Sapience and sentience is what you are looking for.

Most animals are sentient but not all sentient animals are sapient.

An ape can realize its him in the mirror while a goldfish can't

As of non biological neurons, computer simulated neural networks are the closest thing. But they are neither sentient nor sapient yet.

Well what you described isn't really a blur function (it'd be a brightness shift). But if we want to call it that then yes it is reversible there.

There are several other mathematical operations you can do that are just reversible like that. However none of them are anywhere close to actual blur functions.

Likely not if every pixel is blurred.

In that case all original pixel values are lost and replaced by blur pixel values.

Since every original pixel is blurred there is no information to extrapolate from for a undo and so knowing the method is useless.

Its like listening to music on a old telephone, you can make out the sound but all the details of the sound can't be recovered from the audio you are listening to

Does the transplanted organ keeps deteriorating even with immunosuppression? Or are immunosuppressive medication 100% effective?

The human beings (us) that are doing genome manipulation are also created by evolution , hence this genome editing is something we evolved to do.

There are aquatic animals that can change their biological sex while alive, it's the evolution taking its course.

Dip it into a drop full of hexane?

That's basically a billion year of trial and error before we arrived to the first spider.

All of life and evolution is basically trial and error by nature until something sticks. It happens on all sides, the predator , the prey and environment.

It's still happening right now.

A few hundred millions of years from now we'll have humans that unrecognizable from what we consider humans today