Imaginary Numbers

Mathematicians taken up with finding the square roots of algebraic equations have had the niggling problem that such solutions involve illogical square roots of negative numbers.

Mathematicians taken up with finding the square roots of algebraic equations have had the niggling problem that such solutions often involve square roots of negative numbers, something which is seen as nonsensical and illogical to the mathematical mind. In fact until the 1700s it was believed that the square roots of negative numbers simply couldn’t exist because they be positive numbers. This is because conversely a negative multiplied by a negative is always a positive. Whereas a squared negative must achieve a negative solution. "There seemed to be no hope of finding numbers which, when multiplied by themselves, would give negative answers. We’ve seen crises like this before. They occur whenever an existing operation is pushed too far, into a domain where it no longer seems sensible. Just as subtracting bigger numbers from smaller ones gave rise to negative numbers and division spawned fractions and decimals, the free-wheeling use of square roots eventually forced the universe of numbers to expand…again. Historically, this step was the most painful of all. The square root of –1 still goes by the demeaning name of i, this scarlet letter serving as a constant reminder of its ‘imaginary’ status."

Why a federal judge ordered White House to restore Jim Acosta's press badge

A federal judge ruled that the Trump administration likely violated the reporter's Fifth Amendment rights when it stripped his press credentials earlier this month.

WASHINGTON, DC - NOVEMBER 16: CNN chief White House correspondent Jim Acosta (R) returns to the White House with CNN Washington bureau chief Sam Feist after Federal judge Timothy J. Kelly ordered the White House to reinstate his press pass November 16, 2018 in Washington, DC. CNN has filed a lawsuit against the White House after Acosta's press pass was revoked after a dispute involving a news conference last week. (Photo by Alex Wong/Getty Images)
Politics & Current Affairs
  • Acosta will be allowed to return to the White House on Friday.
  • The judge described the ruling as narrow, and didn't rule one way or the other on violations of the First Amendment.
  • The case is still open, and the administration may choose to appeal the ruling.
Keep reading Show less

Russian reporters discover 101 'tortured' whales jammed in offshore pens

Protected animals are feared to be headed for the black market.

(VL.ru)
Politics & Current Affairs
  • Russian news network discovers 101 black-market whales.
  • Orcas and belugas are seen crammed into tiny pens.
  • Marine parks continue to create a high-price demand for illegal captures.
Keep reading Show less

Water may be an inevitable result of the process that forms rocky planets

New research identifies an unexpected source for some of earth's water.

Surprising Science
  • A lot of Earth's water is asteroidal in origin, but some of it may come from dissolved solar nebula gas.
  • Our planet hides majority of its water inside: two oceans in the mantle and 4–5 in the core.
  • New reason to suspect that water is abundant throughout the universe.
Keep reading Show less