... assuming that tables allowed for nested non-primitive values.

I'm trying to think of any instance where data cannot be represented as tables (or a series of tables)... and I can't think of any. However, I'm skeptical of myself on this one... its seems too simple to defined a pseudo-law which state "all data can be represented as tables".

Can anybody think of instances where this isn't true?

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    $\begingroup$ Just make a 1x1 table and put your data in it $\endgroup$ – theonlygusti Nov 7 '20 at 20:57

One way or another any data can be represented in a table or even in a big binary string, since after all the physical memory of a computer is just one big binary sequence. But the question is whether the table format adequately represents the semantics of any data, and the answer is definitely no: while there are tabular representations for graphs, text, images or videos, these representations simplify and/or make assumptions about the nature of the data. Virtually any representation is a simplification of the data it represents, but some representations are more faithful to the original data than others.

  • $\begingroup$ what an amazing answer with so much content in not so many words $\endgroup$ – German C M Nov 9 '20 at 14:00
  • $\begingroup$ @GermanCM thank you! It's funny, I didn't expect this answer to receive much attention. In retrospect I think I was influenced by my vague memories of linguistics, where the distinction representation vs. meaning is a fundamental principle. $\endgroup$ – Erwan Nov 9 '20 at 15:48
  • $\begingroup$ Actually this is faulty: some data cannot be represented in a table. For example a continuous function cannot be represented in a table. As the table loses information on what happens between the "points". The function itself holds the information. -- I'm wondering however if the OP also would consider this, or only discrete "data" and not the more general idea of information/data. $\endgroup$ – paul23 Nov 9 '20 at 16:09
  • $\begingroup$ @paul23 you're right, in my answer I assumed that OP was talking about data as a discrete subset of some original data. $\endgroup$ – Erwan Nov 9 '20 at 17:20

Not sure that's impossible but some data is inherently hard to represent tabularly :

  • Cloud points like the ones processed in this paper : https://arxiv.org/pdf/1612.00593.pdf Similarly time series with variable sampling frequencies
  • Graphs that evolve in time like the relations in a social network

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