Similarity / Dissimilarity

Similarity / Dissimilarity

We’ll mix it up this time. Correct: Not I, but We. Because you’re going to get involved in this one. One simple question, many answers. Take your time to think about it before reading on; here comes the question:

Are the following pictures similar?

Let’s start with the basics: They are digital pictures shown on a website, saved in the same digital format. Not known to you, they also have the same number of pixels along the long side. To be exact, 1000 pixels as all pictures here in order to not occupy too much space (and to not get stolen – but who will steal them anyway…). Color information is stored in Adobe RGB color space, however, since all are black and white, the information for red, green, and blue is identical for every pixel anyway.

Not so fast, you will intervene. And you are right in doing so: While the long side is always 1000 pixels, they do not share the same aspect ratio, nor the same orientation. And it won’t be a stretch to claim that between every two pictures no single pixel is identical. So already after these first simple investigations we see a problem emerging: They are similar to a specific degree, identical in some respects, but disparate with respect to other criteria.

Let’s dive deeper: Are the images we see here the actual images, let alone do they inherit or show some of our reality? First of all, they do not show the full data gathered, since the original pictures are much larger, also encode color, and a variety of additional information in their RAW format. And in any case, they are just some arbitrary representation of reality without any real connection to it. One of endless possible portrayals of reality. While this does not directly touch on the original question, it is important to keep this in mind when we search and interpret their similarity.

Lastly, how do the overall pictures appear? Even if the single pixels are different between all images, combined they create patterns that can be alike. The pixels combine to a variety of forms, which, in turn, are received differently by different viewers. Waves, scales, oscillations, geometrical forms. And are they really creating these patterns or does the viewer infer them? Can we infer different patterns from the same picture?

I could go on for a while, but it’s getting too long. Let’s move on to the second question: Now, we also need to quantify the difference between every pair of pictures. On a scale from 0 to 100, how different are these two?

And what about these?

I think you are getting my point. We can create an endless list of metrics and choose what we think is best. We can apply these metrics to these simple images, or we can gather more data, larger pictures, RAW data, and then apply the metrics. We can weight and combine metrics to generate an overall score of similarity, we can try to assess how it performs in comparison to other scores. We can compare pairs of pictures and create a hierarchy of similarity. But it will never be the same when done by different people. And in the end, it’s quite arbitrary. Do we look at pixels, color, form, format, derived patterns, povoked emotions?

Most of the day I am doing such arbitrary comparisons. Not between images, but between DNA strands. Instead of pixels I am looking at sequences of A, C, G, and T. Depending on the chosen metric, a variety of results emerges. There is no correct metric, no correct similarity measure. There is no correct way to describe reality, neither to analyze and exploit it. There is an infinite number and every single one creates another distinct result.

But fortunately, in the end, it somehow seems to work – at least sometimes, when it solves a problem in biology research or medicine; but most of the time I don’t get how.

Polyommatus Icarus

Polyommatus Icarus

Primrose Optimization 2.0: The common blue (Hauhechel Bläuling), or Polyommatus Icarus. Hiding the blue upper side, but showing the yellow spots underneath the tips of the wings. When flying high his wings don’t melt – when sitting still, a lovely subject for a photographic study during sunrise. His favorite plant: Lotus corniculatus; here: on wheat.

There is never a single point of view. The multiplicity of different perspectives can convey a sense of completeness; however, infinitely many other perspectives always remain unexplored. It’s important to be able to exclude, to simplify, to stop exploring. It’s also important to disconnect from everyday life, slow down, take a break, and relax. Even on vacation I struggle with this. There is always the drive to do stuff, otherwise I am afraid to miss something. I cannot switch off my brain and sit still; the limited time needs to be used to climb the next mountain, to find the next boulder, to photograph the changing landscapes. It remains unknown if and how I can resolve this constant struggle – I’ll let you know when I found a solution…

But still, I have to get up to find a butterfly and at least a hundred different perspectives, enjoy.

Photo Post: Printing

Photo Post: Printing

When we are not away on weekends I mainly do two things: Writing blog posts or printing photos (however, this weekend we also prepared our van for the upcoming holiday!). By now, I have stashed quite a few prints and I need to figure out what to do with them; I think we still have plenty of free space on our walls (my significant other does not agree…), but it also takes time and money to properly frame the prints. So far, I have created mainly A6 postcards on matte paper, A5 prints on semi-gloss paper, A4 matte prints with white margins, and occasionally a large A3+, all on fine art Hahnemühle-paper. I also tried some lower quality paper, but have to agree with their slogan: ‘Paper makes the difference’, visually as well as haptically it’s outstanding. While in the beginning I needed several tries for the right settings, now I can get (most) prints as I want them from the get-go. Additionally, I slowly figured out which pictures do work as print in the first place, and which pictures just do not translate to paper. And as mentioned earlier: The printing also changed my progress of photographing itself, regarding the settings, lighting, composition, and subjects. The first charge of cartridges is empty and already replaced for the next prints to come.

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.

Colors of the Morning

Colors of the Morning

On several occasions I have been asked by family and friends: ‘Do you edit your photos?’ I understand where the question comes from and probably would have asked other photographers the same question myself before I bought a camera. But when you start taking pictures the answer becomes irrelevant, and also more philosophical. The question assumes that the truth can be captured; that there is a real representation of the environment. And this is simply not true. It is impossible to depict the world as it is and every representation is disconnected from the environment and just represents itself.

Pastel colors illuminate receding mountain ranges separated by morning haze; 45 minutes before the rising sun.

Thus, when people ask this question, what they often really mean is: ‘Do your photos look like it did in reality?’ And again, there is no right answer. Different people see different things in reality, pay attention to different details, some see green and red, others only see browns instead. Additionally, the effect of a scene is not only influenced by sight, but also many other senses that cannot be transported in a simple photo. So maybe the photo looks somewhat like the reality to me, but not to you.

An additional layer that is often forgotten: The picture is already hugely edited in camera. The photo receptors just capture some limited amount of light which is very different from reality. Besides this raw data, cameras often produce JPEG-images with already applied color profiles that interpret the raw data. This profiles can boost colors, contrast, or luminosities; or decrease them. Let’s take one of the easier settings that is present in all modern cameras: the white balance. The idea is to tune the information received from red, green, and blue light photo cells to display neutral colors (white, grays, or black) as such. The automatic white balance often fails during sunrises or sunsets because there are no neutral colors in the frame: everything is tinted with deep blues, shy purples, defiant magentas, or lush yellows. Take a look at the following two pictures. Both show the exact same frame only with different in-camera white balance settings:

Two different settings of white balance on the same photograph; 20 minutes after sunrise.

So which one is more correct? Impossible to answer. It depends on what I want to show and what you want to see in the image. Because cameras are not as powerful as computers, it often makes much more sense to edit photographs in a specific software instead. Then, you can fine tune the picture without depending on the limited options that are present in the camera.

So, yes! I edit my photographs! Sometimes only in camera, sometimes heavily in software. It depends on what I want to show. Sometimes the edited photos look more accurate to my perceived reality than the unedited photos; sometimes I use editing deliberately to transfer a feeling or message and don’t care about a ‘realistic’ depiction. Sometimes the photo is perceived as unrealistic even though it’s straight out of camera. Sometimes a photo is perceived as realistic even though it’s heavily edited. Ultimately, photography is just one of many arts, I will create what appeals to me, and if it also appeals to someone else: even better.

The color of light is getting warmer with the rising sun and illuminates the meadows below.

All these photographs were taken on last Saturday. Again, my dad and I started at 4 a.m. in the morning to view the sunset. This time not in the Harz Mountains but from a smaller peak in Hessen close to Hoher Meißner. During the two hours on the peak we saw many different colors and I tried to represent all of them in the next pictures. Enjoy.

Completing the Last Step

Completing the Last Step

I finally did it! I started printing photos and I can’t stop anymore. And it is at least as much fun as I hoped for. But getting there was also quite stressful, so what happened?

As written in my last post, I bought a used photo printer on the internet as well as a full set of ink. In this case it’s the Canon Pixma Pro-1 that is running on 12 pigment ink tanks costing approximately 25€ per tank. When it arrived I enthusiastically started to test it out – and sadly had to realize that one of the print nozzles was clogged. No matter what I tried I couldn’t resolve the issue. Thus, I did not only buy an unusable printer, but also wasted a lot of ink during my iterations of cleaning the print head and trying to print. While I could get back the money for the printer, I still lost a lot of the ink. And more importantly: I couldn’t print even though I was eager to do so.

After two weeks of weighing my options I finally bought a second printer, also used, but this time in person. I had to travel two hours one way to get it; however, the hassle was worth it and this time everything went well: Not only does the printer work flawlessly (at least for now), but furthermore the seller gave me lots of high quality paper for free. And this paper is at least as expensive as the ink: Only later I realized that a single A3+ sheet goes for over 5€.

That’s it. My small adventure of buying a printer. What follows is my still ongoing adventure of figuring out how to use it properly. I still have very little knowledge of what I am doing; but the printer and paper already produce results I am really proud of. I tried to capture it on camera, but unsuccessfully. It’s very different to hold a print in your hand than to see a picture of it: The stunning overall visuals, all the little details when you examine the print closely, the texture of the paper, the smell of paper and ink, the weight of the print: I love it. And thus, I have chosen three of my first prints I will give some short additional information on:

The first picture is one of my all-time favorites: Two goose in the morning fog at our local lake which is only a few minutes by bike. It’s printed on a matte and thick paper, the Hahnemühle Photo Rag, 308 gsm. Texture and details in the print are marvelous.

The second one is an abstract black and white photo of grass and frost I took in the Harz mountains when I went out to photograph the sunrise. It was one of my first dedicated photo trips and until today I never had such good conditions again. I think I still took several of my best photos so far on that morning. It’s printed on the Hahnemühle FineArt Pearl, 285 gsm, which is a semi gloss paper that works beautifully with contrasty black and white photos.

The last one is a picture from our early morning adventure I already talked about here. Clouds blend with rows of trees while the sun hasn’t quite conquered the horizon. Again, there is so much to discover on this photo when you hold it in your hand printed out. So many details I have missed before when just looking at the digital version. It’s printed on Hahnemühle Photo Rag Baryta, 315 gsm.

I have compiled an additional small collection of some detailed shots of further prints. For now, I have only printed A4 and A6 with one exception: I created one A3+ print of a photo from Mädchen Klitzeklein; it’s the one hanging already on the wall. For now, I only have to sell the broken printer again…

Exploration / Exploitation

Exploration / Exploitation

Reinforcement Learning is one of three main approaches for machine learning and can be described as follows: An autonomous agent observes the environment and performs actions to reach a pre-defined goal. A reward function gives feedback to the agent according to how close it was to reach the desired goal; otherwise, the agent has no information on which actions lead to the largest reward. The agent tries to maximize its gained reward in each learning iteration. And in every learning iteration the agent is caught in the exploration / exploitation dilemma: It could either exploit the already gained knowledge of the environment to safely receive the highest reward that it currently knows. But then it may miss other, still unknown options with potential higher reward. Or it could explore the still unknown environment to search for even greater reward. However, it may potentially walk off with even less than when taking the save option.

Solving the dilemma efficiently is difficult, but one intuitive way is as follows: In the beginning, most of the environment, and thus potential reward, is unknown, so the agent has to start by exploring a lot. With time, the agent knows more and more of the environment and can start to utilize its knowledge from time to time. After many iterations, it can then maximize the reward with the known options and only infrequently explore new ones.

The same applies in photography: I could either exploit a known place with known reward, or I could explore an unknown location. If I only choose the first option, I will never find all the beautiful spots out there. And if I always choose the latter, I will miss many good opportunities at good locations while checking out some new places.

Last weekend we decided for the latter: My father and I entered the parking lot at 5 a.m. to, again, get on top of Achtermannshöhe in the Harz Mountains before sunrise (check out Clear Skies and Minus 14 Degrees). From the weather forecast it was unclear if we will be engulfed in clouds or if the clear sky would stretch out above us. Luckily, it was mostly the latter, with some distant orange strips of haze and clouds illuminated by the rising sun. We persevered for 90 minutes in the freezing cold with numb hands and feet, but a breathtaking view made it worth it. In the North, the silhouette of the Brocken towers; in the East, black trees in contrast to orange and purple plains stretching behind; rolling hills dipped into pastel colors in the South; and in the West, the Upper Harz in blue and purple with alternating rows of dead and healthy trees.

After the hike back down we entered the parking lot for a second time, but this time with good memories and full SD cards. For the next adventure, I think I will choose exploration instead.



I am quite fascinated by patterns; they are abundant, in nature and in the human-made environment. They help to order and classify, to understand and comprehend. During my work, I am regularly searching for patterns in sequences of characters (more on that in a later post). However, mostly it is not only about finding the pattern, but finding the irregularity, the absence, or the variation of the expected pattern.

If you consult the most-visited nonprofit website, there is a whole list of different types of patterns that occur in nature; a non-exhaustive extract: symmetry, which can occur along multiple axis and dimensions. Trees and fractals are commonly found in plants. The former also emerge naturally as patterns in more complex concepts such as evolutionary relationships. Spirals are a common feature for animals. My favorite category includes chaos, flow, and meanders, the latter ones often caused by flowing water. I have seen countless examples of such wonderful patterns in the nature of Iceland, e.g. check out these photos by Kai Hornung. Waves and dunes are formed by the wind – the ocean is beautifully captured by Rachael Talibart. And then there are all the other ones like tessellations, cracks, spots, or stripes.

All of these are often represented in abstract macro or landscape photography. In the following you find a collection of patterns that we encountered in frozen puddles during our last hike in the Harz Mountains. You can already spot a bunch of the mentioned types, however, I will be looking out for all the other ones I missed so far with the hope to continue this collection in the future.

Know Your Resources

Know Your Resources

On an ordinary day during the last autumn, I saw, for the first time, the common kingfisher – what a beautiful bird. Despite its divergent blue and orange coloring, it is quite hard to spot when sitting still. Only when the kingfisher changes its branch from which it hunts you see a brief blue shimmer darting close above the water. It belongs to the family Alcedinidae whose species are scattered across the whole globe; and most of them are at least as colorful as the common kingfisher (e.g. check out the oriental dwarf kingfisher!). Since then, we have seen the common kingfisher multiple times at a lake close to our home and I have tried to get in on camera at multiple other locations around our town. I spoke with others where to find it, I spent lots of time waiting for it, and I made hundreds of photos of empty branches and little blue dots in the far distance. On some occasions I was somewhat successful, but the clear sight was always interrupted by branches at the locations I visited. Then, last Friday evening after another day of home office, I sought out one of the last spots around our town I haven’t been before during my search for the kingfisher. It’s only 3 minutes from my normal working location but due to the current situation I haven’t been there for a year. And there, directly at a small pond, the perfect location for the king fisher is prepared: A stick curved above the water, a sign that warns uninterested bystanders of the curiosity, and nearby benches and bushes for the interested photographer. I guess, I have to come back next autumn and try my luck here; in the photos below you see my best attempts from this winter.

Work often feels similar to this experience: You search something for a long time before you unexpectedly find it somewhere else. And sometimes you find even more: In this case it was a wonderful sunset and the first spring flowers: