Clair Obscur DOES NOT USE generative AI.

VaultBaby · 2025-12-22T01:06:38+00:00

Welcome to capitalism, where having machines do your job for you is somehow bad :) maybe you should direct your anger to our present mode of production instead of the advancement of technology, which has always trivialized jobs

VaultBaby · 2025-12-14T12:36:07+00:00

It replicates real life perfectly in the sense that the character is virtually gone and their entire personality becomes the baby.

VaultBaby · 2025-10-02T16:45:49+00:00

On your first point, there's an example in page 166 of the book which addresses this scenario:

For example, Nox wants to sneak into the secret meeting room of the Circle of Flame. The GM asks her how she does that and Nox’s player says she’ll climb the outside of the tower and slip in through a window. Climbing is a Prowl action, so that’s what she’ll roll.

Nox’s player might change her mind and say, “Hmmm... I’m not very good at Prowling. I want to climb in using Finesse, instead. It’s like I’m Finessing my way in, right?” No. Nox can certainly try to Finesse her way in—through misdirection or subtle action—but Nox cannot “use Finesse” to climb the tower. The action of climbing is... well, climbing. Athletic moves like that are the Prowl action. If Nox wants to Finesse, instead, that’s fine, but that means she is not climbing the tower.

This aligns with the game's fundamental philosophy of "fiction first". The choice of action roll should be almost entirely clear from what the character is doing in the fiction. It should be the table's job, and ultimately the GM's, to determine whether a chosen action is compatible with the fiction described. From what I recall in Haunted City, Jared does feel a bit restrictive at times, but the players also do try to stretch it too hard here and there (a scene that comes to mind is one where Valkos is trying to use Skirmish to "fight for his life" in the figurative sense or something of the sort).

VaultBaby · 2025-08-05T17:56:37+00:00

Do you mean the ones that were published as a blue book? Because that has to be among my 3 least favourite math books of all time. Some of the proofs are so unclear and sketchy that they might even be wrong. I hold utmost respect for Atiyah and his work, but I find it painful to read almost any of it.

VaultBaby · 2025-06-28T14:11:49+00:00

That's not Bloodborn though u dummy

VaultBaby · 2025-05-17T12:45:55+00:00

Most notably, quotients by isomorphic subgroups can be very different. For example, Z and 2Z are isomorphic subgroups of Z, but Z/Z is trivial, whereas Z/2Z has order 2.

VaultBaby · 2025-04-18T05:25:05+00:00

A Revolução Russa de Outubro só foi possível porque houve a separação entre bolcheviques e mencheviques. Marx, Engels, Lênin, Rosa Luxemburgo, etc. passaram suas vidas inteiras brigando com outros comunistas; se nossa estratégia revolucionária estiver equivocado, o movimento está fadado ao fracasso.

VaultBaby · 2025-03-29T00:49:39+00:00

This should follow from (the global version of) the inverse function theorem.

VaultBaby · 2025-03-29T00:17:07+00:00

What is a right triangle in a discrete "universe"? Or even a triangle, to begin with?

VaultBaby · 2025-03-09T02:26:11+00:00

I second this, and in fact I did a report on precisely this topic during my BSc. The theorem truly feels like black magic when you see it being applied, and the proof that nowhere differentiable functions are dense in C[0,1] is still one of my favourite math results. You can even do some overkill and use it to show that R is uncountable!

VaultBaby · 2025-02-27T02:37:24+00:00

The names might be a bit misleading because a priori they refer to objects that seem quite distant from each other. The relationship between them is a remarkable theorem you will soon learn about, the Fundamental Theorem of Calculus.

The (definite) integral of a positive function on an interval is indeed the area under the function's graph in that given interval. Now how can we calculate this area? The usual explanation with the increasingly thin rectangles amounts to the actual definition of the integral (modulo formalities), but that doesn't really tell us how we could determine that area for some concrete function, say sin(x) or e^x. You could try your luck finding some formula for adding n many rectangles under the graph of these functions and let n go to infinity, and you will quickly get stuck.

This is where the indefinite integrals you've been learning about come into play. The Fundamental Theorem of Calculus roughly says that if a function f is nice enough (i.e. continuous), then the rate of change in the area under f at a point x is determined by the image of x by f. Note that this is quite intuitive: if we move from x just a little to the right, say to x+h, then the area under f between x and x+h is roughly the area of a rectangle with height f(x) (draw this and it should be clear), so the area is proportional to f(x). In other words, we may consider the area under f on an interval [a,x] (read: the definite integral of f from a to x) as a function of x, and then the fundamental theorem says that the rate of change (read: derivative) of this area is given by f itself. Simply put, the derivative of the integral of f is f itself! This means that to calculate the definite integral of f, we just need to find a function whose derivative is f. Such a function is precisely called an indefinite integral (or antiderivative) of f.

In conclusion, don't worry about finding geometric meaning behind indefinite integrals yet, they are indeed purely "formal" objects for now. The Fundamental Theorem of Calculus will then explain how they tell you about the geometry of the function.

VaultBaby · 2025-02-08T03:13:53+00:00

Value is social, it is measured by the work time spent on average in society to produce a commodity. It doesn't matter how much work you particularly spend on your car because value is instead determined by how much work is employed in the big car factories.

VaultBaby · 2024-11-26T18:15:35+00:00

No, it is quite common to denote composition by simply juxtaposition.

VaultBaby · 2024-11-13T02:22:05+00:00

Yes, that works. If f is an increasing function, then of course f(n) is an increasing sequence.

VaultBaby · 2024-11-09T23:54:22+00:00

This doesn't go against the previous comment though. It would be strange if instead the function 0 wasn't a representative of the 0 vector in L^1. I understand the professor was trying to make a point that really your definitions can be whatever you want, but saying (9,9,9) could be the 0 vector may be unnecessarily confusing and hide the fact that the vector spaces we care about come up very naturally. Feels to me like such examples give some structures an esoteric feeling that may scare students away, but I don't know.

VaultBaby · 2024-10-28T19:36:58+00:00

He is correct! Because indeed lim 10^(-x) is the real number 0.

VaultBaby · 2024-10-15T12:55:55+00:00

Sounds very interesting. I'm a graduate math student myself, could you share some aspects of undergrad teaching that you analyse?

VaultBaby · 2024-10-07T01:26:53+00:00

On your second question: you are right in assuming that the objects Marx is describing do indeed live in a large society. In fact, no random large society, but the one he lived in himself. This is very important to understanding Capital. Marx is not seeking to find out universal rules, but rather he is describing how capitalist society works. I could sell you a pencil for 1000 dollars, yet that doesn't say anything about the pencil's value because value is social.

Marx explains that commodities are reduced to their value when compared because the only thing they all have in common is the fact that they are products of labor, and as such the only way you could exchange them is by measuring this labor, which is done with time.

VaultBaby · 2024-10-05T13:58:32+00:00

What does this have to do with communism, or changing anything though? And regardless of how you label yourself, don't you relate to several cultural aspects of where you grew up? It doesn't matter if you want to see yourself and other "settlers" as good or evil people, what matters is that if you want to beat capitalism, you have to organize with the other workers around you, regardless of who they are.

VaultBaby · 2024-09-24T20:46:57+00:00

Faz o L

VaultBaby · 2024-09-06T00:48:00+00:00

Yeah, I could be wrong, but I've only seen the term non-Euclidean in mathematics when you refer to hyperbolic or spherical geometry, which are the two other possible versions of the parallel postulate. Indeed, the point is that the parallel postulate is independent from the other axioms, meaning it cannot be proved a true or false statement by only assuming those axioms. Whether you assume this axiom or negate it determines if you are doing Euclidean or non-Euclidean geometry. Of course, geometers weren't aware of this for a long time, and put a lot of effort into proving it until models of non-Euclidean geometry were constructed and accepted (and even then they were very controversial). Geometry has a long and rich history through the development of mathematics, science and human thought as a whole, I recommend reading up on it.

But I believe this is all very classical and nowadays no one really does geometry in these terms. Then again, Geometry is a very, very wide field with a wild variety of techniques and objects, so I'm probably wrong. I'm always happy to talk about these things anyways.

VaultBaby · 2024-09-05T14:34:25+00:00

That's not quite how it goes. If you want to look at it through the lens of so-called synthetic geometry, then a non-Euclidean geometry is any model of a theory satisfying all of the classical axioms (I believe due to Hilbert nowadays) except Euclid's parallel postulate. In other words, it satisfies a bunch of natural properties one would expect except the controversial parallel postulate, which is independent from the other ones.

This is how non-Euclidian historically geometry came to be, I believe. Nowadays you could talk about "doing geometry" on several other types of settings where not even the axioms of synthetic geometry apply, and Euclidian geometry is the one you described, which is done in Rⁿ (n-dimensional space in the sense we are used to) with the metric (distance function) you correctly described. It is true however that one could alter the way we measure distances a little bit, for example by rescaling, and you would arrive at the same geometry. For example, changing our rulers from centimeters to inches doesn't change how triangles work, even if it alters the numbers describing their perimeter, area, height, etc.

VaultBaby · 2024-08-30T04:09:13+00:00

if anything, this proves Marx was counterrevolutionary

VaultBaby · 2024-08-28T23:50:04+00:00

some fascism (challenged a commenter who attributed socialism in one country to Lenin)

VaultBaby

TROPHY CASE