BY LETTER
TopoGo
Topological Go, or TopoGo, is a game that dates from pre-Singularity
Earth. The inventor of the game was reputedly a baseline interested in
modelling wormhole networks. It is a variation of the classical game
of 2-Go, with several levels of play. The deeper levels add increasing
complexity to the game.
TopoGo is typically played by youth to develop spatial intuition and
facility with accounting, and by strategists to develop game theory
algorithms. It is rumored that playing higher levels of the game can
provide a fairly accurate model of historical resource conflict among
the Archai. The popularity of the game has waxed and waned throughout
the centuries, with reports of particularly talented players being
tutored and/or subsumed by various avatars. Interestingly, the rating
system, scoring, and topological variants on gameplay have been the
most well documented among the Metasoft Version Tree.
Indeed, the classic Metasoft algorithms for TopoGo are considered
canonical by serious contestants, and superb play can bring
substantial economic incentives.
At various points in time, there have been contests in TopoGo from
such normally dissociated empires such as Metasoft and the Zoefic
Biopolity. In 8300 A.T., a thought-coral reef was reputed to have
defeated a MoonBrain and 5,000 other KnownNet participants in a
Version Tree 23.5 Game. However, there have been no recorded contests
between players of greater than S3 ....
Non-Metasoft players typically decide upon a Version Tree protocol to
fix the rules of the game, which tends to completely describe the
parameter space for the Board. Although a highly mathematical game,
sophonts with good spatial modelling/visualization can usually grasp
the basic rules.
However, published higher level contests often have enigmatic results.
There are numerous examples of games that have a declared winner
different from what a standard algorithmic assessment of the rules
would indicate. There is some speculation that deep study of these
published contests lends insight into higher toposophic game theory,
and some ascensions have been reputedly linked to that line of study.
The TopoGo Board:
1.TopoGo is played on a continuous, rather than discrete, board. 3+1
TopoGo, otherwise known as standard TopoGo, typically using a 3D
display. The defined boardspace can be any size desired, but beginning
boards start out as a cube 500 units on a side, marked identically to
a 3-Go game cube for ease of use. Adjacent is defined to be any
Distance (as defined by the boardspace metric) < 1.
2. Any number of sides > 1 may contest the board; beginning games
start with two sides. Each side has a fixed Starting Point from which
to begin their moves. This Starting Point provides a set number of
Resources per unit of Time, and may be adjusted to determine the
Handicap.
3. The boardspace has a number of defined resource Nodes scattered
throughout its volume; each Node provides Resource equal to its value
per unit of Time. Distribution of Resources across the board also
determines the Handicap.
Actions and Interrupts:
4. Interrupts occur whenever an Action by a side is possible. An
Action consists of Creating Pieces, Movement, Acquiring Resource,
Weighting, Destroying Pieces, or in advanced versions of the game,
Capture, Transport, and Declaring/Breaking Alliances. For basic games,
an Interrupt happens by default for every integer unit of Time.
5. Any number of Actions may be performed by a side at any time as
long as the total of their Resources > 0.
Accounting:
6. Accounting of Time, Distance, Weight, and Resource is kept to
whatever degree of precision desired. Basic games proceed in integer
units of Time; full games proceed by Interrupt.
Creating Pieces:
7. A side may create at its Starting Point one zero Weight Pair of
Home/Travel stones in ten units of Time for each unit of Resource.
Legal Moves:
8. The basic piece in the game consists of a Pair of stones, called
Home and Travel, linked by a Red Edge (or line) between them. A side
may move any number of pieces in its possession, subject to Resource
constraints (see Rule 5).
9. Except for the one Red Edge, all stones in the game are linked by
Black Edges to every other stone. The value of the Black Edge between
each and every stone is their Euclidean distance (henceforth
Distance).
10. The Home stone remains fixed in location; the Travel stone moves
forward to occupy territory. Each unit of Distance traversed requires
one unit of Time.
11. The value of a particular Red Edge is a fixed constant times the
Distance between the Pair of stones. In basic games, this constant is
1/3.
12. It costs one unit of Resource to move a Travel stone 10 units of
Distance. This cost must be prepaid in full before the Travel stone
can be moved. Only Weight 0 Travel stones may be moved. The value of
the particular Red Edge and all Black Edges for all Travel stones is
updated during each Interrupt.
13. It costs one unit of Resource to give the Home/Travel Pair a
Weight of one unit. There is no way to reduce the Weight of a Pair of
stones.
Acquiring Resource:
14. A non-zero Weight Home/Travel Pair adds the Resource value of any
node it is Adjacent to to the sides Resource.
Destroying Pairs:
15. Unlike standard 2-Go, Pairs in TopoGo are destroyed, rather than captured.
16. A Pair in TopoGo is destroyed if it forms a cycle on the board
such that the value of the Red Edges in that cycle exceeds the value
of the Black Edges in that cycle.
Aim of the Game:
17. The purpose of the game is to obtain more Resource than all your
opponents. The game is finished when all Resource nodes are occupied,
when no more moves can be made, or when all sides have agreed upon a
winner.
Handicaps: Resources can be adjusted to give weaker players an
advantage over a stronger ones.
These basic rules can be layered with increasingly more complicated
algorithms. Some examples include:
Level 2:
Creating Pieces:
7a. Creation of Pairs requires 10 Resource-Time Units.That is, one
Unit of Resource for each of 10 Time Units, two Units of Resource for
each of 5 Time Units, etc. If the expenditure of Resource falls below
one unit per unit Time, the Pair is destroyed.
7b.Creation of Pairs requires a new type of stone called a Forge,
which can be created using 50 Resource-Time Units. Each Starting Point
begins with one Forge. A Forge can be Created at any Node which has
the appropriate amount of Resource per unit Time. If the expenditure
of Resource falls below one unit per unit Time, the Forge is
destroyed.
Legal Moves:
10a. The is no distinction between Home and Travel stones in a Pair.
Either stone may be moved.
11a. The value of the Red Edge depends upon the relative Velocity
(Distance per unit Time) between the two stones.
12a. (The Grazer rule part I) A non-zero Weight stone can be moved, at
a cost of (Weight)^2 units of Resource per unit of Distance.
13a. (The Grazer rule part II) A Home/Travel pair can be given a
variable Weight at one unit of Weight per (Weight)^2 units of
Resource.
13b. (The Grazer rule part III) The total Weight of a Pair can be
distributed separately between stones.
Acquiring/Transporting Resource:
14a. Each Node accumulates Resource per unit of Time, unless moved.
Transport of Resource along Red Edges in a Pair takes a small constant
amount of Time. Transport of Resources along Black Edges requires the
same cost as a legal move. Resources are considered to have a Weight
of 0 for purposes of Capture and travel cost, and may be escorted by
Fleets (see Rule 18).
Destroying Pairs:
16a. A Pair in TopoGo is destroyed if:
1) It forms a cycle on the board such that the value of the Red Edges
in that cycle exceeds the value of the Black Edges in that cycle
2) The Weight of that Pair is less than the weight of the other Pairs
in that cycle.
Capturing Pairs:
18. A new type of stone called a Fleet can be constructed at any Node
for a cost of 10 Resource-Time Units * (Weight)^2. Fleets are not
harmed if expenditure of Resource halts during their construction; the
Weight of the Fleet is given by Sqrt(Resources/10).
19. Fleets can be broken down separately or combined, with Weights
given by the Resource formula in 18. Breaking down or combining
requires a small constant unit of Time.
20. A Fleet can traverse an Adjacent Pair in a small constant of Time
as long as the Weight of the Pair on both stones exceeds the Weight of
the Fleet.
21. It costs one unit of Resource per unit of Weight to move a Fleet
10 units of Distance. This cost must be prepaid in full before the
Fleet can be moved.
22. A Fleet captures any stone when the Weight of the Fleet exceeds
the Weight of the Adjacent stone. For purposes of Capture, the Weight
of a Forge is equal to Sqrt(Resources/50).
Capitols and Alliances:
23. Each side must have a stone called a Capitol, which is by default
at the Starting Point. A Capitol may be moved to any Node along any
sequence of Red Edges.
24. Capture of a sides Capitol by an opposing Fleet transfers control
of that sides Nodes and Pairs to the opposing side. Any Fleets in
control of the side with the captured Capitol remain under their
control, however.
25. For a game with n>2 sides, a side may declare or break an Alliance
with another side. Declaration of an Alliance begins at the point of
contact between the two sides, and spreads along all Red Edges in the
Alliance in a small constant unit of Time. Along Black Edges, the
declaration spreads at one unit of Distance per unit of Time. An
Alliance cannot be declared between two sides not in contact.
26. Alliances are non-transitive. (If A is allied to B, and B is
allied to C, A is not allied to C.)
27. Alliances may Acquire/Transport Resource as given in Rule 14a, and
combine Fleets as given in Rule 19.
28. An Alliance may be broken by any side at any time. Breaking of an
Alliance begins at the Capitol, and propagates as given in Rule 24.
Any Combined stones (Fleets, Pairs, Capitols, Forges) immediately
revert to control of the side with the greatest individual Weight (see
rule 22).
Level 3:
The TopoGo Board:
1a. The Boardspace is defined by the metric of its topological space.
Legal Moves:
9a. The Boardspace metric replaces the Euclidean distance in
determining Distance and the values of the Black and Red Edges.
10a. Each unit of Distance travelled requires a variable amount of
Time depending upon the local metric of the Travel piece.
11a. The value of the Red Edge depends upon the local metric of the
Travel piece.
12a. It costs a variable amount of Resource depending on the local
metric to move the Travel piece ten units of Distance.
Level 4:
Information and Signal Propagation (the Affine rules):
29. All stones (Pairs, Nodes, Forges, Capitols, Fleets, and Resources)
have an initial Information equal to their Weight.
30. A Signal can be broadcast from any stone at any time. The
Information value of the Signal is equal to the cube root of the
Information of the broadcasting stone. A Declaration is considered to
be a broadcast Signal of Information value 0 originating from the
Capitol.
31. A Signal can be narrowcast from an origin stone to a destination
stone along the Black Edge between the two stones. The Information
value of a narrowcast Signal is equal to Sqrt(Information of
narrowcast stone).
32. All Signals start at their declared origin, and propagate through
Black Edges at 1 unit of Distance per unit of time.
33. All Signals may propagate through Red Edges, if allowed by the
controlling side, for a small constant unit of time per Red Edge.
34.The Information of any stone can be increased at a Resource cost
equal to the square of its Fibonacci sequence of its new Information
(e.g. Info 4 costs (1+2+3+4)^2 = 100)
35. A Signal, upon intersecting a stone, will capture the stone if its
Information value exceeds either the Information or the Weight of that
stone.
36. If a Signal fails to capture a stone, that stone may broadcast a
counter-Signal of Information 0 which will grant immunity for any
receiving stones against that particular Signal. (Note: to be
effective, the counter-Signal must traverse at least one Red Edge in
order to arrive before the Signal).
Level 5:
Reputedly played using Resource/Distance/Metrics obtained from
detailed galactic maps.
Level 6:
Reputedly played using brane-theoretic landscapes.
Level 7:
Reputedly the real thing ....
Earth. The inventor of the game was reputedly a baseline interested in
modelling wormhole networks. It is a variation of the classical game
of 2-Go, with several levels of play. The deeper levels add increasing
complexity to the game.
TopoGo is typically played by youth to develop spatial intuition and
facility with accounting, and by strategists to develop game theory
algorithms. It is rumored that playing higher levels of the game can
provide a fairly accurate model of historical resource conflict among
the Archai. The popularity of the game has waxed and waned throughout
the centuries, with reports of particularly talented players being
tutored and/or subsumed by various avatars. Interestingly, the rating
system, scoring, and topological variants on gameplay have been the
most well documented among the Metasoft Version Tree.
Indeed, the classic Metasoft algorithms for TopoGo are considered
canonical by serious contestants, and superb play can bring
substantial economic incentives.
At various points in time, there have been contests in TopoGo from
such normally dissociated empires such as Metasoft and the Zoefic
Biopolity. In 8300 A.T., a thought-coral reef was reputed to have
defeated a MoonBrain and 5,000 other KnownNet participants in a
Version Tree 23.5 Game. However, there have been no recorded contests
between players of greater than S3 ....
Non-Metasoft players typically decide upon a Version Tree protocol to
fix the rules of the game, which tends to completely describe the
parameter space for the Board. Although a highly mathematical game,
sophonts with good spatial modelling/visualization can usually grasp
the basic rules.
However, published higher level contests often have enigmatic results.
There are numerous examples of games that have a declared winner
different from what a standard algorithmic assessment of the rules
would indicate. There is some speculation that deep study of these
published contests lends insight into higher toposophic game theory,
and some ascensions have been reputedly linked to that line of study.
The TopoGo Board:
1.TopoGo is played on a continuous, rather than discrete, board. 3+1
TopoGo, otherwise known as standard TopoGo, typically using a 3D
display. The defined boardspace can be any size desired, but beginning
boards start out as a cube 500 units on a side, marked identically to
a 3-Go game cube for ease of use. Adjacent is defined to be any
Distance (as defined by the boardspace metric) < 1.
2. Any number of sides > 1 may contest the board; beginning games
start with two sides. Each side has a fixed Starting Point from which
to begin their moves. This Starting Point provides a set number of
Resources per unit of Time, and may be adjusted to determine the
Handicap.
3. The boardspace has a number of defined resource Nodes scattered
throughout its volume; each Node provides Resource equal to its value
per unit of Time. Distribution of Resources across the board also
determines the Handicap.
Actions and Interrupts:
4. Interrupts occur whenever an Action by a side is possible. An
Action consists of Creating Pieces, Movement, Acquiring Resource,
Weighting, Destroying Pieces, or in advanced versions of the game,
Capture, Transport, and Declaring/Breaking Alliances. For basic games,
an Interrupt happens by default for every integer unit of Time.
5. Any number of Actions may be performed by a side at any time as
long as the total of their Resources > 0.
Accounting:
6. Accounting of Time, Distance, Weight, and Resource is kept to
whatever degree of precision desired. Basic games proceed in integer
units of Time; full games proceed by Interrupt.
Creating Pieces:
7. A side may create at its Starting Point one zero Weight Pair of
Home/Travel stones in ten units of Time for each unit of Resource.
Legal Moves:
8. The basic piece in the game consists of a Pair of stones, called
Home and Travel, linked by a Red Edge (or line) between them. A side
may move any number of pieces in its possession, subject to Resource
constraints (see Rule 5).
9. Except for the one Red Edge, all stones in the game are linked by
Black Edges to every other stone. The value of the Black Edge between
each and every stone is their Euclidean distance (henceforth
Distance).
10. The Home stone remains fixed in location; the Travel stone moves
forward to occupy territory. Each unit of Distance traversed requires
one unit of Time.
11. The value of a particular Red Edge is a fixed constant times the
Distance between the Pair of stones. In basic games, this constant is
1/3.
12. It costs one unit of Resource to move a Travel stone 10 units of
Distance. This cost must be prepaid in full before the Travel stone
can be moved. Only Weight 0 Travel stones may be moved. The value of
the particular Red Edge and all Black Edges for all Travel stones is
updated during each Interrupt.
13. It costs one unit of Resource to give the Home/Travel Pair a
Weight of one unit. There is no way to reduce the Weight of a Pair of
stones.
Acquiring Resource:
14. A non-zero Weight Home/Travel Pair adds the Resource value of any
node it is Adjacent to to the sides Resource.
Destroying Pairs:
15. Unlike standard 2-Go, Pairs in TopoGo are destroyed, rather than captured.
16. A Pair in TopoGo is destroyed if it forms a cycle on the board
such that the value of the Red Edges in that cycle exceeds the value
of the Black Edges in that cycle.
Aim of the Game:
17. The purpose of the game is to obtain more Resource than all your
opponents. The game is finished when all Resource nodes are occupied,
when no more moves can be made, or when all sides have agreed upon a
winner.
Handicaps: Resources can be adjusted to give weaker players an
advantage over a stronger ones.
These basic rules can be layered with increasingly more complicated
algorithms. Some examples include:
Level 2:
Creating Pieces:
7a. Creation of Pairs requires 10 Resource-Time Units.That is, one
Unit of Resource for each of 10 Time Units, two Units of Resource for
each of 5 Time Units, etc. If the expenditure of Resource falls below
one unit per unit Time, the Pair is destroyed.
7b.Creation of Pairs requires a new type of stone called a Forge,
which can be created using 50 Resource-Time Units. Each Starting Point
begins with one Forge. A Forge can be Created at any Node which has
the appropriate amount of Resource per unit Time. If the expenditure
of Resource falls below one unit per unit Time, the Forge is
destroyed.
Legal Moves:
10a. The is no distinction between Home and Travel stones in a Pair.
Either stone may be moved.
11a. The value of the Red Edge depends upon the relative Velocity
(Distance per unit Time) between the two stones.
12a. (The Grazer rule part I) A non-zero Weight stone can be moved, at
a cost of (Weight)^2 units of Resource per unit of Distance.
13a. (The Grazer rule part II) A Home/Travel pair can be given a
variable Weight at one unit of Weight per (Weight)^2 units of
Resource.
13b. (The Grazer rule part III) The total Weight of a Pair can be
distributed separately between stones.
Acquiring/Transporting Resource:
14a. Each Node accumulates Resource per unit of Time, unless moved.
Transport of Resource along Red Edges in a Pair takes a small constant
amount of Time. Transport of Resources along Black Edges requires the
same cost as a legal move. Resources are considered to have a Weight
of 0 for purposes of Capture and travel cost, and may be escorted by
Fleets (see Rule 18).
Destroying Pairs:
16a. A Pair in TopoGo is destroyed if:
1) It forms a cycle on the board such that the value of the Red Edges
in that cycle exceeds the value of the Black Edges in that cycle
2) The Weight of that Pair is less than the weight of the other Pairs
in that cycle.
Capturing Pairs:
18. A new type of stone called a Fleet can be constructed at any Node
for a cost of 10 Resource-Time Units * (Weight)^2. Fleets are not
harmed if expenditure of Resource halts during their construction; the
Weight of the Fleet is given by Sqrt(Resources/10).
19. Fleets can be broken down separately or combined, with Weights
given by the Resource formula in 18. Breaking down or combining
requires a small constant unit of Time.
20. A Fleet can traverse an Adjacent Pair in a small constant of Time
as long as the Weight of the Pair on both stones exceeds the Weight of
the Fleet.
21. It costs one unit of Resource per unit of Weight to move a Fleet
10 units of Distance. This cost must be prepaid in full before the
Fleet can be moved.
22. A Fleet captures any stone when the Weight of the Fleet exceeds
the Weight of the Adjacent stone. For purposes of Capture, the Weight
of a Forge is equal to Sqrt(Resources/50).
Capitols and Alliances:
23. Each side must have a stone called a Capitol, which is by default
at the Starting Point. A Capitol may be moved to any Node along any
sequence of Red Edges.
24. Capture of a sides Capitol by an opposing Fleet transfers control
of that sides Nodes and Pairs to the opposing side. Any Fleets in
control of the side with the captured Capitol remain under their
control, however.
25. For a game with n>2 sides, a side may declare or break an Alliance
with another side. Declaration of an Alliance begins at the point of
contact between the two sides, and spreads along all Red Edges in the
Alliance in a small constant unit of Time. Along Black Edges, the
declaration spreads at one unit of Distance per unit of Time. An
Alliance cannot be declared between two sides not in contact.
26. Alliances are non-transitive. (If A is allied to B, and B is
allied to C, A is not allied to C.)
27. Alliances may Acquire/Transport Resource as given in Rule 14a, and
combine Fleets as given in Rule 19.
28. An Alliance may be broken by any side at any time. Breaking of an
Alliance begins at the Capitol, and propagates as given in Rule 24.
Any Combined stones (Fleets, Pairs, Capitols, Forges) immediately
revert to control of the side with the greatest individual Weight (see
rule 22).
Level 3:
The TopoGo Board:
1a. The Boardspace is defined by the metric of its topological space.
Legal Moves:
9a. The Boardspace metric replaces the Euclidean distance in
determining Distance and the values of the Black and Red Edges.
10a. Each unit of Distance travelled requires a variable amount of
Time depending upon the local metric of the Travel piece.
11a. The value of the Red Edge depends upon the local metric of the
Travel piece.
12a. It costs a variable amount of Resource depending on the local
metric to move the Travel piece ten units of Distance.
Level 4:
Information and Signal Propagation (the Affine rules):
29. All stones (Pairs, Nodes, Forges, Capitols, Fleets, and Resources)
have an initial Information equal to their Weight.
30. A Signal can be broadcast from any stone at any time. The
Information value of the Signal is equal to the cube root of the
Information of the broadcasting stone. A Declaration is considered to
be a broadcast Signal of Information value 0 originating from the
Capitol.
31. A Signal can be narrowcast from an origin stone to a destination
stone along the Black Edge between the two stones. The Information
value of a narrowcast Signal is equal to Sqrt(Information of
narrowcast stone).
32. All Signals start at their declared origin, and propagate through
Black Edges at 1 unit of Distance per unit of time.
33. All Signals may propagate through Red Edges, if allowed by the
controlling side, for a small constant unit of time per Red Edge.
34.The Information of any stone can be increased at a Resource cost
equal to the square of its Fibonacci sequence of its new Information
(e.g. Info 4 costs (1+2+3+4)^2 = 100)
35. A Signal, upon intersecting a stone, will capture the stone if its
Information value exceeds either the Information or the Weight of that
stone.
36. If a Signal fails to capture a stone, that stone may broadcast a
counter-Signal of Information 0 which will grant immunity for any
receiving stones against that particular Signal. (Note: to be
effective, the counter-Signal must traverse at least one Red Edge in
order to arrive before the Signal).
Level 5:
Reputedly played using Resource/Distance/Metrics obtained from
detailed galactic maps.
Level 6:
Reputedly played using brane-theoretic landscapes.
Level 7:
Reputedly the real thing ....
Appears in Topics
Development Notes
Text by Adam Getchell
Initially published on 31 December 2007.
Initially published on 31 December 2007.
