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sniffnoySo today Rosenberg was talking about amenability of groups, and how it's very nice in that it transmits very well from one group to another - subgroups of amenable groups are amenable, as are quotient groups, and if you have a group with an amenable normal subgroup such that the quotient is amenable, the original group is amenable. And he said, not many properties transmit this nicely, except possibly being abelian - no, wait, not even that. Anyway, he decided to contrast it with being a normal subgroup, and he was saying about how "amenable" really means "friendly", so we ended up with
Rosenberg: If you're friendly, it tends to make the people around you friendly, but if you're normal, it doesn't tend to make the people around you normal.
[pause]
Fergie: What? Why is everyone looking at me?
So today Eli was trying to do weird math with the English language. "Harry! Do you know any linguistics?" "Not really..." "Good!"
Apparently this all started when Matt asked him to find a dual to the English language, the idea being like a dual geometry, where points go to lines and lines to points. If I recall, Eli started out with a weird chain of illogic which led him to the idea that the dual of "truth" was "knowledge", and was trying to do things with dualizing the language by... well, I suggested all this was a bit off track, and so they started over with how to put a geometry on the English language, which led to the question of how do we find an angle between nouns, and I for some reason I suggested we should really try to find an angle between adjectives. How to do that? Put an inner product on adjectives, of course! Now, adjectives are functions from nouns to nouns[3], so obviously we should do this by integration! How to integrate adjectives? Well, we need to know how to add nouns, and how we can put a measure on them. Adding nouns is easy; the sum of two nouns is their disjoint union. It's commutative, associative, has an identity - does it have inverses? Does it need inverses? I suggest inverses can be done with antimatter, though Eli prefers using Platonic element inverses, i.e., fire↔water, wind↔earth, pants↔British[0]. Regardless, we get inverses. Now, how to put a measure on nouns?
I suggest maybe we should start over, and just try to put a metric on nouns. When someone asks how, I say "Just use the word metric!" More ridiculously, though, I point out that since we can already subtract nounse, we only have to put a norm on nouns. How to do that? Well, clearly, we can verb any noun, and once we have it as a verb, we just multiply by all its conjugates! (Yes, that awful pun confused two different uses of the word "norm". Oh well.) Now, how do we multiply verbs? Well, very often multiplication is composition, so clearly, a times b is the verb of doing b and then doing a. But that's not commutative - maybe a verb commutes with all its conjugates, though? So we decide to try a numerical example; what's the norm of "run"? (No, that's not a noun, but this works for verbs, too.) I initially suggest that it's run·ran·runs·running, which reduces to run·runs·running, as to run and then to have run is the same thing as just to run, with the question of whether "run" should be counted twice as it's also the past participle, but, well, firstly it's pointed out that "running" isn't a verb, and that secondly, it was decided to just restrict to present tense for simplicity. Also to active voice and indicative mood, and to just take the product over the persons ("people", as Eli insisted on calling them) and numbers, so it's run5·runs. I suggest we take a 6th root to make it more like the type of norm we were originally talking about. Now, what's (run5·runs)1/6? Well, I suggest maybe runs=runmiddot;s, even though that violates our earlier definition, giving us that |run|=run·s1/6. Now they start trying to calculate the numerical value of s, saying that it should be related to its pluralizing property. Eli suggests for something that the plurality of singular should be 1, and of plural should be 2, and I point out that it should be 3, as some languages have dual forms. (Hey, dual! But we never picked up on that...) So we want to find the numerical value of s; I suggest we take the product over all words in the dictionary of the ratio of the plurality of a word with s tacked on to the plurality of the original word. Thus s1/6 is a positive real; but since |run| is also a positive real, this means that run itself is a positive real. Somehow we come to the conclusion that run=1, which causes the problem that s=1; I suggest that maybe we should just take the product over general rules for parts of speech, so nouns give us times 3, verbs give us times 1/3, and the other parts of speech don't affect it. Then the question comes up as to what sort of geometry English has, and Matt and Eli decide it's not anything they already know. I go over and tell this to Tom, about how we decided to put a metric on nouns, and he also immediately says "Just use the word metric!"
Then, once we've done this, we start all over again. Someone suggests the dual of a transitive verb ought to be the verb that takes subject and object in reverse order, i.e. its passive form. So dual nouns should be... passive nouns? I suggest they really ought to be active nouns. We start over. The dual of a noun is clearly a verb. So what's the dual of an adjective? The obvious answer is that it's an adverb, but working from the "jective" part, I suggest it's an interjection. What's the dual of a pronoun? Obviously, says Phil, a proverb! The dual of "I", for instance, is "A penny saved is a penny earned", Eli suggested, though Phil thought it ought to be "Beauty is in the eye of the beholder." To get the duals of others, we started going from the Latin roots of the names - so the dual of an adjective is an ejective, the dual of an adverb is an enoun, the dual of a preposition is a postposition, and the dual of a conjuction is a sinjunction. I think there was something for interjection, but I don't think it made much sense and I don't remember it. Now, a postposition is clearly something you put after a verb - I suggest it should be the same word, so the dual of "to" is "to", just with a different meaning, as it's now acting on verbs. Then I think, what comes after a verb and acts on it? An adverb! Thus the dual of a preposition is an adverb, so adverbs are postpositions and prepositions are enouns. I think that's about where we stopped...
-Sniffnoy
[0]I don't believe I've explained this one in previous entries, so I suppose I have to now. Apparently some time ago Anton and Eli, I think it was, noted that pants are not made of any of the Platonic four elements (and no, they're not made of ether either), and so, clearly, pants are the fifth element. Neither, it was pointed out, is British made of the other elements; thus it is the sixth. (This is how Eli tells it; Anton says they came up with British first, then pants.) Now, each Platonic element has an opposite - fire opposes water, wind opposes earth. By process of elimination, then, clearly pants is the opposite of British! And this has been a running joke ever since (most especially insisting that Victoria is a British spy and wears imitation pants).
[3]This comes from an idea I came up with a while ago - that we can consider "noun" and "sentence" to be primitive parts of speech, and all others to be function types. Note that these are not like ordinary functions, but rather like functions in some sort of typed lambda calculus (as, for instance, adverbs can apply to themselves). So intransitive verbs are functions from nouns to sentences, and transitive verbs are functions from nouns to transitive verbs. Adjectives are obviously functions from nouns to nouns. I did more, but I don't remember and it got really messy.
Rosenberg: If you're friendly, it tends to make the people around you friendly, but if you're normal, it doesn't tend to make the people around you normal.
[pause]
Fergie: What? Why is everyone looking at me?
So today Eli was trying to do weird math with the English language. "Harry! Do you know any linguistics?" "Not really..." "Good!"
Apparently this all started when Matt asked him to find a dual to the English language, the idea being like a dual geometry, where points go to lines and lines to points. If I recall, Eli started out with a weird chain of illogic which led him to the idea that the dual of "truth" was "knowledge", and was trying to do things with dualizing the language by... well, I suggested all this was a bit off track, and so they started over with how to put a geometry on the English language, which led to the question of how do we find an angle between nouns, and I for some reason I suggested we should really try to find an angle between adjectives. How to do that? Put an inner product on adjectives, of course! Now, adjectives are functions from nouns to nouns[3], so obviously we should do this by integration! How to integrate adjectives? Well, we need to know how to add nouns, and how we can put a measure on them. Adding nouns is easy; the sum of two nouns is their disjoint union. It's commutative, associative, has an identity - does it have inverses? Does it need inverses? I suggest inverses can be done with antimatter, though Eli prefers using Platonic element inverses, i.e., fire↔water, wind↔earth, pants↔British[0]. Regardless, we get inverses. Now, how to put a measure on nouns?
I suggest maybe we should start over, and just try to put a metric on nouns. When someone asks how, I say "Just use the word metric!" More ridiculously, though, I point out that since we can already subtract nounse, we only have to put a norm on nouns. How to do that? Well, clearly, we can verb any noun, and once we have it as a verb, we just multiply by all its conjugates! (Yes, that awful pun confused two different uses of the word "norm". Oh well.) Now, how do we multiply verbs? Well, very often multiplication is composition, so clearly, a times b is the verb of doing b and then doing a. But that's not commutative - maybe a verb commutes with all its conjugates, though? So we decide to try a numerical example; what's the norm of "run"? (No, that's not a noun, but this works for verbs, too.) I initially suggest that it's run·ran·runs·running, which reduces to run·runs·running, as to run and then to have run is the same thing as just to run, with the question of whether "run" should be counted twice as it's also the past participle, but, well, firstly it's pointed out that "running" isn't a verb, and that secondly, it was decided to just restrict to present tense for simplicity. Also to active voice and indicative mood, and to just take the product over the persons ("people", as Eli insisted on calling them) and numbers, so it's run5·runs. I suggest we take a 6th root to make it more like the type of norm we were originally talking about. Now, what's (run5·runs)1/6? Well, I suggest maybe runs=runmiddot;s, even though that violates our earlier definition, giving us that |run|=run·s1/6. Now they start trying to calculate the numerical value of s, saying that it should be related to its pluralizing property. Eli suggests for something that the plurality of singular should be 1, and of plural should be 2, and I point out that it should be 3, as some languages have dual forms. (Hey, dual! But we never picked up on that...) So we want to find the numerical value of s; I suggest we take the product over all words in the dictionary of the ratio of the plurality of a word with s tacked on to the plurality of the original word. Thus s1/6 is a positive real; but since |run| is also a positive real, this means that run itself is a positive real. Somehow we come to the conclusion that run=1, which causes the problem that s=1; I suggest that maybe we should just take the product over general rules for parts of speech, so nouns give us times 3, verbs give us times 1/3, and the other parts of speech don't affect it. Then the question comes up as to what sort of geometry English has, and Matt and Eli decide it's not anything they already know. I go over and tell this to Tom, about how we decided to put a metric on nouns, and he also immediately says "Just use the word metric!"
Then, once we've done this, we start all over again. Someone suggests the dual of a transitive verb ought to be the verb that takes subject and object in reverse order, i.e. its passive form. So dual nouns should be... passive nouns? I suggest they really ought to be active nouns. We start over. The dual of a noun is clearly a verb. So what's the dual of an adjective? The obvious answer is that it's an adverb, but working from the "jective" part, I suggest it's an interjection. What's the dual of a pronoun? Obviously, says Phil, a proverb! The dual of "I", for instance, is "A penny saved is a penny earned", Eli suggested, though Phil thought it ought to be "Beauty is in the eye of the beholder." To get the duals of others, we started going from the Latin roots of the names - so the dual of an adjective is an ejective, the dual of an adverb is an enoun, the dual of a preposition is a postposition, and the dual of a conjuction is a sinjunction. I think there was something for interjection, but I don't think it made much sense and I don't remember it. Now, a postposition is clearly something you put after a verb - I suggest it should be the same word, so the dual of "to" is "to", just with a different meaning, as it's now acting on verbs. Then I think, what comes after a verb and acts on it? An adverb! Thus the dual of a preposition is an adverb, so adverbs are postpositions and prepositions are enouns. I think that's about where we stopped...
-Sniffnoy
[0]I don't believe I've explained this one in previous entries, so I suppose I have to now. Apparently some time ago Anton and Eli, I think it was, noted that pants are not made of any of the Platonic four elements (and no, they're not made of ether either), and so, clearly, pants are the fifth element. Neither, it was pointed out, is British made of the other elements; thus it is the sixth. (This is how Eli tells it; Anton says they came up with British first, then pants.) Now, each Platonic element has an opposite - fire opposes water, wind opposes earth. By process of elimination, then, clearly pants is the opposite of British! And this has been a running joke ever since (most especially insisting that Victoria is a British spy and wears imitation pants).
[3]This comes from an idea I came up with a while ago - that we can consider "noun" and "sentence" to be primitive parts of speech, and all others to be function types. Note that these are not like ordinary functions, but rather like functions in some sort of typed lambda calculus (as, for instance, adverbs can apply to themselves). So intransitive verbs are functions from nouns to sentences, and transitive verbs are functions from nouns to transitive verbs. Adjectives are obviously functions from nouns to nouns. I did more, but I don't remember and it got really messy.
no subject
Date: 2005-08-10 02:50 am (UTC)