Complex analysis
Dec. 11th, 2025 09:54 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
posicПокуда нет досуга небесам,
досуг земной казнит и судит.
Закон для всех, но кто казнится сам —
авось по всем статьям судим не будет.
Кем слово «прав» и слово «невредим»
устранены из лексикона,
тот сам судья. Хотя — закон един.
Вольно ж тебе не знать закона.
... All of this is largely based on a perhaps deeply heretical theological idea, which may be thought of as diminishing the omnipotence of God (as compared to the traditional Jewish and Christian concepts). Coming as it is from the mouth of a mathematician, this theological idea is well illustrated by a mathematical metaphor.
The relevant metaphor is the comparison between the real and complex analysis (on the level of understanding accessible to a person with a university education). In the real analysis, you can modify a smooth function locally however you want while keeping it unchanged outside of a small neighborhood of the area where you have modified it to the best of your heart's desire.
In the complex analysis, with a complex-analytic function, you just cannot do that. There are many complex-analytic functions, and so many degrees of freedom in choosing one; but any local changes will have global consequences throughout the whole domain.
The perhaps deeply heretical theological idea suggests that God's omnipotence is more akin to choosing a complex-analytic function than a smooth real one. God is free to choose among a multitude of options, but whatever choices He makes, it will have repercussions throughout the whole system, and not all of such repercussions God Himself considers to be in themselves desirable. Of course, God always makes the best possible choices, but these are still choices within a realm of interconnected phenomena that cannot be chosen or changed in isolation from one another.
The point is, God cannot fix the evil that people do. You and I make our own decisions, and it is your and mine responsibility to make good choices. You are also working on your kind of complex-analytic function, which is qualitatively less important than God's one, but still very important. Whatever choices you make will also have global consequences throughout the system. You want some of these consequences and do not want some others, but you cannot help it. Your best possible choice will still inevitably have some consequences that are, in themselves, undesirable. Nevertheless some choices are good and some choices are bad; you must make good choices. The same applies to me.
When the effective sum total of the choices that people make (whatever it means) is really bad, the earthly world just goes to hell, and it is useless to blame God for not fixing it. It is not God who is supposed to fix it. It is you and I who should have made better choices. God is making the best possible decisions. It is your and my decisions that are far from the best ones, and therefore have room for improvement.
досуг земной казнит и судит.
Закон для всех, но кто казнится сам —
авось по всем статьям судим не будет.
Кем слово «прав» и слово «невредим»
устранены из лексикона,
тот сам судья. Хотя — закон един.
Вольно ж тебе не знать закона.
... All of this is largely based on a perhaps deeply heretical theological idea, which may be thought of as diminishing the omnipotence of God (as compared to the traditional Jewish and Christian concepts). Coming as it is from the mouth of a mathematician, this theological idea is well illustrated by a mathematical metaphor.
The relevant metaphor is the comparison between the real and complex analysis (on the level of understanding accessible to a person with a university education). In the real analysis, you can modify a smooth function locally however you want while keeping it unchanged outside of a small neighborhood of the area where you have modified it to the best of your heart's desire.
In the complex analysis, with a complex-analytic function, you just cannot do that. There are many complex-analytic functions, and so many degrees of freedom in choosing one; but any local changes will have global consequences throughout the whole domain.
The perhaps deeply heretical theological idea suggests that God's omnipotence is more akin to choosing a complex-analytic function than a smooth real one. God is free to choose among a multitude of options, but whatever choices He makes, it will have repercussions throughout the whole system, and not all of such repercussions God Himself considers to be in themselves desirable. Of course, God always makes the best possible choices, but these are still choices within a realm of interconnected phenomena that cannot be chosen or changed in isolation from one another.
The point is, God cannot fix the evil that people do. You and I make our own decisions, and it is your and mine responsibility to make good choices. You are also working on your kind of complex-analytic function, which is qualitatively less important than God's one, but still very important. Whatever choices you make will also have global consequences throughout the system. You want some of these consequences and do not want some others, but you cannot help it. Your best possible choice will still inevitably have some consequences that are, in themselves, undesirable. Nevertheless some choices are good and some choices are bad; you must make good choices. The same applies to me.
When the effective sum total of the choices that people make (whatever it means) is really bad, the earthly world just goes to hell, and it is useless to blame God for not fixing it. It is not God who is supposed to fix it. It is you and I who should have made better choices. God is making the best possible decisions. It is your and my decisions that are far from the best ones, and therefore have room for improvement.
