Decidability 2

Decidability 2

In my first post on Decidability, I wrote about the Halting problem and how everyday life decisions seem undecidable. Still, we are deciding many things, from minute to minute, from hour to hour, that shape our life, surroundings, and possibly the future. But: Do we decide in the first place or is it arbitrariness? Does it matter which one it is? And if it is not arbitrary, how can we decide?


Only those questions that are in principle undecidable, we can decide.

Heinz von Foerster, Ethics and Second-order Cybernetics

Some time ago, I would have said that decisions are guided and derived from environmental data. The deciding person merges and weights the available data to arrive at a conclusion on how to decide. However, this model has flaws: If the data would lead to a clear answer, there would be no need to decide in the first place; the data just gives the answer. Consequently, only if the data is insufficient to derive a clear answer, the need to really decide arises. Thus, decisions also always result in uncertainty; inherently, we are deciding only the things where the outcome is unclear. Also, in most cases it is an arbitrary choice which data is considered and how it is weighted; infinitely many and equally reasonable decisions are always available – the decision itself is arbitrary.


If you can’t decide between two options, throw a coin. Before it touches the ground you will know which side you want it to land on: Decision made.

My best friend; around when we were in 6th grade

I always liked the idea of this approach to decisions. While in essence it’s not very spectacular, this proposed trick addresses the time component of decisions: If a decision is difficult, we tend to postpone it to an uncertain moment in the future in the hope for more data (or that someone else decides for us). Throwing the coin makes the decision pressing and imminent; and, if, the correct decision cannot be induced by data but is arbitrary, this trick lets us make a decision right now. And this decision comes down to the gut feeling of the deciding person, but it doesn’t matter because the decision is arbitrary whatsoever. My version, by now, is simpler: ‘If you can’t decide between two options, throw a coin and take the option it selects.’


Draw a distinction.

Georg Spencer Brown, Laws of Form

Thus, the coin method is congruent to the proposed mark or cross by G. S. Brown as used by Luhmann: There is no way to decide correctly. You never know the outcome, otherwise there would be no need to decide. The only thing that matters is that you decide in the first place.

Thanks to input from my dad. This post probably deserves a re-write as soon as I have more time to properly study the provided material. Since I decided that all posts also have pictures, I chose some older ones from a vacation last year in Sächsische Schweiz. Back then, I still had borrowed his camera and had even less knowledge about photography than now…

Photo Post: P1

Photo Post: P1

Last weekend we walked a hiking trail around the mountain Hoher Meißner. Unfortunately, the only time the alarm clock wakes me up lately is on weekends. The sun rose at 4:30 a.m., so in order to have good light, one needs to be up on time. While we were early, the sun already was high above the horizon when we started hiking. Nevertheless, the cold air and wet grasses made it feel like morning. The landscape was wonderful, but difficult to photograph during plain sunlight; thus the abundant insects had to serve as objects, including additional species of the soldier beetle, ladybugs, and bees.

DoF 3: Summer Evenings

DoF 3: Summer Evenings

Mini-Summer-Evening-Bucket-List:

  • Go outside
  • Eat strawberries
  • Listen to the clicking of your bike
  • Appreciate the barley fields
  • Smell the elderberries
  • Finish with ice cream
Birds at the river greet the evening.

Cantharis fusca & Triticum aestivum

Cantharis fusca & Triticum aestivum

Exactly a month ago, in my post on botanical gardens, I made the promise to inform myself (and you) about one combination of plant & insect I am coming across. Thus, I think it is time to fulfill this promise even though I did not manage to visit the botanical garden in the mean time.

We stumbled across many individuals of this beetle species already on our hike on P23. However, we had no idea what kind of species it exactly is:

Last Friday, I finally managed to go outside again and did some macro photography. And, again, I saw multiple of these bugs in the grasses, weeds, and fields. It also felt like the first genuine summer evening: Warm air coated the landscape, undulating fields of barley stretched in golden rays, the city vanished behind endless rows of trees, and its inhabitants escaped the asphalt towards the deep blue bathing lake.

And I stood in the fields and waited. Waited for this bug, waited that it flies in front of my lens, and that I don’t miss to press the shutter. And then it came:

It is (presumably) a Cantharis fusca, a species within the family of Cantharidae, in English also known as soldier beetle or leatherwings. The last name refers to its soft body; this is also why it is called ‘Weichkäfer‘ in German. There are many different sister species and often they only differ by minuscule details, at least to the untrained eye. In Germany alone, there are 86 different described species; worldwide more than 4500 – for a single family of beetles! The diversity and complexity that nature creates can be mind-boggling. They are mostly colored red, black, or golden. A wonderful visual overview is given here.

The plant it was landing on seemed rather uninteresting; most of all because it is so common on the fields in our area. At least, that’s what I thought at first:

It’s simple wheat – isn’t it? By now, I am not even sure anymore. Wheat is one of the most cultivated crops and it is an important source of food in uncountably many countries. The first record of wheat seems to be around 9600 years BC. This means, today we are 2000(!) years closer to Abraham, the patriarch of several religions, than Abraham was to the first use of wheat. I find it difficult to comprehend such time scales. However, this also means that there are countless different cultivated wheat species by now, including Common wheat, Spelt (‘Dinkel’), Durum, Emmer, Einkorn (the wild form), and many many more. Genetically speaking, a large difference between these species is the number of copies of each chromosome they have in their cells. While humans and many animals are diploid (they have two copies), it’s rather common in plants to have even more than two copies of each chromosome – this is referred to as polyploidy. (It also makes our life more difficult when dealing with their DNA sequences; but more on that at a different time.) The wild form of wheat is also diploid, but the other species are mostly tetra- or hexaploid. I still think that what I photographed is the most common form Triticum aestivum, but there are several more detailed distinctions to be made within this species.

Also, all information here is pure speculation from dubious internet research, also see this post on information.

Decidability 1

Decidability 1

Life is about decisions, large and small ones. What should I study? Which bread do I buy? Should I reach out to a long lost friend? Which approach to life should I take? What values are important to me? Do I buy the next lens or do I save up the money? Do I go outside for sports? Do I keep working for another evening? How do I want to spend the limited time I have in my life?

Some questions seem irrelevant, others may determine several years of our future life. So, how can we decide all these questions? Or: Is it even possible to decide all these questions? How should we approach and deal with any possibly life changing matter and decide: This or that? Now or later? Yes or no?

The more difficult the questions become that I face, the more I am convinced that they are inherently undecidable at any given moment in time. We do not have enough information to know all outcomes, the uncertainties are always large, and we cannot weigh in all factors because of their multitude and complexity. This also won’t change in the future. Maybe the options we decide on shift. Maybe it’s too late for a decision and we did not even have the opportunity to deliberately decide it ourselves. Some things we were sure that we chose correctly turned out to be terribly wrong; other things work perfectly even though we thought we made the wrong turn earlier.

Decidability is also infamous in computer science. In its simplest form it is known as the Halting Problem and was presented by Alan Turing. The problem formulation is as follows: Given an arbitrary algorithm and its input, is it possible to find another algorithmic solution that decides whether the given algorithm stops on the given input, or continues to run forever? If a solution can be found, then the problem is decidable. If no solution exists, then the problem is undecidable. In the case of the Halting problem, it can be shown that no algorithmic solution exists that solves the stated problem; thus, it is inherently undecidable. If you’re interested, keep reading for the proof:

We proof the above statement by contradiction. Imagine there exists an algorithm that can decide our problem statement: Given, as input, an arbitrary algorithm and its input, it can always decide whether this algorithm stops on the input or not. We call our deciding algorithm h and our input x. Given h, we now define a new algorithm h* that is a modified version of h: If h determines that the input algorithm stops, then h* keeps running in a loop. If h determines that the input algorithm keeps running, then h* stops. What happens if we feed our algorithm h* as input to itself (of which our original deciding algorithm h is part of)? This can be seen as a self-referential operation. We refer to the h* that is the deciding algorithm to h(h*) and to the input h* as x(h*). Both, h(h*) and x(h*) are the same algorithm. We have two possible outcomes: Either h decides that its input x(h*) stops – however, in this case h(h*) would keep running: a contradiction because x(h*) and h(h*) are the same algorithm. Or h decides that its input x(h*) doesn’t stop – but now, h(h*) would stop: again, a contradiction. Thus, the halting problem is not decidable.

To be continued in one of the next blog posts about how to decide anyways.

DoF 2: Coffee and Cake

DoF 2: Coffee and Cake

Flavors of a city evening:

  • 1st Cake & tea appears
  • Sirens pass
  • People relish the passing warmth
  • Swifts call
  • Pigeons coo
  • Closing windows reflect last beams of the sun
  • Chocolate taste
  • Flower scent blends with neighbors dinner
  • Thoughts caught between the past and future
  • 2nd cake & lemonade disappears
Swifts speed through the streets and announce the emerging thunderstorm.

I made some city photos and like the following quite a lot:

There is a lot going on. Old and new mix: In the foreground, and the background. Glimpses insight are allowed by the low-standing sun, outside mirrors in the polished windows. Remains of the last visitors are present, while new guests are awaited eagerly after a period of little freedom. In fact, I liked it so much that I printed it big directly afterwards:

Cake from the best cafe in town with lots of vegan options! (However, the two shown here are not vegan…).

DoF 1: Van Weekends

DoF 1: Van Weekends

Packing List:

  • Time
  • A direction
  • Calmness
  • Sleeping bags
  • Hot tea
  • Chocolate spread
  • Porcino ravioli
  • Book: Migrations
  • Camera body, lenses, tripod, filters
  • Solarlight
  • And Ernie (our van)
And these are the sounds at 5:30 a.m. in the middle of nowhere.

More info on this trip here (as well as earlier posts).