Yes, indeed, I totally agree, although I'm not much persuaded by pseudo equations, which are not generally helpful.
Nothing that I have said suggests that knowledge is the same as information and your example illustrates the point perfectly. My point is that we cannot advance our understanding so long as researchers continue to confuse the two concepts. And in most km writing, the two are totally confused. The key point, as Deming acknowledges, is that they are different and as Drucker says, 'knowledge is between two ears and only between two ears' - in order to pass on what we know to others, we have to 'inform' them. We do that by sending messages of one kind or another (spoken, written, etc.) that have the potential to inform - we speak of those messages as 'information'.
The recipient of that 'information' now has the possibility of incorporating his or her understanding of it into his or her personal knowledge of the relevant area, but the information clearly undergoes some further transformation to do that: indeed, if the 'message' is not understood correctly (i.e., as the sender intended) what the recipient is then led to believe may be false and, therefore, not 'true' knowledge. On the other hand, the recipient may interpret the information in a novel way and reach a true understanding NOT intended by the sender. In other words, 'knowledge' is always the personal construct, while 'information' is the external realisation of that construct.
If we confuse the two, we are confusing what we know with what we are able to express about what we know.