Lambda the Ultimate

My impression of this business of named tensors is that it's another form of the units of measure feature that comes up from time to time in PL design, either in statically or dynamically typed form. Though that in itself may say something about the nature of thought versus computation.

Truthfully, I don't grok tensors. I consider it a major gap in my mathematical toolkit. From what I've heard, I'm not alone in not grokking them, either. I've been stuck partway through Penrose's Road to Reality for several years, now, because I decided his overview of tensors just wasn't enough for me to move on past, and I was going to need to go off and get a feel for them elsewhere and come back (by now, I s'pose I'd have to start over from the beginning). So far, for all the explanations of tensors I've read, I haven't got a handle on them. Though I've got a new appreciation of the difference between reading a textbook and taking a well-taught class based on a textbook.

Interesting that The Morning Paper picked a paper that highlights a similar issue:

Machine Learning Systems are stuck in a rut

For example:

Named dimensions improve readability by making it easier to determine how dimensions in the code correspond to the semantic dimensions described in, .e.g., a research paper.

This is a good idea. When I read "named tensor", my mind interprets it as "tensor that's been given a name" (as in "named baby") and not as "tensor with named dimensions" (perhaps "baby with named arms and legs"?). I can't seem to think of a better name though.

On the other hand, do we need a new name for this? I think it would be better if we just called them "tensors" and augmented the old API to support string-named dimensions as well as integer-named dimensions. Would that work?

Is not this a relation/table?

This exactly why I'm aiming at my own little lang (http://tablam.org). I have explored using a NDArray as core internal type. And each relation have a schema (so all is named).

I hope to provide things like:


city ?where .population > 100_000 ?select .name, .country
points ?sort .x


For numerical indexes:


city ?where #3 > 100_000 ?select #1, #2
points ?sort .#1
city # 1


One of the things that made Lotus Improv much superior to Lotus 123 and its descendants is that instead of giant 2D sheets with numbered rows and columns, it has arbitrary-dimensionality cubes with named dimensions and named entries.

Similarly, the database language D beats SQL which beats Codd's original RA, because D gives all attributes of a relation unique names, SQL gives them non-unique names, and Codd's model has only positional labels.

While Improv is defunct, Quantrix Modeler is not, but unfortunately it costs $.