Brains over calculators, part 2.

I recently found another calculation that I would consider reasonable for my students to perform that their calculators cannot. On my Calc II students’ final exam, I asked them to evaluate the infinite series $$\displaystyle \sum_{n = 1}^\infty \frac{4}{(n + 3)(n+5)}$$. As a hint, I told them to rewrite in telescoping form using partial fractions. However, the TI-89 cannot evaluate this series. Since it’s hard to take a good photo of the calculator screen, I’ve instead included a screen shot of the TI-Nsipre CAS iPad app.

Congrats, Oregon! Welcome to marriage equality!

On Monday, a federal judge in Eugene struck down Oregon’s state constitutional ban on same-sex marriage, which was enacted by citizen initiative nearly a decade ago. This ruling was unsurprising, given that the defendants in the lawsuit, such as Oregon’s attorney general, agreed with the plaintiffs’ contention that the ban violated the federal constitution, leaving no one with standing willing to defend the ban’s constitutionality.

I cannot tell you how happy I was about this ruling. I grew up in Oregon, and lived there through the first decade of my adult life. I voted against Measure 36, the ballot measure that added discrimination to the Oregon Constitution, and was quite upset when it passed in 2004. Seeing pictures of Oregonian couples finally able to be married was really heartwarming to me.

Furthermore, my wife and I were married in Oregon; a framed copy of our marriage record from the Oregon Department of Health Services hangs on the wall near my desk in my home office. We chose our officiant, a senior judge, because she was on record as enthusiastic to marry same-sex couples during the brief window in 2004, before Measure 36 passed, when Multnomah County was issuing marriage licenses to same-sex couples. We encouraged our wedding guests to donate to Basic Rights Oregon, in the hope that same-sex couples could someday be married under the same laws we were. I am very happy to see that day finally come.

Yet, I must echo the sentiments expressed by a friend, who wrote on Twitter:

I am sad that marriage equality didn’t come to Oregon by the voters or their elected representatives, but through the actions of a federal judge. Now, please don’t get me wrong, I think it’s completely appropriate that a judge strike down a law if it violates the constitution. I’m not saying it’s bad that a judge overturned the will of the people—judges absolutely should overturn the will of the people when the people want to violate the constitution. But I am much less happy when a state does the right thing because it’s forced to, rather than because it chose to.

Fate has decided that my wife and I make our home in the wonderful state of Minnesota. I have discovered a number of reasons to love and be proud of my new home state. One reason (out of many) I am proud is that, a months after we moved here, Minnesotans rejected at the ballot box a state constitutional ban on same-sex marriage. Furthermore, within a year after that, Minnesota enacted marriage equality through a legislative process. I am proud that Minnesotans did the right thing without needing a judge to force them to.

There is some talk of a ballot measure in 2016 in Oregon to repeal Measure 36. I do hope Oregon voters have a chance to formally repudiate Measure 36 at the ballot box at some point.

By the way, I was inspired by the beautiful language in Judge McShane’s ruling. I think it’s worth quoting at length:

Generations of Americans, my own included, were raised in a world in which homosexuality was believed to be a moral perversion, a mental disorder, or a mortal sin. I remember that one of the more popular playground games of my childhood was called “smear the queer” and it was played with great zeal and without a moment’s thought to today’s political correctness. On a darker level, that same worldview led to an environment of cruelty, violence, and self-loathing. It was but 1986 when the United States Supreme Court justified, on the basis of a “millennia of moral teaching,” the imprisonment of gay men and lesbian women who engaged in consensual sexual acts. [. . .] Even today I am reminded of the legacy that we have bequeathed today’ s generation when my son looks dismissively at the sweater I bought him for Christmas and, with a roll of his eyes, says “dad … that is so gay.”

It is not surprising then that many of us raised with such a world view would wish to protect our beliefs and our families by turning to the ballot box to enshrine in law those traditions we have come to value. But just as the Constitution protects the expression of these moral viewpoints, it equally protects the minority from being diminished by them.

[. . .]

My decision will not be the final word on this subject, but on this issue of marriage I am struck more by our similarities than our differences. I believe that if we can look for a moment past gender and sexuality, we can see in these plaintiffs nothing more or less than our own families. Families who we would expect our Constitution to protect, if not exalt, in equal measure. With discernment we see not shadows lurking in closets or the stereotypes of what was once believed; rather, we see families committed to the common purpose of love, devotion, and service to the greater community.

Where will this all lead? I know that many suggest we are going down a slippery slope that will have no moral boundaries. To those who truly harbor such fears, I can only say this: Let us look less to the sky to see what might fall; rather, let us look to each other … and rise.

Brains over calculators!

I enjoy finding calculations that I would consider reasonable for my students to perform that their calculators cannot.

Using a double-angle identity and the pythagorean identity, it’s pretty straightforward to show that $$\sin\left(2\sin^{-1}\left(-\frac{4}{5}\right)\right) = -\frac{24}{25}.$$ However, my TI-89 returns an unhelpful -sin(2*sin-1(4/5)) instead.

Amusingly, the calculator does know that $$2\sin\left(\sin^{-1}\left(-\frac{4}{5}\right)\right)\cos\left(\sin^{-1}\left(-\frac{4}{5}\right)\right) = -\frac{24}{25}.$$

(My calculator is running the 2005 version of the software. It’s possible this has been fixed since then.)