"Because math is the language of science, scientists who want to translate their work into popular parlance have to use verbal or pictorial metaphors that are necessarily inexact." For example:
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"Consider the demonstration many physicists use to describe the bending of space by matter: putting a bowling ball on a rubber sheet and watching it produce a deep indentation. This nicely shows how the sun curves space around it and how this affects the motion of other objects moving nearby. But it's also a scam. The ball bends the rubber sheet and pulls in other objects simply because the whole apparatus is sitting in Earth's gravitational field. This image also gives many people the false impression that when we talk about curved or flat spaces, we are talking about two-dimensional surfaces embedded in a three-dimensional space and not about three-dimensional curved spaces themselves."
As another example, genes aren't really "selfish," but Dawkins's metaphor "is a brilliant and simple way to explain that natural selection relies on the self-perpetuation of genes that promote higher rates of survival."
Since my doctroral dissertation was on metaphor theory, to include the use of metaphor in science, here are some thoughts I now have.
- All language is fundamentally metaphorical. Even our verb "to be" ('isness') was originally a Sanskrit metaphor. Language we now call "literal" was once someone's figure of speech, trying to express something we don't have adequate words for. Like, e.g., the "leg of the table." Today "leg," when applied to tables, is considered a use of the word "literally." As in: I bumped my foot on the leg of the table.
- I think a strong argument can be made for the "necessary inexactness" of all language. I think this could include mathematical language. This is because "numbers" are themselves words that persons use. See here, I think, J.L. Austin's How To Do Things With Words.
- Does math "exactly describe" reality as it is? I don't know, or am not sure, what this means or even could mean. Surely a theory of description is needed. How do "numbers" refer. If numbers themselves do not refer, then human agents use numbers to refer. And with this we enter, it seems inexorably, into the world of inexactness. (I assume Krauss thinks there is a way of speaking of reality or describing reality that is "exact" since his critique of metaphorical language is that it is "necessarily inexact.")
- I'm guessing that the ontological status of numbers or lack thereof would be part of this discussion.
- I'm certain Krauss is correct in saying that in science some metaphors are more apt (and this less deceiving) than others. I'll add that this is the case with all attempts to speak of things as they really are. Here I'll raise the Kantian objection: can we really get at the ding an sich?
- If Krauss is claiming that math or the use of math non-deceivingly describes things as they really are, then this sounds to me like a return o some kind of logical empiricism or positivism.
- Let me try something. I'm using a mouse to maneuver on my laptop. Let's say the mouse weighs 5 ounces. Is "weighs 5 ounces" descriptive of the reality of the mouse? I'm not certain this is the case. Because if I were using the same mouse while floating in space it would be "as light as a feather." So "weighing 5 ounces" does not seem to be literally or exactly descriptive of the mouse as it really is. Now take this example and apply it to all cases of using numbers to what Krauss calls "the real universe." Have we really described reality without remainder?
- I don't think metaphorical language is necessarily inferior to so-called "literal" language in describing reality. There are things, as I think Philip Wheelwright once said, that the steel nets of literal language cannot capture.
