Science and Technology links (December 7th 2019)

  1. Incredibly, there is a new simpler way to solve the quadratic formula. I used to rely on the completion of the square, but this is better! There is a video report on the finding.
  2. Surgeons are putting patients in suspended animation (biostasis) during surgery, replacing their blood with a cold saline solution, for time-sensitive interventions.
  3. Statins are a widely prescribed class of medications. They may adversely affect cognition.

Published by

Daniel Lemire

A computer science professor at the University of Quebec (TELUQ).

4 thoughts on “Science and Technology links (December 7th 2019)”

  1. Yes, the quadratic derivation is amazing but it raises more questions about intelligence than it solves:
    The occurrence of the key insight is still miraculous, there is no “motivated path” from the statement of the problem to the useful decomposition as (x – R)*(x – S).

    1. The author addresses this in the article. I don’t thinks it’s a question of intelligence, but rather, of having the right conceptual framework. The latter is a product of culture and history.

      Ancient people who solved quadratic problems wouldn’t have conceptualized things in terms of factorizations. That requires the notion that a reducible quadratic equation generally has two roots, which in turn requires having come to accept negative quantities as numbers. Negative numbers were in use in China by about 200 BCE, but it’s not clear that full understanding of the arithmetic of negative numbers was in place until Brahmagupta (7th century CE). European mathematicians during the Renaissance and later were still avoiding negative numbers by treating the general quadratic as a bunch of separate cases with positive coefficients.

      In contrast, modern people–even beginning algebra students–naturally think in terms of factorizations. Students learning algebra will have already learned negative numbers. They will likely have graphed parabolas and practiced factorizing them by hand before learning to solve the general quadratic.

      1. My point isn’t that there is a lack of intelligence of anyone but that despite mathematicians being well honed in quadratics and negative numbers for centuries no one before stumbled on the right formula because there is no “rational” explanation for how it comes about.
        It looks like an entirely random stroke of luck.

        1. I think the author wants to claim that writing the factorization (x-R)(x-S) and making the key substitution R=-(b/2)+z, S=-(b/2)-z IS a motivated, rational way to proceed in comparison with completing the square. Naturally, not everyone is going to agree with that.

          It’s worth pointing out that the parabola’s axis lies midway between the roots and that z is the distance of the roots from the axis. Students with graphing experience may find the substitution natural for that reason.

          It is likely that many people have solved quadratics this way over the centuries. One of the author’s webpages points to an old article by an algebra teacher in Ontario describing essentially the same method. The question is why it it isn’t taught this way in elementary books.

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