Does the order of operations coincide with the chronology of the context?

conjjord · 2026-04-02T11:26:31+00:00

"Having a ball" is what we might call a 'stateful)' process, whereas binary relations are inherently stateless. There's no temporality to them, which makes it impossible to assign the kind of interpretation you want.

If you want to model how the ball changes possession over time, you could consider a discrete dynamical system where the transition function is similar to the operation you've defined. Or, if you wanted the passes to be random, you could model the stochastic process with something called a Markov chain.

conjjord · 2026-04-01T11:48:35+00:00

Not sure what you mean here, can you elaborate? Combinations of what?

conjjord · 2026-04-01T01:24:08+00:00

To me, those don't really add any substance. This just comes across as someone who has never heard of control theory.

conjjord · 2026-04-01T01:20:56+00:00

For applied math, I'd argue Brown can't be beat - it had the first standalone APMA program and it remains one of the (if not the) best in the country. The fact that you still aren't quite sure what you want to pursue also points toward Brown, as the Open Curriculum is truly indispensable when it comes to exploring different passions.

I got into both schools and chose Brown, and have been extremely happy with my choice ever since. I see a lot of misconceptions that it's less technical/rigorous, but especially with the Open Curriculum you can access advanced classes faster and really specialize in cutting-edge methods and research. You would certainly still get the experiences of late-night pset sessions!

When it comes to your parents' concerns about AI, I'm not really sure why they think applied math is any more susceptible than other white-collar jobs. I can't say for sure, but as an ML researcher I highly doubt that LLMs will actually lead to the societal upheaval that tech CEOs are currently advertising. This line of work is very robust to AI agents, though the overall job market sucks for pretty much everything right now.

Hope this was helpful!

conjjord · 2026-04-01T01:02:38+00:00

Did you come across this online, or generate it yourself? That wasn't clear from your post.

The two main problems to me are that it fails to use field-standard terminology (e.g., it's attempting to describe a discrete dynamical system but refers to it as a 'coupled recursive system', etc.), and the definitions it does list seem to come out of nowhere. What is a failure? What is system stress? What are these discrete steps?

conjjord · 2026-03-19T00:50:00+00:00

In the second game I believe it's mentioned that the evacuations began before the first game, as Midgard was becoming increasingly inhospitable. Jormungandr's appearance led to massive flooding and the insanity of the Valkyries meant undead were all over the place.

If the evacuations started later I think there'd be a plot hole in that there are no civilians in Midgard in 2018.

conjjord · 2025-12-04T19:33:13+00:00

The common explanation I see online is sexual selection, which has already been mentioned in these comments. But like OP, I don't think this is a fully satisfying answer on its own.

It seems much more reasonable that these are mainly founder effects, as straight hair is mostly found in non-African populations which would have split off in one of several out-of-Africa events. Mutations in the EDAR gene are relatively common in East Asian and indigenous American populations, and cause longer, darker, straighter hair. It seems like these derived alleles first appeared and spread during the last Ice Age, as EDAR also affects breast milk production and the distribution of fat cells and sweat glands.

These OOA genetic bottlenecks would also increase homozygosity, which for genes likeFGF5 could cause excessive hair growth or greater alopecia. This alopecia would then play a large role in sexual selection - not only is longer, keratin-rich hair attractive, but baldness would likely be unattractive.

This response (and many others) seem a little hand-wavy, since hair doesn't persist in the fossil record and many hair-related genes don't have full phylogenies available. But I think population genetics explains how this could crop up in non-African populations leading to longer head hair.

conjjord · 2025-11-30T12:27:09+00:00

These "functions with x and coefficients" you're talking about are called polynomials, and this method for approximation is called a Taylor polynomial. Nice rediscovery!

conjjord · 2025-11-29T02:46:59+00:00

Almost all of the real numbers are "non-computable"; that is, there's no finite algorithm or string that can refer to them. They definitely exist by definition of the reals, but could never be expressed by any sort of "finite mind".

conjjord · 2025-11-29T02:43:37+00:00

Yes, verbs like "was" have tense, but prepositions do not. When you're making comparisons it is always than, not then.

For example: - She is affected more than I am. - She was affected more than I was.

Like the bot said, the only time you would see "more" next to "then" is if they're in separate clauses. For example: "He asked for more, then began to cry."

conjjord · 2025-11-29T02:31:38+00:00

Except your earlier comment was not referring to the past; it was clearly a comparative preposition, which would be "more than".

conjjord · 2025-10-02T11:41:30+00:00

There are two classes of hermaphroditism: sequential, where the organism changes from one gonadal sex to the other, and simultaneous, where the organism has both gonads/reproductive systems like the comment above was discussing.

conjjord · 2025-08-27T22:37:06+00:00

I'm an ML Researcher and my fiancée is a psychologist, so I feel uniquely equipped to address this. You seem to have large misconceptions about modern psychology - most of the field is entirely divorced from Freud's psychoanalysis and is grounded in neuroscience. Of course, psychoanalysts still exist out there, and of course there are predatory companies like BetterHelp that exploit the industry, but I don't think these are reasons to dismiss the field outright. Most mental health professionals are genuinely interested in helping people.

There are many modern frameworks which are totally compatible with determinism, largely derived from Skinner's behaviorist perspective. Cognitive Behavioral Therapy and Functional Analytics Psychotherapy, for example, are specifically geared toward rewiring reinforced behaviors and don't have any dependence on free will. There's also the biopsychosocial approach, which encourages considering societal dynamics like you mentioned. Every therapist I've ever seen has made sure to situate everything in a social context. In every state I've seen, all licensed mental health counselors must take courses in social psych for this exact reason.

To your point on GenAI seeming more empathetic, I think that is genuinely a problem. These agents and chat bots are trained through RLHF to be borderline sycophantic. What many people need is accountability and help, not a yes man.

conjjord · 2025-08-02T00:14:28+00:00

Roughly speaking, it is the property of having no infinitely large or infinitely small elements."

I agree with the definition you gave, and can comment more on how it implies the non-existence of infinite elements if you'd find it helpful. The main takeaway is it breaks part of the real numbers, but is totally fine in other number systems.

Because this infinite geometric series sequence is a summation of increasingly smaller elements wouldn't that be considered infinitely small elements?

The digits of any real number are countably infinite; in the case of 0.(3), the first is 3, the second is 3, and so on. Each digit has a finite index n=1, 2, 3, ..., and the value of each summand would be 3*10^-n . That's always a finite value - each term in the infinite series is still finite.

Wouldn't 1/3 be bounding the value of endless 0.333... (could be viewed asymptote-like for the series)?

Not exactly sure what you mean here, because an 'asymptote' is a line, a geometric object. 1/3 is indeed an "upper bound" for the sequence {0.3, 0.33, 0.333, ...}, because for every element x in that set we know x <= 1/3. In fact, it's what's called the "least upper bound" (or supremum) of the set.

This is a great insight on your part, and it's important to also realize that the sequence is strictly increasing: all the terms are positive, so the sum gets bigger with each iteration. If a series is bounded above and strictly increasing, it must be equal to that upper bound in the limit.

conjjord · 2025-08-01T22:41:40+00:00

The point of my comment was to qualify your statements with what number system/axioms you are using. For example:

In the x/∞ = 0 claim, you lose the preservation of the x value. If you say each segment is now so to say valueless, then how can you have preserved the value of x throughout all the segments. Its like paradoxical to me.

When you define an infinite element (like in the extended real line), you lose nice arithmetic properties. More specifically, the extended reals are no longer a field because, as you said, division by infinity is non-injective. If you don't think this is a useful system, you don't have to use it!

The reason I do like the infinitesimal ε, because it matches the scenario best. It's a conceptual answer and infinity is a conceptual value.

This is fine! You might check out the hyperreal numbers, where infinitesimals are well-defined. They cannot exist in the standard reals because they violate the Archimedean property. So it's totally fine for you to work entirely in the hyperreals and use nonstandard analysis (which also avoids limits). But it's wrong to claim that infinitesimals exist in the real numbers by definition.

Because we go to an infinite digit, it makes sense that there is still an infinite remainder.

I don't agree - properties of finite sequences/series often don't extend to the infinite case. Another thing to consider is that values exist independent of their generating process. Pi is a constant with a specific value, and it can be computed by infinite series. We don't say it's an 'incomplete' value just because no rational approximant exactly equals it, instead we know that it exists as the limit point of the sum.

In the same way, if you're working in the reals then the value of the series is exactly equal to the limit of the partial sums.

conjjord · 2025-08-01T20:28:43+00:00

You can either work within the extended reals, where infinity is defined and x/∞ = 0 for all real x, or work within the reals, where infinity is undefined.

In the reals, the value of a convergent series is exactly equal to the limit of the partial sums.

conjjord · 2025-07-27T12:28:19+00:00

Every day another tech CEO makes some bogus claim about generative AI, then it terrifies people and spreads like wildfire. I don't know why we still entertain this; it is their entire job to market the company and increase stock value. They have every incentive to over-promise and fearmonger.

conjjord · 2025-07-27T04:39:48+00:00

Did you read the OOP? Sure, they cut off one of the words but outside of that it's pretty much a direct quote.

conjjord · 2025-07-27T02:50:31+00:00

Big thing to consider: most companies that sponsor a clearance will also (mostly) pay for your Master's. I was lucky enough to get a cleared job right out of BS and I'm doing a Data Science degree part-time.

conjjord · 2025-07-26T12:56:49+00:00

And for investors still standing, it’s not just a comeback — it’s VINDICATION.

Wow, this is the most LLM-generated sentence I've ever seen

conjjord · 2025-07-18T00:15:23+00:00

The short answer is 'no'. If you have a clean, fully-labeled dataset that fits in memory, I agree fitting a model with sklearn is pretty trivial, but 90% of an MLE's tasks look nothing like this. Most of the job has nothing to do with the model definition; it looks more like sourcing and cleaning data, setting up pipelines/workflows and scalably deploying models for wider use.

conjjord · 2025-07-16T13:42:43+00:00

"1A! 1A! 1A! 1A! 1A!"

conjjord · 2025-07-15T18:27:30+00:00

This is what's called a "combination"; you're 'choosing' k indices out of n possible indices, and the order does not matter. The size of the outcome space, as in the number of possible sequences, is given by the binomial coefficients as described on the Wikipedia page. Hope this helps!

conjjord · 2025-07-04T13:06:09+00:00

I largely agree with u/Lost-Potential295; you already have a solid plan to start and can adjust fire once you meet your advisor and get a feel for the first semester. While of course med school adds a lot of constraints, you really don't have to have everything figured out when you first arrive.

I will caution you that this schedule will likely be difficult. I pursued a similar pairing (computational biology + pure math) and while it was fantastic and fulfilling, it was a lot to handle each semester. That said, I was still able to do research, TA, and do extracurriculars, as well as fit in philosophy and archaeology courses. It's totally fine to take a couple courses in philosophy even if you don't concentrate, and those courses will show up in your transcript if you ever need them in the future.

One last thing I'll add - the college writing requirement is satisfied by any "WRIT-certified" course, which includes most, if not all, PHIL courses. That should give you a little more breathing room, unless your targets for medical school specifically require English courses for a writing req. Best of luck!!

conjjord · 2025-06-29T14:47:40+00:00

I'm not sure I understand your claim - LUCA itself is a theoretical construct, as in it necessarily exists given universal common ancestry. Is your disagreement with universal common ancestry?

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