In some platformers, your character has momentum. It can take a moment to stop, and you may be able to get a speed boost (from a spring or slope, for example) and keep it for a while. Sonic the Hedgehog is a good example of this.

In other platformers, your character does not have momentum. Stopping is instantaneous, and things like slopes will not give you speed boosts, or if they do, they don't last. Castlevania 1 is a good example of this (though that game does have the mechanic where you can't control anything about your movement while in the air).

So, do you like having momentum in platformers, or do you prefer not to have that mechanic? Does the type of game matter? (I note that Castlevania has more of a combat focus than Sonic the Hedgehog; note that Castlevania gives you a weapon, while in Sonic you instead kill enemies by hitting them while rolled up into a bomb.)

It really depends because you are talking about a physics based game engine. Older games and retro style would likely not have this feature. Overall I think the question is about the use of physics which is something that can be impactful and either make or break the game depending on the quality of its implementation.

In my opinion, if the player does not have to struggle to understand it and the game play can be naturally facilitated then I think it is a more fun and realistic experience.

Honestly, I think Mario figured it out pretty early on, while somehow Sonic the Hedgehog unfigured it out as the series went on. (The DIMPs made Advance games, for example.)

Platformers need momentum, but there's a point where it gets to be too much (I'm looking at you, Bubsy). Just the right amount can be a valuable asset. I was a Genesis kid, and I thought the momentum in the sonic games were fine. I haven't played the Advance ports, though. I assumed it was just a graphics upgrade. Why did they change the physics? Were they trying to re-invent the series?

Of course they were trying to reinvent the series, you try going back to 2D after you thought the forseeable future of your series was in 3D. So they're post Adventures, and are considered part of the "Rush" style.

One advantage to the momentum of the avatar is interacting with other environments, like the icy ground in the arcade game Wonder Boy. If you recall the classic arcade game, Asteroids, it was a foregone conclusion that the protagonist ship would need to move from the stable central spot whence it begins. It is also possible to accelerate the ship surprisingly quickly, to zoom linearly, as well as the mandatory exigent manoeuvring around larger eponymous chunks. It would be a poorer game without this mechanic, but it becomes progressively suicidal, even though the game tempts the player with a clear moment between sets.

Fun fact: like a comet, which is simultaneously one of the largest and smallest phenomena in a solar system, since its tail can reach many astronomical units, radially, but typically only encompasses a dozen miles or so in diameter; so too an asteroid field is almost totally empty for any vehicle that transects it (like the various Earth-launched probes from the Voyager series, onward) whilst still containing asteroids as large as a dwarf planet. So the famous Star Wars scene is almost nonexistent. H2G2, Introduction, cited in Douglas Adams (1978), The Hitchhiker's Guide to the Galaxy, Chapter 8, p63.

I have seen mathematical definitions, like that of Moser's number, that describe numbers that make the universe's size look so close to 0 it might as well be 0. In fact, I'm pretty sure there isn't enough space in the entire universe to represent that number.

And, of course, there are defined numbers that make Moser's number look tiny, but actually verifying this requires a full mathematical proof (you can't just eyeball the numbers and spot which one is bigger).

That's funny, it looks pretty big from here! :)

Thanks for the tip, I had not heard of Steinhaus–Moser notation (for expressing certain large numbers, extended by Leo Moser from Hugo Steinhaus's polygon notation).
It's interesting (and inevitable, don't you think?) that the numbers are self-referential, a Douglas Hofstadter (1980) strange-loop meta-algebra. (One of the rabbit holes I plumbed at university was trying to make every algorithm recursive —— which is not possible, but a seriously interesting passtime.)

What is the magnitude of the Steinhaus mega? 256²?
For n=2, the triangle of 2 = 2², which is nested inside another (4⁴), to make SMN square-2 = 64, sì?
which is then replicated for a Steinhaus circle / Moser pentagon. I reckoned on the square of the eighth power of 2, which equals two raised to the sixteenth power, our old friend 65536.

I like the conclusion in the wiki: Further Graham's number is too big to use a system of nested symbols, even when each symbol is as small as it can possibly be (one Planck volume). I suppose you could interlace the symbols in some multiplex of synchronized strings of Planck volumes … Graham's number itself seems to have only one use, which makes it vanishingly insignificant as a number. (Aside from its semantic significance, of course! :)


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† I would assert definitely, we cannot measure anything smaller than Planck volume, it is beyond any scale we can apply by dint of physical law.

That multiple would be a number that, in a sense, is almost as big; it would still be too big to represent. Hofstadter really does like his self-reference. I once went to a talk he gave, and during part of the talk he was talking about such talks and (IIRC) how people tend to fall asleep during part of them.

By the way, I've been towing with set theory a bit in my mind, and one quiestion I've asked is, "if the comprehension axiom (or its closest equivalent) requires that the property be primitive recursive, what happens"?

No preference if the game is well designed around the controls, momentum or not.

Since you brought it up I tend to dislike not having mid-air control though it's usually because of cheap hits or the game expecting you to take it slow and learning the levels thoroughly. It's not conducive to good flow.

Momentum as in "slides on ice for a moment until it stops, instead of instantly stopping" is fine.
Or maybe I should write: can be fine...depending on the game, and how exactly that mechanic is implemented.
But in general, I don't need "momentum" in my platformers.

And since you brought it up: I especially loath it, when I can "move" while in mid-jump.
That's simply not how jumps are supposed to work.
If I can change directions in mid-jump - I don't call it jumping anymore - I call that flying.
And that's fine, as long as I'm playing a fly, or a bird, etc.,...but if the character I play isn't of some kind that's expected to be able to fly - I don't want that "ability to float" in my jumps.

Perhaps NBG set theory would avoid the mess?

It depends on the dependency, doesn't it? Unless you are trying to construct a paradox (or using naive set theory), then one simply must avoid a counterfactual axiom that would obviously invalidate it. For example:
φ(x) to be ¬(x ∈ x) [i.e., the property that set x is not a member of itself]
The question remains as to why one would insist on this. (A good reason would be to create a new mathematical system, like hyperbolic geometry, which specifically invalidates Euclid's fifth postulate, the pons asinorum, as you know. :) I cannot see a good (prima facie) reason for this axiom.

Did you have a specific instance that encapsulates the problem?

It's just an idea I've had, as I am often curious about how things would behave under unusual sets of axioms. I'm wondering if, for example, you'd have a proper class whose elements are all contained inside a set in this strange set theory. (Example: The set of all real numbers obviously contains all computable real numbers, but the computable real numbers might form a set.)

As for me, my biggest issue with ZF/ZFC set theory is unrelated; I don't liie the foundation axiom, as I feel it's rather limiting, and it's not actually necessary. It just feels that it's unnecessary limiting, and I am not aware of any useful results that require said axiom.

They're not ports, they're entirely original games.