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with 2PB of storage, what resolution could you store of a full-frontal pic of the average woman? what feature size could you get down to?
!theydidthemath@mander.xyz !theydidthemath@lemm.ee
The average woman's height is 1.588 m and the average woman's shoulder width is 0.367 m.
Assuming that this average woman fits exactly in this photo, the photo's "area" would be 1.588 m × 0.367 m = 0.583 m².
Assuming the pixel format is RGB and 8 bits per colour channel, each pixel in the photo would consist of 3 bytes. 2 PB is equal to 2 × 10¹⁵ B, which divided by 3 B for each pixel means there could be at least 6.67 × 10¹⁴ in this photo. In reality most of the time images are compressed so in practice you could get even more pixels. How much more depends exactly on the image and the desired image quality.
To calculate the area of each pixel, divide the photo's area by the number of pixels. This gives 0.583 m² / 6.67 × 10¹⁴ = 8.74 × 10⁻¹⁶ m² for each pixel. To get the side length of each pixel, take its square root to get 2.96 × 10⁻⁸ m = 29.6 nanometres!
Dividing the widths and heights in metres by the length of each pixel gives (width, height) = (1.588, 0.367) m / 2.96 × 10⁻⁸ m = an image resolution of 12,412,583×53,708,941 pixels!
When it comes for feature size, the bottleneck isn't actually the pixel size. Assuming the image is in visible light, the shortest wavelength visible to the human eye is 380 nm, so increasing the resolution beyond that point is useless.
In such a photo where features as small as 380 nm can be identified. To quantify the resolution you can see these features in, define an "effective pixel" to be a pixel of side length 380 nm. The actual pixels in such an image aren't relevant at this point.
Individual skin cells can be identified being 30 μm / 380 nm = 79 effective pixels wide. With similar calculations, blood cells can be identified with a width of 18 effective pixels, and you might be able to even identify individual bacteria. An E. coli bacterium has a length of 2 μm, which is 5 effective pixels.
A few comments as yours is close and I'm too lazy to do the write up myself, bumming off your work:
If you took the image with an electron microscope you can easily get better than 30 nm resolution. Would be in black and white though. And you would need to cover your mom in carbon or gold. And expose her to a vacuum. For biological samples they typically freeze them so they don't boil in there
thank you for your service, you have saved me from having to do this myself
OK, so assuming that each Hard drive has A size of 16TB we have 12 Hard drives per layer and 20 layers so in total we have
12 * 20 * 16TB = 3840 TB of storage.
This is The same as 3840 * 10^12^ bytes
In RGB a Pixel has 3 Values (Red, Green and Blue) each having a value ranging from 0 to 255, so 256 possible valuesbin total. A single byte can store numbers up to 256. This means, that storing a single pixel takes 3 Bytes.
3840 * 10^12^ / 3 = 1280 * 10^12^ Pixels that WE can store.
To get the maximum length of one side of the image we have to take the square root of this so
√(1280 * 10^12^) = 35.777.087
So if I didnt miscalculate this server could store a single image with the size of approximately 35.777.087 x 35.777.087 Pixels in RGB encoding.
We also assume that no other space on the server gets used and we can utilize the full 16TB of each Hard drive. It is probably impossible to view the image, due to its size, but you could store it.
Small miscalculation, 1 TB is only 10¹² bytes, not 10¹⁵ bytes, so you would only have 3840 * 10¹² bytes ⇒ 1280 * 10¹² pixels, so the width of a square RGB image with 3 bytes per pixel would only be around 35,777,088 pixels.
Damn, thanks for the correction, I will correct it.
I'm trying to see her taste buds