Business Cycles are well-known to Economists. Periods of boom and bust exist regardless of the health of an Economy. In this presentation, Money and Infinity, we will consider far longer cycles. In fact, not Economic Cycles but Civilisation Cycles. How it started and how it will end. Our Ariadne thread will remain a proper mathematical modelling of Monetary Flows. We will begin by explaining what we mean by Accounting Circuit (Part 1), then move on to the mathematical structure of these circuits (Part 2). And finally by taking time to +∞ or -∞, this will allow us to answer the questions (Part 3): How did it all start? Where will it all end? We will close the discussion by showing that it is the Revolutionary Act which in fact keeps Civilisation alive by taking it out of the Eternal Return of the Same which Money, like Power, cannot escape !!

1. MONEY
&
INFINITY
©
North
Delta
College
2015
Mathema'cs
applied
to
Business
Theory
1

2. INTRODUCTION
Business
Cycles
are
well-­‐known
to
Economists.
Periods
of
boom
and
bust
exist
regardless
of
the
health
of
an
Economy.
In
this
presentaNon,
Money
and
Infinity,
we
will
consider
far
longer
cycles.
In
fact,
not
Economic
Cycles
but
CivilisaNon
Cycles.
How
it
started
and
how
it
will
end.
Our
Ariadne
thread
will
remain
a
proper
mathemaNcal
modelling
of
Monetary
Flows.
We
will
begin
by
explaining
what
we
mean
by
AccounNng
Circuit
(Part
1),
then
move
on
to
the
mathemaNcal
structure
of
these
circuits
(Part
2).
And
finally
by
taking
Nme
to
+∞
or
-­‐∞,
this
will
allow
us
to
answer
the
quesNons
(Part
3):
-­‐ How
did
it
all
start?
-­‐ Where
will
it
all
end?
We
will
close
the
discussion
by
showing
that
it
is
the
RevoluNonary
Act
which
in
fact
keeps
CivilisaNon
alive
by
taking
it
out
of
the
Eternal
Return
of
the
Same
which
Money,
like
Power,
cannot
escape
!!
Mathema'cs
applied
to
Business
Theory
2

3. SUMMARY
Mathema'cs
applied
to
Business
Theory
3
Part
I:
WHAT
ARE
ACCOUNTING
CIRCUITS
?
A)
Purpose
of
the
Concept
B)
Macro/Micro
Zoom
in
Part
II:
THE
LOCAL
STRUCTURE
A)
The
3
basic
Money
Flows
B)
Where
all
these
Flows
are
heading
to
…
Part
III:
MONEY
AND
∞:
THE
BOOK
OF
KINGS
A)
The
Monetary
Chessboard
B)
Origins
of
Time
C)
Ends
of
Time
D)
Concept
of
RevoluNon
Final
Statement

4. PART
1:
WHAT
ARE
ACCOUNTING
CIRCUITS
?
The
concept
of
AccounNng
Circuit
transcends
the
framework
of
Finance
and
belongs
to
some
of
the
deepest
concepts
in
Philosophy
or
Hard
Sciences.
It
is
under
its
MathemaNcal
format
that
we
will
study
it
in
this
presentaNon
in
order
to
see
what
happens
at
Infinity.
The
Goal
is
to
model
how
Money
flows
through
Nme.
From
one
person
to
another
person.
From
a
person
to
an
organisaNon.
From
an
organisaNon
to
another
person
or
organisaNon.
There
is
a
chain
of
Senders/Receivers.
Money
is
never
Lost.
There
is
a
principle
of
conservaNon
of
Money,
the
same
as
in
Chemistry,
where
nothing
is
ever
lost.
Mathema'cs
applied
to
Business
Theory
4
Purpose
of
the
Concept
Picture
2:
Picture
1:
Sender
Money
Receiver
A
chain
of
Senders/Receivers

5. What
happens
at
the
Macro
Level
If
we
look
at
the
High-­‐end
point
of
view:
Money
transits
from
one
Monetary
System
(person
or
organisaNon)
to
another
Monetary
System.
This
is
how
the
Chain
looks
like.
Mathema'cs
applied
to
Business
Theory
5
Picture
3:
Picture
4:
If
we
look
at
greater
Intervals
of
Nme,
we
can
see
a
network
taking
shape.
DefiniNon:
An
accounNng
circuit
is
a
given
path
taken
by
money
through
this
network
of
chains.
PART
1:
WHAT
ARE
ACCOUNTING
CIRCUITS
?
MS
MS
MS
MS
MS
MS
MS
MS
=
Monetary
System
Chain
3
Chain
2
Chain
1

6.
Mathema'cs
applied
to
Business
Theory
6
What
happens
at
the
Micro
Level
If
we
look
at
the
Micro
level,
the
Atomic
level,
the
same
structure
repeats
itself
but
this
Nme,
the
nodes
are
the
accounts
of
a
given
Chart
of
accounts
inside
a
Monetary
System.
Remark:
It
is
worth
noNng
that
at
the
Micro
level,
the
flow
is
only
going
one
way.
From
one
account
1637
to
another
account
6254
and
not
the
reverse.
Example:
For
the
Cost
Flow
(Money
going
out
of
the
MS
[Monetary
System]),
we
go
from
Cash
to
COGS
(Cost
of
Goods
Sold)
and
not
the
Reverse.
Cash
is
used
to
pay
Salaries
and
not
the
other
way
round.
Picture
6:
PART
1:
WHAT
ARE
ACCOUNTING
CIRCUITS
?
Picture
5:
Account
D
Account
C
Account
B
Account
A
Account
1637
Account
6254

7. We
now
want,
in
this
Part
2,
to
study
the
Local
Structure
of
an
AccounNng
Circuit.
By
Local,
we
mean
the
behaviour
of
the
Monetary
flows
near
a
given
Monetary
System.
Global,
on
the
other
hand,
will
mean
the
behaviour
when
Nme
goes
to
-­‐∞
or
+∞
(which
we
will
study
in
Part
3)
for
all
possible
Monetary
Systems.
Any
Monetary
System
has
3
Flows
of
Money
alached
to
it.
This
is
the
standard
FRC
structure:
Funding,
Revenues
and
Costs.
Funding
and
Revenues
are
in-­‐going
Flows,
Costs
is
an
out-­‐going
Flow.
Mathema'cs
applied
to
Business
Theory
7
The
FRC
Structure
PART
2:
THE
LOCAL
STRUCTURE
Picture
7:
Picture
8:
Local
vs.
Global
in
Maths
A
Geometrical
Object
=
Global
Local
behaviour,
i.e.
:
I
zoom
in
R
F
C
Flows
inside
a
Monetary
System
The
FRC
Structure

8. The
hidden
Channel
Two
of
the
previous
FRC
Flows
are
connected
by
a
hidden
Channel.
F
and
C
are
linked.
The
outgoing
Flow
C
is
iniNally
an
ingoing
Flow,
namely
F.
This
is
a
Fundamental
Principle
of
Monetary
Systems
and
explains
why
Funding
is
so
crucial.
Without
it,
a
Financial
EnNty
doesn’t
even
exist
as
it
cannot
even
pay
the
most
basic
expenses.
We
get
the
following
Diagram.
Mathema'cs
applied
to
Business
Theory
8
Picture
9:
PART
2:
THE
LOCAL
STRUCTURE
R
F
C
The
Hidden
Channel

9. A
key
point
about
the
F
and
C
Flow,
is
that
it
cuts
through
the
Monetary
System
transversally.
Mathema'cs
applied
to
Business
Theory
9
What
do
we
mean
by
that?
1.
First,
this
Flow
cuts
through
the
Monetary
System
through
and
through,
visiNng
all
its
aspects,
from
the
Entry
Nll
the
Exit,
leaving
no
space
for
virgin
areas.
2.
It
re-­‐energises,
from
the
AccounNng
standpoint
the
whole
Monetary
System.
3.
The
organisaNonal
layers
of
the
Monetary
System
stand
in
some
sense
orthogonally
to
this
Energy
path
going
through
them.
Picture
10:
A
Transverse
Flow
Picture
11:
PART
2:
THE
LOCAL
STRUCTURE
Transversal
Cut
Monetary
System
The
whole
of
the
MS
is
impacted
Money
coming
Out
Funding
Gate

10. The
Time
Inversion
Line
Let
us
look
more
closely
at
the
F
and
C
behaviour.
We
will
call
our
first
Monetary
System
Kurt.
Kurt
has
a
Funding
entry
F
coming
from
a
Funding
source
we
will
call
F1
and
a
cost
exit
C.
The
cost
goes
to
another
monetary
system
that
we
call
Karl,
which
itself
has
an
F
and
C
flow.
The
chain
Kurt
à
Karl
is
the
base
of
our
AccounNng
Circuit.
It
goes
forward
in
Nme.
The
key
point
is
that
all
Funding
nodes
F0,
F1,
F2
…
sit
on
another
Time
axis
which
goes
in
a
backward
Time
direcNon
compared
to
the
base
accounNng
circuit.
Mathema'cs
applied
to
Business
Theory
10
PART
2:
THE
LOCAL
STRUCTURE
Picture
14:
Picture
13:
Picture
12:
C
Kurt
F
Funding
Source
=
F1
F
F
F1
F0
C1
C2
Karl
Kurt
Flow
of
Time
F1
F0
F2
Kurt
Karl
AccounNng
Circuit
Chain
Time
Inversion
Line

11. The
Pool
of
Present
:
R-­‐∞
Similarly
we
can
look
at
the
R
Flow.
The
R
Flow
stops
in
the
Monetary
System.
However
if
we
ask
where
it
comes
from
we
can
start
going
backward
Nll
the
Source.
At
the
Limit,
we
find
the
UlNmate
Source
R-­‐∞
of
all
possible
Revenues.
R-­‐∞
is
the
Pool
of
Present,
situated
exactly
at
the
same
Nme
t0
than
the
TransacNon
Kurt
à
Karl.
Mathema'cs
applied
to
Business
Theory
11
Picture
15:
Picture
16:
PART
2:
THE
LOCAL
STRUCTURE
c
c
R
R
Kurt
Karl
R’
R’’
AccounNng
Circuit
Chain
Kurt
Karl
R’
R’’
R3
R2
R3
R-­‐∞
R-­‐1
R01
R0

12. The
Bigger
picture
We
now
want
to
look
at
the
bigger
picture.
What
happens
when
we
consider
all
the
possible
AccounNng
Circuit
Chains
and
start
taking
Nme
t
towards
+∞
or
-­‐∞.
We
get
in
fact
the
following
diagram:
Mathema'cs
applied
to
Business
Theory
12
CEO
PART
3:
MONEY
AND
∞:
THE
BOOK
OF
KINGS
Picture
17:
The
Monetary
Chessboard
R-­‐∞
:
The
Pool
of
Present
Time
t
=
+
∞
Time
t
=
0
=
NOW
Time
t
=
-­‐
∞
Time
Inversion
Line
THEN
The
IniNal
Ocean
The
Future
The
Past
All
the
Possible
AccounNng
Circuits
with
usual
Flow
of
Time
F1
F2
F∞
Kurt
Wendy

13. Few
Remarks
on
the
Monetary
Chessboard
Remark
1:
Because
of
the
existence
of
F∞
the
Model
we
have
built
is
Asymmetric
with
respect
to
Nme.
The
Ler
Hand
Side
(the
Past)
doesn’t
look
like
the
Right
Hand
Side
(the
Future).
Remark
2:
F∞
and
R-­‐∞
are
the
Energy
givers
whereas
the
Monetary
Systems
sisng
on
the
Material
Realm
are
like
the
motors
taking
the
Game
forward
as
they
consume
this
Energy.
Remark
3:
F∞
is
properly
a
pump
as
it
acNvates
the
whole
Game
by
aspiring
the
Monetary
Flow
sisng
on
the
Time
Reversal
Line.
Mathema'cs
applied
to
Business
Theory
13
Picture
18:
PART
3:
MONEY
AND
∞:
THE
BOOK
OF
KINGS
F∞
R-­‐∞
Present
Past
Future
Material
Realm
Finance

14. Philosophical
InterpretaNon
Mathema'cs
applied
to
Business
Theory
14
It
is
possible,
although
not
as
accurate
as
the
Model
itself
to
rephrase
everything
in
a
more
tradiNonal
Language.
Indeed:
R-­‐∞
=
“Society”
F∞
=
“The
Capital”
c
=
The
Working
Force
We
also
have
the
Following
Theorems:
Theorems:
F∞
>
Fj
,
for
any
j
R-­‐∞
changes
as
t
(the
Nme)
moves
forward
wF
moves
ahead
in
Nme
We
will
now
try
to
understand
what
happens
at
Nme
t
=
+∞
or
t
=
-­‐∞
+
∞
=
Ends
of
Time
-­‐
∞
=
Origins
of
Time
PART
3:
MONEY
AND
∞:
THE
BOOK
OF
KINGS

15. Origins
of
Time
If
we
go
back
to
the
Origins
of
Time,
we
see
a
very
mobile
Monetary
System,
that
we
call
the
WASP
(Wise
Adrenalin-­‐Savvy
Pervert)
injecNng
Cash
Energy
inside
the
first
few
monetary
systems
present
at
that
Nme
near
the
wasp.
The
Wasp
is
bustling
with
Energy,
Cash
and
is
profoundly
out
of
Time.
The
Energy
it
injects
as
a
seed
in
the
few
early
Monetary
Systems
is
neither
Good
Energy
or
Bad
Energy,
but
has
a
tremendous
momentum
that
none
of
the
early
Monetary
Systems
can
handle
fully.
Mathema'cs
applied
to
Business
Theory
15
Picture
19:
PART
3:
MONEY
AND
∞:
THE
BOOK
OF
KINGS
Monetary
System
Monetary
System
No.
136
The
Wasp
At
the
Dawn
of
Times

16. Origins
of
Time
Mathema'cs
applied
to
Business
Theory
16
The
first
few
monetary
systems
come
back
in
the
Society
or
their
Nme.
Their
key
challenge
is
to
use
this
Energy
that
they
almost
plucked
at
a
metaphysical
level
into
a
CivilisaNonal
purpose.
To
their
great
surprise,
they
discover
the
Funding
rounds
never
ends,
despite
the
iniNal
Life
injecNon.
A
category
of
the
populaNon
decides
suddenly
to
control
the
gates
of
funding
and
realises
they
can
control
all
the
monetary
flows
and
take
a
porNon
of
revenues
out
of
it.
Picture
21:
Picture
20:
PART
3:
MONEY
AND
∞:
THE
BOOK
OF
KINGS
Funding
Starts
Beginning
of
the
Time
Line
Inversion
for
the
Funders
Energy
Channeled
into
A
CivilisaNonal
Purpose

17. Origins
of
Time
Very
strangely,
a
third
party
comes
in
the
picture
of
this
very
strange
business.
Let’s
call
him
T
As
the
AccounNng
circuits
start
funcNoning
the
MS
(Monetary
Systems)
start
generaNng
a
whole
new
CivilisaNon.
The
Funders
make
money
while
at
the
same
Nme
sinking
in
a
spiritual
Black
Hole,
as
for
a
short
period
T
reaches
the
summits
of
Material
Wealth.
This
tri-­‐parNte
game
goes
on
for
a
certain
interval
of
Nme.
As
we
move
forward
towards
the
future,
there
is
only
one
Certainty.
Arer
Nme
T
=
tK
T collapses
The
Funders
remain
funders
The
MS
build
Military
Power
Mathema'cs
applied
to
Business
Theory
17
Picture
22:
PART
3:
MONEY
AND
∞:
THE
BOOK
OF
KINGS
MS
T
Funders

18. Mathema'cs
applied
to
Business
Theory
18
Ends
of
Time
The
neighbouring
communiNes
start
parNcipaNng
in
the
game
as
Nme
t
goes
forward.
Each
one
choosing
which
role
to
play.
The
game
repeats
itself
except
the
ulNmate
Myth
of
T ‘s
supreme
wealth
once
reached
in
the
Golden
Age
which
is
never
repeated
but
generates
the
desire
to
pursue
the
game!
At
the
End
of
Time,
T ,
The
MS
and
the
Funders
meet
again.
They
could
very
well
shake
hands
and
end
the
Game.
Unfortunately,
they
repeat
the
same
game,
on
a
parody
version,
inverNng
roles,
on
Level
-­‐1
(A
lower
level
than
the
iniNal
version)
and
R-­‐∞
starts
moving
to
chaos.
Picture
24:
Picture
23:
PART
3:
MONEY
AND
∞:
THE
BOOK
OF
KINGS
The
WASP
Chaos
History
of
a
Full
Cycle
Time
t
The
triparNte
game

19. How
to
stop
this
Cycle?
How
does
one
stop
this
endless
cycle?
By
a
RevoluNonary
act
of
an
absolute
defiance
and
denying
precisely
the
rules
of
this
game.
Example
1:
Introduce
a
700-­‐page
revealed
text
on
the
planet
which
denies
from
A
to
Z
the
rules
of
the
game.
Example
2:
Land
on
Mars
Example
3:
Introduce
principles
of
civilisaNon
absolutely
alternaNve
and
based
on
acNviNes
not
listed
on
the
paper-­‐roll
of
the
iniNal
game.
Example
4:
Ler
to
the
reader
It
is
vital
to
escape
the
Eternal
Return
of
the
Same
and
we
leave
the
Intelligence
of
the
reader
to
decide
for
her/himself.
Mathema'cs
applied
to
Business
Theory
19
Picture
25:
PART
3:
MONEY
AND
∞:
THE
BOOK
OF
KINGS
Chaos
One
cycle
Another
cycle
Start
Start
End
End
Cyclical
History

20. Final
Statement
Arer
a
Long
journey
into
MathemaNcal
Modelling,
we
finally
came
out
with
a
cyclical
vision
of
civilisaNon,
starNng
with
the
WASP
and
ending
up
in
the
usual
chaos.
It
is,
in
fact,
not
that
far
from
Nietzsche’s
point
of
view.
Except
that
we
refuse
the
concept
of
Eternal
Return
of
the
Same.
There
are
key
events
in
human
history
that
Nietzsche
doesn’t
explain:
1) The
InvenNon
of
WriNng
2) The
Koranic
RevelaNon
3) The
Landing
on
the
Moon
These
are
clearly
one
Shot-­‐events
and
are
fundamentally
Non-­‐Reversible
This
shows
two
things:
1) Some
events
in
human
history
shape
its
future
more
than
Money
2) A
RevoluNonary
Act
is
always
possible
We
leave
the
Reader
to
conclude…
Mathema'cs
applied
to
Business
Theory
20
FINAL
STATEMENT