If we measure a basket of 1,000 products that is direction and magnitude in a 1,000 dimension space. Those are not the important things of that vector. What's important is that we have 1,000 measurements of inflation for 1,000 different products. One of the points of the article is that it could be possible to collapse that vector into a single scalar number as governments do, but it usually isn't because the variance between each component is too big and makes that number meaningless.

And yet it's useful to be able to tell my customers that I have to raise my fee because of a 6% inflation instead of "gas went up 20%", "but clothing went down 5%."