Rebel Physics

Peter J. Carroll

Latest Blog Post

  • Late May 2020

    Magic News.

    An enthusiastic correspondent has started putting together an online forum for THE EPOCH OWNERS CLUB, in which participants can discuss their work and experiences with it. I have had a look at the layout and format. It looks good and I will participate when he declares it open. Watch this space for further details.

    Now Online at epochownersclub.freeforums.net

    Haute Cuisine.

    Oat Cuisine recipe number 3 of 8,127 – (a large sack of oats lasts an exceptionally long lockdown). - Savoury Oatcakes from Porridge Oats.

    Note the non-quantitative nature of the entire Oat Cuisine Range. Cooking becomes so much more intuitive and creative and fun without measurement. After a hard day’s painstakingly accurate cosmological and quantum hypersphere mechanics, sculpting and cooking by eye comes as blessed relief.

    Oil up a shallow baking tray and heat an oven to about 200 C. Mix porridge oats with about a fifth flour and a dash of oil, and add anything savoury to hand, like grated cheese, herbs, pepper, seeds, spices, etc. Stir in a little water till the mixture becomes a thick paste. Spoon dollops of the paste onto the baking tray and squish them flattish. Bake for about a quarter of an hour or until agreeably brownish and crispy. Delicious and fortifying, hot or cold. 


    Beach detritus fantasy creations continue with this: -

    Arachnid Empire Outpost, with nest cone, spidership, and termite slave towers.

    The nest cone and base consist of some sort of lightweight building composite that washes up here, and which grinds away easily against flat stones or bits of scrap metal. The termite towers consist of lengths of sea rusted iron rod. The spidership started off as a grapnel fishing weight, a covering of araldite smeared all over it provided a surface which when gone over with a thick black marker came out with an insectoid sheen.

    Pandemic Thoughts.

    A Shub-Nigurath - Cthulhu perspective.

    Life on earth only tried high intelligence comparatively recently. For billions of years it experimented with other strategies like giant reptilian bodies, aerial flight, and hundreds of millions of species of insect. Will the high intelligence strategy pay off? The most ‘intelligent’ species that has so far evolved has already done spectacular damage to most of the rest of life on earth. The so called Anthropocene (Human created) Mass-Extinction of other species proceeds at a terrifying pace, we have ripped up the earth and polluted the land, the skies, and the seas, and our numbers seem set to grow by billions more who will want gigatons more of everything.

    Covid 19 looks like the biosphere taking a swipe at a rogue species, not a particularly vicious swipe because it probably won’t kill more than a mere one percent of us, but it could do much worse next time.

    High intelligence seems a risky strategy for life on earth to pursue. In the long term it will only pay off if the high intelligence species manages to plant life from earth in other star systems. Otherwise life on earth will probably have shortened its own life expectancy by trying this experiment, unless the ‘intelligent’ species becomes truly intelligent.

    Octachoron and Hypersphere.

    Some Azathothian musings…….

    Herewith a 3-dimensional representation of a 4-dimensional hypercube.



    (Scrap wire and superglue, the araldite having run low, the whole perched on a spare pyramid,)

    A hypercube can assist with the visualisation of the geometry and topology and rotation of a hypersphere in both cosmological and quantum contexts.

    The hypercube consists of a four-dimensional cube, and it has many possible perspective representations in the 3 spatial dimensions that we can perceive.

    Some preliminary thoughts on the applicability of hypersphere mechanics to cosmology and particle physics now follow: -

    The 4-dimensional hypercube, sometimes also known as a tesseract, also has the mathematical name of an Octachoron as it has eight cubic cells. The eight cubic cells appear in the above model as the more obvious inner and outer cubes and the less obvious six truncated pyramids that join the inner to the outer cubes. In this 3-dimensional representation these six cubes become distorted by perspective into truncated pyramids. In a real four-dimensional cube, all eight cubes have the same size, so perspective has also made the ‘outer’ cube appear much larger than the ‘inner’ cube.

    The Octachoron has the usual x, y, and z axes of a cube and of 3-dimensional space, and its fourth spatial axis w corresponds to the ‘diagonals’ joining the ‘inner’ and ‘outer’ cubes. In a hypersphere the fourth spatial dimension w will appear to 3-dimensional observers as a curvature or an acceleration.

    This makes the Octachoron a useful visualisation tool when considering the dynamic behaviour of a hypersphere which we usually represent in three dimensions as either a point surrounded by a spherical surface representing the antipode of that point, or as two spheres of equal size with every point on the surface of each sphere in contact with a corresponding point on the other, (imagine them rolling all around each other) and the centres of each sphere representing the observer and the observer’s antipode.

    In the Octachoron each of the six truncated pyramids lies antipodal to the one opposite to it across the ‘inner’ cube. Strange as it may seem, the ‘inner’ cube lies antipodal to the ‘outer’ cube, analogous to the way in which the ‘central’ point of a hypersphere projected into 3 dimensions has its antipode point spread out into a spherical surface around it.

    Visualising the rotations of a hypersphere remains exceptionally difficult as it has no obvious planes or edges to act as reference points. However, the Octachoron does provide a model of four-dimensional closed space which also comes with built-in three-dimensional Cartesian axes x, y, and z, corresponding to the edges of the undistorted ‘inner and ‘outer’ cubic cells.  

    As these videos show, rotating an Octachoron through a plane of one of the x or y or z directions and the fourth-dimension w, turns it inside out and back again: -

    VIDEO https://www.youtube.com/watch?v=q5Qh2XpoCsY

    The following diagram shows a side view of an Octachoron undergoing an 1800 rotation about a wx plane from one end of the diagram to the other. Note than in addition to turning the figure inside out, the rotation also turns each cell into its mirror image.

    Using the quaternion algebra of rotations, we can equate an 1800 rotation with i2 as it inverts the figure (i2 = -1).

    Thus, by Hamilton’s formula i2 = j2 = k2 = ijk = -1

    if we equate i, j, and k with a 900 rotation about the wx, wy, and wz planes then a 900 rotation simultaneously about each will completely invert the Octachoron or Hypersphere and turn it ‘inside out’ and into its mirror image, a further 900 rotation of this kind will restore the original configuration. Note that each rotation can have two possible directions designated + and -, or r and l. Such rotations about three planes simultaneously only work as above if they all have the same direction.

    An Octachoron rotating in the -i-j-k mode would effectively act as an Anti-Octachoron to an Octachoron rotating in the +i+j+k mode. This may underlie the manifestation of fermion quanta as either particle or anti-particle.

    This triple rotation involving the w axis would appear in three-dimensional space as a spherical wave traveling either inwards or outwards depending on its sign. It may explain the origin of gravitational and electromagnetic and perhaps nuclear fields. On the cosmological scale it provides a model for the hyperspherical vorticitation, the special kind of rotation which prevents the cosmic hypersphere from collapsing under its own gravity.

    Now all fundamental particles have a measurable Spin corresponding approximately to rotations in three dimensions by rotation about a single xy, xz, or zy plane. The somewhat peculiar nature of this Spin may arise from its origin as an isoclinic double plane spin such as xy/wz.

    In addition to Spin, fundamental particles can also have one or more of two properties which can come in THREE possible ‘strengths’ viz-

    Electromagnetic charges of 1/3, or 2/2, or 1 (or their negatives)

    Particle Generation (charges?) of 1, 2, or 3 (or their negatives)

    Plus, fundamental particles can in principle have one of three possible Nuclear Charges (designated red, blue, and green (or their anti-colours)) although only composite particles exhibiting all three or a charge - anti-charge configuration have any kind of stability.

    Now if time has three dimensions rather than just one as commonly assumed, and all three lie mutually orthogonal (at right angles) to each other (as with space), then the two time dimensions orthogonal to the direction of observation used by an observer constitute an imaginary time plane corresponding to probability lying at right angles to time. Imaginary time would constitute a sort of ‘Pseudo-Space’ by the Minkowski formalism that counts time as an imaginary space.

    As the two axes of pseudo-space, which we can designate u and v, must also lie mutually orthogonal to all the spatial dimensions x, y, and z, a number of further rotational possibilities and degrees of freedom become possible, viz-     

    ux  uy uz        vx  vy vz        wu  wy  wz

    Between them these ‘exotic’ spins may somehow account for the electromagnetic, nuclear, and generational charges of fundamental particles.

    Work continues………… I put this out there to see if it ignites any sparks.

    Written on Monday, 18 May 2020 19:48 in Blog Read 175 times

Latest Games Post

  • Frontier Space War

    Herewith a recent sci-fi board game system. The board represents space using star systems as nodal points connected by posible jump routes. All movement takes place simultaneously on the declaration of pre-wriiten destinations for starships. Combat between opposing ships that land on the same star system takes place by the simultaneous revealing of ship order of engagement and chosen tactical cards, the effects of which appear on the combat octagon charts. The system does not use dice or other sortilege procedures, everything depends on trying to anticipate an opposing commander's intentions in movement and tactical combat. Does this make it a game of chance or not?

    The various classes of starship and the starsystem bases all consist of various nuts and bolts and masonry anchors and plumbing fittings painted matt mettalic. Such pieces have the advantage of standing upright and not cluttering the board, vessels of the same class all have the same appearance, and the pieces have a pleasing weight. Combat takes place only at star systems. Although the system used a 2D board to represent 3D space we can consider the stars as lying both above and below the plane of representation.

    Legemeton flotilla threatens a Terran position.

    Legemeton ~ Little Green Men of unknown origin and appearance. 

    Frontier Space War.

    A boardgame system for modelling interstellar conflict as it may develop in coming centuries. This system uses concealed simultaneous choice of movement and concealed simultaneous choice of combat tactics rather than sortilege procedures to model the uncertainties of conflict.

    1) Starships in the FSW Universe.

    Common Classes of Vessel.

    Common Name      Firepower       Defences              Cost  

    Battleship                     5                     5                       5

    Cruiser                         3                     3                       3

    Destroyer                     1                     1                       1

    Factory                         1                     1                       5

    Reinforcement Vessels.

    Common Name      Firepower      Defences               Cost

    Battlecruiser                5                     3                         3

    Heavy Cruiser             3                     5                         3    

    Frigate Carrier FC       3                     3                         3          (Carries up to 5 Frigates)

    Frigate                         1                     1                     2 for 1.     (Not jump capable)


    2) Ship Movement in the FSW Universe.

    At each turn all ships on all sides can move simultaneously.

    All ships that move must move two star systems, slingshotting via an intermediary system at hypervelocity. (The presence of other ships at the intermediary star makes no difference)

    Commanders write down the next position of each of the ships under their control on a log-sheet and then all commanders reveal their secret orders and move their ships accordingly.

    A log-sheet for a small flotilla might look like this: -

    Ship           Initial position      1st Move,      2nd Move,    3rd Move,    4th Move,       etc  

    Battleship          N36                     D43            H67    

    Cruiser              N36                    X14             L65

    Destroyer          N36                    D43             H67

    Destroyer          N36                    D43             H67  

    Destroyer          N36                    X14             L65

    Here the flotilla starts at star system N36. On successive moves the flotilla splits in two with a pair of Destroyers accompanying the Battleship to D43 and then on to H67, whilst the other Destroyer goes with the Cruiser to X14 and then to L65.

    3) Ship Combat in the FSW Universe.

    When opposing vessels meet at a star system, combat occurs if any commander elects to attack opposing vessels. Combat proceeds by combat rounds until only the vessels of one side remain, the others having become destroyed or having managed to evade, or all commanders elect not to attack further.

    A combat round begins with the Assignment of vessels. Commanders put forward a piece concealed within a hand against an enemy commander who must then put forward a concealed piece and then both reveal them simultaneously, until all attacking ships become paired.

    If one side’s ships outnumber that of the other, then the commander(s) of the greater number may then assign any spare ships to join in where desired.

    Combat rounds then take place between vessels assigned against each other. Each commander selects a tactical card for a vessel and puts it forward, both commanders then reveal their tactics and consult the tactical chart to assess the result.

    If vessels from both sides survive their individual duels, then any vessels which did not evade successfully can go through another cycle of assignment and combat rounds. Ships which manage to evade during a combat round can voluntarily de-evade and participate in another cycle of assignment and combat rounds if desired.

    Where more than one vessel becomes assigned to attack a single vessel the commander(s) of the multiple vessels may order them to attack individually and put forward a concealed tactical card for each. In this case commanders assess the effects of each of these chosen tactics against the single tactic chosen for the single vessel. Alternatively, the commander of the multiple vessels may coordinate Destroyers or Frigates with other vessels (subject to certain restrictions below) and chose a single tactic for them.

    Ships coordinated together on a single tactic simply pool their firepower and defences and act in effect as a single more powerful vessel.

    Restrictions on the grouping of Destroyers or Frigates arise from the telemetry problems associated with closely coordinating their actions:

    a) A single Destroyer or Frigate can coordinate with a heavier vessel such as a Cruiser or a Battleship or a Jump Carrier or a Factory.

    b) Two Destroyers or Frigates can coordinate with each other.

    c) Destroyers or Frigates cannot coordinate with vessels from different allied civilisations.  

    The arrows on Combat Octagon 1 show the effects of eight possible tactical choices upon each another. A thick arrow shows that one ship has scored 3 against another. Middleweight arrows add a score of 2. Lightweight arrows add a score of 1. Red arrows or red circles show a score of 1, 2, or 3 against both ships.  

    If adding the arrow score to the firepower of the ship that scored the hit gives a number higher than the defence value of the target, the target ship becomes destroyed. In the unforgiving environment of space, shield and generator breaches invariably prove fatal.

    Dotted lines show that a vessel which has chosen tactic 7 or 8 has achieved an evasion. To achieve an evasion against multiple opposing ships, a ship must evade them all.

    When Ships attack Factories based on planets, commanders use Combat Octagon 2 in which they have fewer tactical options.

    When a Factory comes under attack, commanders treat the Factory in the same way as a Ship for the purposes of Assignment. If all defending Ships have become destroyed or have managed to evade, the attacking commander may simply declare an evasion of remaining attacking Ships if an attack no longer appears worthwhile.

    After the resolution of all combats, another turn begins, and commanders write new movement destinations for all the Ships they wish to move.

    Thus, a complete turn consists of the following three phases.

    a) Spending of Ship Units to create Ships which appear at the Factory.

    b) The writing of movement orders on a ship-log. The mutual revealing of movement orders and the implementation of movements.

    c) Combat resolution.

    e) Production of Ship Units at Manufactories which lie on planets and have not moved during the turn. (Only one Manufactory can operate at any Planet.)

    4) General Notes on Scenarios, Strategy, and Tactics in the FSW Universe.

    a) The FSW system uses Topological Nodal Mapping of the contested areas of space. Points on the map denote star systems. Yellow points or markers show stars with inhabitable rocky worlds in an appropriate temperature range. Blue and Red points show stars which do not have such planets, Ships can go to such systems or slingshot past them whilst jumping but they cannot establish bases there. In most areas of space, uninhabitable star systems outnumber habitable ones by about five to one. Lines joining star systems show those within navigational range of each other and hence the possible ‘jump routes’.

    Two dimensional representations of contested areas (with the stars and jump routes understood as projecting both above and below of the plane of representation and with some jump routes thus perhaps appearing to cross each other) prove most convenient. The scale of the map in relation to the sizes of the pieces should allow for the unambiguous positioning of groups of pieces around any star system.

    To settle larger battles at star systems commanders may temporarily move all involved pieces off board to a convenient space and then replace the surviving ones on the board afterwards.

    b) Scenarios.

    In Tournament Scenarios both or all commanders start with equal forces on a board with an appropriate (if somewhat unrealistic) symmetry, and the contest continues until one side achieves set victory conditions such as the elimination of all enemy Factories or Ships or the establishment of a set number of new Factories.

    Initial set ups and dispositions should ensure the dispersal of forces between well separated Bases to avoid excessive force concentration and cataclysmic battles too early in the scenario.

    Asymmetric Scenarios.

    Empire Building. Players start with some Factories placed and strive to expand their spheres of influence. Alliances may form and break.

    Raids. An empire can over-extend itself by providing insufficient protection to peripheral areas or to areas where it has started to establish new Factories. This may offer opportunities for cost effective raids by smaller vessels against areas defended by too few heavier vessels. Deep Penetration Raids against Factories designated as politically important can also justify the commitment of heavy warships.

    Convoy Operations can involve moving Factories or designated warships carrying items of great value from one side of an area to another against enemy interdiction.

    Insurrection Scenarios can arise after cyber-warfare and/or political propaganda causes some Factories and Ships to rebel and fight for independence.

    Tactical Notes. Jump Carriers enter combat with their Frigates already launched. Thus, a fully loaded Jump Carrier could in some circumstances engage several opposing ships by effectively reconfiguring itself as (3+1), (1+1), (1+1). Alternatively, the Jump Carrier could attempt to evade carrying its Frigates.

    The civilisations from which fleets originate may not wish to allow commanders to become too powerful and may limit the number of replacements and reinforcements they can build.

    5) Diplomacy and Treachery in the FSW Universe.

    Scenarios involving more than two players provide opportunities for the making and breaking of alliances.

    The simultaneous movement of ships requires trust between allies, and treachery can exploit this.

    During a multi-player battle of several combat rounds, ships can change allegiances.

    Diplomacy can proceed openly and/or by the passing of private notes.

    The complexity of FSW lies above that of ‘family game’ but below that of ‘afficionado game’. However, game aficionados can easily complicate to game to any required degree of sophistication by adding house rules.

    Whilst a two player game becomes a straight conflict based on bluff and an asymmetric rock-paper-stone type combat, multiplayer games tend to also involve elements of Diplomacy and Poker.

    The rules do not forbid the use of psychic powers.



    Written on Thursday, 07 November 2019 15:20 in Games Read 813 times

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