Bang this unfurling is still happening until we get down to dimensions at which the size of the hyperspheres get much larger, and this itself could account for the expansion of the universe and dark energy. In other words in this speculation dark energy is really the expansion of hyperspheres that occurs at lower dimensions eventually we hit the F theory and then the M theory levels, and the unraveling continues until the universe hits the fourth dimension, and at that point a phase change occurs because the fourth dimension has no set topology and thus that is where our physics is rooted with its set constants for the universe, but then a further symmetry breaking produces three dimensionality and the asymmetry between spacetime or timespace and that the realm we experience, but the actual universe itself is four dimensional and that is inscribed in relativity and quantum mechanics and their use of imaginary numbers in their formulation.

If this picture were true it would explain a lot. It would explain dark energy as merely the continued unfolding of the higher small dimensions into the larger big dimensions which then produces an expanding universe. In this theory the universe is expanding because it is unraveling into lower dimensions and they are bigger than the containing dimensions. If lower dimensions are bigger than the containing dimensions that is going to produce an inflationary pressure. If that unraveling is continual rather than just something that happens once and then is set, then that is a constant inflationary pressure. But to your question, we are still nested in these very small hypespherical high dimensions at the same time we are in the lower ones that are bigger and so in this sense we are right on top and gathered to everything in the universe all the time at these higher dimensions. But whether as three dimensional creatures we could travel in them is another question, and that is to my mind doubtful. But another consequence of this idea is that it might explain some of the structure of the universe in as much as there is a concentration of mass in the universe. These hyperspheres get larger until they get to around the fifth or seventh dimension in terms of size and volume but then they get smaller until they get to the fourth and third dimensions. In the fourth dimension there is no set topology so that is like reaching a point that is fully freeform and where there is perfect movement which is like an Bose-Einstein condensate. I think that the paradoxes at the Planck scale may be resolved by this topological anomaly. But then the symmetry breaking out of that produces spacetime/timespace out of the matrix of four dimensional time or four dimensional space, which together is eight dimensional. These eight dimensions occur within the fourth dimension as the double covering of that space by the Octonion. So with respect to the Octonion it is as if four dimensional space were folded back on itself and that folding is the difference between four dimensional space and four dimensional time and all possible symmetry breaking between time and space between. The fact that there is perfect motion within the fourth dimension, and the fact that spacetime/timespace is folded in that dimension though the octonion suggests that it might be possible to slip through if we were able to actualize ourselves at that level because there should be no topological constraints and the folding in the Octonion suggests that there is some sort of reflexive superpositioning of the  matrix on itself.

If it is true that we are nested in higher dimensional hyperspheres of some arbitrary high dimension then actually everything that is spread out as spacetime or timespace is literally interprenetrated, and we know that effect physically as entanglement under Bells Theorem which has proved to be correct. Since all matter in the universe was together at the big bang that means everything in the universe is entangled with everything else. So this leads to a second argument for interpenetration of everything which is the Mahayana position of Fa Tsang and other nondual philosophies in other traditions as well.

Suggest you read the summaries that exist on the internet and then if you are still interested listen to The Bernstein Tapes podcasts of Professor Bernstein on Kant First and Third Critiques. Don’t know of any good podcasts on the Second Critique. But Bernstein more or less explains that too as he goes along. Really when it comes down to it summaries really don’t do you any good. Either you want to understand Kant in his own terms or you should probably forget it, because Kant is difficult and dry and unless you want to know how Western Science works probably too much to be bothered with. However if you must there is always the commentaries of Patton which are in my view the best. Basically I spent a whole summer reading Critique of Pure Reason, the only critique I was interested in, with the Commentary of Patton as my guide. I thought I understood Kant by the time I had finished, more or less, at least well enough to read Heidegger’s books on Kant which was my real goal, and probably the best thing in Heidegger. But years later I ran into Bernstein on Hegel who I had never been able to get into, and he helped me over the hurdle. So I decided just to brush up on Kant by listening to those podcasts as well. Well I just did not realize how much I had missed both of the big picture, the details and the significance of Kant. When it comes right down to it there are only four figures in our tradition Plato, Aristotle, Kant and Hegel. The first two are fundamentally the same for all their differences and the last two are fundamentally the same for all their differences. If you know these four figures you know pretty much everything else by extrapolation if you know them well. I still don’t know Aristotle all that well. But the others I think I have a decent grasp of, and Kant and Hegel only by way of Bernstein. Plato by way of John Sallis.

Which leads me to the important point: Read commentaries, good ones are hard to find, but are indispensable.

Basically if you read a summary you still don’t know anything. If you give up and read the actual philosopher you still don’t know anything. Then read some commenters enough to figure out what the disagreements are and you still don’t know anything. Then you must find the commentators that really explain what the philosopher meant within his philosophical context, and then you can claim to know something.

In other words you cannot know anything based on help, and you cannot know anything based on your own reading of the original text, and you cannot know anything significant based on knowing what the commentators argue about, but for each figure there is one or two commentators that actually understood what was being said in context and can explain it cogently and clearly, and when you grasp that then you can say that you know something.

Knowledge is cutting though the crap. There is just so much garbage said about Kant, strange self-serving interpretations that only make him more obscure. The summaries might give you a clue what the whole thing might be about, but you will never know until you actually read the philosopher himself and what he has to say, because most summaries are unjust in some way, or so abstract that the core is left out.

But even if you are reading the philosophers own words you do not know the context in which he was writing, and so you are interpreting it in relation to the later philosophers that you have read, and this can be an endless source of confusion. Then if you see what the commentators are arguing about with regard to the philosopher this only tends to obscure his thought more. However, if you look at all the commentators there will probably be one or two who have risen above their own agendas to tell you what Kant was trying to say himself, like Patton. Bernstein says that the problem with Kant is like in mathematical proofs steps are left out in the argument and left as an exercise for the reader, and if you don’t realize that those steps are needed, or substitute the wrong intermediate left out steps then you get a different philosophy from the one that Kant intended. You have to find a commentator that actually understood Kant and the right left out steps and then you get a reasonable facsimile of his thought. It makes astonishingly good sense once you know what he is not telling you, because he assumed you already knew it.

Patton does this by taking one sentence at a time and writing a paragraph for each one first explaining why the sentence is there given the prior context, and then explaining the sentence, and then saying why it is important to the argument. After you go through all that you realize that Kant was just too brilliant for his own good. He was a genius and you are not going to be better than him, no matter how hard you try, no matter how many hundred years of other commentaries you have to lean on. As Bernstein quaintly put it, he was a bastard because he left out key points that makes the arguments cryptic and the whole game is to figure out what is missing that he left out just because he assumed we were as brilliant as him. So because of this fatal flaw of genius very few commentators have had any idea what he was talking about all this time, and he is the key figure in our tradition, because of the few things we all did understand. This problem only gets worse with Hegel. Between them they used up most of the available philosophical genius in our tradition and the rest of us are just floundering about with less than a full deck of cards compared to them.

If you really want to get crazy you need to read Kant with Milton and Hegel with Blake after reading Dante. That will keep you occupied and make sure you stay out of trouble for a long time.

The best evidence I have found that they may exist is . . .

“On a class of solutions of the sine-Gordon equation” Mikhail Kovalyov Journal of Physics A: Mathematical and Theoretical Volume 42 Number 492009 J. Phys. A: Math. Theor. 42 495207 doi:10.1088/1751-8113/42/49/495207

This article talks about anti-breathers. It basically says that there are real and imaginary breathers and anti-breathers in the what I have been calling the Super-breather. There are only two articles that I could find that spoke of anti-breathers at all. But it took me days to figure out what search term to use to find this article. But having just one article that claims that they exist is hardly sufficient.

Why is it a good question whether Superbreathers exist? I have had a theory since around 1995 that predicted that Superbreathers existed. And every now and again I try to look for someone who has discovered them. But recently I was writing an article where I suddenly needed to know whether they existed for my argument to hold weight. So I started a frantic search. It turns out in the meantime a lot has been learned about solitons and breathers, and all sorts of odd types of solitons and breathers have been discovered, but no mention of the missing predicted superbreather. In my formulation a super-breather is a combination of a breather and an anti-breather just as a breather is a combination of a soliton and an anti-soliton. These are mathematical and physical anomalies which are waves that are both particle and wave at the same time in macro phenomena.

Why do we care? Because like super-conductivity, solitons, breathers, and if they exist super-breathers call into question some of our traditional views of science. Like super-conductivity or Bose-Einstein Condensates they call into question our ideas about Thermodynamics. They are counterexamples and as such they are important. It took twenty years to come up with Cooper Pairs as the explanation of superconductivity, and it took us a very long time to realize that solitons are everywhere in physical equations, and to work out how to tease them out and then find out whether the equations described something real or not once the math was known. Now we know pretty much that the equations are correct and solitons and higher order derivatives like breathers and other strange soltonic phenomena are just about everywhere in physics. They are important because they are unexpected side effects of our physical equations that are counter intuitive. When we tease them out and find out that they are real that means our equations are better than we thought they were at predicting reality. This is a very fortuitous and unexpected finding that says that our equations really do predict the nature of the world, even in ways we did not intend in the first place when we created those equations.

Good question.

The answer is that the higher dimensions are more real than our experience isolated to the third dimension. But to understand why this is the case is difficult. In order to understand it you have to rethink your view of the world somewhat. In our worldview Logos/Physus is the most basic duality. But between them is the Nomos (Order, Math) which allows theory to connect to experimental results. All good scientific theory mimics math in operationalized words that reflect how phenomena works. Without all three you could not have science. But Nomos being nondual comes before (is a priori to) the split between Logos/Physus. How do we know this? because if the universe did not have anything in spacetime there would still be the math. And the math has some very odd characteristics and those actually drive our world and constrain it in specific ways that show up in physical phenomena. The simple answer is that Logos and Physus describe Being and the Nomos describes existence as it looks from the Physus/Logos split. Being is in fact a unique Indo-European linguistic kink and thus is not universal in any stretch of the imagination, except by fiat of killing off many of the other peoples and worlds, and languages that did not have Being. So that means that nomos is nondual and prior to the rest of nature that appears when there is something in spacetime but it has structure even if nothing ever articulates that structure. Part of that structure is N-dimensions. But N-dimensions though infinite are not all the same. In fact the fourth dimension which is the dimension that we really live in has some pretty unique properties compared with the other dimensions. But dimensions are different from each other. And we see this best in the size of hyperspheres which get bigger then tail off into the infinitely small. The peak of size of hypersperes is around the 5th to the 7th dimensions. So although they are infinite this does not mean that the structures that are interesting go on forever, but rather oddly the interesting structures all exist at the lower dimensions, near where we are. The oddities like the hypercomplex algebras drive a lot of structure in the low dimensions. Also the fact that the fourth dimension uniquely has no set topology is important. So since Math constrains the physics it must be real, in fact in some sense more real than the physics, because those constraints would be there even if the matter were missing.

There is more to this answer than what I have mentioned but this is a good place to start to answer the question of why mathematical dimensions are real, more real than the phenomena that fills spacetime that the math constrains. The math has to constrain it otherwise science could not rely on mathematics to guide its theorizing about phenomena.

=========================================================
How do we know that mathematics (Nomos) is prior to phusis (Nature, Physics)?
(responding to a comment from Chase Quinton)

What you have to grasp to understand this idea is basically the essence of Kantian Philosophy. What we need to see really how deep the Kantian picture is in order to accept this idea. Basically he worked out an answer to Hume’s Skepticism. But more than that what has come out of Kant’s approach is the very basis of our scientific endeavors since his time. In effect no one has figured out how to surpass the limits he set on reason, nor the way that he has tied reason to experience to produce understanding, or the way he has managed to rescue causality from the mire of mere sequences of events. In other words Kant’s view has become our predominant view in our worldview concerning the efficacy of Science. And that view demands Transcendental Idealism as the route to Transcendental Realism. Everything else has gaps that cannot be explained. Kant got rid of the gaps, by saying first we project spacetime which we understand through math, and then we project the categories by which we get objects within spacetime and causality that may be objective, and the only way to know what is real is through these projections that we make unconsciously. What it does is by basing everything on projections is to make sure there is no gaps between us and what is real. Those projections we make are the reality, but that does not mean we are constructing that reality we see, but it means that what comes through the medium of the projections IS real, as real as anything gets. All other views have unexplainable gaps between reality and our attempts to be objective as subjects, and cannot explain things like causality on which Science is based.

Now since Kant philosophers have tried every possible way out of this box that Kant put us in. But they all fail one way or another and if you look at both Continental and Analytical philosophers they all accept and harken back to Kant one way or another. Because without his Copernican Turn toward critical philosophy by weakening reason and tying it to experience to produce understanding there is no way to explain how science actually works. All the other opinions are just tweaks to this basic positions or reactions that merely entrench it further. In other words we know that nomos comes before physus because logically spacetime has to come before anything can be in it. And Nomos is how we understand spacetime. And we can understand it become it comes out of us a a projection prior to our experience. Then we know that objects that are physical come next because things in space logically have to come after the place that they are in, and we know them because we are projecting the categories after spacetime. And we know these things because of our judgments that are aligned to the projections, and the judgments are in language. We project what we can then understand and interpret as judgments. Essentially this means that objects have to adapt to us and our projections rather than us adapting to them. We can only know what we are prepared in advance to know, we cannot know anything that we are not prepared to know prior to the knowing by our projections. Everything I am telling you is explained by Bernstein in his lectures of Kants at Page on bersteintapes.com. So if you want to know more then listen to those tapes. We are projecting synthetic a priories, because that is the only way we can know anything. Whatever we know is already part of us from the beginning. And because of that what we know via our prior projections is the only thing that is Real to us.

It is like a current author (of Is that a Fish in your Ear) on translation said at the LA Times Bookfair recently. If we sent people off into space and they met aliens and learned their language and spoke to them, and they came back we would ask them what the Aliens said. If they said we would like to tell you but their language is untranslatable, we would doubt their veracity. By its very nature if they learned the language of the aliens and spoke to them then somehow what the aliens said would be translatable into something. This I think is another version of Kant’s argument. The very nature of language is that it is translatable into any other language somehow, to some degree, with some fidelity, perhaps not accurate or correct but to be language at all it must be translatable. Kant is merely saying the same sort of things about nature. Nature has to be experienceable. To be experienceable there are certain rules that it must adhere to and if the phenomena does not adhere to those rules governing our experience, we cannot experience it, and those rules come from inside us, not from outside. We may not be able to experience everything, what is real to us is what we are capable of experiencing and understanding. We use reason to aid in understanding. Left to its own devices reason makes up fantasies about the world, but with respect to interpreting phenomena by the rules of judgment to produce understandable experience reason does a good job and giving us access to the realities we can handle. Elliot’s quip about this is that Human beings cannot take too much reality, but the reality we can take is as real as anything gets.

I don’t want you to get confused about whose idea this is. It is Kant’s idea. Please argue with him if you must. People have been arguing with him ever since he writes the First Critique, but no one has found a way around this argument. You cannot accept it, in which case Science as we know it breaks down for you, or you can accept it in which case Science sorta works, and just enough to discover amazing things, but not enough to tell you how real the things are that they have discovered. So you have to kind of decide if you want Science to appear to work at least half way OK, or not at all. For Kant there are no noumena. He only posited noumena so he could show that this is an empty concept. Noumena do not exist because everything we experience via our projections is itself real, as real as anything can be. if there were nounena, i.e. realities that we cannot know, we would not know them, and so speaking about them would be a moot point.

This is not Platonic. For Plato and other metaphysicians before Kant there are unknowables, and the metaphysicians from their privileged position will tell you about them. But Kant is going to say every time to these in his critical philosophy, if it did not come from me ultimately then I cannot know it, and so it is irrelevant. I would rather than a science that told me novel things about the world that are interesting that I can know, that myriad unknowable things no matter how fascinating. If you want to know a little that is real about the universe then Kant is the only show in town. If you want to know a lot that is not knowable about it then there are other metaphysical paths to follow. There are a lot of problems with Kant’s thinking but on the essential point of the lack of value of ungrounded metaphysics there is unanimity. Un-grounded here means not grounded in our nature as human beings, and tied down to our experience, such that it produces understanding of the world. Another way to say this is what is real is what we can understand, and things e cannot understand ultimately because they go against our reason are not real, and are worthless to us.

I hope this helps.

That would probably be Kant because he made Transcendental Idealism respectable, and laid the foundation for science and no one has gotten past those foundations that he laid yet as far as I know.

Most art is self indulgent. It is produced by the self to express the self either to the self or others. So somehow if the artist is not indulging the self then then there is little to express. I would say that indulgent art is allopoietic in the sense that it is producing something other than one’s authentic self. But good art is autopoietic in the sense that it is genuinely producing the self qua self which is the unique individuation of the artist. But of course this is just a guess. What it means to be  “self” indulgent is open to interpretation. But art qua art is an expression of the self no matter how abstract or minimalistic or conceptual we attempt to be. Good art is not just a self-expression but also is archetypal in some sense. As Kant says Beauty is intersubjective in some sense. Great art hits a chord we all can appreciate somehow, or at least ought to appreciate to the extent we realize our humanity within ourselves.

To me the art of Bacon that Deleuze praises is self-indulgent. I don’t see what Deleuze sees in it.

But for instance the statue of Laocoon cannot ever be called Self-indulgent because the self that expressed it expressed purely the human condition. The self of the artist is effaced in its immersion in the human condition. But by that it does not lose its individuality, but instead heightens it to embrace everyone somehow  which is what Jung calls the individuation of the self.

Kant in his Critiques. He really started it all in the modern period.

David Bohm See http://en.wikipedia.org/wiki/Bohm_Dialogue