This may just be my physical science education speaking, but adding two quantities of unit “sheep” and getting a quantity of unit “sheep” and a quantity of unit “sheep interaction” bothers me immensely. In every situation I’ve ever encountered where quantities were added, and I trusted whoever was doing the adding to have a very good understanding of when you get to describe something as “addition”, the resulting quantity had strictly the same dimensions as the originals. Whatever’s going on here, it’s probably not best described as addition (as Bundle so wonderfully explained).
It’s not the abstract process of addition. It’s an entirely different way of counting reality; the abstract processes are necessarily different.
It’s very close to addition, though, and may reflect reality better than addition. Could you work with a mathematical system in which new units come apparently out of nowhere?
If you’re not talking about addition, then why in the name of Odin’s glorious beard did you use phrases like “+”, “addition”, and “counting” in reference to whatever this mathematical operation is? I hope you can imagine why that would be horribly confusing to us. You’d have to specify what this operation is before I contemplate the relation between its input units and output units.
I believe that was the point the article was attempting to get across. To my impression, OrphanWilde seems to be attempting to convey a concept he does not yet fully understand for which there have not yet been any formalizations and/or for which no words or accurate english/human-linguistic description exists.
My own interpretation tends towards a “feeling” of the following being an approximate description of this operation: “model the first element, model the second element, model the joining of these two elements, model the two elements as a whole of ‘firstandsecondelement’”
To me, this seems clearly nonequal to “first element” + “second element”, but I’d also agree that not mentioning this crucial distinction is confusing.
Reread my post. I didn’t use them in reference to that mathematical operation, except in the end, where the problem domain would be different (and hence the operators could conceivably mean something different). I in fact said that “Which is not to say that one plus one does not equal two. It is, however, to say that one plus one may not be meaningful as a concept outside a very limited domain.”
I -did- do this in my response to you, because the confusion was in a sense important; you can’t outright deny the existence of sheep interactions, you can only point out that this isn’t addition. Which allowed me to make this point: “It’s very close to addition… and may reflect reality better than addition.”
I’m not attempting to define this operation, only present its conceivable existence. There are two points to this post: First, that any defined subset of mathematics is not universal. (That is, mathematics is not in fact a universal language, any more than “Language” is a universal language.) Second, that any defined subset of mathematics is a nonideal representation of reality, and that it would frankly be surprising if an advanced intelligence chose to use the same mathematics we chose through our biased processes.
In terms of units, 1 sheep + 1 sheep = 2 sheep + sheep interaction.
The additional sheep adds more to the field than another quantitative sheep.
This may just be my physical science education speaking, but adding two quantities of unit “sheep” and getting a quantity of unit “sheep” and a quantity of unit “sheep interaction” bothers me immensely. In every situation I’ve ever encountered where quantities were added, and I trusted whoever was doing the adding to have a very good understanding of when you get to describe something as “addition”, the resulting quantity had strictly the same dimensions as the originals. Whatever’s going on here, it’s probably not best described as addition (as Bundle so wonderfully explained).
That’s deliberate.
It’s not the abstract process of addition. It’s an entirely different way of counting reality; the abstract processes are necessarily different.
It’s very close to addition, though, and may reflect reality better than addition. Could you work with a mathematical system in which new units come apparently out of nowhere?
If you’re not talking about addition, then why in the name of Odin’s glorious beard did you use phrases like “+”, “addition”, and “counting” in reference to whatever this mathematical operation is? I hope you can imagine why that would be horribly confusing to us. You’d have to specify what this operation is before I contemplate the relation between its input units and output units.
I believe that was the point the article was attempting to get across. To my impression, OrphanWilde seems to be attempting to convey a concept he does not yet fully understand for which there have not yet been any formalizations and/or for which no words or accurate english/human-linguistic description exists.
My own interpretation tends towards a “feeling” of the following being an approximate description of this operation: “model the first element, model the second element, model the joining of these two elements, model the two elements as a whole of ‘firstandsecondelement’”
To me, this seems clearly nonequal to “first element” + “second element”, but I’d also agree that not mentioning this crucial distinction is confusing.
Reread my post. I didn’t use them in reference to that mathematical operation, except in the end, where the problem domain would be different (and hence the operators could conceivably mean something different). I in fact said that “Which is not to say that one plus one does not equal two. It is, however, to say that one plus one may not be meaningful as a concept outside a very limited domain.”
I -did- do this in my response to you, because the confusion was in a sense important; you can’t outright deny the existence of sheep interactions, you can only point out that this isn’t addition. Which allowed me to make this point: “It’s very close to addition… and may reflect reality better than addition.”
I’m not attempting to define this operation, only present its conceivable existence. There are two points to this post: First, that any defined subset of mathematics is not universal. (That is, mathematics is not in fact a universal language, any more than “Language” is a universal language.) Second, that any defined subset of mathematics is a nonideal representation of reality, and that it would frankly be surprising if an advanced intelligence chose to use the same mathematics we chose through our biased processes.