Isadora Duncan and Ernst Haeckel first meeting

Ernst Haeckel and Isadora Duncan in front of the Festspielhaus in Bayreuth, Germany, 1904

This photo was never before published. According to book" THE ARYAN CHRIST: THE SECRET LIFE OF CARL JUNG" this photo was taken on the first day of their meeting. Just a few hours later, they sat in the Wagner family's private box and viewed a performance of Parsifal.
Here how Isadora  recalls about Haeckel and their meeting:
When I was in London, I had read the English translations of the works of Ernst Haeckel in the British Museum. I was greatly impressed by his lucid and clear expression of the different phenomena of the Universe. I wrote him a letter expressing my gratitude for the impression his books had made on me. There must have been something in this letter which arrested his attention, for afterwards, when I danced in Berlin, he replied to it.
At that time Ernst Haeckel was banished by the Kaiser, and could not come to Berlin, on account of his free speaking, but our correspondence had continued and when I was in Bayreuth I wrote and asked him to visit me and attend the Festspiel.

One rainy morning I took a two-horse, open carriage, as there were no autos in those days, and went to the train to meet Ernst Haeckel. The great man descended from the train. Although over sixty, he possessed a magnificent, athletic figure, with a white beard and white hair. He wore strange, baggy clothes, and carried a carpet bag. We had never met, but we recognised each other at once. I was immediately enfolded in his great arms and found my face buried in his beard. His whole being gave forth a fine perfume of health and strength and intelligence, if one can speak of the perfume of intelligence.
He came with me to Phillip's Ruhe, where we had his room decorated with flowers. Then I rushed down to Villa Wahnfried to tell the good news to Frau Cosima, that the great Ernst Haeckel had arrived and was my guest, and would come to hear "Parsifal." To my surprise this news was received most coldly. I had not realised that the crucifix over Frau Cosima's bed, and the rosary hanging on the night table were not merely ornaments. She really was a church-attending Catholic and a believer. The man who had written the "Riddle of the Universe," and who was the greatest iconoclast since Charles Darwin, whose theories he upheld, could not find a warm reception at Villa Wahnfried. In a naïve and direct manner, I expatiated on the greatness of Haeckel and my admiration for him. Frau Cosima reluctantly gave me the coveted place in the Wagner loge for him, for I was a very close friend of hers and she could not refuse me.
That afternoon, before the astonished audience, I promenaded during the entr'acte, in my Greek tunic, bare legs and bare feet, hand-in-hand with Ernst Haeckel, his white head towering above the multitude.
Haeckel was very quiet during the unfolding of Parsifal. Not until the third act did I understand that all this mystic passion did not appeal to him. His mind was too purely scientific to admit of the fascination of a legend.
As he received no invitation to dine or to be fêted at the Villa Wahnfried, I had the idea of giving an Ernst Haeckel Festival in his honour. I invited an amazing assembly of people, from King Ferdinand of Bulgaria, who was then visiting Bayreuth, and the Princess of Saxe-Meiningen, sister of the Kaiser, who was an extraordinarily broad-minded woman, to the Princess Henri of Reuss, Humperdinck, Heinrich Thode, etc.
I made a speech praising the greatness of Haeckel, then danced in his honour. Haeckel commented on my dance, likening it to all the universal truths of nature, and said that it was an expression of monism, in that it came from one source and had one direction of evolution. Afterwards, Von Barry, the famous tenor, sang. We had supper, Haeckel acting as gaily as a boy. We feasted and drank and sang till morning.
Nevertheless, the next day, as every morning during his stay at Phillip's Ruhe, Haeckel rose with the sun. He used to come into my room and invite me to walk with him to the mountain top, which, I confess, I was not as keen to do as he was. But these walks were wonderful, because he commented upon every stone in the road, every tree and every geologic earth strata.
Finally, arriving at the mountain's height, he stood like some demi-god, observing the works of nature with a completely approving eye. He carried on his back his easel and paint-box, and made many sketches of the forest trees, and rock formations of the hills. Although he was a fairly good painter, his work naturally lacked the artist's imagination. It portrayed, rather, the skilled observation of the scientist. I do not mean that Ernst Haeckel could not appreciate art, but, to him, it was simply another manifestation of natural evolution. When I used to discourse to him of our enthusiasm for the Parthenon, he was much interested to know the quality of the marble, from which strata and which side of Mount Pentelicus it came, rather than to hear my praise of a gem of Phidias.