Hi Antony,

I found yours to be an interesting essay about numbers, their relationships and properties. You suggest a connection between Fibonacci sequence seed values and Wheeler's 0 and 1; you discuss Fibonacci numbers found in nature (in the structure of plants and bees) suggesting that these numbers and their relationships are a type of information known to nature at some level; and you suggest that Fibonacci numbers are a type of numeric information that relates to the properties of black holes and the reasons for a spatially 3 dimensional universe.

You may recall that in my essay I developed a bit of a case that numbers are things that really exist; they are what I would call hidden information category self-relationships (not that anybody has commented on this assertion either positively or negatively). So I'm interested in asking other people about numbers: I wonder how you see the nature of numbers including Fibonacci numbers i.e. in what sense do you think they exist in relation to physical reality? (I hasten to add that this is not a quiz question that will be marked!!)

I am giving you a good rating. Best of luck in the contest,

Lorraine

    Dear Margriet,

    I agree the contest is fantastic for sharing ideas! I like your explanation. It fits with my essay in that the numbers in the Fibonacci sequence represent geometry, in this case the simplexes, being the simplest form of the n-dimensionality.

    Best wishes,

    Antony

    Hi Lorraine,

    Thanks very much for your kind comments and rating. I'm also relieved that I won't be marked on the answer to your question as I don't think my nerves can take another contest ;o)

    I think you are dead right that hidden information exists. I explain spooky action at a distance as hidden fixed constants, a play against hidden variables.

    My geometries explain the cosine non-linear relation between entangled particles in spin Alice/Bob type experiments exactly!

    As mentioned to Margriet - I think at least in the case of Fibonacci numbers, that they represent real geometry in the form of simplexes.

    From this I get symmetry breaking from complete nothingness, that also conserves the nothingness. In short it solves Baryon Asymmetry.

    I think this should apply to all numbers and that they apply to dimensionality and simplexes are the most fundamental geometry in n-dimensions.

    Great question!

    Best wishes for the contest!

    Antony

    Dear All,

    I'd just like to thank you for reading and commenting on my essay! I find it an honour that you have considered my reasoning. I've thoroughly enjoyed reading ALL the other essays!

    Best wishes to you all for you future's.

    Antony

    I'd just like to sum up my essay with one of my favourite comments above:

    "A thought-provoking take on the subject and an intriguing exploration of Pythagorean link between numbers and nature. In an accessible manner which can be convincing and comprehensible even to a layperson, the author successfully presents in few logical steps an attempt to combine the Fibonacci sequence with the questions of reality and its underpinning - information. What seems to be especially appealing is the intellectual effort to prove the possibility of deriving functions inherent to the fabric of realty from binary choices. In this concise essay the author skillfully manages to interweave the great questions of modern-day science such as the theory that information is fundamental to the physics of the universe, Hawking Radiation, entropy and quantum fluctuations. Fine base for further research that might possibly turn out to be an important jigsaw puzzle piece in tackling the problems of fundamental parameters, black hole information paradox and holographic principle".

      Dear Antony,

      I have now finished reviewing all 180 essays for the contest and appreciate your contribution to this competition.

      I have been thoroughly impressed at the breadth, depth and quality of the ideas represented in this contest. In true academic spirit, if you have not yet reviewed my essay, I invite you to do so and leave your comments.

      You can find the latest version of my essay here:

      http://fqxi.org/data/forum-attachments/Borrill-TimeOne-V1.1a.pdf

      (sorry if the fqxi web site splits this url up, I haven't figured out a way to not make it do that).

      May the best essays win!

      Kind regards,

      Paul Borrill

      paul at borrill dot com

      Dear Paul,

      There is a link page http://fqxi.org/popups/forum/links.

      I've read and commented on yours and the other 180. 182 in total. I can't believe there were so many great essays!

      Really enjoyed it.

      Best wishes,

      Antony

      Dear Antony,

      Sorry about my Thumper's dad's response to your essay. In some respects I did like it; but when it comes to black holes I've got so many personal issues that I just couldn't see how to respond without feeling like I was on a psychiatrist's couch. With that said, if you are interested to hear all I have to say on the matter, please feel free to email me at the address on my essay.

      All the best,

      Daryl

        Dear Daryl,

        No problem. I had to Google that term, but i can't find a Thumper's Dad response ;)

        I will email you at some point soon, as I'd like to hear different points of view on this. It doesn't just have to apply to Black Holes though!

        Best wishes,

        Antony

        Hi Antony,

        Congratulations for doing so well in the contest!

        Thanks for replying to me about numbers. Are you saying that numbers derive from or even ARE geometry, which in turn comes out of nothing because of symmetry? Does this mean that you have a platonic view?

        Cheers,

        Lorraine

        Right, obviously that was way too cryptic. Why the heck would you have Bambi on the brain at a time like this.

        Thumper: He's kinda wobbly, isn't he?

        Thumper's mom: Thumper, what did your father tell you this morning...?

        Anyway, I meant to say that it's not even like I couldn't say something nice, but whenever I sat down to say something I inevitably ended up going on to say something like "but I find the whole black hole concept so utterly inconsistent..." and launching into something that I just don't think would have been appropriate to get into here.

        With that said, my opinion is obviously very unpopular, and will have no bearing on the judging of your essay in the final round. I wish you the best of luck. And please do keep in touch.

        All the best, Daryl

        Many thanks Jonathan and congratulations to you too!

        Best of luck to you too in the finals! I'm really looking forward to the judges questions!

        Kind regards,

        Antony

        Hello Daryl or should I say Thumper's pal - ha ha.

        Firstly congratulations on making the finals!

        I think it is good to examine reality from an objective point of view. So any view should not be considered unpopular. That's what I do in my research, I think why something shouldn't work and only if it overcomes those obstacles do I continue.

        Tha essay is about more than just Black Holes, in fact in some respects it suggests that singularities might exist mathematically, but information doesn't remain within Black Holes. Also the essay came about from a broader theory about simplex type geometry resolving Baryon Asymmetry and producing an arrow of time.

        Best wishes,

        Antony

        Dear Antony,

        Thanks for the reply. I realised that while I mentioned that I could say something nice about your essay, I didn't say what that was. I found your idea both neat and intriguing. I personally think both mathematically and physically, anything beyond a black hole's event horizon is a dead end, because I think the solution simply doesn't exist there--i.e., I don't think r goes from being "space-like" to "time-like", but from being "space-like" to invalid at the coordinate singularity--but as I said, that's not an opinion that anyone else shares, so don't lose any sleep over it.

        So, while I could honestly have just posted that I find your idea neat and intriguing, I didn't do that because I thought it would have looked superficial, like I didn't really bother to read through your essay. Since I'd have had a difficult time showing an appreciation for the details of your essay, due to my own personal issues, I just didn't post, because I feared that a brief comment like that would have appeared dishonest, and I like to avoid that.

        Finally, I thought I'd add a point that you may like to ponder, since you read and liked my essay: if time objectively passes in the way that I've described, as opposed to not passing at all (in the case of a real block universe), then the usual justification for the collapse scenario is invalid, because it takes reality to be synchronous in general reference frames.

        Cheers,

        Daryl

        Hello Lorraine,

        Many thanks. It was touch and go, as there seemed to be plenty of low votes late on. But I expected the rough with the smooth so to speak. There is talk of collusion to group vote, which is a shame. I'm furious that somebody else thought I was part of one such group. I think there is an element of human nature that if you're nice about somebody, they may be inclined to be nice to you, but that's just how some people lead their lives.

        Anyway getting back to science ;)

        I'm suggesting that numbers correspond to information exchange in different dimensionalities with regard to the Fibonacci sequence in the first instance.

        But I then explored the concept further, so that the simplest geometries in n-dimensionality are the simplexes, which of course are self-dual Platonics in their respective n-dimension.

        So I proposed that the information content at n-dimensionality in its simplest form is the simplex, going on to use this to represent entropy, where we get the interesting results in the table as we drop downwards along the sequence.

        The coming out of nothingness is because the 0-simplex is an infinitesimally small point, which the sequence passes through. However, I have other research which similarly suggests equivalency between 0-simplex and higher simplexes - they all conserve the central point for instance.

        So the Fibonacci numbers I'd say are linked to geometry. However, curiously as shown in the table the +1 pattern remains only up to 3 spatial dimensions.

        I could go on for hours about my symmetry breaking system that considers 3-dimensions a limit. I'll just summarise here that we condsider the 1 and 2-simplexes in 3-dimensional space and Electromagnetism, Mass, Weak interaction and Residual Strong are all shown. Further, a mass relationship between the Proton, Neutron and Electron to 99.999988% of prediction is obtained.

        Great questions!

        Cheers,

        Antony

        Hello Daryl,

        I've just seen your reply - sorry. I'll ponder the question and re-read your essay in that context, then get back to you on your thread. As I said above, it's a great approach to consider time's role in reality!

        Regards,

        Antony

        Hi Antony,

        Thanks for getting back to me about numbers. I am still trying to digest your concept of a number i.e. in what sense it really exists, and how physical reality might apprehend particular numbers as opposed to all other numbers that exist. Also how would you characterize the numbers that we obtain from measurement of fundamental reality e.g. mass or momentum or relative position?

        Cheers,

        Lorraine

          8 days later

          Hi Lorraine,

          Sorry for late reply!

          Great way to think about this! In this respect I'd suggest physical reality apprehends numbers as dimensions. So a singularity is zero with regard to spatial dimensionality. 1-dimension could exist as equivalent if we look at simplexes as fundamental geometry.

          The two vertices of a line segment are equidistant to their average position - a point - 0-dimensional simplex. So creating 1-dimension from 0-D conserves 0-D point.

          We can indeed then do this equivalency for any n-dimension simplex. However, starting at 0 and moving to the next dimension 1 allows us to then follow Fibonacci.

          As you rightly say - why this rather than all numbers?

          To answer this I'd point to the negative part of the sequence. The -1, 1, 0. Without this we would be saying that 0D can fluctuate to higher dimensions, but always must fluctuate back down to nothingness again.

          If 0D however fluctuates of "decays" to -1 +1 we have two 1-dimensionalities. One positive and one negative (whatever that means).

          I'd suggest this is the real approach to solving Baryon Asymmetry.

          With -1 AND +1 existing, we could of cause have a type of annihilation. BUT a further "decay" of each dimensionality would do this:

          -1 -> -3 +2 AND (+1 -> 0 +1 then +1 -> +2 -1)

          Giving us -3, 2, AND 2, -1.

          We'd have an asymmetry with two distinct spaces. One made of -3+2 dimensionality and another of +2-1 dimensionality.

          I.e. one overall -1 the other overall +1. But geometrically unable to annihilate.

          Not getting sidetracked from your question, but this highlights why the sequence might be foundational and special.

          The other point re- numbers obtained from measurement. I'd say they are cumulative just as we know them.

          For example, the geometries arising from my theory are quantised yet real numbers, as angles such as the dihedral angle of the tetrahedron and Pi apply.

          Best wishes,

          Antony