OBJECT
对象Object
M-01 到 M-08 是被描述的设备。M-01 through M-08 are the devices being described.
01 · 想象仓库货架01 · Imagine warehouse shelving
同一箱零件按重量摆一遍、再按尺寸摆一遍，箱子变了吗？If the same boxes are arranged once by weight and once by size, did the boxes themselves change?
023D 散点换轴实验3D Scatter Axis-Reorder Lab
唯一变量：轴顺序One variable: axis order
对象Objects
8
始终不变always unchanged
特征Features
3
temperature · vibration · hours
移动点Moved points
0
换轴后位置变化positions changed by mapping
正在生成固定设备点云…Generating the fixed device cloud…
x temperature · y vibration · z runtime
拖动旋转 · 换轴看点云重排drag to orbit · remap axes to rearrange
03空间里的 4 个零件Four Parts of a Coordinate Space
same data · new viewFEATURE
特征值Feature values
温度、振动、时长是每台设备携带的三个数。Temperature, vibration, and runtime are three values carried by each device.
AXIS
坐标轴Axis
轴把一个特征值翻译成某个空间方向。An axis translates one feature value into one spatial direction.
POSITION
位置Position
三个轴坐标合在一起，才得到点的位置。Coordinates on all three axes combine into a point position.
04最小机制：坐标是按轴排列的特征值Minimal Mechanism: Coordinates Are Axis-Ordered Features
features → position
p = (fx, fy, fz)
M-01 的原始三元组不变；只要把 T、V、H
重新分配给
x、y、z，显示位置就会重排。M-01 keeps the same raw triple. Reassign T, V, and H to x, y, and
z, and its displayed position rearranges.
选择轴顺序Choose axis orderT · V · H
重新映射坐标Remap coordinates(T,V,H) → (V,H,T)
点云移动Cloud moves对象和值均未变objects and values remain
05边界实验：重复一条轴会压扁信息Boundary Test: Duplicating an Axis Flattens Information
主动制造失败Create a failure让 x 和 y 都表示温度Make both x and y mean temperature
点会被限制到 x=y 的斜平面，振动信息消失。仍然是 3D 画面，却不再是三个独立特征。Points collapse onto the x=y plane and vibration information disappears. The view is still 3D, but no longer carries three independent features.
尚未执行。先尝试三种有效换轴。Not run yet. Try the three valid mappings first.
✗ 点移动就说明对象变化。A moving point means the object changed.
→ ✓ 也可能只是坐标映射改变。The coordinate mapping may simply have changed.
✗ 画出三根轴就一定有三类信息。Three drawn axes guarantee three information
types.
→ ✓ 每根轴必须承载独立、明确的特征。Each axis needs an explicit independent feature.
✗ 坐标距离天然就是有意义的相似度。Coordinate distance is automatically meaningful
similarity.
→ ✓ 量纲、缩放与特征选择都会改变距离。Units, scaling, and feature choice all change
distance.
06 · 一句话带走06 · One line to keep