Is humankind understood to be currently in the first of the four yugas?

Humankind is currently in the last of the four yugas.

A kalpa is a day of Brahma, and one day of Brahma consists of a thousand cycles of four yugas, or ages:

1) Satya-yuga;
2) Treta-yuga;
3) Dvapara-yuga;
4) and Kali-yuga, this is the present yuga.

The cycle of Satya is characterized by virtue, wisdom and religion, there being practically no ignorance and vice, and the yuga lasts 1,728,000 years.

In the Treta-yuga vice is introduced, and this yuga lasts 1,296,000 years.

In the Dvapara-yuga there is an even greater decline in virtue and religion, vice increasing, and this yuga lasts 864,000 years.

And finally in Kali-yuga (the yuga we have now been experiencing over the past 5,000 years) there is an abundance of strife, ignorance, irreligion and vice, true virtue being practically nonexistent, and this yuga lasts 432,000 years. In Kali-yuga vice increases to such a point that at the termination of the yuga the Supreme Lord Himself appears as the Kalki avatara, vanquishes the demons, saves His devotees, and commences another Satya-yuga. Then the process is set rolling again.

These four yugas, rotating a thousand times, comprise one day of Brahma, and the same number comprise one night. Brahma lives one hundred of such "years" and then dies. These "hundred years" by earth calculations total to 311 trillion and 40 billion earth years.