Great question. Inflation is SUPPOSED to be a group valued field. In the case of bilateral trade it’s an element of GL(2,R) although the economists haven’t gotten there yet. But it is mostly not a field on Geography. It’s a field on path, Loop, preference and geographic spaces.
Q1: Why is it a field on Preferences?
A1: Because a true COLA is not an index on baskets (mechanical index) but on welfare derived from baskets (economic index). BLS misrepresents CPI being COLA-driven abusing work of Erwin Diewert on Superlative indices. A COLA prices WELFARE.
Q2: Why is inflation a field on LOOP spaces of preferences?
A2: Tastes are seasonal. In USA “We never spill Egg Nog on our bikinis.” What you both want & price HAS to be made seasonal to avoid the Cycling Problem (Holonomy) in index number thy. So we have LOOPS of tastes/prices.
A2 Continued: If you don’t make loops of tastes and prices, you will show meaningless regular inflation if prices, quantities and tastes Circle back to their initial Jan 1 values. This confuses economic experts (Like Diewert) when it comes to chain/path indices…which is up next.
Q3: Why is inflation a field on Path Spaces of Looped Preferences/Prices?
A3: Loosely, Index number theory really died w/ work of Ragnar Frisch (rightly) destroying Irving Fischer’s misguided work on axiomatic tests for bilateral (2 period) mechanical index numbers. Here’s why.
A3 Cont.: As Ken Arrow challenged us “Frisch showed we can’t solve the bilateral index problem because a single agent at multiple points in time is *exactly* dual to multiple agents at a single instant of time. Which is exactly my ‘Impossibility Theorem’ in Social Choice. QED.”
A3 Cont.: Our response: “Ah. That would be true but for 2 differences! First, Indices live in markets with *prices*. Our methods *don’t* live in social choice voting paradigms. Second, agents evolve into their future selves via paths. There’s no ‘morphing path’ in social choice.”
A3 Cont.: “This is why index numbers will one day be properly understood as parallel translation in Fiber Bundles wrt Economic Gauge Potentials. But Zoe doesn’t become Cam morphing into Fatima when voting. So parallel transport is unavailable. Even in topological social choice.”
Q4: Why do you say indexes are Group-Valued? Isn’t inflation just a number?
A4: Here goes. In the most famous case you *can* get away with a number. But that 8.9% style CPI nonsense is actually secretly a 1×1 matrix in GL(1,R). And that actually matters! Why? B/c Non-linearity.
A4 Cont.: Only 1×1 matrices commute. NxN matrices do not! And if A.B isn’t B.A, the system goes non-linear. So if you have 2 countries with 2 currencies, the commutative case doesn’t work at all. You need to use Freeman Dyson’s system of Time Ordered Products to save inflation.
A4 Cont.: But even in the case of one Currency like the Dollar, economists don’t get the group issue. True COLAs are valued in an *infinite* dimensional non-commutative group called DIFF_0(R^+) equivalent to increasing differentiable functions from 0–>♾ reparameterizing ‘Utils’.
Q5: So let’s see. Inflation is a field like temperature. But a field in a fiber bundle over ♾-dimensional path spaces of loops of preferences/prices valued in non-commuting groups leading to non linearities not addressed by economists? What about actual geography!”
A5: Fair. ?
A5 Continued: Prices vary by zip code. So throw in a geographical map as a reward for getting to the end!
Just try to understand my bewilderment when @BLS_gov says 7.9% and everyone pretends that they aren’t really raising taxes & slashing social security. You’re being screwed.
Your life savings are being stolen through seignorage as you are being taxed into oblivion with your social Security beaten to a pulp. Meanwhile @paulkrugman and Robert Reich are playing with finger paints.
If you want help, do let me know. But I can’t watch this massacre again.
Either do something to save yourselves or continue to sit & wait to be eaten by the Fed and @BLS_gov’s fakely precise single number CPI.
I’ll debate ANYONE on this high enough up for you. But I can’t watch & I’m done w economist abuse & yelling at clouds.
Thanks for asking.?