Essay Abstract

Assumptions about what is a theory and what is a mathematical model are considered related to the question "How can mindless mathematical laws give rise to aims and intentions?". Theory cannot be reduced to a mathematical model and requires conceptualization. So aims and intensions arise from the concepts, not the mathematics. From this the question of whether we have the appropriate mathematical tools to model aims and intensions is considered.

Author Bio

Trained as a mathematician, Donald Palmer has followed the world of computers in his career. He received a BA in Mathematics from Earlham College, then a Masters in Mathematics from Villanova University. He ran his own computer services and software development company for 11 years, before entering the bio-pharmaceutical world, where he now works designing software. He has worked on numeric representational concepts and written a short book on modeling of scale in the physical world.

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Dear Donald,

Good essay, which makes many important points.

I agree that "It would be a dangerous mistake to think the mathematical models are either the reality or, by themselves, can define reality.", and that

"If we consider 'random' to mean 'without rules or laws', then it seems difficult to understand how directed change, with or without 'aims' and 'intensions', can occur. Some action that changes randomness into directed change (according to some rule or law) would be required, which would seem to violate the initial assumption of randomness everywhere. So the concept of 'random' as meaning 'without rules or laws' can be easily discarded. Science presumes there are rules and laws (that humans can understand) that govern the universe.", and that

"Mathematical structures are needed for the 'how' of directed change as well as the 'where' and 'when', but not the 'what' and 'who' and certainly not the 'why' of change. The 'what', 'who' and potentially 'why' involve conceptualizations and theory - not mathematical laws.", and that

"Does this inclusion of all possibilities mean we have an explanation or even a model of aims and intensions? The model purports to 'explain' our universe, but, as noted before, the mathematical model is not reality. If the model accurately mimics reality, then using probability we should be able to provide the specific results of one or the other situation (will the tossed coin come up 'heads' or 'tails'?). However, this is precisely the results that the mathematical structure of probability cannot provide - the results of a specific situation."

    Donald,

    Great essay, beautifully written and compellingly argued. It helps that I agree on every point. Would you agree my logical 'Law of the Reducing Middle' (removing the problematic 'excluded middle') so Bayesian between 2 of anything including sheep!?

    I greatly appreciated reading from a trained mathematician; "The mathematics of a physical theory is an attempt to model physical concepts using mathematical structures. The physical concepts and how they interact are the center of the theory, not the mathematical equations."

    I see it's been trolled with a 2 (mine had had four 1's!). My score should get it where it should be. But what I really want to discuss refers to;

    It would be a dangerous mistake to think the mathematical models are either the reality or, by themselves, can define reality. . ... "(does the Schrodinger equation 'collapse' or not?)".. ..".These random actions are modeled via mathematical structures of probability. So we use probability to model non-random laws. Is this mathematical structure sufficient to provide for aims and intensions in intelligent humans? ..the mathematical structure of probability cannot provide - the results of a specific situation." . "....is this mathematical structure simply the best we can find, at this point in history, to model reality?"

    You'll know that QM has the mathematical model which predicts results, but no 'theory'. My essay does what's considered inpossible; identifies a classical mechanism producing the findings so corresponding the the mathematics (essentially Diracs twin stacked orthogonally offset/complementary Cos[sup2 'spinors').

    I do so after explaining why this will be 'invisible' to most because it's already well explained by the maths and wierdness! (really cognitive dissonance). But you may be who I need to 'see' it and collaborate with the slight refinement of the mathematical model required (for accuracy but mainly to convince those who still believes maths is primary)

    I do hope you'll get to read my essay and discuss. There are also long and very short (100sec) videos, the latter; Classic QM https://youtu.be/WKTXNvbkhhI

    Very well done and thank you for yours, which I'm scoring now.

    Best of luck.

    Peter

    pj.ukc.edu@physics.org

      Thank you for the kind words, Peter,

      I have read your essay and find it quite interesting. Only having mathematical aspects of a theory can lead to mis-understanding of what we are doing.

      I agree we do need to re-consider certain assumptions underlying current physics. In particular is the assumption that we have the appropriate tools (mathematical as well as theoretic) in order to properly model reality.

      I have argued, in a few places, that we need new (rather extended) mathematical tools in order to measure aspects of the universe we currently are unable to measure. In addition, we need to consider if we have a correct theoretic concept of the universe - do we really only experience three dimensions?

      Let us all work toward a new understanding!

      Take care,

      Don

      Dear Donald,

      I found your essay interesting. I have also focused in the fact that aims and intentions are not in the bare math, they arise from us when looking into that math. You have stressed the more conceputal part of this idea, I dealt with the information flow that I believe to take place in the observer's mind. I would appreciate your thoughts about it.

      By the way, just before reading your essay, I read Ian Durham's - whom I do not know, and have no connection with. I just thougth it was funny, because the two of you seem to show opposite points of views, and I happened to read them consecutively. If I understood him right (you should read it yourself) he seems to argue that directed change can indeed arise from a random world - whether the same happens with free will, intentions and so forth is less clear. I am curious to know what you think about his toy universes.

      Thanks for the interesting read!

      inés.

        Thank you for your insights, Ines

        I will read the other essays and get back to you

        Don

        Dear Don Palmer,

        Thanks for your comments and for your essay.

        You begin your essay by noting the physical concepts and how they interact is at the center of the theory, not the mathematical laws.

        You also note that the mathematics of the physical theory is an attempt to model physical concepts using mathematical structure. This seems in complete agreement with my contention that mathematical structure is projected onto reality. In early days the structure was intuitive, probably because our neural nets were 'tuned' by survival to identify mass, force, momentum, speed, etc. Once Planck's constant entered, we began projecting matrix structures and other non-intuitive structures, and the 'conceptions' couldn't keep up.

        Your example of a pendulum as a specific physical model that shares 'harmonic motion' with many very different models is excellent.

        Your perspective fits well with my model. I conceive of the consciousness field as a real physical field that possesses the properties awareness plus volition. I do not try to model these mathematically. I'm not sure it makes any sense to model subjective self-awareness, which is non-linear and non-measurable. On the other hand, if the field is to interact physically with the material world, which it obviously does, then it should be capable of being modeled in that sense. So I do have equations that describe the input/output interactions; what the field physically senses and how the field can act on matter. I do not model the 'aims and intentions' mathematically.

        Thus, as you so clearly state, the field cannot be reduced to a mathematical model, yet it's physical interaction behavior is modeled mathematically. The theory is mathematically modeled in physical interaction, but only conceptually modeled in the 'mental' properties. It certainly matches your key point that the conceptual model is primary, rather than the mathematical structures.

        You note that it would be a mistake to think that the mathematical models are either the reality, or, by themselves, can define reality. This is congruent with my discussion of quantum theory, so buried under complex structures that reality vanishes at times.

        To summarize, you observe that if we only consider the mathematical structures, we will not see any 'what', 'who', or 'why' involved. These relate to conscious awareness and volition. We see 'how' the fields interact with matter, sensing or directing change.

        So thanks again, your essay has helped me elaborate on my own theory.

        Best regards,

        Edwin Eugene Klingman

          Edwin,

          Thank you for reading my essay and your congruent thoughts regarding it.

          Having read yours, I think we have a good bit in common - as you note your 'math maps projected onto physical territory' is the same as mine (using different words).

          A number of physicists have commented on the need for new mathematics in order to progress physics. I will suggest that the direction of these new mathematical tools is the need to 'upgrade' our 500 year old system of numeric representation (decimals and positional numeric cousins) in a way that expands numeric representation to complex numbers. There is a price for this change, which involves some re-routing of current paths - however the gains are many entirely new paths.

          If we could put a numeric value to sqrt(-1) (or 'i'), then the 2-part character of complex values (x iy, which is not a complex number, but the representation of a complex number) simplifies to a single value. We would not need to 'throw out' the 'imaginary' part in order to produce 'real' observable results (what does this part represent is where some new paths emerge). This could radically change how and even what we can calculate.

          Note that Donald Knuth already did this more than 50 years ago, so this is not a fantasy.

          Some ideas that could assist physics and mathematics expansion...

          Don

          Dear Donald G Palmer,

          Please excuse me for I have no intention of disparaging in any way any part of your essay.

          I merely wish to point out that "Everything should be made as simple as possible, but not simpler." Albert Einstein (1879 - 1955) Physicist & Nobel Laureate.

          Only nature could produce a reality so simple, a single cell amoeba could deal with it.

          The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

          A more detailed explanation of natural reality can be found in my essay, SCORE ONE FOR SIMPLICITY. I do hope that you will read my essay and perhaps comment on its merit.

          Joe Fisher, Realist

          Hi Palmer

          I am in total agreement with you regarding the mathematical structures being different from physical conceptualizations. While the former can lead us astray without the guidance of the latter (monkeys on a typewriter was a great analogy), the latter on its own will not help us either (it would be a world where mathematical predictions cannot be undertaken). I also agree that the what, who and why belongs with physical conceptualization, while the other three - when, where and how belongs to mathematical domain.

          It is good that you devoted your essay to make this subtle, but essential point. I had struggled with this distinction subconsciously while composing my essay, and that struggle is perhaps evident in the way the title of my essay was framed.

          However, I differ with you on current mathematics being unable to support a theory dealing with 'aims and intention'. My essay might be offering a possible glimpse of how really simple such a theory could be. The main challenge is to deal with the physical conceptualization in a way that is sensible enough.

          Warm Regards, Willy

            Nice essay Palmer,

            Your ideas and thinking are excellent

            Theory cannot be reduced to a mathematical model and requires conceptualization. So aims and intensions arise from the concepts, not the mathematics.

            A more direct concern for understanding where 'aims' and 'intensions' come from is the assumption that the universe is basically random (defined loosely). If we consider 'random' to mean 'without rules or laws', then it seems difficult to understand how directed change, with or without 'aims' and 'intensions', can occur

            ............... At this point I want you to ask you to please have a look at my essay, where ...............reproduction of Galaxies in the Universe is described. Dynamic Universe Model is another mathematical model for Universe. Its mathematics show that the movement of masses will be having a purpose or goal, Different Galaxies will be born and die (quench) etc...just have a look at my essay... "Distances, Locations, Ages and Reproduction of Galaxies in our Dynamic Universe" where UGF (Universal Gravitational force) acting on each and every mass, will create a direction and purpose of movement,

            Universe is not chaotic but moves under UGF

            I think intension is inherited from Universe itself to all Biological systems

            For your information Dynamic Universe model is totally based on experimental results. Here in Dynamic Universe Model Space is Space and time is time in cosmology level or in any level. In the classical general relativity, space and time are convertible in to each other.

            Many papers and books on Dynamic Universe Model were published by the author on unsolved problems of present day Physics, for example 'Absolute Rest frame of reference is not necessary' (1994) , 'Multiple bending of light ray can create many images for one Galaxy: in our dynamic universe', About "SITA" simulations, 'Missing mass in Galaxy is NOT required', "New mathematics tensors without Differential and Integral equations", "Information, Reality and Relics of Cosmic Microwave Background", "Dynamic Universe Model explains the Discrepancies of Very-Long-Baseline Interferometry Observations.", in 2015 'Explaining Formation of Astronomical Jets Using Dynamic Universe Model, 'Explaining Pioneer anomaly', 'Explaining Near luminal velocities in Astronomical jets', 'Observation of super luminal neutrinos', 'Process of quenching in Galaxies due to formation of hole at the center of Galaxy, as its central densemass dries up', "Dynamic Universe Model Predicts the Trajectory of New Horizons Satellite Going to Pluto" etc., are some more papers from the Dynamic Universe model. Four Books also were published. Book1 shows Dynamic Universe Model is singularity free and body to collision free, Book 2, and Book 3 are explanation of equations of Dynamic Universe model. Book 4 deals about prediction and finding of Blue shifted Galaxies in the universe.

            With axioms like... No Isotropy; No Homogeneity; No Space-time continuum; Non-uniform density of matter(Universe is lumpy); No singularities; No collisions between bodies; No Blackholes; No warm holes; No Bigbang; No repulsion between distant Galaxies; Non-empty Universe; No imaginary or negative time axis; No imaginary X, Y, Z axes; No differential and Integral Equations mathematically; No General Relativity and Model does not reduce to General Relativity on any condition; No Creation of matter like Bigbang or steady-state models; No many mini Bigbangs; No Missing Mass; No Dark matter; No Dark energy; No Bigbang generated CMB detected; No Multi-verses etc.

            Many predictions of Dynamic Universe Model came true, like Blue shifted Galaxies and no dark matter. Dynamic Universe Model gave many results otherwise difficult to explain

            Have a look at my essay on Dynamic Universe Model and its blog also where all my books and papers are available for free downloading...

            http://vaksdynamicuniversemodel.blogspot.in/

            Best wishes to your essay.

            For your blessings please................

            =snp. gupta

            Dear Willy K,

            Thank you for reading my essay and for commenting on it.

            You have a number of interesting ideas and provide some great quotes.

            This appears to be me to be a model of how humans could be manifesting extrinsic intelligence, but it seems build upon a single governmental structure. How would this model the government of a singular leader (eg. a King or Emperor)?

            While I grasp that you are putting forth a model, I find it difficult to understand how this model is mathematical, beyond being a set of nested squares. Typically, a mathematical model involves measurements and/or quantifiable characteristics that are related in some operational (eg. arithmetic) manner. I do not see any of these defined in your essay and so do not understand how this is a mathematical model.

            I wish you well in developing your model.

            Don

            Hi Donald,

            Your essay is clear and takes the mysticism out of mathematics. Very nicely done. Do look at my essay and let me know what you think.

            Thanks for one of the best essays,

            Don Limuti

            Dear Palmer

            First of all, thanks for allowing the possibility that humans could be manifesting extrinsic intelligence. That is the real major point of my essay and I am glad you are positive there. Everything else can be improved given time.

            Regarding dictatorial governments, my essay would simply note that such a structure does not qualify as an intelligent system. But that does not mean that the dictatorial system is not successful in carrying out some basic regulatory functions. As far as comparisons go, we could compare it to the difference between chimpanzee brain and human brain. I have actually already expanded my work to include this comparison (not yet published). You showed great insight in anticipating that expansion.

            On the work not being a mathematical model, I actually agree! I have only claimed that it is a 'mathematical structure'; because it is clearly more than just a conceptual structure (conceptual structure would just imply human language). I did claim 'goal-free mathematics' and 'mathematical laws' because I thought they are inherent in all mathematical structures. I am not sure but you may disagree here. Regarding the modeling itself, it has got lot more ground to traverse before it can claim to be a formal mathematical model with all the definitions that are well laid out.

            Thanks so much for taking the trouble to review my essay. I rate your own essay highly since it brought up those difficulties I was struggling with in such a poignant manner.

            Warm Regards, Willy

            Dear Donald

            Well, I could not agree more with you! Of course that mathematics is a tool, a powerful tool but just a tool. In spite of being an essential tool.

            Mathematics allows an easy way to have control over phenomena. You take any set of data and it always possible to make a mathematical model that fits the data. It is like determining the polynomial that fits a set of points in a plane. It is just a question of adding enough parameters. Do you know when we know that a model has no physical information, it is just a mathematical model that in no way is a model of reality? When to each new kind of data it is necessary to add a new parameter. Of course that to these parameters are given fancy names, like dark matter, dark energy or even neutrino. The parameters are easy to identify because they represent just one property - a field, or an energy - while a physical entity is always a set of parameters.

            But it is not just a question of having control: Mathematics are a fundamental, essential tool for discovering the universe. It is thanks to it that we can make first models of data, which allow the discovery of more data, which can then lead to physical models. Take the case o Ptolemy model. It was a fantastic mathematical model of data. Thanks to it, cosmic data could be acquired and organized. Without it, the work of Copernicus until Newton could not have been done.

            We have nowadays important mathematical models - the atomic model, quantic mechanics, the cosmological model. The important think is to be aware that these are largely mathematical models, like the Ptolemy model, and that we must keep looking for the respective physical models, as Copernicus, Galileo and Newton did. Sadly, most of us do not understand this.

            Now, if you want to get a glimpse on how a random universe could have evolved until human society as if it was guided by an intelligence towards a goal, you can find a surprisingly simple answer in my essay; it may clarify some aspects of your wondering.

            All the best,

            Alfredo Gouveia Oliveira

            12 days later

            Hi Donald

            I welcome your essay as I see there your clear position on the significance of the contest question. I see you are one of small quantity of people who have inclined to critical approach to significance this or that questions in whole. That is why I invite you to open my work. I am hopeful we can find many common points that will allows us to talk on this matter. Please let me know in my page (as I see you are not so active now)

            My best wishes

            6 days later

            Dear Mr. Palmer

            Your conclusion is:

            But do we even have adequate mathematical tools to model and aims

            intensions? This author believes we do not.

            But then my essay is worth nothing. So, please, as a mathematician to find a mistake in a very simple mathematics of my essay. In my essay, there is a aims and intention of the universe to produce a proton.

            Regards,

            Branko

              Dear Sirs!

              Physics of Descartes, which existed prior to the physics of Newton returned as the New Cartesian Physic and promises to be a theory of everything. To tell you this good news I use «spam».

              New Cartesian Physic based on the identity of space and matter. It showed that the formula of mass-energy equivalence comes from the pressure of the Universe, the flow of force which on the corpuscle is equal to the product of Planck's constant to the speed of light.

              New Cartesian Physic has great potential for understanding the world. To show it, I ventured to give "materialistic explanations of the paranormal and supernatural" is the title of my essay.

              Visit my essay, you will find there the New Cartesian Physic and make a short entry: "I believe that space is a matter" I will answer you in return. Can put me 1.

              Sincerely,

              Dizhechko Boris

              Dear Branco,

              I am not a physicist (I was trained in mathematics), so some of your essay I can only attempt to get my head around. Based upon some other comments, you seem to be onto something.

              Like a couple other commentors, I am unsure how your essay relates to the main question. How do these equations imply intention for, say, humans?

              Putting that issue aside, I do not see how you have accounted fr error terms in your values and equations. Your value for 2(pi) is only an approximation to 11 decimals, while pi is a transcendental number, also called a non-terminating decimal value. A similar point can be made for your other constants, which use transcendental numbers pi and e. So your concept of accuracy needs to be bounded by error terms, which I do not see.

              Your quote by RuÄ'er BoÅ¡ković is an implicit agreement that this is only a mathematical model that uses non-realistic mathematical points. This also brings into question how close the model can come to the physical world. Related to this (and I think to Gary Simpson's comment on your essay), making the mathematical model work does not mean you have provided an underlying principle that gives useful knowledge about what is going on (in my terms, you have not provided enough conceptualization of the model beyond the mathematical aspects).

              There are some questions you might addresss that are connected to the essay topic: How can actions on the particle level cause human beings (at a very different physical scale) to build devices that then cause actions on the particle level? How can a reductionist model, that implies all actions stem from the smallest scales account for human intentional actions, at a very different and larger scale, that then impact and change what happens at the smallest scale? Example - how can actions at the particle scale cause human physicists to create experimental devices that cause all sorts of havoc back at the particle scale?

              To me, this is the crux of the dilema involved in the essay topic.

              From my perspective, mathematical tools that cross levels of scale are what is currently missing for the next level of physical models to be developed.

              Don