When you shorten a description in a lossy way, you are deciding a priori that some differences in the object don't matter, and it's not because you understand the object, but because it serves your goal of shortening the description.
You can't just assume smaller is better but it often is. And very often it's more information-dense.
A compression program can compress a book written in a language that the author of the program doesn't understand, on a topic he knows little about.
I think "losslessly even" is the wrong way to think about it. Lossless compression often requires less understanding than high quality lossy compression. If you can do a lossy compression that correctly decides what details are unimportant, that's a good sign of understanding.
This is the crux and reminds me of things like mp3 that exploit the nature of human hearing being limited to a frequency range.
But it's frankly a philosophical question what's real or not. No model is going to capture absolutely everything about the thing it models - at that point, it would be the thing. The best we can hope for is that it captures everything we care about.
And no experiment or metric can tell you if you care about the right things. At best it can tell us if we care about a thing given other things we care about. "No cares in, no cares out".
To make it a little more concrete: you could compress a string from back to front. You could build an LLM to help you do that. If you care about file size, that's almost certainly a bad idea, the forward LLM will be better for that purpose. But are there purposes for which the backward LLM might be better? I think that's not so hard to imagine. Often we wonder about "what came before".
I mean, my interpretation is that the question Turing tried to answer is equivalent to "How can we determine whether machines understand humans/human thought?"
This only works when both systems can talk about pretty much arbitrary things, but if you want a more general method for less complex systems, perhaps having one system simulate another system is sufficient. (Which is also another Turing invention)
At this point, I am unaware of a better definition. I know the Chinese Room argument (and I disagree with it), but I'm not aware whether the proponents of that argument have a better definition of understanding other than "well, the Turing Test isn't enough"...
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PS: Interestingly the issue of compression is highly relevant regarding the Chinese Room argument -- the essential element in the Chinese Room argument is that the information is not compressed...
No. Teaching is compression. Understanding and application is decompression.
You don't memorize the specific details, you memorize the flow of systems. But you get back to the details to put things into practice.
So was I.
> One decompress it when they can generalize and apply it.
Generalizing is compression. Generalizing and applying are very different things.
> So understanding is compressed, but is not the act of compressing.
Understanding (noun) is compressed. Understanding (verb) is the act of creating understanding (noun) and is compression.
> The larger data it represents never existed.
The larger data is everything you take in about the subject. Experience and instruction.
What is it compressing from?