first of all thank you for your detailed comment. You raise important issues and I actually have some posts planned to address/clarify some of the points you raise, so I will only say a few short things here.

I haven’t yet made up my mind about Tegmark’s argument.

Well, the only thing I’m certain about is that pancritical rationalism (link to Max More, I like his writing) is the way to go. With metaphysics, I am very careful. I like Tegmark’s ideas and I want to explore them at the moment, but “a made up mind” is a fixed mind, and thinking is dynamic, so my mind is never made up

First, explicity is not usually a boon, at least not in subjective experience, which constitutes the majority of human knowledge good mathematicians if every act they make or symbol they manipulate is explicit. So, this inference goes against plenty of our well-established knowledge.

You must differentiate between 1st Person Point of View (1POV) and 1st Person Plural Point of view (1PLPOV); 1POV is implicit. This is what it is like to “be” someone. 1PLPOV is about shared knowledge. The aim of science is to make knowledge public, easily accessible to most everyone (otherwise we would have “occult circles”).

So this is just the difference between subjective experience and public knowledge, but it is an important point on which I will do an extra post in the future (it also has to do with the distinction “subjective”/”objective” which is deeply problematic IMHO, but more in the future post).

Second, speaking in math does NOT ensure that everybody associates the same meaning with what is said. Indeed, the very purpose of math is to remove (abstract out) the concrete meaning, semantics, referent to which the symbols point. This is why math is successful. Hence, it is not only false that math ensures the same meaning; but it’s not even the purpose of math _to_ ensure the same meaning. It is the purpose of math to remove the semantics to whatever extent possible.

The “meaning” that remains is only the structural relation; the symbol manipulations which everybody performs in the same way; the syntactic side. From the bird view, syntax is all there is; semantics arise from the inside (frog) view. This is a very pleasing feature of the Mathematical Universe, because the universe as seen from the outside (which we only manage to incompletely reflect via mathematical structures) should not have any meaning. Because meaning only exists for _someone_; outside the universe (multiverse if you like) there is no-one; hence, no meaning. No baggage, in the words of Max Tegmark.

There are _many_ potential reasons why math is so successful at describing reality. The first and foremost reason is because _we_ humans supply most of the semantic grounding for any math construct.

Agreed! But: the meaning exists, does it not? – inside our heads. Where does it come from? It must be part of the universe – but only in the inside view; meaning arises when mathematical relations are juxtaposed. The radical approach (mathematical universe) comes from taking seriously the monist postulate: there is one reality; humans have no special position. So everything which concerns “only humans” also concerns reality, because humans are part of this reality.

But I think that the question of how meaning arises on the inside is deeply intertwined with the question of what mathematical structures give rise to universes with observers (for instance the Computable Universes). I have not yet studied this enough

Hence, we humans, with math construct in hand, can spend our lives hunting for places to use that construct. To the man with a hammer, everything looks like a nail.It’s important to note that this is not merely pattern matching. The psychological arrogance noted here has more to do with the nature of abstraction than it does with matching patterns. It has to do with psychological bias, selective perception, and ambiguity.

Actually, the position you propose above would have been mine two years ago, I was radically anti-platonist (and I still am in the way most mathematicians are platonists). But for evolution to select abstract thinking etc (and even to select for biases!) there has to be something in reality which “responds” to this abstraction (otherwise it would not add to inclusive fitness). And, second, as mentioned above, the patterns, abstractions etc now reside in minds – but minds are part of reality! So you have mathematical objects as parts of reality the moment you think of a circle.
The Mathematical Universe is, IMHO, also a first big promising crack at the mind-body problem, unifying idealist and materialist monism in a yet to be explored way.

o “An issue well pointed out by Max himself is maximal independence from word fluff: only relationships made explicit in formalisms, computations or structures constitute knowledge. This ‘making explicit’ is a first boon, because when we speak in ‘normal’ words everybody has different connotations and associations bundled with them; only by speaking in mathematics can we ensure that everybody associates the same meaning with what is said.”

First, explicity is not usually a boon, at least not in subjective experience, which constitutes the majority of human knowledge. Implicity is almost always the boon, in practice. Musicians cannot become good musicians, one cannot learn to ride a bicycle, indeed, mathematicians cannot become good mathematicians if every act they make or symbol they manipulate is explicit. So, this inference goes against plenty of our well-established knowledge.

Second, speaking in math does NOT ensure that everybody associates the same meaning with what is said. Indeed, the very purpose of math is to remove (abstract out) the concrete meaning, semantics, referent to which the symbols point. This is why math is successful. Hence, it is not only false that math ensures the same meaning; but it’s not even the purpose of math _to_ ensure the same meaning. It is the purpose of math to remove the semantics to whatever extent possible.

o “Everybody who denies the mathematical nature of reality is welcome to present more plausible alternatives for the effectiveness of mathematics.”

There are _many_ potential reasons why math is so successful at describing reality. The first and foremost reason is because _we_ humans supply most of the semantic grounding for any math construct. Hence, we humans, with math construct in hand, can spend our lives hunting for places to use that construct. To the man with a hammer, everything looks like a nail.

Math is extraordinarily successful because it is abstract, and by definition, can be applied to great success in many different concrete circumstances.

“The Unreasonable Effectiveness of Math” is merely conspiratorial thinking … like those guys who see the number 23 everywhere they look… or the one’s who believe there are secret codes in the bible.

It’s important to note that this is not merely pattern matching. The psychological arrogance noted here has more to do with the nature of abstraction than it does with matching patterns. It has to do with psychological bias, selective perception, and ambiguity.

I’ve been to your site, it’s very nicely done; I’ve included a link to it on the links page on my main site http://www.complexitystudies.org/.

As to Max’s theory: I think it will get more and more attention with time, as the riddle (of mathematical effectiveness) is not going to go away by itself.

I’ve added a bit to my own blog on this (it includes one link to your site), halfway down this page:

http://www.ipod.org.uk/reality/reality_mathematical_universe.asp