Dear Amazigh,

interesting essay. I agree that duality is important and for me it is a cornerstone in philosophy too.

Thats the reason why I rated you rather high.

Best

Torsten

Dear Michel,

the Hopf fibration is a non-trivial bundle but I had a trivial bundle in mind. So it is the simple cross product S^2x[0,1] but with a non-trivial foliation.

But it has some parallels to Matlock's construction in his essay.

All the best

Torsten

Dear Torsten,

Thanks for drawing my attention to your essay. You're right that I'm interested in a geometrical explanation of accelerated expansion, and I'm glad that you picked this up from my comment on Sean Gryb's essay, and that it drew your attention to my essay. I see that we have some common interests, and will therefore read your essay with interest. In the meantime, I thought I'd direct you to the discussion thread I opened up on Ken Wharton's page (near yours at the top), because that pretty much outlines how I think a geometric description of the observed expansion rate should be handled.

Anyway, thanks for reading my essay. I'll comment again when I've read and rated yours. I hope you do rate mine as well before tomorrow night (since you've said you found it interesting ;)).

All the best,

Daryl

    Dear Torsten,

    I found your essay intriguing in many ways, yet highly technical (unfortunately, I think beyond the scope of this contest in that respect). I was also puzzled why, when you've already assumed a model that is spatially homogeneous and isotropic, you would be interested in recovering inflation? It doesn't seem to fit.

    But those two things aside, you have some very interesting results, and I see a lot of overlap with what I'm thinking about, although we're approaching the problem in some ways differently. I wonder if, when the dust settles here, you'd be interested in reading through the discussion thread I began on Ken Wharton's essay page and emailing me your thoughts on what I've put there. I think I see a possibility from your essay that would really be of mutual benefit, and I imagine you'd pick that out as well from my posts.

    As I said, interesting and intriguing essay. I rated it accordingly. I look forward to hearing more from you.

    Best of luck, here and always,

    Daryl

    Greetings Torsten,

    I found your essay deeply meaningful and engaging. It was not light or easy reading, but I found myself learning something meaningful with each paragraph I read. I think I was able to understand most of your technical points, although the depth of your coverage was astounding, which attests to the clarity of your exposition. I especially like the observation that the smooth and triangulated or PL constructions of the manifold are equivalent, and find greatly satisfying the idea of a tree-like branching spacetime.

    There is much to like about your essay, and I gave you a high rating. I had started to read it at least twice before, but it was so dense with content as to take as much time as 3 or 4 lighter ones. However; I felt I needed to come back to it, before the deadline, and give you your due. You might enjoy my essay as well. I'll say more later, if there is time. Good Luck!

    All the Best,

    Jonathan

      Dear Jonathan,

      I also read your essay (giving them a high rang), it is really interesting.

      But I will also read it again.

      Best wishes

      Torsten

      Dear Michael,

      thanks for your rating and I do the same for you.

      very interesting essay, I agree with you completely, information has a hierachical structure with many layers (including also its semantic).

      It was ghood that Matt brought us together.

      All the best

      Torsten

      Dear Jonathan,

      thanks a lot for your words. Yes, finally I got it (with one of the last votes).

      Congratulations for you rank.

      Best

      Torsten

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