3 ms·

I know that one: 1, 2, 4, 8, 16, 31... https://oeis.org/A001591 https://oeis.org/A001591

jonathanstrange 6y ago
Off-topic but this made me wonder. As the name implies, Solomonoff Induction only works for inductive inference from empirical data. Is there something similar for mathematics that would allow us to list the simplest sequences first, then more complex sequences, and so on? Or does the complexity of the formulation of a sequence depend on the choice of a foundation of mathematics and/or arbitrary conventions?
- FeepingCreature 6y ago
  Why not do the same thing? Run a dovetailer, print sequences that terminate... (Dovetailer: for all n from 0 up, for all m from 0 to n, treat m as a Turing machine and run it for n steps. If it halts, yield its output.)
- yters 6y ago
  why wouldnt solomonoff induction work for number sequences?
- qnsi 6y ago
  sorry this is also offtopic. Saw your link 2 years ago to https://sites.google.com/view/lvu18lisbon https://sites.google.com/view/lvu18lisbon can you recommend some decision theory reading? Maybe more on a practical side?
  - jonathanstrange 6y ago
    Depends on what you're interested in and your level of mathematical maturity. I assume you're interested in real-world, actually applied decision making rather than philosophical debates, right? Then you have to look for multicriteria decision making (MCDM) and multi-attribute utility theory (MAUT). Eisenführ/Weber/Langer: Rational Decision Making. Springer 2010. This is a good practical introduction in the standard methodology. Keeney/Raiffa: Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley & Sons 1976. This is an older work, but very good. It's mathematically more rigorous and important if you want to understand additive and multiplicative models. Both of them are practical and give good examples. The first one is easier to read. If you're not afraid of more complicated mathematics, I can also give you some more other references. I guess you wouldn't be asking me then, however, because there is plenty of sources. I generally recommend Peter C. Fishburn's work, insofar as I can understand it -- some of it is too hard for me.
    - qnsi 6y ago
      thank you so much for taking time to reply! it really means a lot and I will follow your recommendations

Off-topic but this made me wonder. As the name implies, Solomonoff Induction only works for inductive inference from empirical data. Is there something similar for mathematics that would allow us to list the simplest sequences first, then more complex sequences, and so on? Or does the complexity of the formulation of a sequence depend on the choice of a foundation of mathematics and/or arbitrary conventions?

FeepingCreature 6y ago
Why not do the same thing? Run a dovetailer, print sequences that terminate... (Dovetailer: for all n from 0 up, for all m from 0 to n, treat m as a Turing machine and run it for n steps. If it halts, yield its output.)
yters 6y ago
why wouldnt solomonoff induction work for number sequences?
qnsi 6y ago
sorry this is also offtopic. Saw your link 2 years ago to https://sites.google.com/view/lvu18lisbon https://sites.google.com/view/lvu18lisbon can you recommend some decision theory reading? Maybe more on a practical side?
- jonathanstrange 6y ago
  Depends on what you're interested in and your level of mathematical maturity. I assume you're interested in real-world, actually applied decision making rather than philosophical debates, right? Then you have to look for multicriteria decision making (MCDM) and multi-attribute utility theory (MAUT). Eisenführ/Weber/Langer: Rational Decision Making. Springer 2010. This is a good practical introduction in the standard methodology. Keeney/Raiffa: Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley & Sons 1976. This is an older work, but very good. It's mathematically more rigorous and important if you want to understand additive and multiplicative models. Both of them are practical and give good examples. The first one is easier to read. If you're not afraid of more complicated mathematics, I can also give you some more other references. I guess you wouldn't be asking me then, however, because there is plenty of sources. I generally recommend Peter C. Fishburn's work, insofar as I can understand it -- some of it is too hard for me.
  - qnsi 6y ago
    thank you so much for taking time to reply! it really means a lot and I will follow your recommendations