I've read the 'object class' definitions and pretty much understand them, but I'm curious as to what the word 'euclid' actually means. I see there is a definition for the word 'keter' in the object class definitions as being "crown" in Hebrew. The only definitions I can find online for 'euclid' are horrifyingly mathematical explanations that my non-mathematical brain cannot absorb.

This has always annoyed me as Euclid really doesn't have a logical explanation to it. Keter is obscure enough that one might assume that the systems were based on the Sephirot/Qliphoth as a sort of code or, to suggest the terminology to be a relic of a more occult language - prior to the Foundation approaching things in a strictly scientific manner. I actually came up with a system that would cover both threat level and type using the Sephirot/Qliphoth but rather pointless because really, there is no way people are going to realistically change the system now.

Oddly it's Safe that bothers me. Euclid seems meaningless and therefore could be a randomly or obscurely assigned codename.

I think it was chosen just because it sounds cool, mysterious and vaguely important.

Euclid was a Greek guy who did a lot of math-related things. He's famous for geometry in particular: angles, shapes and whatnot. All his theories and stuff worked out for flat surfaces (eg. angles of a triangle equal 180 degrees). That's Euclidean geometry. On odder surfaces, like on a sphere, Euclid's laws don't apply too well; that's non-Euclidean geometry. On a sphere, a triangle's angles don't add up to 180 degrees.

As for why Euclid is the name of a classification, I have no idea. It came from 173, and we don't know why that writer picked it.

I've seen the term 'non-euclidian' many times as a huge fan of Lovecraft and his followers' works, and never quite understood it really. Thanks for the clarification on that issue. :)

Technically, we don't live in a universe with Euclidian space (the fabric of space-time is ever so slightly hyperbolic, if I recall correctly), but on the small scale that we experience it, spacetime is "flat" enough that we can use Euclidian geometry to more-or-less accurately describe things.

Lovecraftian non-Euclidian horrors are supposedly from a reality where spacetime is much, much stranger: hyperdimensional beings, beings where realities where space itself is bent obviously wrong, etc.

Giving bearhugs to the unsuspecting since 1872.

now i now why it's called euclid! his works and theories were so confusing no one could comprehend them, *LIKE A SCP!* makes sense, right?

Technically, we don't live in a universe with Euclidian space (the fabric of space-time is ever so slightly hyperbolic, if I recall correctly), but on the small scale that we experience it, spacetime is "flat" enough that we can use Euclidian geometry to more-or-less accurately describe things.

Unless you like draw a triangle on sphere (or sphereoid like you know, fly from London to New York to Miami and back to London)…

It's all a matter of scale:

- Things fall down.
- Things accelerate downward when you drop them.
- Mass moves towards the larger mass
- All objects attract each other with a force of gravitational attraction
- $F_{grav} = G * (m_{1} * m{2}) / d ^2$
- etc.

I don't understand the relevance of Newtonian gravity here. Newton's gravity works generally in Euclidian terms.

If you draw a triangle on sphere (at any scale, provided that the triangle is large enough that the surface is measurably curved in the domain of the triangle) the sum of the interior angles will exceed 180° which violates Euclid's 5th postulate. Curved surfaces are non-Euclidian 3-space. Gravity doesn't have anything to do with it, it works with a sharpie marker and a basketball or even a purely mathematical triangle on a sphere in abstract 3-space.

Drawing a triangle on a sphere isn't ACTUALLY a triangle, as you're not using all the data; specifically the "three straight lines" part - you're using arcs.

So while you THINK you're correct, you just don't have all the data.

Using Euclidian is one of those "Assume a spherical_cow" type questions. You have to ignore or be ignorant certain things; space is warped, time slows with greater gravity or velocity, etc. It's just a matter of how MUCH you're willing to disregard because it doesn't affect the final answer to within six decimal places.

In the case of Euclidian (originally) it's from ancient greek. Effects of gravity on space aren't even imagined, let alone accepted.

tl;dr

Why we use "euclid" is because it sounded cool to whoever wrote SCP-173.

If you *don't* ignore it, lines drawn on the surface of a sphere have non-Euclidian geometry. My point is that you can have non-Euclidian geometry in ordinary two-space by protecting it onto ordinary -3 space. In a way that is very ordinary and familiar (again just look at an airline's flight map). It doesn't require higher dimensional space.

Lovecraft actually knew this by the way, despite the popular perception. If you look at where he talks about non-Euclidian geometry, it is pretty clear that he talking about 3-Space projections on higher dimensional surfaces. Exactly analogous to the triangle projected onto a sphere.

In geometry a line is straight (no curves).

If you dug a hole through the sphere, you could make a line, but if you draw it ON the sphere, it's no longer an actual line, it's an arc.

Technically since space is curved by every gravity source, they actually aren't even that - it's more like a paperclip you've tried to straighten - you can't ever get those last kinks out.

Add in "How big is the universe?" type of questions and it gets even weirder. Keep aspirin ready.

Euclidian geometry is planar geometry. It doesn't describe or attempt to describe the geometry of curved surfaces. It is possible (easy in fact) to make arcs on a surface of a sphere that are not parallel. A 2-space projection of these arcs would be lines in a plane, and would be Euclidian. Yet a sphere is a thing that can exist in 3-space (duh, really) and there is no obstacle to projecting a planar triangle onto the surface. The geometry of this surface violates the 5th postulate and therefore is not Euclidian. Yet a triangle drawn on a basketball isn't a Weird Thing Man Was Not Meant to Know (though it might be a Weird Thing That Flatlanders Are Not Meant To Know). A triangle drawn on a basketball is *both simultaneously non-Euclidian and quotidian.*

You don't need to ignore anything, or dig a hole into the surface, and if you draw it large enough the sum of the interior angles will exceed 180° by far more than six decimal places. This does not have anything to do with gravity or the curvature of spacetime. This is a purely mathematical thing.

Euclidean_geometry BEGINS with plane geometry, which is what everyone is first taught. Later does include 3D solids.

It doesn't include elliptic geometry.

Elliptic geometry is totally not Euclidian geometry but it also isn't mind warping.

Euclidian geometry handles 3-space by projecting it onto planes and then doing planar geometry to it. It doesn't ever project a plane onto a curved surface and do geometry to it there. That is elliptic geometry, which is by definition non-Euclidian.

Indeed. Euclid is the 'baseline' for SCPs. They're things we don't understand, and seem to work outside of established laws. Keter means crown and implies higher level than Euclid. I'm not saying they're superior or even better written or anything. It's just that based on our baseline, which is things we don't understand and need to contain, Keter means it is much harder to understand/contain/stop from XK-ing the world into cheese. Safe goes down from Euclid, it's either more easily understood, or more easily contained.

Euclid is the 'baseline' for SCPs

nnnnnot really, no. That may be how you personally think of it, and that's fine, but that's not the "definition" of how to classify things.

Giving bearhugs to the unsuspecting since 1872.

I kind of assumed he meant that the majority of SCPs fall in the 'euclid' category…

Actually, if you do a tag count, I think Safe and Euclid are about tied.

Giving bearhugs to the unsuspecting since 1872.

Euclid Class is best understood as the 'baseline' Object Class. They require fairly specific containment procedures, but if they're followed, the object's easily contained. Assume your SCP is going to be Euclid from the start. Euclid Class SCPs are some of the most varied SCPs on the entire site; the class includes the first SCP, SCP-173, the Nexus of Abandoned Places, and Demisers.

Sorry if I'm wrong, I just took this from the How To Write an SCP Guide, so I assumed it was a pretty good way to start defining things.

"Safe" is fairly obvious, although used in a "well, in relation to that other thing" way

"Euclid" is the name of an ancient Greek philosopher & mathemetician who did a lot of work with figures on a flat plane. When you were learning plane geometry in school (triangle, circles, angles, etc.), you were learning Euclidian geometry. Geometry that occurs in a non-flat system (triangles drawn on the surface of a sphere, for instance) in non-Euclidian and gets really weird, yet interesting. As Cryokina said, we have no clue why the original author of 173 chose to use it as an Object Class

"Keter" does mean "crown", and, outside of us, it almost exclusively used in reference to the Kabbalah, wherein it represents " 'the most hidden of all hidden things,' and is completely incomprehensible to man."

Giving bearhugs to the unsuspecting since 1872.

Well, not entirly true about Keter- it is a commonly used word in Hebrew in general, and not only in the Kabbalistic sense. Hell, there's a big plastics company called that.

Reading that description of Euclid, I think it was probably chosen because while he put forward a pretty solid set of rules which we understand, they don't explain everything. With Euclid class objects, we have a pretty good idea how to keep them under lock and key, but they're still pretty unpredictable in their own way. It makes very good sense if you think about it like that.

There was a great orientation article written about this. Safe class means that you could put it in a locked room and nothing would happen. Euclid means that you need to put it in a verrrryyy special locked room to keep it locked up. Keter means it wants to bust out of your locked room and eat your grandmother. At least that's how I understand it.

Keter means it can bust out of your locked room and eat your grandmother.

What? I don't mean like it *only* wants to eat your grandmother. Keter class objects don't discriminate based on age.

I was specifying that the object classes are based on the abilities of the SCP, not its motives or temperament.

Well there's a certain amount of motive there. 343 is a reality bender capable of retconning a doctor from existence, and he's classified safe. Because you can put him in a locked room, and he'll just chill. And to be fair there are some Keter class objects that aren't actively malicious but inadvertently have the power to do horrible things. I honestly think it's a very loose term.

Yeh. There is no canon, as long as there is some degree of consistency. Classes are just as reasonably based off of containment procedure only, more than abilities/properties/effects.

As I see it, it should be judged primarily by "potential for destruction if uncontained", secondly by "difficulty to contain", and a nod given to "how far it is outside the bounds of reality as we understand it". Not by abilities, but by real potential for destruction.

343 obviously is incredibly powerful, but from everything that has been observed about him, he has absolutely no desire to do so. He CAN'T be contained, but chooses to be anyway. Everything the Foundation has seen shows that while he may have great capacity for destruction, possibly to the point of being able to end the world with a thought…he will not use it. Thus the potential for him to do so if uncontained is very low. He will stay in the locked box because he's comfortable there and sees no reason to leave. He is very anomalous, but Safe applies very well to him.

Meanwhile 682 can really only kill people one by one as he travels the world. But he most definitely WILL do so, and is very difficult to keep in containment. His potential for destruction is great, even though how much destruction he can do at any given moment is limited. He is at least as anomalous as 343, but because of his probable behavior Keter applies well to him.

And then 173 also will kill anyone that it runs across if given the opportunity. He has shown himself able to inflict incredible amounts of damage to 682 himself, which is insane. Obviously dangerous…and yet containing him is relatively simple. Maintain procedures and he will not get out, so far as the Foundation can tell. He is anomalous, albeit not quite as much so as the previous two. Euclid fits him well.

Safe: not at all dangerous if uncontained, or easily contained, or something very close to it.

Euclid: fairly dangerous, but containable if procedures are maintained. Alternately, not VERY dangerous, but liable to breach containment in undesirable ways. Alternately, unpredictable. or any of a variety of mixtures.

Keter: dangerous, and difficult to contain. If an object is not dangerous if uncontained, and if it is not at least somewhat difficult to keep contained, there is generally little to no reason for it to be Keter.

Ideally it's a largely meaningless codename chosen because it doesn't actually directly relate. This makes both Safe (unless it's like actually Greek or something) and Thaumiel kind of odd.

It is interesting that the Foundation has Keter and Thaumiel exactly morally reversed though. Keter is the sepiroth where God enters the universe and Thaumiel ("twin of God") is Keter's qlippothic opposite; it's where Satan is. This seems to support a general theme of "bad-guy God" that runs through a lot of this site…

Honestly, I always thought that Euclid sounds similar to elusive. Really simple train of thought.