The Validity of Infinite Speed Touhou Project

Hey everyone, I know this isn’t the Kasen Ibaraki vs Fleetway Sonic blog I promised first, but this ended up being something I realized I’d need to cover before that blog. Infinite Speed Touhou seems to be something that’s met with varying reception, and is definitely something that’s not quite understood by many for a variety of reasons, varying from Touhou’s method of storytelling, misremembering how the events occurred, some genuine fair concerns that might need an explanation, as well as a handful of people who just outright think the evidence for infinite speed is invalid or misinterpreted. This blog is meant to showcase that’s not the fact.

To preface this, I was someone who was similarly unsure in infinite speed when getting into Touhou from a Versus sense as well, so I did a lot of research into it. Poured over every angle I could, trying to find ways to potentially punch a hole in the concept and prove that it wasn’t supported within the series. But overtime, I came to realize that I wasn’t able to find anything to dispute it, and began to find myself agreeing with it. There wasn’t just a single instance, no, there are 3 total well known instances of infinite speed within Touhou , and I couldn’t find anything to dispute any of them (there's plenty more as well). So I would begin to become a supporter for the concept of infinite speed 2hu, and would begin to push to get it appended to Touhou VSBW profiles, and would from there continue to defend it in attempted downgrade threads. I would even go on to include it in my blogs, although typically as more supporting evidence than anything due to its currently contentious nature.

Eventually, I realized Infinite speed is something that people will inherently have troubles understanding, and after several incidents with people either trying to downgrade the verse on VSBW or just flat out not understanding the concepts of infinite speed, I realized I’d have to make some kind of blog to make it as bulletproof and solid as possible, and to avoid unnecessary repeated conversations, and so, this blog came to be.

This blog compiles all of the most common debunks and issues brought against Infinite Speed Touhou, and systematically breaks down every single one, showcasing why they’re either invalid, fallacious, or born from misunderstanding. I implore you to read this blog in full if you have any concerns about how Touhou’s infinite speed works or if you have a hard time believing it yourself, as it’s likely this blog will cover one of your potential issues.

One more thing before starting, this blog was created in conjunction with @sukuviolence, aka Fujiwara, who was a massive help in creating this blog, created many of the counter-arguments and frankly some of these segments are taken right from her own words.

Now that we’ve gotten through most of the important preliminary info, there’s a couple things to go over before discussing Touhou’s specific feats and the counter arguments against them. It’ll be best to run over infinite speed as a concept and a major quibble relating to feats of infinite speed in fiction in order to elaborate for the unfamiliar, as well as refresh ourselves.

What is Infinite Speed?:

Infinite Speed, as described by VSBW, is the ability to travel any finite distance in zero time, or to move across an infinite distance in a finite amount of time. Teleportation does not count, as teleportation involves transporting from one location to another, without occupying the space in-between, meanwhile Infinite Speed would involve occupying that space while you travel from point a to point b.

To elaborate fully, in VSBW’s words: “Infinite speed characters are so fast, they move faster than time can flow at any period. They perceive every finite speed character as completely frozen and it takes 0 time to react to any finite speed object or travel a finite speed distance. They can also perform an infinite number of actions or travel an infinite distance within a finite amount of time. An infinite speed character's perception of time only flows when they allow it to flow.”

Now that we’ve covered what Infinite speed is and some of the qualifications for being an infinite speed feat, it’s now time to cover an integral part of one of the qualifications for infinite speed, crossing an infinite distance in a finite amount of time, as all of Touhou’s infinite speed feats fall within this qualification:

The “Edge” of Infinity?:

It is commonly believed that crossing an infinitely sized location in such a manner that one reaches its 'end' cannot be measured as a speed feat, as it inherently contradicts the very idea of infinity; After all, infinity is defined by the lack of an edge. The issue here resides in both fiction itself and VSBW's standards. The first point is that fiction need not abide by the rules of our own reality, as 'the edge of infinity' is a common concept in fiction; A notable example is the Source Wall in DC, which is a wall which resides at the edge of an infinite multiverse. Essentially, at a certain point we must let the internal logic of a fictional verse override the logic of our own universe, which in this case, includes infinite spaces possessing edges. The second point relies on our standards for infinite speed. One of several methods for achieving this speed includes crossing an infinite distance in finite time. However, what most people don't realize is that this requires a paradoxical edge of infinity to be present. Imagine the distance in a speed calculation as a straight line, from point A to point B. A would be the point where one starts moving, and B is the point where one stops moving. In the case of infinite speed, A and B would be an infinite distance away from one another. This presents a paradox where there are two points an infinite distance away from one another, yet each of those points individually could be seen as the "end" of infinity. As VSBW currently accepts speed feats of this nature, it stands to reason that infinite spaces which contain an "edge" should be acceptable as well, especially since a number of feats reliant on this logic are already accepted for other verses.

Now that we’ve discussed infinite speed and the notable aspects of it, we can begin to cover Touhou’s infinite feats, and debunk the arguments that are brought against them:

Kaguya’s Infinite Corridor:

During the events of Imperishable Night, upon reaching Eientei, the protagonists are faced with a choice between two corridors. The first leads them directly to the cause of the incident, Kaguya Houraisan, leading to what will from now on be referred to as stage 6B. The second leads down an infinite corridor, leading to Kaguya's accomplice, Eirin Yagokoro, which will be referred to as stage 6A. The game always forces players to play 6A upon their first playthrough, which makes it a necessary part of the narrative. 

Isn't it Impossible for the Corridor to be Infinite because it's in Gensokyo?

This makes sense on a surface level, as Gensokyo is a small, island-sized space. It holding an infinite space would be contradictory, which is why it's important that the corridor technically isn't inside Gensokyo. This is because of one simple factor: the corridor goes upwards. This can be visibly seen when the protagonists fly through the corridor, reaching its end, and then find themselves in the sky/space. Something of note when it comes to going up in Touhou, is that eventually you’ll find yourself nearing the moon. What you’ll find after that is that the Lunar Capitol resides on the moon. What you'll find before that though, is that between the Earth/Gensokyo and the Lunar Capitol is Heaven! Heaven being an infinitely sized cosmological structure in of itself. So no, going upwards wouldn’t result in them eventually hitting the moon, they would just pass over into Heaven, an infinite realm in of itself.

Getting back to the corridor itself, this corridor is created after Eirin seals off the Earth, and then proceeds to create a chamber of unknown spatial extent, this chamber is where Kaguya resides. The edge of this chamber separates Gensokyo and the Lunar Capital, so its endpoint would have to lie somewhere within Heaven. Kaguya then creates a corridor of infinite size to prevent any intruders on Earth from entering her chamber from Eientei, this corridor extending towards the sky, eventually passing into Heaven by going upwards for an infinite distance, and ending somewhere right below the edge of the sealed chamber.

This means that, in about the span of a minute and 30 seconds, while fighting other entities, the protagonists enter this infinite corridor, fly through it, eventually passing from Gensokyo and into Heaven in the process, before eventually reaching the end of the corridor by pure speed, finding themselves right outside the sealed chamber, faced with Eirin. No contradictions with an infinite space within Gensokyo, as it enters the Heaven, an infinite space.

Couldn't Kaguya have just made an infinitely-looping corridor?

The argument here is that Kaguya "looped" space-time, making it so the corridor is just a single section repeating itself infinitely, while the space it takes up remains finite.

First of all, we know that this simply isn't how Kaguya's ability works. Her ability is that of manipulating eternity and the instantaneous; Essentially infinite time and zero time. To extend something infinitely is the entire purpose of her ability, such as extending the time of something to an infinite extent to make it immune to change. No official description of her ability allows her to make loops in any capacity, so this is purely headcanon. Furthermore, Miko's explanation in Urban Legend in Limbo contradicts the idea of a loop. The way the corridor works is by infinitely linking pieces of the space-time continuum; This in no way implies the corridor being a loop.

Secondly, this isn't even possible under the mechanics of the verse. Within Touhou, there exist three layers of reality: The physical layer, the mental layer, and the memory layer. The memory layer is the most important of the three, as one of the main purposes of its existence is to prevent loops. Thanks to this layer, anything that has happened in the past is remembered, and so long as that memory exists, it is impossible for that exact event to occur in the same way again. In the case of a space-time loop, since time is being repeated, this would cause events within a predetermined time frame to repeat as well, in the exact same manner that they occurred the first time. Obviously, this contradicts the functions of the memory layer, so the space-time loop theory would require Kaguya to literally defy the very laws reality is built on and substitute her own, something we should not assume without a significant amount of evidence.

Third, we know that the corridor isn't looped, as the protagonists aren't having their positions reset. They are clearly moving in a linear fashion, as they are able to reach the space between the earth and false moon. If they were in a loop, they would've still been on ground level, or close to it.

Finally, this presents a rather humorous contradiction. If Kaguya created a space-time loop, the context of the protagonists bypassing it through sheer speed remains. This means we have characters who are able to break through time itself via their speed, which is a blatant case of immeasurable speed. Essentially this argument boils down to "they aren't infinitely fast, they're immeasurably fast".

What if the Corridor Was Never Intended to be Infinite?

This is very easy to disprove. In Cheating Detective Satori, it is explained that the entire purpose of the corridor is to make people wander for eternity. It also makes very little sense to assume that a character would place arbitrary limits on their powers when their primary goal is preventing people from finding them. Making an infinite corridor would be a pretty effective way of not being found, considering that by the process of being infinite in size, anybody who attempted to reach you would be stuck in that corridor infinitely. Considering this is a usage of Kaguya’s ability to manipulate eternity in the first place, it should be even more clear. There’s no reason or purpose for Kaguya to go through the trouble of creating the corridor if it wasn’t going to be infinite for the purpose of keeping people out.

Why did Kaguya bother making the Corridor if the Protagonists have Infinite speed?

There are a few points to go over here, but overall they all fall under a single, major failing of Kaguya & Eirin’s plan. They knew very, very little about Earth, and by proxy, Gensokyo, and thus, heavily underestimated the Protagonists. To start in detail though, let’s begin breaking each point down. The first would be that Kaguya was explicitly not aware of the potential the protagonists held; It is stated on several occasions how the reason she and Eirin lost was because they underestimated the protagonists. Eirin made the oversight of utilizing an illusory fake moon, even though it’s well known that Youkai can see through illusions. She would then go on to say that it was “beyond her calculations” that the Youkai would be bothered enough by said illusion to get the humans involved in the first place. They also severely underestimated the might of the humans and Youkai in Gensokyo in the first place, as Kaguya was shocked to meet anybody on Earth as strong as Marisa and Alice are, comparing them to members of the Lunar Capital themselves. On top of that, everyone within Eientei had lived a relatively isolated life within the Bamboo Forest of the Lost, a location they specifically chose because of its ability to keep others away, before then hunkering down within this forest, with nearly no interactions with those outside of it before the events of Imperishable Night. This likely means they had absolutely no knowledge of any of the Protagonists in Imperishable Night beforehand, and thus, no way to predict their capabilities. Their complete lack of interaction with those on Earth, their lack of understanding of Youkai, and their underestimation of humans and Youkai all combined to make their plan a complete disaster, when the humans and Youkai knocked on their doors and far, far surpassed their expectations.

Couldn’t the Protagonists have nullified the Corridor?

Theoretically, yes. Based on the abilities possessed by all 8 protagonists, all 4 routes had at least some ability to nullify the corridor, whether through power nullification or space-time hax of their own. In practice, however, this is very misinformed. We can see from the dialogue that occurs after the corridor has been crossed that the protagonists didn’t have any indication that the corridor was infinite, until Eirin basically sat them down and explained to them that it was. Essentially, all 4 sets of protagonists just zoomed through the corridor in such a short time frame in such a rush to find Kaguya, that they didn’t even realize it was infinite, until they were told so after the fact, this would continue to play into the earlier point of Eirin severely underestimating the protagonists. So, yeah, the protagonists could have nullified the Corridor. If they even realized it was infinite, and thus, something they could cancel out in the first place, but they very obviously didn’t realize that, thus rendering this point unusable.

Outside of that, there also isn't a single implication, statement, visual or anything of the sorts implying the protagonists did so. Assuming a character used an ability in an instance to perform a pretty insane feat (negating an infinitely sized realm) would be a pretty crazy assumption to make without solid backing.

Why didn’t Eirin react when the Protagonists crossed the Corridor?

Because at this point in time, she had essentially already won. Her goal is to keep Kaguya safe in this situation, so while the protagonists getting lost for eternity is the ideal outcome, leading them further away from Kaguya is still a good outcome for her. Furthermore, Imperishable Night works off of a time limit, where if you fail to beat the game before 6 AM, the Imperishable Night spell cast by the protagonists wears off, and you get a bad ending with the incident going unresolved. In this case, where Eirin wastes time by drawing the protagonists to the end of the corridor, so she essentially forces the player into failure, thus making the outcome of her fight against the protagonists and whether or not they're able to cross the corridor irrelevant. If anything, this still ends up going all according to her plan regardless. Either way, Kaguya goes undetected and wins.

Toyosatomimi no Miko, A character who scales to infinite speed, chose to instead use haxx to bypass the Corridor, is this an anti-feat?:

Long story short, no. While her dispelling the corridor is true, simply choosing to use haxx to accomplish something you can do physically isn't an anti-feat. A real-life comparison would be how many people have no issue walking a mile on their own, but usually prefer to use a car or bike to traverse such a distance. Many people, if they could, would gladly choose to warp space-time to move where they want regardless of physical capability. In the case of Touhou specifically, we know characters generally dislike moving at their peak speed, as we see them complain about the infinite corridor (and complain about traveling infinite distances in the other two feats as well), so someone bypassing it with hax should reasonably be seen as a choice to avoid what is, to a character in-universe, a massive inconvenience. Finally, we know that Miko is characterized as being very over-the-top and commonly displaying impressive feats solely for the sake of making herself look good; Doing something as flashy as nullifying an infinite space-time continuum as opposed to just flying across it would fit that characterization perfectly.

The Palanquin Ship:

During the events of Undefined Fantastic Object, the protagonists start their journey by catching up to a flying treasure ship, known as the Palanquin Ship. By stowing away on the ship, they are able to enter the infinitely sized Makai, before crossing the realm to reach Hokkai, which is located at the edge of Makai. This is done in order to find Byakuren Hijiri, who has been sealed away within Hokkai.

“Corner” doesn’t necessarily mean the edge of something.:

This is a very common misunderstanding, as 'corner' in English can refer to a remote or isolated space. The issue is that this is an English-exclusive definition. The kanji used to represent 'corner' in the original Japanese text, 角, is defined as as the edge of an object or location. Thus, defining 角 as a remote or secretive location is completely inaccurate, and is essentially replacing the original text with something that never even really existed or was even considered by the author. While 角 can also be defined as a street corner, this isn't really applicable in context, as Makai doesn't have any streets.

Why did the Protagonists need the ship if they have Infinite speed?:

Makai is separated from Gensokyo by a powerful miasma that can't be crossed through conventional means. Only certain things, like the Palanquin Ship, can bypass it, so the protagonists needed to stow away on the ship.

Couldn’t the ship have slowed down or stopped?:

This is contradicted by the descriptions given to the ship. According to Murasa, the ship's captain, she has no real control over the ship, as it runs on autopilot (what a good captain btw), which means we have no real reason to assume it stopped or slowed down manually. Sanae Kochiya then compares this to a bullet train, which functions by moving towards a single destination at top speed without stopping or slowing down. As the Palanquin Ship works the same way, it wouldn't be stopping or slowing down either.

The Sanzu River:

During the events of Wily Beast and Weakest Creature, in order to cross over into Hell and reach the game's antagonist, the protagonists must first cross the Sanzu River to reach Higan. Starting from the lake shore in Gensokyo and ending on the shore of the river in Higan. The Sanzu River has been stated at several points to be infinite in size when it isn’t shortened by a Shinigami, and the protagonists cross the River with no Shinigami present.

Couldn’t a Shinigami have shortened the river?:

For context, Shinigami in Touhou possess the ability to manipulate distance, which is how they ferry souls over the river after their death. The idea here is that this is one of those cases, where a shinigami used their abilities to shorten the river for the protagonist's sake. There are numerous reasons why this is not the case. The most obvious being that the protagonists themselves point out the lack of interference from any Shinigami, going so far as to say that they wish they had enlisted the help of one. Furthermore, the context of the game makes the idea of anyone shortening the river very strange; Gensokyo is being invaded by hostile beast spirits attempting a takeover, so shortening the river in a case like this would be willingly assisting a hostile faction for no benefit, something that would be wildly out of character for virtually everyone in the series, especially since Shinigami serve the Ministry of Right and Wrong, which exemplifies order and tries to keep control over various afterlives such as Hell. Finally, we cannot simply assume a character showed up and performed a plot-convenient feat without any sort of direct showing or implication; This argument exists solely on the basis that something could theoretically happen, rather than use evidence to show whether or not something actually did happen.

What if the river was shortened to make things easier for the Protagonists?:

We have direct confirmation from Kutaka that the Yama (Eiki Shiki) was deliberately making things more difficult for the protagonists as a test. Shortening the river would be contradictory to that intention.

Is the river just finite normally, with it being extended to infinity by Shinigami?:

As explained by Ran Yakumo (who, to note, is considered one of the most hyper-intelligent characters in the franchise), the river and its relationship with those crossing it can be described using a mathematical formula showing an inverse relationship between the width of the river and the amount paid to the shikigami ferrying you across. As one pays more money, the width shortens and you'll have an easier time crossing. Conversely, if you pay less money, the river's width gradually becomes greater until it is virtually impossible to cross if you pay no money at all.

Essentially, this shows that the river is only altered in response to external stimuli (the shinigami being paid), with no stimuli (the shinigami NOT being paid) being what causes the river to be infinite. As the protagonists obviously didn't pay the shinigami during the events of WBaWC (as per their own admission), they would be dealing with the River while it is infinite.

All of this is further supported by a bit of common sense. The Sanzu River is meant to separate the world of the living from the afterlife. It is not something intended to be easily crossed, so keeping it at a short distance that anyone can conveniently cross at their leisure and only extending it infinitely on rare occasions

The Shinigami could just be creating more water when they expand the river?:

Given that all depictions of shinigami manipulating the river relies on the manipulation of distance, this isn't possible. Spatial manipulation cannot create matter from nothing; At most it can separate the space between molecules of matter and make it appear as though there's more of it, but at a certain point it will become so sparse that there might as well be nothing left at all. While it's true that shinigami have some degree of water manipulation, they merely summon pre-existing water from the Sanzu River. They have never been depicted as creating it out of thin air, let alone an infinite amount of it.

Conclusion:

Most, if not all of the points brought up against Touhou's infinite speed ratings are reliant on headcanons, or ignorance of either the original context or VSBW’s own rules. Many of them simply propose alternatives to the feats, while neglecting to show any in-universe demonstrations of those alternatives being true. The feats presented here are consistent enough to be able to avoid being called an outlier as well, as most verses rarely have a single infinite speed feat, let alone four.

Many people may have issues with the fact that these feats make nearly the entire verse infinite speed, due to the fact that several characters scale to Reimu, Marisa, Yukari, Alice, Remilia, Sakuya, Youmu, Yuyuko, Sanae, and Reisen, the main characters to perform these infinite speed feats. Some people are fine with the fact that it scales to all the high tiers, but take issues with many Touhou low-tiers also being afforded Infinite speed, after all, the feats are only performed by high tiers, correct? Well, yes, all of them… except the Sanzu River crossing. The Sanzu River is actively crossed by an absurd amount of Beast Spirits, in fact, this occurring is the main reason for 17’s plot occurring. Beast Spirits in of themselves only pose the threat that they do due to their massive quantity and abilities to possess others, otherwise, they’re a complete fodder race within Touhou, easily surpassed by even most low tier youkai. This essentially means even low tier Touhou characters upscale to infinite speed based off of the Beast Spirits, and can also be argued to downscale from the high tiers’ speeds due to at least being able to contest with them in battle to a degree, meaning essentially, infinite speed scales to nearly the entire verse of Touhou, with only a few exceptions.

So, in the end, Touhou’s infinite speed ratings are incredibly solid within VSBW’s own rules, are supported with in-universe statements, in-game visuals, canonical feats, and quotes from ZUN himself, and due to the characters that have performed these feats and how they scale across the verse, nearly the entirety of Touhou as a verse scales to infinite speed.

I hope this blog answers many of your concerns that come with Infinite Speed Touhou, or helps make it make sense even a little more. Keep an eye out for my initially planned blog, Kasen Ibaraki vs Fleetway Sonic, which will release only a couple days after this one, I had a blast writing it and researching it was absolute insanity! Edit: 12/29/2023, been meaning to do this for a long while, but I removed the Dream World Crossing segment from the blog due to issues with the feat (none of which were covered in this blog), as well as adjusting one explanation for the Heaven segment that was changed due to new findings. I'd also like to add that this blog does not cover every single infinite speed feat in the verse, just the 3 most major and well known ones, and the ones that are more frequently picks at in terms of validity.