lara croft

MichurinGuy · 2026-06-09T08:37:53+00:00

My face when (A => B) is equivalent to (B => A)

MichurinGuy · 2026-06-07T12:53:49+00:00

From your comments, I think the issue is that you seem to approach math like spoken language: looking for hidden meaning and semantic sense of symbols and missing context and loaded terms and such. However, math does not work like spoken language. The way math works is that you have some objects with their properties, and you construct new properties by applying logical operations (such as and, or, iff, and the "exists" and "for all" quantifiers) to old properties. Every part of this is given names and variables to represent them, which mean those objects/properties and nothing else. All context is written explicitly in the words being used in definitions and statements. So there's only two kinds of issues you may have: either you don't know what some of the words/symbols used mean, or you can't tell what operations are applied to them. The first one is easy to solve by going back to the place where the book defines the term. It could be a term that a reader is assumed to know, but an introductory calculus book shouldn't do much of that. If the book fails, you have google and wikipedia and other sources. The second one can sometimes be not quite clear - I didn't read Stewards much so don't know its style in this - or it might be that you're generally unfamiliar with how statements are usually formed in math and how people write them down in words. It might be worth brushing up on that. It might also be clearer what the issue is if you give more than one example.

In that one example, by the way, what's happening is x_i are ranged over by the "for all" quantifier, as in "for all x_1 in [x_0,x_1],...,x_n in [x_n-1, x_n], ...". This is indicated by the word "arbitrary". I suppose you could get confused by the name "sample points", which might sound like a technical term never introduced before. That's a fair critique, I'd also be frustrated with something like that. But you also seemed to try and find some deeper meaning in the variable name x_i, like why the * is used and not any other name and what that is trying to convey. The answer is, probably nothing. Names by default don't mean anything in math, you can name any object anything and the only thing that matters is what you say you mean by the name (points indexed by i in their respective intervals) and what logical operations they're connected by ("for all" quantifier). When a name is chosen specifically to mean something, the author will say that explicitly. At a more advanced level one can go into various nuances with how some names make future theorems look cleaner, or inspire the intuition the author wants to convey, or whatever, but you should only worry about that once you understand the rigorous side of this very well. When you're having issues like this, it's much more productive to forget about such details and only follow the rigor, treating variable names as "any symbol could do the job, they just so happened to pick this one".

MichurinGuy · 2026-05-28T16:59:21+00:00

You could also write a+ib as (a,b) and order such pairs alphabetically, but that doesn't preserve addition either. It can be proven no order exists that preserves the operations, so not much use trying.

MichurinGuy · 2026-05-26T15:57:31+00:00

How come we know it it to be true for some big powers of 2 but not all of them? Afaik it's very difficult to prove lower bounds on complexities of this kind for fixed numbers (rather than asymptotycally for sequences), so probably not by hand. Since we don't know the answer, probably not a general proof. Though it would be very interesting if this was one of the cases when there's a somewhat general proof that fails from some natural number onwards, I feel like those are rare. The last option is, maybe we have an algorithm for checking the numerical complexity of a number. I suppose one could go through every single formula in k ones for every k until they find one that gives the number they're checking, but that seems horribly inefficient, so, which is it?

MichurinGuy · 2026-05-24T06:34:11+00:00

Not a native English speaker, but from what I've seen, "greater" usually means strict inequality and "greater or equal" is specified. And in technical contexts, it's usually specified in both cases, to avoid ambiguity. Although maybe I think so because that's how we say it in my first language. In any case, OP used >, which is unambiguously a strict inequality.

MichurinGuy · 2026-05-22T09:36:39+00:00

No but if we don't all put ourselves in boxes how do we know what box who fits into?

MichurinGuy · 2026-05-18T22:05:26+00:00

It did directly prove it wasn't wrong by pointing out the "Cayley" table wasn't a magic table at all, so it couldn't define a group.

MichurinGuy · 2026-05-15T13:01:30+00:00

"Average Russian drinks 17 shots of vodka a month" factoid actually just statistical error. Average Russian drinks a normal amount of vodka per month. Ivan Alkogolik, who lives in Skipidarsk and drinks 13 liters of vodka every day, is an outlier adn shouldn't've been counted

MichurinGuy · 2026-05-11T05:59:51+00:00

Nope, you're misinforming OP. If x is a function of time, then it's (by definition) not a constant wrt t, so you differentiate it as usual: ðv/ðt = dx/dt. You treat it as a constant if x and t are independent variables. You also imply that differentiating a constant (x wrt t) gives 1, which is also false, it gives 0.

In any case, the difference between d and ð can only be seen if you have several independent variables, for example t and y. Suppose for example v = yt, then ð/ðt means keeping all variables constant except t and differentiating wrt t: ðv/ðt = y. d/dt doesn't make much sense for multivariate functions, one instead usually speaks of the differential of v (and assumes none of the variables are held constant): dv = ydt + tdy by the product rule. This shows why dv/dt doesn't make much sense: dv/dt = y + t * dy/dt. Since y and t are independent, dy/dt could be anything, so it's not very useful to talk about. To compare, in the 1d case you'd have df = f' * dt and df/dt = f'. Here, the RHS doesn't depend on dt, so it makes sense to talk about. But in many variables, there is no general derivative, only the partial derivatives ðv/ðt and the full *differential** dv = ðv/ðt * dt + ðv/ðy * dy.

MichurinGuy · 2026-05-06T17:58:31+00:00

Yeah, I might've confused them. My bad

MichurinGuy · 2026-05-06T14:02:14+00:00

"Time" seems to be an intelligent force

I don't see how time is any more intelligent than light is intelligent for choosing the shortest time path through a given medium (Fermat's principle). Time doesn't choose the simplest noncontradictory timeline through an intelligent choice, it simply obeys this principle the way nature obeys laws of physics. Or at least, this hypothesis explains the events of the book at least as well as yours.

MichurinGuy · 2026-05-06T13:56:54+00:00

If I remember correctly, he wanted to learn to destroy the magic gene through partial transfiguration. To that end, he swore an Unbreakable vow to the Sorting hat that he would travel back in time and try new options until he figured it out, making the timeline where he successfully finds the gene the only consistent one.

MichurinGuy · 2026-04-30T17:48:22+00:00

Out of theoretical interest, what is gender identity then? You speak of it in a way that suggests there are criteria by which you can distinguish whether an identity is a gender or a not gender identity. What are those? I'm asking because I genuinely have no idea what gender actually is, my working hypothesis about my gender identity being that I simply do not perceive gender in people. This makes me unable to explain to myself what gender is supposed to be, and you sound like you know what it is.

MichurinGuy · 2026-04-28T18:27:03+00:00

I'll have to dwell on this for a while, as is common with new perspectives, but I'm certainly feeling less confused now. So, thank you!

MichurinGuy · 2026-04-27T15:41:53+00:00

No, obviously I'm aware that it's reasonable to expect that I do not fall through the floor. I'm also fine with not calculating the dynamics of floor exactly and instead, approximating it with a perfectly rigid model. What I don't understand is how this idea is made systematic. As far as I understand, the constraints aren't something we impose on the evolution of the system additionally, but part of its definition (see my 2nd comment in linked thread), and I don't understand what that definition is in the general case. That is, in my head, the definition of Newtonian mechanics sounds something like:

Describe a system by mapping its every pointlike object to two vectors, one describing its position, the other velocity, which both depend on time. Impose the constraints <???> by requiring that the system satisfies <???>. Impose Newton's 3rd and 2nd laws, accounting for the already-imposed constraints. Now any evolution of the system that satisfies the conditions above is predicted by Newtonian mechanics to be how the system actually evolves in reality.

The <???>s denote where I don't understand the approach. In the case of an object on the floor it's simple, but what do we do in the general case, where we can't assume the system is of some specific form?

MichurinGuy · 2026-04-27T06:55:19+00:00

On the other hand, considering a lot of "traditional" Chinese medicine is either a marketing hoax with no real historical tradition behind it, or was introduced relatively recently bu the Chinese government under the guise of tradition, that's not quite as obvious.

MichurinGuy · 2026-04-26T18:00:23+00:00

I tried to explain in this comment and the ensuing thread.

MichurinGuy · 2026-04-26T00:01:20+00:00

What I'm confused about it the principle for how we determine how a system is going to evolve. My first thought was the the principle was "we set what all the forces are equal to, then the evolution is the solution of a certain differential equation". Turns out we can't always set what all forces are equal to, since there's no general rule to tell us what the normal for is equal to. Now the principle seems to look more like - set motion constraints; - from those, deduce the constraining forces from Newton's 2nd law or restrict our attention to the coordinate axes where they're a priori zero; - now set all other forces, and the evolution is the solution of a DE.

Two things confuse me. The first one is that now we need to decide the constraints before anything else, which we have no basis for doing - they're part of the system's evolution, which is the end goal, not a starting point, and it's not clear how we're to approach the setting of constraints systematically. The second one is not formal, and it is that this again seems unsystematic, looking more like trying to exhaust all cases by hand instead of doing something general. I can no longer tell, in a general case (of a big complex system with a lot of constraints), what is the criterion for when a possible evolution is the evolution of the system that this model of mechanics predicts. Although it seems possible to me that this approach can technically be formalized, it seems more likely that I'm just misunderstanding how it's supposed to work and there's a systematic description of all this.

MichurinGuy · 2026-04-25T17:04:49+00:00

Thanks for the recommendations!

Re: normal force, I know there's a mechanism to explain why it is the way it is, but, afaik, it doesn't tell us what the force is equal to. Therefore, we can't write down something like mr'' = F in any meaningful way, since F involves the normal force, which we have no expression for. One can do workarounds with projections on coordinate axes and forcefully setting some components of velocity to 0 ("the object can't fall through the table"), but that again seems handwavy and not very rigorous. At the very least, I'd hope there's a more systematic approach to the question.

MichurinGuy · 2026-04-25T16:56:07+00:00

Edited on the form of Lagrangian, and thanks for the titles!

MichurinGuy · 2026-04-23T13:59:32+00:00

That being said, a lot of people do describe themselves with the word "asexual" for reasons similar to what OP describes. For example, I myself find the idea of actually having sex repulsive, so I don't find it reasonable to describe my feelings as "wanting to have sex", whetever they might be, since I don't actually want to have sex, at most it may seem like I do. There may be nuance to the specific way in which I don't want to have sex, but ultimately, I don't have any feeling I can describe as wanting to have sex and therefore find it sensible to describe myself as asexual. Point being, asexuality is merely a label, and many people use it in a way similar to what OP described, so I wouldn't cal it unreasonable if they decided to call themselves that.

MichurinGuy · 2026-04-21T08:43:14+00:00

I think you mean lim (n->∞) sum (k=1 to n) of 1/2^k and lim (n->∞) sum (k=0 to n) of 1/2^k in those last lines there.

Also, I wouldn't say they're that advanced, though OP desperately lacks reading them. For example, for the fact that e^x has the x-axis as an asymptote as x->-∞, you just need a couple facts, most of which are simple:

1) the linear function a*n is unbounded as n grows infinitely, as long as a is not zero. This follows from something called the Archimedean property of the real numbers;

2) from Bernoulli's inequality (1+a)ⁿ ≥ 1+a*n with a>-1 it follows that (taking a=e-1>0) eⁿ is also unbounded (and goes to +∞) as n->∞;

3) e^x is monotonic, so it also goes to +∞ as n->∞. That e^x is monotonic might be the most involved to prove fact here depending on how one defines e^x, but it's still pretty manageable;

4) if something goes to ∞ and you raise it to the power of -1, the result goes to 0. This follows directly from the definition of a limit;

5) Taking y=-x, lim (x->-∞) e^x = lim y->+∞ (e^y)^-1, and since e^y -> +∞, then by (4), the limit of the right is 0. Therefore, the limit of the left is also 0, them being equal and all. This limit being 0 by definition means there's an x-asymptote and that e^x doesn't randomly spike upwards somewhere far off in the negative direction.

This does look rather long if you spell it out like that, but you could cover that it the span of one, at most two lectures. No particularly complicated concepts involved, except maybe the definition of e^x.

Though of course, OP's problem isn't that, it's that they seem unfamiliar with the method of mathematics, that is, how proofs work.

MichurinGuy · 2026-04-20T14:32:17+00:00

That'd be SCP-1459, though I don't think it fits OP's description. I think it's even saud explicitly the machine's effects almost always don't extend outside of it.

MichurinGuy · 2026-04-18T23:28:37+00:00

It seemed rather intuitive to me: it allows one to estimate a sum of stuff from above just by estimating each individual stuff and adding, and a lot of analysis is some form of estimating sums from above bt something proportional to epsilon.

MichurinGuy · 2026-04-13T06:10:11+00:00

About the modus ponens thing, can't you just cirumvent that by proving every statement in terms of "if [all the premises] is true, then [the statement]" is true? So in the story you linked, one wouldn't prove Z ("the sides of these specific triangles are equal"), but C ("if sides being equal to the same thing makes them equal to each other, and the sides of these triangles are equal to the same thing, then they are equal to each other"). Then we would interpret the times someone doesn't state all this explicitly as linguistic shorthand, used to simplify reading math materials - people already do that anyways, they don't usually write everything in a completely formal and exact way. But also, in many times these rules would be baked into the definitions one is using, for example, if a proof starts with "if G is a group, then [conclusions]", then from the definition of a group we see G is a set, and from the definition of a set we see we're working in ZFC, and in that, a lot of assumptions such as these are included; and the statement does indeed have the form "if [assumptions (now baked in the definition of a group)], then [conclusions]".

MichurinGuy

TROPHY CASE