To really explain what I mean by the Asymptote, I need to explain another construct which I call “the Hypermind” ( Kawoomba’s commented motivated me to invest in the terminology :) ).
What is identity? What makes you today the same person like you yesterday? My conviction is that the essential relationship between the two is that the “you of today” shares the memories of “you of yesterday” and fully understands them. In a similar manner, if a hypothetical superintelligence Omega would learn all of your memories and understand them (you) on the same level you understand yourself, Omega should be deemed a continuation of you, i.e. it assimilated your identity into its own. Thus in the space of “moments of consciousness” in the universe we have a partial order where A < B means “B is a continuation of A” i.e. “B shares A’s memories and understands them”. The Hypermind hypothesis is that for any A and B in this space there is C s.t. C > A and C > B. This seems to me a likely hypothesis if you take into account that the Omega in the example above doesn’t have to exist in your physical vicinity but may exist anywhere in the (multi/)universe and have a simulation of you running on its laptop.
The Asymptote is then a formal limit of the Hypermind. That is, the semantics of “The Asymptote has property P” is “For any A there is B > A s.t. for any C > B, C has property P”. It is then an interesting problem to find non-trivial properties of the Asymptote. In particular, I suspect (without strong evidence yet) that the opposite of the Orthogonality Thesis is true, namely that the Asymptote has a well-defined preference / utility function
This seems like a rather simplistic view, see counter-examples below.
My conviction is
“conviction” might not be a great term, maybe what you mean is a careful conclusion based on something.
that the essential relationship between the two is that the “you of today” shares the memories of “you of yesterday”
except that we forget most of them, and that our memories of the same event change in time, and often are completely fictional.
and fully understands them.
Not sure what you mean by understanding here, feel free to define it better. For example, we often “understand” our memories differently at different times in our lives.
Thus in the space of “moments of consciousness” in the universe we have a partial order where A < B means “B is a continuation of A” i.e. “B shares A’s memories and understands them”
So, if you forgot what you had for breakfast the other day, you today are no longer a continuation of you from yesterday?
“The Asymptote has property P” is “For any A there is B > A s.t. for any C > B, C has property P”
That’s a rather non-standard definition. If anything, it’s close to monotonicity than to accumulation. If you mean the limit point, then you ought to define what you mean by a neighborhood.
To sum up, your notion of Asymptote needs a lot more fleshing out before it starts making sense.
the essential relationship between the two is that the “you of today” shares the memories of “you of yesterday”
except that we forget most of them, and that our memories of the same event change in time, and often are completely fictional.
Good point. The description I gave so far is just a first approximation. In truth, memory is far from ideal. However if we assign weight to memories by their potential impact on our thinking and decision making then I think we would get that most of the memories are preserved, at least on short time scales. So, from my point of view, the “you of today” is only a partial continuation of the “you of yesterday”. However it doesn’t essentially changing the construction of the Hypermind. It is possible to refine the hypothesis by stating that for every two “pieces of knowledge” a and b, there exists a “moment of consciousness” C s.t. C contains a and b.
“The Asymptote has property P” is “For any A there is B > A s.t. for any C > B, C has property P”
That’s a rather non-standard definition. If anything, it’s close to monotonicity than to accumulation. If you mean the limit point, then you ought to define what you mean by a neighborhood.
Actually I overcomplicated the definition. The definition should read “Exists A s.t. for any B > A, B has property P”. The neighbourhoods are sets of the form {B | B > A}. This form of the definition implies the previous form using the assumption that for any A, B there is C > A, B.
Why postulate that such a limit exists?
To really explain what I mean by the Asymptote, I need to explain another construct which I call “the Hypermind” ( Kawoomba’s commented motivated me to invest in the terminology :) ).
What is identity? What makes you today the same person like you yesterday? My conviction is that the essential relationship between the two is that the “you of today” shares the memories of “you of yesterday” and fully understands them. In a similar manner, if a hypothetical superintelligence Omega would learn all of your memories and understand them (you) on the same level you understand yourself, Omega should be deemed a continuation of you, i.e. it assimilated your identity into its own. Thus in the space of “moments of consciousness” in the universe we have a partial order where A < B means “B is a continuation of A” i.e. “B shares A’s memories and understands them”. The Hypermind hypothesis is that for any A and B in this space there is C s.t. C > A and C > B. This seems to me a likely hypothesis if you take into account that the Omega in the example above doesn’t have to exist in your physical vicinity but may exist anywhere in the (multi/)universe and have a simulation of you running on its laptop.
The Asymptote is then a formal limit of the Hypermind. That is, the semantics of “The Asymptote has property P” is “For any A there is B > A s.t. for any C > B, C has property P”. It is then an interesting problem to find non-trivial properties of the Asymptote. In particular, I suspect (without strong evidence yet) that the opposite of the Orthogonality Thesis is true, namely that the Asymptote has a well-defined preference / utility function
This seems like a rather simplistic view, see counter-examples below.
“conviction” might not be a great term, maybe what you mean is a careful conclusion based on something.
except that we forget most of them, and that our memories of the same event change in time, and often are completely fictional.
Not sure what you mean by understanding here, feel free to define it better. For example, we often “understand” our memories differently at different times in our lives.
So, if you forgot what you had for breakfast the other day, you today are no longer a continuation of you from yesterday?
That’s a rather non-standard definition. If anything, it’s close to monotonicity than to accumulation. If you mean the limit point, then you ought to define what you mean by a neighborhood.
To sum up, your notion of Asymptote needs a lot more fleshing out before it starts making sense.
Good point. The description I gave so far is just a first approximation. In truth, memory is far from ideal. However if we assign weight to memories by their potential impact on our thinking and decision making then I think we would get that most of the memories are preserved, at least on short time scales. So, from my point of view, the “you of today” is only a partial continuation of the “you of yesterday”. However it doesn’t essentially changing the construction of the Hypermind. It is possible to refine the hypothesis by stating that for every two “pieces of knowledge” a and b, there exists a “moment of consciousness” C s.t. C contains a and b.
Actually I overcomplicated the definition. The definition should read “Exists A s.t. for any B > A, B has property P”. The neighbourhoods are sets of the form {B | B > A}. This form of the definition implies the previous form using the assumption that for any A, B there is C > A, B.
Hmm, it seems like your definition of Asymptote is nearly that of a limit ordinal.