this post was submitted on 28 May 2024
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I’m not an Information Theory guy, but I am aware that, regardless of how clever one might hope to be, there is a theoretical limit on how compressed any given set of information could possibly be; and this is particularly true for the lossless compression demanded by this challenge.
Quote from the article:
The skepticism is well-founded, said Karl Martin, chief technology officer of data science company Integrate.ai. Martin's PhD thesis at the University of Toronto focused on data compression and security.
Neuralink's brainwave signals are compressible at ratios of around 2 to 1 and up to 7 to 1, he said in an email. But 200 to 1 "is far beyond what we expect to be the fundamental limit of possibility."
The implication of a 200 to 1 algorithm would be that the data they're collecting is almost entirely noise. Specifically that 99.5% of all the data is noise. In theory if they had sufficient processing in the implant they could filter the data down before transmission thus reducing the bandwidth usage by 99.5%. It seems like it would be fairly trivial to prove that any such 200 to 1 compression algorithm would be indistinguishable in function from a noise filter on the raw data.
It's not quite the same situation, but this should show some of the issues with this: https://matt.might.net/articles/why-infinite-or-guaranteed-file-compression-is-impossible/
Ugh? That's not what it means at all. Compression saves on redundant data, but it doesn't mean that data is noise. Or are you using some definition of noise I'm not aware of?
I can try to explain, but there are people who know much more about this stuff than I do, so hopefully someone more knowledgeable steps in to check my work.
What does ‘random’ or ‘noise’ mean? In this context, random means that any given bit of information is equally as likely to be a 1 or a 0. Noise means a collection of information that is either random or unimportant/non-useful.
So, you say “Compression saves on redundant data”. Well, if we think that through, and consider the definitions I’ve given above, we will reason that ‘random noise’ either doesn’t have redundant information (due to the randomness), or that much of the information is not useful (due to its characteristic as noise).
I think that’s what the person is describing. Does that help?
I agree with your point, but you're arguing that noise can be redundant data. I am arguing that redundant data is not necessarily noise.
In other words, a signal can never be filtered losslessly. You can slap a low pass filter in front of the signal and call it a day, but there's loss, and if lossless is a hard requirement then there's absolutely nothing you can do but work on compressing redundant data through e.g. patterns, interpolation, what have you (I don't know much about compression algos).
A perfectly noise free signal is arguably easier to compress actually as the signal is more predictable.