Chapter 833: Chapter 833 - Taming the Fifth Year - Mathematics of Power "The amount of terrain manipulation alone..." another professor trailed off, shaking his head. They were not used to Ren, so very obviously not from the Central Academy... The audience hadn’t seen the Jade Wolverine launch powerful lightning bolts of the type the hydra had used to devastate opponents, but most knew that was in a certain way more a specific skill of the hydra species with added elemental control than a pure elemental control lightning in its most fundamental form. Species-specific abilities versus raw manipulation... different categories entirely. Feats like controlling the entire field in little more than an instant, generating dozens of massive stakes and transforming the terrain so completely that it seemed a beast of superior rank had executed the technique with just elemental control, were too "different in nature". So it was a demonstration of control that exceeded what the supposed simple multiplier of around two(x2) would suggest, something that defied intuitive understanding of how power scaling should function. The calculations weren’t adding up, and the more knowledgeable spectators knew it. Instead of having the (Hy(25×7) + Ma(25×3) + Wo(50×6)) = 550% total buff as the shared multiplier of the (Minimum expected) 175 (Actually true Hydra power) - 210 (Maximum expected by audience) elemental control points like the hydra, the wolverine didn’t seem to have 300 control points multiplied by the same increase. It should be lower, its maximum around double the hydra, very likely less, never more. There was a general understanding of the basics. Everyone knew Ren’s wolverine wasn’t Gold rank while his hydra obviously was... They knew the maximum ceiling of the wolverine’s elemental control was 50 points per level, and they knew Ren’s strange jade-mana hydra had to have around 30 points per level based on what was seen. Only 25 points being the absolute minimum theorized for some species that seemed to be slightly weaker even in the same tier 1. But even with the theorized minimum being the case for Ren’s hydra, there was still too much difference. ♢♢♢♢ Some seconds ago... The math wasn’t working out in their mind like normally. "How is a Silver 3 doing that?" someone whispered. "Maybe his weird cultivation methods affect the base multipliers too?" "That doesn’t make sense. The mana print and the aura size and feeling is weirdly energetic but normal, and even if weirdly colored the core sizes are normal too." "Indeed, after exhaustive investigation and now data sharing with Ex-Yino’s people, even corruption or mutation didn’t change the base multipliers. They are more fundamental than most things..." (Ren’s beasts multipliers. Some did change slightly...) "Then what are we seeing?" Selphira smiled upon hearing some of the murmurs expressing exactly that sentiment of confusion about the magnitude of the wolverine’s power they were witnessing. She thought to herself that normally only students consistently misunderstood power levels... but for professors despite having such clear and mathematically proven studies with numerous tests it was a bit unexpected. Still understandable though.. The increase in strength through multipliers was so simple to see, and yet it was dramatically underestimated time and time again. It was a common mistake that even experienced tamers made when trying to estimate relative capabilities, even with appropriate and very basic mathematics, even more when they lacked sufficient combat experience. Selphira valued deep understanding over superficial knowledge, but she didn’t blame them. That perspective had changed for her only when she was already quite old... Now she appreciated any opportunity to contemplate exactly why people’s intuitions failed so consistently in this particular aspect. She’d taught some students over the decades. This kind of misunderstandings appeared in every generation without fail, no matter how thoroughly they explained the underlying principles. It was as if the human mind simply resisted accepting all but one of the sides of what the mathematics clearly demonstrated. For example, she’d observed while still watching the wolverine maintain vigilant position over the incredible sphere containing the wisp, if you compared 100 points of elemental control and theoretically transformed them into the range of a projected fireball, say, 100 meters maximum distance before the spell structure dispersed, then 200 points of elemental control would give you 200 meters range. It was a direct linear increase that seemed very simple to understand. Double the control resulted in double the range. Simple. Clean. Easy to grasp. And there, most people stopped analyzing, satisfied with a superficial understanding that seemed to capture the essence of the multiplier. It’s double, obviously double as effective. Reasoning that sounded correct until you began considering multiple aspects of how that power actually applied in real combat. But people tended to minimize various aspects when thinking in such simplified terms. 𝐟𝚛𝕖𝚎𝕨𝗲𝐛𝚗𝐨𝐯𝐞𝕝.𝐜𝗼𝗺 A tamer always received their omnibust percentage to all their capabilities when cultivating a rank of their beast appropriately, an increase that varied from 10% to 30% depending on tier. Those percentages seemed small when declared like that, almost trivial in the context of battles where complete rank differences determined outcomes. Just 10%, just 20%. Numbers that felt manageable, comprehensible, safe. But like the magic range example Selphira had been contemplating, now not only the magic didn’t just have double straight-line range but that range applied in all directions when considering "radius" of effect. That was where intuition started to fail people. And that range, if taken forward and backward and in all dimensions with an ability unlocked at higher rank that allowed an "area attack" instead of just a directed projectile, then the tamer could generate a fire explosion in volume that would be 8× larger than the initial area. Not double. Not even quadruple. Eight times. Because you had to consider height multiplied by width and length of the affected space. If each dimension doubled from 100 to 200 meters, then the theoretical total volume affected went from 1,000,000 cubic meters (100 × 100 × 100) to 8,000,000 cubic meters (200 × 200 × 200). It was an 8× increase in total effective area derived from simply doubling the underlying elemental control. Geometry didn’t care about human intuition. The mathematics were absolute and unforgiving. And that was only considering basic geometry of area attacks. It didn’t account for energy density, penetration against defenses, duration of sustained effects, or dozens of other factors that also scaled with improved elemental control in ways that weren’t perfectly linear. Each of those factors multiplied against each other, creating compound effects that far exceeded simple addition. Energy density might increase by 50%, penetration by 30%, duration by 40%, and all those percentages multiplied together to create the final damage that was exponentially higher than the base increase would suggest.