Journal of Theoretics
Transcription
Journal of Theoretics
Journal of Theoretics The Difference Between Mathematical Physics and Physical Mathematics: The Christmas Plum Pudding of Mathematics XPP Model J Harri T Tiainen PO Box 5066 Chatswood West NSW 1515 Australia [email protected] Abstract: By using a simple method – arithmetic is quantized. This quantization procedure reveals an extra mathematical ‘counting-force’ that is equivalent to the partitioning of all physical ‘counting’ objects. This ‘counting-force’ is shown to be the process of entropy that is the partitioning of all physical objects from an initial state (maximum temperature and minimum entropy) into a final state (maximum entropy and minimum temperature). Keywords: Arithmetic, Quantization, Entropy. Journal Home Page The difference between Mathematical Physics and Physical Mathematics On the quantisation of counting, or on counting one white stone and one black stone ○ + ● = 2 stones. The language of ‘1+1=2’ is quantised using three objections to the classical Greek picture. XPP (Xmas Plum Pudding) is a counting model based on 1+1=2, the familiar equation 1+1=2 is the most basic symbolic representation for arithmetic. 1+1=2 is the quintessential counting equation it is the archetype event chain for simple reckoning. In XPP; mathematics as a subject is the study of the interaction of the logic objects +,= with the action of the counting objects 1,1, and 2. In XPP we look at this simple equation in some detail and show that the traditional Greek model of addition is based on a number of false assumptions that makes it incompatible with QM. Objections to the old model of 1+1=2. LHS (Left Hand Side) = RHS (Right Hand Side) 1+1 2 = ○● ○● = objection 1 objection 2 objection 3 LHS 1 logic = RHS Equals logic logic ○ ● It is the ‘=’ sign that combines the RHS logic and the LHS logic systems respectfully. ‘=’ logic is an all operation. 2 The RHS uses a logic that is any general two. LHS = RHS ○ ● = ○ ● 1 1 + Stage one of 1+1=2 The two labeling laws for elementary objects 2 Stage two of 1+1=2 There are two logic systems for the labels. = Stage three of 1+1=2 The equals sign transcends the LHS and RHS logic to describe. Objection Three Think of it this way, the LHS uses a mode of interaction between each and every element, since each and every primitive object must be labeled with a ‘one’. At this stage of the event of 1+1=2 we have uncounted objects labeled ‘one’ that are the elementary constitutes of the ‘+’ logic system. Only a mixed system of logic can connect a LHS that uses exclusively each and every object with a RHS using any particular collection of the elementary entities. The point is that RHS and LHS use the primitive axiomatic objects differently. In other words the ‘=’ logic system acts on the labels but not on the objects. LHS is an uncounted system and the RHS is a counted system, and the ‘=’ sign is the logic that transcends, RHS and LHS labels. (See objection two diagram.) 1 Objection Two I know, I know, I know the whole point of counting is that the LHS elements (and it doesn’t matter how many) became one combined ‘grouping’, a collected whole, a counted object on the RHS. Commonly counting changes ‘many’ uncounted objects (LHS) into ‘one’ counted object (RHS). Think of it like this, on the LHS the ‘+’ sign collects the objects to be counted, and this ‘+’ sign is an independent logic system to the RHS. That is the ‘+’ sign has hidden paths to the RHS. The LHS has parts waiting to be counted by the ‘+’ sign the ‘+’ operates on each and every object. The ‘+’ logic is a distinguishable each and every system, quite different from the RHS indistinguishable any operation logic. The ‘+’ sign deals with each and every object while the RHS deals with any general counted two as a collection but it is the LHS label and RHS label that coordinates all ‘=’ operations of the event of 1+1=2. (See objection one diagram.) ○+● Objection One Look at objection three, on the LHS there is one white stone and one black stone and on the RHS there is also one white stone and one black stone. Exactly how does counting the LHS elements change one white stone and one black stone into two stones on the RHS? Because by inspection after the so-called count we still have each side exactly the same. There is no difference before the event of counting and after the event; there is no way of knowing whether any individual white stone or any individual black stone has been counted or not counted. Look at objection three ○●=○●. Look at the elements on both sides of this well-known equation. By inspection nothing has changed there is no difference. On the LHS we have one white stone and one black stone and the RHS we have one white stone and one black stone. Counting does nothing and can do no change to the objects on the LHS and RHS of 1+1=2, because the LHS equals the RHS by definition. The ‘+’ sign is an independent logic system to the RHS. The ‘+’ uses each and every object. That is ‘+’ is a hidden variable to the RHS. LHS RHS ○ ● ○ ● 1 1 LHS has ‘many’ uncounted objects called distinguishable 2 RHS has ‘one’ counted object called indistinguishable LHS ○ ● 1 1 + RHS ○ ● 2 LHS = The LHS is an each and every system. The objects of the LHS are in many distinguishable states that can be labeled by ‘+’. These elements are ‘counting’ fermions. Uncounted interaction mode of the LHS. This is how the distinguishable logic works for each and every object of the event of ‘1+1=2’. These ‘1’ ‘+’ ‘1’ variable labels are hidden to the RHS. The LHS ‘1+1’ has a different interaction mode than the RHS. This is the distinguishable mode of counting. Clearly LHS objects of the event act as fermions, there are many different LHSs that are available to be ‘condensed’ into one RHS. Many LHSs →one RHS. Or in QM language the available configuration space of the LHS is different than the RHS. See bottom figure. The RHS is an any system. The objects of the RHS are in one indistinguishable state that is labeled ‘2’. These elements are ‘counting’ bosons. Counted interaction mode of the RHS. This is how the indistinguishable logic works for any object of the event of ‘1+1=2’. The ‘2’ variable label transcends the hidden LHS paths of uncounted objects. The RHS interaction is the indistinguishable mode of counting. Think of it like this from counting we cannot construct the objects that where counted to give us a general two. Examples of LHSs 1+1 = 8−6 = 5+10−13 all equal two there is no way of coordinating the logic of the elements of the LHS with the elements of the RHS. The RHS objects of the event acts as bosons, all the objects are in one ‘counted’ state labeled two. The RHS is a Bose-Einstein condensate. See bottom figure. RHS ○ ● = ○ ● 1 1 + 2 = The = logic is an all system. The labels of the in toto interaction transcend the distinction fermions and bosons. Combined ‘counting’ interaction (un/counted) mode of the LHS and RHS. This is how the combined in/distinguishable logic works for all objects of the event of ‘1+1=2’. The variable label ‘=’ of ‘1+1=2’ transcends the labels of both RHS and LHS objects. This is the in toto interaction mode of the event, this interaction can transcend the logic of fermion and boson ‘counting’ and must be associated with a SUSY supersymmetric ‘Higgs’ logic that can connect particles of these two different basic counting modes, (if counting applies to nature at all). See bottom figure. What connects fermions’ and distinguishable bosons’ labels? The ‘=’ sign. states of the LHS The logic interaction for the labels RHS and LHS is ‘=’. It The hidden works by making equal the paths of each RHS and LHS labels. Or 1 and every logic more simply there are three interaction modes for the are the variable + event of ‘1+1=2’. The LHS is states for the ‘many’ ‘fermionic’ and the RHS is 1 uncounted ‘bosonic’ and the in toto objects on the interaction of the LHS and LHS. RHS labels must transcend Fermi-Dirac the component entities of the gas of particles count of ‘1+1=2’. In QM the mechanism that breaks the impasse of bosons/fermions labels is the SUSY ‘Higgs’ mechanism ie anti/symmetric wavefunction. indistinguishable state of the RHS The counted state that is the same for any fermions on the LHS. This state is called the ‘one’ counted object. 2 Bose-Einstein condensate The ‘=’ all Higgs SUSY logic The new XPP model for 1+1=2 is a representation where the inherent difference of the LHS and RHS is respected always in the structure of the model. The LHS is always a fermionic system for each and every object of the event of 1+1=2. The RHS is always a bosonic system for any object of the event of 1+1=2. And the labels LHS and RHS are always a SUSY logic to combine all objects of the event of 1+1=2. Counting is a loss of configuration from the LHS system to the RHS system and to the in toto system. The fermionic system LHS. Think of how the left hand sides of the counting equation 1+1=2 behave. 1+1 3+4+9-15 4+8-10 etc’s = = = = many LHSs 2 2 2 2 only one RHS The LHS of the counting equation is made up of many distinguishable configurations; a few are shown left. Notice how we have hidden paths to the RHS. The LHS deals with the bedrock counting objects; we have knowledge of each and every object. The LHS system is made up of Left Hand Sides, LHSs, it is this distinguishable system that acts as the ‘ultimate’ hidden variable to the event of the count. The bosonic system RHS. Think of how the right hand side of the counting equation 1+1=2 behaves. 1+1 fermions distinguishable each and every = 2 bosons indistinguishable any ○+● LHS ○● RHS The RHS of the counting equation is made up of one indistinguishable configuration; this is shown left. Because of the hidden paths on the LHS, the RHS does not contain information about the distinguishable objects. You cannot ask the RHS which numbers where added to give the ‘count’. The only information on the RHS is the one indistinguishable configuration - the counted state. The SYSU system ‘=’ Think of how the left hand side and the right hand side of the counting equation 1+1=2 behave as a combined system. LHS = all logic system RHS The LHS and RHS must follow a ‘Higgs’ super-symmetric SUSY logic where the label LHS and the label RHS are made equivalent. The result of counting is to inflect the injury of loss of identity of each and every object, into a indistinguishable state ‘object’ called counted, and these two sides must be symmetric in both directions (starting from the left side going to the right side, or vice versa.) Comparisons between XPP and the old model of 1+1=2. The various laws of counting (=algebra) are examples of fermionic counting laws that is LHS laws. In the new XPP model, we also have the bosonic counting law for the RHS and the SUSY rules for the count of the LHSs logic = RHS logic LHS label and RHS label. The SUSY super-logic acts on the labels LHS and RHS respectively, and x+y=y+x = ‘one counted object’ not on the elementary objects. In counting we first must label fermionically the elements, and these x ( y + z )= xy + xz = ‘one counted object’ obey the normal (classical) laws of algebra. Then we label bosonically to form a condensate of the etc’s = ‘one counted object’ fermions, we go from fermions on the LHS to bosons on the RHS, and how we combine fermions laws of uncounted states singlet state called counted and bosons is by a super-symmetric label exchange. are the laws of algebra 1+1 fermions The LHSs are the old model for counting = SUSY mode for the in toto picture 2 bosons The RHS is a condensed singlet state interaction This is how the LHS and RHS labels are joined The fundamental difference between the classical Greek picture and the new XPP model is that the distinction between the uncounted LHSs and the counted RHS is maintained always in the structure of the model; whereas this distinction is lost almost immediately in the normal picture. In the classical picture, there is no automatic sense of loss of configuration space for the three interaction modes of the event of 1+1=2, but in the XPP model we keep in the structure the past histories of the count. By the model we must accept that the label ‘boson’ and the label ‘fermion’ are combined by the SUSY rules and not that the actual bosons and fermions have ‘counter-particles’. It is the labels that we equate in XPP. In the new XPP model we have three logic interaction systems that work as a seamless whole. That is the fermionic LHSs and the bosonic RHS and the SUSY in toto system. XPP starts with this simple idea of the bosonic RHS, which is the obvious issue in counting; ‘many different LHSs all make the same RHS’ this is the basis of the new quantum model of counting called toy XPP. This very simple and obvious idea is the basis for counting and it is made one of the pillars of a new conceptual basis for quantum counting of elementary objects. The quantisation of math’s must start, from the simplest of basis that of the fundamental counting event 1+1=2. If we can make the basic counting equation 1+1=2 use QM language exclusively then a lot of the mysterious behaviour of the theory should disappear. To quantise counting is to quantise mathematics that is make mathematics more of a physics model. We force the structure of counting to conform to basic QM considerations. And by this one simple change of emphasize to the old model of ‘1+1=2’, that many different LHSs all give the same RHS we can generate a very simple model quantum system, that is a ‘toy’ XPP universe. Old model 1+1=2 One interaction mode only LHSs No hidden variables No automatic connection to quantum mechanics New model 1+1=2 Three interaction modes i) each and every fermion ii) any boson iii) all SUSY label exchange Hidden LHS ‘+’ logic variables to the RHS Automatic structural connection to QM concepts There is no classical analogue for the three interaction modes, yet they can be understood in terms of wellestablished quantum mechanical concepts. Notice the ease that XPP’s ‘1+1=2’ connects naturally to QM considerations. XPP fermions in the model follow the classical algebra laws. The fermions are distinguishable, that is no LHS particles have exactly the same state (= quantum numbers). In XPP this is the reason why we can separate out identical objects labeled 1, on the LHS. In the model we have ‘1+1’, we have two identical objects that are distinguishable. This ‘contradictory’ idea is a very simple and well-known phenomenon in quantum mechanics. The well-known algebra rule x + y = y + x or more concretely 6 + 7 = 7 + 6 is an LHS Fermionic gas example of LHSs distinguishable configurations of 1+1 identical objects. This is why LHS particles are each and every Fermi-Dirac statistics are algebra called fermions because ‘1+1’ must obey exactly the Distinguishable identical particles at same laws as Fermi-Dirac statistics in quantum maximum temperature and in a physics. Toy XPP is a model of mathematics where minimum entropy state. the elementary objects are forced by language The false vacuum are the ‘+’ states structure to obey quantum conceptions. In QM terms the LHSs are a fermionic gas. We have gas particles with maximum internal degrees of counting freedom; the uncounted objects have hidden “internal” variables to the RHS because LHS configuration space is different. The temperature of the gas is at maximum (hottest) since the thermal states are labeled by each and every. And the average kinetic energy is at maximum (highest) because any configuration is defined by each and every motion. The gas is at minimum (zero) entropy because no available states since the particles have maximum available degrees of freedom, the particles seem to have inherent motion to the RHS. The LHS particles labeled 'fermions' act as in a state of zero entropy and max temperature and are the initial state of any configuration. In physics the name for this state is the ‘big bang’. The LHSs are the toy universes’ ‘initial’ partition that is at the big bang everything became ‘distinguishable’ and the ‘+’ states are the toy’s false vacuum. XPP bosons in the model follow the Bose-Einstein statistics. Bosons are indistinguishable and act as a minimum configuration for the LHSs, since no available degrees of freedom, because there is only one state that is labeled ‘counted’. The bosons are at min temperature because there are no available states and the label each and every is meaningless. Or more RHS Bosonic condensate simply the label ‘each and every’ behaves as an 2 ‘internal’ hidden variable to the RHS. That is we any cannot consistently construct the behaviour of the Bose-Einstein state is the vacuum. LHS (fermions) from the behaviour of bosons Indistinguishable particles at (RHS), since each and every is a hidden interaction minimum temperature and in a mode to any. Each and every path leads to the any maximum entropy state. state of all histories of the event of 1+1=2. The vacuum state fully occupied. The ‘final’ counted partition is a singlet state, where each and every fermion is ultimately labeled by one over-riding RHS quantum number in our case ‘2’, in the general case the ‘one counted state’. In QM terms the RHS is a BoseEinstein condensate with hidden ‘internal-LHS’ variables, that is inherent motion of the bosons, even if no quantum (LHSs) states. We have maximum occupation but with the minimum configuration, that is max entropy and min temperature. Toy XPP bosons do not see barriers, their range is maximum (infinity) and their kinetic energy is minimum. The boson state is the true vacuum state for the LHS. It appears to be a fully occupied state to the LHS. Again this ‘contradictory’ idea, that the quantum vacuum is full is a very simple and well-known QM phenomenon. The normal quantum vacuum is a heaving melee of ‘everything-ness’; from the vacuum spontaneously anything can appear because of the time-energy uncertainty principle. This is also true in the toy XPP model from the RHS ‘2’ any LHS can be generated by the SUSY rules (the toy’s time-energy uncertainty principle). The RHS represents the exemplar of behaviour for the LHSs. The behaviour of the RHS is the ‘ideal’ final partition of the particles of the LHS. LHS particles cannot behave as the RHS, but the course of any path of each and every history of all objects of ‘1+1=2’ does lead to ‘2’. The bosons have min temperature and max entropy and the label ‘bosonic state’ is the final state for counting, this is why it is called the big crunch state, since this is the same behaviour as the normal physics big crunch. To the RHS each and every is only one ‘history’ of all interactions of 1+1=2. Creation is the singular bang of distinguishability and the crunch is the demise of identity into one common state of indistinguishability. The various correspondences LHS Initial Max temp Each + Every of toy XPP and normal physics The False Vacuum + 1+1 Partition Min Entropy distinguishable and thermodynamics. The fermions Big Bang spectrum all system counting equation 1+1=2 can Final Any Counting Vacuum RHS Max Entropy indistinguishable be forced to resemble a toy Partition 2 state is fully Min temp spectrum Big Crunch universe from fermionic bang bosons occupied. to bosonic crunch. XPP’s SUSY logic in the model follows a ‘thermodynamic work cycle’ and is the in toto interaction. The SUSY logic is the in toto interaction mode and is the toy’s time-energy uncertainty principle. Since in the toy XPP counting model the only event is the counting interaction symbolically labeled ‘1+1=2’. The toy XPP time-energy uncertainty principle is made equal to ‘1+1=2’ entropy-temperature cycle. Always in the model we force the language of the count to be quantum we always use QM articulation always, everything is always in QM terms always always always. The in toto mode is the following 1+1=2 , 2=1+1 and is the super-symmetric SUSY logic, it only involves the label LHS and the label RHS. max Temperature Configuration Fermions min LHS Entropy Configuration RHS SUSY logic table IN/OUT max Bosons RHS label LHS label LHS label RHS label min LHS RHS Final counted ‘state’ (min temp, max entropy) 2 Entropy SUSY ‘=’ LHS RHS Initial uncounted ‘state’ (max temp, min entropy) 1+1 Temperature Phase diagram for 1+1=2 Big Crunch SUSY IN/OUT Entropy Big Bang Temperature Entropy - Temperature work cycle for 1+1=2 , 2=1+1 The table above is the final stage of the logics that are needed to make ‘1+1=2’ completely symmetric. The final logic is called SUSY IN/OUT and makes the count 1+1=2 , 2=1+1 1+1=2 IN to table 2=1+1 OUT of table totally symmetric label-wise, mathematical counting takes no physical time to complete and the table expresses this condition and is equivalent to all paths of all histories. Think of it like this we have three descriptions going on at once; the LHS the fermionic story, the RHS the bosonic story and the SUSY story and all these stories (=logics) must join seamlessly, because everything is based on ‘1+1=2’ which is the basis of counting for mathematics. And mathematics would become suspect if doubt could be cast on the one equation one and one equals two that is totally comprehensible and totally believable. Nobody doubts 1+1=2 and that is the root trouble. The objections stay fixed in the structure of the model, the objections are handled or ‘over-come’ by introducing ‘larger’ and ‘larger’ logics that contain the elementary elements and logic images (=labels) until at SUSY we have that the logic doesn’t involve the elementary elements directly, only through all paths of all histories can the whole picture for the count of ‘1+1=2’ be quantised. The story of ‘1+1=2’ so far. The toy XPP LHS fermions, live in an environment with a true quantum vacuum (the RHS) which cannot be directly accessed by the fermions (since it is a bosonic state) where anything can be spontaneous generated (=projected) at random (because there is no direct connection between the label exchange SUSY rules that complete the work cycle of the elementary objects for counting). The RHS bosons are the carriers of a universal ‘force’ that seems to bind the fermions for any configuration for each and every motion. This counting ‘force’ is mediated by a boson of infinite (max) range and zero (min) mass. This universal ‘force’ connects everything via counting. Because of the SUSY rules it appears that an extra counting ‘force’ is working additional to the normal classical rules and the RHS condensate rule. In toy XPP we have an additional counting tendency ‘force’ for elementary objects of the event, this is the basis for thermodynamics in normal physics. The automatic counting of everything via a process is a natural phenomena of toy XPP ‘1+1=2’. In the toy model entropy the process is a consequence of SUSY rules. Notice the ease and the method that the language of normal thermodynamics can be very naturally draped over the normal classical ideas about counting. After all thermodynamics is a counting partition theory. Think of it like this the LHS spontaneously goes to the RHS. The LHSs have an ‘irreversible’ tendency to proceed via counting processes to a final ‘ensemble’. This is the basic idea about counting (and thermodynamics), that the LHS elements are forced by an irreversible process (that happens spontaneously) to behave such that the course of each and every motion of any of the LHSs all go to one final degenerate counted state that is the same final partition called the RHS. The thermodynamics for the counting equation writes itself. The LHSs partition can be generated ‘spontaneously’ if a measure for entropy can be defined. The initial distinguishable partition of objects is at max temp and min entropy since there are min degrees of freedom and max configuration as compared to the RHS. The final indistinguishable partition of objects is at min temp and max entropy since there are max degrees of freedom and min configuration as compared to the LHSs. The RHS state acts as the quantum vacuum counting state. From the vacuum ‘2’ anything that is each and every Left Hand Side can be generated but the LHSs of ‘2’ and the RHS of ‘1+1’ are coordinated by the SUSY rules. The RHS bosonic state, is the ideal state for the LHSs that is due to the SUSY logic structure of the quantum count there is a automatic tendency for fermions in the LHSs false vacuum ‘+’ states to ‘conspire’ mysteriously to go to the same final condensed state, using false RHS bosons. Consider the following example 1 + 1= 8 + (-6) = 15 + (-10)+ (-3) = … = ‘2’ many uncounted LHSs 1 + 1= 8 + (-6) = 15 + (-10)+ (-3) = … = ‘2’ always the same condensed counted state The LHSs acts as the states of motion where in the toy XPP fermionic particles of nature obey algebra. The reason why thermodynamics (=counting) works at all in the toy is because of the super-exchange of labels, entropy the process is due to SUSY logic. And SUSY is an external logic to nature if nature (where counting stones happens) is defined to be the LHS and the RHS. This external logic to nature is a pure symmetry unbroken SUSY. In QM terms this external pure symmetry is CPT (in a singlet state). In toy XPP the SUSY ‘=’ logic is equivalent to the CPT symmetry (as a singlet state) in the real-physical universe. Also in toy XPP the SUSY IN/OUT logic is equivalent to entropy. How to obtain the bare mass and the rest mass of the false fermions and bosons? It wouldn’t be a complete catastrophe if our mathematics was constructed such that the counting equation is based on this logic 1+1 ≦ 2 and 1+1 ≧ 2 so long as it isn’t possible to observe violations of the strict 1+1=2 counting equation. The rest mass spectrum 1+1>2 The False Vacuum LHSs Counting Vacuum state is fully occupied. The quantum counting reservoir =2 RHS is ‘2’ RHS > = < The Higgs field 1+1<2 This is how the LHSs and the RHS ‘interact’ there is no possible mechanism to ‘force’ bosons/fermions out of the vacuum/s and to appear as two species of particles with rest mass and mass of motion interacting via the normal force concepts of quantum mechanics. The mechanism that connects bosons/fermions in the toy is the Higgs field and the Heisenberg uncertainty relationship. That is the structure of the less than < and greater than > leads to distinguishable counting mass and indistinguishable counting mass, from the point of view of the infinite reservoir of the counted object ‘2’. This reservoir is the true vacuum state. The bare and observable mass of the particles is the mechanism of less than and greater than. How do you connect consistently these three types of logic seamlessly? false vacuum states SYSU IN/OUT true vacuum state LHS = RHS Think of the objections like this. In what sense does the LHS equal the RHS? If the ‘=’ sign is constrained by objection three ○●=○● which is a tautology nothing is gained because there is no difference of the parts of ‘1+1=2’ if by ‘=’ we mean that the LHS is exactly the RHS. What does counting do to the LHS to make it the RHS? In XPP the ‘=’ sign must deal with the LHS label and RHS label respectively. The major objection to the old Greek counting model is that the LHS and the RHS and the ‘=’ form their own independent logic systems, that is how the LHS and RHS treat the elementary objects are different. uncounted LHS 1 1 ‘+’ objects of the event internal LHS logic of the event external RHS logic of the event counted RHS 2 ‘=’ Simple picture of the objections to the normal (Greek) ‘1+1=2’ XPP is a new model for simple counting based on quantum concepts. To quantise counting is to quantise arithmetic. Conclusion The difference between Mathematical Physics and Physical Mathematics. Nearly everybody is familiar with mathematical physics, whereby physics principles are used in conjunction with the methods of mathematics to capture a picture of the interaction of the physical elements of reality. In XPP we are doing physical mathematics we use mathematical principles in conjunction with the methods of physics to capture the interaction of the mathematical elements of reality. Supposedly 1+1=2 applies to nature in some direct and obvious manner because it is widely believed that ‘1+1=2’ is observed to be ‘true’ most of the time; well at least for two stones, that is one white stone, and one black stone. What is not widely appreciated is that arithmetic is doable in our universe, Paul Davies in his book The Mind of God in the section called Why does arithmetic work? expresses this idea concisely “Arithmetic operations such as counting seem so basic to the nature of things that it seems hard to conceive of a world in which they could not be performed. Why is this?” and goes on “The mathematician R.W. Hamming refuses to take the doability of arithmetic for granted, finding it both strange and inexplicable. ‘I have tried, with little success,’ he writes, ‘to get some of my friends to understand my amazement that the abstraction of integers for counting is both possible and useful. Is it not remarkable that 6 sheep plus 7 sheep make 13 sheep; that 6 stones plus 7 stones make 13 stones? Is it not a miracle that the universe is so constructed that such a simple abstraction as number is possible?’” and “The fact that the physical world reflects the computational properties of arithmetic has a profound implication.”… “ this capability hinges on a deep and subtle property of the world. There is evidently a crucial concordance between, on the one hand, the laws of physics and, on the other hand, the computability of the mathematical functions that describe those same laws. This is by no means a truism. The nature of the laws of physics permits certain mathematical operations — such as addition and multiplication — to be computable.” Physical Mathematics explains why we can count at all because the interaction of the mathematic elements of reality are so constructed that all physical elements must form one counting event countable by entropy. Recall entropy (the all SUSY ‘force’) is the spontaneous counting (=partitioning) of each and every thing in the universe to a final degenerate state of any collection of objects. Mathematics Physics Physics Mathematics Mathematical Physics Physical Mathematics Journal Home Page In mathematical physics we have that physical principles are the foundations of reality, while in physical mathematics mathematical principles are the foundation of reality.