Bo'ness Dynasty Pt3 - King Maine McCinaed 'the reveler' of Lothian

(This is an AAR for Crusader Kings III. Year 867 start with the Earl of Fife - renamed to the Bo'ness Dynasty.)
Pt1 - High Chieftan Drystan
Pt2 - High Chieftan Cinaed of Lothian

Trained as an adequate bargainer, Maine made is name as the life of the party. A dear friend to vassals, foreign rulers and wandering knights, Maine's feasts brought many to Edinburgh and most stayed to add their sword or skills to the glory of Lothian. Under Maine's rule the Bo'ness line strengthened in number and power with most finding desirable matches around the banquet table and landed titles flowing from continued expansion throughout Ireland, England, Norway and Denmark.  

Although the Bo'ness family tree grew greatly, Maine himself had only one daughter, Anna, through his early years. Maine's dearest held the family hopes of alliance with France together with early betrothals to Armagnac, but by the time the marriage proposal came to fruition Aquitaine had split from Francia, taking Armagnac with them. Adding to the strife, the Bouchard rulers were swayed to Messalianism, a new heretical offshoot of the Christian faith. For this they were hounded and purged through holy war, leaving Anna stranded without a husband. Before Maine could bring her home, Anna's elderly father-in-law, Duke Bouchard, forced another marriage to the young genius, dashing hopes of future children and alliances. This would not do. Maine plotted to bring her home through any means to keep the Bo'ness heir safe. Soon Duke Bouchard died to mysterious circumstances.

With Maine approaching 40 and still no male heir to the throne, the marriage to 'Anna the wise' was annulled under suspicion of infidelity. Maine's 2nd wife, Alix de Trainel (also gifted with a marvellous intellect) soon lifted to become a magnanimous host of the ever more impressive feasts crowding the halls of Edinburgh. 2 more daughters graced the family line, but concerns were finally laid to rest when Adam, heir to the Lothian throne, was born with Maine over 45. Alix continued to have children, leaving 8 to share the heritage left behind by the time Maine died.

With lineage secured, Maine's final years were devoted to becoming a King in his own right. The kingdom of Alba had flourished in large part to the growing power base of Lothian, but increases in land and levees for Maine also meant increases to his leige. Coupled with King Cinaed V's tight relationship to the Bavarian King, he held a dominant position fielding almost 14,000 men at the height of his power. Another concern was the tanistry elective process limiting kingdom candidates to only those of the Ailpin house; it couldn't be ousted by Bo'ness candidates no matter their standing. An exit strategy had to be found. 

Maine's opening came with the mysterious death of King Cinaed V to a spider bite, succeeding to King Conchenn. While the new liege had lower prestige and less alliances, he could still field 8,000 souls if needed. Maine's troops had grown to over 6,000, but was unsure how the generally reliable family alliances would hold since all swore fealty to Alba as well. With additional alliances garnered through his children to Wessex and as far-flung as Florence, Maine pressed for independence alone as Conchenn returned from raiding Ireland. The Lothian elite were also bolstered by mercenary warbands to field over 17,000 once raised. As Alba's levees returned to their lands, the Retinue of Hengist and other warbands tore into Gowrie, demolishing the standing army and laying siege the capital. Unable to recall Lothian levees, King Conchernn's army depleted to a measly 4,800 that even his own mercenary hires could not recover from. After the first month the campaign had largely been won, leaving only a few harried skirmishes and sieges to seal independence.

Shortly after breaking the shackles of Alba, the Kingdom of Lothian was announced with all lands from Edinburgh to York under rule as well as holdings in Ireland, Norway, Denmark and the Netherlands. As the embarrassment of Alba's sudden fall from dominance over the northern realms sunk in, King Conchernn switched primary titles to the Kingdom of Norway to signify where his power base now lay. Alba is no more.    

Maine's drunken excesses finally took their toll as the obese king revelled his last feast. King Adam may be young, but has his own destiny and domain to lead now.  

Bo'ness Dynasty Pt2 - High Chieftan Cinaed of Lothian

(This is an AAR for Crusader Kings III. Year 867 start with the single title of Earl of Fife and the start of the Bo'ness Dynasty.)

Pt1 - High Chieftan Drystan

Cinaed took up the mantle of patron to the Bo'ness line amidst the turmoil of Viking battles for Scotland (Alba) and Northern England. With internal bickering between sons of Ivar the Boneless, other nations descended onto the confusion to tear out a piece for themselves. Cinaed helped himself to most of Lothian to surround his new capital at Edinburgh. Other regions of Ireland and Northumbria also came under the control of the Duke of Moray to add to Alba's dominance of the northern lands. 

In between local skirmishes and clams on the mainland, Cinaed also strengthened his presence on the Nordic coastline to completely supplant the Danes all the way to the Finnish peninsula as well as all mountain passes over into Swedish lands. 

Mercia moved in on Danes holding York to put even more pressure on established viking conquests. Cinaed also saw the opportunity to move in and take the prized capital of York, but missed the opportunity to compliment it with the fertile lowlands around Leeds, with the West Riding capital ceding to Mercia. Spoils were split on the Lancastrian coast as well with Cinaed holding Westmorland and the rest falling to an expanding Mercia. 

All was not happy families within the Alban Kingdom as easy Danish targets dried up. Strife started with the Earl of Lennox declaring rightful ownership of the Irish lands of Oriel, held by Cnes Bo'ness along with her norwegian estates in Traendalog. Mormaer Tadg from Atholl supported the claim to add vastly superior numbers to the equation and tore through the local Oriel defenses. With no formal alliance to assist, Cinaed changed tack and found an avenue to claim Lennox itself through somewhat dubious heraldry. He pressed the claim immediately and swept through the midland holding with ease and pushed into Atholl while their forces were preoccupied overseas on the nordic coast. As they pinned Cnes's troops into a final pitched battle, word reached Flaithbertach Neill that his domain is no more and, as a landless lord, his claim to Oriel is no longer valid.

Even though a few more petty claims over Danish lands rounded out the Cinaed's reign as one of expansion, the internal fractures of Alba hinted at an independent future for the Bo'ness line. 

Bo'ness Dynasty Pt1 - High Chieftain Drystan

 (This is an AAR for Crusader Kings III. Year 867 start with the Earl of Fife - renamed to the Bo'ness Dynasty.)

Drystan is the earliest known landholder for the Bon'ess Dynasty. Although there is no record of his early life or even how he came to hold the Mormaerdom (Earldom) of Fife, Drystan is likely to have come from Gaelic tribal lands between Edinburg and Linlithgow during the time of viking raids and great upheaval.  

Under the Kingship of Causantin II of Alba, Drystan had relative independence and sought a path to take over Edinburg to claim his homeland. With Ivar the Boneless raiding from the west and Jorvik pushing up from York, Drytan's meagre army could not hold claim for long on the Lothian capital, and eventually fell to Danish hands along with Northumbria. Disheartened, Drystan looked to Linlithgow instead. 

Both Sterling and Linlithgow were held by fellow vassal MacMuirdach. Although internal fighting was not unheard of, MacMuirdach held double the lands and could command almost 1000 tribesmen. Through marriage of Drystan's youngest son into the line of Prince Rhodri 'the great' of Gwynedd, the alliance yielded almost 2000 men to call upon and press the homeland claim. Stirling would fall 5 years later.

With Danish kings vying for Ireland, a small window of opportunity opened to allow Drystan to pinch Oriel from one of the smaller invaders. Alba also allied with Meath to control the top of Ireland until Bjorn 'Ironsides' headed west and dominated. 

Alba turned back to the mainland and forced claims on Strathearn's heart, taking Glasgow from the independent Kingdom. Drystan followed in on the weakened Cumbrians to pick up Kyle and surrounds, leaving Carrick and Galloway to fall soon after to Ivar the Boneless, giving continuous land from east to west across Scotland.

As a more established Earl and finding favour with Moray, Drystan continued tussels with smaller independent Danes on the Nordic coastline, gaining foothold in Bjorgvin and pushing north all the way round to Raumsdale. Enough land was gained to usurp the Vestlond title and elevate Drystan to High Chieftan. 

As an ill-fated holy war between Alba and The Isles was drawing to a close, Ivar the Boneless succumbed to injury and left his nation shattered between siblings. With Lothian falling to Jarl Godfrid separate to The Isles, Drystan pounced on the opportunity to take entire duchy in one bold claim. Calling on all allies and additional mercenaries the weakened Danes fell to a 4,500 strong army, but before the final sieges ran their course Drystan succumbed to old age. His dream of ruling from Edinburgh came 3 months later for the Bo'ness line. 

Nothing can stop a cheater?

A recent discussion on the Capitalism Lab forums led to the issue of optimising vs exploiting vs cheating in single player games. Below is a response to this quote:

While I think there is room for exploitation, in the end this comes down to the desire of the player for fair game - nothing can stop a cheater from cheating. - JasonLJ on BankingDLC

As a starting point, the simplest way to define cheating is operating outside the rules. In a computer game the rules are set by the designer and embedded into the simulation. In general this also means that you can interpret cheating as "operating outside the simulation", given the provision that if there are unintended consequences (bugs, etc) the designer can rectify them to clarify / enforce the rules.

On top of the simulation rules there can also be additional "house rules" where players in corporate or individually agree to abide by different rules to achieve a different goal to that which the designer intended. This can be anything from custom mods, scenarios, competitions, the obligatory "one city challenge" in Civ, to someone choosing to only buy and sell purple items. In this case it is the responsibility of the agreeing parties to enforce the rules and if this cannot be done absolutely through the simulation (Eg: turning off all imports at a port for a tougher CapLap challenge) then a level of trust that all players are "playing fair" starts to exist. Note that most sports and even collaborative play operate in this space.

Saying "nothing can stop a cheater" isn't quite right. The simulation space can be hardened against attacks from outside of the simulation, and within the simulation it is almost completely possible to stop cheating by encoding the rules into the simulation.

Now from the other side:
Within the simulation, the aim is to optimise play to maximize whatever the winning criteria is defined to be. In a competitive sense this is the heart and soul of the challenge and the main striving factor. To achieve greater and greater optimization requires deeper and deeper understanding of the rules (and therefore the simulation) and the skills needed to execute optimal play.

This still holds true for "house rules" games, although if there are rules that need to be enforced from outside the simulation, the line between "breaking the rules" and "optimal play" is not as clear cut and opens a window for debate about what is or isn't "fair play".

With JasonLJ's comment:

Cons
- Could be exploited by some players to bankrupt AI competitor banks. However, this is a matter of "willingness to cheat" not "capability to cheat" - even if deposit cap was 20%, players who wanted to use the same trick to cause a liquidity crisis with AI firms could still do so.

There are 2 different angles to view the question of cheating (not sure which one Jason is using, but both are worth discussing anyway):
- If Jason is referring to "tricking" the AI because they don't know how to handle it, then Jason is expressing the fact that any other player wouldn't fall for that, or, more officially, the AI is not playing like a real company would in the real world. Jason is expressing a desire to play with a house rule of "only do what would work in the real world", therefore taking advantage of a dumb AI would be cheating. Unfortunately since CapLab is actually trying to simulate the real world, there is some legitimacy in thinking that the game you are playing is operating under the same rules as the real world, however this isn't the case; the game's rules are enforced by the simulation. That said the designer should, as much as possible, encapsulate the desirable rules from the real world and embed into the simulation to enhance the simulation's relevance to people with this particular house rule. In the scenario above, making the AI aware of their liquidity risk exposure would remove this element of cheating from those expecting the "real world" house rule regardless of any changes to the deposit cap.

- But what if the AI knew about liquidity risk exposure and still got itself into a vulnerable position? Would it then be Ok to punish them? What if the the player got into a vulnerable position, would/should the AI bankrupt them? If Jason was thinking that the ethical choice of intentionally bankrupting someone is available in the game but classified as cheating, then he is putting a new house rule in effect; "Don't bankrupt opponents". Once again the designer COULD choose whether this rule is enforced in the simulation through some sort or anti-competitive behaviour legislation and enforcement (as would likely happen in the real world).

Although it sounds like I'm advocating a wild-west anything-goes-inside-the-simulation approach, it's more the opposite that the designer has the LUXURY of controlling exactly what is or is not simulated, what rules are or are not enforced, what ethical choices do or do not appear, and what learnings the player can take away from the game to apply to the real world. Ideally all players uptake the rules as intended, obviating the need for house rules and potentially divergent views on how to play the game.


Onto the game-breaking strategy:
As mentioned I generally play single-player games until I "break" them by discovering a strategy that guarantees a win, because all that is left is to execute the strategy over and over again. What I REALLY enjoy are complex games where the balance allows a variety of strategies packed full of interesting choices along the way. CapLab is one of those games and I've been playing on and off since the original Capitalism. When I started using the land pre-purchase strategy it felt wonky, but somewhat believable since it seemed to simulate the land-developer mindset. After investigating exactly what was going on and finding the edge cases (especially infinite money generators) it seems FAR more likely that this is unintended and would be classified as a bug or at least needing clarification / enforcement of the intended rules. If so, I look forward to a new version with many more optimising challenges ahead.

TournamentCompare v0.005 prep

A recent Math binge has brought me back to predicting confidence levels in the montecarlo method approach to assessing what the bias is in a tournament. Previously I had kept a running total of averages as 1000's of randomly seeded tournaments rolled by, but it looks like I can also keep a running standard deviation. Once I have both the sample standard deviation and the number of tournaments sampled, I should be able to calculate the 95% confidence interval for the trial. Hopefully I can blow the dust off the old code and get it running again.  

14.5

Although I missed an excellent opportunity to hit Burners after work for 30+Kn, Sunday was almost ideal for Burners with a full tide at 4pm and winds above 20Kn. First session felt good, but not as special as 2 weeks ago and I greeted a 13.1m peak height with a knowing nod. At least it's the Burners record by a fair way.

Francis came down for a late session and I'd recovered enough to hit it once again. Unfortunately the wind was down a few knots and it really felt the heights weren't there. Luckily a strong surge for about 2 mins launched me unexpectedly up above the trees. A few more boosts through the surge saw me up over 14.5m! another PB!

Of the 4 boosts during the surge, the most telling was the 2nd one of only 12.1m where I distinctly remember being pulled off my edge in the leadup. Although I was still riding fully powered, it's the first sign that I might be getting close to the peak wind performance of the kite. The next jump I'd held my edge better and that's what registered the 14.5 monster. 15m is definitely on the cards, but going past that will need better technique.    

Woo rank #1

After an excellent demo over a year ago, I have had my sights set on an Ozone Edge v9 as my next potential kite. The problem had been that the 10m Edge that I tested felt like it provided the power of my 14m Bandit, yet nimble like my 10m Bandit. Do I get one kite that replaces both? I wasn't willing to give up on the Bandits that soon. Fast forward a good 9 months and the Bandit's had their fair share of running repairs that kept them out of the sky. It finally feels like the maintenance is going to be costing more than replacement. The last piece to fall was a bit of a discount through Wardy.

The first session was great. 10.1m jump off a pretty average session (maybe 18Kn winds) at Elliott. I'd settled on a slightly larger 11m Edge to mainly knock out the 14m Bandit and keep just a bit more sail up in the sky for boosting in the standard 20kn range, and it immediately felt like it was going to bring in the height department.

Unfortunately the next few outings were in lighter winds, and it wasn't as good at the low range as expected. Admittedly I was sometimes the only one out on the 11 when others on 12's and 14's were parking, but it didn't quite have the bottom end of the 14 Bandit as I'd hoped.

18th November was the weekend I was waiting for; steady 20+Kn winds with a full tide to really push the kite into boost mode. After 2 hours on the water I came in and downloaded the woo stats hoping for at least a new personal best. C'mon, 10.5 metres! 12 possibly? The reading floored me. 13.7 metres! a new PB by over 3.5m. Maybe an outlier? Nope, analysis of the session showed several boosts over 12m and the 11 over 11m badge. YES!

As it happened the day was also the QLD boosting comp down in Brisbane. I kept refreshing to see the boosts come in and was pleasantly surprised that they maxed out at 11m. WINNING! Granted I wasn't at the event to share the exact conditions and had over 2 hours to put in a good one, but it looked from the reports to be close enough to give me hope I'm in the right ballpark. Maybe February's Wind Slasher and state freestyle titles might have a boost off?

The day rolled into night and I stayed above the rest. More due to WA missing out on their normal 25+ winds than anything else kept me and David (boosting at Lake Weyba just down the coast) out in front to claim my first (and probably only) daily win on the woo charts:

Another notable improvement was my overall rank. previously a 10.2m still had me in the bottom 33% of all Woo owners, but moving to 13.7m put me right up into the top 20%. There must be a massive bubble of people about the 11-12m mark, which likely means that there's a typical peak jump on standard equipment at that mark. The Edge is certainly the catalyst for going bigger as my technique hasn't changed much in the past 2 years. 

Also notable was that I still has the Edge fully powered all session. I'm pretty sure I can hold down another 5Kn, which means going higher is definitely possible. 

Send out the disciples

There was a group of people who wanted to establish a new Surf Life Savers Club on a new beach:

• Between them they gathered enough funds for a building.
• Turned up weekly to go inside and practice
• Marching in straight lines,
• Overhead line pass
• Brought in specialists. Famous names.
• Taught the theory of swimmingSwimming while holding another afloat
• Talking calmly to others to let them know that the shoreline isn’t too far away.

Months of training. Years of training. Yet they didn’t enter the water once, and people kept drowning. 

In the reading today we hear Jesus equipping and sending out his disciples:

Mark 6:6-8  Then Jesus went around teaching from village to village. Calling the Twelve to him, he began to send them out two by two and gave them authority over impure spirits. These were his instructions: “Take nothing for the journey except a staff—no bread, no bag, no money in your belts

Jesus’ instructions seem to be an odd way to equip your followers. No food (not even a lunchbox) no bag, no money. But he did equip them with spiritual power. The authority over demons was the main tool needed for this journey. The rest is not a concern right now. It will be provided when the time comes. Have faith. The point is to go. Right now. 2 by 2.

And they should have had faith. By this time they had been with Jesus for about a year. They had seen him start off his ministry and drive out impure spirits, then go on to heal the sick, then those with Leprosy, even the paralysed. They had front row seats to see Jesus exercising his authority.

So did they Go? Yes, yes they did.

Mark 6:12-13 They went out and preached that people should repent. They drove out many demons and anointed many sick people with oil and healed them.

That authority was real and evident in them.

So what about us disciples gathered here in the present. Do we feel trained and ready? Do we feel confident to step outside in faith? Or are we more like the surf life saving club afraid of the water?

If these services each Sunday were training sessions, how many would you need to feel ready? Here’s an experiment. Close your eyes and think how many years you have been a Christian. A rough guess is fine. Now half that number (divide by 2), then multiply by 100. That’s roughly how many hours spent in church.

Not only that we have the bible with us. An instruction book that even tells us how it’s going end.

Yet sometimes it feels like we’re strangely inadequate (myself included), unable to head out in faith, to seek and save the lost.

There was a period where the disciples from Mark’s gospel faltered. They watched their source of power be falsely accused, be stripped and humiliated, and laid bare on the cross. They ran away, their faith all but gone.

But Jesus wasn’t done with them, and he’s not done with us. Rising again Jesus not only claimed authority over death, but authority over everything. When ascending up to heaven he repeated the sending out:

Matthew 28:18-20 Then Jesus came to them and said, “All authority in heaven and on earth has been given to me. Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything I have commanded you. And surely I am with you always, to the very end of the age.” 

Actions speak louder than words

This is a sermon based on Matthew 21:23-32 :

The Authority of Jesus Questioned
23 Jesus entered the temple courts, and, while he was teaching, the chief priests and the elders of the people came to him. “By what authority are you doing these things?” they asked. “And who gave you this authority?”
24 Jesus replied, “I will also ask you one question. If you answer me, I will tell you by what authority I am doing these things. 25 John’s baptism—where did it come from? Was it from heaven, or of human origin?”
They discussed it among themselves and said, “If we say, ‘From heaven,’ he will ask, ‘Then why didn’t you believe him?’ 26 But if we say, ‘Of human origin’—we are afraid of the people, for they all hold that John was a prophet.”
27 So they answered Jesus, “We don’t know.”
Then he said, “Neither will I tell you by what authority I am doing these things. 

The Parable of the Two Sons
28 “What do you think? There was a man who had two sons. He went to the first and said, ‘Son, go and work today in the vineyard.’
29 “‘I will not,’ he answered, but later he changed his mind and went.
30 “Then the father went to the other son and said the same thing. He answered, ‘I will, sir,’ but he did not go.
31 “Which of the two did what his father wanted?”
“The first,” they answered.

Jesus said to them, “Truly I tell you, the tax collectors and the prostitutes are entering the kingdom of God ahead of you. 32 For John came to you to show you the way of righteousness, and you did not believe him, but the tax collectors and the prostitutes did. And even after you saw this, you did not repent and believe him.

2 Kids

When the father asks his 2 sons to help out, one says he will do it and then doesn’t, the other son says he won’t do it, then eventually turns around and does it. Who did what the father wanted?

When Jesus posed this question to the religious leaders, they answered by choosing the son who eventually turns around and helps out. Do you agree?

I’m sure the parents among us see this as a simple yes. From the Father’s perspective there is work to be done, and at the end of the day, no matter what was said, the work just has to be done. If not by the sons then, most likely, by the Father.

It’s disappointing to hear your son whinge and whine about doing what was asked, but it’s even more disappointing to be told it’s all under control and find out later on that nothing got done.

Actions speak louder than words.

Hypocrites

There is a name for people who say they are going to do something and then don’t. Anyone know? Hypocrites (Politicians?)

The word “hypocrite” was originally used to describe a greek actor about 400 years before Jesus. These actors would literally have a mask on to display the type of person they were portraying and their mood. This is a happy scene? Wait a minute and I’ll just go get my happy mask. From there the word branched out to cover people that hid behind a figurative mask; people looking happy even when they were sad, people saying one thing and doing another, people hiding their true intentions.

As an aside: Politics? Demosthenes, a respected politician in Athens ridiculed Aeschines because he used to be an actor. An untrustworthy man used to hiding behind a mask. A hypocrite. They have no place in such a respected profession...

Jesus had branded the Pharisees as hypocrites several times, but they weren’t alone. Earlier on in the chapter, Matthew writes about Jesus entering the temple. What appears from the outside to be a magnificent structure and the spiritual centre of the Jewish religion had been infested with moneymakers. A den of robbers. After that Jesus came across a fig tree. All leafy and green on the outside, but no fruit at all! What good is it!?

Now the Jewish leaders and elders come to Jesus to ask about his authority, but Jesus has a question back: where did John’s baptism come from?

They discussed it among themselves and said, “If we say, ‘From heaven,’ he will ask, ‘Then why didn’t you believe him?’, But if we say, ‘Of human origin’—we are afraid of the people, for they all hold that John was a prophet." 

So they answered Jesus, “We don’t know.”

Both answers show that deep inside, they really just wanted to maintain their OWN authority in the sight of others. They don’t want to be ridiculed and are more interested in saving face than actually seeking the answers they asked for. An outward appearance of seeking God, while an inward selfish preservation of the status quo.

Repenters

So what of the second son, the one who said no, but later went and helped? Isn’t that hypocrisy too?

It’s interesting to read that something happened between the second son’s response and his action:

29 “‘I will not,’ he answered, but later he changed his mind and went.

The son quite possibly had every intention of not helping, but something changed his mind. He dropped his selfish ways and turned back to the request of the Father.

Jesus drives home the parable:

Jesus said to them, “Truly I tell you, the tax collectors and the prostitutes are entering the kingdom of God ahead of you. 32 For John came to you to show you the way of righteousness, and you did not believe him, but the tax collectors and the prostitutes did.

John the Baptist was preaching about repentance, which, in the original greek, can also mean a “changing of the mind”. Those that started out disobeying the will of the Heavenly Father, the crooks and whores, were the ones that changed their minds. They were the ones that went. They were the ones that started to do the will of the Father, They were the ones bearing fruit.

Of the 2 sons, the hypocrite and the repenter, which one are you? I’ve been a Christian all my life, I’m now an Elder. Like it or not, I identify more with the religious leaders in this story than the lost-and-now-saved. Am I a hypocrite? Do I say one thing and do another? Sadly, sometimes the answer is yes ...

The real hypocrisy - not seeing the need to repent.

32 For John came to you to show you the way of righteousness, and you did not believe him, but the tax collectors and the prostitutes did. And even after you saw this, you did not repent and believe him.

Our heavenly Father had offered John’s message to the Jews, yet those most entwined in the Law failed to act. They believed their words and actions kept them in high regard, yet ALL fail to meet the perfection required. There was only one whose actions carried out the will of the Father perfectly, Jesus.

Even from an early age the bible says Jesus had a thirst for God’s Word. We hear that he stayed in the temple soaking up the Jewish teachings, discussing and debating with the religious teachers of the time. He prayed to His Father, especially before big events, to keep the lines of communication open.

Jesus loved others. He wasn’t afraid of how it looked to eat with tax collectors and sinners, he saw the need in others and acted. Even to the end, in the garden Jesus prayed “Let not my will but Your will be done”. Loving us enough to lay down his life.

Jesus message echoed John’s. Repent and believe. All have sinned and all need saving. I have come to seek and save the lost. Through my sacrifice you can be made whole with the Father. Through my sacrifice you can walk with him in the garden again. Turn from you ways and remain with the Father. Change your mind to be in tune with the Father. Don’t just say you’ll love other, actually love others!

Father, change our minds so that we are always listening for your call.
Father, change our minds so that we have the courage to answer “Yes, you can count on me”
Father, change our minds so that we do what you ask.
May our actions speak louder than words. 

Introduction to Adaptive Grids

Summary: 
Adaptive Grids are a procedural generation technique for area and point based topologies that can expand to n-dimensional space.

 Preamble: 
Although ROAM was a technique that inspired temporal ROAM (Later, VRWorlds), there has been an unresolved question on how to adapt the self-similarity of right triangles to 3 dimensions and above. I’ve been considering a square / cube based approach that exhibits the near-parent properties of ROAM, but have usually run afoul of being unable to conceptualize it into a working model past the main recursive function. A breakthrough in going from 3x3 to 4x4 grids as a starting point has spawned a lot of additional pieces to fall into place.

 Introduction: 
Realtime Optimally Adaptive Meshes (ROAM) have certain key features when attempting to build procedurally generated content (like terrain).
 - Scaleable depth: ROAM allows one part of the map to be generated more deeply than another part of the map. This is important in terrain generation as a potentially infinite terrain can be generated without infinite memory / storage requirements to generate the entire world at the proposed granularity.
 - Deterministic depth: ROAM can be configured to always return the same division given the same parents. This allows the scaleable depth to continue to generate the same result given a very high level starting parent set, which in turn allows ROAM to roll up and forget previously expanded areas in favour of the currently viewed area.
 - Continuous mesh deformation: Any change made by ROAM continues to keep the mesh cohesive and continuous due to the reliance of splitting pairs of right triangles together based on known parents. This largely removes issues of creasing and tent-poling inherent in many terrain generation techniques.
Adaptive Grids attempt to mimic these traits, but be based off a grid (of squares for 2-dimensional space, cubes for 3-dimensional space, etc).Continuous mesh deformation is currently not retained for the eventual mesh itself, but utilises parental involvement to remove creasing.

Adaptive Grid core algorithm:
(The algorithm is explained for a 2-dimensional surface using squares. Extensions to higher dimensions are trivial, but covered formally later.)
Given a set of parents arranged in a 3x3 grid of squares, the Adaptive Grid generates a 3x3 grid ½ the size centered on the middle square. The new squares rely on the parents that they overlap with. This means that the new middle square is determined solely by the middle parent; the new cardinal squares are determined by the middle square and the adjacent parent (Eg: New square to the north requires the middle parent and the northern parent); and the new corner squares are determined by the middle square and the 3 other parental squares in that diagonal direction (Eg: New square to the NorthEast requires the middle, North, East & NorthEast parents).

 Since the algorithm produces another 3x3 grid at a deeper layer, the algorithm can be recursively applied to create an arbitrary depth.

 Top Layer: 
 If a top layer of 3x3 is used to initiate the algorithm, it can continue to develop infinite depth, but no method of developing breadth of grid when at an arbitrary depth. Any requirement to develop anything other than the centre grid requires the rebuilding of another parent in the previous layer to make the requested square a centre square. The parent would also require a grand-parent in the layer above, and so on, eventually breaking due to the absence of a parent outside of the initial 3x3 layer.

 To allow a defined space for breadth generation, the Adaptive Grid is initiated with a 4x4 grid. This allows the generation of a grid of arbitrary size or arbitrary depth to be generated within a 1x1 size square centred on the midpoint of the 4x4 grid. (Eg: an initial grid of 4x4 squares of 128 unit length can generate a 64x64 grid with 2 unit length inside a 128x128 space centered on the middle of the initial grid)

 4x4 grid layer progression: 
When initiating an Adaptive Grid with a 4x4 layer, the amount of squares in each fully expanded subsequent layer increases with this observed sequence:

Layer 1	Layer 2	Layer 3	Layer 4	Layer 5
4	5	7	11	19

The calculation for each layer follows the sequence: Layer(n) = Layer(n-1)*2-3

 Proof of defined space:
Since the child 3x3 grid is located centrally over the parent 3x3 grid, the middle child is a direct shrinking of the parent middle square. Continued shrinking makes the centre square reduce the area around the centre point, but never will reduce the centre point to nothingness or deviate from the centrepoint. The sides of the square asymptote to the central point. Since the side length of each square is the same across the entire grid, as the middle square side length reduces toward 0, so too does the outer squares. Therefore the outside of the outer squares also asymptotes toward the central point, which is 1.5 units in from the outside of each outer square. 

Applying this asymptote to a 4x4 grid means that the outside of the outer squares will only ever need to be brought in by 1.5 units when creating a grid of infinite depth. Removing 1.5 units from the borders of the 4x4 grid leaves a 1x1 unit area that cannot be reached, thus leaving the area to be rendered by an arbitrary grid size (Eg: If the requirement for a 1000x1000 grid is needed covering an area of 100 m2 (side 10m), a starting Adaptive Grid of side 40m or larger is required).

Simple Scratch application to help demonstrate Adaptive Grids