Hasmukh,

A good read. Thank you.

I like your use of "eyes-closed" and "eyes-open" to describe mathematics and reality. That is an excellent description and it definitely is a source of confusion.

You should really attribute the symbols used for modern numbers to the Arabs. It seems that we use Arabic numerals and Phoenician style writing.

I have frequently found that in order to understand where I am and how I got to where I am, I must retrace my steps and think about the motivations for the decisions at each step. You have done a nice job of retracing the development of some of the ideas of Mathematics.

Best Regards and Good Luck,

Gary Simpson

Dear Gary Simpson,

Thank you very much, Dear Gary Simpson, for reading my essay, and for your comments.

I too read your essay, Calculus II. You have discussed a specific point in details, and you suggest a way of improving relativity theory. Very Nice.

Yours sincerely,

Hasmukh K. Tank

Hi Hasmukh,

I can see from the other posts that I am not the only one that believes that the some from the west are coming together with the eastern concepts of mind. In my essay, I quote Sir James Jean ...... "the universe begins to look more like a great thought than a great machine". I wrote in my essay "Based on what I presented, it appears that there was information before the big bang. I don't have a problem ascribing this to a great mind". I also emphasize that our view of reality is information and always viewed from within the mind. So we agree on this point and the view that mathematics should not be confused with reality.

I was interested in your thinking about gravitationally bound objects. If one is thinking about the whole galaxy or whole solar system there could, as you point out, be a discontinuity at a boundary. I developed a concept called cellular cosmology and it is reviewed in my essay. Cells are spaces defined by the laws of nature at the quantum level. They define the dimensions of time and space and do not change. Cells become non-quantum as they expand. Just like cells of the body come in different sizes and fit together as a whole, the cells of space (each containing a proton) fit together and accommodate one another. It is my view that there is no discontinuity but I am open to your thoughts.

The wavelength of light is inversely related to its energy. It travels through space based on the dimensions of space, time and energy established at the quantum level. Since it is traveling away from us it appears to be red-shifted. My thinking is that its energy is only changed relative to us.

Dear Hasmukh K. Tank,

As you mentioned about conception of physically real and math, I believe as long a physical observation have such pattern that fits into a mathematical equation, then there is a upright joining between math and physics.

But either physics or math can't be mapped and associated entirely with the other. But one thing that is the intersecting factor between the two is a quantity itself.

Many scientist believe that math and physics are not the perfect match or mirror of each other, therefore I trust that is not possible to have a theory of everything as math and physics only intersect to some extent, this is what I try to address in my essay. Good luck.

Sincerely yours

Koorosh

    Dear Gene H Barbee,

    Thank you very much for reading my essay, and your comments.

    I agree with you, that there can not be any discontinuity in space at the boundary of gravitationally-bound objects, like the galaxies; and perhaps your cellular structure of 'space' may avoid the discontinuity. What I want to show is: the mathematics of general relativity, and big bang cosmology, leads to the anomaly, of discontinuity in space at the boundary of gravitationally-bound structures, like galaxies. So mathematics, when extended beyond a limit, leads to anomalies.

    I will read your proposal of cellular structure of 'space', and express my comments. Currently, I believe that 'space' is a super-flexible-continuum (SFC). 2. Spontaneously generated fluctuations in it automatically assume spherical wave-packets of micro-microscopic dimensions, which appear to us as 'the particles'; as was described in my last year's essay contest, titled On the emergence of physical world from the ultimate reality.

    Yours sincerely,

    Hasmukh K. Tank

    Dear Koorosh Shahdaei,

    Thank you very much for your comments.

    Mathematics was originally invented to correspond completely with the real physical world; and real numbers correspond completely with the physical world.

    Then the mathematicians extended the concepts of mathematics; like n-dimensional space, complex-space, curvature and expansion of space...etc. Such mathematical extensions sometimes do not match with the real physical world. Any theory of everything, which is based on mathematical-extensions of space, may or may not prove to be correct. Therefore, we need to make judicious use of mathematics, while doing physics.

    Moreover, in the real physical world, we find electrons, protons, photons. When we collide them at very high energy, we create an artificial-world. There is some regularity and patterns in the artificial world too. So mathematical-extensions describe the artificial world created by colliding the particles at high energies, and we observe some short-lived particles matching with theories based on mathematical-extensions! It was hoped that unification of forces will be observed at Planckian energies; but in a paper titled: "An insight into Planck's Dimensions" (Published in Progress in Physics, and available open access on INTERNET) it was shown by me that Planck-length is a 'geometrical-mean' of 'gravitational-radius' and 'Compton-wavelength' of every particle, so it is not a fundamental-unit of length. Similarly, Planck-mass is a 'geometrical-mean' of 'total-mass-of-the-universe' and smallest possible mass (h H / c^2), where h is Planck's constant, H is Hubble's constant and c is 'speed-of-light'. Planck-mass is obtained by 'mathematically equating' G m m = h c, so Planck-mass is mathematically equivalent to 'electric-charge'. Thus Planck-units are geometrical-mean-values. To get truly fundamental units of 'mass' 'time' and 'length' we should get them without taking 'square-root' or 'cube-root'!

    Yours sincerely,

    Hasmukh K. Tank

    Dear Sir,

    Yoga Vaashishtha is a book for intelligent learners, which explains some of the most difficult subjects through allegories. Thus, it should not be interpreted literally. For example, 'manah' does not refer to mind in all cases. It may refer to the emotions (hrdayaakhya manah) or Consciousness proper (Shwavashiyas Manah) depending upon the context.

    What you have said regarding origin of numbers actually relates to development of the script to denote numbers. Numbers developed in India during remote antiquity. We have written a book on number theory in which we have discussed this in detail including why one is the first number, why two follows one, why three follows two, why four follows three, why zero comes after nine, why the number system repeats thereafter, why these numbers are called one, two, etc, etc. We have also discussed the negative numbers, irrational numbers, zero, infinity, etc. We have also explained why complex or imaginary numbers are not mathematics, but manipulations in the name of mathematics. Scientists further manipulate the distorted statement to get some accidental physical representations, which they call unreasonable effectiveness of mathematics. Our book is free for research scholars and can be obtained by writing to mbasudeba@gmail.com.

    Dimension is the perception of differentiation between the internal structural space and external relational space of objects. Since we perceive through electromagnetic interaction, where the electric and magnetic fields are perpendicular to each other and both move perpendicularly, we have three mutually perpendicular dimensions. These are invariant under mutual transformation and can be resolved into 10 different combinations. Thus, the n-dimensional space is a figment of imagination. After failure to find the extra large or compact dimensions, we should not continue with this and scrap all papers dealing with fantasy.

    Regarding space, we have replied against your comment in our thread.

    Much has been talked about sensory perception and memory consolidation as composed of an initial set of feature filters followed by a special class of mathematical transformations which represent the sensory inputs generating interacting wave-fronts over the entire sensory cortical area - the so-called holographic processes. It can explain the almost infinite memory. Since a hologram retains the complete details at every point of its image plane, even if a small portion of it is exposed for reconstruction, we get the entire scene, though the quality may be impaired. Yet, unlike an optical hologram, the neural hologram is formed by very low frequency post-synaptic potentials providing a low information processing capacity to the neural system. Further, the distributed memory mechanisms are not recorded randomly over the entire brain matter, as there are preferred locations in the brain for each type of sensory input.

    The impulses from the various sensory apparatus are carried upwards in the dorsal column or in the anterio-lateral spinothalamic tract to the thalamus, which relays it to the cerebral cortex for its perception. However, both for consolidation and retrieval of sensory information, the holographic model requires a coherent source which literally 'illuminates' the object or the object-projected sensory information. This may be a small source available at the site of sensory repository. For retrieval of the previously consolidated information, the same source again becomes necessary. Since the brain receives enormous information that is present for the whole life, such source should always be illuminating the required area in the brain where the sensory information is stored. Even in dream state, this source must be active, as here also local memory retrieval and experience takes place. This illuminating source (shuddha prakaasha maatra roopa) is the Consciousness (vigyaanam).

    How do our sensory agencies function? At any moment, our sense organs are bombarded by a multitude of stimuli. But at any instant only one of them is given a clear channel to go up to the thalamus and then to the cerebral cortex, so that like photographic frames, we perceive one discrete frame at every instant, but due to the high speed of their reception, mix it up - so that it appears as continuous. Unlike the sensory agencies that are subject specific (eyes can only receive electromagnetic radiation, ears only sound, etc.); the transport system within the body functions for all types of sensory impulses. This occurs against concentration gradients with the input energy like the sodium-potassium pump in our body, which moves the two ions in opposite directions across the plasma membrane through break down of Adenosine triphosphate (ATP). Concentrations of the two ions on both sides of the cell membrane are interdependent, suggesting that the same carrier transports both ions. Similarly, the same carrier transports the external stimuli from sensory agencies to the cerebral cortex and back as a command. This carrier is the "indriyam" called mind. The existence of mind is inferred from the knowledge or lack of it about external stimuli. Only if the mind transports different external impulses to the brain for mixing and comparison with the stored data, we (Self) know about that (for the first time impulse received about something, there is no definite 'knowledge').

    The brain acts like a computer. In communication technology, in addition to encryption (language phrased in terms of algorithms executed on certain computing machines - sequence of symbols), compression (quantification and reduction of complexity - grammar) and data transmission (sound, signals), there is a necessity of mixing information (mass of text, volume of intermediate data, time over which such process will be executed) related to different aspects (readings generated from different fields), with a common code (data structure - strings) to bring it to a format "it is like/ not like that". Such mixing is done through data, text, spread-sheets, pictures, voice and video. Data are discretely defined fields. What the user sees is controlled by software - a collection of computer programs. What the hardware sees is bytes and bits.

    In perception, data are the response of our sensory agencies to individual external stimuli. Text is the excitation of the neural network in specific regions of the brain. Spreadsheets are the memories of earlier perception. Pictures are the inertia of motion generated in memory (thought) after a fresh impulse, linking related past experiences. Voice is the disturbance created due to the disharmony between the present thought and the stored image (this or that, yes or no). Video is the net thought that emerges out of such interaction. Software is the memory. Hardware includes the neural network. Bytes and bits are the changing interactions of the sense organs (string) with the respective fields generated by objects evolving in time.

    It requires an agent to mix these signals and convert them to electro-chemical information and submit to a conscious agent (operator) to cognize and utilize them. In perception, the former tasks are done by a transitory neural activity in brain called intellect. Though, it is not directly perceptible (prakrhtilayaah), it is inferred from its actions - firing of positrons in specific areas of brain during perception. Hence even after the breath stops, a person may not be brain dead as the intellect (and not the mind) may still be functional. While mind facilitates the transport of various external impulses, the interpretation after mixing of the state of superposition of various thoughts/inputs in memory (vikalpa), is done by transitory intellect. The Conscious Self that cognizes is different from all these.

    Regards,

    basudeba

      Dear Joe Fisher,

      Thank you very much for reading my essay, and for your detailed comments.

      I agree with you that every star, every galaxy and every structure is unique.

      Since we human beings are somewhat lazy, we try to derive some common features from the unique structures; and try to formulate some laws.

      I have read your essay once; and i will read it again more carefully.

      Yours sincerely,

      Hasmukh K. Tank

      Dear Shri Basudeva Mishra Sir,

      Thank you very much for your illuminating comments. I agree with you that the books like Yoga Vashishtha need to be studied under the guidance of good teacher; as there is a possibility of misinterpreting important terminologies.

      Regarding your hologram-model of brain, a thought comes to my mind; that:

      The real physical world is like a full-band, full-size hologram. And our mind is like a small piece of it. Our perceptions of the physical world are band-limited, and do not contain fine details. If we can perceive the full hologram, then we may hardly need any mathematical model, or theory.

      Thanking you once again,

      Yours faithfully,

      Hasmukh K. Tank

      N.B. I also request you for e-copy of the book, referred by you.

      9 days later

      Hello Hasmukh,

      Your essay was nice and straight to the point.

      You said, "Mathematics is good and quite useful, but we should be careful that we do not mistake 'mathematical-space' for 'physical-space'; as many current scientists appear to be doing". But you did not tell in detail how to differentiate the two. I will also like to know your opinion on the question whether physical space is continuous or discrete debate.

      On your interesting observation that "...according to the Big Bang Cosmology, the space between the galaxies is expanding; but the space within the galaxy is not expanding, because galaxy is a gravitationally-bound-structure", I wish to ask what you think is preventing the masses within the galaxy from collapsing into a single mass after attracting each other for billions of years? Could it not be that the space within the galaxy is what is preventing this?

      Why has the Moon not fall on our heads, since both Earth and Moon are attracting each other or why has the Earth not collapsed into the Sun? Rather we see a cycle like a vibrating spring - extension and compression. A force compresses the orbit and another force is extending the orbit, hence perihelion (maximum compression) and aphelion (maximum extension). Compression we can attribute to force of gravity . Who is the force doing the extension since it cannot be gravity, and according to Newton's law, a body cannot change its direction unless a force acts on it.

      All the best in the competition.

      Regards,

      Akinbo

        Dear Akinbo,

        Thanks for the questions; and my answers are:

        1.In a paper titled: "An Insight into Planck's Units" URL:

        www.ptep-online.com/index_files/2011/PP-27-04.PDF

        you will find three references describing experimental results, that 'space' has no quantum structure.

        2. The stars in a galaxy do not collapse to a single point; and the Moon does not fall on our head because: they have tangential-velocities, such that, the centrifugal-force(v^2/R)= [(G M m)/ R^2], the force of gravity

        Your symbolic representation of physical and mathematical aspects of nature are quite symbolic with your work, Sir!

        Sincerely,

        Miss. Sujatha Jagannathan

          You are right, Sujatha, I should have included more details!

          Dear Friends,

          1. I wish to tell something more about mathematics:

          At night I was trying to do some calculation and derivation while resting in bed.

          As I go to next step the first step was getting evaporated from my memory. Ultimately I got up from the bed, switched on the lights and finished the calculation. from this incidence I found that mathematics provides an aid to our memory, and thus boosts our ability to think. So with the aid of mathematics we can solve some problems of physics, which we can not solve only with our memory available in our brain. Therefore, just as an automobile boosts our ability to run, so exactly mathematics boosts our ability to think!

          2. It seems that now we have arrived at the correct explanation for the cosmological red-shift, as described in: http://vixra.org/abs/1502.0104

          This mechanism also explains: (i) the non-observation of dark-energy,(ii) Large-number-coincidence and (iii) the cosmic coincidence.

          Your valuable comments and criticisms are most welcome!

          Yours sincerely,

          Hasmukh K. Tank

          7 days later

          Dear Hasmukh,

          I was wondering whether all the steps of the transformations in Fig 1 are documented, or only the first and last of each row. Interesting anyway!

          You write: '...subjective-space, which we perceive with our eyes closed, and objective-space that we see with our eyes open.' Then I am not sure that curved spacetime as described by Einstein can be seen as mathematical extensions of subjective space, as you suggest. The curvature of spacetime due to mass is a perfectly observable phenomenon, e.g. when Eddington observed the deflection of light passing near the sun, in 1919.

          The view that math and the physical world may be aligned because they are 'created', respectively, by the cosmic mind and by the human mind, is, in my opinion, somewhat appealing. I realize it is only a philosophical (or mystical) idea, but at least it is an attempt to answer the precise question posed by the Contest - something that several other essays prefer to ignore.

          As for the relation of mind and matter, I do believe that there must be some truth in Wald's idea that mind (or consciousness) may be present as a complementary aspect of all matter. However, I do believe that consciousness is a byproduct of the complexification of matter, which happens during evolution. This idea was pioneered by Pierre Teilhard de Chardin (I believe before Wald). An attempt to make it formal has been recently carried out by Giulio Tononi with his notion of Integrated Information, as I discussed in my 2014 essay. Also in my current essay I let a fictional character discuss briefly the issue of matter/consciousness, in the context of a potential evolution of Tegmark's Mathematical Universe Hypothesis (take a look if you have time... I'm running short of posts!)

          Best regards

          Tommaso

          Dear Tommaso,

          Thank you very much for your careful reading of my essay, and your following comments:

          " Then I am not sure that curved spacetime as described by Einstein can be seen as mathematical extensions of subjective space, as you suggest. The curvature of spacetime due to mass is a perfectly observable phenomenon, e.g. when Eddington observed the deflection of light passing near the sun, in 1919."

          You are right, i can not call it 'subjective space'. I should only cal it 'mathematical extension'. This mathematical extension has helped explaining 'bending of star-light' and 'the precision of Mercury's perihelion.'

          Regarding 'expansion of space': If the space between the galaxies is expanding, but the space within the galaxy is not doing so, as a galaxy is a gravitationally-bound-structure, then what happens at the boundary of the galaxy? If a real object like glass experiences such uneven expansion, then glass would break, and space may get torn out. Therefore, 'expansion-of-space' is a mathematical-terminology in my opinion, and not a physically-real-process.

          It is good that GR could explain deflection of light, still it does not mean that 'time' and 'space' get physically 'curved'; this is my opinion.

          Regarding your comment:

          "The view that math and the physical world may be aligned because they are 'created', respectively, by the cosmic mind and by the human mind, is, in my opinion, somewhat appealing. I realize it is only a philosophical (or mystical) idea, but at least it is an attempt to answer the precise question posed by the Contest - something that several other essays prefer to ignore"

          In my opinion, the physical universe is a 'hologram', a full-band, full-size, dynamic, hologram. And our 'mind' is a band-limited, small-piece, slow-motion, hologram of the physical world. Therefore, some patterns of our thoughts correspond with the physical world. This is why our mathematics matches with the physical world. You may be delighted to read the following articles:

          On the Nature of Consciousness, Space &Omnipresence of ...

          scigod.com/index.php/sgj/article/viewFile/290/335

          Hasmukh K. Tank, On the emergence of Life from Matter ...

          philpapers.org/rec/TANOTE

          I have read your essay once, I will read it again more carefully, and try to comment. Rating is a confidential matter, but be sure, I always try to be fair!

          Yours sincerely,

          Hasmukh K. Tank

          Dear Hasmukh K. Tank,

          Your essay is fine, but I much more enjoy reading your viXra papers. Your conclusions about physical mining of red shift, accelerated-expansion of the universe and some other I may just copy past. Of course, I disagree with you in details. I think you're overly influenced by the authorities. For example, when you mention Weinberg interesting formula it is also for you pi meson in formula. When you explain the important relationships in the universe you are using Hubble parameter. I think it would be more consistent, not to use pi meson and Hubble parameter. In my essay, you can convince that your shiny conclusions can be drawn in a much simpler manner of looking at the universe as a unity of the whole and the parts.

          Best Regards,

          Branko Zivlak

          Dear Hasmukh K. Tank,

          1. When I say Large number I mean 10^121, that may be reason that I cited Scott Funkhouser.In " An explanation for the 'Large Number Coincidence' 10^40 in astrophysics". In formula (18) you ingeniously re-write Newton Gravitational formula. So, I have same for Universal Gravitational constant as you in 1997 year, but with quite diferent approach. And, it is both quite good without mentioning Hubble.

          2. The dimensionless expression of a cycle, in my essay give results similar to yours. The difference is that you are using pion parameters but I am using fundamental particle defined as you can see in my articles.

          3. About: „How should we think of infinity?" I cited RuÄ'er BoÅ¡ković [1, paragraph 391]. "Now, although I do not hold with infinite divisibility, yet I do admit infinite componibility". More you can see in paragraphs 391 to 396. Therefore I say: mass and radius of the universe are not physically real mass and radius of the universe; but the mass, radius and any other fenomenon is finite but the number of their combination is infinite.

          4. The base 2 of logarithms is usefull tool (see FQXi contests, 2013 year). For calculating values of gravitational constant you can use formula from [2] (You alsow know that h=c*mp*lambdap), so, the proton parameters are used for both, Planck-constant and gravitational constant.

          5. Mentioned attempt gave results with accuracy of 12 significant digits for numerous phisical constants;

          You do not mentioned anything about pion and Hubble parameters in your articles. Maybe you would think about that later.

          Best Regards,

          Branko Zivlak

          [1] Boscovich J. R.: (a) "Theoria philosophia naturalis redacta ad unicam legem virium in naturaexistentium", first (Wien, 1758) and second (Venetiis, 1763) edition in Latin language; (b) "A Theory of Natural Philosophy", in English, The M.I.T. Press, Massachusetts Institute of Technology, Cambridge, Massachusetts and London, England, first edition 1922, second edition 1966

          [2] Branko Zivlak, Universal Gravitational Constant Via Proton, http://viXra.org/abs/1310.0018

          Dear Branko Zivlak,

          I read with interest your following paper:

          Universal Gravitational Constant Via Proton, http://viXra.org/abs/1310.0018

          Try to submit it to some peer reviewed journal, like Astrophysics and Space Science, so that you can get expert reviewer's opinion on it, which will help you to up-grade it; making it suitable for publication.

          With my best regards,

          Hasmukh K. Tank

          8 days later

          Dear Hasmukh,

          Your short essay is pleasant to read. In particular,I did not know your Fig. 1. "According to an ancient spiritual book Yoga Vashishtha, the physical world too is an imagination of the cosmic mind". How this old view of consciousness can be reconciliated with the modern ones? You talk about the patterns of cosmic mind, does it mean neurons flashing together?

          Thanks,

          Michel