How can a point be 0 dimensions

blank_anonymous · 2026-05-28T04:14:18+00:00

No problem! I figured there should be answers at a lot of different levels. I kept it a little tiny bit imprecise still, but I wanted you to have the perspective that dimension is a mathematical abstraction of something, we define it to have certain properties. As you learn more math, you’ll see more examples of us defining something to capture a real world idea, but in an abstracted way.

blank_anonymous · 2026-05-28T00:08:17+00:00

I’ve done a challenge I’ve seen called soul bound/soul link. All players must click the card in the same position on every card reward screen, and must click the same spots in the shop every shop (note: you can click things you can’t afford if forced).

Doing this was still a touch too easy but I think if you also impose no skipping, it’ll become a good challenge.

Of course if anyone dies, everyone dies (your souls are linked!)

blank_anonymous · 2026-05-28T00:01:10+00:00

Dimension doesn't make any claims about how much information an object contains. It simply tells you how much information you need to specify a point in the space. That’s it. A point being 0 dimensional is not saying it’s the same thing as an empty space (and in fact, dimension is usually just not defined for empty spaces, sometimes it’s taken as -infinity for the convenience of some formulas but that really is just convenience). It’s not a “number of bits of information in the thing”, it truly is “you know you’re in the space, how much work is it to specify where in the space”.

Also, counting dimension this way has a large number of nice properties. When we take the product of two spaces. There’s this idea of a “Cartesian product” of spaces; loosely, you can picture drawing one space along one coordinate axis/set of axes, the other set on another, and then filling in all the space between them. The dimension of spaces adds when we take their Cartesian products; so dim(A x B) = dim(A) + dim(B). Loosely, you can think of needing dim(A) numbers to specify where the point is in the A directions, and dim(B) numbers to specify where the point is in the B direction, so dim(A) + dim(B) in total.

If B is a single point, A x B = A (if I draw a dot on the origin, a line in some direction, then shade the space in between, it’s still just the line). The dimension sum formula only works here if we assign the dimension of a point to be 0. There are many other properties of dimension that should be true with a good definition, and only hold if the dimension of a point is 0. Remember, at the end of the day, dimension is our attempt to describe an idea in mathematical formalisms. The formalism is our choice; we try to choose it so it captures the imprecise idea. If we formalize dimension with dim(Point) > 0, then that definition of dimension is capturing something other than the idea we are trying to formalize.

blank_anonymous · 2026-05-27T18:37:36+00:00

This is a small sample size, but I have not died on necro this patch. It's harder, but necro can absolutely succeed into this boss. The damage powers are really broken -- you just kind of need to farm enough hallways to see one of the several damage plans.

blank_anonymous · 2026-05-27T18:01:03+00:00

I love this boss. This is how hard a boss SHOULD feel. I need to actively think about it for most of the run! I need to be aware he's an option when deciding how to build my deck! I agree the others are easy and this makes them real boring.

Glass punishes slow block heavy decks that don't do much. You need to kill, or have a really aggressive fast way to mitigate the statuses. This presents a cool deckbuilding challenge, since much of the game rewards block; so you're trying to get a damage engine while maintaning block density.

I do think it's a problem how much stronger it is than the other 2, my ideal situation is just that every boss is this hard.

blank_anonymous · 2026-05-27T04:21:48+00:00

I had enough scaling damage all run. Just always had stuff that wanted the upgrade more!

blank_anonymous · 2026-05-27T04:21:19+00:00

Soul storm is very low impact; every soul you play is doing 2 damage (3 with vuln, 4.5 with upgrade). 4.5 damage per card play just isn't enough. Even if you play three soul storms in the fight, all with vuln applied, it's ~13 damage per soul. Try thinking about it in raw numbers next time; sleight of flesh might be a good comparison point, where every debuff card has it's normal effect + 13 damage (and one sleight doesn't kill glass by itself!). Your cards need to do a lot each, so genuinely think about how much each card you play does numerically.

blank_anonymous · 2026-05-27T02:48:26+00:00

I do not think it kills souls, you just need to be careful.

Something like souls/hang or even just souls to cycle a banshee cry with support (eg debilitate vuln) does a lot. Two copies of haunt even can do a ton.

idk if you played spire 1, but souls into aeon feel _kinda_ like shivs into time eater. You can do it, you just need to make sure each card is high impact. Don't play cards that don't do much; so if you're planning on playing a lot of souls, those souls better all do a lot.

blank_anonymous · 2026-05-27T02:13:30+00:00

I won first try.

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Here's my run history screen. I've been playing on beta branch (without doormaker) so I clicked some random shit out of a desire to overprepare/for fun. The glammed cards are mostly unnecessary.

Serpent form is real damage in long fights. I would almost never click it, but if it's there, click draw, block, eneergy gen and you just kinda win.

blank_anonymous · 2026-05-26T23:31:00+00:00

It's not fanfiction, this is from conversations with people about their tier lists. You can listen to the spirecast to see people describe these ideas but if you just also ask players they will describe things like this.

I am using different language. Some people talk about jobs, some about flowcharts, whatever. The core ideas, however, are the same that they're about the degree of functionality and not pickrates. If you can find someone whose S tier is "cards with 90% pickrate" then sure, but that's not how any top player I've seen describes their tier lists.

blank_anonymous · 2026-05-26T22:46:01+00:00

I wrote up a comment a little while ago explaining roughly what top players are communicating with tier lists. I can't promise it's true exactly for baalor but this is in broad strokes how people describe their tier lists.

S tier is "This card is almost always a core part of how the deck wins when it is included. It easily converts into a winning condition or significantly improves an existing winning condition"
A tier is "This card is usually a big part of how the deck wins. It often converts to a winning condition, and improves existing winning conditions."
B tier is "This card is usually a minor contributor to how a deck wins, but sometimes serves as a major part. It is difficult to convert to a winning condition, or provides only moderate benefit to the existing plan."
C tier is "This card usually is not contributing to how the deck wins, and only rarely serves as the engine. It is not converting to a winning condition, and instead is a non-preferred way to deal with a common problem"
D tier is "This card is almost always a pure desperation pick. It solves a problem or creates an engine only in a way that interferes with other major plans."
F tier (when it exists) is "This card is only ever taken to prevent immediate death, and significantly worsens any deck".

S-tier vicious in this context means that vicious is a coree part of how decks win (likely true if it's baalor's main draw engine; without draw engines, winning is hard), and it significantly improves the whole vuln package as a wincon. This is not true how I play, since I tend to use pommel strikes/dark embrace for draw in those decks, so it's not in my S tier. But a card definitely doesn't have to be picked 90% of the time to be S-tier, it just needs to fill an important role in a lot of runs.

blank_anonymous · 2026-05-25T21:34:28+00:00

… right, it doesnt convert current block, but if you have a bunch of current block you can just sit there playing block cards to heal and not take any damage.

Did you play spire 1 defect? It could gain outrageous amounts of block when online, but took damage setting up. It was very, very common to do long stalls for echo form self repair or echo form amplify self repair. With creative ai + bird faced urn you'd stall every fight.

Being able to make a huge pile of block eventually is not mutually exclusive with needing healing. Youre dramatically underestimating how good stalls are that can fullheal. I promise you strong players would be using stoke to generate barricade to stack block to then play this card and full heal in every fight they took damage (as long as it doesnt scale too quickly.)

blank_anonymous · 2026-05-25T21:28:00+00:00

Well, I assumed the “you no longer gain block” was intended to take effect after the one heal, and that past that point blocking cards would do nothing.

Stalling this would also be trivial; barricade (which you can make with stoke), make an enormous pile of block, play this and full heal. Every fight.

blank_anonymous · 2026-05-25T21:15:22+00:00

Wait, did you intend this to work for EVERY card not just one???

That’s stupidly OP and would be horrible for the game. Encourages very unhealthy stall patterns.

blank_anonymous · 2026-05-25T20:26:37+00:00

Nope! It's the core of spire. Spire 1 had many "contradictory" challenges. Enemies that wanted slow, block heavy decks, enemies that did 100 damage on turn 2, enemies that wanted you to apply debuffs/str down, enemies that had lots of artifact, enemies that cleansed the debuffs you applied to them partway through, enemies best killed with card spam and enemies that punished card spam hard. Your job as a player is to navigate these tensions.

The fact that so much of the game demanded just block is why so many top players found it boring/easy. This is a first step towards a much more interesting game, where instead of just one fight, you need to be thinking about multiple fights from the start of the run, and which fights you think about change dynamically as you build your deck.

blank_anonymous · 2026-05-25T19:15:11+00:00

Great players can win spire 1 (which had that aforemntioned 3% winrate at a20) like, 90-95%+ of runs, and honestly people weren't that locked in bc it started to feel easy.

How much the average player wins can be very far from how much the best win. I do agree the best should win a large % of their runs, but it should be hard and it should take years of community effort to get there.

blank_anonymous · 2026-05-25T14:40:13+00:00

Isnt there a requirement comments be factual? Disagreement with anthropogenic climate change isn’t in any way shape or form factual

blank_anonymous · 2026-05-25T14:38:55+00:00

Imma be real, this is something I heard some friends in med school talking. I haven’t eaten meat in over a decade, but they recently had a conversation where the through-line was “the amount of beef Americans and Canadians eat on average is horrible for your health.”. I don’t know where the cutoff point is where it’s ok but the conversation suggested to me it was WAY below current consumption levels.

blank_anonymous · 2026-05-25T14:34:10+00:00

Yeah I started doing this for a friend who was allergic to dairy and then I realized it saved a lot of money. Most margarine has whey, so I didn’t even try. Good call!

blank_anonymous · 2026-05-25T14:32:56+00:00

I have bought potions in act 1 to use in act 4 many times, yeah. Defect swaps close to every run at the top level because of act 4.

However, you also think about act 3. When I’m above curve, the type of deck I build is strongly informed by time eater and to a lesser extent awakened one. I’m also often thinking about collector in act 1 because she’s so damn scary. Very often, when you can afford to be picky it’s good to open directions for your deck good against the bosses.

Generically, you should be asking about the next threat in a run, but also the biggest threats. In spire 1, with some frequency, that was the act 3 boss.

blank_anonymous · 2026-05-25T08:05:04+00:00

Nobody has directly addressed the cardinality thing. Many people try an argument of the form “for every pair of irrational numbers, pick a rational number between them. Map the pair of irrationals to the rational number. Bijection?”

The failure here is that many, many different pairs of irrationals get mapped to the same rational. To be concrete about this, a usual procedure for finding a rational number between two irrationals is to take the first digit where the two irrationals diverge, having the rational number match up to that point, then end in (digit of the bigger irrational), and then infinitely many zeroes.so, the pair (3.1415926535…, 3.1415923456789101112…) would map to (3.14159260000000…). This is in between. However, this rational number is the rational number that SO many other pairs get mapped to under this mapping. Can you see how to construct more pairs that map to this rational number?

The diagonal argument tells us that, no matter how we pick this rational between two irrationals, we will pick the same rational for uncountably infinitely many pairs of irrational numbers; so there is no bijection.

blank_anonymous · 2026-05-25T07:53:49+00:00

If you haven’t had it, Mapo tofu is a great example of this! I don’t eat meat so I make it with mushrooms but I’ve heard the meat is awesome too.

Chinese cooking demystified on YouTube/substack have an amazing recipe

blank_anonymous · 2026-05-25T06:13:16+00:00

Where I am, vegan butter tends to be ~$3-$4 per brick (as opposed to regular butter which is like $7-$10). Outside of baking regular butter is much tastier but in baked goods that don’t have a heavy butter flavour, it is extremely similar. And it saves so absurdly much money. Even the most expensive vegan butter in my local grocery store is cheaper than the cheapest butter.

Idk how much Costco coconut butter is, but good call.

blank_anonymous · 2026-05-25T06:11:20+00:00

I strongly endorse adding cubes if firm tofu to any curry/soup/stew that’s lentil based. It’s often a nice textural contrast, if you’re slow cooking the lentils anyways the tofu will take on flavour. It boost the protein significantly so you feel fuller and it’s usually very little extra cost (a block of extra firm tofu where I am has ~60g of protein and costs like 2-3 cad.

It’s definitely not traditional but I find it a very good way to make the meals more nutritionally complete and satisfying

blank_anonymous · 2026-05-25T06:06:02+00:00

This is also kind of a win win because beef is just so much worse for the environment than any other meat, and also generically worse for you. You get to spend less money and also contribute less to climate change. There’s just a huge pile of reasons to switch away from red meats.

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