The Kanoka Equation
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- เผยแพร่เมื่อ 21 ก.ย. 2024
- Kanoka disks are a widespread technology within the Matoran Universe, with many different powers and abilities. In this Knowledge Tower investigation, we take a closer look at the Enlarge and Shrink Kanoka and derive brand new equations to predict their effects.
New Bionicle Science investigations every month. What part of Bionicle lore do you want to see investigated next? Give your suggestions in the comments below!
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power level 9 shrink disk sounds like it's either a disk of implosion or disk of miniature black hole
Oh no
Gah, tricking me into doing math by using my childhood nostalgia! Devious!
I did approximate math in my head and got "something under 2 meters, at minimum 1.6m"
that's alright for the accuracy Vakama was looking for in the heat of the battle I think.
Could have used an exponential growth / Decay function to describe the growth rates instead. Not sure exactly how this would have changed the math but it would have been an option.
I'm not sure it would make much sense to use that model. For one, an exponential function always goes to 0, unless you add a minimum value, but the equation would become h(P) = hmin+(h0-hmin)*e^-P, which just looks inelegant.
Plus it would mean that you are gonna have a huge size drop from 1 to 2, and then tiers 5-8 will be practically indistinguishable. That would call into question why have all these tiers. I think the linear model is more appropriate so that each tier makes a difference.
@@Yan_Alkovic
I attempted a different approach, namely a simple power law. The formula I devised is:
h[P] = h0^(1-Abs[P]/8) * c[P]^Abs[P]
where P is the disc's power (negative values refer to shrinking, and positive to enlarging; P = 0 is not getting hit by a disc lmao) and c[P] is hMax^(1/8) for P > 0 and hMin^(1/8) for P < 0. For hMax = 18.29 m and hMin = 0.15 m this works out to be:
c+ = 1.438 m^(1/8) ; c- = 0.790 m^(1/8)
I tried finding a constant factor that would work for both positive and negative values, but couldn't find one that reproduces both given min/max sizes.
All resulting sizes of a Toa getting hit by each power level are then (in meters and feet):
LVL m feet
-9 0.11 0.36
-8 0.15 0.50
-7 0.21 0.70
-6 0.30 0.97
-5 0.41 1.36
-4 0.58 1.90
-3 0.81 2.64
-2 1.12 3.69
-1 1.57 5.15
0 2.19 7.19
1 2.86 9.37
2 3.72 12.21
3 4.85 15.92
4 6.33 20.76
5 8.25 27.07
6 10.76 35.30
7 14.03 46.02
8 18.29 60.00
9 23.84 78.23
I think the size differences between each level are still reasonable enough. The only problem I can see is that the resulting sizes you get for power level 9 are dependant on the original size, e.g. a Toa getting hit by a level 9 enlarge disc would become 23.84 m (see above), but a Tahtorak (~12 m) would become 19.28 m, and similarly for shrinking. This could be resolved by setting the max/min sizes to be the result of getting hit by a lvl 9 disc instead of a lvl 8, in which case you'd have to replace all 8s in my equation with 9s.
It’s amazing how enjoyable stuff like this is when it’s explained clearly.
Could you explore what exactly the webs of the Visorak are composed of?
plot device material~*
but realistically i'd guess something of a spider silk fiberglass type mixture, can't really say why, it just feels right to me
@@prcervi I was thinking some polymer plastic, but the way they release a puff of dust as they are broken looks more life micro fibers that break into very small particles
Agreed entirely.
I go onto youtube to watch a specific video.
I see a bewildered ko-matoran staring at me.
I watch that video instead.
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Jokes aside, this was a great video! Getting into the nitty-gritty of how certain powers and abilities work is always a good time, and everything was very well explained. One thing that could have made it even better would be a more gradual "reveal" of the final equation in the "play along at home" section. Overall tho, that section was very fun, and it did feel great to figure it out for myself and then seeing the correct answer pop up on screen.
Great vid again! Well done
I love that I came for a video on the great discs and also got a lesson in maths notation
Awesome video, especialy the interactive part and the aclaration of the x *
I think there's something wrong with the wiki's shrink disk entry as I clearly recall a matoran having been hit with a level 8 shrink disk and he became so tiny that he was never found again. I found this in one of the novels from the same novel line as Time Trap.
If I had to guess about the theoretical great shrink disk, so as to not break the laws of physics, it would probably shrink the target down to an arbitrarily small size such as 1mm or a more universally small yet functional size like some number of microns (small enough that molecules can still exist, so not quite atomic)
Another fun puzzle for the vakama example would be to have to determine the ideal power level of disc to use to shrink the rahi so it is small enough to handle but not so small it can escape
Perhaps you could examine how much antidermis is in one Makuta... if we go by the tank the piraka used, it looks like a lot, but Teridax's models (and the fact he presumably staffed all of his gas into Matoro to possess him) implies that antidermis is very compressible. Perhaps too conpressible?
Great video.
The problem with writing x(y) is that my programmer brain sees it as a function, that is we are asking x to do something with y. To maybe explain, I could provide a function, multiply(), that multiplies two numbers, multiply(x,y), and that's how I look at the syntax. It's not a huge mental whip to go "wait, no" but I'd much rather see it as x⋅y for the sake of balancing readability with verbosity, while avoiding the x×y problem.
A tangent, yes, but I like going on tangents
Of course, this under the assumption that the minimum and maximum heights are the fixed values for a level 8 disk and not an overflow/underflow error failsafe.
Say for example an enlarge disk multiplied the size of a target by 0.75 times their default height for each level. If you hit something that was 15 m tall with level 6 disk. Suddenly you'd have something that's 67.5 m tall, and that'd be *too* big for the Great Beings' various security measures, so the disk deactivates and stops feeding its "enlarging power" when the target reaches 18.29 m. On the flipside if you used a level 8 disk with that same 0.75 multiplier on something that's only 2 m tall. They'd hid 12 m and then stop growing because the ran out of "enlarging power" before they even hit the upper limit.
I want a video theorizing why each of the Great Disks have the specific disk power they have and how do those powers factor in the Great Disk of Time. Enlargement could factor in enlarging the effect of the Time distortion for example.
remember when league of legends changed their ability cooldown reduction stat into ability haste? (flat percentage reduction vs percentage faster cooling down). That reminds me of this problem, and how you could avoid the negative size result. Remind me to try and solve this and I might do it.
I have additional takes on kanoka (mosly the logic of kanoka combinations in maskmaking) if you are interested in hearing them
Go for it, I'd love to :)
@@theknowledgetower208
I might have figured out the logistics of mask-making through the disk combinations we are provided (admittedly, a small sample size of 13)
any mask made with one disk gets a literal translation of the power, while masks made with multiple causes the disks to become less literal
reconstitute: blanket alteration of other powers
freeze: reduces something involving a select target (am least sure of this one)
weakness: reduce external force
remove poison: relates to the user's body/abilities
enlarge: projection/broadening
shrink: focusing
regenerate: provides extra force or capacity
teleport: relates to distance (namely speed and sight)
example: the matatu is shrink+teleport or the focusing of motion on a selected object or the pakari being remove poison+enlarge+regenerate or the user's strength projected and amplified
true elemental disks can apparently be used for this as well, but we have no examples of this
@@theknowledgetower208another I thought of: mask making has to be a more complex process than just molding the metal given kanohi last seemingly indefinitely (toa Mata masks made at beginning of MU) while kanoka denatured (all depleted between toa metru and toa mata)
There was that one rahi which had the powers of the kanohka discs and enlarged itself so much that it's atoms could no longer keep themselves together.
I wonder if the rahi's powers let it bypass the usual size limit of the disc powers or if when using that disc power to go beyond the size limit causes that effect.
I'd guess the former since if something was already at the size limit it's atoms should still be densely pact enough to keep it together.
Ohhhh! Is he doing it?! The combination formula?!
Oh, no, different kanoka formula. As always, amazing video!
1.63 m, that's just a little shorter than me lol
My question is this: Is the difference in effect from the power levels linear like you've been calculating, or is it exponential?
What is the maximum power of? Tahu and kopaka nuva fire and ice powers so we can figure out what The resistance of those respectful elements, Makuta have after all official sources say they can resist their respective toa tools of the 2003 storyline aren’t those just to channel their powers
😊👍
I got about 1.5m cause I did it in my head. Close enough I say
why's it gotta be linear?
Given there are distinct power levels, it makes sense that each one would have a set effect, otherwise you wouldn't be able to predict what amount of growth or shrinkage the disk would cause, making the levels themselves somewhat moot.
It could've been an exponential scale rather than a linear one, but again this wouldn't really be a practical system. You would get basically no change at all between lower levels like 1 and 3, and the change between levels 7 and 8 would be larger than all the previous changes combined, so again not really a practical system for use by the Matoran.