PART 01
数值Value
25 是此刻的大小读数，可以在同一数轴上与 20 比较。Twenty-five is the current magnitude and can be compared with 20 on the same line.
01 · 空调面板上的一个数01 · One number on a thermostat
温度显示 25 °C 时，这个数还需要第二个方向才能说清吗？When the display reads 25 °C, does the temperature need a second direction to be complete?
02温度数轴Temperature Number Line
单值拖动型Single-value slider数值Value
25
°C
分量数Components
1
一个位置one position
湿度对照Humidity contrast
60
%
03一个标量的 3 个零件Three Parts of a Scalar
一个数值位置One numeric positionPART 02
单位Unit
°C 说明数值如何解释；单位不是第二个方向分量。°C tells us how to interpret the value; it is not a second directional component.
PART 03
一条数轴One number line
温度只需一个位置；左右移动就涵盖所有可选值。Temperature needs one position; left and right cover every available value.
CONTRAST
向量对照Vector contrast
[温度, 湿度] 需要两个位置，因此不是标量。[temperature, humidity] needs two positions, so it is not a scalar.
04最小机制：一个变量对应一个位置Minimal Mechanism: One Variable, One Position
s ∈ Rs = 25 °C
拖动上方滑块验证：s 改变时只需更新一个数，分量数始终等于 1。Drag above to verify: changing s updates one number while the component count stays at one.
拖动滑块Drag the slider一个读数改变One reading changes
单点移动One point moves仍在同一数轴Still on one number line
标量更新Scalar updates没有新增方向No direction is added
05边界实验：用一个数硬定位二维点Boundary Test: Force One Number into a 2D Position
主动制造失败Create a failure只给温度，不给湿度Give temperature but omit humidity
点击后尝试用当前温度定位下方二维箭头。横坐标已知，纵坐标仍有无数可能。Try to place the 2D arrow using only temperature. Its x-coordinate is known, but infinitely many y-values remain possible.
尚未执行。一个数能否同时回答两个独立问题？Not run yet. Can one number answer two independent questions?
✗ 标量就是没有单位的数字。A scalar is a unitless number.
→ ✓ 标量可以带单位，关键是只有一个数值分量。A scalar may carry units; the key is one numeric component.
✗ 数值很大就叫高维。A large value means high-dimensional.
→ ✓ 大小回答“多少”，维度回答“需要几个数”。Magnitude asks how much; dimension asks how many numbers.
✗ 一个标量能完整表示二维位置。One scalar fully specifies a 2D position.
→ ✓ 两个独立坐标需要两个标量。Two independent coordinates require two scalars.
06 · 一句话带走06 · One line to keep