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> In theory, there is no domain (or finite set of domains) that cannot be accurately modeled using tuples of things and their relations. That seems right to me

> In theory, there is no domain (or finite set of domains) that cannot be accurately modeled using tuples of things and their relations. That seems right to me, but is it really provably true?

Scarblac 3y ago
At least, if it can be modelled by some type of finite database stored on disk or in memory, then you can store the entire contents of that database as one binary blob. Now you just need one tuple ("our_system", "the_db", the_binary_blob) QED :)
bob1029 3y ago
Provably? I'll leave that up to the academics. Practically? I've never had someone throw a problem at me I couldn't model in SQL. Not saying I can guarantee performance, but in terms of abstract modeling I've never encountered something that can't be done "clean". I'd like to use the analogy of painting. What can't you paint on that canvas that isn't trivially-hindered by the available media? Can you actually describe that space of things? In my estimation, premature optimization is why most people can't work in these terms. You wind up with a tuple like WorldObjects and immediately go off the deep end about a billion row scale before you are done naming things.
Legend2440 3y ago
No. Many real domains like natural language are too complex and fuzzy to accurately model with tuples. To be truly universal, your model needs to be computationally stronger - it needs to be turing complete. For example fractals could never be modeled by any number of tuples, but can be perfectly represented by very short computer programs.
- Mikhail_Edoshin 3y ago
  Can a program be modeled by a finite number of tuples?
  - bostik 3y ago
    Probably yes, but for any program of sufficient complexity, that finite number may have an inconvenient number of digits.
  - Legend2440 3y ago
    The program's output and behavior can't. The source code can.
kaba0 3y ago
I think there is some "Turing-completeness" for this category as well, that is quite trivial to achieve, though the practical usability may be negligible. One hacky equivalence I can come up with is that you have a tuple with a single string value, and encode something in that string.
refset 3y ago
Maybe https://plato.stanford.edu/entries/relations/ https://plato.stanford.edu/entries/relations/
Kinrany 3y ago
This is not the right question. A Turing machine can model any algorithm, but no one uses Turing machines in practice.

> In theory, there is no domain (or finite set of domains) that cannot be accurately modeled using tuples of things and their relations. That seems right to me, but is it really provably true?

Scarblac 3y ago

At least, if it can be modelled by some type of finite database stored on disk or in memory, then you can store the entire contents of that database as one binary blob. Now you just need one tuple ("our_system", "the_db", the_binary_blob) QED :)

bob1029 3y ago

Provably? I'll leave that up to the academics. Practically? I've never had someone throw a problem at me I couldn't model in SQL. Not saying I can guarantee performance, but in terms of abstract modeling I've never encountered something that can't be done "clean". I'd like to use the analogy of painting. What can't you paint on that canvas that isn't trivially-hindered by the available media? Can you actually describe that space of things? In my estimation, premature optimization is why most people can't work in these terms. You wind up with a tuple like WorldObjects and immediately go off the deep end about a billion row scale before you are done naming things.

Legend2440 3y ago

No. Many real domains like natural language are too complex and fuzzy to accurately model with tuples. To be truly universal, your model needs to be computationally stronger - it needs to be turing complete. For example fractals could never be modeled by any number of tuples, but can be perfectly represented by very short computer programs.

Mikhail_Edoshin 3y ago
Can a program be modeled by a finite number of tuples?
- bostik 3y ago
  Probably yes, but for any program of sufficient complexity, that finite number may have an inconvenient number of digits.
- Legend2440 3y ago
  The program's output and behavior can't. The source code can.

kaba0 3y ago

I think there is some "Turing-completeness" for this category as well, that is quite trivial to achieve, though the practical usability may be negligible. One hacky equivalence I can come up with is that you have a tuple with a single string value, and encode something in that string.

refset 3y ago

Maybe https://plato.stanford.edu/entries/relations/ https://plato.stanford.edu/entries/relations/

Kinrany 3y ago

This is not the right question. A Turing machine can model any algorithm, but no one uses Turing machines in practice.