[The
title above is an ironic take on Donald Hoffman's

__'Reality is Eye Candy'__, which was a presentation he gave in 2017 at a__SAND__conference.)
i) Introduction

ii) Conscious
Realism

iii) Why
the Maths?

iv) Models
as Idealisations

v) Examples
of Hoffman's Models

vi) Conclusion

__Professor Donald Hoffman__

**often (very often) uses phrases such as “precise mathematics” and “mathematical models” in reference to his own philosophical position -**

__conscious realism__. Hoffman explains why he does so in the

__following words__:

“Part
of my background is in psychophysics. This is the science of studying
conscious experiences and building mathematical models. Your
conscious experiences are not random things. We do careful
experiments and can write down mathematical equations that actually
describe the conscious experiences you will have. They're
mathematical, so conscious experiences can be described by
mathematics.”

As
just stated, Hoffman often mentions “mathematical models”; though
he rarely says what he means by those words. And he rarely offers us
any examples of these models. (The ones I've found will be discussed
later.) There may be a good reason as to why Hoffman doesn't give us
any examples. For example,

__he says that__**we must**
“admit
that maybe consciousness can be described with mathematics”.

Hoffman
doesn't say that consciousness

*has been described by mathematics*here: he uses the word “maybe consciousness can be described with mathematics” instead. Yet elsewhere Hoffman keeps on talking about his mathematical models of consciousness (as well as of experiences).
Models
of “conscious experiences”?

What
form do they take? And what does it mean to claim that

__psychophysicists__like Hoffman
“can
write down mathematical equations that actually describe the
conscious experiences you will have”?

Does
Hoffman mean that he has mathematical models of the physical bases or
physical correlations of what he calls “conscious experiences”
(or consciousness itself)? That would be fine. But to have
mathematical models of conscious experiences

*themselves*seems like a__category mistake__.
The
point here, then, is that mathematical models exist in physics,
biology, economics, etc. Can there also be mathematical models of
experiences and conscious agents? In terms of the latter, the answer
is 'yes'; though only if the physical and behavioural nature and
actions of a conscious agent are being modelled. However, that's not
what Hoffman is attempting to do.

**Conscious Realism**

Donald
Hoffman often uses the word “we” when he should really use the
word “I”. Take this eulogy to his own conscious
realism.
Hoffman

__writes__:
“Here
there is good news. We have substantial progress on the mind-body
problem under conscious realism, and there are real scientific
theories.”

It
can be conceded that Hoffman has a few postgraduate workers, and even
a few fellow professors, working with him on his conscious realism.
However, phrases such as “we have substantial progress on the
mind-body problem” seem a bit too grand for anyone's liking.
However, it's the passage which follows which is relevant to this
piece. Hoffman

**continues:**
“We
now have mathematically precise theories about how one type of
conscious agent, namely human observers, might construct the visual shapes,
colors, textures, and motions of objects..”

Now
that's fair enough. It can easily be seen how scientists (

__cognitive____scientists__) can construct “mathematically precise theories” about how “human observers might construct the visual shapes, colors, textures, and motions of objects”. The thing is that Hoffman goes much further than this. He has done so by entering the domain of speculative philosophy. Not only that: the reference to constructing shapes, colours, and the motions of objects can all be placed under what's often called__“third-person science”__. That is, in such a science the researchers will rely primarily on two things:
1)
The “reports” of the subjects in scientific experiments.

2)
The neuroscience, etc. of vision.

Hoffman
moves beyond all this. He claims to have constructed a
“mathematically precise” theory (or “model”) of
consciousness, experiences, cognitive agents, etc. too. In addition,
Hoffman also uses such mathematical models to defend (or simply
describe)
his philosophical position of conscious realism. Now what we have
here is a huge jump from the neuroscience/cognitive science
(mentioned in the quote above) to Hoffman's speculative

*philosophical*positions.**Why the Maths?**

My
question is simple: when Hoffman

__says that__his theory
“gives
mathematically precise theories about how certain conscious agents
construct their physical worlds”

what
does he mean by that? More precisely, in what way are numbers and
other mathematical tools used to explain how “conscious agents
construct their physical worlds”? This can easily be answered in
one way. Numbers or mathematics can be used to describe or explain
just about anything. For example, if I randomly throw a deck of cards
on the floor, the positions of all the individual cards can be given
a mathematical description. But why bother?

The
other question is about how precisely maths makes sense of what goes
on in minds or consciousness. Here again maths can be used (perhaps
arbitrarily or pointlessly) to do so. More to the point, what work,
precisely, is the maths doing in Hoffman's philosophical position of
conscious realism?

Hoffman
compares what he's doing to what

__Alan Turing__**did. In Hoffman's own words:**
“[T]he
tip from Turing is that Alan Turing decided to give a theory of what
is computation and he came up with this really simple formalism. A
little machine that has a finite set of states finite set of symbols
some simple transition rules and it turned out he could prove that
any computation could be done by this simple little device called the
Turing machine and that was what launched the theory of computation
computer science...”

Consequently,
Hoffman continues by asking us this question: “[C]an we do the same
thing for consciousness?” That
is:

“Can
we come up with a simple formalism which will handle all aspects of
consciousness?”

And
again in the following we may have a category mistake when Hoffman
asks this
question:

“Can
we come up with a mathematically precise theory of consciousness and,
from that, boot up space, time, and matter?”

What's
more, Hoffman tells us that he

“think[s]
[that] a precise mathematical science of consciousness is possible”..

**Models as Idealisations**

No
one will have a problem with the fact that mathematical models can –
or always do –

*idealise*what it is they're modelling. For example, this is the case with__ideal____gases__, point particles,__massless ropes__, and lots of stuff in boxes (see__Lee Smolin__'s__“physics in a box”__). However, it's often the case that these “idealisations” (or simplifications) go too far. So is this true of Hoffman's models of consciousness, conscious agents and the rest?
Here
we'll also need to stress the fact that real situations (or things)
in the world are very complicated and thus models – especially
Hoffman's models – may be extremely approximate in nature. However,
perhaps the problem is not even

*approximation*when it comes to “modelling” consciousness, experiences, etc.
Yet
idealisations and simplifications are often good things.

For
a start, a model must provide us with more than “empirical data”.
Put simply, models serve a purpose that's beyond any painstaking
description of every aspect of what it that's being modelled. And
it's precisely because models – all models (by definition) – go
beyond that data (or beyond description) that there can be the
following problems:

i)
Models can oversimplify.

ii)
Models can bear little relation to what it is they model.

iii)
The relations between the model and what they model can be very vague,
weak and even purely metaphorical/analogical – and that can even be
the case when the model utilises mathematics.

Now
how much of all the above applies to not only Hoffman's models
themselves; but also what Hoffman claims about them?

Thus
each mathematical model also has to take into account the to
and thro between accuracy and simplicity. These and other scientific criteria are
always being played against each other. This means that other factors
must come in, such as the “predictive power” of the model. In
addition, simplicity is supposed be cherished in the theories of
physics and when it comes to mathematical modelling. Thus, if a model
is complex, then it will more faithfully reflect the thing that is
modelled. If it's too complex, on the other hand, then it won't serve
the purpose of being a model very well. (That is, the complex model
may be hard to analyse and difficult to understand.)

All
this means that Hoffman's mathematical models (if they

*are*mathematical models) need to account for the question as to whether or not they really do describe systems (or reality) accurately. In that sense, Hoffman's models face the same problem which he stresses human “perceptions” face in his (part) evolutionary account of conscious realism.**Examples of Hoffman's Models**

The
following are a few examples of Hoffman's “mathematical models” -
or mathematical graphs.

Firstly,
we have this mathematical model of what Hoffman calls a

__“conscious agent”__:
Hoffman
uses the (supposedly) mathematical symbols of

*W*,*X*and*G*in the above*:**W*= the world

*X =*an experience

*G*= a conscious agent's action

Now
once you have these symbols you can of course play with them. In
Hoffman's

__own words__:
“We
can translate this into some mathematical symbols. We have a world

*W*, experience*X*and action*G*.. and then we have a map [see next image], a Markovian kernel... and an integer counter [*n*] which is going to account for the number of perceptions you have...”
And
so on. And where you have mathematical symbols, you often also have
maps, graphs, grids

**and suchlike. Hoffman makes use of them too.**
So
what we have is a triadic set of relations between

*W*,*X*and*G*. Does it tell us anything? Is it gratuitous? And even if it's not actually mathematical in nature, does it still help us in some way?
For
one, as mentioned earlier, this model is certainly an idealisation
(or a simplification): all we have represented is the world (

*W*), an experience (*X*) and an action of a conscious agent (*G*). So why only these three phenomena? Why a*single*experience and a single action? (Unless*X*is meant to be a symbol for*experiences*or*experience in general.*) And how are*X*and*G*taken in separation of the rest of*W*? How would an externalist**or anti-individualist take this almost Cartesian position on a world, an experience and an action? (Of course Hoffman isn't a Cartesian from either a philosophy of mind or an ontological point of view – he's against “dualism”.) What about the agent (***G*) and his/her/its embeddedness in the world (*W*)?
It's
of course the case that Hoffman's conscious realism will provide all
the answers to these questions

So
to recap.

Hoffman's
graph above is very sexy and seemingly scientific. We have the
symbols

*W*,*X*and*G*for a start. Not only that: the letters are connected in a geometric graph. But so what? How does this graphic and symbolic representation help matters? More importantly, what does it really say? And is this really a*mathematical model*?
Then
Hoffman goes deeper – or at least his next graph is more complex.
Now we have this:

Here
we have extra “mathematical symbols” and thus more scientific
deepness. In addition to the symbols

*W*,*X*and*G*, we now also have the symbols*P*,*A*and*D*. Thus:*A*= “action map”

*P*= “a

__Markovian__

__kernel__”

*D*= “a perception map” or a “decision map”

*N*= “an integer counter” which “counts the number of perception which you have”.

According
to Hoffman, “a conscious agent is just

**[***sic*] a sextuple” - that is, “(*X*,*G*,*P*,*D*,*A*,*N*)”.
Thus,
the connecting line from

*W*(a world) to*X*(an experience) is symbolised by*P*(a “markovian kernel”). And*X*'s connecting line to*G*is symbolised by*D*(a “perception map” or a “decision map”). That is, an agent carries out an “action” in the world.
Again,
how does the model help? And is the model accurate? What sort of
world (

*W*) – if a conscious agent's world - can be summed up by a “sextuple” (*X*,*G*,*P*,*D*,*A*,*N*) – even if we acknowledge the importance of idealisation or simplification?
(I'm
willing to concede that I may have partly misread Hoffman's
symbolisations or models. Nonetheless, I don't believe that would
have even a slight effect on my criticisms.)

Things
get even deeper here:

Here
we have a symbolic and graphic representation of “two conscious
agents”, not one. In addition, we have

*N*_{1}and*N*_{2}(both “integer counters”) But what does the image above really tell us? If we didn't get much meat out of the left-hand side of this image (as quoted above), then how can we get any more meat when we've put both sides put together?
Finally,
we have this:

In
the above, “each dot is a conscious agent” and “each link is a
connection between conscious agents where they are communicating with
each other”. Even Hoffman must admit that the placings of the
agents (the pink dots) and the resultant shapes of these agential
interrelations are completely arbitrary. (There are symbolisations of
triadic
interrelations and quadratic
relations; which, in turn, are related to other geometric relations.)
This, however, may not matter to the philosophical point that Hoffman
is attempting to get across.

Two
things are worth mentioning here. One: the use of the
mathematically-sounding title “combination
theorem”
(see mathematical

__combination__). Two: what does that graph actually give us? Indeed why is the above a__theorem__? (Or, more mundanely, why use the word “theorem” at all?)**Conclusion**

To
offer a final sceptical conclusion.

Perhaps
all that Hoffman means by his frequent references to “using precise
mathematics” (or, more often, to using “mathematical models”)
is simply the use of what he calls “mathematical symbols”; which,
in turn, are then placed in graphs

**(such as in those above). But mathematical symbols alone can be used for anything and they can be used by anyone.**
This
also raises the question:

What does Hoffman
mean by the words “mathematical symbol”?

Finally,
is Hoffman doing something that's really that different to what

__Julia Kristeva__did? Take this passage (which is replete with mathematical symbols and references) from Kristeva:
And
here's an “equation” from

__Jacques Lacan__:
Finally,
I'm not saying that Hoffman's models are completely in the same
ballpark as the other two outre examples. However, they are, I
believe, still gratuitous. And they're also used to tart
up
(as it were) his extremely speculative philosophical positions.

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