#math post

[mega-gaymer-party]

[tumblingxelian]

The Missed Potential for a Dignified Bow Out for Yamcha:

I'm not alone in thinking Yamcha was done dirty by the writing of Dragon Ball more and more as time went on.

& while I'd have preferred it if he get to be more relevant in general, if he needed to be removed from the story, I think they had the set up for a very dignified last hurrah and completely whiffed it.

Early in the Cyborg/Android Saga, Gero mistakes Yamcha for Goku which implies Yamcha is at a fighting power comparable to what Gero estimated Goku would be four years after fighting Vegeta.

I crunched some numbers on this that any one can read below, but imagine if Yamcha had that kind of power just on its own, or he had learned the Kaio-Ken and he actually got to put up a fight?

I imagine the fight would basically go:

Yamcha finds the Cyborgs victims and is saddened he was too late before realizing "They were only her a second ago, in fact this seems like the perfect set up for an- Ambush!"

He dodges 19's dive-kick but has to use Kaio-Ken to avoid the follow up strike, but he guesses where his second attacker will be coming from and uses times two to take the brunt.

Realizing that was still too heavy of a blow to take more than once he lets himself go flat to avoid Gero's charge and as the man stops above him, Yamcha hits times 3 and sends Gero flying into the air.

19 comes in for another attack forces Yamcha to use times 4 to counter and he thinks he's figured these guys out.

They are scavengers, ambushers, strong enough to take people out before they know who or what they are fighting.

They are in essence not martial artists.

After all he didn't hear how the others died or that they could take on Trunks, just that Trunks hadn't been able to kill them.

At times four he's able to more than match Gero, but seeing 19 coming back in, Yamcha launches himself back to gain some distance and loads up his newest technique, the Kaio-Hama-Ha.

Basically a super Kame-Hama Ha, that turns all the power of his times 4 Kaio-Ken + a little extra into a times 5 style attack and fires.

Then Gero absorbs the attack and Yamcha has a moment to think, "Oh that's how they got us" before Gero's hand is through his chest & the man's mocking him:

"Impressive Son Goku, even stronger than I had anticipated but your might was no match for my genius!" Yamcha starts smirking, "Me… Goku? Hah… You got… No idea… What's coming…"

Cue the others arriving & being furious.

After that things basically follow canon, save that rather than being afraid, Yamcha initially just dismissed the Cyborgs as a threat.

He has no interest in attending a fight he thinks will be a stomp fest & only changes his mind upon wondering if the Cyborgs absorbed energy leads to a permanent stat boost over a temporary one.

My extensive calculations can be seen below:

Realistically getting a proper scale for the characters growth is hard, but Yamcha went from 177 to about 1480 in a year without ten times gravity, and with four years of training after that was considered to be at the same level Gero expected Goku to be at after four years of training post King Kai.

Which logically is super impressive, too bad it didn't amount to anything 😦

Anyway, in one year, Yamcha's Ki multiplied by about eight, even just assuming that continues we have:

1 Year - 177 times 8 equals 1480 2 Year - 177 times 16 equals 2,832 3 Years - 177 times 24 equals 4,248 4 Years - 177 times 32 equals 5,664

However, this doesn't account for the growth stacking, which looks more like this:

1 Year - 177 times 8 equals 1480 2 Year - 1480 times 8 equals 11,840 3 Years - 11,840 times 8 equals 94,720 4 Years - 94,720times 8 equals 757,760

Which is very impressive, but then we have to factor in how Goku's gravity training expedited his growth & add it to our calculations.

Goku had about six months training in ten times gravity and went from about 416, to 8000, which means his Ki multiplied by 19.

This is a useful reference because of Gero's aforementioned assumption in mistaking Yamcha for Goku, so we can assume the two have at least semi similar growth levels. Logically Yamcha's would actually be better than Goku's own minus transformatons.

However, Gero wouldn't know Goku spent half a year just running, or how much time was spent on the Spirit Bomb or Kaio-Ken trainign. So his projections are kind of off, but that's neither here nor there.

If we follow the 19 principle then we have:

1 Year in the time chamber is - 177 times 19 equals 3,363

But technically Yamcha would also have spent a year training before or after than to its more like:

1 Year training + the time chamber is - 177 times 27 equals 4,779

& if the defends of Earth wanted to be double super safety sure they'd be ready they could go for a second spin, leading to:

1 Year training + two years time Chamber is - 177 times 35 equals 6,195

However this again doesn't strictly factor in the benefits of gravitational training or the way training tends to stack, which is much harder to quantify. Nor does it tell us how Yamcha got to Goku's presumed level.

Though if we again draw a line between Gero mistaking Yamcha for Goku & assume they have similar base level growth potential then gravity train in more than doubles the results of your efforts, IE:

1 year = times 8 half a year + gravity = times 19 (IE two eights plus 3)

But we can't ignore the benefits of a mentor, or discount the difficulties learning the Kaio-Ken and Spirit Bomb and how they might have slowed Goku's progression in terms of raw power by splitting his focus.

If we try and even things out based on that, then I'd say that: a full year + gravity would likely = times 24 IE,

1 Year Time Chamber is 177 X 24 = 4,248

If we factor in the year spent training before/after then it goes up to 32 assuming a consistent growth level and so Yamcha's Ki upon the Sayian invasion would potentially be around:

1 Year Training + 1 Year Time Chamber = 5,664

Or

1 Year Training + 2 Year Time Chamber = 7,080

As said though this doesn't really account for how growth tends to build up as characters get stronger, presumably one could argue it'd be more like:

1 Year of Training - 177 X 8 = 1470. 1 year training + Time Chamber - 1470 X 24 = 35,280 1 year training + Years Time Chamber - 38.280 X 24 = 846,720.

Though one could argue for diminish returned as time went on, or follow the initial training outline I provided, or even the two out into a medium gradient leading to:

846,720 divided by 7,080 = 119,593

Or anything really, this is all speculation, but it is fun and now that I have shown my work, let us discuss how strong Yamcha could get.

If we follow Gero's presumption about Goku's yearly growth and account for growth stacking as times goes on then we get this:

8000 × 9.5 = 76,000 (Year 1) 76,000 × 9.5 = 722,000 (Year 2) 722,000 X 9.5 = 6,859,000 (Year 3) 6,859,000 X 9.5 = 65,160,500 (Year 4)

Which is a VERY respectable fighting power and would put Yamcha as superior to final form Frieza but not 100% Frieza, which would give good cause to him feeling it was worth showing up to the fight, even if he figured he'd not be the front liner.

Gero would also have likely scaled his & 19's power for the Kaio-Ken and assume he figured it couldn't go substantially higher than times 3, he and 19 were likely around: 260,642,000

IE, 65,160,500 X 4 = 260,642,000

Which would be substantially stronger than Final Form 100% Frieza whose max was 120,000,000

This is also being rather conservative with Gero's estimates given how bloated canon powers became & also doesn't convey how absurd Yamcha's growth rate must be to have reached that. I estimate his exponential growth rate from this as being: 14.6-ish

1470 x 14.6 = 21,462 21,462 × 14.6 = 313,345.2 313,345.2 × 14.6 = 4,574,839.92 4,574,839.92 × 14.6 = 66 792 662.8

Which as established, is an incredibly respectable growth rate!

Added notes & other musings:

& let's keep in mind Yamcha's starting point for power was lower than Goku's, IE, based on Gero's calcs, Goku was gonna go from 4000, to 65,160,500 in four years.

But Yamcha went from 1470 to 65,160,500 in four years; which puts his yearly growth rate as being much higher and that is without gravity training, using the original 65,160,500, & then the Kaio-Ken:

65,160,500 + Kaio-Ken plus 16290125 = 81 450 625 65,160,500 + Kaio-Ken times 2 = 130,321,000 65,160,500 + Kaio-Ken times 3 = 195,481,500 65,160,500 + Kaio-Ken times 4 = 260,642,000 65,160,500 + Kaio-Ken times 5 = 325,802,500 65,160,500 + Kaio-Ken times 6 = 390,963,000

Basically, strong enough to definitely pose a threat to 19 and 20, and keep pace with the others is the point.

Damn you King Kai why did you not teach them!?!?

Aside but this was all inspired by seeing a video:

& using my calculations if we go by what the various fights could accomplish based on their 1 Year training + the time chamber is:

Chi-Chi (Estimated) 100 times 27 = 2,700 Chaozu (Estimated) 120 times 27 = 3,240 Yajirobe (Estimated) at 125 times 27 = 3,375 Kami (Shounen Jump Magazine) 220 times 5,940 & Roshi - 139 times 27 = 3,753 Yamcha -177 times 27 = 4,779 Krillin - 206 times 27 = 5,562 Tenshinahn - 250 times 27 = 6,750

Basically four of them could school Nappa solo and three of them could put up a damn good fight.

If I went with Chi-Chi's fighting power in the 23 Budokai she'd be bumped up into the "Give Nappa a good fight" category with a fighting power at 3,510, but I assume that she let her skills and training atrophy somewhat & would need time to make them back.

I didn't bother to calculate Piccolo or Gohan's cos Piccolo would not have been allowed on the Lookout at this point in time and likely would have refused to go on principle & I doubt 4 year old Gohan could handle the time chamber given teen Goku almost died in there, but if they sensed the others….

Piccolo - 408 times 27 = 11,016 Gohan (Estimated) 3,310.875

Determining Gohan's Ki is really hard cos he has bonkers growth going from like 5 to 981 in a year, so I just divided that by 8 (122) and then multiplied it by 27 like the others. Still not sure they'd be let in, or be able to use it effectively however, but good to know.

Sad part is, Vegeta could still rock their shit at this level 😢 But at least they could treat Nappa like a volleyball lol.

Final thing!

Assuming the original Kikoho multiplies the users power by let's say 4, (as that would allow the very injured 1880 Tenshinhan likely working at 915 to lightly wound Nappa and shock Vegeta)

Then the time chamber Tenshinhan could unleash a Kikoho at: 27,000

If injured like canon, he'd be able to unleash a Kikoho at: 13,500

This is of course speculative, the characters all likely have different growth rates, and there's no exact metric to guess how much Tenshinhan's Ki went down or up by, but this is pretty handy as a general guideline I think.

I tis also funny to think about how many storylines could have been resolved with Tenshinhan coming out swinging with the Kiko-ho.

"Oh fuck a villains here!"

"KIKO-HO!"

"Hooray the villains dead!"

[harloqui]

The Mathematics of Shifting

I went to the doctor the other day, for the typical autoimmune issues I've mentioned on this blog. While I was talking to one of the doctors about my issues, they offhandedly confirmed my feelings with a "we noticed your eosinophils were quite high." I'd always suspected that, but I hadn't had any tests to confirm, and although it was likely I just wanted to confirm medically before I started claiming something... Although googling it it's almost a fact that if you have autoimmune issues you'll have high eosinophils, so I guess I could have claimed it anyway.

But as I was leaving the doctor's office, it occured to me that maybe this is why at least some shifters are the way they are. A symptom of my autoimmune condition is that I don't get cold; when it's flaring I could be out in sixty or even fifty degree weather and still be hot. A lot of shifters also describe this same symptom, and while it's not always tied to being a shifter (many conditions are tied to high eosinophils) enough shifters have mentioned it that I think there may be something there. Eosinophils are white blood cells that are responsible for a bunch of functions in the body, including wound healing and chemical signaling.

And then later on it occured to me that with this information, maybe shifting is less like breaking a bone and more like self-cannibalism? Eosinophils in eosinophilic diseases attack the human body and its organs, but it doesn't outright cause damage the way a broken bone or serious physical injury might. I've seen therians try to disprove shifting by using calculations for injuries as a gotcha - the logic being that if you were to injure yourself a thousand times over you'd die from shock or an energy deficit. But if shifting isn't a critical injury, and your calorie source is yourself, then you can bypass those restrictions.

So I decided to do some calculations. I found an academic journal which goes into the calories of an average adult male organ by organ. Total calories of an adult male is around 143,771.33cal, and their weight is around 65.99kg. Now, googling how long it takes to heal an injury (I know I said shifting isn't like healing an injury but unfortunately there isn't any data on how long it takes to heal from eosinophilic diseases and the calories burned from them) it would seem as if it takes 30cal per kilogram of weight. 30cal × 65.99kg = 1,979.7cal/kg. (I'm going to treat the entire body as if it is a giant "wound" instead of tiny unspecified cuts and injuries.) Different sources say that the human body is composed of 40% skeletal muscle, 18-24% fat, and 14% bone (for men). I'm assuming the rest is things like cartilage, keratin (hair, nails), smooth muscle, organs and other bodily byproducts that don't fit into this.

So assuming our 65.99kg man has 40% skeletal muscle, 18% fat, 14% bone, and 28% everything else, we can take the percentages of 1,979.7cal/kg, since I'm assuming that the 30cals would be distributed evenly around the body, or to the parts that need it the most. 40/100 × 1,979.7cal/kg = 791.88cal/kg, 18/100 × 1,979cal/kg = 356.346cal/kg, 14/100 × 1,979cal/kg = 277.158cal/kg and 28/100 × 1,979cal/kg = 554.316cal/kg. We'll really only need skeletal muscle and bone, since as far as I know fat isn't modified (it may be redistributed on the body or used, but it itself doesn't appear to be touched by the shifting in the same way), and hair, nails, etc. simply don't have a rate attached since they tend to be negligible. Organs may not be severely affected as well (if they were, shifting would kill people immediately) and I'd have to assume they're largely untouched.

(Note that for me and other shifters I've talked to, bones do not break, they moreso flow? into an area. This is why I'm not calculating for the breaks of a bone or anything like that, there's nothing to break.)

Muscle damage is graded on a severity of 1 to 3, with grade 3 injuries taking months to heal and grade 1 a few weeks. I chose a grade 2 injury to represent shifting since it would most likely mimic a severe injury, but not to the point where you couldn't use the muscle or function with it. Grade 2 injuries take at most 16 weeks to heal, so 791.88cal/kg of muscle × 7 days = 5,543.16cal/kg per week so then 5,543cal/kg × 16 weeks = 88,690.56cal/kg. Bone takes 12 weeks to heal at the latest, so 277.158cal/kg × 7 days = 1,940.106cal/kg and 1,940.106cal/kg × 12 weeks = 23,281.272cal/kg.

88,690.56cal/kg skeletal muscle + 23,281.272cal/kg bone + 554.316cal/kg everything else + 356.346cal/kg fat = 112,882.494cal/kg total to heal bone and muscle, or reform a shifter's body.

Calories of adult male (143,771.33cal) - calories of "shifted" male (112,882.494cal/kg) = 30,888.836cal/kg left over, meaning that if you were to shift using your body as energy, you'd have 30,888.836cal/kg to spare. Now, if we were talking about calories you need to ingest needing 112,882 of them would be an unreasonable amount, unless you healed over a period of weeks or days. However, since the body is our energy source, it will be the source of calories used while shifted, and we'll assume the process is sped up.

The human body is imperfect at digesting calories - off the top of my head I've heard 65% of what we eat is actually used as energy, with the rest being burned while processing those calories or simply lost while processing, but more recent estimates have it at 95%. I know reusing parts of the body isn't exactly like digesting external matter through your stomach, but assuming it's similar enough, 95/100 × 112,882.494cal/kg = 107,238.369cal/kg so 112,882.494cal/kg − 107,238.369cal/kg = 5,644.1247cal/kg lost. So transforming would (assuming you were efficient at digesting matter) cause you to lose around 5,000 calories, which actually lines up with the claims I've heard from other shifters, who say they get really hungry after shifting but not overly so to where they'd need medical assistance or the like. 5,000 is around the amount athletes eat, so it's not an unreasonable amount to build back either.

Going a little bit further... If that's how many calories athletes burn, the body temperature of athletes in action should be applicable to shifting, right? A body temperature above 40°C is dangerous for long periods of time, because it denatures proteins and destroys the body. But it would seem athletes regularly go past that without necessarily suffering ill effects, indicating that at least on some level the body can handle high temperatures short term. (If you're disabled however, the risks increase due to physiological differences, so this doesn't apply across the board.)

So shifting (if my math is right and all this is applicable to the real world) should typically lead to a calorie deficit of around 5,000 calories, a body temperature above 40°C (but not too far) and exhaustion similar to that of experienced athletes. It does not destroy the body, because everything is in accepted ranges and the body is being "digested" and used as a source of food.

Feel free to check my work. A lot of the math surrounding this stuff is hard to do because a lot of the values necessary to calculate it have never been studied. I was trying to find the amount of calories hair growth would take even for an average adult human, but hair is considered negligible and the people I've come across tend to use sheep's wool as a replacement, which might distort the calculations a bit. If you have any values for me to work with though, you're more than welcome to send them to me! I'll see how I can work them into my calculations, if possible.

[art-of-mathematics]

I am asking in the crowd:

Do you have recommendations for reading and (re-)sources about category theory and graph theory?

I want to learn about it, but do not know where to start.

[punedrr]

Physics is just applied math, and chemistry is just applied physics, and biology is just applied chemistry. Math is the quantum particle of subjects. Everything is so cool and I love everyone

[here-by-chance]

im obsessed

[lolipoptheclown]

If The Character won't let me stop thinking about them during class then they better make themselves useful and help me with my fucking math

[nolinno-art]

I've developed mathematics for a non-human mind, for my comic "The book written by tiny paws"

Sapient distant descendants of rats, known as packers, living on Earth millions of years after the extinction of humans, began to develop mathematics using cognitive mechanisms never intended for such tasks. Due to an evolutionary quirk, multiplication came more naturally to them than addition, and their mathematics reflects this.

Packers write numbers as shapes, with each number having a corresponding number of corners.

And they write large numbers as nested shapes. The number inside is multiplied by the number outside.

Examples of some numbers:

Packers haven't invented 0 yet. They haven't even invented 1! In fact, they don’t need the concept of "one" much in their system. There's no need to say "I ate one fish" when they can simply say "I ate fish".

Packers can't yet write large prime numbers, like 101 or 10,501, because they would have to draw a huge shape to represent them! Even writing 17 or 19 would be quite difficult if they only used convex shapes.

So packers use non-convex shapes too!

Many years later, some packer noticed that large prime numbers look suspiciously symmetric.

So this packer improved the notation system and made it clearer.

Later, another packer simplified this system even more, deciding that there was no point in writing the same shapes twice.

This packer was the first in their culture to declare that "a dot isolated from a number" should also be considered a number. The packer called this dot "the wonderful number that's less than two".

Many years later, another packer made an important innovation: the "dot isolation" could be repeated multiple times as long as the result remained odd. When the result became even, it could undergo a "two isolation" (division by two). The final result will be a series of dots and twos.

This invention led to the creation of a binary system based on one and two, which had a significant impact on the technological advancement of packers.

The comic "the book written by tiny paws" talks about all of this in more detail. There will be mistakes, debates, the invention of rational, irrational, multivariate numbers, and some other stuff. Some stuff will be very much like human math, and some will be different. After all, math is still math, only the point of view has changed.

[lemongogo]

life of regret

[moshaeu]

umm whos gonna tell him

[anpilled]

cheers :3

[multimemes]

[morganbritton132]

The cameras at the VMAs: *cut to Eddie Munson’s husband when he’s on stage to present an award*

Steve’s students, past and present, watching at home: Was that my math teacher??

[micamone]

hewwo

[echo-has-queries]

Writing multiple fics about the same characters at the same time is so wild. Like: What are you in the mood for today, blorbo? Do you want to experience the harrowing ordeal of growing up in an impoverished neighborhood that has increasing amounts of monstrous murder happening? Or do you wanna go to math camp?

[gayarograce]