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| | On Mathematics, Mathematical Physics, Truth and Reality NOTE: These pages deal with the Ph | |
[size=50]On Mathematics, Mathematical Physics, Truth and Reality[/size] NOTE: These pages deal with the Philosophy and Metaphysics of Mathematics and the Mathematical treatment of the Wave Structure of Matter (WSM). The theoretical physic pages (Quantum Theory, Einstein's Relativity and Cosmology) are treated separately. Mathematics is, I believe, the chief source of the belief in eternal and exact truth, as well as a sensible intelligible world. (Bertrand Russell) Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identity fades out of sight. (Johann Wolfgang Von Goethe) ContentHello Everyone, This page has the following content;What is Mathematics and how can it Exist in the Universe.Newton replaced Causal Connection of Reality with Causal Connection of MathematicsMathematics Does not Describe Reality, only its QuantitiesMathematical (Axiomatic) Truths Vs. Truths of Physical RealityEmpirical Facts Vs. Theoretical InterpretationsEssays on Philosophy / Metaphysics of MathematicsMathematical Treatment of the Wave Structure of MatterHope you find it interesting! Geoff Haselhurst What is Mathematics and how can it Exist in the Universe?One reason why mathematics enjoys special esteem, above all other sciences, is that its propositions are absolutely certain and indisputable, ... How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality. (Albert Einstein)Given the Wave Structure of Matter in Space it is now possible to explain what mathematics is, how it can exist in the universe, and thus why it is so well suited for describing physical quantities (mathematical physics). For mathematics to exist physical reality must; i) Contain discrete / finite quantities (that can thus be counted / numbered). ii) These discrete things must be necessarily connected to one another (so they interact in a logical manner).The Wave Structure of Matter confirms this.Logic comes from the necessary interconnection and behavior of the spherical in out wave motions of Space, which is determined by the properties of Space (existing as a wave medium). In particular, waves form into complex wave patterns that interact logically / necessarily, and which are represented by our larger scale patterns that we call numbers.Quantities include the wavelength, velocity, frequency and amplitude of the waves, their energy, and the number of wave center 'particles' that exist in Space.And now, thanks to some great wave machine technology you can actually see how waves can form patterns / numbers. Thus you can see for yourselves how mathematical logic can exist in the universe due to the logical interconnection of wave patterns. | Researchers at Akishima Laboratories (Mitsui Zosen), working in conjunction with professor Shigeru Naito of Osaka University, have developed a device that uses waves to draw text and pictures on the surface of water. The device, called AMOEBA (Advanced Multiple Organized Experimental Basin), consists of 50 water wave generators encircling a cylindrical tank 1.6 meters in diameter and 30 cm deep. AMOEBA is capable of spelling out the entire roman alphabet. Each letter or picture remains on the water surface only for a moment, but they can be produced in succession on the surface every 3 seconds. | Mathematics and MusicThe relationship between mathematics and music (vibrations / sound waves) is also well known, and in hindsight it is obvious that mathematics, maths physics, music (sound waves) and musical instruments exist because matter is a wave structure of Space. This is why all matter vibrates and has a resonant frequency.Mathematics may be considered as a logical relationship language developed upon the concept / definition of one. From this one, we can logically define two, three, etc. which we call numbers. Hence a number is some relationship to one. Once we have whole numbers then we can define add, subtract, multiply and divide. Fractions, squares, cubes, etc, all became possible, as more and more complexly defined relationships between numbers evolved. From this unity of one, a language with a set of logical rules has evolved which enables us to exactly compare the quantitative relationship between different things. As Bertrand Russell wrote;Mathematical knowledge is, in fact, merely verbal knowledge. "3" means "2+1", and "4" means "3+1". Hence it follows (though the proof is long) that "4" means the same as "2+2". Thus mathematical knowledge ceases to be mysterious. (Bertrand Russell, History of Western Philosophy)The next thing we must consider is how our mind can create and understand this precise mathematical logic, as Brouwer states;One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics. (Luitzen Brouwer)If we consider life on earth one billion years ago, humans did not exist. Thus mathematics existence must be found by considering the evolution of the human brain and mind. Why has the brain evolved such that it is able to develop and understand mathematics, which then allows a mathematical 'description' of Nature?The answer is found by considering our evolution. The mind can be considered as a relationship machine which has evolved to understand the logical consistency of the world about us and hence relate things in a systematic and logical manner. e.g. Once eating poison fruit was related with dying, then this relationship remained true and consistent. In this way a logical mind is a natural evolutionary consequence of the logical universe (as it enhances our survival). This is why we are able to think in terms of mathematics. Our brain is a logical relationship machine, and mathematics is a logical relationship language. (And yes, we are also highly emotional creatures too - so our mind has a complex mix of logical and illogical / emotional aspects.) Newton replaced Causal Connection of Reality with Causal Connection of MathematicsSince Newton mathematics has replaced reality as the source of causal connection, where continuous forces connect discrete matter particles in space and time. Even Newton realised this limitation, but since mathematical physics works so well it was forgotten. As Newton and Einstein wrote;It is inconceivable that inanimate brute matter should, without mediation of something else which is not matter, operate on and affect other matter without mutual contact. ... That gravity should be innate, inherent and essential to matter, so that one body may act upon another at-a-distance, through a vacuum, without the mediation of anything else by and through which their action may be conveyed from one to another, is to me so great an absurdity that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it. So far I have explained the phenomena by the force of gravity, but I have not yet ascertained the cause of gravity itself. ... and I do not arbitrarily invent hypotheses. (Newton. Letter to Richard Bentley 25 Feb. 1693)In Newtonian physics the elementary theoretical concept on which the theoretical description of material bodies is based is the material point, or particle. Thus matter is considered a priori to be discontinuous. This makes it necessary to consider the action of material points on one another as action-at-a-distance. Since the latter concept seems quite contrary to everyday experience, it is only natural that the contemporaries of Newton - and indeed Newton himself - found it difficult to accept. Owing to the almost miraculous success of the Newtonian system, however, the succeeding generations of physicists became used to the idea of action-at-a-distance. Any doubt was buried for a long time to come. (Albert Einstein, 1950)"When we attribute this strange attractive property to massive particles, aren't we indulging in metaphysics? For we are saying, indeed, that matter has a inner, active principle: matter attracts matter. At the time, physicists (who called themselves "natural philosophers") accused Newton of doing exactly that, indulging in metaphysics, and the followers of Descartes (mostly in France) couldn't stomach the law of gravitation. What can we say in Newton's defense? Well, surely he was indulging in metaphysics, but with a difference: he wasn't just saying, like others had been doing for centuries, that things have an inner, active principle and leaving it at that; he gave a mathematical law for that inner, active principle. That made a lot of difference. He abstained from answering the metaphysical question, "What is this attractive force?" Rather, he just gave a mathematical formula for it. Still, the main reason for the acceptance of Newton's gravitation was its tremendous success. As the saying goes, nothing succeeds like success." (Prof. Ricardo Nirenberg, 1997)This is why mathematicians now seem so skeptical of Metaphysics as they use their mathematics to connect things instead. But mathematics does not exist in some magical realm - it exists in physical reality and depends upon it for its necessary connection. We now know this causal connection - matter is a spherical wave structure where the wave center 'particle' is in continual two way communication with all other matter in the observable universe due to its spherical in and out waves. So one substance space (and its wave motions) is the ultimate foundation for the causal connection of both physical reality and mathematical physics. | |
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