Welcome to my Tavern. I had to close shop for a bit due to grad school and all, but I’m almost done. Today, I’m going to dive into something other than fantasy… well, kind of fantasy but not Dungeons and Dragons.

I. Introduction

The question “Who wins in a fight: Superman or Goku?” is an old one with many different takes. This is not one of those. To be honest, I’m tired of asking it and searching for an answer because it’s absolutely irrelevant. Sure, it may be fun to wonder who would win when you are bored with nothing else to do, but it’s really not an important question even in the nerd space. Aside from that, the characters are impossible to compare; they were created in different regions of the world with different rules. They can’t be compared.

That doesn’t stop people however. I recently saw this picture floating around on social media:

I favor Goku a lot more than Superman so it’s strange that this picture got me irritated. I think what really hit me was the final line: “Goku wins. Science proves it.” You can’t use *science* to prove that one of these two characters would win over the other. Not only that, but you shouldn’t credit science for your conclusion when your own scientific reasoning is flawed. It gives a bad name to actual science. This essay is not to settle the debate on who would win, but rather why this picture is absurd.

II. “Superman peaks his lift around 100 tons”

The first topic to be discussed is the first claim: Superman peaks his lift around 100 tons. However, in order to contest this fact we must first debunk a different claim that, if true, would lean the argument in Superman’s favor considerably. That claim is that Superman can lift infinity pounds. This train of thought reached prominence when Screw Attack made a final verdict in their YouTube Death Battle series where Goku and Superman were the subject matter (it should be noted that they concluded that Superman would win). I will paraphrase the claim as summed up by gamespot.com:

Final Crisis Superman Beyond 1& 2

Superman and Shazam travel to the Library of Limbo to read a book housed in a sphere which details all the histories in the DCU, at a time when there were 52 multiverses. They read the book in order to learn how to escape Limbo.

Superman states “A book with an infinite number of pages occupying the same space”,” this contains every book possible!”.

Superman and Shazam attempt to take the book to a spaceship

Superman “The Ultima Thule’s onboard computer has infinite memory capacity”

Shazam “Which means it could read every page of the book at once.”.

When attempting to move the book pages start falling out and they drop it. The book reads itself.

Every book possible is a finite number of books, not an infinite number of books. There is no context to the weight. On our own Earth (Earth 1 in the DCU) we are moving away from printed content to digital content. It’s safe to assume that is the case in other (theoretical) multiverses.

The conclusion that can be drawn from this text is that Superman did not lift an infinite weight, but rather a weight that seemed relatively infinity by our standards. Using averages, we can come up with a reasonable estimation of this weight. Gamespot.com continues with this thought using other sources, but I will instead refer to the sources themselves.

Software Engineer Leonid Taycher published an article in 2010 on the actual number of the books in the world as calculated by Google’s advanced algorithms. As of the date of publication, Google Books estimates that 129,864,880 books have been published. This number increases daily, so an accurate representation would require meticulous research for a number that would quickly be outdated. This does not pertain to the subject matter at hand, so 129,864,880 will be used as the total number of books in the world with a few caveats: 1.) The number of books is always increasing. 2.) The sphere in the Library of Limbo would have data on every book ever written, but to make conjectures on this actual number would increase the probability of error. 3.) All the books ever published on earth does not mean all the books ever published in our multiverse, let alone 52 of them in DC.

Even if we used the heaviest hardback book weights for our calculation, this number will be outrageously conservative. I don’t see an issue then using the heaviest hardback book weight in this calculation.

Calculating the weight of this object using averages would require the following equation:

# of books * average book weight (heaviest hardback book) * number of DC multiverses

129,864,880 * 1 lb 15 oz (1.9375 lbs or 0.8788 ks) * 52 =1.308 x 10 ^ 10 lbs = 6.54×10 ^ 6 U.S. tons, 5.84×10 ^6 Imperial tons, or 5.94 x 10 ^ 9 kg

So in conclusion, while Superman may not be able to lift infinity, he can lift a considerable amount more than the picture would lead you to believe even if you consider that the weight was shared by other heroes.

III. Power levels: A linear, exponential, or logarithmic relationship?

The picture utilizes power levels as the basis of their calculations and reasoning on Goku’s sure victory. It is implied that if Goku’s numbers exceeds that of Superman in the Vegeta saga, then of course Superman couldn’t stand a chance against Goku at later points in the series or in Dragon Ball Super. It fails to mention that power levels were only used in the beginning of Dragon Ball Z, up to the Frieza Saga, and only once after that when we were introduced to Trunks. It is sometimes referred to by other characters: King Kai will commonly warn Goku that the “power level” of his enemies will outweigh his own, but I wonder if this is a mistranslation from the original Japanese (ki vs. power vs energy vs power level and their apparent interchangeability). This leaves any quantification of any DBZ character beyond that point up to mere conjecture and resulted in obscenely high numbers.

In regards to why Scouters existed in the first place, and therefore power levels, Akira Toriyama says:

My number-one goal in coming up with it was because, if an opponent’s strength could be seen as a number, it would be very easy for the readers to understand when I put it in the comic. However, I could foresee that it’d be an inconvenience for me down the line, because if you knew a concrete number, then you could tell who would win or lose, so with regards to Goku & co., I decided that [their power] would change due to “Ki” and couldn’t be adequately measured.

In addition, it’s a very convenient item to create peril, since with enemies equipped with them, their location could become known, and they could be reported. http://www.kanzenshuu.com/translations/saikyo-jump-tell-us-toriyama-sensei-qa/

Scouters were a way to introduce tension into the show when it picked up from Dragon Ball. Though more than a match for both Goku and Piccilo, Radditz was simply a plot device to hint at bigger challenges to come. Power levels allowed early fans to have an idea on the coming challenges.

As Mr. Toriyama predicted, the number thing soon became irrelevant when the heroes learned how to hide their powers by controlling how much ki they could channel to fuel their abilities. It was the Ginyu Force’s downfall and also Frieza’s upon meeting Trunks. One could imply that Toriyama was telling his readers and viewers “This system doesn’t work, so stop trying to make sense of it.” Yet this is disregarded in the picture.

The flaw with using power levels as a metric is that at its core it makes no sense. In order to use it as a measurement between the strength of Superman and Goku, it must be understood and quantified.

…but let’s try anyway.

Using the Dragon Ball Z Wiki, I compiled a list of all instances of recorded power levels. There was nothing to plot against, so the graph is simply Power Levels vs. Each instance of recording and shows the growth of the numbers. Here is the undoctored data in ascending order:

Each tick mark is an instance when an actual number was recorded. We can scale it to show all numbers below 1,000,000 if it gives us a better perspective of the numbers. Here it is below:

Many suggest that power levels follow an exponential trend to explain why battles earlier in the series seem greater in difficulty for the heroes even though numerically the gap was considerable smaller (Goku and Radditz with approximately 1000 difference in power levels vs pre-super saiyan Goku and Frieza with a difference in the 100,000s). Though as I look at the data, I decided to scale it logarithmically and got the following results:

(In case you were wondering what that super small power level is, it’s the turtle clocked at 0.001).

Ok so what does all of this imply? What’s the point? What do we do with this data? In short, nothing. Power levels are a joke ad shouldn’t be used for comparisons.

Long answer: they only seem to make sense when you look at them logarithmically. It shows that even though two opponents have a difference in power level in the 10,0000’s, the fight can be considered “close”, even if you went into Dragon Ball Super’s god forms and ultra-instinct forms. You must be orders of magnitude greater than your opponent to make a difference in battle. But honestly, would the author of a manga and anime come up with a consistent model of power scaling using a logarithmic approach? Probably not. How many people think in terms of logarithmic scales anyway?

IV. The physics of a lift vs. a strike

The picture creates a correlation between power levels and lifting capacities while implying that those two factors equate battle prowess. This is a troubled approach as it doesn’t explain how “strength” is defined. Here are some initial questions one might have:

Is lifting or striking more influential in battle? What’s the difference? How do you mathematically model this? What are the influential factors we should look at? But of course, answering those questions would make too much damn sense and we need to instead rely on the abstractness of *power levels* from DBZ.

We can make an attempt by defining the differences between lifting and (what I consider more important in a fight) striking. First, we need to determine what it means to lift something. There are multiple equations that model this, but the one we will use is kinetic energy. The equation is:

*K.E. = 0.5 * m * v2*, Kinetic energy is equal to half of mass multiplied by velocity squared.

Kinetic energy is a form of a concept called work. Work can be thought of in a different way: applying force to an object to move it a distance. When you lift weights at any speed, the object you are applying force to is the weights. When you punch or kick something, the object you are applying force to is your fist or foot (at least until the moment of impact). The picture fails to make this distinction and confuses lifting strength with combat prowess. In reality, lifting capacity is not a real measure of fighting capability.

Since we are on the topic of striking, punching, and kicking, let’s break it down further. Look at the equation again while remembering that “mass” refers to the person that is punching or kicking. Something you might notice is that the two factors that influence how hard someone can hit an opponent is mass and velocity (speed).

So… who is faster? Who weighs more?

About weight: One can say that Superman is extremely dense because bullets bounce off him. The problem with this is that high density requires Superman to be extremely heavy. This doesn’t appear to be the case because normal humans have been able to lift an unconscious Superman. If you consider Superman Returns as cannon, he’s even on a hospital bed without breaking it. The same goes for Goku who stands on Bulma and Vegeta’s bed without breaking it after accidentally teleporting there. So if Superman and Goku are relatively similar in weight, it can be concluded that the deciding factor of who punches harder would be speed.

Speed is kind of unanswered for Goku. We don’t really have a measurement of how fast he can be. Instant transmission is teleportation and can’t effectively be converted to a measurable quantity. When he travels Earth or Namek during normal flight, we aren’t sure about the distance he is travelling or the rate that he is covering that distance. During the Cell games, nobody present was able to see Goku and Cell fight with the exception of Gohan. Blurring due to object speeds is extremely difficult to figure out due to a variety of factors like distance and size. An example would be how a jet plane can travel faster than a bullet yet the bullet is practically invisible to our eyes. Even with the camera equipment most likely operating at 24 frames per second, the distance between the two combatants and the equipment is an unknown factor.

Superman however DOES have a recorded speed. In Flash v2 #220. Here is the comic frame:

Flash states that Superman is moving at over 2000 miles/sec, which is also over 120,000 miles/minute, and also 7,200,000 mph. That’s Mach 9350. Not only that, but this is within Earth’s atmosphere. He can break light speed in the vacuum of outer space.

That’s a really hard punch.

To be honest we still don’t have enough information about who is faster between Goku and Superman, but these numbers are a tall order for our beloved Goku. I’m leaning toward Superman being faster, implying that he can probably punch harder too. So in short, the power level comparison picture is lame. Don’t believe it. And certainly don’t credit science for it.

There. I finally got that off my chest.

## GrimlyFiendish