Just because statistics and quantum theories cannot be axiomatized doesn't mean that math is not a part of nature to be discovered. Probability is merely the first, invented step in detecting a pattern that is caused by some structure described by discovered math and physics.

Another universe: The universe needs a way to disperse the energy inserted into it. S it created cooling flows between galaxies and inflows in galaxies. Life as we know it is a means to increase the rate of entropy increase for the universe in the infall models.

a month later

William,

Perhaps there was too much compressing of various subtopics into the allotted space, when it could be more fruitful to focus on one or a few in more depth, however - your essay was well-written, thought-provoking, and seemed to me to provide some novel insights and speculations. It certainly deserves more attention and credit than it has so far. Cheers,

    Dear William,

    I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

    All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

    Joe Fisher

    Dear William Nelson,

    In your essay you wrote, "... the dimensionality that we experience does not have to be the full dimensionality of the underlying theory; additional dimensions could exist which are wrapped up so tightly that we can't perceive them. This very natural idea was first proposed by Kaluza in 1919, and string theory famously requires it." String theory with the infinite nature hypothesis suggests the wrapping up or curling up of extra dimensions. I say that string theory with the finite nature hypothesis suggests that there is no curling up of extra dimensions. Google "witten milgrom" for more information. According to the Gravity Probe B science team, my quantum theory of gravity has already been ruled out. However, I say that the Gravity Probe B science team misinterpreted their own data and that they empirically confirmed what I call the "Fernández-Rañada-Milgrom effect." I say that the 4 ultra-precise gyroscopes functioned correctly and did not malfunction in a surprisingly predictable way. Have your personally studied the Gravity Probe B results, the space roar results, and the photon underproduction crisis results?

    Dear William,

    You ask:

    Why do we see three space and one time dimension? Could it have been diferent?

    My answer is:

    Earth is a consequence of the laws of nature, not the cause. From the perspective of a whole universe dimensions are not essential. You can see in my essay that is quite good results are obtained without using Dimensions.

    Regards,

    Branko

    Dear William,

    I just found your essay to be one of the few great essays in this contest, and I just gave it a boost. I also added it to the list of best essays in my general review of this contest. Sorry I did not notice it earlier. I think you will be particularly interested with these two other essays:

    Genesis of a Pythagorean Universe by Alexey and Lev Burov, which addresses some common issues with yours, even if the kind of reasoning is different.

    My own, A Mind/Mathematics Dualistic Foundation of Physical Reality, where I give precise reasons, other than those you mentioned, for the necessity of quantum physics with its "paradoxical" features, with the non-mathematical aspect of probabilities and the measurement problem, in order for a universe to be able to host conscious life.

    6 days later

    If according to you, no mathematics are involved in this creation.

    How you would essentially do the astronomical calculations and the numbering?

    - Sincerely,

    Miss. Sujatha Jagannathan

    Dear Bill,

    Having just read your essay, I really liked your introduction involving the deeper questions one should think to ask about unicorns (what a wonderful way to teach a child to think more deeply about things in the world, let alone adults) and was struck by how methodically you covered all the areas relevant to your argument.

    Concerning your comments on probability, if you permit me, I would like to share some of my own ideas and views: I believe that, ultimately, probability is a measure of "coming into existence" relative to other possibilities. This "coming into existence" could be the outcome of a single event or many (i.e. a frequency) or, if one wishes to treat probability epistemically, the "coming into existence" of certainty of belief.

    The problem you pointed out with probability, namely "What kind of mathematical axiom can distinguish the probabilities from the rest? It seems that a probability interpretation must be added separately, and lies above and beyond the definition of the mathematical structure." stems in my opinion from the fact that Kolmogorov's axioms do not distinguish this special kind of measure from other more ordinary ones, such as, say, length and mass.

    In fact, I believe it cannot do this because denoting "coming into existence" is not a feature of the measure but of the sets on which the measure is taken, so in reality the problem manifests a limitation in the current foundations of mathematics, namely ZFC set theory.

    I am working on developing a foundation in which such a distinction naturally appears. The key, I believe, is to extend classical logic to what is called free logic, which permits the definition of what is called an outer domain. Sets in the outer domain fail to satisfy the criterion of "existence" in the domain of discourse, which is now called the inner domain.

    I believe that probability is naturally a measure over sets in the outer domain because the sets it measures cannot already "exist" in order for the interpretation of probability to be applied to that measure. If I am right, then this would allow for a natural means of formally incorporating the interpretation of probability, at least in the sense that it is distinct from other kinds of measures, into mathematics.

    I am not sure how this would impact your argument against the universe being a mathematical system, but I hope that you find these ideas at least interesting.

    Best wishes,

    Armin

    PS. I read the sample chapter of your "Relativity Made Real" book and found it to be very lucidly written. Given that you have written an entire book on relativity, I would very much like to know how you would respond if someone asked "what does it mean that for an object traveling at c, a zero proper time implies that a hypothetical observer at rest with respect to that object would measure his own duration of existence in spacetime to be precisely zero?"

      17 days later

      Neil,

      Thanks for the encouraging remarks :-D I know it became kind of telegraphic but I figured I may as well go for it since I probably won't be writing on this topic again, or at least I don't know of an appropriate venue. It's mainly food for thought, not an effort to present a fully developed philosophical position, something that would be beyond my abilities.

      Armin,

      Regarding probabilities, let me think about that and get back.

      Regarding relativity, an observer moving at speed c will not be able to measure anything because none of his/her measuring apparatus can function. This is because signal propagation is completely disrupted since two sub-components which are both moving at speed c cannot exchange signals. It's not possible to build any kind of working machine or even a cyclical process like a clock, out of purely massless matter.

      So it's not exactly correct to say the observer would "measure zero" for anything. There simply can be no such observer in any meaningful sense.

      4 months later

      Dear Bill,

      I only saw and read your response now, and would like to mention that at least in my view, the meaning of what you wrote concerning SR is really the same as what I wrote, because of all possible things one could measure, measuring one's own duration of existence to be zero would seem to be the one thing that would preclude any sort of measurement in the first place.

      What I really wanted to find out was your view about the implications one could draw from this, and whether you took any of these to be hints of a deeper understanding about what relativity really tells us about the world. I agree that it is not possible to have a spacetime frame that moves at the speed of light in space, but, it seems unlike virtually everyone else, I do not believe that this necessarily implies that such frames are altogether impossible. I wonder whether we are in this respect caught in a situation like our ancestors, who about 500 years ago, thought that the earth, moon, sun and a few planets was all there was to our world, and who could never fathom that (at least in principle) it was possible for observer frames to exist beyond the boundaries they recognized (e.g. frames on Andromeda, in which the entire Milky Way would be a small speck in the sky).

      If you had some thoughts on my remarks about probability, I would love to hear them.

      Best,

      Armin

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