a dreamt visit to Malta, the land of model theory
I had an interesting dream last night, which I first just dismissed as a meaningless dream with pleasant images. But then when I started thinking about it more, the significance started showing through.
In the dream, I am on vacation on an island in the Mediterranean. The island is called "Malta", though I have actually been to Malta and this island was much bigger and grander. In fact, in my dream, I was aware that I had visited a smaller Mediterranean island before, but this one was better and was called "Malta". The dream starts out on a beach, where the French are trying to build a fort, except they are making it out of sand, so it's flimsy and only about a foot tall. There are many ships in the ocean offshore, including several warships which are hiding under the foliage of floating islands so that they don't get picked up on radar. I get into a car with Alice (ajawa_took) and someone else (perhaps Kenny? easwaran) and we drive along a road towards the main city on the island. I make a weird turn through some alleyway and suddenly we have driven into someone's house; the road just was paved right into their foyer or something. We apologize to the owner of the house, but leave the car parked in his foyer and walk outside into this neighborhood that looks like a cross between Chinatown and a medieval outpost. There were a lot of banners and heavy wood structures, and a heavy wooden gate was lifted for us as we walked into this old Russian market hall. We pass a pastry shop and Alice spots a chocolate cake that she wants unconditionally. She points and points and starts foaming at the mouth until she finally is able to eat it. Then we all split up and I head off to the center of the city. I emerge from an underground walkway into a small grassy park surrounded by beautiful skyscrapers stretching to a clear sky. The one directly in front of me can only be described as artistically majestic: bronze color, with tiered levels that come to a point on the side. The whole building is tilted about 30 degrees off vertical, like an enormous sundial. Then a sunshower starts and the whole scene is basked in sun-filled, glistening sparkles.
----
So, yeah, it was a dream that clearly left me in a really good mood. But these images actually had some ready interpretation. Just before going to bed that night, I had come up with a new "solution" to my model theory problem. I was a little uneasy about it because the contradiction seemed stronger than it should be (yes, you can derive anything from a contradiction, but the contradictions you actually derive in a proof are never all that far from plausiblity, and this contradiction just seemed flat out implausible). Well, musing about this in bed before falling asleep, I came up with a satisfactory explanation, and went to bed with the feeling that I had actually solved the problem this time. So, this dream is all about solving the problem and all the pride and confidence I have now that I've solved it.
In the beginning of the dream, there are warships, representing obstacles to my proof, and then the car ride was me "arriving at my solution". The gate lifting was the obstacles being lifted and the solution presenting itself, namely the chocolate cake. Alice symbolizes expert model theorists who devour my theorem as a sign of approval that it's quite a tasty result. And then the magnificent skyscrapers and sun signify my growing confidence as a capable mathematician. Malta was my favorite vacation of recent memory, so the island in the dream being called Malta means that I am in a happy place. Except in the dream it's a bigger Malta, because my happiness has grown from now actually having proven a novel result in model theory. Even the presence of the French building that sand fort was not absurdity: the main school for the model theory of groups is in Lyon, and it's somewhat surprising that one of them hadn't solved this problem yet. But like their fortress made of sand, maybe they never made a serious enough effort to tackle the problem.
In any case, I'm still in a good mood from this dream, and today I'm going to look through my solution to the model theory problem and hopefully iron out all the details. Hopefully on Monday I will have a complete theorem typed up to show Scanlon.
In the dream, I am on vacation on an island in the Mediterranean. The island is called "Malta", though I have actually been to Malta and this island was much bigger and grander. In fact, in my dream, I was aware that I had visited a smaller Mediterranean island before, but this one was better and was called "Malta". The dream starts out on a beach, where the French are trying to build a fort, except they are making it out of sand, so it's flimsy and only about a foot tall. There are many ships in the ocean offshore, including several warships which are hiding under the foliage of floating islands so that they don't get picked up on radar. I get into a car with Alice (ajawa_took) and someone else (perhaps Kenny? easwaran) and we drive along a road towards the main city on the island. I make a weird turn through some alleyway and suddenly we have driven into someone's house; the road just was paved right into their foyer or something. We apologize to the owner of the house, but leave the car parked in his foyer and walk outside into this neighborhood that looks like a cross between Chinatown and a medieval outpost. There were a lot of banners and heavy wood structures, and a heavy wooden gate was lifted for us as we walked into this old Russian market hall. We pass a pastry shop and Alice spots a chocolate cake that she wants unconditionally. She points and points and starts foaming at the mouth until she finally is able to eat it. Then we all split up and I head off to the center of the city. I emerge from an underground walkway into a small grassy park surrounded by beautiful skyscrapers stretching to a clear sky. The one directly in front of me can only be described as artistically majestic: bronze color, with tiered levels that come to a point on the side. The whole building is tilted about 30 degrees off vertical, like an enormous sundial. Then a sunshower starts and the whole scene is basked in sun-filled, glistening sparkles.
----
So, yeah, it was a dream that clearly left me in a really good mood. But these images actually had some ready interpretation. Just before going to bed that night, I had come up with a new "solution" to my model theory problem. I was a little uneasy about it because the contradiction seemed stronger than it should be (yes, you can derive anything from a contradiction, but the contradictions you actually derive in a proof are never all that far from plausiblity, and this contradiction just seemed flat out implausible). Well, musing about this in bed before falling asleep, I came up with a satisfactory explanation, and went to bed with the feeling that I had actually solved the problem this time. So, this dream is all about solving the problem and all the pride and confidence I have now that I've solved it.
In the beginning of the dream, there are warships, representing obstacles to my proof, and then the car ride was me "arriving at my solution". The gate lifting was the obstacles being lifted and the solution presenting itself, namely the chocolate cake. Alice symbolizes expert model theorists who devour my theorem as a sign of approval that it's quite a tasty result. And then the magnificent skyscrapers and sun signify my growing confidence as a capable mathematician. Malta was my favorite vacation of recent memory, so the island in the dream being called Malta means that I am in a happy place. Except in the dream it's a bigger Malta, because my happiness has grown from now actually having proven a novel result in model theory. Even the presence of the French building that sand fort was not absurdity: the main school for the model theory of groups is in Lyon, and it's somewhat surprising that one of them hadn't solved this problem yet. But like their fortress made of sand, maybe they never made a serious enough effort to tackle the problem.
In any case, I'm still in a good mood from this dream, and today I'm going to look through my solution to the model theory problem and hopefully iron out all the details. Hopefully on Monday I will have a complete theorem typed up to show Scanlon.