Phil,

Well up to you usual high standard and with signs of greater maturity of view. I hope my score helps keep you at the top. I particularly like your identification that the question can be just as well reversed (why is it that physics...). I do however have a couple of questions;

1) Do you really believe there must be a greater or 'super' symmetry hiding away behind the 'dipole' symmetry considered 'breaking' by Green and most particle physicists? ..and what would it bring. Do you think of the concept that the dipole may perhaps be the very quiescence of 'matter' (inc anti) as opposed to (maybe dark?) 'energy' alone?

2) This may be semantic, but suggesting a 'map of all things logically possible" would seem to many to be excluding QM and non-locality. Do you suggest QM; a) CAN have a 'logical' explanation. Or b) ??

Re 2; I hypothesise a 'quasi classical' mechanism that seems to reproduce it and reveal the mathematical 'sock switch' trick that hides it in my essay, so prefer a).

I hope you get to read mine. I feel that in 'stabbing in the dark' I've felt something, but how can we then expose what it really is when each of us has a different vision? Perhaps the value of reading these a essays is in converging those vision.

Well done, and very best of luck with the definitive judging.

Peter

    Dear Philip,

    Because universality is the central concept in your ontology, I wonder whether it would be appropriate to put logic at the point of universality. We usually think of universal concepts as the concepts which apply to everything. Similarly, universal principles are defined as those principles which apply to everything. The common view seems to be that the concepts and principles of logic are universal in this sense. Your chart includes all logical possibilities. If we try to organize and understand the realm of all logical possibilities, then I think we would begin by using the concepts and principles of logic. In a sense a very basic part of the meta-laws are the laws of logic. Of course, there are more specific meta-laws as well, including meta-laws for physics. But maybe I am misunderstanding the role of universality here. In any event, thank you for a stimulating essay.

    Best wishes,

    Laurence Hitterdale

      James, the world seems classical but that is only superficial. Quantum mechanics plays many roles in life.

      If the BICEP2 discovery had stood up it could indeed have allowed us to explore the effects of quantum gravity in the early universe. Sadly that seems not to be unless we can find a clear enough window through the dust. Other opportunities to see similar effects may come from direct observation of primordial gravitational waves or low frequency radio waves.

      Peter, supersymmetry was first conceived as a component of quantum gravity where it may be very hard to detect. If is important in making perturbative quantum gravity more consistent. In my idea of "complete symmetry" where there is a degree of symmetry for every degree of freedom supersymmetry is essential simply because there are fermions. All this is specualtive of course. I dont think there is any good evidence even in dipole measurements.

      So called quantum logic can be described using ordinary ideas in logic. We can pretend that it is something more general but I dont see it that way. Of course there are some mysteries in quamtum mechanics but I dont see them as questions beyond logic. Perhaps I am wrong.

      Laurence, I dont think you have misunderstood it. You have expressed it very nicely.

      Philip,

      Shark time when some are pulled under, so I am revisiting essays I've read to assure I've rated them. I find that I rated yours on 4/20, rating it as one I could immediately relate to. I hope you get a chance to look at mine: http://fqxi.org/community/forum/topic/2345 as the hours tick down.

      Thanks,

      Jim

      11 days later

      Dear Philip,

      This is very well written essay, and an enjoyable read.

      I read quite a long time ago, and I think I am now on my third read. I guess that I really have a different perspective.

      You have a logically-ordered ontology of mathematics which you present metaphorically. And central to this is the idea that there is some sort of universality around which the mathematics converges rather like a critical point.

      While on the surface, there is something attractive about this idea. However, there are some seemingly paradoxical aspects that arise the more that I think about it. First, you don't seem to differentiate between types or classes of mathematical theories or descriptions. And because of this, it then seems odd to develop such an ontology, since in doing so, the act of creating an ontology (or ordering) would be inherently mathematical. So this then begs the question "What type of mathematics allows you to develop an ontology of mathematics and where does this fit into the resulting ontology?" There is something circular about this that is unsettling.

      On a different point entirely, I think that it is very telling that you (even in your title) are relying on a metaphor. This creation of models via metaphor is a critical aspect of science. David Hestenes' essay takes this stance, which leads to mathematics as being an analogy-based tool for thinking.

      I agree strongly with his approach. Symmetries are particular cases of analogies, and in my essay, I show explicitly how the symmetries of associativity and commutativity (along with closure and ordering) result necessarily in additivity (up to invertible transform). Thus, any description of a system that has those symmetries must result in an additive theory. This suggests that the universality lies in fundamental symmetries (such as commutativity, associativity, distributivity---which are not the same as physics-based (higher-order) symmetries such as isotropy of space, gauge invariances, etc).

      Now, you actually make some comments about symmetry and note that some people see symmetries as being emergent. I believe that some are. They are emergent from the chosen description. But they still could be the source of the laws. Another objection that you point out is the fact that some theories known to be dual to one another are based on different symmetry groups. However, this is not an argument against the universality of symmetry. Instead it highlights consistency in/and among the chosen description/s.

      In the post above from Laurence Hitterdale, he points to logic as being the universal principle. In your response, you seem to agree with this. However, it is not specified which logic you two are discussing. But either way, logic is a particular example of symmetry/order, which again places those concepts at center stage.

      To me it seems that your exercise in constructing a metaphor for an ontology of mathematics highlights the critical nature of metaphor and analogy in science, which supports symmetries as being central as Hestenes and I discussed in our essays.

      I think that there are some deep ideas/insights here that can be extracted. I would like to know your thoughts if you have a chance.

      Again, thank you for a very enjoyable and thought-provoking essay.

      Kevin Knuth

        Kevin

        Thank you for your insightful comments

        I don't think there are really different types of mathematical theories. There is just one self-referential logical whole. We see it from the inside as participants and like children who rep4eatedly follow every answer with the question "why?" we are never satisfied with a final answer. Yet I think that the class of logical possibilities is as far back as you can go. We have to accept that it is consistent because we know that cannot be proven from within the system other than by the fact of our own being.

        I may overstate the metaphorical aspects of my ideas but I do so to try and keep things separate from the physical models and ideas that our minds are programmed to look for. Sometimes we seek explanations for things that are not there. Inspired by the words of Marc Seguin I would put it like this , consciousness is biology plus noithing else, biology is physics plus nothing else, physics is maths plus nothing else, maths is logical plus nothing else and logical is just nothing else. We look for more in our minds by trying to decide what exists and why and where it came from. We can only express these questions by analogies from our physical experiences. This is a good way to gain some philosophical understanding but we should not lose sight of the fact that they are just metaphors

        I agree on te importance of symmetries is algebra but I think that gauge symmetries are the same thing. That is where they come from. In fact the meta-laws have much more algebraic symmetry and the symmetry we know of in physics must be part of a much greater whole. This is the only way to explain the holographic principle for example. The algebraic symmetries are more fundamental but the physical gauge symmetries are what remains of them when the solutions of the algebraic equations are mapped to emergent space and time. I hope one day people will understand in detail how this works using the principles of category theory, algebraic geometry and the like.

        I think computers would understand real numbers the same way we do, through symbolic logic. You dont have to be able to understand every individual real number to be able to explore the properties of real numbers as a whole. This is the same for humans as it is for an AI. Mathematica and other symbolic logic programs can already handle real numbers in this sense.

        I think that once we know the rules for constructing the possible vacuum states it is going to be a huge challenge to work out exactly what it is.

        It may turn out not to be so hard or it may be so hard that we can never work it out completely, either because the necessary experiments are out of reach or because the computation is too complex.

        The most interesting scenario would be that it is possible but only after some very clever experimentation and computation, but we will have to accept whatever nature has in store for us.

        It was the most abstract, complete and general algebraic object I could think of.

        Science works both ways. Sometimes theorists make predictions that are then verified by scinece, but sometimes experienters find things that were not predicted and theorists have to find the right theory for them. There are plenty of examples of the latter e.g. the muon, law of black body radiation, constancy of the speed of light etc.

        Particle accelerators search for predicted particles but they can also find things that were not predicted. This is done by continually measuring every quatity at higher and higher energies and checking to see whether they match predictions from accepted theory.

        While accelerators are limited in energy scale, the other experiments I mentioned are not. proton decay could give us information about the GUT scale for example.

        You dont need a formal framework to find something new. As soon as something does not match the existing framwork you can start looking for what might explain it.

        Sorry, but I dont see this contest as an exercise in popularisation. If we had to write for people who dont know any fundamental physics we could not explain very much in nine pages.

        basudeba, the "unexplained" questions you ask about string theory are very ordinary questions whose answers are well understood by string theorists. I am afraid you will just have to accept that it is only to you that they are not explained or understood.

        The "new way of thinking" is not "giving up" . That is just the opinion of the old guard who does not understand the unexpected truths that new discoveries are telling us. That has always been the way science has progressed.

        8 days later

        Thanks to everyone who commented and rated my essay. This was a subject that I started thinking about 25 years ago so I was very happy to have the chance to write about it here. I dont take the final placements seriously. I used to wish for a prize place in these contests but now I realise that the winners tend to be those who take the safer options. If I win I will feel that I was not sufficiently controversial. I like to imagine that in a hundred years time someone will revisit the essays to rate them in the light of future discoveries. I aim to write for that rather than the present judging. Perhaps it is a good thing I wont be here to see the result.

        Questions I would like to see for future contests are:

        - Can we explain consciousness?

        - Is there merit in the multiverse?

        - Why is there symmetry?

        - Why the quantum?

        - Where are the aliens?

        - What is the long-term future for humanity?

          a month later

          I am very honoured to receive a prize in this years contest. Congratulations to all the winners. To those who did not make it I say dont be disheartened. These contests are a bit like mother and baby contests and we all think our baby is the most beautiful. It is hard not to feel offended when someone elses baby is judged to be better but the judges are only human and following their own opinions. My guess is that the unknown judges are not always the high level experts we imagine them to be so the result is just one set of opinions and not necessarily the most important one. The truth is that all the babies are beautiful in their own way and we will have to wait for them to grow up before we have the hindsight to judge their real ptoential.

          I suppose that I should now follow my words prior to the announcement and say that my essay was not radical enough because it won a prize. However I have to point out that they had to invent a new lowest ever fifth level of prizes and a special category of non-academic author to get me in :-) Some people are going to think that I dont fit the non-academic label bacause I have a PhD and have published in academic journals, but all of my work on this topic has been carried out independently of any academic institution over 28 years so I think it is right. I dont think I am the only prize winner that fits this description. It is good to see that top places are going to some non-FQXi members this year.

          A lot of the prizes went to people who argued against the mysterious nature of mathematics in physics. Most notably the first prize to Wenmakers who argued that mathemaricians are just following the influence of the physical world. Most pure mathematicians would strongly dispute this and they are right. They are very capable of exploring abstract ideas independently of any kind of real world application yet such applications frequently appear later. The manner in which ideas from physics are unexpectedly applied to problems in pure mathematics is even more striking. The moonshine conjecture is just the most obvious example of this.

          Looking forward to the next essay or video contest. Thanks to the people at FQXi who worked hard behind the scenes to make this work.

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