What is the connection between Kali and Kaliyug? Kaalii is the goddess that takes the darkness away (Kali) but which scripture does it come from? And is there an explanation of the close connection of the the two words? Thanks
In Hinduism (or Sanatana Dharma), there is a beautiful concept where even the non living things and abstract ideas also exist in personified form. It is because Consciousness runs everything as Shrutis/ Vedas state:
प्रज्ञानं ब्रह्म (Aitreya Upanishad 3.3)
ie. Pure Consciousness is Brahman
And Shrutis/Vedas also state:
सर्वं खल्विदं ब्रह्म (Chhandogya Upanishad 3.14.1)
Sarva Khalvidam Brahman
ie. Everything is Brahman
So, from above as we know everything is Brahman and we also know pure consciousness is Brahman. So,we can say Everything is Pure Consciousness.
So, even non - living things and abstract ideas also exist in personified form. For eg. Days and Nights are phenomenon but there exists a personified form of Days and Nights.
Similarly Vedas are eternal voices. But they also exist in personified form. For eg. RigVeda has it's own form, own shape. And same for other Vedas like Samaveda, YajurVeda and Atharvaveda.
And not only this there are personified form of Anger (Krodha), Attachment (Moha), Buddhi (Intellect), etc...
And in the similar way among the four Yugas namely:
Satya Yuga, Treta Yuga, Dwapara Yuga and KaliYuga.
They all exist in their personified form also.
Kali Yuga as the name implies is the age of darkness. So, Kali is personification of age of darkness.
As per Puranic accounts the present age running is Kali Yuga / Kali age. And the personified Kaliyuga is the Kali. Kali has it's respective forms and attributes as reflected by the present age.
His main agenda is to spread violence, adharma and cruelty in the society. He tries his best to trigger such events. He will be defeated by coming incarnation of Lord Vishnu named Kalki.
Here is the description of Kali demon from Kalki Purana:
After the annihilation, the secondary creator of the universe, Lord Brahma, the grandfather of everyone, who was born on the universal lotus flower, created Sin personified, having a black complexion, from his back. The name of Sin personified was Adharma By faithfully hearing about, chanting, and remembering the descendents of Adharma, one quickly becomes freed from all sinful reactions. The wife of Adharma (Irreligion), was named Mithya (Falsehood), She was very beautiful, and had eyes like those of a cat They had a son named Dambha (Pride), who was always very angry and eneigetic. Dambha had a sister named Maya, and within her womb, he begot a son named Lobha, (Greed), and a daughter named Nikrti (Cunning), Lobha begot a son named Krodha (Anger), in the womb of Nikrti. Himsa (Violence), was Krodha's sister. From the womb of Himsa, Krodha begot a son named Kali. Kali is always seen to be holding his genitals in his left hand. His complexion is very black, like black ointment that has been mixed with oil. Kali's abdomen is like that of a crow, his face is frightening to behold, and his tongue is red and appears to be full of greed. His appearance is very fearful and a bad smell emanates from his body. Kali is very fond of playing chess, drinking wine, enjoying the company of prostitutes, and associating with gold merchants. Kali's sister was Durukti, (Harsh Speech). From Durukti's womb, Kali begot a son named Bhaya, (Fear), and a daughter named, Mrtyu (Death). Bhaya begot a son named Niraya (Hell) from the womb of Mrtyu and Niraya begot ten thousand sons in the womb of his sister, Yatana (Excessive Pain). Thus I have described the destructive progeny of Kali, who were all blasphemers of genuine religious principles. All these relatives of Kali were the destroyers of sacrifice, study of the Vedas, and charity, because they transgressed all the Vedic principles of religion. They were reservoirs of mental distress, disease, old age, destruction of religious principles, sorrow, lamentation, and fear. [Kalki Purana 1.14-22]
So, his form and birth clearly describe his attribute. As seen above he is born from Violence and Anger. Harsh speech is his sister. From his sister he begot a son named Fear.
One doesn't need to wonder or be surprised seeing the above description. How can Violence and Anger be father and mother and etc.. etc.. questions.? As I already told before, everything, even the abstract ideas have their own personified form.
On the other hand Kaali (with long 'a') is name of Goddess and she is one of the forms of Goddess Durga. She is Supremely merciful and mother of all and at the same time She is also terrible Annhilator of even time. Kala means time and Kaali is one who rules or even annhilates time.
Here is one of the story of Godesses Kali when she was invoked during encounter with two demons named Chanda and Munda and she emerges from Forehead of Ambika. It is inside Devi Mahatmyam of Markandeya Purana:
ततः कोपं चकारोच्चैरम्बिका तानरीन् प्रति।
कोपेन चास्या वदनं मषीवर्णमभूत्तदा॥५॥
काली करालवदना विनिष्क्रान्तासिपाशिनी॥६॥
सा वेगेनाभिपतिता घातयन्ती महासुरान्।
सैन्ये तत्र सुरारीणामभक्षयत तद्बलम्॥९॥
Thereupon Ambika became terribly angry with those foes, and her anger her countenance then became dark as ink. Out from the surface of her forehead, fierce with frown, issued suddenly Kali of terrible countenance, armed with a sword and noose. Bearing the strange skull-topped staff, decorated with a garland of skulls, clad in a tiger’s skin, very appalling owing to her emaciated flesh, with gaping mouth, fearful with her tongue lolling out, having deep-sunk reddish eyes and filling the regions of the sky with her roars, and falling upon impetuously and slaughtering the great asuras in that army, she devoured those hosts of the foes of the devas.
There is a connection between Kali and Kali yuga, but Kali in this regard is not a goddess but is the personality of Kali, who is the cause of all irreligion, the master of Kali-yuga, who was lower than a śūdra, disguised as a king.
You can read about that in the Bhagavatam, canto 1, chapters 16 and 17 at http://www.vedabase.com/en/sb/1
I suggest you to read those two chapters and you'll see in detail who exactly Kali is and how is he related to the age of Kali or Kali yuga.