#bad math

It's hearing rant time. I'll try to keep it light on the math and heavy on the logic; no matter what, it should be real obvious real quick that Ukyo's hearing is literally superhuman.

This is exhilarating. Get excited!

Alright, SO *claps* what's happening in this exact moment is Ukyo hearing Ibara give a command to the Medusa. Now, Ibara actually commands the medusa three times over a short period here, but I think we can safely rule out the first (petrifying Kirisame, where he speaks somewhere between a regular and quiet speaking voice) and the last (literally underwater and in his mouth). This mean he hears the command used against Yo, which is reinforced by the fact that we see Yo's statue briefly while Ukyo is thinking about what he heard. Ibara does raise his voice to give this command, but only somewhat (from what I can tell, this is true in both the English dub and in the original Japanese).

As you probably know, sound is most often measured in decibels (dB) from the point at which it is being recorded, which for average volumes of things like speaking volume is typically one (1) meter away from the point of origin. For Ibara, I chose to round up a bit and say he gave the command at a volume that would measure 70 dB at one meter.

The bigger question is, how far Ukyo was from Ibara? Here, Ukyo was already running inland while Ibara was right by the boat, which was itself some distance from the shore. What I ended up plugging in was a distance of 400 meters. I chose this number as being 1/10 of the final, island-consuming diameter (he says 2,000 meters, and unless I'm mistaken, the affected range is the radius of the outgoing beam), which barely misses the ship from somewhere I can only assume was near-ish the center of the island. I will go ahead and admit that I may have overestimated this number, however perhaps the extra meters could be making up for other complications I did not account for in running the calculation, such as interference from the commotion of other people running and shouting, the waves, or the climate.

One thing that confused me for a while is that while stated in plain numbers and dB, when calculating what a sound will be at a certain range, it is instead written out in scientific notation and marked as intensity. This is the point that caused me the most grief and that I may be the most wrong on, but if I'm not mistaken, I believe intensity is basically one-to-one with dB.

I won't bore you with the math itself, not in the least because my past self didn't bother to write it down somewhere I could find it now, but the intensity I got for how Ukyo would hear Ibara's voice from 400 meters was about -5 x 10^-2, or -.05 dB. Yes, decibels can be negative; 0 dB is considered the threshold for the softest noise a human can hear. Anything softer is recorded as negative. Already, it seems Ukyo can hear .05 dB below that threshold.

Here's the kicker; he was also able to understand what Ibara said. According to the only source I apparently bothered to keep track of, the quietest level for understanding a conversation with background noise is 12 dB SNR (sound-noise ratio), which I think implies that Ukyo’s hearing reaches to sounds about 12.5 dB softer than what a normal person can make out, at minimum.

I’m no physicist, so I don’t know exactly how impossible that is or how much better that makes his hearing than a regular person (it’s not a neat 1:1 calculation), not to mention this isn’t necessarily Ukyo’s limit. We don’t know what the softest sound he can hear would measure in decibels, which is what we would need in order to come up with a “this many times better than a normal human” calculation. Especially when you start looking at inconsistencies like him not hearing Moz sneaking into the cave. 

Again, I am not a physicist nor a mathematician. I am a creative writing major who happens to go a little insane about fictional media sometimes. If someone who actually understands these calculations wants to try their hand at it, absolutely be my guest. 

However, I would like to briefly go over one other, much simpler calculation, for context.

This shot is from season 2, episode 8, when Ukyo hears Tsukasa and Hyoga approaching. He says, and I quote, "No way. They're fast, but not that fast!"

Earlier, just before the fight, he was able to inform Senku and the others that Tsukasa and Hyoga were at the grave site. We know, from seeing their side of things, they were there for only a short period of time, having a short conversation at regular speaking volume, before they found the cell-phone.

Now, according to a commenter on this Quora post, the average human can understand a conversation held at regular volume (65-70 dB at 1 meter, according to them, which is higher than the averages I was seeing on other sites for my previous calculations regarding Ibara) from only around 4-6 meters away in quiet conditions, and can hear it from up to 8-15 meters away (again, in quiet conditions). Now, I suspect this estimate may be somewhat skewed, but we'll work with it for the scuffed version of calculations.

Already, we know Tsukasa and Hyoga must be a good deal greater than 15 meters away because even from the treetops, the clearing with the grave site isn’t even in view. But let’s keep going, just for the heck of it.

According to my half-baked calculations, the average adult male can run somewhere around 100 meters per minute (1 and 1/3 meters per second) normally, or (for athletes running the 100 meter dash [world record being around 10.5—after a bit more research, the average athlete would be more like 6 and 2/3 meters per second]) up to 10 meters per second at a sprint. Given Ukyo’s reaction, it’s safe to assume they were sprinting, so probably closer to that 10. The battle was 20 seconds, and we can say at least five seconds passed in-story after it was won, given the dialogue that occurs around then. We don’t know exactly when relative to the battle Hyoga and Tsukasa started running, especially since the scene occurs in-show before the battle starts, but let’s give it a minimum of 5 seconds and a maximum of 30 seconds.

Even if we assume Hyoga and Tsukasa weren’t particularly fast sprinters, that already sets our minimum distance at 40 meters (more than twice the quora user's estimate); our max is as high as 300 (with the likely distance being closer to 100 meters or so). For him to hear. And recognize. Their voices. (Even if he couldn’t recognize what was being said, that’s ridiculous).

TL;DR: This man is either an alien or a government experiment. There is simply no other explanation for hearing that good.

Basically I’d just be outlining the facts of the case, the plaintiff/prosecution, the defense, the various arguments, evidence (for interest I’m not going to use just the videos, it would be like, the weapon, ect. Destruction of evidence would be FREQUENT), interesting trial moments, the holding, ect.

My ideas:

Google, what happened to you?

Edit: if Google was smart, they would keep metrics on people taking screenshots of queries. They control Android and Chrome, it's completely doable for them