The way to quantify it is to see what has been printed, the amount of money supply that has increased in a year.
Indeed. That's the most accurate approximation, in my opinion. But inflation is more complex than that. I think that, money supply plays the biggest role, but the government can influence with taxes and subsidies, as well. So, it'd still be false to rigorously treat money printing as the only variable of the complex equation that is inflation.
Imho something fixed should be used as an unit of measure, like for everything else (maybe like the good old international prototype of kg was). But what?
I believe the fundamental flaw lies in trying to quantify inflation. The reason is that there are simply too many variables to account for. In fields like physics or chemistry, quantification works because complex information can be simplified into equations. However, economics is not an exact science where you can conduct experiments or verify outcomes in the same way.
As I have made clear, even if we assume that we know
everything about the economy, inflation remains a questionable metric of value. This is because I might rely on goods and services that have increased in price far more than the average. If inflation isn't a useful measure on an individual level, perhaps it holds more value collectively-- such as when assessing the average prosperity of a population. However, certain products are simply more essential and have inelastic demand compared to others. How can your equation account for this?
For example, olive oil may represent a relatively small portion of the market, but it is essential for most people. Even if every other good in the economy experiences 0% inflation, a 300% rise in the price of olive oil would barely impact overall inflation, yet it would be deeply felt by the majority of people.
If you think about it, every metric in economics carries a significant degree of unreliability on how accurately it represents what it presumably measures; inflation, minimum wage, unemployment rate, gross domestic product, consumer price index, interest rates, tax rates. Every measure is the result of humans trying to quantify the economy. This overconfidence, coupled with a lack of humility in believing we can fully understand and predict human behavior, is undoubtedly, in my view, why these metrics are inherently flawed and fallible.