5 ms·

> That's not true. To give a trivial example, a set or sequence of numbers is composed of numbers but is not itself a number. 2 is a number, but {2,3,4} is not

> That's not true. To give a trivial example, a set or sequence of numbers is composed of numbers but is not itself a number. 2 is a number, but {2,3,4} is not a number. That's still a number because everything in a digital computer is a number or an operation on a number. Sets are often encoded by binary bit strings and boolean operations on bitstrings then have a corresponding denotation as union, intersection, product, exponential, powerset, and so on.

skissane 2y ago
> That's still a number because everything in a digital computer is a number or an operation on a number. I feel like in this conversation you are equivocating over distinct but related concepts that happen to have the same name. For example, “numbers” in mathematics versus “numbers” in computers. They are different things - e.g. there are an infinite number of mathematical numbers but only a finite number of computer numbers - even considering bignums, there are only a finite number of bignums, since any bignum implementation only supports a finite physical address space. In mathematics, a set of numbers is not itself number. What about in digital computers? Well, digital computers don’t actually contain “numbers”, they contain electrical patterns which humans interpret as numbers. And it is a true that at that level of interpretation, we call those patterns “numbers”, because we see the correspondence between those patterns and mathematical numbers. However, is it true that in a computer, a set of numbers is itself a number? Well, if I was storing a set of 8 bit numbers, I’d store them each in consecutive bytes, and I’d consider each to be a separate 8-bit number, not one big 8n-bit number. Of course, I could choose to view them as one big 8n-bit number - but conversely, any finite set of natural numbers can be viewed as a single natural number (by Gödel numbering); indeed, any finite set of computable or definable real numbers can be viewed as a single natural number (by similar constructions)-indeed, by such constructions even infinite sets of natural or real numbers can be equated to natural numbers, provided the set is computable/definable. However, “can be viewed as” is not the same thing as “is”. Furthermore, whether a sequence of n 8-bit numbers is n separate numbers or a single 8n-bit number is ultimately a subjective or conventional question rather than an objective one - the physical electrical signals are exactly the same in either case, it is just our choice as to how to interpret them
- soloist11 2y ago
  > However, “can be viewed as” is not the same thing as “is” Ultimate reality is fundamentally unknowable but what I said about computers and digital circuits is correct. We have a formal theory of computers and that is why we can construct them in factories. There is no such theory for people or the biosphere which is why when someone argues for intentionality or some other attribute possessed by both people and computers I discount whatever they are saying unless they can formally specify how some formal statement in a logical syntax (program) corresponds to the same attribute in people and animals. This confusion between formal theories and informal concepts like intentionality is why I am generally wary of anyone who claims computers can think and possess intelligence. The ultimate endpoint of this line of reasoning is complete annihilation of the biosphere and its replacement with factories producing nothing but computers and power plants for shuttling electrons. The people who believe computers are a net positive might not think this way but by equating computers with people they are ultimately devaluing the irreducible complexity of what it means to be a living animal (person) in an ecology with irreducible properties and attributes. I'm obviously not going to convince anyone who believes computers and algorithms can think and possess intelligence but it is clear to me that by elevating digital computers above biology and ecology they are devaluing their own humanity and justifying actions which will ultimately end in disaster.
  - skissane 2y ago
    > We have a formal theory of computers and that is why we can construct them in factories. Formal theories and physical manufacturability are two different things, with no necessary connection with each other. People have been manufacturing tools for thousands of years without having any “formal theory” for them. People were making swords and pots and pans and furniture and carts and chariots long before the concept of “formal theory” had ever been invented. Conversely, one can easily construct formal theories of computers which are formally completely coherent and yet physically impossible to construct (such as Turing machines with oracles, or computers that can execute supertasks). I’d even question whether formal theories of computation (Turing, Church, etc) were actually that relevant to the development of real world computers. One can imagine an alternate timeline in which computers were developed but theoretical computer science saw far less development as a discipline than in ours. The lack of theoretical development no doubt would have had some practical drawbacks at some point, but they still might have gone a long way without it. I mean, you can do a course in theoretical computer science and have no idea how to actually build a CPU, and conversely you can do a course in computer engineering and actually build a CPU yet have zero idea about what Turing machines or lambda calculus is. The theory actually has far less practical relevance than most theoreticians claim > The ultimate endpoint of this line of reasoning is complete annihilation of the biosphere and its replacement with factories producing nothing but computers and power plants for shuttling electrons. The people who believe computers are a net positive A very alarmist take. Personally I am at least open-minded about the possibility of an AI having human-like consciousness/intentionality, at least in theory. But even if we could build such an AI in theory, I’m not sure whether it would be a good idea in practice. And I absolutely am opposed to any proposal to destroy the biological environment and replace it with electronics. Some people may well be purveyors of mind-uploading/simulationist woo, but I’m not. Interesting philosophical speculations but no interest in making them a reality (and I think their actual technological feasibility, if it ever happens at all, is long after we are all dead)

skissane 2y ago

> That's still a number because everything in a digital computer is a number or an operation on a number. I feel like in this conversation you are equivocating over distinct but related concepts that happen to have the same name. For example, “numbers” in mathematics versus “numbers” in computers. They are different things - e.g. there are an infinite number of mathematical numbers but only a finite number of computer numbers - even considering bignums, there are only a finite number of bignums, since any bignum implementation only supports a finite physical address space. In mathematics, a set of numbers is not itself number. What about in digital computers? Well, digital computers don’t actually contain “numbers”, they contain electrical patterns which humans interpret as numbers. And it is a true that at that level of interpretation, we call those patterns “numbers”, because we see the correspondence between those patterns and mathematical numbers. However, is it true that in a computer, a set of numbers is itself a number? Well, if I was storing a set of 8 bit numbers, I’d store them each in consecutive bytes, and I’d consider each to be a separate 8-bit number, not one big 8n-bit number. Of course, I could choose to view them as one big 8n-bit number - but conversely, any finite set of natural numbers can be viewed as a single natural number (by Gödel numbering); indeed, any finite set of computable or definable real numbers can be viewed as a single natural number (by similar constructions)-indeed, by such constructions even infinite sets of natural or real numbers can be equated to natural numbers, provided the set is computable/definable. However, “can be viewed as” is not the same thing as “is”. Furthermore, whether a sequence of n 8-bit numbers is n separate numbers or a single 8n-bit number is ultimately a subjective or conventional question rather than an objective one - the physical electrical signals are exactly the same in either case, it is just our choice as to how to interpret them

soloist11 2y ago
> However, “can be viewed as” is not the same thing as “is” Ultimate reality is fundamentally unknowable but what I said about computers and digital circuits is correct. We have a formal theory of computers and that is why we can construct them in factories. There is no such theory for people or the biosphere which is why when someone argues for intentionality or some other attribute possessed by both people and computers I discount whatever they are saying unless they can formally specify how some formal statement in a logical syntax (program) corresponds to the same attribute in people and animals. This confusion between formal theories and informal concepts like intentionality is why I am generally wary of anyone who claims computers can think and possess intelligence. The ultimate endpoint of this line of reasoning is complete annihilation of the biosphere and its replacement with factories producing nothing but computers and power plants for shuttling electrons. The people who believe computers are a net positive might not think this way but by equating computers with people they are ultimately devaluing the irreducible complexity of what it means to be a living animal (person) in an ecology with irreducible properties and attributes. I'm obviously not going to convince anyone who believes computers and algorithms can think and possess intelligence but it is clear to me that by elevating digital computers above biology and ecology they are devaluing their own humanity and justifying actions which will ultimately end in disaster.
- skissane 2y ago
  > We have a formal theory of computers and that is why we can construct them in factories. Formal theories and physical manufacturability are two different things, with no necessary connection with each other. People have been manufacturing tools for thousands of years without having any “formal theory” for them. People were making swords and pots and pans and furniture and carts and chariots long before the concept of “formal theory” had ever been invented. Conversely, one can easily construct formal theories of computers which are formally completely coherent and yet physically impossible to construct (such as Turing machines with oracles, or computers that can execute supertasks). I’d even question whether formal theories of computation (Turing, Church, etc) were actually that relevant to the development of real world computers. One can imagine an alternate timeline in which computers were developed but theoretical computer science saw far less development as a discipline than in ours. The lack of theoretical development no doubt would have had some practical drawbacks at some point, but they still might have gone a long way without it. I mean, you can do a course in theoretical computer science and have no idea how to actually build a CPU, and conversely you can do a course in computer engineering and actually build a CPU yet have zero idea about what Turing machines or lambda calculus is. The theory actually has far less practical relevance than most theoreticians claim > The ultimate endpoint of this line of reasoning is complete annihilation of the biosphere and its replacement with factories producing nothing but computers and power plants for shuttling electrons. The people who believe computers are a net positive A very alarmist take. Personally I am at least open-minded about the possibility of an AI having human-like consciousness/intentionality, at least in theory. But even if we could build such an AI in theory, I’m not sure whether it would be a good idea in practice. And I absolutely am opposed to any proposal to destroy the biological environment and replace it with electronics. Some people may well be purveyors of mind-uploading/simulationist woo, but I’m not. Interesting philosophical speculations but no interest in making them a reality (and I think their actual technological feasibility, if it ever happens at all, is long after we are all dead)