Yes, information and negentropy are measuring the same thing, and can be directly compared and just differ by a constant scale factor.
But this introduces a problem when talking about the valuable information in a book, brain, or computer, because the valuable information is overwhelmed by the relatively numerically gargantuan entropy of the arrangement of the mass that is storing that information. This problem, though, is often easily solved by asking information questions that are phrased in a way to select the information of interest. So in a computer, where this separation is more obvious, for example, it's important to differentiate between the entropy of a transistor (a crystalline structure with very high information) and the information contained in its logical state (a much much lower information, but usually more interesting).
Therefore, the question ends up being only, do we understand the system well enough to determine what information we are interested in? Once we know that, it's usually possible to estimate it.
are negentropy and information measuring the same thing?:
Yes. This is spelled out very clearly by many people, including this answer on PSE, but I'll go with an old book by Brilluoin, Science and Information Theory (i.e, this is the Brilluoin of Brilluoin Zones, etc, and also the person who coined the term "negentropy").
The essential point is to show that any observation or experiment
made on a physical system automatically results in an increase of the
entropy of the laboratory. It is then possible to compare the loss of
negentropy (increase of entropy) with the amount of information
obtained. The efficiency of an experiment can be defined as the ratio
of information obtained to the associated increase in entropy.
information vs valuable information:
Brilluoin also distinguishes between "information" and "valuable information", and says that a priori there's no mathematical way to distinguish these, although in certain cases we can define what we consider to be the valuable information, and in those cases we can calculate it.
We completely ignore the human value of the information. A selection
of 100 letters is given a certain information value, and we do not
investigate whether it makes sense in English, and, if so, whether the
meaning" of the sentence is of any practical importance. According to
our definition, a set of 100 letters selected at random (according to
the rules of Table 1.1), a sentence of 100 letters from a newspaper, a
piece of Shakespeare or a theorem of Einstein are given exactly the
same information value. In other words, we define “information” as
distinct from “knowledge,” for which we have no numerical measure. We
make no distinction between useful and useless information, and we
choose to ignore completely the value of the information. Our
statistical definition of information is based only on scarcity. If a
situation is scarce, it contains information. Whether this information
is valuable or worthless does not concern us. The idea of “value”
refers to the possible use by a living observer.
So then, of course, to address the information in the Pricipia, the question is to separate information from valuable information, and note that a similar book with the same letters in a specific but random sequence will have the same information, but different valuable information.
In his book, Brilluoin provides many ordinary examples, but also computes some broader and more interesting examples that are closely related to some subtopics of this questions. Instead of a picture (as the OP's question suggests), Brilluoin constructs a way to quantify what is the information of a schematic diagram. Instead of a physics text (as the OP's question suggests), he analyses a physical law (in the case, the ideal gas law), and also calculates its information content. It's not a surprise that these information values are swamped by the non-valuable information in the physical material in which they are embodied.
a specific case, the brain:
Of the three topics brought up by the question the most interesting one to me is the brain. Here, asking what is the information in the brain, creates a similar ambiguity as for a computer, "are you talking about the crystalline transistors or are you talking about their voltage state?" But in the brain it is more complex for various reasons, but the most difficult to sort out seems to be that there is not a clear distinction between structure and state and valuable information.
One case where it's clear how to sort this out, is the information in spikes within neurons. Without giving a full summary of neuroscience, I'll say that neurons can transmit information via voltages that appear across their membranes, and these voltages can fluctuate in a continuous way or exist as discrete events called "spikes". The spikes are the easiest to quantify their information. At least for afferent stimulus-encoding neurons where people can make a reasonable guess what stimulus they are encoding, it's often possible to quantify bits/spike, and it is usually found to be 0.1 to 6 bits/spike, depending on the neuron (but there's obviously some pre-selection of the neurons going on here). There is an excellent book on this topic titled Spikes, by Fred Rieke, et al, although a lot of work has been done since its publication.
That is, given a model of 1) what's being being encoded (eg, aspects of the stimuli), and 2) what is the physical mechanism for encoding that information (eg, spikes), it's fairly easy to quantify the information.
Using a similar program it's possible to quantify the information stored in a synapse, and in continuous voltage variations, although there's less work on these topics. To find these, search for things like "Shannon information synapse", etc. It seems to me not hard to imagine a program that continues along this path, and it if it were to scale to the large enough size, could eventually estimate information in the brain from these processes. But this will only work for the processes that we understand well enough to ask the questions that get at the information we are interested in.