![[Serious] (No infinity, no RCT) Gojo might just barely not be able to survive Tsar Bomba.](https://preview.redd.it/1gpudeibiouh1.png?auto=webp&s=983876914d24682e4933cd8240cb04fc143dc481)
[Serious] (No infinity, no RCT) Gojo might just barely not be able to survive Tsar Bomba.
It's said that Gojo leaving his infinity on for the duration of three days was able to hurt his brain enough to make it turn off, before he used RCT to compensate.
You can take that given a few more days sustained injury would occur.
Surface area and bits Gojo uses per refresh:
You can calculate Gojo's surface area using any estimate for his surface area for a build with his height 6,3 (canon) from 80kg to 85kg (estimated):
Lowball: 2.01 m² (uses Fujimoto calculation at 80kg)
Highball: 2.15 m² (uses Takahira calculation at 85kg)
You can scale this by an infinity factor (just the distance between Gojo and infinity boundary), that should very miniscule like <0,1
S (Infinity) = S (Gojo) × (1 + I²)
Lowball: 2.01 m²
Highball: 2.1715 m²
Now Gojo has atomic level precision for what he can actually see, as stated multiple times in the manga. For him to detect where something is, he essentially divides it into atomic little squares. It doesn't really what atom we use, we can use anything from helium-4 to cesium-133
Helium-4: 9.61×10¯²² m²
Cesium-133: 8.8804×10¯²⁰ m²
Number of cells of information states Gojo has:
| m² | Infinity | Spacial resolution |
|---|---|---|
| Lowball (to minimize cells) | 2.01 | 8.8804×10¯²⁰ |
| Highball (to maximize cells | 2.1715 | 9.61×10¯²² |
Cells = S (Infinity) / Spatial resolution
Lowball: 2.263411558×10¹⁹
Highball: 2.2596253902×10²¹
If Gojo had perfect compression (we'll get to this) then you can simply take the log2 of the cells, for him to know where a cell is everytime he refreshes. You can then scale this by some bit factor for Gojo to evaluate the particle under (mass, energy, etc.) this should be at least under 100, because bits are logs they aren't usually too much. (100 bits would be 2¹⁰⁰ possible states)
Bits per refresh = (bits to test if it's safe) log₂ Cells
Lowball: 2057.44424761 bits (Using 32 bits)
Highball: 8244.04853621 bits (Using 128 bits)
How many times he has to do it?
You can get the average flux (number of molecules that hit per square meter per sec), through this formula:
Collisions per second = Pressure √( Degrees of freedom / 6 m kB T)
Take Temperature 298.15 (Room temperature at Kelvin), and atmospheric pressure (101 325 Pa)
The particle in air with the highest mass is O₂ (5.3137250206×10¯²⁶ kg)
and using N₂ (4.649509393×10¯²⁶ kg) as they both make up 99% of air:
(Diatomic molecules have 5 degrees of freedom)
| Temperature (°Κ) | Mass (kg) | Surface area (m²) | |
|---|---|---|---|
| Lowball (to minimize collisions) | 298.15 (25℃) | 5.3137250206×10¯²⁶ | 2.01 |
| Highball (to maximize collisions) | 293.15 (20℃) | 4.649509393×10¯²⁶ | 2.175 |
Collisions hitting Gojo per second = Flux × Pressure √( Degrees of freedom / 6 m kB T)
(Diatomic molecules have 5 degrees of freedom)
Lowball: 1.4376628123 ×10²⁸ collisions per second
Highball: 1.663842196 ×10²⁸ collisions per second
Gojo's bitrate
Gojo has to do 1.4-1.6 refreshes per second, multiplying this by the bits per each refresh:
Bitrate = Frequency of collision × Bit per refresh
Lowball: 2.9579110831 ×10³¹ bits/s
Highball: 1.371679582 ×10³² bits/s
Power and energy
Since information can't be destroyed, it will always generate heat for Gojo to erase a bit of information, i.e.: update information, you can use the Landauer principle to get the limit for the minimum wattage dissipated:
Power (in watts) ≥ Bitrate × kB T ln 2
Landauer limit (lowest power to be dissipated)
Lowball: 8.2981973077 ×10¹⁰ W
Highball: 3.9137783946 ×10¹¹ W
However unfortunately for Gojo, the human brain operates really close to the Landauer limit, only losing about 28% in compression (compared to computers which lose like 99.9998%), so the actual power dissipated is slightly higher, you can multiply the calculated launder limit to get the power to hurt Gojo's brain, to get the heat dissipated for each bit erased:
Power to hurt Gojo = 1.26 × Landauer limit
Lowball: 1.0455728608×10¹¹ W
Highball: 4.9313607772×10¹¹ W
Now obviously this completely dwarfs the power generated from a nuclear bomb, a nuclear bomb lasts about 10s
Even for little boy, it's only about a tenth of its power output
Little boy: 6.3 × 10¹³ / 10 = 6.3 × 10¹²
Now. This power was only able to hurt Gojo over a few days. The only problem is we don't know how much Gojo could theoretically survive really, but we do now is the difference in timeframe.
For early nuclear arsenal like little boy, he survives it easily. Even just taking that another 4th day would be enough to kill him, the total energy released from little boy is like nothing:
Energy = 4 × 86400 ×1.0455728608×10¹¹ = 3.6134998068 10¹⁶ J ≫ 6.3 × 10¹³ J
You still have to consider that your cells are more resistant to long term energy than short energy. The difference is massive when you're comparing multiple days to a few seconds.
You can reverse this formula to see how Gojo compares against the tsar bomba (2.1×10¹⁷ J):
Days = Energy /( 86400 × Power )
Lowball: 4.92877253436 days
Highball: 23.2461614752 days
This is the total days he could supposedly strain from using infinity before getting lethal injury. The range is pretty massive but doable depending on how much you think he improved from then in terms of durability.
However this ignores that the longer the days are, the better Gojo's natural human healing factor can take into place, and also the fact that Gojo can consciously reinforce his brain much better than a total dispersion throughout his body, means that something like a bomb is a lot harder to deal with than a strain over a few days.
I would say that Gojo couldn't survive a modern nuclear bomb, but could survive early nuclear just based of pure durability.