Max himself posted about this on the everything-list here:
A popular article was also the feature in last week's 'New
Now is a good time for me to summarize my objections once again.
As I said recently to Bruno, here's the problem with the idea that
everything is mathematics:
"I think we need to draw a careful distinction between the *process*
reasoning itself, and the external entities that reasoning is *about*
*(ie what it is that our theories are externally referencing). When
you carefully examine what mathematics is all about, it seems that it
is all about *knowledge* (justified belief). This is because math
appears to be the study of patterns and when meaning is ascribed to
these patterns, the result is knowledge. So:
so Math <----> Meaningful Patterns <--------> Knowledge.
Since math appears to be equivalent to knowledge itself, it is no
surprise that all explanations with real explanatory power must use
(or indirectly reference) mathematics. That is to say, I think it's
true that the *process* of reasoning redcues to pure mathematics.
However, it does not follow that all the entities being *referenced*
(refered to) by mathematical theories, are themselves mathematical.
It appears to me that to attempt to reduce everything to pure math
runs the risk of a lapse into pure Idealism, the idea that reality is
'mind created'. Since math is all about knowledge, a successful
attempt to derive physics from math would appear to mean that there's
nothing external to 'mind' itself. As I said, there seems to be a
slippery slipe into solipsism/idealism here."
Another major problem is this idea of pure 'baggage free' description
that Max talks about (the removal of all references to obervables ,
leaving only abstract relations). The problem with this , is that, by
definition, it cannot possibly explain any observables we actually
see. Notions of space and agency (fundamental to our empirical
descriptions), cannot be derived from pure mathematics, since these
notions involve attaching additional 'non-mathematical' notions to the
pure mathematics. As I pointed out in another recent thread on this
thread, the distinctions required for physical and teleological
explanations of the world appear to be incommensurable with
mathematical notions. We cannot possibly explain anything about the
empirical reality we actually observe without attaching additional
*non-mathematical* notions to the mathematics.
"I've talked often about 'the three types of properties' (for my
property dualism) : Mathematical, Teleological and Physical. These
three properties are based on three different kinds of distinction:
Mathematics: The distinction is *model/reality* (or mind-body,
Teleology: The distinction is *observer/observerd* (self-
or 1st person/3rd person, intention)
Physics: The distinction is *here/there* (space, geometry).
These are simply three incommensurable types of distinction. You
(believers in comp) can try to derieve the observer/observed and
there distinctions from the model/reality distinction all you want,
you just won't succeed."
There are yet more problems with Max's ideas. For instance, he says
in the New Scientist article that: 'mathematical relations, are by
definition eternal and outside space and time'. Certainly, there have
to be *some* mathematical notions that are indeed eternal and platonic
(if one believes in arthematical realism), but it also makes sense to
talk about some kinds of mathematical objects that exist *inside*
space-time and are not static. As I pointed out in another thread
here, implemented algoithms (instantiated computations) are equivalent
to *dynamic* mathematical objects which exist *inside* space-time:
"Let us now apply a unique new perspective on mathematics - we shall
now attempt to view mathematics through the lens of the object
oriented framework. That is to say, consider mathematics as we would
try to model it using object oriented programming - what the classes,
methods and objects of math? This is a rather un-usual way of
at math. Mathematical entities, if they are considered in this way
all, are not regarded as 'Objects' (things with state, identity and
behaviours) but merely as static class properties. For instance the
math classes in the Java libraries consist of static (class)
and class methods.
But consider instead that there could be mathematical 'objects' (in
the sense of entites with states, identities and behaviours). What
could these mathematical 'objects' look like? if there are
mathematical objects they have to be dynamic. This conflicts with
standard platonic pictures of math as entities which are eternal and
static. What could these 'dynamical mathematical objects' be?
The obvious answer, based on the previous points made, is that
*algorithms* (reasoning procedures) are identical to *mathematical
objects*. The implementation of the algorithm (ie running the
program) would be equivalent to the state changes in the mathematical
Again, if it were really the case that all mathematical relations were
outside space-time, they could not, by definition, ever explain
anything we actually see from the perspective of observers inside
Nor, as I pointed out in the earlier paragraph, is it neccesserily
true that the platonic forms consist only of *mathematical notions*.
Plato/Plotinus talked about ethical/aesthetic forms as well (for
instance beauty). So there appear to be immutable relations which are
teleological in nature (ie beauty), not mathematical. In addition,
there are abstract physical concepts as well. It is not clear at all
that geometric notions should be classified as mathematics. Instead,
a strong case can be made that these are asbtract *physical* forms.
Geometry involves an additional *non-mathematical* distinction which
attaches to purely mathematical notions (ie the here/there
Nice try Max. But no cigar. The world is a long long way from a true
TOE yet. Indeed, it is not even yet understand by main-stream science
what the actual explanatory scope of a TOE would be.
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