Dear Sophia,

Your essay is near the top in quality of those that have appeared so far. Your topic sort of overlaps the last part of mine

http://fqxi.org/community/forum/topic/2320

I discuss largely the nature of mathematics I see shaping up that will be used by physics.

The reason that mathematics is used in physics is that we measure things and express that according to numbers. This of course goes way back with measuring weights, or distances and so forth. Physics of course has taken this to considerable extremes with measuring quantum eigenvalues and using measurements of scattering cross sections to back out quantum amplitudes and strengths of gauge interactions.

There are of course sciences that do not as heavily rely upon mathematics, such as biology. We have subjects such as psychology that have some small overlap with science, and this tends to reach a limit with sociology. Even these have some mathematics enter into their practice.

At the end you mention the linking of brains or minds, which will be facilitated with cybernetics. That might happen, and that will pave the way towards humanity becoming something other than it has been. We may become something completely different in the long run. This is of course assuming that we can survive far into the future. Under those conditions we can't know now what sorts of mental structures we will be thinking, or maybe groking or mind-melding, about.

Much of these alternatives you discuss are I think not demonstrable, or at least I see nothing either empirically possible or logically provable in order to support of verify one of these.

LC

    Thanks for your essay Sophia. It is interesting and well written.

    In the chapter "How to do science without mathematics", you explain that a computer might simply compare two subsets to find solutions without the need for a mathematical model. I might be wrong, but comparing two subsets is simple maths but it is still mathematics?

      Hi Christophe,

      I am glad that you liked my essay! It is a topic very to my heart. I am not sure what you refer to exactly, maybe it is a misunderstanding? In the examples that I mentioned, the computer is one of the subsystems, it does not do a comparison. The comparison would be a test of the hypothesis that the computer is a good model. Ie, you'd make some measurement and see if your model (the one subsystem) is good to describe (or predict) the other subsystem. Or were you referring to something else?

      -- Sophia

      Dear Lawrence,

      Thanks for the kind words :) I will go and check out your essay! I have been travelling and I am somewhat behind reading.

      Yes, I share your opinion that we may become something completely different in the long run. It's one of the reasons I don't buy into the idea that artificial intelligence is a danger to mankind. I don't think we will actually get to see a split in "intelligences", rather we will come to combine with that what we now call "artificial", to form something new that is "natural".

      You are right in that the alternatives cannot be verified, but then nothing in science can ever be verified. As Pragmatic would say, the question is which one works best.

      See, consider for a moment that the Human Brain Project (Google will tell you if haven't heard of it) will not work in the sense that the computer model, based on some algorithm (math) will not be a good model for the human brain. Imagine then that instead of programming one of the presently existing computers, we design another artificial system with connections much like the human brain, but rather than running an algorithm on it that is executing what we think it should be executing, we design the system so that its own interactions (laws of nature - maybe not math?) mimic that of the human brain. What is the difference? In the first case we push the time-evolution of the system into a mathematical form that we *believe* to be correct. In the second case we don't, we just map one system to another, regardless of whether the underlying laws are mathematical or not. The second case is very close to the idea of adiabatic quantum computing which I touch on in the essay.

      So imagine that was so, this would lend support to the idea that math either doesn't always work or that at least it might not be the most useful way to deal with the system. That for example would shed doubt on all the version in which math describes all of our observations. As I said, you can never really verify any of these, but then verification isn't within the scope of science anyway. I am convinced that philosophers will never run out of things to think about ;)

      -- Sophie

      Hi Sophia,

      I agree that the math approach is the easy approach. That's why current theoretical physics developments are conducted almost exclusively on a mathematical basis. However as you pointed out the math fist approach may not work. The math of super string theories requires eleven dimensions of space and time and there is no way to confirm the existence of these extra dimensions experimentally.

      I have chosen the physics first approach and I was able to come up with a physical model of our universe called Model Mechanics. The different aspects of Model Mechanics can be used to replace the various abstract math objects (such as field/virtual particles, curvature in space-time dark energy, dark matter....etc.) in our current math theories.

      I invite to read my essay and give me your informed comments. Thanks.

      Regards,

      Ken Seto

      I agree, the pragmatic physicist does not have the right to risk knowledge advancement on ethical restraint, on social conventions, nor on philosophical disputation. Predictability is the dominant reality. This is not unlike Machiavelli for the world of true science. Use what works.

        Hi. Interesting essay. Here are some thoughts about it:

        You pointed out that when we need to approach or make predictions about processes from the world (subsystems of our universe), solutions ("models") can be developed not only in the form of mathematical theories but also as other processes from the world that somehow "behave the same". My opinion is that almost all processes in the world are so relatively complex and depending on many parameters (both physical constants and initial states of systems), that it would be extremely unlikely to discover 2 processes that behave the same (give the same result), except for a few very simple phenomena, or if they are made of the exact same stuff, or if one of them has been precisely well-designed for the purpose of matching the other. And I think only 2 kinds of systems (that you mentioned) are generally able to receive that needed amount of design for this purpose: well-programmed computers, and intelligent minds understanding a subject.

        I mean, I don't believe in large usefulness for the other kind of "model" that you mentioned with the example of Analogue Gravity : they might provide vague similarities for specific processes but no full similarity, and cannot approach any accuracy I guess (sorry I did not check the article you gave as reference). For example, space-time outside the horizon of a black hole remains perfectly time-symmetric (if not distorted by a falling big mass); the time asymmetry only concerns what crosses the horizon. The acoustic model with a moving fluid does not show this fact, or at least does not make it intuitive. It can suggest some aspects but cannot be accurate because, well, moving fluids remain in a Galilean space-time and just cannot have a faithful correspondence with the curved space-time of General Relativity. Generally, digital computers can reproduce quite well any results that analogue models could provide (as any kind of analogue physical process can be described by known laws of physics, thus analyzed by these laws with methods of numerical analysis, except for quantum phenomena where classical computation would be inefficient, in which case making a quantum model, either "different stuff" quantum analog or by quantum computation, would be a hard problem anyway), with the advantage that they can be programmed to apply the exactly right law, while analog processes being subject to the specific laws ruling the stuff they are made of, are unlikely to behave the same as what we want.

        Strictly speaking, computer simulations are mathematical stuff, even if they can look quite different from what is usually presented as "mathematics" at school. However, computer solutions can be considered largely non-mathematical when they heavily depend on the input of big data, which has a non-mathematical origin (see Jaron Lanier's talk on the myth of AI describing the situation of automatic translation systems).

        Intelligent minds can also have both mathematical and non-mathematical abilities, that can be developed depending on needs. The advantage of mathematical abilities being their capacity of perfection to match a given rule, in case it would happen to be the right one; but I consider that only a mind can understand another mind, which is an ability beyond maths.

        Now about your attempt at classifying views with sentences such as "Observations can be math", "Observations are described by math but are not math". I don't think such sentences make much sense. You don't seem to take them very seriously in the rest of your essay, but why did you develop them in the first place ? In particular, I doubt anyone would claim an observation "is math". An observation may be said to be "described by math" if some mathematical structures can be found there, in the sense that the observation is shown to not be entirely random. However I do not see it as a binary question "can be described or cannot be described by math", but rather a roughly continuous, quantitative question "how much can it be mathematically explained" in the sense of "compressed by some algorithm". So it is another sort of mathematical way of describing how mathematical something is, but it takes more subtle mathematical concepts than such basic set theory concepts as you did. See more explanations in my essay.

          John,

          I'm not sure what you mean with "does not have the right". Who says what these rights are? My perspective on this is more one based on the mechanism of selection and adaption. That what works is what will bring us progress. It's somewhat tautological. The question whether scientists should conform to ethical codes or engage in philosophical disputation isn't that easy to answer because ethics also "work" towards something, so does philosophical discussion. They just work towards something different than describing nature. That's why I have been very careful with explaining what I mean with "it works".

          -- Sophia

          Hi Ken,

          Thank you for drawing my attention to your essay, which I will be happy to have a look at. It is not true though that there is no way to confirm the existence of extra dimensions. If you have enough energy to excite string states, this would have observable consequences. The problem is that at least in the simplest models, the energy necessary for this is way too high for us to reach. There may be other signatures of the additional dimensions though, such as the dynamics in the early universe. You are probably aware of this, I am just saying it to remind you that in contrast to other aspects of the landscape (multiverse), some properties of string theory are testable - in principle.

          -- Sophia

          Hi Sylvain:

          Thanks for your thoughtful comment. I am not sure why you say that "it would be extremely unlikely to discover 2 processes that behave the same" because that's what all of science presently works like! And the fact that it does then speaks against your opinion "that almost all processes in the world are so relatively complex and depending on many parameters". Or maybe I am misunderstanding what you are saying? As a matter of fact most systems that are presently described in physics are dramatically simple and depend on very few parameters. Think harmonic oscillator.

          The reason I have distinguished between the options that observations are math or can be described by math is that both are represented in the literature, and it seems a very fitting topic for the question of this essay contest. Y

          ou write "I doubt anyone would claim an observation "is math"." Then you haven't read Tegmark's paper, and apparently you also missed the explanation of it in my essay. If you do not think that observations are math, then what it is that makes an observation different from math? It can't be describable by math, can it?

          In any case, the whole point of my essay is to point out that while we may differ on the philosophical underpinning of science, in practice it doesn't matter.

          -- Sophia

          The threat of AI is not something that keeps me awake at night as much as other things. Our species has been very good at exploiting the environment to engineer positive feedbacks for us. We are now converting the planetary biosphere into a garbage heap. We are demolishing our life support system. These things keep me far more concerned than the problem of AI.

          The problem of AI taking over is worth keeping in mind though. I think we are seeing the integration of digital technology into us. Now we have wearable tech and Microsoft has its holographic view system, even though it has nothing to do with real holograms. I do see a real prospect for more direct brain computer interfaces (BCI) in the next few decades. We may see this intrude into the inner aspects of our consciousness, and we may in many ways end up in a sort of cyber mind-meld. Star Trek had the BORG, and I would not be too surprised if we end up in that state in the second half of this century.

          The question of AI "taking over," assuming there is much left here worth taking over, may come if we have adaptive and learning AI systems hooked to human brains. They might adapt and learn how to become more like the brain, which could in the end supplant the brain. These might form the basis for von Neumann probes that migrate out into the solar system and after hundreds of millions of years migrate across the galaxy. I see some prospect for this sort of thing happening.

          Cheers LC

          ``The pragmatic physicist - first name Pragmatic, last name Physicist - wants to describe observations and only bothers to think if thinking seems useful for this description.''

          I didn't notice any ethical restraint in this description. Ethical restraint, social conventions, and philosophical disputation have had a tendency to inhibit knowledge advancement.

          Survival is the only moral goal of life suggests ``rights'' come from the ability to survive. Those technologically advanced societies overcome lesser societies. Humanists would like to think Kant's view would win. But history has shown Hobbes' view of the leviathan is what nature allows over a long term. Kautilya's ``Arthashastra'' and Machiavelli's ``The Prince'' are good descriptions of international relations.

          5 days later

          Dear Mr. Fisher:

          You write "There is a real Universe." Please define "real" and "universe". Without that, your statement is meaningless.

          -- Sophia

          Dear Ms. Magnusdottir,

          I hope you are not admitting that you do not know what the words "real" and "universe" mean after admitting in your essay that your "Pragmatic Physicist did not care what the words reality and the universe meant.

          Curious Joe Fisher

          Hi Joe,

          I don't understand your remark. I am telling you that I do not know what you mean with the words "real" and "universe", and that I cannot reply to your comment unless you explain what you mean.

          -- Sophia

          Hi Sophia,

          I did appreciate your point in the conclusions section that there is no particular reason why models must be mathematical to be useful.

          I agree with this and I think there is a great value in spending time to get the descriptive model correct. It should be obvious to everyone that having a quantum theory in which there is no agreement on interpretation is missing something.

          I do however, feel that a model which has a clear top level description regarding properties that can be measured and related to a mathematical model is the most convincing and useful type of model.

          Thank you for reading my essay titled Solving the Mystery and I hope I answered your question on realism to your satisfaction.

          With best regards

          Richard

          Dear Sophia,

          Those words do not bear my definitions. When I entered the inquiry "definition of real?" into the GOOGLE Search Engine programmed into my desktop computer, the first definition it provided was:

          1. actually existing as a thing or occurring in fact; not imagined or supposed.

          When I entered the inquiry "definition of universe?" into the GOOGLE SEARCH ENGINE programmed into my desktop computer, the first definition it provided was:

          1. all existing matter and space considered as a whole; the cosmos.

          There is no real need for you to respond to my comments. I am right about the real Universe. I used the words real and universe correctly. Your abstractions filled essay about an abstract Pragmatic Physicist dealing with an abstract universe was entertaining, and I thoroughly enjoyed reading it and I do hope that it does well in the competition.

          Peacefully,

          Joe Fisher

          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