No, that's not quite right. If you blur the same picture twice using the same blur filter, then yes, you end up with the same final image. But that's not the same as saying that if you blur two different pictures you end up with two different images. Two different pictures blurred with the same filter can end up being identical blurred images.

You can think of a blur filter as a set of vectors that move pixel information around, but the step you're missing is that the pixel information isn't moved to just one other pixel. It's spread around over several neighbouring pixels, and then added together with the information spread from other pixels that overlaps it. That adding together operation muddies the waters, so to speak - once the blurred pixel info is added together to form the final blurred image, you can't work out how to un-add them to separate them again. There will be multiple possible solutions to the problem of going backwards to an unblurred image, and no way to decide which is the correct solution.

> Let’s say you take a photo and then digitally blur it in photoshop. The only possible image that could’ve created the new blurred image is your original photo right?

No, that's not correct. Many different images could give you the same blurred image.

When you blur an image, fine detail below a certain scale is lost. If two images are the same at large scales, but different in the fine details below the scale where the blur filter removes them, and you blur them, you won't be able to tell the difference. So you can't decide which of the two images you started with. You can make a guess, but given there are infinitely many images that will blur to the same blurred result, you are likely to be wrong.

It's important to understand that colour sensation is entirely psychophysical. The colours we sense are a product of the construction of our eyes and nervous systems - they don't really exist outside the context of a human observer (or an observer with the same visual architecture).

A spectrometer can easily tell the difference between (light of wavelength 580nm) and (mix of light with wavelengths 480nm and 650nm). There is a physical difference. But human vision cannot tell the difference - our brains sense both these as "yellow". Which one is really yellow? Neither. "Yellow" has no physical reality outside a human brain - it's our label for a sensation that we have.