占星上星座和宫位0°0‘0“的数学定义难题及其解决方法

占星上星座和宫位0°0‘0“的数学定义难题及其解决方法

占星上一个星体如果处于某一星座占星上0°0‘0“的位置、常常会带来它究竟属于哪个星座的混沌定义模糊，某一星座、宫位的0°0‘0“本身在定义上也是模糊的，所以如果采取如下标准，即把某星座对准的0°0‘0“的位置，视为上一个星座的30°60‘60”，在0°0’0“这个弧线位置上应该是上一个星座的30°，刚才在这个极限位置上发生了朝向下一个星座的极限趋于0的无限小位移了之后、才进入到下一个星座，就是下一个星座0°x”（x—>0）的位置，就会带来在定义上与数学意义不能兼容的难题得以解决的好处，虽然会带来四轴点（春分点、秋分点、夏至点、冬至点，对应白羊座、天秤座、巨蟹座、摩羯座的0°0’0“）位置上需要澄清和解释的新问题，但对这方面的新问题的解决将在后文中详细解说。

如果取【星座A：θ ∈ [0°, 30°)，星座B：θ ∈ [30°, 60°)】的划分方法的话，就会带来每个星座都把“0°0′0″”这个点作为自己的一部分、“占了”0度，但却“并为占实际范围”，带来代数意义上的问题，好像一块面积包含了0平方单位的部分、一段曲线包含了长度为0的区间那样，要知道一个分界点自身是没有长度意义的，“0”这个实数的意义本身就是”这个抽象位置上、某一意义事物的单位含量不存在”（负数则表示相反意义的事物），在数学测度意义上，当“可测空间”对应的数字为0的时候，对应的函数的自变量的集合为空集合，即不属于该函数的自变量取值范围。因此，我觉得应该左开右闭的区间区分：星座A：θ ∈ （0°, 30°］，星座B：θ ∈ （30°, 60°］，这样就能解决0面积领域的难题了。

然后对于四轴点、则可以标注得更加清晰，因为太阳实际日射位置有实际面积和实际物理意义、不是数学抽象意义上无长度、无面积等测度意义的点，当太阳直射南北回归线（夏至、冬至），太阳直射位置自南向北或自北向南扫过赤道而直射赤道（春分，秋分）的时候，直射春分点和秋分点这一0度位置的太阳光照并不会“0面积”（物理上的光子也是在各个方向上有波长、有波动性、因此有面积的）其所对应的星座含义，比如“太阳此时处于春分点，位于白羊座0°”的实际意义，其实是太阳直射赤道的日光落在白羊座0°的白羊宫（座）宫内一侧所产生，对应的占星上的灵验共时性也由白羊宫内非0度数（有长度意义）的曲线所对应的太阳光光照面积所带来，所以在抽象处理四轴点的抽象位置点的时候、可以采取微积分的方式将其定义为【春分点∈（白羊座0° 0’0”，白羊座0° 0’0” +Δα），其中α—>0“且<1“】，【夏至点∈（巨蟹座0° 0’0”，巨蟹座0°+Δα），其中α—>0”且<1“】【秋分点∈（天秤座0°0‘0“，天秤座0°0‘0“ +Δα），其中α—>0”且<1“】，【冬至点∈（摩羯座0°0‘0“，摩羯座0°0‘ 0”+Δα），其中α—>0”且<1“】。

不过，在占星实践的名称上应该保留白羊座0°、天秤座0°、双鱼座0°等包含回归黄道的四轴点所在的宫位在内的黄道十二宫的0°名称，以便方便称呼和直观理解，避免使用过于抽象、过于复杂的数学定义从而使得陈述四轴点的重大意义及其共时性时带来不必要的麻烦与共时性神秘意义被稀释，只是保留“某星座0°位置”这种通俗称呼的同时、心中有数要知道那对应的是该星座0° 0‘0“+ Δα（其中α—>0° 且<1“）即0°0‘0“位置的”下一星座”一侧的极限领域的实际作用，这样四轴点的0°0‘0“的几何意义得以保留的同时、与星体位于四轴点的0°0‘0“的位置上应该对应着星体的光照在屋里事实上落入四轴点宫位大于0°0‘0“的度数位置的物理事实相兼容，同时解决了占星上0°0’0“所带来的占有星座区间0长度的难题，与此同时黄道十二星座的每个星座可的区间标记可以增加到满30°，后天十二宫同理处理，这就好办了！

The Mathematical Definitional Difficulty of 0°0′0″ in Zodiac Signs and Houses—and How to Resolve It

In astrology, when a celestial body is located at exactly 0°0′0″ of a zodiac sign or astrological house, it often leads to definitional ambiguity: to which sign or house does it actually belong? The point 0°0′0″itself is inherently vague in its definition, both mathematically and astrologically. To resolve this ambiguity, we may adopt the following convention: treat the position defined as “0°0′0″” of a given zodiac sign as conceptually equivalent to the 30°60′60″ mark of the previous sign — in other words, the theoretical end-point of the preceding sign.

At the point labeled “0°0′0″” of a new sign, the celestial body has just undergone an infinitesimal displacement directed toward the next sign, having departed from the final moment of the previous one, approaching the next sign as x → 0⁺, and thus should be considered to have only just entered the new sign — at a position like 0°0′x″ where x → 0⁺. This convention resolves the contradiction between traditional astrological labeling and the strict requirements of mathematical definition and measure theory, although this approach introduces new questions regarding the cardinal points—the equinoxes and solstices (i.e., the vernal equinox, autumnal equinox, summer solstice, and winter solstice, corresponding to 0°0′0″ of Aries, Libra, Cancer, and Capricorn, respectively). These issues, however, can be clarified and will be discussed in detail in the following sections.

If we adopt the interval-based division such as Sign A: θ ∈ (0°, 30°] and Sign B: θ ∈ (30°, 60°], it leads to a subtle contradiction: both signs appear to claim ownership of the 0°0′0″ point—each treating it as part of its own boundary—yet that point has no measurable extent. This creates a problem in terms of algebraic and geometric logic: it’s as if a surface area were said to include a region with zero square units, or a curve to include a zero-length segment. One must remember that a boundary point itself carries no length, area, or quantity in the measure-theoretic sense. The real number zero signifies precisely this: that at this abstract location, the amount of any meaningful entity is nonexistent. (A negative value, by contrast, would imply the presence of something of opposite nature.)

In the context of mathematical measure theory, when the measure of a given space is zero, the corresponding set of input values (the domain of a function) is effectively an empty set—meaning that such points do not belong to the valid domain of the function.

Therefore, I propose that the division of zodiac signs (and similarly of astrological houses) should follow a left-open, right-closed interval format—for example: Sign A: θ ∈ (0°, 30°], Sign B: θ ∈ (30°, 60°]. This approach elegantly resolves the conceptual issue of “zero-area occupation” and avoids assigning ambiguous measure to boundary points.

As for the Four Cardinal Points, their definition can be clarified even further by acknowledging the fact that the Sun’s position of direct illumination has real physical area and measurable extent—unlike the abstract, zero-length points in pure mathematics.

When the Sun is directly overhead at the Tropic of Cancer or Capricorn (during the summer or winter solstice), or when it crosses the celestial equator moving northward or southward (during the vernal or autumnal equinox), the point of solar illumination is not a point of zero area. On the contrary, it is a region affected by actual solar radiation, which is distributed across space by photons that have wavelengths and wave-like properties, and thus occupy nonzero physical area.

This means that even at the exact moment of the vernal or autumnal equinox, when we say the Sun is at 0° Aries or 0° Libra, the astrological meaning of that position is not derived from an abstract mathematical point, but from the actual solar energy falling on the portion of the zodiac that lies just beyond 0°0′0″—within the measurable interior of the sign itself.

For example, when we say “the Sun is currently at the vernal equinox, at 0° Aries,” what this actually means is that the Sun’s direct rays are falling on the equator, and the solar illumination is entering the interior side of Aries at 0°, within the sign’s own spatial domain. The astrological synchronicityassociated with this moment arises from the solar energy falling upon a curved segment of Aries that lies beyond the exact 0°0′0″ mark, a segment that has measurable length and area.

Therefore, when abstractly defining the positions of the four cardinal points, it is appropriate to use a calculus-based limit approach, such as:

【Vernal Equinox ∈ (0° 0′0″ Aries, 0° 0′0″ Aries + Δα), where α → 0″ and < 1″】,

【Summer Solstice ∈ (0° 0′0″ Cancer, 0° 0′0″ Cancer + Δα), where α → 0″ and < 1″】,

【Autumnal Equinox ∈ (0° 0′0″ Libra, 0° 0′0″ Libra + Δα), where α → 0″ and < 1″】,

【Winter Solstice ∈ (0° 0′0″ Capricorn, 0° 0′0″ Capricorn + Δα), where α → 0″ and < 1″】.

However, in astrological practice, it remains appropriate and even necessary to retain the conventional terminology of 0° Aries, 0° Libra, 0° Pisces, etc.—that is, the named 0° points of the twelve zodiac signs, which include the locations of the four cardinal points along the ecliptic. This ensures ease of reference and intuitive understanding in interpretation. Avoiding overly abstract or mathematically complex definitions in the practical naming of these points helps prevent unnecessary confusion when conveying the symbolic importance and synchronicity of the cardinal transitions, thereby preserving their mystical and symbolic potency. When astrologers continue using familiar terms like “0° of a sign” in practice, they should keep in mind that this refers to 0° 0′0″ + Δα of that sign (where α → 0″ and < 1″)—namely, the infinitesimal domain just beyond the 0°0′0″ boundary, on the side of the new sign.

This reframing both preserves the geometric meaning of the 0°0′0″ point and resolves the paradox of “zero-length occupation” (that is, a paradox that arises from trying to assign spatial extent to a point that has none).