Dear Madam,

Your essay is poetry written in prose format. We wish you could have used a gender neutral format like 'it' because there is no bare charge or bare mass. Every perceivable information / object is composite with positive (male) charge in the center (central like bone) confined by negative charge (female exterior like flesh) with both protecting each other differently. Their net internal dynamics makes them male or female (if one extra y chromosome, then male; if in pairs, female. If moves out, positive; if moves in, negative). Human consciousness might have "a non-physical component", but it is revealed only through a physical body. Reality or existence is whatever has a limited structure that evolves in time and is perceivable / measurable directly or indirectly, is intelligible (perceivable or knowable as the result of measurement) and communicable universally (describable in a language as defined in our essay: Transposition of information to another system's CPU or mind by signals or sounds using energy. The transposition may relate to a fixed object/information. It can be used in different domains and different contexts or require modifications in prescribed manner depending upon the context). Thus, wittingly or otherwise, you have included reality in your discussion - "not a follower of the shut-up-and-calculate doctrine".

A model can explain reality, but can we be sure that it fully explains it, particularly when manipulations of its theory-laden characters are influenced by the thinking of the scientist, which in turn are influenced by the social factors - spirit of the age! Reductionism has its own limitations. There is a story about six blind men, who went to see an elephant. Each touched only one part of the creature - leg, trunk, ear, belly, tooth, tail - and described the elephant by that experience only. Though all their descriptions are valid, one who has not seen an elephant cannot make any sense out of their combined statements. The Universe does not duplicate itself. Though all quarks look same and cannot be distinguished from each other, they are different. When you stretch a quark too much, it gives rise to another quark by drawing material from the environment. It does not 'become two'. Thus, you have rightly pointed out that "it also must contain a prescription to identify the mathematical structure with observation".

While science without technology is lame, technology without science is blind. With over-emphasis on the effectiveness of technology, its 'blindness' is increasing, which is manifest in various social and environmental problems. A very large number of people enjoy a cozy life in pursuing and teaching nothingness or self-destruction. We may enjoy temporarily, but ultimately everyone is going to suffer. We have discussed these subjects elaborately in our essay. You are welcome to read it because of many similarities.

Dear Sophia,

I find the quality of many of the essays in this competition below expectation. Yours is a refreshing exception, although I would have wanted to challenge Mr Pragmatic Physicist with some questions about what is real and what is not. I also find refreshing the subtle mix of humour in a serious discussion. I think the essay is destined to do well in my opinion at least.

Since in matters of physics and mathematics, you seem to have a pragmatic and practical mind all rolled into one, I might want to ask you a few questions on what is real, if it is pragmatically correct to ask it here or will do so at my thread, whichever is your preference.

Regards,

Akinbo

    Dear Akinbo,

    I agree on what the quality of the essays is concerned... :/ what bothers me even more though is this weird rating procedure in which participants rate each other's essays. To make matters worse, they can even see the average rating from other's ratings. I certainly wish that the responsible FQXi folks would read Surowiecki's "Wisdom of Crowds", esp the part about information cascades, then they'd see that nothing sensible can come out of this.

    In any case, it seems rather futile to complain about this. It must be difficult for FQXi, one the one hand to be open-minded, on the other hand to not be overrun by low quality entries, and then find a fast way to sort out the trash.

    I don't know what is real, or let me say Pragmatist doesn't know, just so we can get over somebody's personal (your or mine) experience. The only way Pragmatist can make sense of it is as a relative measure. You could say then that something "is as real as" something else. The question then is whether mathematics is "as real as", say, you. This is a question which seems well-defined. I don't know what to make of an an absolute "reality", I cannot find any basis for it. I myself have an unfortunate tendency towards solipsism, based on some personal experience, but Pragmatist would discard this as useless. I will check out your thread.

    -- Sophia

    Dear Joe:

    Proof by Google! Oh-oh. What do we get? Explaining "real" as "actually existing" is recursive. You now have to explain what it means to "exist". Will you explain that existing means it's real? (What does Google say?) As to the universe, this is certainly the origin of the word, but as I explain in my essay it is as a matter of fact not how physicists use the word today.

    -- Sophia

    Dear Pragmatic,

    very pleasant read indeed. A message that builds up during reading but also, it seems, during writing! Nice narrative idea and style.

    Perhaps my favourite passage is the one in which you admit to ignore why the All displays recurrent, reproducible, often self-similar subsystems, but identify in these features the key for an effective coupling with the mathematical language, which delivers simplified universal models that are reproducible and reusable. So, the marriage between a world with much regularity and a language with much 'universality' (absence of human baggage) and reproducibility appears, at least at first sight, very possible, although your treatment, being necessarily concise, cannot dig into the details, where the devil is often hidden (in marriages in particular...).

    With respect to the question of why features such as regularity and self-similarity, interspersed with chaotic ones, are so frequently observed in the subsystems of this world, let me just point out that the assumption of a fundamentally algorithmic nature of the universe appears to some physicists, e.g. S. Lloyd, as a very attractive explanation (the last figure in my essay illustrates the idea).

    Your essay is one of the few I've read so far that offers - starting from the title - a generous attempt to address the very hard question about possible alternatives to mathematics for modelling the observable world. The requirement for such an alternative model to support predictions beyond the 'wait and see' barrier, and to describe many subsystems, not just one, is also very well stated in several passages.

    The answer you provide to this hard question is appealing, at least at first sight: use subsystems for modelling subsystems - establish a reproducible link between them. It's also a very economic solution, in that it does not bring on stage new actors. The example of Analogue Gravity explains well the idea.

    But your proposal triggers a question.

    The marriage between mathematical model and physical subsystem is asymmetric, in the sense that the model abstracts away the details of the modelled object: it represents an equivalence class of phenomena (subsystems), each happening at different places and times. In the subsystem-subsystem marriage, this is lost: both subsystems have fuzziness, so to speak. One might suspect that mathematics is still necessary, for extracting the universality behind BOTH of them.

    Thanks and best regards

    Tommaso

    P.S. Is there not any Pragmatic Computationalist in your wider family tree?

      Dear Ms. Magnusdottir,

      I enjoyed your story of Pragmatic Physicist.

      I am a pragmatic physicist with a vivid pictorial imagination. In my mind's eye, I see real waves and particles propagating through space and interacting with each other. I believe that this physical intuition provides a better insight into physical theory than mathematical formalism. Indeed, humans have a natural propensity for visual image processing; mathematics is more difficult. However, theoretical physicists are taught to reject physical intuition since it is unreliable, relying only on mathematical formalism. I believe that this is a mistake.

      In my essay, "Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory", I argue that premature adoption of an abstract mathematical framework prevented consideration of a simple, consistent, realistic model of quantum mechanics, avoiding paradoxes of indeterminacy, entanglement, and non-locality. What's more, this realistic model is directly testable using little more than Stern-Gerlach magnets.

      Alan Kadin

        Physics without math appears impossible because we need numbers when we make measurements. Numbers are part of math. I do see see how we can do physics without math. Probably someone who knows no math can conceive a physical theory but physics goes beyond conception and requires measurements. Measurements are impossible without math. Can you offer a compelling argument about the possibility of measurements without any math? That would be really interesting.

        There is also another alternative: Math progresses so much that humans are no longer necessary, they can described mathematically and saved on a chip along with their world.

          Dear Tommaso,

          You have picked out a very important point indeed, one that I had to gloss over due to lack of space. The real mystery is, in fact, why do we find ourselves in an environment that has so many self-similarities - both over space and over time?

          I don't think that mathematics is really necessary to extract them, but it is definitely useful, and I think that this is essentially the reason why we find mathematics useful, 'unreasonably useful' even.

          One may suspect - and I apologize in advance for the anthropic smell ;) - that these self-similarities are necessary somehow for the evolution of life, or for that life to be able to start recognizing any regularities at all, which is essential for evolution. See, if nature wasn't so reproducible and, in a sense, reliable, life would never adapt and could never evolve.

          Somewhere in the multiverse there is a Computationalist in Pragmatic's family tree...

          -- Sophia

          Dear Alan,

          I agree with you that humans have a natural propensity for visual image processing. In fact, the human eye-brain team is still vastly better at analyzing visual information than any computer. I think that the relevance of data vizualisation for human understanding and, ultimately, scientific modeling, is often underestimated. Alas, I see no reason why not this should eventually be possible to do by a computer.

          I am vary of the idea though that intuition is better than mathematical formalism. Human intuition did not develop to explain phenomena that we have no physical perception of. I will look at your essay and read it with interest.

          -- Sophia

          Numbers are an intermediary. They are handy, but you don't need them. You can determine for example whether the height of a quicksilver column is as high as the height of a sandpile without ever writing down the height of either. What you need to make predictions is not the number, you need to know what to do in reaction - you need a model system, but that system doesn't have to be numerical in any sense.

          Besides, the point isn't that we should do science entirely without math, but that math might not be sufficient, and that's no reason to give up on doing science all together. Ie, use numbers where useful, but what do you do when they're not useful? That's the point I addressed in my essay.

          Hi Sophia,

          I certainly agree with you that regularities and self-similarities are very useful, perhaps necessary, for the appearance and support of life, and for us to have some chances to make sense of this universe; and I certainly accept your apologies for the anthropic smell of the idea :-}

          But you can't imagine how cheap and frequent it is to obtain periodic and selfsimilar structures from randomly chosen algorithms that run on simple or random inputs - as your remote computationalist relative could confirm.

          When I first bumped into self-similarity (I bought Mandelbrot's 1977 book on Fractals in 1978) I thought these were cute but rather abstract and abstruse forms. In fact, it is easy to see that they are simply another form of periodicity. And, for example, out of 256 elementary cellular automata (with elementary initial conditions), over 20 develop self-similar patterns. Fractals are the A-B-C of the infant computational universe.

          Ciao

          Tommaso

          PS - I replied to your kind comments in my page.

          "Numbers are an intermediary. They are handy, but you don't need them. You can determine for example whether the height of a quicksilver column is as high as the height of a sandpile without ever writing down the height of either."

          What about determining the volume of a hypersphere? Is there anything to compare it to? I do not only disagree with what you say but I also argue that as long as we establish a comparison we have essentially established a number system: we can call the standard element "1" and start from there, out standard meter for example.

          ",,, but that math might not be sufficient,"

          I agree with that. Obviously math is a tool but not what reveals the truth, if truth exists anyway. Thanks.

          Hi Sophia,

          your "mathological" classification is really cute. Introducing the word "ALL" for those wishing a multiverse with 1e500 universes is very instructive. All in German means really all, i.e. everything including infinite in space and time.

          I read your essay from the first line to the last and liked it.

          Best

          Lutz

            How can a non-physicist take the perspective of a pragmatic physicist? Is it beyond grasp.

            I think this essay is the result of a lack of understanding of what physicists do.

              You downrated my essay because I'm not a physicist? This will give me something to think about...

              Hi Lutz (Susanne?),

              I am glad you liked it :) Do you think somebody really "wishes for" a multiverse? I have the impression it's more like they're trying to make the best out of it, even tough nobody really likes it. Best,

              -- Sophia

              5 days later

              Dear Sophia,

              Your narrative is beautiful. Words speak volumes that numbers cannot begin to represent. You don't need to be a physicist to think; indeed one cannot think without words. You are correct in pointing out that 'It is shortsighted to just dismiss philosophy.' We do not need to be reminded of Plato's perception that philosophy is the 'spectator of all time and all existence' (i.e. your 'O' for all possible observations). Thus philosophy can be viewed as a reasonable link between physics and mathematics.

              Mathematics is a number of things, none of which add up to a plausible description of anything. I appreciate that you are not led astray by the sheer weight of 'nothing'.

              Certainly some 'observations are described by math but are not math and not all observations can be described by math'. What is the mathematical description of the observation of love? The same question can be applied to all our immeasurable affections. Where was math when they were first experienced?

              How many math descriptions are required to adequately cover the multiple meanings of the word 'course'? Forgive the question, but to assume that there is any such mathematical equation is a non-sequitur, an illogical inference - of course!

              It is unfortunate that some refer to 'The laws of nature'. Laws, like mathematics, are inflexible. Nature is nothing if not flexible. Substituting the term 'principles' for 'laws' is more fitting insofar as principles accommodate ranges of flexibility.

              In speculating upon the possibility that 'the day will come when we can link human brains and language will become an unnecessary intermediary of communication', are we not overlooking the point that the brain's network of consciousness (aka the mind) relies upon language as the means by which to transmit, receive and thereby share 'useful' information.

              Thank you Sophia. Keep unloading your 'network of consciousness' upon the rest of us.

              Gary Hansen

                Dear Pragmatic Physicist -

                Thank you for such a delightful essay! Such a practical and commonsense approach, I admire it greatly - Hakuna Matata!. I was thinking you had given me a great new way of thinking about mathematics, physics and the world - one that really made sense. But then you asked whether M is in M, and I must admit I've been spinning my wheels ever since. It also made me wonder - I observe myself, so I am in O, but since O is that which I observe, O must be in me, and then I think this statement must be false. Oh dear, I just can't keep this all straight, and I just can't see how taking the math our\t of physics is going to help......

                Hoping you can enlighten me! With sincere regards - Musing Metaphysician (aka George Gantz)

                .

                I must beall that I observe, so I must be outside of O. isn't O in me or outside of O since I make observations in O, and one observation is that I observe myself making observations in O.

                n O are about mysel making statements so am I in O?