Dwelling more on symmetry and Arthanaareeswara, a scientific point of view is available with several references https://pmc.ncbi.nlm.nih.gov/articles/PMC3705693/ . While this is Lord Siva's tattva, Bhagavata provides many instances of Lord Visnu taking the feminine forms like Mohini that is more of a ploy than a tattva. That means, Lord Siva is not just making appearances to save mankind or making temporary truce between devas and asuras. He is an embodiment of the human condition.
As said many times, "Lord Siva leaves no child behind including those wrestling with bisexuality, hermaphroditism, homosexuality, gender identity disorder, gonadal dysgenesis, chromosomal defects, etc." that are often referred to as LGBTQ factors that are physiological. Freud and Jung agreed that there is neither perfect masculinity nor complete femininity based on psychological studies. That means, every jiva falls into the gray areas between the two gender extremes.
The creation after going through many maha yugas is trying to achieve perfection, like a pure diamond sans inclusions, which is akin to a computer that never fails. Sometimes the manufacturing defects are passed on to the consumer. The Law of Karma may have something to do with this.
In the symmetry debate, mainstream science only accepts certain combinations of matter or energy that lead up to satisfying conservation laws that are thought to be of paramount importance ("all laws of nature originate in symmetries"). Mathematicians are more precise by looking for invariance (changelessness) under transformations such as translation (moving from A to B), reflection (like in a mirror), rotation (like earth around its axis) and scaling (changes in multiple dimensions). And the development of supersymmetry to understand the plethora of subatomic particles MSS discovers, rather conjures up everyday. Whereas, MSS has turned from us vs. dogma to us vs. universe where contrarian views and thought experiments have lesser importance than personalities.
So that leads to my inference that Mainstream Science and Mainstream Media enjoy reflection symmetry. If I said they are a happy couple, I'd be breaking the symmetry. So I leave it upto them to figure out.
However, as hindus built temples such as Arthanareeswarar Temple in Tiruchengode, and made carvings of arthanaareeswara, is it like having a third pole? I think it is like advaita where all we see is oneness or unity. When there is no second, where is the question of the third?
I can imagine some non-savaites thinking that siva-sakti unity is a blight and a blemish. To support my claim the Wiki page (Ardhanarishvara - Wikipedia) draws parallels to Yama-Yami of Rig-Veda which in my view is incorrect. Here is from Rig Veda translated by Dr.Wendy Doniger
10.10 Yama and Yami
Yama, the first son of the sun, is regarded in later mythology as the first mortal man and king of the dead, while Manu, the sun’s other son, is regarded as the ancestor of the human race. In Avestan mythology, the primeval incest of the twins, Yama and Yami, remains an important episode in the procreation of the human race; in India, Yama rejects the erotic solicitations of his sister in the Rig Veda and is never again exposed to them, for later Indian mythology is significantly silent about the affair. The hymn is not, however, a commentary on a social charter (‘Thou shalt not commit incest’), but rather a speculation – ultimately negative – on a possible cosmogony, the male and female twins functioning as a variant of the androgyne.
The hymn begins, as is usual with those of the ‘conversation’ genre, in medias fires. Yami invokes gods of procreation and argues that the human race must be preserved; Yama counters by invoking moral gods and their laws. Unlike the similar conversation between Agastya and Lopamudra (1.179), this hymn ends with the rejection of the woman, who finally loses her temper completely.
1 [Yami :] ‘Would that I might draw my friend into intimate friendship, now that he has gone far across the ocean.{1} A man of foresight should receive a grandson from the father, thinking of what lies ahead on earth.’
2 [Yama:] ‘Your friend does not desire this friendship, in which a woman of his kind would behave like a stranger.{2} The heroes, {3} the sons of the great spirit,{4} supporters of the sky, see far and wide.’
3 [Yami:] ‘The immortals desire this, that off spring should be left by the one mortal. Let your mind unite with my mind;{5} as a husband,{6} enter the body of your wife.’
4 [Yama :] ‘ Shall we do now what we have not done before? Shall we who spoke truth out loud now whisper false- hood?{7} The divine youth in the waters{8} and the woman of the waters – such is our source, our highest birth.’{9}
5 [Yami:] ‘The god Tvastr,{10} the creator and impeller, shaper of all forms, made us man and wife even when we were still in the womb. No one disobeys his commands; earth and sky are our witnesses for this.’{11}
6 [Yama:] ‘Who was witness of that first day? Who has seen it? Who can proclaim it here? The law of Mitra and Varuna is high. Yet what will you say to men, wanton woman, to seduce them?’
7 [Yami:] ‘Desire for Yama has come upon me, Yami, the desire to lie with him upon the same bed. Let me open my body to him as a wife to her husband. Let us roll about together like the two wheels of a chariot.’
8 [Yama:] ‘These spies of the gods, who wander about here below, do not stand still, nor do they bunk their eyes. Wanton woman, go away fast with another man, not with me. Roll about with him like the two wheels of a chariot.’
9 [Yami:] ‘ She would do what he wished in the nights and in the days; she would deceive the eye of the sun for the instant of the blink of an eye. We twins are related in the same way as sky and earth. Let Yami behave toward Yama as if she were not his sister.’
10 [Yama:] ‘Later ages will come, indeed, when blood relatives will act as if they were not related. Make a pillow of your arm for some bull of a man.{12} Seek another husband, lovely lady, not me.’
11 [Yami:] ‘What good is a brother, when there is no protector?{13} What good is a sister, when destruction breaks out?{14} Overcome with desire, I whisper this again and again:mingle your body with my body.’
12 [Yama:] ‘Never will I mingle my body with your body. They call a man who unites with his sister a sinner. Arrange your lustful pleasures with some other man, not with me, lovely lady. Your brother does not want this.’
13 [Yami:] ‘Dammit, Yama, how feeble you are. I have not been able to find any mind or heart in you. Some other woman will surely embrace you like a girth embracing a harnessed stallion or a creeper embracing a tree.’
14 [Yama:] ‘You too, Yami, will surely embrace another man, and he will embrace you, as a creeper embraces a tree. Seek his mind, and let him seek yours. Join with him in proper harmony.’
Notes
1. The ocean may be the metaphorical ocean separating mortals (like Yama) from immortals (as Yami may be), in which case ‘he’ is Yama. But ‘he’ may be the avenging god whom Yama fears (vv. 2, 6, and 8), or the sun in the water (v. 4), in which case Yami is assuring her brother that he need not fear, as the spy is absent across the ocean.
2. This may mean that Yama does not wish the woman of his kind (his sister) to act like a stranger (like a woman with whom sexual contact is allowed); in caste terms, he avoids marriage within the subgroup (gotra). Less likely, but possible, is the interpretation that Yama fears that a woman not like him (an immortal) will behave like one of his kind (a mortal woman, one who may have sexual contact with him). In caste terms, he avoids marriage outside the group (varna).
3. The gods, or perhaps just the Adityas, the particular servants of Varuna.
4. Varuna, most likely, as guardian of the moral law; or Rudra, punisher of incest (in which case the ‘heroes’ would be the Maruts).
5. The word (manas) can designate mind or heart, the seat of both rational and emotional functions. But since it is later contrasted with a word for ‘heart’ (v. 13), it is here probably limited to the first connotation.
6. Here Yami implies that Yama actually is her husband, a thought which she makes explicit in v. 5; later, however (v. 7), she merely asks him to behave as if he were her husband, as her resolve weakens.
7. The word, anrta, means not merely to speak a lie but to say something that violates the moral order, to say something that may be true but should not be.
8. Probably the sun, born of the waters, but perhaps just any Gandharva.
9. Yama argues both that people born of such lofty parents should not break the moral law, and also that he and Yami, having the same parents, cannot procreate together.
10. The god of procreation, and the artisan of the gods, fashioner of the embryo in the womb. Cf. 10.184.1, 4.18.3.
11. Here and in verse 9, Yami argues that sky and earth are as closely related as she and Yama are, that their procreation was not only permitted but even archetypal.
12. ‘Bull’ is Vedic slang for a virile man, like ‘stud’ in American; cf. 1.179.1 and 1.179.4.
13. She argues that a brother should protect his sister, even if this involves incest, to keep her from going unsatisfied and un fertilized. Ironically, it is the brother who should find a husband for his sister and avenge her if she is rejected.
14. Destruction (nirrti) both in the wider sense of the destruction of the human race (as she argues in verse 1) or in the more particular sense of the destruction that comes upon a man who dies son- less.
Regards
