alt Hacker NewsGood point! Maybe indexing is a bad term here, and it's more like feature extraction (and since embeddings are high dimensional we extract a lot of features). From that point of view it makes sense that "the index" takes more space than the original data.
Why would the embeddings be higher dimensionally than the data? I imagine the embeddings would contain relatively higher entropy (and thus lower redundancy) than many types of source data.