4 ms·

That makes you a bread-oracle O, but doesn't define bread. Since there are some inputs x where O(x0) = False, some where O(x1) = True, and the laws of physics

That makes you a bread-oracle O, but doesn't define bread. Since there are some inputs x where O(x0) = False, some where O(x1) = True, and the laws of physics are continuous(yes, even in quantum mechanics), Buridan's Principle implies that you are incapable of deciding the breadness of arbitrary input in bounded time.

whatshisface 5y ago
I agree that I cannot decide the breadness of arbitrary inputs in bounded time, although I contend that does not stop me from claiming to have defined bread, on the grounds that the set of Turing machines that halt is well-defined but also has the same difficulty you're describing.
- MichaelBurge 5y ago
  A definition doesn't change: The prime numbers or Turing Machines are the same set regardless of who Putin invades next or what law Biden decides to veto. But the set of inputs that an oracle implicitly defines, could change if the oracle changes. And you could change your mind or die tomorrow. So you would need a very large number of definitions of bread, indexed by (time, person). Any one of them could be a valid definition - it's theoretically possible to make you look at 1000 pictures of bread so your brain is encouraged to make a bread-detector neuron, and then scan your brain and calculate its response on any input - but you don't know which one is correct to use for any purpose. i.e. If I want to start a bakery, should I use your current bread-oracle to define "marketable bread", your bread-oracle as of 5 years ago, should I take a statistical ensemble of brain scans from millions of people, or should I use my own? It seems like just having a function that returns true on some inputs and false on others doesn't tell you much, whereas traditional mathematical definitions have strict relations to other things.
  - gryn 5y ago
    > A definition doesn't change but they do, the definition of many words changed over time some to even start to mean the opposite of what they initially did.
    - deleted 5y ago
      [deleted]
addaon 5y ago
I don't think this is true? Suppose I define "bread" as "that which has a net positive charge" [1]. Can I not put the bread candidate in an electric field in flat spacetime and measure (the direction of) its acceleration in a bounded time? I suppose I might be depending on its mass being finite, but the observable universe supports that assumption. [1] I don't think this is a very useful definition of bread.
- MichaelBurge 5y ago
  The original paper in Section 6 looks at the case of a magnetic field: https://lamport.azurewebsites.net/pubs/buridan.pdf https://lamport.azurewebsites.net/pubs/buridan.pdf It's a practical issue that affects CPU design, which is also mentioned in the paper under the name "Arbiter Problem".

whatshisface 5y ago

I agree that I cannot decide the breadness of arbitrary inputs in bounded time, although I contend that does not stop me from claiming to have defined bread, on the grounds that the set of Turing machines that halt is well-defined but also has the same difficulty you're describing.

MichaelBurge 5y ago
A definition doesn't change: The prime numbers or Turing Machines are the same set regardless of who Putin invades next or what law Biden decides to veto. But the set of inputs that an oracle implicitly defines, could change if the oracle changes. And you could change your mind or die tomorrow. So you would need a very large number of definitions of bread, indexed by (time, person). Any one of them could be a valid definition - it's theoretically possible to make you look at 1000 pictures of bread so your brain is encouraged to make a bread-detector neuron, and then scan your brain and calculate its response on any input - but you don't know which one is correct to use for any purpose. i.e. If I want to start a bakery, should I use your current bread-oracle to define "marketable bread", your bread-oracle as of 5 years ago, should I take a statistical ensemble of brain scans from millions of people, or should I use my own? It seems like just having a function that returns true on some inputs and false on others doesn't tell you much, whereas traditional mathematical definitions have strict relations to other things.
- gryn 5y ago
  > A definition doesn't change but they do, the definition of many words changed over time some to even start to mean the opposite of what they initially did.
  - deleted 5y ago
    [deleted]

addaon 5y ago

I don't think this is true? Suppose I define "bread" as "that which has a net positive charge" [1]. Can I not put the bread candidate in an electric field in flat spacetime and measure (the direction of) its acceleration in a bounded time? I suppose I might be depending on its mass being finite, but the observable universe supports that assumption. [1] I don't think this is a very useful definition of bread.

MichaelBurge 5y ago
The original paper in Section 6 looks at the case of a magnetic field: https://lamport.azurewebsites.net/pubs/buridan.pdf https://lamport.azurewebsites.net/pubs/buridan.pdf It's a practical issue that affects CPU design, which is also mentioned in the paper under the name "Arbiter Problem".