Local truth

I meant actual fundamental physics, not the standard model, which is already known to be a (very good) approximation. There are some statements we can make which at least have the possibility of being exactly correct - the general form of the Schrodinger equation, General Relativity, conservation of momentum... that sort of thing.

As for truncated series etc, that fits exactly into the sort of approximation I was talking about.

At the most trivial level, look at wikipedia's article on diamond, the phase change diagram in particular. Diamond starts to be thermodynamically preferred over graphite at around 100k atmospheres, and has been known about for a century.

For a 2012 paper, there's this. Note that the first thing in the paper is the unquestioned statement "High pressure can fundamentally alter the bonding patterns of light elements and their compounds, leading to the unexpected formation of materials with unusual chemical and physical properties."

Here's a 2006 paper from Germany that directly looks at how high pressures affect the chemistry of alkalai metals, including sodium.

And a 1998 reference book containing five hundred pages of high pressure chemistry notes, including a handful of sodium compounds.

Seriously, nothing new here. Vastly overblown and irresponsible hype.

Oh man! Disagreement! I like disagreement!

How do you mean this?

• You enjoy disagreements. In this case that I proposed opportunities for that.

• You are happy to get an apportunity to disagree with what I wrote.

• You see my comment as a disagreement with established truth.

There is a universal arrow of time.

I don't think this is actually accepted as truth by physicists.

That is mostly so because physicists know about falsifiability and are mostly ready to revise a theory for one that makes better predictions (provided it's not their own).

In particular, physics is supposed to work the same in reverse.

That's not what I meant. I thought more about something like Segals chronometric cosmology which "presents a continuation of the nonanthropocentric tradition, in that it distinguishes between the observed time x_0, which takes the same form as in special relativity, and global time t, which is sychnonous with x_0 in the short run ...". The development of the universe is usually pictured to have started with the big bang. But in Segals theory that is only because it looks that way due to the curvature. Every point in that universe model would see a different point (at 90°) as 'big bang'. Note that Segals theory was found to make wrong predictions, but that doesn't mean that other alike theories might be found which don't.

"Markets tend towards efficiency in the absence of outside influences."

That is exactly the 'non-locality of truth' meant by Nancy. The question is: What (kind of) influences.

Capitalism requires continuous economic growth.

Why do you think this is true - or if you don't, why do you think other people think it is true?

I have heard this often. Ad hoc I can give only a German link: http://www.uni-protokolle.de/Lexikon/Wachstum_%28%D6konomie%29.html

First order reals [...] are "interesting" systems (in the sense that we study them and there are open problems that can be phrased in terms of them) and are consistent and complete.

I wasn't aware of that. Can you give some link?

Politics/economics: People don't have much sense, whether they're in business or government.

I'm not sure whether this is meant as a proposal for a 'local truth' or some reply/explanation to something else.

Organized crime is a significant part of economies and governments, and ignored by most theories.

You mean most economic theories I take it. I'd guess that from an econimicsts point of view (organized) crime is not different from other economic transactions only that it involves a penalty of (temporarily) exclusion from trade or other costs that could be translated into monetary amounts.

The question is how much this aspect has actually been taken into account.

There is also Rational choice theory.

Most of the economy isn't measured or considered.

Yes. I also have always wondered why there seem to be no statistical approaches to modelling social population development. E.g. by measuring and predicting the moments of Bourdieus types of capital of a sample of the population.

Such an approach should allow to much better predict (and thus address) effects like social inequality, aging society, precariat development. It shoud be simple (much less particles involved that in climate models) and I really hope that it is not already employed to actually do steer society (to the unjust).

Truths [...] which are complex beyond the human ability to manipulate ideas.

Interesting.

As a limit on ideas this implies truth (structures) which show no observable effect (otherwise the effect would allow to at least name the truth even if it cannot be understood fully).

As a limit on understanding of truth (structures) this implies irreducibility not only in the horizontal dimension (the number of parallel items cognitively manageable - those can be offloaded to computer) but at least also in the vertical dimension (the number of reduction steps required).

Examples of the latter might be structures which

• change so little with each reduction step as to make the reduction undetectable in itself and build an unmanageable number of these on each other. Or

• Contain reductions which feed back on lower reductions thus creating cycles. Something like humans which on a high reduction level (social) but feed back on effects observed under the microscope (an effect that probably (note: 'probably' is a catch-word) cancels out on the social level).

My intuition on these structures is that they are indistinguisable from noise. If they were there they couldn't have an effect at all (except being there).

Theological note: Some beliefs in god imply exactly such irreducible undetectable truth.

I'm hoping for more specificity about where a generalization might break down.

My comment was more about horizontal exploration (before it most comments were physics-related) than about elaborating any details.

No one that I've asked seems to know much about how mathematicians choose axioms-- there's got to be some process of choosing axioms which are likely to generate interesting mathematics.

That is one aspect of my first item "Mathematics is explained by reduction of propositions to axioms". The axioms as "premise so evident as to be accepted as true without controversy" (Wikipedia) still possess or require some structure - albeit a non-mathematical implied and/or often 'soft' one. I once had a discussion with a mathematician about this and also a longer web dialog about how vague notions crystalize into concrete structures but couldn't convice anyone that this is a real problem instead of a wishy washy relativization of the truth of math.

I will address your other items with separate comments.

It could mean that the dimensionless constant "alpha", also known as the "fine structure constant", varies, and the simplest way to express that change mathematically is as a change in C rather than in one of the other parameters (such as the charge of the electron).

(I read a book about this.)

Taboo 'fundamental'; what distinction are you trying to get at? Change the speed of light holding other parameters constant, and the fine structure constant changes; and vice-versa. Whether you want to consider this a "change in the speed of light" or a "change in alpha" seems to me pretty strictly a matter of taste; and the speed of light (especially its constancy) is much more familiar to most people than is alpha. (Which anyway may not be so constant at high energies, in spite of having 'constant' in the name.)