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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
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In mathematical physics we
have that physical principles
are the foundations of reality,
while in physical mathematics
mathematical principles are the
foundation of reality.