Gaming philosophy conundra

[SolemnGolem]

What does a 1-sided die look like?

And moreover, under what circumstances would it need to even be rolled?

[Agemegos]

Originally Posted by SolemnGolem

What does a 1-sided die look like?

And moreover, under what circumstances would it need to even be rolled?

In a game of lawn bowls.

[whswhs]

Originally Posted by SolemnGolem

What does a 1-sided die look like?

And moreover, under what circumstances would it need to even be rolled?

Its one side would be a Möbius strip or something analogous.

[The Colonel]

Originally Posted by whswhs

I suspect that thinking of the outgroup as not really being people may go back to the Paleolithic, even if the word for "not really people" changes.

I'm told that a great many primitive cultures tend to have an endonym which, on translation simply means "people" and refer to all of the rest of humanity as "not people" (although polite translators sometimes parse this as "other people"). Sort of like a cultural equivalent of that theory of mind deficiency that makes toddlers hide by covering their eyes.

[whswhs]

Originally Posted by The Colonel

I'm told that a great many primitive cultures tend to have an endonym which, on translation simply means "people" and refer to all of the rest of humanity as "not people" (although polite translators sometimes parse this as "other people"). Sort of like a cultural equivalent of that theory of mind deficiency that makes toddlers hide by covering their eyes.

In an RPG, is the distinction between PCs and NPC a theory of mind deficiency?

[TGLS]

Originally Posted by SolemnGolem

What does a 1-sided die look like?

And moreover, under what circumstances would it need to even be rolled?

It's a sphere. It never needs to be rolled, as you can reduce +Xd1 to +X, but if you had a system that increases or decreases the number of sides based on some variable, it may be called for.

[whswhs]

Originally Posted by TGLS

It's a sphere. It never needs to be rolled, as you can reduce +Xd1 to +X, but if you had a system that increases or decreases the number of sides based on some variable, it may be called for.

Technically, a sphere is an infinite-sided die.

[Anthony]

Originally Posted by whswhs

Technically, a sphere is an infinite-sided die.

No, a sphere is a sphere. Increasing the number of sides on a polyhedron can come arbitrarily close to a sphere, but fundamentally a sphere has a single curved surface, a polyhedron has multiple flat surfaces.

[whswhs]

Originally Posted by Anthony

No, a sphere is a sphere. Increasing the number of sides on a polyhedron can come arbitrarily close to a sphere, but fundamentally a sphere has a single curved surface, a polyhedron has multiple flat surfaces.

At the very least, a solid body with C sides all equidistant from its center seems to be a sphere. Whether a body with aleph sub null sides is a sphere depends on whether you require a sphere to have a continuous surface.

But you can define a plane that is tangent to a sphere at a single point; that single point is a limiting case for a flat surface.

Addendum: What's sort of a dual case to this may help with the intuition. Say you toss a sphere onto a table. Let the surface of the sphere be printed with colors, in such a way that every point is a different color. For any throw of the "die," the surface of the table must be tangent to one point of the sphere, distinguishable as being one particular color. That is equivalent to a polyhedral die landing on one side, except that the "side" of the sphere is a single point. Now, how many sides does the sphere have? It clearly is larger than any finite integer.

[ravenfish]

From the point of view of tabletop gaming, the sphere is indisputably one-sided rather than infinite-sided, unless you have found one that can produce an infinite number of possible displayed results depending on the point at which it stops rolling.

(Anyway, if you argue that the sphere has a number of sides equal to the number of possible tangent planes, then any actual die becomes a d[huge number] due to the fact that its "faces" are not perfectly flat, and any actual roll will be undetectable cocked at one of a vast number of possible angles.)