In particular, Bertil Petersson of New York stated that:
"The quote comes from a question and answer period during a seminar in
Copenhagen where Danish Physicist Niels Bohr laid out the fundemental nature
of quantum physics for the public. Included was the description of the
Heisenberg Uncertainty Principle which basically says that you can't predict
where a particle will be at a specific place in time, or vice versa. The
question that triggered the answer was: What do you predict the influence of
Quantum Physics will have on the world in the future? and Niels Bohr said,
somewhat tongue in cheek due to the prominence of the principle, that 'it is
exceedingly difficult to make predictions, particularly about the future'
(because we can't even know what the state of our situation is NOW, much
less in the future)."
This is the most common explanation and the one that I am most familiar
with. However, in a letter published in the July 19, 2007 Economist,
Felicity Pors, Neils Bohr Archive in Copenhagen, Denmark states:
"A letter attributes the following comment to Niels Bohr: Prediction is very
difficult, especially about the future. It is said that that Bohr used to
quote this saying to illustrate the differences between Danish and Swedish
humour. Bohr himself usually attributed the saying to Robert Storm Petersen
(1882-1949), also called Storm P., a Danish artist and writer. However, the
saying did not originate from Storm P. The original author remains unknown
(although Mark Twain is often suggested)."
So it appears that the most widely accepted attribution is suspect. Indeed,
even the suggested correct attribution (Mark Twain) is suspect since it is
frequently popular to attribute sayings to him when they sound like they
should have come from him.
Perhaps Fred Shapiro is closer to the answer in the Yale Book of Quotations
who cites the quotation as, "It is difficult to predict, especially the
future." He states the quotation is attributed to Bohr by Mark Kac in
Statistics (1975). He says that Kac also goes on to suggest that the saying
may have been an old Danish proverb. In addition, Shapiro notes that K. K.
Steincke in Goodbye and Thanks (1948) quotes it as a pun used in the Danish
parliament in the late 1930's.