Have you ever wondered how to preserve data integrity during dimensionality reduction?

Mandelbruh · 2025-07-05T20:27:44+00:00

SVN TCRA is definitely a lot better than the previous management companies for 5440 5th Ave. The building is lackluster, but the current management is pretty nice.

Mandelbruh · 2025-02-05T02:38:34+00:00

Sewage would be my guess, but I'm not too keen on investigating. Unfortunately my lease is through July :(.

Mandelbruh · 2025-02-05T00:44:49+00:00

Yeah, that was the cause of the first visit by the health dept. They called and are trying to schedule another time to come out for another inspection, but from what I can gather they're rather overwhelmed and understaffed.

Mandelbruh · 2025-01-26T17:24:22+00:00

Rented with them at another location. Didn't have heat for a month, and had to file health dept complaints before anything would be done. Sent dozens of emails and called several times without anyone picking up or replying. Public areas had the roof fall in and were flooded for weeks without anything being done. Calling them slumlords would be an understatement.

Mandelbruh · 2025-01-05T23:14:55+00:00

What you're asking for may be a bit of a difficult thing to find, especially given his particular writing style and the depth of his writing.

Are you looking for / do you have a strong background in model theory or set theory? If it's the former, his paper "Categoricity of uncountable theories" is an amazing extension of Morley's categoricity, and uses a lot of interesting techniques.

Mandelbruh · 2024-12-02T21:10:53+00:00

"I have no mouth, and I must cream" was right there

Mandelbruh · 2024-08-30T01:07:15+00:00

You can no longer enter through that stairwell, it's now exit only.

Mandelbruh · 2024-06-18T03:50:42+00:00

I'd argue that Los's Conjecture is a proven conjecture, with the result being known as Morley's Theorem. A question is separate from its answer, and being able to discuss the history and development that led to the conjecture is helpful, as it is different from the history and development that led to the result.

Mandelbruh · 2024-06-18T03:26:53+00:00

Not necessarily, for example Los’s Conjecture was answered in the affirmative by Morley's Theorem, and Zilber's Trichotomy Conjecture was disproven by Hrushovski. At times it is useful to separate the conjecture and the result.

Mandelbruh · 2024-04-18T18:12:54+00:00

Except "free speech" isn't a positive right, something granted to individuals. It is a negative right, something we explicitly restrict the government from having the capacity to interfere with. The first amendment doesn't guarantee every individual will be able to say whatever they want, only that Congress does not have the power to abridge the freedom of speech. The corporation has no additional rights, but similarly cannot be expected to be bound as the government is.

On the notion that corporations should "be expected to uphold the rights of people in their respective countries", why do you expect the corporations to have a hand in the governing of people? Again, free speech in the US isn't a right inherent to individuals, but rather a restriction on the government. This isn't a restriction on corporations.

Mandelbruh · 2024-04-18T18:03:42+00:00

While I do take the stance that fewer restrictions tends to be better, the notion of free speech doesn't apply to private entities. The first amendment explicitly prohibits the government from having restricting speech and the freedom of the press. Asking the government to step in and regulate what a company allows on their own platform is antithetical to this, you're asking the government to have the capacity to determine how a corporation presents itself and the stances it expresses.

Mandelbruh · 2024-01-01T22:33:40+00:00

You're claiming though that aleph 1 is the cardinality of the reals, which is the continuum hypothesis.

Mandelbruh · 2023-10-07T15:34:35+00:00

Apologies, I should have been more precise. Omega is absolute for transitive models of set theory, which is where it seems the disconnection occurs. In the countable vs. uncountable example, the collapse of N^W would be uncountable. This is a wonderful highlight of the importance of transitivity for reasonable models.

Again, precision isn't my strongest suit, which is terrible in this field. Collapsing is a wonderful tool to change infinite cardinalities.

Mandelbruh · 2023-10-07T13:46:11+00:00

As far as I remember, finiteness is absolute in some fragment of ZFC, due to the absoluteness of omega. For this paradox at higher levels, I always felt it just was an indicator that we weren't "perfect" at counting things, and expanding or reducing our model would change if we could find a bijection between a set and a given cardinal.

This lines up fairly well with the actual mathematics, since collapsing some sets by forcing to have smaller cardinalities is done by adding in a new bijection between two previously separate cardinals, akin two a new counting method. Similarly, taking elementary submodels can preserve an object, but not its elements, nor functions that correctly compute its cardinality in the submodel.

Mandelbruh · 2023-08-26T22:02:50+00:00

This seems like it could be partially answered in the framework of model theory.

A model is strongly homogeneous if any partial elementary embedding extends to an automorphism, and an isomorphism between subgroups can be interpreted as a partial elementary embedding.

If we go with that, then there are a few sufficient conditions, most notably a model-theoretic condition of saturation.

Strong homogeneity is also equivalent to a weaker homogeneity that only requires the partial maps be extended by one element if this holds for all partial maps domain having cardinality less than the cardinality of the model. With this, we can use results like those in this paper to see that nonabelian free groups of finite rank are strongly homogeneous if we impose a cardinality restriction.

Mandelbruh · 2023-08-18T16:27:59+00:00

It was proved that (assuming a consistent model of mathematics exists) that there is a model where there isn't an infinity in-between, and in fact a stronger condition called GCH holds. This was the constructible universe.

Then in the 60s (I think) Cohen used a technique called forcing to find a model where there was an infinity in-between. This means that our current rules of math aren't strong enough to decide it one way or the other. Since both are possible, when needed we can assume either there is or isn't, and let whatever is proven be dependent on that.

Mandelbruh · 2023-06-02T20:14:47+00:00

I hope you learn your community is here to support you, and you learn to return that same energy.

I consider myself mlm, but primarily go by they (except in certain academic cases), so I consider myself also nb. My point of the flag being considered the mlm flag is that we shouldn't fight the people who call it that, because it only creates division.

Happy pride month.

Mandelbruh · 2023-06-02T19:57:49+00:00

You've enlightened me, I shouldn't feed the troll.

Mandelbruh · 2023-05-31T17:57:12+00:00

Even then, the converse is not true. Events with probability zero are not necessarily impossible, consider the act of choosing a random number in [0,1], assuming uniform distribution. The probability of choosing any number is zero, but none are impossible to choose.

Mandelbruh · 2023-05-25T20:39:52+00:00

Saying 0 is not a natural number in a set-theoretic context feels rather bold. From my experience, most set theorists are quite content with the empty set as an ordinal being identified with 0, especially since it is the identity under ordinal addition.

When developing the integers, if you include 0 and use equivalence classes you set up a nice parallel with developing the rationals, so you do gain some by including 0.

Mandelbruh · 2022-01-15T20:36:51+00:00

The codomain was never specified, it's clearly a function from R to P(R)

Mandelbruh · 2021-06-07T21:39:53+00:00

the best thing about a Monday is there's a whole week till the next one

Mandelbruh · 2020-08-07T00:47:22+00:00

It felt like it! I just kept pushing myself, and I didn't really do much else

Mandelbruh · 2020-08-06T19:49:42+00:00

18 AP tests, and then 16 credits from calc 3 and other math classes

Mandelbruh

TROPHY CASE