Who was the sage who witnessed Mahabharata and Ramayana multiple times?

Question

I recently heard about time travel and am curious to know about the sage who had seen Mahabharat and Ramayan multiple times.

Answer 1

He is Kakbhushuda(काक​ भुशुण्ड). There is a story of Kakbhushunda in Yogvashishtha, Nirvan Prakaran Purvardh, Sarga 14-25.

Quoted text is from Yogvashishtha English translation part-3.

Vashishtha discussed about Bhushunda to Rama:

8. Among them there was a crow's nest, belonging to one old raven by name of Bhusunda, who lived quite happy with himself; as the god Brahmá dwells ontent in his lotus-bed.
9. There is no one in the womb of this world so long lived as he, nor even the gods in heaven, can boast a greater longevity than he among the feathered tribe; and it is doubtful whether there may be another as old as he in times to come. (Old as Adam and as old as Methuselah).
10. This crony crow was beauteous even in old age, and had become passionless and great-minded by his long experience. He remained quiet with the tranquility of his mind, and was as graceful as he was full of knowledge of all times. (Acromatic[**Achromatic?] as old Nestor of the present, past and future-trikálajna).
11. If any one may have the long life of this crow, his life becomes meritorious, and his old age is crowned with sapience. (The vigour of life is productive of meritorious works, and its decay is fraught with wisdom).

............

30. He witnessed the course of ages and periods, and marked their advent and exodus in repeated succession; and was thereby known as the time worn Bhusunda in this world, and a being of stout and unflinching mind.
31. He was weary with counting the revolutions of the Kalpa cycles, and with recounting the returns of the preserving divinities of the world; such as the Sivas, Indras, the gods of the winds and other......

(When Vashishtha visited toKakbhushundi)

Following part is from conversation between Vashishtha and Kakbhushunda.

Wwhen Vashishta asked him:

27. Sir, you have seen the many changes of the world, and have been experienced in all things in the repeated course of creations; must be best able to tell me the wonders that you have witnessed during the revolution of ages.

Kakbhushundi discussed what he have been seeing for many kalps.

Quoting the part that related to the title of question.

17. I bear in my remembrance the overthrow of tripura thrice ten times by Siva, and the discomfiture of Dakhas' ceremony for more than once by the irritated Hara; and I recall to my mind the downfall of ten Indras by the offending God, who bears the crescent moon on his forehead, (and the confinement of their thunder-bolts within the caverns of volcanoes glass).
18. I recollect the battle that has been fought eight times between Hari and Hara, and the first appearance of Vishnu and Siva, jvaras or the cold typhoid fevers in these] conflicts. (This means the rising of the malarious fevers of Dinajpur, whichraged among the belligerent forces on both sides).
19. I remember, O silent Sage! the difference in the intellects of men at every succeeding age, and the various readings of vedas at the ceremonial observances of mankind. (This means the varieties of reading of the vedas as pointed in the prati sákha, and the difference of phonetic intonation as shown in the sikshas, have greatly tended to the depravity of vedic recitation, and consequently to their inefficacy in producing their desired consequence also).
20. O sinless saint! The purans also though they agree in the main substance, are so full of interpolations, that they have been greatly multiplied in successive ages. (It is quite true of works in manuscript and without their gloss).
21. I remember also many historical works, which have been composed by authors learned in the vedas in the succeeding ages. (These works are called Itihásas or legendary accounts, as the epics of Rámáyana and mahábhárata[**Mahábhárata] by Valmíki and Vyása respectively).
22. I have the recollection of the other wondrous composition of legendary accounts, under the title of the Mahárámáyana a work comprising one hundred thousand slokas or tetra stichs, and replete with sound wisdom. (This was revealed by Brahmá to Vasishtha and Viswamitra).
23. This work presents the conduct of Ráma for the imitation of the men, and sets the misbehaviour of Rávana to the opprobrium of mankind. This precept contains the essence of all wisdom, and serves as the luscious fruit of the tree of knowledge, placed in the palm of all people. (The substance of these instances is, that virtue is true happiness below and vice is baneof life).
24. This work is composed by Valmíki, who will compose some others also in time; and these you will come to know, when they will be presented to world in time: (as I have known them before hand by my foreknowledge of things.[** ,?] gloss) (This work is called Vasishtha Ráma samváda in the form of a dialogue as those of Socrates and Plato).
25. This work whether] it is a composition of Valmíki, or the composition of some other person, is published for the twelve times, and is now going to be allmost[**almost] forgotten by men.
26. The other work of like importance, is known under the name of Bhárata; I remember it to have been written by Vyása at first, but is becoming obsolete at present.
27. Whether it is the composition of person known by the name of Vyása, or a compilation of some other person, it has upto[**2 words] this time undergone its seventh edition, and is now going fastly to be forgotten.
28. I remember] also, O chief of Sages! many tales and novels and other sástras, composed in every age and Yuga; which have been written in a variety of styles and diction.
29. O good sage! I remember to have seen also many new productions and inventions, following one another in succeeding age; and it is impossible to innumerate enumerate this innumerable series of things.
30. I remember the Lord Vishnu descending many times on earth, for the destruction of ferocious Ráksasas], and is now to appear here the eleventh time under the appellation of Ráma.
31. I know the lord Hari to have thrice comedown[**2 words] in his form of Nrisinha or leonine man, and thrashed the demon Hiranya Kasipu as many times, as a lion kills a gigantic elephant. (i. e. Although the gods are of smaller forms and figures, yet they got the better of the giants, by means of their better arms and knowledge of warfare).
32. Vishnu is yet to be born in his sixteenth incarnation at Vasudeva's bode, for the purpose of rescuing the earth from the burthen of the oppression of its tyrannic lords and despots.

So, He is kakbhushunda. If you want to know more about Kakbhushunda, read the whole story of Kakbhushunda from Yogvashishtha Maharamayana. Kakbhushundi is also mentioned in Ramcharitmanas.