The society recognizes and honors its most accomplished members by making them fellows. The Technical University of Munich lists 22 members of its faculty who have been so honored. One of these IEEE Fellows is Professor Gordon Cheng.

Professor Cheng worked with others to develop an exoskelton. This device provides support and force that supplements what a person’s own bones and muscles can provide. It can enable paralyzed persons to move in ways that their unaided bodies cannot. The technology must communicate to the person information about movement, position, and force (giving a sense of touch) while also reading from the person’s muscles and brain that person’s intentions. Professor Cheng and his collaborators demonstrated the potential of this technology at the FIFA 2014 World Cup in Brazil. A paralyzed man, wearing their exoskelton, kicked a ball during the opening ceremony.

]]>Some of our students might understand this excerpt:

Physiker glauben häufig, dass die besten Theorien schön, natürlich und elegant sind. Was schön ist, muss wahr sein…

Here is a profile of the author, Sabine Hossenfelder.

]]>One of my students impressed me and her classmates yesterday with her recitation of the first one hundred digits of pi. In a subway station we saw the number pi written on the wall (part of an exhibit of interesting numbers and statistics). Kat walked to the “3”, put her finger on that first digit, turned her back to the wall, and walking slowly while dragging her finger on the wall recited from memory the first 100 digits of pi.

Ferdinand Lindemann, a German mathematician, was the first to prove that pi is a transcendental number. Lindemann completed his career at the University of Munich.

Mathematicians recognize several kinds of numbers.

- Z (for Zahl) is the set of
**integers**(whole numbers). - Q (although the word is the same in both languages, MathWorld, a wonderful online encyclopedia of mathematics, says Q is from the German word Quotient) is the set of
**rational numbers**. These are the numbers that can be expressed as ratios of two integers (fractions such as 3/4). - R is the set of
**real numbers**. Z and Q are subsets of R. However, R includes numbers that are neither integers nor the ratios of integers. Some real numbers are irrational—it is not possible to specify their value with a finite number of digits (such as 0.123) or with repeating sequences of finite length (such as 0.33333….). **Algebraic numbers**are another subset of the real numbers. An algebraic number is the root of a polynomial equation (we all saw these in high school). For example, the square root of two is a root of the equation x^2 – 2 = 0. Some algebraic numbers (such as the square root of 2) are irrational.- A
**transcendental number**is an irrational number that is not algebraic. Pi is an important example.

There are algorithms that will approximate pi to any desired degree of precision. If you are patient enough, you can have as many digits of pi as you like. This property makes pi a computable number.

There are **non-computable numbers**. In fact most numbers are non-computable.

Alan Turing, then a young English mathematician, published a paper in 1936 with the title “On Computable Numbers, with an Application to the Entscheidungsproblem.” The title refers to challenge posed by German mathematician David Hilbert in the previous decade, but has roots that go back to Gottfried Leibniz’ dream in the seventeenth century of a machine that could answer any question posed in logic.Turing built his proof that some numbers cannot be computed (and that we can describe some problems for which there is no computer program that will produce a solution) by building on a method that Georg Cantor, yet another German mathematician, had developed in the late nineteenth century. Cantor had proved that there are degrees of infinity—the set of integers and the set of real numbers both have infinite size, but the reals are more infinite. Turing wrote his landmark paper only five years after Kurt Gödel (then at the University of Vienna, later Albert Einstein’s colleague at the Institute for Advanced Study in Princeton) uncovered limits to the methods of proof.

Turing’s paper marked the start of the study of computer science. Every student of computer science sees the word “Entscheidung.”

Once mathematicians believed that any mathematical proposition could, with enough time and effort, be proven true or false. No longer.

Similarly, once physicists believed that they could, with enough time and effort, measure with arbitrary accuracy, and then predict future positions and velocities with as much accuracy as desired. No longer. The physicists’ story is also filled with German names (e.g., Werner Heisenberg and his Uncertainty Principle).

]]>Wladimir Klitschko ist ein sehr bekannter Boxer. Er ist viele Jahre Welt-Meister gewesen. Jetzt hat er gesagt: Ich höre auf. Klitschko ist 41 Jahre alt.

I wanted to make sure that I understood the meaning of “aufhören.” I found an article that provided this mnemonic:

Now before we get to the grammar, let’s take a quick look if aufhören has any connection to hören after all. So imagine some cave-men sitting around their fireplace doing cave-men things and then all of a sudden there is a noise in the woods. Naturally they all would stop their activity and try to listen closely…. they stop doing their thing and … listen up… aufhören. Over time the listen part has disappeared and aufhören only kept the stop whatever you are doing part as its meaning.

I suppose that if I were teaching music, I might say to my students: “Wann der Dirigent spricht, hören Sie auf, alles das Sie tun.”

In any case — “Sie und ich müssen alle Sommeraktivitäten bald aufhören!”

Roughly: “When the sun hangs low in the sky, even dwarves cast long shadows.”

An Austrian, Kraus criticized the political culture of the 1920s and 1930s.

]]>Gott ist bei uns am Abend und am Morgen und ganz gewiß an jedem neuen Tag.

(God is with us in the evening and in the morning. Completely and certainly, He is with us in each new day.)

Ich will diese Tag mit dir leben und mit dir gehen in ein neues Jahr.

(I want to live with you this day and go with you in a new year.)

This is my prayer for you as we close 2016 and begin 2017!

]]>Edgar ist klug und, Sie werden entdecken, nicht allein!

This film is available from Film Movement on a DVD whose main feature is titled *Bomber*.

Meiner theuren, heimgegangen Schwester Franziska Ilgen, zum Andenken in herzlicher Liebe gewidmet, von ihrem Bruder

Manches Blümlein hab’ ich nah’ gefunden

Manches pflüchte ich in weiter Fern’

Doch zum Kranze hab’ ich sie gewunden

In der Stille unterm Kreuz des Herrn

Mögen sie zu seiner Ehre blühen

Mög’ uas ihnen manches fromme Herz

Einer höhern Welt Genüsse ziehen

Dies wunscht der Verfasser allerwärts

Dedicated with deep love in the memory of my precious sister Franziska Ilgen, who has gone home to the Lord, by her brother.

I found some flowers nearby.

I plucked some flowers from farther away.

I have wound them into a wreath

beneath the stillness of our Lord’s cross.

May these blooms honor our Lord

and pull us to a higher and more enjoyable world.

This is the author’s wish always.