The author and naturalist, who has written about the experience in her new book The Soul of An Octopus, is in Vancouver for a talk at the Vancouver Aquarium.
She spoke with CBC Radio One's Rick Cluff on The Early Edition.
On her first meeting with an octopus
"The first was named Athena and I met her at the New England Aquarium. The keeper opened up the top of her tank and I was surprised to see her turn red with emotion and slide over to greet me, and her eye swiveled in its socket and locked into mine.
"And then, her arms started boiling up out of the water ... I plunged my arms into the 47 F (8 C) cold water and her arms came up to greet mine and soon I was covered in all of these strong, white, supple suckers ...
"I realized, not everyone would like this, but I was thrilled because as I petted the octopus on her head, she started to turn white, which is the colour of a relaxed octopus."
On mourning the death of an octopus
"I just started to get to know (Athena). She was so special ... because our meeting, to me, represented a kind of portal to the sea itself.
"These octopuses, they changed my way of thinking. They changed my way of living on the planet. They are the ones that introduced me to the sea."
On lessons learned from octopuses
"They've taught me that there's many different ways of knowing and thinking and feeling, all vivid and all important.
"These animals' brains are so different from ours, their lives are so different from ours, their bodies are so different from ours... they taste with all of their skin, including their eyelids ...
"They can know you and know you are different from this other person ... and that to me expands the moral universe quite a bit."
On octopuses' creepy reputation
"It has something to do with being an invertebrate, and being covered with slime ... and those suckers. But the suckers are great, it's kind of like being hugged and kissed at the same time.
"You go home and you've got hickeys on your arms to explain to your husband, but you've been having this meaningful interaction with an octopus."
On octopuses' ability to escape
"They love to play with the same toys we give to our children. Octopuses need to be occupied and people give them Mr. Potatohead, they give them Legos ... they love to solve puzzles.
"They're very smart and they're great Houdini-like escape artists too, so when you design an octopus tank, it's got to be octopus-proof or else they'll get out and if they get out, they're likely to get into someone else's tank and eat the inhabitants."
To hear the full interview with Sy Montgomery, listen to the audio labelled: Octopuses 'expand the moral universe' says researcher.Suggest a correction