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    Is math inherently part of the structure of the universe?
    By Rafe Furst | November 22nd 2010 11:23 AM | 90 comments | Print | E-mail | Track Comments
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    Rafe Furst holds an M.S. in Computer Science and B.S. in Symbolic Systems, both from Stanford University. He is an entrepreneur, investor and business...

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    In another thread on Science 2.0 we got onto the nature of existence and what we can say for certain about the universe (if anything).  Given that physics and math seem so intimately linked in practice, I often wonder if this link is "real".  In other words:
    Do numbers and other mathematical entities actually exist, or are they made up by the human mind?

    This is a question I've asked in a number of forums before and have only gotten one interesting reply.  Derek Abbott said he doesn't know, but thought it was a paradox.  To paraphrase Derek: "Nowhere in the universe does a perfect circle exist; only approximations.  Yet we can imagine a perfect circle in our minds, and unless you believe cognition is epiphenomenal, our minds exist in the universe, and thus so do perfect circles...."

    I struggled on whether to post this in Physics or Math, but I'm more curious as to the physicist's answer.  Anyone?

    Comments

    Hank
    Math was, for reasons you note, the hardest to categorize here, because we have to have a math section but it is not a science.   Science is explaining the world according to natural laws and mathematics does not do that, though it is systematic knowledge and is the language of science.

    There is obviously a broader philosophical issue.   Did Einstein invent E=MC^2?  No, he discovered it, it was in nature speaking to us and he simply learned how to listen, which is generally why I think people refer to math as the language of science.
    Aitch
    Do numbers and other mathematical entities actually exist, or are they made up by the human mind?

    I was always of the opinion that nature just is

    It is us, as humans who struggle to 'understand it'
    I prefer the concept of 'overstanding it' which I believe to be the Philosopher's viewpoint,
    as if looking from a vast mountaintop looking down, and also that Philosophy,
    or wondering what it all means, came well before Math in human understanding

    There always seem to be arguments about what is real, or truth, or existence
    .....always expecting 'the everything' to have to be proven, yet, gravity can only be proven
    by its effect, as anyone who ever jumped, or fell knows

    It seems that nature has led us a merry dance with pi, the golden ratio, and plenty more examples
    .....and that's without trying to do complex math by computer needing double precision arithmetic
    If we didn't have Math we would need to invent it, as it is a descriptive language, with logical  functionality

    My question would be; Can you imagine how silly we will feel, if by chance one day we discover a different system of describing what we now think of as numbers, based on 10 base Math, and find that Nature's anomalies fit perfectly in that new system AND make better sense of our current struggle to makes sense of it all?

    Has anyone messed with base 13, for example? ;-)

    Some related Quotations
    * A youth who had begun to read geometry with Euclid, when he had learnt the first proposition, inquired, "What do I get by learning these things?" So Euclid called a slave and said "Give him three pence, since he must make a gain out of what he learns." - Stobaeus, Extracts
    * "The laws of nature are but the mathematical thoughts of God." - Euclid
    * "If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker." - Albert Einstein
    * "I tell you that I accept God simply. But you must note this: If God exists and if He really did create the world, then, as we all know, He created it according to the geometry of Euclid." - Ivan, in The Brothers Karamazov, by Fyodor Dostoyevsky (1821-1881)
    * "Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions." - Eric Temple Bell

    Aitch
    Gerhard Adam
    Yet we can imagine a perfect circle in our minds, and unless you believe cognition is epiphenomenal, our minds exist in the universe, and thus so do perfect circles...
    Actually that's not true, since we don't have any way to distinguish a circle that is "perfect" from any other kind of circle (certainly not in our minds).  We imagine that there is such an ideal, but what would be the criteria for actually formulating such an entity in our minds?

    Mathematics is a logical tool that we can use to find the patterns in nature.  As a result, we find that there are logical inconsistencies in the tool despite the fact that it works with a high degree of reliability.  Infinity and values like pi are logical inconsistencies since they are the product of our analysis.

    Some may argue that there are deeper meanings here, but the physical world isn't nearly granular enough for such discrepancies to matter, so consequently we have the paradox of a mathematical explanation that requires more accuracy or rigor than the physical reality it represents.  This is no different than trying to imagine a dimensionless point, or a line with only length.  These are abstractions that have no corollary in the real world, and yet they have a mathematical definition and existence.

    Of course, it always seems curious when we discover something in the universe that seems to imply some mathematical origin, but if we believe that such patterns exist in nature, then it should be no surprise if our human method of symbolic expression should also operate in that realm.
    Mundus vult decipi
    vongehr
    "I'm more curious as to the physicist's answer.  Anyone?"

    If you insist, here it goes:

    "actually exist" = silly undergrad/stoner "philosophy" of no value whatsoever

    Sorry to be so harsh, but in face of "really real reality" I cannot help it.
    socrates
    Okay, Sascha, I too am "curious as to the physicist's answer" and I do understand your distaste for what you call "silly undergrad/stoner philosophy". So let me put my question a little differently than Rafe's. Putting aside the question of whether mathematics "actually exists" in "really real reality", can you tell me the current view in physics as to the disagreement between Einstein and Bohr? Would you say nothing is determined until it is observed, as Bohr insisted, or do events occur independent of our observation of them, as Einstein argued?

    Einstein, as I understand it, disagreed with Bohr, saying "I cannot believe the moon ceases to exist when we are not looking at it." The Copenhagen interpretation seems to say, on the contrary, the cat in Schrodinger's box is neither alive nor dead until it is observed and the moon, and all else, is equally indeterminant until observed. Do I have that correctly? I must say I'm with Einstein on that one. However, as I understand it, main stream physics sided with Bohr. The Copenhagen interpretation became the orthodox position. So my question is, is that still the case today? Does the physics community still side with Bohr? All there is is what is observed? Nothing behind the curtain? No hidden variable, as Einstein argued? Just asking.
    Citizen Philosopher / Science Tutor
    socrates
    P.S. Just discovered Don Howard's articles here.

    Revisiting The Einstein-Bohr Dialogue
    Revisiting the Einstein-Bohr Dialogue Part 2
    Revisiting The Einstein-Bohr Dialogue Conclusion

    Will need to spend some time studying them. Gosh, this Science 2.0 has so much good stuff. Thanks for being here.
    Citizen Philosopher / Science Tutor
    Hank
    I agree about those articles.  It took a philosopher to write about physics so adeptly, I think.  I don't know a physicist who could have done it as well as he did.
    This inquiry reminds me of a fantastic quote from Nietzsche.

    “Mathematics . . . would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.“

    Nietzsche in Human, All Too Human, sct. 11 (1878).

    It took me a while to find the quote. My memory thought this was from Wittgenstein.
    While scanning Wittgenstein, I came across the following from Wittgenstein.

    “Like everything metaphysical the harmony between thought and reality is to be found in the grammar of the language.”

    Here’s another from W for those (like S) who cannot but help from being silly 'n harsh.

    “Never stay up on the barren heights of cleverness, but come down into the green valleys of silliness.”

    and this

    “It is one of the chief skills of the philosopher not to occupy himself with questions which do not concern him.”

    Notice that he said “philosopher”, not “physicist.”

    In conclusion, here’s a a quote from Lewis Carol:

    “Yet what are all such gaieties to me
    Whose thoughts are full of indices and surds?”

    How are we doing here Rafe?

    I really like the ironic quote from Nietzsche. It has rung true to me for many years.

    Who’s fooling who?

    make that,

    Who 's fooling whom?

    Bitten anon by the "grammar of language" ...

    socrates
    Good question Rafe. The way I see it, yes, of course, mathematical entities really, really, exist. How else could we talk about them. The question is, what is the nature of their existence? Do they exist in the same sense as rocks and trees? I think we would all agree, no they don't. So does that mean there are different kinds of existence? Perhaps a hierarchy of existences? In my opinion, yes.

    For example, how real is a rainbow? I would say a rainbow is more real than a thought, but less real than a rock. (Perhaps a better term would be "manifest". A rock is more manifest than a rainbow, but a rainbow is more manifest than a private thought.) A rock has simple location in time and space. A rainbow does not. Nor does any virtual image. You can point to a virtual image and even have a colleague look at it with you. The virtual image exists in time, but not in what we would call real space.

    Mathematics exists not in manifest space nor in manifest time. That is to say time and space do not apply to mathematics. I believe it is a category error to speak of mathematics existing in time or space. We tend to think of things having simple location as real (or some say physically real) and all else as not "really real". This is a false duality, in my opinion. We must allow for a greater spectrum with finer gradations. (There is more to say, but I will leave it at that for now.)
    Citizen Philosopher / Science Tutor
    rafefurst
    Steve, I like your answer best, but I ultimately side with the observer-dependent view, in which time and space are both constructs.

    Regarding the rainbow...
    ...neither electricity nor magnetism have visual properties.... there is nothing inherently visual, nothing bright or colored about that candle flame.  Now let these same invisible electromagnetic waves strike a human retina, and if (and only if) the waves each happen to measure between 400 and 700 nanometers in length from crest, then their energy is just right to deliver a stimulus to the 8 million cone-shaped cells in the retina.  Each in turn sends an electrical pulse to a neighbor neuron, and up the line this goes, at 250 mph, until it reaches the warm, wet occipital lobe of the brain, in the back of the head.  There, a cascading complex of neurons fire from the incoming stimuli, and we subjectively perceive this experience as yellow brightness occurring in a place we have been conditioned to call "the external world."  Other creatures receiving the identical stimulus will experience something altogether different, such as a perception of gray, or even have an entirely dissimilar sensation.


    Regarding the rock...

    What about if you touch something?  Isn't it solid?  Push on the trunk of the fallen tree and you feel pressure.  But this too is a sensation strictly inside your brain and only "projected" to your fingers, whose existence also lies within the mind.  Moreover, that sensation of pressure is caused not by any contact with a solid, but by the fact that every atom has negatively charged electrons in its outer shells.  As we all know, charges of the same type repel each other, so the bark's electrons repel yours, and you feel this electrical repulsive force stopping your fingers from penetrating any further.  Nothing solid ever meets any other solids when you push on a tree.  The atoms in your fingers are each as empty as a vacant football stadium in which a single fly sits on the fifty-yard line.  If we needed solids to stop us (rather than energy fields), our fingers could easily penetrate the tree as if we were swiping at fog.


    Both quotes are from Robert Lanza's new book, Biocentrism.
    Rafe Furst http://emergentfool.com
    socrates
    "I ultimately side with the observer-dependent view, in which time and space are both constructs."

    Rafe, I agree that time and space, and everything else for that matter, are, in one sense, constructs of the observer. However, this can be a tricky issue. One most distinguish between the map and the territory. The map is the construct. The territory is the given. Unfortunately, we use the same words for both. We say, "I pick up the book," rather than, "I pick up my experience of a book as I have constructed it."

    All I can know is my own experience but I have reason to believe that at least some of what I experience has an existence independent of my own.

    Language is a map or metaphor used to describe the world we experience. Mathematics is also a language. It is a model that simulates and clarifies what we know about the world. Much more subtle is the idea that the material world, itself, is also a language - a pre-verbal, pre-rational, language we all learn so early that we mistake it for the world itself. That is not to say there is no world. We have ample evidence of it. It is just that all the evidence we have, and can have, is indirect and that we take the evidence to be the world itself.

    Citizen Philosopher / Science Tutor
    Amateur Astronomer
    Raef, your question was a major topic in mathematics about 50 years ago, and led to the rewriting of mathematics based on set theory to replace the geometric basis that had been built up by mathematicians since antiquity. Technically speaking mathematics is classified as a pure science in contrast to the physical sciences and the social sciences. Part of mathematics is found in nature beyond the human area of influence. Integers are found in nature both in cardinal numbers and ordinal numbers. Decimal fractions are not found in nature as a general rule. Binary numbers are found in nature, but octal and hexadecimal numbers are not. Much of discrete mathematics is found in nature, and was for a long time the only chance to get a completely correct calculation. That was before the rewriting of mathematics. Continuum mathematics has been redefined in terms of mapping and limits of a discrete sequence, making it acceptable now for many scientific works that previously had to be done with discrete functions. I keep Paul Dirac’s book on quantum mechanics handy as a reminder of the dilemma that science had with mathematics before the rewriting of math. Dirac really wanted to use continuous functions, but also wanted to avoid the criticisms that surrounded continuum mechanics in his early years. His remedy was to write quantum mechanics both ways, once with continuous functions and again with discrete mathematics. His great achievement in doing so was to demonstrate that the two systems give equivalent answers if the continuum is defined in the new way. Your concept of what really exists in nature needs to be expanded to fit into a physical system. Some time ago we had a discussion about particle beam splitting experiments. The conclusion is that there is more than one reality coexisting at the same time in different contexts. In physics you get an argument that we will not be able to end here. Albert Einstein couldn’t resolve it with Niels Bohr, and Roger Penrose couldn’t resolve it with Stephen Hawking. The argument is about quantum mechanics, for example the particle and the wave. When we look for a particle we find a particle, and when we look for a wave we find a wave. The great minds tried to attach a physical reality to the object before a measurement was done. Their failure leads to a representation of wave functions that no one would ever accept without a lot of experimental data. The two slit experiment and the beam splitters are just a continuation of the same argument. Finally with the beam splitters the situation is well enough defined and controlled to show that there is one reality for the laboratory detectors, and a different reality for the photons. Both realities are regarded as valid in the context where they are measured. It comes from special relativity. In mathematics sometimes you get more than one right answer. Other times the right answers are mixed in with wrong answers. The only way to separate them is to test the results and challenge the conclusions. Mathematics can produce a lot of results that have no physical reality in any context. I guess Physics can do the same thing. That’s why we still do experiments.
    rafefurst
    Part of mathematics is found in nature beyond the human area of influence. Integers are found in nature both in cardinal numbers and ordinal numbers.... Binary numbers are found in nature, but octal and hexadecimal numbers are not.


    Or perhaps we are discovering the structure of our minds and mistaking that for "found in nature".

    What if observation / consciousness / life comes first and existence/nature/universe is the consequence?
    Rafe Furst http://emergentfool.com
    Gerhard Adam

    What if observation / consciousness / life comes first and existence/nature/universe is the consequence?
    I'm not clear on what this is supposed to mean, nor do I see how it explains anything.
    Mundus vult decipi
    socrates
    Well this is actually a very eastern philosophy and I do myself subscribe to it, myself. However, language is very tricky and this philosophy can be, and is, interpreted in many different ways. Because it is often used to promote the possibility supernatural/religious worlds or forces, this very idea can be very repugnant to the rational thinker. Having said that, I myself have come to the conclusion that the physical world is a subset of the metaphysical world (and emerges from it); that is, the material is a subset of the ethereal (and emerges from it). I don't mean anything supernatural by that. What I mean is very close to simply stating that the Newtonian world is a subset of the quantum world and emerges from it.

    My understanding of the history of physics is that Bohr's view (as opposed to Einstein's) was related. What became known as the Copenhagen interpretation (if I understand it correctly) was that conscious observation of the world brings the world into being. That the observation of an event is the event and that there is nothing "behind it". I have always had a problem with that. I always found myself siding with Einstein on this one, for like Einstein, I cannot accept that "the moon ceases to exist when we stop looking at it."

    So the way forward for me is to recognize that we each construct our own world as we experience/observe it, but THE world (as opposed to my world) has an existance independent of me and my observation of it. So who is observing/creating THE world? God? One might use that language, but I would simple say the universe. The universe is observing itself. Every collision is an observation.

    I would be curious to hear from Jerry on this as relates to the Bohr vs Einstein debate and the orthodox position of quantum physics. Jerry correctly points to the relevance of this classic debate to your question. I may not have understood/presented it exactly correctly.

    Citizen Philosopher / Science Tutor
    Amateur Astronomer
    Steve, the reference to beam splitters is the key to understanding the Copenhagen interpretation. You can do the Lorentz transformations from the laboratory point of view to the photon point of view. Then for the photon all of the decisions are made at the same time and in the same place. With that in mind the laboratory results are reasonable. Both realities are valid, but in conflict if you don't account for transformations. Relativity alters not only the time and distance, but also the sequence of events. Fortunately there are some groups of variables that are invariant in transformations. Science is always looking for new invariants.
    socrates
    My understanding is that the beam splitter experiments were designed to use Bell's Inequality Theorem to test whether one could in fact show what Einstein disparaged as "spooky action at a distance" was possible. The experiments have been conducted and supposedly show that Einstein was wrong. According to Bell's Theorem, the experiments using entangled photons seem to prove that yes, one can have "spooky action at a distance". I don't think everyone accepted that conclusion, however. So, is the question of observer dependence resolved, or is it still an open question whether Einstein's hidden variable could still be possible?
    Citizen Philosopher / Science Tutor
    Amateur Astronomer
    Beam splitter results are not in doubt. Interpretation of the data is disputed. Two main groups are debating spooky versus non spooky interpretations. Einstein didn't like quantum mechanics because it was irrational in a human context. He was proven wrong by over whelming data, but the argument continues. Now I'm suggesting that special relativity can explain all of the results, and be used to prove that Einstein was wrong about quantum mechanics. String theory gives us hidden dimensions, so I don't feel too bad about hidden variables, as long a s there is a chance to find them later. You don't need hidden variables if you apply special relativity to look at the experiments from a particle's point of view. All you need are the transformations from one reality to another. When ever possible science should be described by things that can be observed and measured. Quantum wave from entanglement has some of the issues you described. Photons or electrons remain connected together at great distances for a fairly long time in the human point of view. In the particle view point they are close together and no time has passed. Still the human reality can separate the particles and use the entanglement for communication. Both realities are valid. We just have to discover all of the transformations . We need to have some fun with the math on this page. Remember I said the that decimal fractions are not found in nature. Still we call them real numbers. At the same time we have imaginary numbers, but they are found in nature. Physics uses a lot of imaginary and complex numbers. Now maybe I can misquote Roger Penrose about complex numbers. If there are hidden dimensions and hidden variables, the complex numbers have already found them and described any properties that apply to the experiments we can do. That's what the imaginary part of a complex number is. It is the evidence of a physical component that we can't find in our human reality of 4 dimensions. Imaginary operators in quantum mechanics are just a way of transforming numbers from one reality to another and back again. There is always some transformation that can convert an imaginary number to a real number in a different context. If you look at quantum mechanics from the particle point of view it is a lot easier to understand and less spooky than when we describe it in human terms. I guess some of the transformations have not been discovered yet. When we find them modern science will become a lot easier to understand.
    rafefurst
    Is there a case to be made that each scale (particle, atom, molecule, cell, etc) defines its own variant of "time" and "space"?  This would make it easy to see how applying our human-scale notions of spacetime to sub-atomic realms yields spooky interpretations.
    The interesting question (from my perspective) is what a scale-dependent spacetime means for the biological scales...
    Rafe Furst http://emergentfool.com
    socrates
    Jerry, you speak of mathematics and transformations and how mathematics sometimes does and does not correspond to natural processes. The challenge, then, is to find the right match/correspondence between a mathematical model and the natural process under study. With that in mind, I have often wondered why I haven't seen any attempt to use Fourier transforms to model the quantum world. It would seem to me to be the obvious model, once it was established by Broglie and Schrodinger and others that all is waves, so to speak.

    Also how come it is usually just the time-independent wave equations that are written about? I get the idea of standing waves of electrons fitting into the space around an atomic nucleus. What is important in that situation is the wave length and how it "fits" into the given space. What is rarely mentioned (I'm still looking for it) is the frequency and velocity of the electron matter wave, for instance.

    If we really are talking about waves with a time dependency, what would things look like transformed into the frequency domain via the Fourier transform. Time would be eliminated and only frequency would remain. That would certainly be a different perspective. Perhaps that perspective would be a better fit to describe nature at its most fundamental level. All emerging from fundamental oscillators, so to speak. Sounds a little like string theory, as I understand it - fundamental vibrating strings and all that.
    Citizen Philosopher / Science Tutor
    Aitch
    Steve, Jerry, Rafe

    I find this line of discussion very interesting, as I am into eastern philosophy, myself, so Rafe's question, "What if observation / consciousness / life comes first and existence/nature/universe is the consequence?" sort of rang a bell for me, and reminded me of an experience I had a few years ago....
    I was sat talking with a downstairs neighbour, and the subject of consciousness came up, with my neighbour asking me what I thought was the causal factor; consciousness or reality/the universe we live in and experience?
    I started to explain my understanding that the 2 are inter-related, but differently, to 2 independent observers, though both may live in the same reality/universe, and that each observer may influence the universe of the other's perception, if not the universe itself. It was, I perceived, the task of groups of beings of like mind, to have sufficient power of effect on the universe itself, unless the observer were an enlightened being [I was studying under a Guru at the time, and felt his presence to be very close at that moment]
    Suddenly, the light in the room changed as if someone had turned on 3 floodlights, and I was a bit taken aback as my neighbour asked, 'What just happened? Did you see a light flash and light up the room'
    It has to be said, we were in a basement, below ground level, and the curtains were drawn partially across the window, yet the effect seemed more connected with our conversation, and, it later transpired, my friend said he had a sort of inner realisation of something as I spoke, and he said he sensed my Guru in his mind, almost as though he [the neighbour] wanted to meet him, and described him, by what he remembered. It was an accurate picture, even though I hadn't told him about having a Guru or what he was like.
    I have never been able to explain that or other similar experiences, other than by accepting a similar stance to that in Rafe's question, despite maintaining an interest/curiosity in the Scientific explanations about the Universe which doesn't usually include consciousness in its theories, which to this day puzzles me......
    I still think reductionism, and looking for causal factors to be 'on a different plane of under/overstanding of our place in the universe', and I prefer the overstanding philosophy, to the understanding science, if you get what I'm trying to express?

    Aitch
    rafefurst
    Yes, I understand what you are trying to express.  Putting it into words is difficult (impossible really).
    Have you looked into the Global Consciousness Project?  http://noosphere.princeton.edu/

    I am someone who has made most of his living off of relying on the results of statistical reasoning.  And yet I know that the fundamental assumption (that of independence of events) is a fiction.  As complexity in our world increases, the fiction becomes greater.  Nothing is independent.

    I have been pondering recently what a theory of coincidence would look like (as in co-incidence).  Most scientists would think this worse than intelligent design, I suspect.
    Rafe Furst http://emergentfool.com
    Aitch
    I had a look at your link, to Global Consciousness Project, but it made me shudder, however I found a link, there,  to the Noetics Institute, with which I feel an affinity

    http://www.noetic.org/

    I haven't looked for links like this, as, to be honest I got disillusioned quite a few years ago, so maybe it's time for me to do some fresh research

    This interview with Edgar D Mitchell is fascinating, for example, as I had personal experience with Cancer/healing, and I particularly like his thesis that intuition be regarded as a fundamental 1st sense, rather than a sixth sense. I had no idea he was so responsible for much of current thinking about entanglement mind and group patterns

    http://d3uiy70t9jk1bx.cloudfront.net/library/audio/mitchell_e__intention...


    Aitch
    Amateur Astronomer
    Steve, a lot of the original quantum mechanics including string theory was written in terms of Fourier series. Especially it was used when many frequencies were described coexisting together like in a wave function. Fourier series created infinities in quantum calculations that had to be renormalized out by matching pairs of terms with opposite sign. In recent times work was done to get a better generating function. Quantum mechanics has a lot of expertise behind it, and is very far advanced from the level of general science studies. There are few chances for a non specialist to contribute. About the only original work I’ve done in QM was the Vacuum Partition theory to remove the objections of general relativity to quantum field theory.
    socrates
    Thanks, Jerry, for that clarification. Certainly, quantum theory is extremely complex. My primary objective is to learn as much as possible about the workings of the world on the most fundamental level and to share that understanding with others. That's what teachers do. Any contribution to science or philosophy on my part would be incidental.
    Citizen Philosopher / Science Tutor
    rychardemanne
    Back to history. One of the main philosophical locking of horns between the Catholic Church and Galileo was over the nature of mathematics. The argument from CC ran somewhat like this: we accept that the Ptolemaic construct is not perfect because it is merely a mechanical device with which to obtain fairly accurate predictions; the true course of the heavenly bodies is subject to heavenly will and therefore the mathematical construct is there to merely "save the phenomenon"; your heliocentric system and elliptical orbits are merely a better construct to "save the phenomenon"; therefore your victory remains hollow - the planets may appear to move with a certain order but that is a consequence of divine will and not a consequence of your mathematics. Galileo took the opposite view: the solar system had a certain structure because the mathematics was simpler. It took Newton to make Kepler's laws a consequence of one attractive force. There was still a ghost in the machine but it had no willpower. The angels were sacked and subsequently revolted, although certain chroniclers dated this to an earlier era.

    In a now obscure but popular medieval text, The Marriage of Mercury and Philology, Arithmetic is considered to be above the gods, so much so that even Zeus bows to her. Allegory or not, the idea that the universe is mathematical goes certainly back to Pythagoras and the Vedas. It's a hard idea to break when the mathematics very often precedes the physics. However, like in much of history, we rarely get to look at the failures; how many branches of mathematics are there, or have there been, that have proved completely useless to science? And where are they?



    Richard King
    Mathematics
    In modern use
    (a) the abstract science of quantity, including arithmetic, algebra, etc.
    (b) in a wider sense, those branches of research which consist of the application of the abstract science to concrete data (applied or mixed mathematics)
    Shorter Oxford Dictionary

    Aitch:
    I was always of the opinion that nature just is

    Agreed, except it is the “Is” rather than the “is”; not limited to the perceptions on which most human reasoning is based.

    I'm more curious as to the physicist's answer. Anyone?

    The physicist’s answer is limited:

    If you insist, here it goes:
    "actually exist" = silly undergrad/stoner "philosophy" of no value whatsoever
    Sorry to be so harsh, but in face of "really real reality" I cannot help it.
    Q.E.D.

    There is a great deal of difference between the “real reality” of the physicist, et al, and “Real Reality”, though you will not find a great deal of the latter in science, at present. Those aware of Real Reality are rarely harsh. That level of awareness does not really go with harshness, or similar attitudes.

    Steve Donaldson:
    Well this is actually a very eastern philosophy and I do myself subscribe to it, myself. However, language is very tricky and this philosophy can be, and is, interpreted in many different ways. Because it is often used to promote the possibility supernatural/religious worlds or forces, this very idea can be very repugnant to the rational thinker. Having said that, I myself have come to the conclusion that the physical world is a subset of the metaphysical world (and emerges from it); that is, the material is a subset of the ethereal (and emerges from it). I don't mean anything supernatural by that. What I mean is very close to simply stating that the Newtonian world is a subset of the quantum world and emerges from it.

    Supernatural is a somewhat subjective description. There are matters that many of us experience which some regard as supernatural and we as entirety natural. Much, most, of what we take for granted today would be supernatural to the peoples of a few centuries ago.

    I agree that the Newtonian world is a subset of the quantum world; that was also the thinking of David Bohm. On an experiential, reasoning and other knowledge basis I am equally sure that the quantum world is a subset of another world and so on, though I am not sure how “deep”, actually “high”, they go; it is to do with energy levels and frequency levels, which is one of the reasons why the physicists are having such a hard time getting there.

    Mathematics, like science, and most other things, is simply another heuristic; perceived as useful in certain contexts and situations, while being fallible and, ultimately, unprovable.

    As far as “the nature of existence” is concerned, both mathematics and science in general still have quite a way to go; the surface is barely scratched.
    rafefurst
    Those aware of Real Reality are rarely harsh. That level of awareness does not really go with harshness, or similar attitudes.
    I have also noticed this.
    On an experiential, reasoning and other knowledge basis I am equally sure that the quantum world is a subset of another world and so on, though I am not sure how “deep”, actually “high”, they go; it is to do with energy levels and frequency levels, which is one of the reasons why the physicists are having such a hard time getting there.
    Yes, "turtles all the way down". You might resonate (so to speak) with Norm Hirst's work (see autognomics.org). "Reality" is Life-itself (which is vibrational in nature). Matter, energy, et al are projections or manifestations of that universal pattern. Of course words are too course to do justice to the profundity of the message and render it silly-sounding.
    Rafe Furst http://emergentfool.com
    socrates
    "Mathematics, like science, and most other things, is simply another heuristic; perceived as useful in certain contexts and situations, while being fallible and, ultimately, unprovable."

    In the defense of science, I must say that while science is fallible and limited, it is less fallible and less limited than any of the alternatives. I say that as someone who considers himself to be more of a philosopher than scientist. Philosophy has a critical contribution to make to science but can never be a substitute for science. Philosophy can help in the formulation of new hypotheses and whole new world views, but we need science to test our ideas and possibly disprove them. That is why I seek the counsel of the scientists. They have the data. They know the facts better than anyone. When man's ideas contradict natures behavior, it is man that is wrong, not nature.
    Citizen Philosopher / Science Tutor
    rafefurst
    I would put scientists and philosophers in the same general camp of "cognitive explorers".  Both can learn much (I have found) from practitioners (i.e. those who experience directly).  As for what realm of practice, it hardly matters.
    Rafe Furst http://emergentfool.com
    Aitch
    When man's ideas contradict natures behavior, it is man that is wrong, not nature.
    There is something to this, however, I feel 'wrong' to be too harsh, merely disillusioned is perhaps nearer.
    I feel an affinity to Richard's understanding, but recognise that the thing that gives Science the edge over the 'Spiritual minded' is the fact that the language is more universally agreed. I've lost count of the number of times I've heard 'Spiritual' people say something like, 'If you were on my level of vibration, you wouldn't think/say/do that'...and immediately I cringe......'levels' just doesn't fit well with me, though I struggle to find a better description of heirarchical perspective consciousness, and it seems to fall into the category trap of 'little boxes' needed to make everything neat
    I envision more  something akin to 'spiral dna chains' which one metaphorically 'exist in' and  transcends only upon finding the key to transition to the next 'opportunity for consciousness growth' [as substitute for 'level']

    Rafe, glad to see you give experiencers credit

    Aitch
    Richard King
    Rafe:
    Matter, energy, et al are projections or manifestations of that universal pattern.
    Essentially, agreed.

    Steve:
    In the defense of science, I must say that while science is fallible and limited, it is less fallible and less limited than any of the alternatives.
    I do not attack science, nor do I attack scientists. I am very enthusiastic about science and have been since the 1950s. However, I am aware of the limitations of science, both professionally and non-professionally, as well as many other human endeavours. I am somewhere between dismayed and appalled at the direction science, at least “mainstream science” has taken in the last decade, or two; that direction essentially seeming to be that materialistic, atheistic, science, usually applied at a rather basic, bog standard, level, similarly with the attendant logic and reason, is all, everything, the ultimate authority, and that everything else is rubbish, delusional and stupid.

    If engineers did not recognise the limitations of science and go beyond it, find ways around, particularly if we took the “evidence based” on science alone route, the world as we know it would not exist; just one example is applying knowledge and experience of real materials rather than keeping to the theoretical models and the science of those materials.

    How fallible science is depends on how and where it is applied and by whom. Engineers tend to know, have to know, the limits of science and the rest is based on their judgment; actually, all is based on their judgment. Along with others I also know areas where science is currently limited in its capability, though much of that limitation is down to the knowledge and ability of those who endeavour to apply science in those fields. I am well aware of instance where people, respected in their field by many, mainly because they come up with the “right” results, are engaged in rubbish science and proving nothing really because they have not a clue about the matters with which they are dealing. I have even had a professor “run away” from questions I asked him about a subject on which he professes to have knowledge; I happen to know more than he does on a particular subject but he declines to answer queries on his published errors. I was thinking about blogging about it on Science 2.0 and continuing the discussion through his website but, although the professor is engaged in what others deem to be science I was not sure that the subject he wrote about would be considered scientific. That is one of the other problems about science these days, some subjects are not acceptable, thought he science with which I grew up had no boundaries.

    I say that as someone who considers himself to be more of a philosopher than scientist.
    I say what I have said as an engineer and also as a scientist, even though science is only a relatively small fraction of engineering, and as a mystic, healer, etc. I therefore, consider myself to be entirely capable as far as science is concerned, plus engineering, certainly those areas of engineering which are within my knowledge and experience, plus higher matters, though I know my limitations there as well.

    By mystic I mean a person who is aware of and can comprehend a reality beyond the usual general level of physical human understanding, as well as routinely link with it. We are all part of that Reality, whether we understand it, or not, can sense it, or not.
    Aitch
    By mystic I mean a person who is aware of and can comprehend a reality beyond the usual general level of physical human understanding, as well as routinely link with it
    There are as many ways of 'linking with it' as there are mystics, methinks, as few agree on what or how, they 'link'.....or on what 'level' [see my earlier comment] they are at
    I think the idea of frequencies and consciousness is something which Science could test, but most Scientists seem to have preconceived ideas as to what is meant by 'frequencies' and restrict themselves to the wrong area of frequency and the wrong test equipment
    Certainly a common theme amongst 'enlightened wise men' of eastern teachings is that of higher frequencies of resonance being connected to lower inner vibrational mind waves, so maybe the only Scientists capable of answering these questions are those who know how to put 'the experimenter/themselves' into the 'state of mind' of the experiment and slow their own vibrations?

    Aitch
    Richard King
    Aitch:
    There are as many ways of 'linking with it' as there are mystics, methinks, as few agree on what or how, they 'link'.....or on what 'level' [see my earlier comment] they are at
    Of course there are and each to his own. Everyone has to find their own way; that is part of the experience.

    I think the idea of frequencies and consciousness is something which Science could test, but most Scientists seem to have preconceived ideas as to what is meant by 'frequencies' and restrict themselves to the wrong area of frequency and the wrong test equipment
    In general, scientists are do not have the knowledge, experience or requisite trains of thought to investigate such areas successfully. It is difficult to do good science without at least some understanding of the subject under investigation and many so-called, self-styled, experts have not a clue about those matters, or, at the very least, significant parts of them, they profess to investigate and/or have knowledge of, e.g. Professors Edzard Ernst, Richard Wiseman and Chris French, to name but three. I was going to say, write, “to a slightly lesser extent” as regards Chris French but a recent blunt comment, in the “know it all” category, quoted in a recent newspaper article, changed my mind.

    The exceptions are people like those involved with organisations like the Scientific and Medical Network (www.scimednet.org) and the ISSSEEM (www.issseem.org), for example. I have attended some of the Network’s “Mystics and Scientists” annual Conferences (www.scimednet.org/the-nature-of-dreams) at the University of Winchester (www.winchester.ac.uk/Pages/home.aspx) and feel entirely comfortable in such company; as an engineer, I am also a scientist, by default, and, being well aware of more than just the physical, material, on a semi continuous basis, with the ability to achieve a much stronger connection at will, I would fall under the definition of a mystic. There is discussion, exchange of views and opinion in an atmosphere of mutual understanding and respect for each others views, knowledge and experience.
    Certainly a common theme amongst 'enlightened wise men' of eastern teachings is that of higher frequencies of resonance being connected to lower inner vibrational mind waves, so maybe the only Scientists capable of answering these questions are those who know how to put 'the experimenter/themselves' into the 'state of mind' of the experiment and slow their own vibrations?
    The vibrations of the physical world are slow, very low frequency, the connection being at higher frequencies. The frequencies are somewhat beyond technologies with which I am familiar, beyond Zitterbewegung, even Planck frequency, as far as my understanding and knowledge is concerned. I have thoughts about how to transducer those frequencies down but only very first thoughts and that is for the future, anyway.

    It is not exactly a case of “only Scientists capable of answering these questions … etc.,” in quite the way that you put it but their is the perennial problem of scientists experimenting in areas that they do not understand, thereby using assumptions and procedures that are not suitable, coming up with rubbish results, though the rubbish results frequently, invariably (?), fit limited mainstream, flatland, thinking, so that is what is “proven”. By such means Edzard Ernst proved, essentially, that placebo does not work because placebo is no better than placebo. He also “ran away” when I asked him specific questions on a subject he professes to be knowledgeable, though that is another story; I happen to have experience and knowledge of that particular field as well as a good science background and he seems not to have been able to handle the combination.
    Aitch
    Thanks, Richard, good to see you posting! I think you probably understand 'where I'm coming from'
    I hadn't seen the ISSSEEM before, although I've seen the scimednet site before, but a meeting I would like to have gone to not so long ago, was about £10, whereas most meetings I go to are free or voluntary contribution...as a Pensioner, I don't have a great deal of spare money to explore my interest, but I understand why you feel comfortable with them
    Did you make it to CamExpo at Earls Court this year, as that's a place I feel 'at home'?

    Aitch
    Richard King
    Aitch:
    My posting is spasmodic because I am trying to get back to it while, at the same time, finalizing my book manuscript and chasing several other matters. There are some issues to do with the delay of the book, which will make a story in its own right; not all are psychological, in the conventional sense, though I am, hopefully, going to post a blog on the psychology of such matters when I do manage to get it finished and felt it go. Recently, one of my colleagues from the Havant Healer’s Group offered to help with proof reading, following a passing mention of finishing the initial corrections, etc., in early October, but still finding errors during the first reread. I have already put in my original corrections, along with those that Sylvie Lucas (www.richardspsychicrealm.com/RPR_familiar_spirit_richard_lucas.htm), my editor and also a member of the Healers’ Group, found, along with most of her suggestions for modifying the text.

    Also, I take rather a long time to write, then check, double check, etc. I have not mastered the art of writing quickly and just letting go; the manuscript has been a serious letting go problem.

    I first came across the ISSSEEM (www.issseem.org) a year, or two, ago, maybe more given the way that time seems to fly. At least in part that was because Professor Brian Greene, author of “The Elegant Cosmos, etc., was giving a paper at one of their conferences. I also noticed that Christine Page (www.christinepage.com) was a member of the ISSSEEM. I met Christine back in the 1990s when she give talks at COMPASS (Chichester Open Meetings Psychical and Spiritual Studies, as I recall) in Chichester. Her description of my old petit problem, in the book Through Healing to Wholeness” (www.hk4health.co.uk/frontiers-of-health-from-healing-to-wholeness-by-dr-...) on a psycho-spiritual basis, was close to being an exact fit of what I experienced. That was in the early 1990s and is in the book. Christine moved to the U.S.A. in the late 1990s, I believe. She was, presumably still is, also a member of the Scientific and Medical Network.

    I could not quite remember the full title of compass, manly the word for which the “P” stood, but, while this comment, mostly finished, has been on my computer for a couple of days, I reached the relevant part of “Remembering Lorelei”, during a re-read of what I hope, will be the finished manuscript; specifically Chapter 5, of twelve, originally entitled “Progress?” but needs a new title.

    No, I did not go to CAM expo at Earl’s Court; I am not sure that I knew it was on. I also have a cost problem, at present, though that is because I am forcibly semi-retired, have been for several years, due to local circumstances; a certain matter of Local Government corruption and resulting cover up which has resulted in me hardly being able to move in Hampshire, in the business sense, with the sole exception of Portsmouth and South East Hampshire Chamber of Commerce (www.chamber.org.uk), now part of Hampshire Chambers of Commerce (www.hampshirechamber.co.uk), Southern Entrepreneurs (www.southernentrepreneurs.com) and their friends. There have been one, or two, partial ways out, which I missed, though the only real one is the book.

    My financial situation is the main reason I have not been to as many meetings as I would wish. I trusted a Council and lost everything, ending up being helped by the Institution of Mechanical Engineers Benevolent Fund (www.bfime.org.uk/index.asp?contentid=73) in some ways; they came to see me after I asked for a deferment of Membership fees – the “rewards” for being an entrepreneur, setting up business in Havant, Hampshire . I even dropped out of the Scientific and Medical Network for a while as I could not justify even £30 per year for membership. Quite a jolt after begin on the brink of Director of a major Technical/Business Centre for which I had won European Funding, plus an almost certain Professorship.

    The hesitancy has resulted from the likely considerable publicity deriving from who Lorelei is, i.e. not just anyone by that name and the extra publicity from local events following me into the public domain. There was also some concern regarding my wife, Jo, though she is now also pushing me to get the book out, a considerable change from her initial hesitancy; Jo is Lorelei’s Soul Sister, though you may have found that out by now, from the Web, as well. On the other hand, Sylvie has maintained that it will go when the time is right. Hopefully, we are now close.
    Aitch
    Thanks for the background, Richard
    Thee and me have had similar experiences with Government corruption, but I think you had more support than I....good fortune, I guess
    I'd agree with Sylvie....perhaps in the theme of the thread, 'it will go when the time is right' adds up to the same as 'when the numbers fit the universe'?
    Good luck - I'd be interested in a copy, if available?

    Aitch
    Richard King
    Henry,

    I have support in the physical, fortunately, as well as from “Upstairs”. Caroline said she was an “Old Soul”, so she may be still around and willing to help but we will see what is meant to be.

    I am not sure if I mentioned it on here before but Caroline is with us in Barbara Ford-Hammond’s book “Past Life Tourism” (www.amazon.co.uk/Past-Life-Tourism-Gateway-Bridging/dp/1902578317), see, for example, www.richardspsychicrealm.com/RPR_Barbara_Ford-Hammond.htm.

    Essentially, I have concluded that I am meant to use the book and the story behind it to get past the “Hampshire Block” as I have tended to refer to it. The result should also be enhanced democracy in Havant, as well as Hampshire, to some extent, at least for a while.

    Current progress on the book is that the manuscript is now complete (currently just over 100,000 words and unlikely to change substantially) and I am two-thirds of the way through the first re-read. I hope to send the file in January, or February, so, assuming I do not need to find other arrangements for publication, etc., it should be available next spring to summer; probably about the time that our third grandchild is due to be born. If that is the case and those who have advised me are right, it could be quite a year.

    The book should be readily available online, or to order through bookshops.
    rafefurst
    Richard,
    Do you know about Kickstarter.com?  Many authors are using it to pre-sell copies of their books.  

    You pick an amount you'd like to raise (e.g. $1000, $10K, whatever) and whomever donates more than, say $30 (or whatever you specify) receives a "free" copy as a gift.  You keep all the proceeds to fulfill the gifts and cover your expenses in writing the book.  The amount raised is treated as a gift so you can technically do whatever you like with it.  You can also be creative with incentives to get people to donate more towards your project.  E.g. for $500 or more you will throw in a healing session via skype video; for $2000 or more, you will fly to visit them for a week to help them problem solve whatever hairy problem they have; etc.
    Rafe Furst http://emergentfool.com
    Richard King
    Rafe:

    Many thanks for the tip about Kickstarter.com. I had a quick look. It may come in useful for the book, though I am hoping that current, or replacement, facilities will be readily available for that. Where Kickstarter.com would be of considerable potential use is for something else that I have in mind.

    As I have a considerable science background, let alone my involvement in engineering, I am well aware of the limitations of science, even more the limitations of those who seek to apply it. My non-physical side has highlighted those limitations even more. On the other hand, the purpose of engineering is to move from one situation to an improved situation, how that is accomplished being, largely, immaterial. Where science is applicable, apply it, where not, do without, find another way. What most people, including scientists (especially scientists?), do not realise is that if engineers only did what was scientifically provable, quite part from the greater part of engineering which is art, not science, anyway, much of what is taken for granted in the “modern world” would not exist. Hence, I regard engineering, the engineering method, as a greater, more powerful means to achieve change and, therefore, logically, the engineering method is more likely to make progress in areas that science finds intractable, is “afraid” of, regards as “pseudoscience”; in reality, of course, that is nothing to do with science, which is neutral, but the limited people have imposed limits on science, or at least what they regard as science; they are keeping science within their limitations, not sciences’ limitations. So, the general thrust of what I would like to do is research in certain areas, taking an engineering approach, applying science as and when and where it is useful, otherwise making progress by other means and leaving science to catch up in due course. That is no different to what engineers have always done but the areas to which I wish to apply it are not strictly engineering at least not in the conventional sense but they are in the Real sense; the capitalization of Real being deliberate, much as Billy Vaughn Koen does is his book on the engineering method in relation to heuristics, where he underscores the second letter of each word that represents a heuristic, including science.

    I am fairly sure that my unusual side, unique from the Lorelei point of view, will be of interest to a sizeable proportion of the population of the U.S.A., quite apart from anywhere else. One possibility that I thought of, in exchange for assistance for funding such research, though I suspect that funds will come from other sources anyway for a number of reasons, was a contribution to the lecture circuit in a particular way. On the assumption that here are organsiations which specialise in arranging such tours, one possibility is for me to, in exchange for funding contributions to do a lecture tour on a little more than at cost basis, though, possibly, combining it with a holiday tour of the U.S.A., given that the circumstances already described have seriously curtailed the travelling that my wife, Jo, and I would have done. Besides, given J’s close connection with the main person in the book, her presence would be appropriate, though how long it will take her to get used to that relationship being so public is quite another matter.
    blue-green
    I’d like to discuss this further … did not know that the
    conversation had continued. As Steve’s evil double, I must traveling ‘till the
    close of this year ….  No one brought up
    Penrose’s Three Worlds or more as in the following diagram.
    [img]http://www.mountainlake.com/mlp/travel/3worldsx.jpg[/img]

    Somewhat distinct from Steve Don’s Three P’s: physics,
    philosophy and psychology.



    Following C.P. Snow’s Two Cultures … one could recognize
    that there are indeed Many Cultures and realize that what is Computable is not
    commensurate with what is Not-computable. Maybe that’s the real measurement
    problem.


    Those who subscribe to “A Theory of Everything” or the
    goal of  “A Complete and Unified Theory”
    ought to perhaps first prove that everything is computable. I am not so
    convinced that such a proof is even possible.


    Photo below is at a library benefit with Igor Gawow (by George) as a visiting author.



    [img]http://www.mountainlake.com/mlp/travel/gamowe2.jpg[/img]






    That’s a pool table in the foreground with some Carlsberg
    elephant beer under it.






    [img]http://www.mountainlake.com/mlp/travel/gamow2s.jpg[/img]









    http://www.mrt.theadventuresofmrtompkins.com/creative-team.html









    (I have to go through the “request a new password” process
    every time I try to sign in here … not because I can’t remember the password …
    maybe because I often clear my cache and cookie jar ….  I usually post as anonymous. Having syntax problems getting the photos to show while signed in ...The quantum
    elephant never forgets.)






    [img]http://www.mountainlake.com/mlp/beyond/elephant.jpg[/img]






    Oh, and the Don Howard articles noted further up … I
    did not know they were here with the man himself. I saw them elsewhere and was
    impressed.
    socrates
    Okay, this is really uncanny. I was just about to respond to Vladimir, below, with a reference to Roger Penrose, when I happened on this post from my evil twin, Prof. Blue-Green (I don't know how I missed it earlier). Yes, indeed, there are those who see mathematics as primary and my understanding is that Roger Penrose is one of them. He calls himself a Platonist, by which I understand him to mean that our experience of the world will always be only an approximation of the real/ideal world. This is essentially what Plato was saying with story about shadows on the wall of the cave. This, in Penrose's eyes, makes mathematics primary and everything else secondary, for only mathematics can describe the ideal, as opposed to that which we measure in front of us.

    However, in light of his reverence for mathematics, almost to the point of sacredness, I would be tempted to call Penrose more of a Pythagorean than a Platonist. It was Pythagoras who elevated mathematics to the status of all powerful and all knowing, that is god-like status. Coincidentally, it was also Pythagoras who anticipated Bohr with the idea of quantized orbits and de Broglie with the reason for the quantized orbits being the necessity of harmonic waves fitting neatly into each allowed orbit. Of course Pythagoras was talking about the orbits of the planets around the sun and not the electron around the nucleus, and so was dead wrong with his specifics. However, his insight, derived from pure mathematical considerations, did prove correct over 2000 years later when applied to the atom. So perhaps there is something to this primacy of mathematics.
    Citizen Philosopher / Science Tutor
    Aitch
    Here's a philosophical and experiential moment of enjoyment, which seems to support the thread's title

    Nature by Numbers from Cristóbal Vila on Vimeo.

    It will go fullscreen HD, if your PC is up to it!





    Courtesy: http://flowingdata.com/2010/05/10/dreaming-in-numbers/

    Aitch
    rafefurst
    Great video, thanks for sharing.
    So does this clarify at all which came first, the math or the biophysical reality?
    Rafe Furst http://emergentfool.com
    socrates
    "which came first, the math or the biophysical reality?"

    There is always the possibility that they are one and the same, or, at least, that they have a common ancestor/origin. I personally subscribe to the latter - common origin.
    Citizen Philosopher / Science Tutor
    rafefurst
    yeah, different manifestations of the same thing, i agree.  i think though, given our "objective reality bias" as scientists and rationalists, it helps to overcompensate and consider how our thinking would change if we indulged these related notions:
    • observer is primary
    • observation creates reality
    • "observer" need not be anthropomorphized or deified, but understand its nature (and the nature of observation) is key to further progress in may areas of science, including physics and biology



    Rafe Furst http://emergentfool.com
    socrates
    Rafe, I don't disagree with you in principal, but I would caution on some of the language. In particular the word "observer".  I think, it is hard for most people to separate that word from the anthropocentric perspective, your disclaimer notwithstanding. For most, I think it will conjure an image a person or person-like deity and I, myself, would not want to leave that impression. If by observer you mean anything that can "collide" with something else then I am okay with that.

    Actually, on a deeper level, the observer is also a construct. It is the observation that is primary. The observation creates both the observer and the observed. The Zen way of putting it is that there is no thinker and there is no thought, there is only thinking.

    Of course all of this talk can cause more confusion than clarity since our language and common experience in this area is so limited. I encourage personal exploration in this area, but I do not think it is necessarily "
    key to further progress in may areas of science, including physics and biology". We work and live our daily lives mostly right here in this higher, constructed realm and there is no shortage of progress to be made right here. That is to say, just because physical reality is a construct, does not mean it is not real or important. It just means it is emergent from more fundamental elements - so what else is new? :-)
    Citizen Philosopher / Science Tutor
    rafefurst
    While we agree on the potential confusion of language, I suggest that because of this it's essential to "go there" and explore/try-on these emotionally-laden and provocative linguistic constructs.  In as much as Science 2.0 aims to improve the methodology by which we gain insight, it is absolutely in-bounds to suggest that this is not just personal issue but rather an epistemological issue, and thus is only effective if we embrace it at the group level.


    Notice how different a research program is implied by these categorical assumptions:


    • "there is no thinker required, things exist independently"  
    • "there is no independent existence, just a thinker (or thinkers)"  
    • "there is one thinker, He creates existence and the Laws by which it operates"  
    • "there is no thinker and there is no thought, there is only thinking"  





    Should we be afraid to explore them all (and others) because we might become confused?  Isn't this reason to confront those fears head on and thereby understand empirically which are chimerical and which advance our ability to make falsifiable predictions?



    Rafe Furst http://emergentfool.com
    Aitch
    Rafe/Steve
    Since this is a twist on the original, I agree about the language confusion...when has it ever been otherwise?

    As to the thinker and the thought, I would add 'the confusion between the self and the mind'

    My Self has many insights which are not borne of thought, and my mind is the greediest beast on the planet, forever asking me to 'take notice of it' as if Ego had some function or value to my journey in the unknown
    Some unknowns, I have discovered have a 'time and circumstance for disclosure' dependent upon my own spiritual awakening/awareness

    Some again, it seems, are destined to be unknowns for longer than I am likely to live.....but we are entering an exciting turning point in human collective consciousness......so who is to know, will be revealed......'as, and when'

    good luck, though I think this may be a personal journey, Rafe

    Aitch
    socrates
    Oops, perhaps I should rephrase the part where I said "I encourage personal exploration". Actually, I encourage both personal and group exploration of this topic. It is a fascinating topic and well worth exploring.

    Nevertheless, I don't believe science is seriously impeded by having this issue unresolved. In fact, I think science might do well to have none of the above assumptions and simply follow the evidence wherever it leads.
    Citizen Philosopher / Science Tutor
    rafefurst
    "science might do well to have none of the above assumptions and simply follow the evidence wherever it leads"

    I can live with that as an epistemological position.  I'm skeptical of it's practicality based on the evidence :-)
    Rafe Furst http://emergentfool.com
    Aitch
    So does this clarify at all which came first, the math or the biophysical reality?
    I don't believe it does!....it's the chicken and egg deal, methinks, and I have to ask, 'What hinges on it?
    Does some important Scientific or Philosophical question?
    Or just a personal/groupthink query?

    Aitch
    Vladimir Kalitvianski
    Is English language inherently a part of the structure of the universe?
    socrates
    Vladimir, I suspect you are being facetious (tongue in cheek / joking) with this question. However, I think we can actually gain some insight from examining it. Yes, there is a similarity between English and mathematics in that they are both a kind of language. And one might argue that language is a human invention and so how could these be in any way "inherent to the structure of the universe"?

    Well, let us ask is there something special about mathematics that makes it different from English. English, certainly, is not a universal language. Would you not say, on the other hand, that there is something universal about mathematics. The
    Pythagorean theorem was known to the Egyptians before the Greeks. And if Pythagoras and the Egyptians had not spoken of it, certainly others would eventually speak of it. Should we some day encounter another civilization on a far away planet, we certainly would not expect them to speak English, but we would expect their mathematics to agree with ours and the sum of the angles of a triangle lying in a plane would still add up to half the way around a circle.

    So then if there is something universal about mathematics - if it is a kind of universal language - then one might ask, what is its relationship to the universe that makes it so, well, universal?

    Oh, and I almost forgot to mention Roger Penrose (see my response to blue-green above). Here is a
    theoretical physicist who certainly thinks mathematics in inherent to physics and the physical world and perhaps is indistinguishable from it. He writes extensively about this in his book, The Road to Reality. (I don't necessarily share this extreme view, myself.)
    Citizen Philosopher / Science Tutor
    rafefurst
    This is a great question.
    Rafe Furst http://emergentfool.com
    Gerhard Adam
    So then if there is something universal about mathematics - if it is a kind of universal language - then one might ask, what is its relationship to the universe that makes it so, well, universal?
    That is a tautology, since it presumes to question the universality of mathematics while using mathematics to perform the measurements by which we evaluate the universe. 

    The question to ask is what is it that mathematics measures?  If it is based on geometry, then it follows that if the universe consists of geometrical shapes, then any symbolic system based on geometry will find corollaries.  In other words, mathematics does not have a separate existence since everything used to verify it, exists in the real world and since mathematics cannot be derived from first principles, then at best we can simply argue that it represents its origins.

    Just as we can't look at the English language and marvel at how every word we use seems to have meaning to another English-speaking listener, so it is with mathematics.  It is a product of its environment and consequently can't help but appear to be intrinsic to that environment.

    Certainly mathematics has been subjected to rigorous logical evaluation, so we would expect it to be consistent in any environment in which it was applied, hence the appear of universal application.

    However, it should also be clear that there are many things that can be expressed mathematically that have no real world existence, so that should be our first clue that it does not represent reality as an inherent property of it.

    In fact, one primary consideration is how frequently the real world can't be expressed mathematically without taking tremendous liberties in how we express it (using approximations, etc.).  What is 'pi' in the real world?  We know it is part of the mathematics of circles, but what is it really?  Can we ever experience its actual value?  Is it even necessary or is it simply an invention of our mathematical processes?
    Mundus vult decipi
    Quentin Rowe
    The question to ask is what is it that mathematics measures?
    I've always thought mathematics at it's most basic represents proportions and/or relations between different elements. That so much richness&complexity can unfold from a system that is by its nature self referencing, is truly astounding to me.

    This raises the issue of how these elements became separate in order to have a difference to measure. Is the assumed separateness artificial or something more fundamental?
    Gerhard Adam
    Is the assumed separateness artificial or something more fundamental?
    I would suspect that it is fundamental, which involves the "arrow of time" as much as anything else.  It's a mark of changes occurring that gives rise to all the phenomenon we experience and the ordering of such events.
    Mundus vult decipi
    socrates
    Yes, mathematics is the language of relationships, or as we would say in physics, laws. Why there should be laws at all, is itself an interesting question. What are the fundamental laws is of course a fundamental question. Lee Smolin suggests in The Life of the Cosmos that the laws that govern our universe are not necessarily immutable. That is, he says the fundamental laws themselves may have evolved over time. For me that begs the question, are there laws that govern the evolution of laws. (I think he would say the law of natural selection would be such a law).

    You ask how how elements became separate so that there could be relationships between them to be measured. If the fundamental elements are laws and laws operating on laws beget more laws you have system that builds on itself. My feeling is that there is one ultimate law and I would call it the Law of Universal Evolution, along the lines of Lee Smolin. It has yet to be perfectly articulated, but would include the universal truth that all is change, first articulated, I believe, by Hericlitus (famous for saying "you never step into the same river twice"). I would call it a universal truth, but not everyone will agree with me, I am sure. I see change as fundamental, because I see time as fundamental, not an illusion as some have suggested. Time comes before space, and space comes before objects in space, and all else we experience as physical comes after that. That is how I see it, anyway.
    Citizen Philosopher / Science Tutor
    Gerhard Adam
    I see change as fundamental, because I see time as fundamental, not an illusion as some have suggested.
    I might suggest you look over a series of articles that Patrick Lockerby put together last year.  There was some interesting discussion there and you might be interested as well.

    http://www.science20.com/chatter_box/blog/theory_time_part_one
    http://www.science20.com/chatter_box/blog/theory_time_part_two
    Mundus vult decipi
    socrates
    Thanks, Gerhard, for the links to Patrick's excellent series on time. (Was there a part 7? I only found 1 through 6, which ended with "In the next part, I shall discuss...")

    It is all a bit overwhelming but the
    gist of what I gleaned from Patrick's presentation is "that time has no cosmic reality" and that it is inertia, not time, that is fundamental. The argument being, roughly, that if it were not for inertia, everything would happen all at once - that is, in no time at all. So, I guess, Patrick contends that time is a byproduct of inertia. I may not have that exactly right, and I don't mean to put words in his mouth, but in any case, it makes for an interesting proposition.

    However, I don't buy it. There is a hidden assumption there, which is that if left to its own, time would pass infinitely fast. Why should that be assumed? One could have also assumed the opposite - that time might pass infinitely slowly. In that case one might argue that what is required to keep time from standing still is not inertia, but force. One could argue then that force is primary for without force there would be no change and without change there would be no time. Then time would be a byproduct of force not inertia.

    I don't buy either of these arguments, though one might note a
    resemblance to Newton's second law here, that acceleration is the interplay of Force and Inertia and what is acceleration, if not change.

    However, I don't see why we need to assume any inherent speed to time. (Indeed one might argue that it is the granularity of time that leads to the invention/emergence of Force and Inertia.) What we need in not any particular rate of change, but we do need change. Without change, there is nothing. For without change there is no effect, and without effect there is no existence. What does it mean for something to exist and yet have no effect? Something that has no effect has no existence. So change is fundamental to all existence and time is the word we use to reference this ongoing change.

    This is not my only argument for the primacy of time/change, but I will leave it at that for now.

    P.S. One more quote about time to add to
    Patrick's excellent collection:

    "Time is what happens when nothing else does" -Richard Feynman

    P.P.S.
    I need to make a slight correction to my earlier post. I mispoke in my list of emergent phenomenon. The correct order is time>object>space, not time>space>object. Objects define
    space. Objects require time, and they create space. Sorry about that.
    Citizen Philosopher / Science Tutor
    Gerhard Adam
    So change is fundamental to all existence and time is the word we use to reference this ongoing change.
    Fair enough, but that gets to one essential point, in that time is not a fundamental characteristic of the universe.  It does not have an existence of its own, but is simply the result of other things occurring by which we measure or notice the change.
    Mundus vult decipi
    socrates
    Yes, time is a concept linked to a process. Time is what we call generic ongoing change. Time, the concept, is not fundamental, but that which we refer to when we say "time", is fundamental. You are hitting on the distinction between a map and the territory to which the map refers. Language can be tricky that way. The map is not the territory. Nevertheless, when I say "time is fundamental", I really mean, "that which time refers to is fundamental".
    Citizen Philosopher / Science Tutor
    Gerhard Adam
    One of the comments I made in Patrick's discussion was:

    While it is true that mathematics is not "reality", it is a logical system that provides us a means by which we can extrapolate results that do reflect the real world.  By analogy, it is like flying an airplane in a dense fog using instruments.  The instruments are not "reality", but they certainly reflect the real world in which we are flying and one ignores their data at one's own peril.  In effect, flying an airplane on instruments is akin to navigating reality using mathematics.
    Mundus vult decipi
    socrates
    By analogy, it is like flying an airplane in a dense fog using instruments.  The instruments are not "reality", but they certainly reflect the real world in which we are flying and one ignores their data at one's own peril.

    Bingo! You are almost there. (I call it the bathysphere insight, but an airplane on instruments works just as well.) We can never experience really directly. We can only experience our experience of reality. Our experience of our experience is our reading of our instruments. All we can read is our instruments. All we can see is the inside of our cockpit. Here it comes... All we can see in the inside of our mind! We infer there is something just on the other side that corresponds to what we see on this side. We come to accept a one-to-one correspondence between our readings on our instruments and what is out there. We master this language at a very early age and call this language physical reality. So you see, your insight applies not only to mathematics and time but to the whole of physical world. That is why I say the physical is a subset of the metaphysical, and the material is a subset if the ethereal. All of which is enough to make your head spin, but this is not my intent.

    Once we accept this insight we still have a lot of questions to answer and everyday problems to cope with. The physical world does not cease to exist. The physical world is what we experience as the physical world and time is what we experience as time. (I don't think mathematics is an experience in the same sense, so I don't think there is as much confusion with the physical there. I think it is understood that mathematics is ethereal all along. The question might be asked, is mathematics proto-physical, that is, is it a precursor to the physical or just an adjunct.)

    Sorry if this is starting to sound too mystical for a science site. (I myself, would prefer to call it philosophical.) So let me reiterate, I do believe in the physical and I believe it starts with time/change.
    Citizen Philosopher / Science Tutor
    Gerhard Adam
    In that case, mathematics is simply the abstraction of the direct experience.  In other words, mathematics is never the experience, but the translation of that experience into symbols which can then be manipulated.

    It's much like the ability to abstract reality in stories (our imagination).  It clearly isn't reality, but it allows us to behave and act as if it were real (i.e. our ability to abstract reality is precisely what gives rise to our ability to solve problems that we imagine to exist).
    Mundus vult decipi
    Gerhard Adam
    Actually it was that ability to abstract is what my argument was regarding the rise of language in humans.  In other words, language is a necessary prerequisite in communicating anything that only exists in our minds.  For everything else, simple sounds and gestures would be adequate.

    It is from this that I personally believe, that animals can be intelligent and solve problems, but that they can only address those that are part of their direct experience, whereas humans can abstract such problems and formulate solutions.
    Mundus vult decipi
    socrates
    Nicely put. I essentially agree on all points. Language and imagination allows us to abstract, manipulate and solve problems in our minds. It also allows us to imagine/invent problems that don't really exist. The same goes for mathematics. It is enormously powerful but can also lead us astray. To use your analogy, we can see things inside our cockpit that have no correlations with what is outside. How can we tell the difference? It is kind of a Turing test in reverse. Are my instruments reading what is out there, or am I just reading myself? This is where we need the ability to reason. Experience alone is not enough. That is, we must reason from experience.
    Citizen Philosopher / Science Tutor
    Bonny Bonobo alias Brat
    I can't help wondering where the autopilot fits into this analogy?
    My article about researchers identifying a potential blue green algae cause & L-Serine treatment for Lou Gehrig's ALS, MND, Parkinsons & Alzheimers is at http://www.science20.com/forums/medicine
    socrates
    Ha, ha, very good questions, Helen. I would say the autopilot keeps things going while we are asleep, and possibly was keeping things going long before we ever woke for the first time. :-)

    (Do you know the footprints in the sand story? It is a religious reference. "Why are there sometimes only one pair of footprints?" I am not religious, but I like that story anyway. http://www.wowzone.com/fprints.htm Now I know the real answer to the question, who is in charge when we are asleep- it is the AUTOPILOT!)
    Citizen Philosopher / Science Tutor
    Gerhard Adam
    Actually you could probably make the case that the autopilot is that which allows you to breathe and keeps your heart going.  That which keeps you standing upright, as well as that which digests your food and extracts energy.

    Mundus vult decipi
    Aitch
    Good Question
    I have a different take on the autopilot
    Trusting your autopilot is something people do when driving, whilst talking on the phone, or when doing something familiar whilst your mind wanders elsewhere, thinking about some time displaced event, like a conversation earlier in the day, where maybe you start worrying about what someone thought about what you said, recalling it and playing it back with a different outcome
    People DO have accidents on autopilot, as it isn't as auto as we'd like...but then it is a mind function, and I personally don't entirely trust it to keep me safe...experience taught me otherwise
    However, it fits the airplane analogy...but see my earlier comment about a space vehicle in reply to Steve

    Aitch
    Aitch
    All we can see in the inside of our mind! We infer there is something just on the other side that corresponds to what we see on this side. We come to accept a one-to-one correspondence between our readings on our instruments and what is out there
    Not ALL we can see, really, as the Self is not the mind
    The mind really is the interpreter and computer that grabs all available information for the Self to use. Mistaking the mind for oneself is probably THE most common misunderstanding - I often say the mind is the greediest thing in the universe, and care needs taking that it doesn't overtake/take over who you are in reality
    Think in terms of your being as in a space vehicle, instead of an airplane...if the mind were in control, we'd have crashed...that is the job of the heart, as the heart's clarity can guide us through insurmountable obstacles on our journey, instead of crashing into them, and being overwhelmed
    There are other aspects to the Self's reality shared in common with others, including consciousness, which knows not only the map, but the whole terrain and environs of what is mapped

    It is said, 'When you change the way you look at things, the things you look at, change'

    I think this will be increasingly important in the next few months, as we enter the final speed up phase of consciousness

    Aitch
    Gerhard Adam
    It is said, 'When you change the way you look at things, the things you look at, change'
    But that isn't really true, is it?  The only thing that may change is our interpretation of those things, which is simply another way of changing your mind.  The "things" themselves are unaffected.
    Mundus vult decipi
    Aitch
    Well, Gerhard

    To me, it is more than simply another way of changing your mind, as the sort of instance I am referring to is more one of a gestalt consciousness shift, which doesn't really take place in the mind, but in the awareness of 'the way things are'...the mind change is as a result of the experience, of perception, and happens in a ripple down way, I found

    I do believe things themselves change, as I have seen, for example, plants and animals affected by a person's positive or negative emanations, and in certain ways, even to see something as a problem in your way, affects others views of it, albeit sympathetically, but many people don't realise how often and how surreptitiously these effects mount up, and in countries where creativity is not so openly utilised, a stranger to a culture can have a huge impact by demonstrating something thought to be normal, by its common application in their home surroundings, which can appear almost revolutionary, in a foreign land, and far more than just our interpretation

    Aitch
    Gerhard Adam
    Sorry, but I fail to see how these are anything except perceptual differences.  Your point about plants and animals is still a matter of interpretation since you're not claiming the animal or person has changed, but rather their behavior has.

    I'm being very specific here in defining an object, so that it isn't behaviorial or subjective.  In an overly simplistic example, it's like looking at a car and decided that you suddenly like the color versus hating it previously.  The color hasn't changed, only your perception of it.  That may sound trivial, but that's the type of specificity I'm referring to. 
    Mundus vult decipi
    Aitch
    Well I can only put this down to the fact that you are much more strongly attached to your mind than I, and find the idea of a shift of consciousness a mere mental exercise, perhaps?
    Being more experientially oriented, I was trying to relate, yet again, to my personal experiences
    To me, from direct experience, behaviour is far more than an effect of  a way of being, it is an intrinsic component of being - in changing behaviour, the being is a completely different entity, not just the same entity with different effects, as if the jacket or coat was changed
    Some changes take place at such a deep core of being, that what appears to be a surface effect is at the core a deep biological/electrochemical/electromagnetic/and psychic energy paradigm shift in consciousness
    I am trying to convey suitable 'specific' meaning to you, but at least look to meet me 1/2 way, else I see no reason to struggle to your benefit when it feels to my disadvantage to be talking to a closed book 'made my mind up' stance - I know you can reach 'that level of being awareness'
    I find your trivial example way off beam in relation to where I'm at, and asking you to consider, 'When you change the way you look at things, the things you look at, change'

    For you to say, you fail to see...
    ....just makes me giggle and go, 'You should've gone to Specsavers' ;-)

    Aitch
    Gerhard Adam
    ... find the idea of a shift of consciousness a mere mental exercise, perhaps?
    What else would it be?  I don't know if you're attaching something more mystical to it, or not.  I can certainly appreciate that you trust your own experiences, but that doesn't render them meaningful to anyone other than yourself.

    I'm always concerned when such ideas get expressed and they sound like little more than psychic mysticism.  No matter how you phrase it, it always ends up sounding like a completely subjective experience. 
    Mundus vult decipi
    socrates
    "Not ALL we can see, really, as the Self is not the mind"

    I have to agree and disagree here slightly, Aitch. You are right to point out that the Self is not the mind. However, you overlook the fact that the Self cannot see the Self. Anything you can see, is not the Self. Anything you can see is not the see-er. So that still leaves you with "All you can see is the inside of your mind." :-)
    Citizen Philosopher / Science Tutor
    Aitch
    Ah, I was using 'see' in the Gnostic sense, but I don't think we are far apart... ;-)

    Aitch
    Vladimir Kalitvianski
    > "mathematics is the language of relationships"

    Let me add: still relationships between still (simplified) entities. In other words, it is a virtual world, not the real one. In the re
    al world every object changes with time but we still call it with the same name.

    Mathematic is a very grateful virtual world. One can obtain so many beautiful results and enjoy them with a proud. Many like to apply their equations A=B to the whole Universe, and some even speak of multiverses. How exciting!

    At the same time we cannot describe even real elementary particles in current theories - our results are divergent. It means our initial approximation is quite different from the exact solution, even for a free elementary particle! And we succeeded in camouflaging these conceptual and mathematical difficulties instead of avoiding them with better physics implementation in our theories. So I think the question of this thread is premature.
    rafefurst
    Gerhard&Steve both assume Time is fundamental and I believe that constrains what else is possible/conceivable.
    In this essay I explore what happens when you assume Infinity is fundamental and derive the material world and spacetime from there.  As an aside (Steve), Universal Darwinism can be derived from a more general Anthropic Principle if you begin with infinity and keep time as an illusory consequence.

    There is another tack, which is to assume that Observation (aka self-reference / reflexivity) is fundamental.  This is the Eastern philosophical worldview as well as that of certain Western thinkers (Mandelbrot, Hofstadter, and others).

    My view is that none of these is (or ever will be) "complete", but if we begin with any one of them and insist only on logical consistency, we end up deriving an approximation of reality that's ever closer to our experience.  It's when we insist on more than one fundamental assumption AND consistency that we get into the world of paradox and confusion.
    Rafe Furst http://emergentfool.com
    Gerhard Adam
    You cannot use infinity (in any capacity) since it is only a concept.  Even if it existed, you could never confirm that it existed, so you immediately begin with an unverifiable element in your discussion.

    Infinity is far to vague a concept to be useful since virtually anything can be postulated with no possibility of ever obtaining a useful proof.
    Mundus vult decipi
    rafefurst
    While I share your skepticism of starting with infinity, it's no different than starting with any concept.  And we agree that it's ALL concept in the end, don't we?
    The problem with infinity is that it's tantamount to starting with False in modus ponens; i.e. in deductive logic, False implies anything.  You can prove anything if you start with infinity.

    This is no different though than starting with time, or object, or process, or whatever.  It's simply an aesthetic choice.

    I would postulate though that starting with infinity is more general than starting with these other choices.  Certainly if you look at the cardinality of the time continuum as compared to Aleph1, Beth1, etc. this is true.
    Rafe Furst http://emergentfool.com
    Gerhard Adam
    I'm not sure where your going with this, with these statements.  Certainly mathematics begins with certain axioms that do precisely what you're talking about, whether it be the definition of a line or a point, etc.  Consequently by considering it axiomatic that these "perfect" representations exist, we already introduce approximations into mathematics that must be accommodated when referencing the "real" world.

    One thing that is abundantly clear is that while mathematics can be a useful vehicle to abstract elements of the real world, it is NOT part of the real world.  It is equally clear that the world tends to operate in ways that are far more complex than our mathematics allows for (or at least our abilities to solve such problems).

    So, let me ask .... what are you "starting with" and where are you going to?  Are you attempting to establish first causes or simply axioms to begin the process with.  In either case, it seems that your beginning will always be arbitrary and you can arrive at any conclusion you think appropriate.
    Mundus vult decipi
    rafefurst
    "while mathematics can be a useful vehicle to abstract elements of the real world, it is NOT part of the real world"
    Ok, so your answer to the question posed by this thread is now clear.  Others disagree.  (But I'm not one of them :-)

    "Are you attempting to establish first causes or simply axioms to begin the process with"


    Simply choosing various starting points and seeing what can be derived.
    Rafe Furst http://emergentfool.com
    Steve’s evil double here (blue-green cat). (The photo link given further up was for Steve to verify that I indeed have his genes. The only difference is that I’m older, the real McCoy).

    On a different thread of this august site, Henry Cox gave a link to Max Tegmark’s, year 2007 paper on “The Mathematical Universe”.

    http://arxiv.org/abs/0704.0646

    I’m a little surprised that it has not directly made it into the discussion here.

    Here is a link to some feedback given on it elsewhere:
    http://backreaction.blogspot.com/2007/10/mathematical-universe.html

    I’d like to say more …. yet I have to hit the road again … Still slogging through it all.
    Will be back soon. …. ribbet

    Dear Rafe Furst,
    In my opinion-
    philosophy is a thought process.
    Physics is reality for human senses.
    Mathematics is a vehicle(or language) as Mr.Hank said.
    1.A thought may be real or imaginary thus philosophy need not be proved practically .But it should be logical. So the logical system developed by some assumptions will be agreed by reasonable means.But the assumptions will not have any basis. Such systematic thought process is called philosophy.
    2. Physics is reality. We can not deny that. The above mentioned thought process is based on certain practically proved concepts that is also called physics but hypothesis. After some exercise(Theoretical) and some experimental proves this will become Theory. This is called physics.
    3.Physics can be recognized by our senses and by instruments. When we generalize this we have to communicate with each other. So we started a system to change this physical reality in to communication. Not only that we have we have developed a system which will accelerate our thought process drastically to discover a physical concept to another physical concept. That is mathematics.
    For example if we take a telephone communication.the sound will be converted in to electrical signal and after receiving by receiver again will be converted to sound. The same way physics concept will be changed in to mathematical equation and will follow some steps and finally it will give an equation that gives us a new physics concept. This physics concept will be proved practically for a perfect physics.

    For a long time we are exercising these methods and day by day we are getting in to sophistication system. Finally we are accepting the reality only( practical proof). So we can not say any of these systems are wrong.If we find any thing wrong that is for a little modification or sophistication only.

    Here I am going to give an idea about mathematics. Let us suppose five mangoes and five people are there. people and mangoes are physical things .that is reality.we can not deny that. now these five man goes to be distributed to five people then each one will get one. But if zero mangoes distributed to zero people .The mathematics is not defined for that. But physically
    The question is' How many mangoes are there'
    The answer is 'No mangoes'. As per our physical communication system this is a wrong answer .Because the question is how many are there so the answer is zero mangoes are there. in the same way zero people are there. Thus it must be distributed.
    It is not satisfying the exact physical meaning and its communication.So there may require some modification for this communication(mathematics). I am not saying the entire number theory is wrong .There may be system which obeys the conventional mathematics at zero and small figures similar to Theory of relativity of physics .Where Newtonian mathematics obeys at small velocities and special relativity will vary with high velocity.

    Thus nothing is wrong in this scientific world its a continual improvement only. Never science regrets it modifies. Mathematics is a good friend to physics It is very help full tool. Mathematicians are sharpening that tool also.

    Thanking you
    Siva Prasad Kodukula

    You guys are on crack. What a bunch of wangers. Physics is Physics. Philosophy is a bit different. Drooling out a stoned combination of the two is annoying and actually such a thing is a silly as eating yourself for dinner. Wang.
    Go do physics alot more.