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Cake day: November 19th, 2023

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  • Also, if you put the same wine in different bottles, they pretty reliably prefer (and describe the rich complexities of) the more expensive bottles.

    I knew an audiophile that believed the government had top secret technology for additional audio channels in surround sound setups, like 17.7 or something. I tried very hard to explain how you can buy an off the shelf 128 channel recorder/playback device, and have as many channels as you can feasibly buy and set up, and the reason a lot of media was recorded in 5.1 was because a 5.1 setup was considered at the upper end of what people would be willing to pay for. He moved his target in response, to now the government has top secret 1000 channel audio equipment.

    I don’t know what the equivalent of the wine world is, but I hope never to meet it.





  • In set theory, sets containing an infinite number things are relatively easy to describe. For example, “All the counting numbers” is a set with an infinite number of things in it.

    Many sets with an infinite number of things have a one to one correspondence to each other, meaning that we can describe a function that takes elements of one set as an input, gives elements of the other set as an output, and spans both sets - no element is skipped on either side.

    “All the even counting numbers” has a one to one correspondence with “All the counting numbers”. You can look into Hilbert’s Hotel for a good demonstration of how this works.

    Not all sets with an infinite number of things correspond with the set of all counting numbers, because some are fundamentally bigger. This difference in size doesn’t happen just once (e.g. there are countably infinite sets, and uncountably infinite sets, and that’s all we need to know), there are actually an infinite number of sets of progressively bigger infinite numbers of elements.

    Because this is a confusing mess, we needed a way to keep track of how infinitely big each infinitely big set is, and the aleph cardinalities are the preferred way to do that. Any set with cardinality of aleph zero (aka “aleph null”) has a one to one correspondence with any other set with cardinality aleph zero. The same is true for every other aleph cardinality. Two sets of cardinality aleph thirty seven have a one to one correspondence with each other.

    Anyways, busy beaver(tree(aleph omega)) is the biggest number.















  • The world trade center was required to be insured against terrorism by the banks in the leasing deal. That was an obvious requirement for the banks to include because of the recent (at the time…) 1993 world trade center bombing.

    Larry Silverstein got the insurance so recently before the attack because he signed a lease that included the insurance provisions, and he signed that lease in July 2001 because negotiations for the deal took from January 2001 until July 2001. Prior to that, the Port Authority was having trouble keeping the occupancy of the building high, and they thought private management of the building would increase tax revenue, and give them money for other projects. The plan for privatization began in the 1990s, and coincided with other revitalization efforts in the area, some managed by the Port Authority, and others stemming from the city government.

    I think in context there’s nothing surprising involved here, and the timeline of the attack was driven by different things than the timeline of the leasing deal. In other words, this is a coincidence.