[Uploader's Note: A huge chunk of the second half is equations. I've thrown them all on the site at groundbreakingsci-stuff dot com/post/170171153987/1point10 ]
[Uploader's Note 2: Uhh, seems like the Professor has found this mirror: groundbreaking-science dot com/post/170171468988/groundbreaking-science-on-ffn ... Oops. He's wrong though, people need to know. Share this knowledge! ]
1.10: Breaking Down the Power Level
From the start of my patchy teaching career, beginning as a brother then a parent, my general ethos towards explaining the world has been to never patronise. I have developed some semblance of self-awareness over the years and so may at times simplify or reign in tangents - not everyone needs to know the minutiae to gain a broad understanding of a topic. My aim though is to never shy away from trying to provide a full answer to a question posed, no matter the age or background of the poser. An earnest and enthusiastic question deserves a considered answer with all the nuance one's expertise can provide in the situation. I trust those listening to instead communicate where clarification would be helpful, or sift through what they need in the moment and chew over the rest later.
In contrast, there's a trend in wider media to cling to 'consumers' of scientific content by ratcheting up the the sensational, the over-simplified, the drama that may or may not be manufactured for entertainment. Narratives within popular science help guide and contain the message within (no one wants to be subjected to a list of facts, even regarding ki) but often the science is so watered down the only substance of the piece is the fluff. Those with a genuine palate for science (or history, or literature, or…) are left underwhelmed on repeated readings and sometimes even mistrusting of the expertise involved.
It is for those reasons I decided to include this section as a hat tip to the insatiably curious, though for those among you with little appetite for a smattering of mathematics, I first bring you a tangential, and completely true, offering in the form of a fish.
I have spoken frequently of a model for ki. By that I mean a story that explains the effects of ki we see using fundamental quantities. The story links cause and effect in the form of equations, transforming the qualitative to the quantitative.
The model presented here is not perfect. All models are an approximation to the truth and there are many simplifications (particularly in this version and I will highlight where), but broadly the model performs well and the limitations of the model are well defined. I trust you to take away what is most useful to you now, and I hope this treatment gives potential undergraduates a taster for some of the more theoretical aspects of a course on ki-use I hope will materialise in the near-future.
When in battle one question sits on the tip of everyone's tongue: "What is the enemy's power level?" This is proxy phrase to ask many questions at once. What is the opponent's potential? How many people will be required to tackle them? How much strength should I use straight out of the gate? What is the risk to the local environment, the nearby populace, the planet? The highest power level will not always win a fight. Power level differences of an order of magnitude, even sometimes two, can be overcome with teamwork and sound strategy. Getting an early indication of the opponent's location and power can give your team vital time to plan and distribute yourselves effectively.
As we discussed in a previous section, the idea of a power-level measuring device - the scouter - was first introduced to us by Freeza's personal army and deconstructed by Bulma.
The original scouters performed perfectly well in the situation they were designed for, searching for clusters of life-forms with power levels of 0-2 (encompassing the vast majority of people in the Universe) to allow the possessors to commit mass murder extremely efficiently. The scouters were able to stretch beyond this range, reaching higher power levels of 5.3; any higher and the harmonic oscillator arrays constructed to respond to the vibrations in the ki field (with technology developed along a similar branch to Dr Gero's) would break. Specifically: the atomic 'pendulums' of varied masses contained within ion traps would be kicked out of the holding magnetic fields and flung away into the rest of the structure, shorting the electronics and usually exploding the device. The designers believed the likelihood of any of Freeza's forces encountering someone that strong so low they didn't deem it necessary to prioritise the scouter-wearer's safety. Clearly Freeza's true strength, peaking above a power level of eight at that time, was hidden from the vast majority of his forces.
The fully artificial scouters were not flexible enough to cope with everything life could throw at it. Life itself on the other hand has an amazing capacity to give as good as it gets. I can sense everything from tiny fogs of ki in less-than-clean water to the brightest kis in the Universe standing almost blindingly close, and I can do it all without shorting my own circuitry. Whilst the mechanical scouters have a range of 0 to 5.3, the newer versions developed on Earth can cope with -1 to 14, (or 0.1 to 100,000,000,000,000 unlogged). That is tested. Hypothetically they should remain accurate up to a power level of 17 but we never want to be in situation where we're reading that. Our method's downside is the loss of precision compared to the original scouter, which was able to differentiate just as well between power levels of 1 and 2 and 10,000 and 10,001. Our scouters do maintain a 0.1% precision however, which is usually sufficient. Anyone wanting finer precision to monitor and argue their progress needs another hobby.
Capsule Corp employees have for the most part stayed away from playing with the biophysics of life, knowing the trouble and potential backfire meddling can cause through the work of Dr Gero. What little research and development that has been done in this field has been led by Bulma and Mai through all above-board personal funding. The new scouters are a result of this off-piste research and utilise a genetic modification of bioluminescent bacteria found in a tropical fish.
The fish in question - the blue-finned angelfish - exclusively inhabits the coral reefs around one of the many South Sea archipelagos. They're crepuscular feeders, making use of the changing light levels at dawn and dusk that other fish and invertebrates struggle to cope with. When hunting for prey like small fish and krill they spread into what can appear to be a dangerously loose shoal. What makes this strategy effective is the beautiful symbiotic relationship the fish has with a bacteria within the fish's transparent skin along the fins and tail. The bacteria glows neon yellow using bioluminescence near low power levels (-2 to -1.5) and flickers in a predictable pattern with the ki signature, the wave of flickering allowing for the triangulation of distance. When the glow starts, the fish play a game of hot and cold until close enough to pinpoint their prey through smell. The now brighter glow brings the rest of the shoal to feed into the early night.
Why then are are these fish known as the blue-finned and not yellow-finned angelfish? Well, they are named as yellow locally, though zoologists from the mainland way-back-when never much listened to local expertise, routinely removing chosen specimens from their natural environment to study in the comfort of the lab. As the scientists approached the fish in the tank back home their fins glowed a bright blue and the fish reacted poorly, racing to escape. It transpires the bacteria can luminesce over two colours, yellow for prey and blue for predators - the latter covering intensities of 0.3-2. This range catches the bigger fish and reef sharks that home in on the yellow glow of a feeding shoal. When a wave of blue creeps across the shoal in the near-dark, the fish know to hide. It just so happens this range encompasses the scientists' own power levels, too. To the scientists with clipboards then, these were only ever blue-finned glowing fish.
[ Figure 1 ]
[ groundbreakingsci-stuff dot com/post/170171153987/1point10#one ]
The locals know of the fish's defence intimately and is a source of great amusement. There's a shallow, natural harbour in one of the smaller islands that, very rarely, a large shoal of angelfish will chase prey into. The harbour is sealed and all the boats dragged onto the shore. A call is then sent to the other islands for an impromptu night-long festival - a spontaneous get-together and chance to catch-up. Traditionally, the arrival of the fish had been seen as a mixed omen, that bad luck is ongoing or shortly arriving. Assembling a group to challenge the fish twice-touched by a creator god (once for each colour) however will guide the selection of the warrior or leader to pull the islands through a time of strife.
The challenge is as follows. Representatives from each attending island volunteer to take on the fish. Their true reasons for participating are varied: trained warriors, children nearing adulthood, people looking to impress an onlooker they're sweet on, older fishermen showing off their talent, the local clown putting on a show. Each representative is then painted over the course of the afternoon by friends and family with a glowing set of pigments (not made from the fish fins, I hasten to add). Some designs are beautifully intricate; most are messy, child-sized handprints. Everyone then waits for twilight with great anticipation.
The participants take their turn to wade in and try to catch a fish in the harbour with only a net - the great difficulty being of course that the fish will glow blue and alert the shoal to avoid the intruder. This leaves an ever-moving empty ring of water around the participant to flounder in, struggling to cast the net and maybe just reaching the shoal edge. The larger their genki, the wider that ring and the greater the challenge. The winner is decided by elected older folk, and is usually a combination of how fast a fish was caught and how much paint was left on the challenger's body. About half of participants catch and release a fish, nearly everyone trips, and the spectators have a great time.
Nowadays the omens and winners are not taken seriously beyond passing on fantastical stories, spooking the children or for gaining bragging rights. Usually.
The year before the 28th World Martial Arts Tournament, a shoal made their way into the harbour. The residents of one of many islands answered the call, the group including the young Papayaman and his family. Their island hadn't been doing so well in recent years; the Moon's twice vanishing and reappearing act dampened the tides for a time and their delicate yellow mangrove trees took a hit. The entire food chain around the islands and reef was disrupted and the trees would take decades to recover. As the slow-growing tree bark is prized for its tannin, the island's economy took a brutal hit, too. The residents, previously relatively comfortable, had eaten into their savings and were near the brink. Going to the festival was supposed to be a rare fun day out. As the eldest sibling at nine years old, the boy who would become Papayaman had already resolved to compete in the hope he would be worthy enough to help his family.
The evening went smoothly until the boy took the long walk down towards the water. As he hit the shoreline the fish retreated, that blue ring growing to taunt him, he believed. When in the water the scale of the challenge stretched before him. There was no way he would be able to throw the net that far out, let alone hold onto it to drag a fish back. He became more and more frustrated as his time and paint dwindled and his anger, something he rarely felt, rose… then burst. For a moment the entire bay was full of blue stars, lighting up the dusk. Then the fish bolted, some even jumping onto the shore in a frantic escape attempt, causing pandemonium amongst the younger children.
The boy did not catch a fish himself in the end. But there was no doubt about his potential throughout the archipelago, and he was brought into warrior training as soon as he returned home. He was then selected to attend the tournament on nearby Papaya Island to earn money for his village. Although he didn't win, due to his efforts and subsequent training the island eventually did recover.
A number of years later the shoal returned and the now young man eventually found a way to catch that fish, finally marking (from his own perspective at least) his graduation from training with my father. And as they say, the rest is history.
My first encounter with the fish was a little more begrudging. I had just "moved" to East City for a postdoctoral position into a cosy office with two others funded on the same grant. We got on well and I was hoping for a relatively relaxing couple of years. That was thrown out the window within the first month when the zebrafish aficionados in the labs two floors below decided to branch out, nabbing a number of blue-finned angelfish to get to grips with the bioluminescence. They'd hypothesised the glowing bacteria were responding to the fish's excitement and stress levels (apologies for not correcting you sooner) and were planning on running behavioural studies.
Those fish hated me. Even at that distance, my natural aura was just the right strength to set them off. No one could figured out why the fish were constantly stressed during lab hours, until of course the news reached our office and I put two and two together. My chronically guilty self had the most fun five months suppressing my genki at work until the lab moved from data collection to analysis and the fish returned home. Still, I'm grateful I got to peruse the results from the bacterial DNA sequencing. I relayed the gist to Bulma and she was able to isolate, then modify, the particular colour and ki range the bacteria glowed at. I've contacted the old lab members for co-authorship on this new work. I hope they're not too mad.
The new scouters use these modified bacteria to read power levels and ki signatures. Stacked into mini vials filled with agar, the bacteria respond to ki much like cone cells in the eye respond to light wavelengths. The spectrum of light emitted by the bacteria indicate the intensity of ki hitting the scouter, and the specific pulsing is monitored and decomposed to identify ki signatures - much like instruments can be isolated from a song. With at least two detector packs and accelerometers to track the movement of the wearer, ki signatures can be triangulated and located. A simple pair of glasses (less conspicuous than the original scouters) can be used display results - one lens for a simple overlay or both for a full 3D effect. The isolation isn't fantastic at a distance as the baseline separation between the detectors isn't that great, but in relatively close quarters they work perfectly. Better yet are the systems Mai built into the jet flier and jeep windshield that give a heads-up display of the scene for both the driver and passenger. Due to "popular" demand there is a smartphone app, though sadly the hardware is not included.
All in all we're pretty well-equipped to quantify overall power level. The measure was rendered completely useless by Earth's martial artists, however. As soon as Freeza's army found we could suppress our ki and therefore their scouters were unable to accurately predict any form of maximal potential, the tech was discarded. With the new scouters, getting beyond that one measure to find all the components - genki boosts, yuuki, shouki, the base power, flow suppressions, effort - is entirely possible and we can fully model a person's ki-use and potential. The equations for the model (omitting the calculus) are as follows.
[[ The derivation: Math is hardcore enough - you really don't want to be flicking between two pages for all the equations, so I put the whole derivation on my side account. - Liberator. ]]
[[ groundbreakingsci-stuff dot com/post/170171153987/1point10#derivation ]]
Given some loose assumptions and probabilities assigned to each of these variables - so-called priors that were discussed in section 1-3 - one can monitor a changing power level and narrow down these assumptions using increasing evidence as time passes to give parameter estimates.
What kind of priors? We know some states of particle flow and genki charge are difficult to reach due to the harmonics inherent in the process, and so ki-users are going to avoid particular power levels due to the increase in effort required to hold them. We can assume ki-users will default to a habitual level of genki amplification. Flow rate will never increase above base without particular techniques like transformation. Charge never drops below the default level unless the flow rate is unnaturally high or the ki-user is exhausted. All of these assumptions can be programmed into the model as prior assumptions.
One must be careful with priors to never attribute zero probability to a possibility otherwise that one-in-a-million chance will never appear in the probable results in the updating model. I could assume that no one with a Earthling appearance could have a power-level above 2, for example. If I turn these assumption on my Uncle Krillin the model will give the best answer it can, maybe trying to say that he has a very efficient genki to field conversion rate to compensate for the lack of flexibility in the model. Instead, by allowing some very small, highly unlikely chance for an Earthling to have such a high natural power level, the updated prior will be pulled to this region with every new data point, showing the unlikely to be more and more possible.
When encountering odd enemies one may 'widen the priors' to encompass highly unlikely scenarios like godly-powered Earthlings. 'Flattening the priors' means allowing all possible scenarios. Whilst that sounds like the best idea, flattening leads to a large number of possible solutions when you know some combination of base stats are more likely to occur than others. Choosing priors for any kind of succession analysis is an art form in itself.
There can be a lot of information and possibilities to process when building up a picture of a ki-user, but with a careful set of tasks to perform in a calm environment, someone's base stats at least can be obtained and updated on a semi-regular basis. This narrows down the parameter space before entering battle considerably, reducing the uncertainty when finding the dynamic variables. Some tasks include running up and down ki output from fully suppressed to maximum, or how quickly one can amplify a set amount of genki. For new enemies the scouter has to work overtime, but with every second of new information our intel improves considerably. Even if all the enemies' parameters haven't been constrained, the more varied their attacks and strategy the faster we can build up a picture to start answering key questions such as whether the enemy is holding back their strength.
For our team, Mai is able to feed us updates about each other's status, allowing us to adjust the plan should someone be running low and too proud to admit it, or the enemy be surprisingly resilient. For all the rudimentary single word or single image telepathy usually thrown around the field,hearing an articulate voice in your ear confirming that you're tired or Auntie Bulma yelling to calm down should the panic be setting in can be very disconcerting. I refer to 'us'; I'm never very careful with the tiny earpiece and I blow it within minutes. As much as the data intrigues me I'm far too used to running from my own observations. I'm not the only one to have been on the sharp end of a scolding, the earpieces are notoriously difficult to keep intact. Pan has the longest survival time of forty-five minutes and even that's contested as for the first half an hour she was deliberately suppressing as a feint.
The scouters are useful in the moment and for review, but their most interesting day-to-day function is how the software can track improvement. This of course leads to competition. Endless competition. From conversations I've overheard, the moment one of the kids feels they've improved the scouters are out. There are often disputes because someone is 'using the scouter wrong' and Mai is dragged in to adjudicate or fix what turns out to be perfectly functional hardware… Bulma put her foot down very quickly on getting drawn into these arguments. Even the old guard cannot contain their curiosity and will play with them at parties for old times' sake.
Realistically though, the live-feed technology is more a gimmick for us. We know each other well enough and are sadly so experienced that our gut reactions, whilst not quantifiable, are usually correct. In actuality, the technology as a whole continues to be developed for future use. It would be well-suited for personal status trackers across a large group to be fed back to a control hub, or to help tailor training for new ki-users to maximise their efforts.
"New ki-users". For those who haven't flicked to later chapters that phrase must be torture to read right now. I understand. This section now closes the 'brief' chapter on the theoretical framework behind ki and we will now move onto the practical elements. You can breathe. Speaking of, if you have been working on those centring exercises I'd hope you'd have found your centre by now, have fantastic posture and felt the first hints of the natural flow of genki with your breath. This is preparation that will, in the coming chapter, pay dividends.
Ah. During this chapter I did promise you a particular story. I hadn't forgotten, nor have I left it deliberately late to tease. I wanted to put myself, friends and family in a wider context before tackling it lest there is any misunderstanding after. I also wanted to put the story front and centre in the textbook chapter I believe will be the most read because of the tale's significance - not just to world history or tangentially to ki but to me.
The story's about the Cell Games, and how I came to be that little boy on the hill.