yes they did meet and exchanged ideas on various topics.I nfact,tesla was deeply influenced by vedic cosmology and philosophy that he started naming few of his discoveries in sanskrit ,after the meeting.

Vivekananda was keenly interested in the science supporting meditation, and Tesla would cite the monk’s contributions in his pioneering research of electricity. “Mr. Tesla was charmed to hear about the Vedantic prana and akasha and the kalpas [time],” Vivekananda wrote to a friend

In 1896, both of these great minds attended the play “Iziel” in which Sarah Bernhardt starred. The play was nothing but ” French reading of the life of the Buddha “, after this show Sarah Bernhardt knew Swami Vivekananda as a yogi and after seeing him in the audience she immediately arranged a meeting with him at the end of the performance, which by coincidence also included Nikola Tesla, at that time he had already invented the AC motor, developed and patented by the age of 39. The evening meeting turned out to be an interesting conversation for both, as they discussed the notions of prana (vital energy), akasha (the ether or matter ) and kalpas ( the ideas of the aeon(lifetime)), three elementary concepts of Vedantic Doctrine.

According to Vivekananda, on that very night, Tesla assured him that ideas of such a long tradition in Hinduism could find an echo in modern Western science. On the other hand, Tesla considered himself capable of mathematically demonstrating that force and material could both be expressed in terms of energy. This notion is, in turn, very close to Hindu religious thought. “In that case,” Swami Vivekananda later wrote in a letter outlining the meeting, “the Vedantic cosmology will be placed on the surest of foundations.”

Nikola Tesla. At 39 years old, he’d already invented the AC motor and developed and patented other electrical inventions, and thus received the income necessary to found the Nikola Tesla Company. At this extremely fertile time in his own life, Tesla was excited not only by what he’d achieved but by the new fields of research that his own discoveries had opened up.

During the evening, Vivekananda and Tesla met and began to speak. To the surprise of both of them, the conversation turned to topics of mutual interest. For Vivekananda, because they covered the very substance of life, and for Tesla, because he unexpectedly found inspiration and confirmation of some of the ideas he could then only barely perceive.

Among other things, Vivekananda and Tesla discussed the notions of prânaâkâsha, and kalpas, three elementary concepts of the Vedantic doctrine. Respectively, these can be understood as vital energy, the ether, and the idea of ​​the aeon. Prâna might be understood as a unit of energy, âkâsha as matter, and kalpas as time. According to Vivekananda, on that very night, Tesla assured him that ideas of such a long tradition in Hinduism could find an echo in modern Western science. On the other hand, Tesla considered himself capable of mathematically demonstrating that force and material could both be expressed in terms of energy. This notion is, in turn, very close to Hindu religious thought. “In that case,” Swami Vivekananda later wrote in a letter outlining the meeting, “the Vedantic cosmology will be placed on the surest of foundations.”

This was also the beginning of the friendship between the yogi and the inventor. Each found an interlocutor who, from his own position, nevertheless had a possibility of proximity to the other. Tesla continued to pursue his interest in the doctrine of the Vedas. Some years later, he didn’t hesitate to use some of its terms (precisely the ideas of ​​prâna and âkâsha) to describe the physical phenomena he’d been researching.

If you want to find the secrets of the universe, think in terms of energy, frequency, and vibration ,” wrote the inventor. One might wonder if, at the moment he realized this universal maxim, he hadn’t been experiencing the rapture of a yogi, or a mystic.

A letter from Swami Vivekananda with a reference to meeting Tesla. Its really surprising how two great minds from two different countries and altogether different fields of study were able to meet that also at a time when travel was not so easy.

LVII Blessed and Beloved

A swell family of my acquaintance arranged the affair. There were besides Madame M. Morrel, the celebrated singer, also the great electrician Tesla. Madame is a very scholarly lady and has studied up the metaphysics a good deal. M. Morrel was being interested, but Mr. Tesla was charmed to hear about the Vedantic Prâna and Âkâsha and the Kalpas, which according to him are the only theories modern science can entertain. Now both Akasha and Prana again are produced from the cosmic Mahat, the Universal Mind, the Brahmâ or Ishvara. Mr. Tesla thinks he can demonstrate mathematically that force and matter are reducible to potential energy. I am to go and see him next week, to get this new mathematical demonstration.

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