Bodies in Play

This is a crosspost from an article, I wrote first on Medium.

Yesterday evening, I gave a talk at the eMedia Research Lab at KU Leuven about “Bodies in Play”. It attracted a surprisingly large audience asking interesting and intriguing questions that challenged and strengthened my theoretical explorations in this area.

Additionally, there seemed to be interest by others to hear about these thoughts, so I’m providing a transcript here. The associated slides are also available on my website and if you’re interested in reading more, the original paper and a short medium blog post are both available for you to peruse.

Colourful drawing of a Virtual Reality Player using a wheelchair with black and white space environments hinted at in line drawing styles.

In Games Research and concerning player experiences, we often talk about embodied play only in certain contexts; particularly, we talk about embodied play, when we specifically use our entire body in play, as in we dedicate our entire movement to play. You know, if we take it for a second out of a digital context: board games then would not be considered bodily play whereas Twister would be.

Now let me trouble that a bit. I assume most of you are familiar with the game Monopoly? Is your body involved? How? It’s restricted a bit by the context, with the table and sitting down, but still moving around, stretching across the board, frustratedly hitting the table, throwing your arms up in the air.

As you can see, I try to think about the body in play a bit differently. Basically, as soon as you have a body (and that’s everyone here), play is *embodied*. If you take one thing away from this talk, it is that whenever you design a game or try to get at a player experience, these players will have bodies and the context of your game and platform will shape that embodied experience by allowing for certain type of movements or prohibiting them.

What helps us in understanding this, is a specific theory within Media Studies. Specifically, Film Studies. Christine Voss has developed this theory on the ‘Surrogate Body’ to understand cultural and mediated immersion in movies. Immersion is the suspension of disbelief, when your reality is encompassed entirely by the movie you’re watching or, in our case, the game we are playing. In other words: Immersion is what happens if you feel like you’re ‘really there’.

Distilled into one sentence, the surrogate body theory says that immersion happens when a viewer lends their affective (and emotional) responses to the film. I want you to recall for a second a scene in a film, that did something with you in that regard, a moment that stuck with you. Take 20 seconds.

Let me share an example from my own experience. I recall the final showdown in ‘The Good, the Bad and the Ugly’, where the movie cuts quickly between close-ups of the eyes of the three protagonists. I always feel queasy and slightly uncomfortable thinking about it, because it creates such a close moment with the characters on screen. That is an affective and an emotional response. And I wouldn’t have that response in that moment if I weren’t watching the movie. Or recalling it. Hence, I’m giving some of that to the movie, figuratively speaking.

Voss then says, that this embodiment of affect leads to a metaphorical body that is made up of the intersubjective interplay between viewers and film and facilitated through physical aesthetic distancing. That means, the surrogate body, she identifies is exactly that interplay between myself and the movie, that creates a figurative, metaphorical body having the affect and that that only happens by me watching that movie.

However, I found this very abstract. So I went, literally, to a drawing board and tried to figure out, what this might mean. Where is that surrogate body? What do people do? As you see here, not a lot, the affective response can be outward or not, the screen is quite far away and has to bridge a large distance and the embodied reactions are fairly limited by the physical constraints of the chairs, seating options and social expectations from other viewers. Shhhhh….

But is it the same for every context?

Christiane Voss, the main person behind the theory, is at Uni Weimar, by the way, where I did my undergrads and master…. a while ago. And for the last five years, I’ve been angry about one particular footnote in which she claims games and digital media to be essentially equivalent to cinematic dispositives. And I was like, Really? And so, I tried to think about what this theory could give us to understand bodies in play more holistically.

Let’s first talk about a very stereotypical gamer image at a personal computer setup. We still have a screen, sometimes multiple, but suddenly we have the surrogate body located in two positions.

What happens if we play a game, is that we also provide input. Games require players to be active, to steer to progress. Even in the most basic of unbranched narratives, people will have to do *something* to advance the plot.

So, players not only lend affective responses, but also *lend their actions* to the game. In playing these games, it’s however, not only the actions players lend. Remember that evocative movie response? Can you think of a game that emotionally stuck with you? Again, no need to share, but take 20 seconds to think.

I am comfortable sharing with you that I enjoy the deeply frustrating experience I have when playing SuperHexagon. On the other hand, playing Undertale, that game made me not only feel intrigued and involved when I played it, it went further and made me question my actions within the game. I don’t want to spoiler it for those of you who haven’t played it but if you want to understand my thinking on convergence of actions and emotions, that’s the perfect game to think about it.

However, emotional responses can also have damning consequences for gameplay. If players become frustrated and yell at the game or their character and kick a glass of water over their equipment…. just think about the horror.

Let’s switch to mobile games then. Mobile devices, such as smartphones and tablets, are readily available to players in a range of different contexts. Private and public settings are equally common, but players tend to play by themselves with one single device. Of course, there is Pokemon Go and the like, but we’re also trying to keep things within single player settings right now, to make it a bit easier on ourselves. So, when interacting with mobile devices, players’ touch input occludes part of the screen. That means, while you interact with the screen, you also don’t see exactly where that is, because the game surface and the surface of your action are the same. Hence, most touch gestures, notably tapping, require players to continuously engage and disengage with the device itself as to be able to take in the entire screen without the occluding hand. This means, there is a temporal separation of how affect and action inputs are actualised. You cannot at the same time see everything and act on it. That means that action and reaction are temporally separated. They do not happen at the same time.

Let’s switch again: What about embodied gaming, like with a wii, kinect? There you don’t necessarily need to be directly connected to the environment But suddenly your entire body becomes a surrogate body with a decided focus on a screen. Any action you do might have consequences for the game, making displays of affect either part of the game or a point of disruption. If you express your frustration, the game can recognise it and react to it. Your frustration becomes immediate part of the gameplay as your entire body is part of it; it is recognised explicitly, not just implicitly as might be the case in our previous examples.

And your body shape and form suddenly becomes relevant as well. What if you have a minority body, but the game expects you to stand? What if someone (like me), twitches and fidgets a lot? They impact the game and that impacts their experience. Though, again, these bodies also might have impact on our previous examples. On desktop games, it means that different players might be able to do different things with different precision or fuzziness (depending on what is desired), in mobile games, small buttons can become really frustrating when you happen to have a tremor.

Can you relate to a playing experience, where you felt your body and the game didn’t quite fit?

For me that’s, funnily enough, again, SuperHexagon because it required me to be super fast and concentrated on one single thing. Something that is super hard for me.

What I’m trying to say is that even if we measure player experiences through questionnaires and assess them across an average, that average might still let people down and you have to reflect on the bodies that are privilege to your immersion. It’s not just the bodies we have that shape our gameplay, though, it’s also what we have done with them, our lived experiences.

Our bodies also have implications for ways of knowing: the more associated certain actions are with things we do outside of games as well. Playing a Switch Labo fishing game, a player can draw from an experience of fishing from carnival games while also practicing this action for different non-digital contexts. Hence, the embodied experiences of players play an additional role in how they lend their body to the surrogate body with the game.

Then the surrogate body can become entirely encompassing, when you lend your entire body to the game environment and, how you see in VR, even suspend some sensory perceptions of your physical environment to the game environment. You don’t even see or hear anything else anymore, you only see and hear the game environment and move within it.

Though, let me also trouble this for just a second again. because what you see here is a majority body, one that you generally tend to design for, one that is ‘more or less like you’. And I want to encourage you to design for radical difference, if you want your game to be playable by many different kinds of bodies.

Besides making the point of expanding the surrogate body theory to play contexts and troubling Christine Voss’ footnote by specifying that in games, we not only lend affect but also embodied actions to a given game in different contexts to the emerging surrogate body, we also encourage game designers to instead of following the latest technological trends, make more conscious choices in designing their games alongside desired embodied experiences — not just in explicitly fully embodied play scenarios.

Piss Perfect: Privacy in Continence Care

On October 27th, 2019, I gave a talk at privacy week. I will edit this post to insert a static video once it is up. Until then, have a look at my slides and the abstract.

With 50% of residents in nursing homes classified as incontinent, continence care is an area in which technological development is hailed as the solution to declining numbers of carers–with deeply troubling consequences for carers’ and residents’ privacy alike.

Ideal continence care is framed around concepts of dignity–for residents as well as carers. This stands in a stark contrast to hierarchical surveillance structures present in the sociotechnical context of nursing homes. Technological development is mandated by governments and managers, rarely with consideration for residents’ or carers’ perspectives. Drawing on a case study from interviews and observations in a Flemish nursing home, I will detail how technology in this space ends up perpetuating these hierarchies, creating a continence panopticon which is deeply rooted in surveillance practices and, ultimately, distrust.

Beyond Transparency — Comments on the Update to Submission and Reviewing Guidelines for CHI

This is a crosspost from an article, I wrote first on Medium.

[This post specifically addresses a recent update for the submission and reviewing guidelines of CHI, a conference within the Human-Computer Interaction (HCI) research community, but might be relevant for readers interested in discussions around what constitutes ‘good research’ more broadly.]

To discuss different aspects of what constitutes quality in research, a myriad of terms and concepts are summoned. We talk about rigour, transparency, accountability, replicability, reflexivity, significance, stringency, consistency and many more. As someone who is passionate about methodology and enthusiastically discusses epistemological consequences of different ways of knowledge production, I was excited to see an update to the submission and reviewing guidelines for CHI 2020. After all, it was a chance to reflect on what we can know and how by looking at how we claim knowledge in the first place.

Given that I have received reviews calling my approaches too critical for the field of HCI and its methods, the description of methodological detail on the one hand (R1) putting others to shame on the other (R2) too excessive, I welcome any approach that aims at a shared understanding of what we might understand as high-quality research and where different conceptualisations might differ, how and why. So, let me start this post by sincerely thanking the authors and contributors that have worked towards updating these guidelines in a concerted effort. They pushed the discussion further and rejuvenated vigour in collectively thinking on this. Let me take here the opportunity to further reflect on the guidelines, synthesising some critique brought up in different social media platforms and adding my own, personal perspective on this.

The overall aim of the update is to increase transparency in reporting research. It is relevant to keep this in mind as an overarching goal, particularly as by focusing on transparency in this update, the initiators have added another dimension to how we, as a community, assess research and what matters to us. This means, that how we assess transparency and what we define as transparent is core to understanding which research is (highly) valued and communicate expectations to authors.

The first key component the initiators refer to is replicability. By starting with this one, they already set the pace. Replicability only makes sense from a post/positivist or critical realist paradigm, one that assumes no standpoint and operates with a notion of disembodied objectivity. However, the initiators do not indicate how the concept of replicability expects a certain kind of research and, given it is the first one listed, potentially excludes others. It implicitly (not necessarily intentionally) disregards those coming from a critical/feminist/queer lens in particular, those, like myself, who root their work firmly in an epistemology that values the privilege of partial perspective and values different kinds of situated knowledges. How do you replicate an autoethnography where the very point is to provide an in-depth, highly contextual analysis? How do you replicate an argument for ‘tangible bits as a new interaction paradigm’ (a paper that has the highest citation count of any CHI paper according to my query)?

Another aspect, the initiators focus on is sharing data. Inspired by (and heavily advertising for) the Open Science Framework, “reviewers may expect that all materials created for this research (such as experiment code, stimuli, questionnaires, system code, and example datasets), all raw data measured, and all analysis scripts are shared.” There is a lot to unpack here, notably the lack of nuance on whether the practices associated with open science are at all achieving what they are set out to do (thanks to stuart reeves for pointing this out). Such a requirement also ignores the vast varieties of institutional particularities that researches have to consider, ranging from supranational levels (EU, GDPR) to individual, local routines. And while the update acknowledges that sharing data might not always be possible (and argues for explaining why), it sets a normative expectation on sharing and, subsequently, a normative expectation for research (and institutional contexts) that allows such sharing. On that note, a discussion in the CHI Meta Facebook group has pointed to a more nuanced discussionand some practical guidelines, though those might not be appropriate when working with marginalised participants. In addition, there is an assumption that all data can be digital or digitalised; if it can’t be provided, it needs to be specified why. According to the update, why data can be shared and which reflections go into sharing which parts of the data is less relevant (a.k.a. sharing as norm), absence has to be defended (a.k.a. diverging from the norm has to be defended and can be attacked).

In consequence, the update also invites authors “to share as much non-sensitive and non-proprietary code as possible to help reviewers scrutinize, replicate and reproduce your results”. Besides the culture of suspicion and mistrust this perpetuates (instead of assuming expertise and knowledge and asking for clarification out of curiosity and respect), this adds an entirely new workload to authors and reviewers without acknowledging the potential effects this might have, particularly with an update published only 6 weeks before the abstract submission deadline. Ignoring that papers introducing datasets have a notoriously difficult time in getting accepted to CHI, merging the publication of data with any type of reporting on analysis, devalues them further and makes it less likely for them to be accepted in the larger field as stand-alone contributions. However, the sentence also drastically increases demands on reviewers. For context, associate chairs are expected to manage reviewers for 8–10 papers and additionally provide in-depth reviews for another 8–10 papers within a time span of only six weeks — all that while the semester starts up again (at least at my university, it coincides with the start of a teaching term) and most of us are expected to continue conducting high quality research and contributing to self-administrative aspects of the academy. If we want to take this seriously (and I am not sure we should to the extent the update implies), we also need to change the practices and frames in which authoring, submission and reviewing occur.

Most of the online critique has centred, though, on the different requirements posed for reporting “technologically oriented” and “qualitative” approaches. Full disclosure on this part: One of the initiators (Matthew Kay) already indicated that this part will be revised. However, the core distinction seems inappropriate as the first category conflates a technology focus with quantitative research, which, in my opinion, is an inadequate reduction of the vast variety of approaches that can focus on technology (including those that make an argument as philosophy research through design).

Lots of buzz has been about limiting positionality, rationale for design, transparency of decision making and ethical contextualisation to qualitative approaches (see my annoyed tweetMelanie Sage questioning this suggestion or further discussions initiated by Sarita Schoenebeck). In my understanding, this should be required of any research. At the very least, expecting some work to provide more detail than others is deeply unfair given that CHI operates with a strict page limit (which was also raised as an issue by Casey Fiesler on Twitter). On a side note, the wording on sharing conveys an entirely different approach as to why and how this valued. Authors are “welcome” to only share data after having obtained explicit consent to do so. This indicates an opportunity instead of implying a requirement.

Before I conclude, allow me to reiterate that I am deeply grateful for the initiative to rekindle discussions around how we present our research and review our peers. My critique and the comments on social media indicate a level of care and an expectation towards the field to keep working on the issues of quality assessment in HCI research. Going forward, we should discuss which implications the high-level expectations we state have for how we organise and value authoring and reviewing processes. As a longer term project, I am interested in collecting actionable criteria for the assessment of a range of contributions, epistemologies and methods present in HCI. Let’s keep talking about it.

Post Scriptum:

Edit Notes:

  • edited the sentence discussing the simultaneous start of the reviewing period with the start of the teaching term to localise it appropriately to my personal context (thanks to Geraldine Fitzpatrick for pointing this out).

“Anonymous Review” says it all

This is a crosspost from an article, I wrote first on Medium.

Ableism is deeply tied into our everyday language. There are countless examples of where disabilities are used to imply negativity very explicitly. Today, though, I want to write about a more deeply entangled case; I am asking people to stop (and I’m only using this term once) saying “blind peer review”.

This is not a new request. However, the term is so persistent in my academic environment that it took me until today to realise that I more fundamentally need to change my own use of language to encourage others to revisit commonly used terminology with me. While some of that is due to the sheer ignorance my sighted privileges allowed me to have, I have a sneaking suspicion that I might not be the only person who needs a refresher — given that just today, I found the term used casually on a conference website related to my field.

So, in revisiting previous debates let me draw on them. A succinct argument for using ‘anonymous review’ instead has been made by Tremain, 2011:

The phrase is demeaning to disabled people because it associates blindness with lack of knowledge and implies that blind people cannot be knowers. Because the phrase is standardly used in philosophy and other academic CFPs, it should become recognized as a cause for great concern. In short, use of the phrase amounts to the circulation of language that discriminates. Philosophers should want to avoid inflicting harm in this way.

Ultimately, I’d assume, that not just philosophers are in this responsibilities, but rather everyone who is engaged in research from a simple perspective of being considerate about people around us. It requires sighted researchers to actively engage with the epistemological consequences of tying ‘seeing’ to ‘knowing’, or as Rodas, 2009 puts it:

Our language bespeaks our unconscious belief that blindness is automatically agnostic, unknowing. Whether we speak of a blind trust or of trusting blindly, the symbolic foundation is the same. Our language depends on the common understanding that not seeing equals not knowing.

Using blindness metaphorically, even in a presumed positive context, then is not helpful either given that the metaphors are built, established and reinforced predominantly by sighted people.

[M]etaphors of blindness are based upon the presumption of what the experience of blindness must be like, rather than the lived experience of blindness itself. (Schalk, 2013)

The damage perpetuating such language does to the blind members of our communities takes form in epistemic violence, to say the least. It ties into powerful dynamics fueling a neglect in terms of making publications, conferences and practices more accessible. This actively excludes blind people from the academy or requires them to put up with extra effort to participate. Both is unacceptable. I have been guilty of this and need to learn how to do better myself. I call on my sighted colleagues to do the work with me. It starts with language. Let’s talk about “anonymous peer review” from now on, shall we?

Rodas, J. M. (2009). “On Blindness. Journal of Literary & Cultural Disability Studies, 3(2), 115–130.doi:10.1353/jlc.0.0013

Schalk, Sami. “Metaphorically speaking: Ableist metaphors in feminist writing.” Disability Studies Quarterly 33.4 (2013).

Tremain, Shelley. “Ableist Language and Philosophical Associations.” New APPS: Arts, Politics, Philosophy, Science. July, 2011.

CHI 2019 Cowl Knitting Pattern

This year’s theme for CHI is ‘Weaving the Threads of CHI’, inviting us to see the connections between different strands of research and how they connect the field. To provide the community with an opportunity to reflect on how different aspects of the field come together to create something each of them could not do individually, we offer up a knitting pattern that visualises the ‘Threads of CHI’.

Yarn: The sample piece uses fairalpaka DK yarn (100m/50g). A finished piece requires about 1 ball o the main colour (MC; teal) and about 20g of the contrasting colour (CC; tangerine).
Needles: We used 3.5mm double pointed needles (dpns) for the sample piece. You might prefer to knit with 40cm circular needles.


  • knit (k)
  • purl (p)
  • knit through back loop (ktbl)
  • twist through back loop (twbl) – insert right needle into second stitch on left needle and purl without dropping, then ktbl into first stitch on the left needle, dropping both together

Stripe Pattern:
Repeat all parts for the round (chart below).

  1. p1,k1tbl,p1
  2. repeat step 1
  3. p1,tw1tbl
  4. p2,k1tbl
  5. move first stitch of the round to left needle, repeat step 3
  6. repeat step 4
  7. repeat steps 5 and 6 twice more

Mosaic Pattern:
Each round seen on the chart is knitted twice, once as a knitted round, once as a purled round. Note that after each garter ridge, colour changes, starting with teal. Essentially, you start with a knit teal round according to the black stitches in the chart slipping all white ones (with teal yarn in back), then you purl the stitches you knit previously, slipping all you slipped previously. Then you switch to the tangerine and knit all white stitches in the chart (indicating row 3), slipping the black (a.k.a. teal) ones and repeating with a purl round. This sounds much more complicated than it really is. You can also find an introduction to garter stitch mosaic patterns here.

The pattern comes in two sizes: S/M and L (sample piece shown in S/M). Instructions are given for S/M (L). The pattern is knit in the round.

  1. with MC cast on 108 (126) stitches; connect in the round be careful not to twist.
  2. purl 1 round, knit 1 round, purl 1 round
  3. knit Stripe pattern 36 (42) times through the round
  4. knit 1 round, purl 1 round (twice)
  5. switch to CC
  6. knit 1 round, purl 1 round
  7. knit Mosaic pattern 6 (7) times through the round
  8. knit 1 round, purl 1 round, cut CC
  9. with MC: knit 1 round, purl 1 round (twice)
  10. knit Stripe pattern 36 (42) times through the round
  11. knit 1 round, purl 1 round, knit 1 round
  12. bind off loosely by purling the last round
  13. weave in ends and block lightly, if desired.

No Blow Hat

Viennese winds can be harsh, particularly if you’re a child. Having had their previously favourite hat blown off their head numerous times, I was asked to please make another hat, that doesn’t do that. Behold, the No Blow Hat, so elastic, it clings onto your head without pressure (and, as a side effect, fits most heads no matter their size).

You’ll need: some sports-weight yarn in as many colours as you want. 3.5 mm needles (double point or hat round needle).


  • ktbl — knit through back loup
  • p — purl
  • k — knit
  • m — make (I do that here by picking up the yarn between two stitches and knitting it through the back loop. This effectively twists the yarn and makes the potential hole smaller)
  • k2tog — knit 2 together


  • Cast on 84 stitches (I use long-tail cast-on); join in the round (be careful not to twist)
  • 7 rows (ktbl, p1) to end 
  • (k7, m1) to end — 96 stitches
  • *row 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21 and 23: knit
  • row 2, 4, 6, 8, 10, 12: (k3, p3) to end
  • row 14, 16, 18, 20, 22, 24: (p3, k3) to end*
  • repeat stitches between * twice
  • For the colour effect above, you want to change the yarn every 12 rows.
  • Optional: repeat rows 1-12 once more.
  • (k10, k2tog) to end
  • knit
  • (k9, k2tog) to end
  • knit
  • (k8, k2tog) to end
  • knit
  • (k7, k2tog) to end
  • knit
  • (k6, k2tog) to end
  • knit
  • (k5, k2tog) to end
  • (k4, k2tog) to end
  • (k3, k2tog) to end
  • (k2, k2tog) to end
  • (k1, k2tog) to end
  • pull yarn through remaining stitches, pull tight and weave in ends.


Bobble Hat

Green Hat version of the Bobble Hat Pattern

I started creating patterns again. So here comes one that is surprisingly easy, but comes with a bunch of interesting different shapes and effects. Still not good at making pictures, though.

You’ll need: about 75g of bulky yarn for main colour (MC); about 20g of bulky yarn for contrasting colour (CC), 4.5mm needles (either double point (dpns) or round), tapestry needle


  • CC – contrasting colour
  • MC – main colour
  • ktbl – (knit through back loop); k2tbl (knit 2 through back loops)
  • k – knit
  • p – purl
  • sskslip slip knit (left leaning decrease)
  • k2tog – knit 2 together (right leaning decrease)
  • x (number) – repetitions


  • Cast on 90 stitches with CC, join in round (being careful not to twist)
  • (k2tbl p2) x 22, k2tbl for 15 rows
  • switch to MC
  • knit 4 rows
  • *(k9 p5 k4) x5, for 6 rows
  • knit 6 rows
  • (p5 k13) x5, for 6 rows*
  • knit 6 rows
  • repeat between * once more
  • knit 2 rows
  • (k1 ssk k12 k2tog k1) x5
  • knit
  • (k1 ssk k10 k2tog k1) x5
  • knit
  • (k1 ssk k8 k2tog k1) x5
  • knit
  • (k1 ssk k6 k2tog k1) x5
  • knit
  • (k1 ssk k4 k2tog k1) x5
  • knit
  • (k1 ssk k2 k2tog k1) x5
  • knit
  • (k1 ssk k2tog k1) x5
  • knit
  • (k1 ssk k1) x5
  • pull yarn through all remaining loops and pull tight
  • weave in ends.

The contrasting part is folded towards the inside as to support warming the ears and creating a neat edge to the hat. Hopefully, you’ll enjoy the resulting pattern as much as they do:

Current Penalty Code Cheat Sheet (March 2016 codes) for Penalty Trackers

While I had the wherewithal to create a new penalty code cheat sheet when the new verbal codes came out… over a year ago and to share it with my league, I’ve kind of forgot to make it available for anyone else, also because I thought that would only matter to me and someone else would surely do it as well and imposter Bla Bla Bla. I got over it. So, have thepenalty codes cheat sheet with the updated codes from March 2016. I will probably soon have to make another one.

Presentation and Journal Paper: Evaluating Experiences of Autistic Children with Technologies.

Last year in Barcelona, I have given a talk about how I plan to evaluate the experiences of autistic children with technologies. You can find the slides for the talk here. They also allow a unique glimpse into a preliminary state of what was later becoming my paper at the International Journal of Child Computer Interaction, which incidentally is available for free until April 7th using this link. Note, for example how in the main graphic there has been a change in the top intersection where ‘interests’ as the defining characteristic of the relationship between child and technology has been replaced by ‘interaction’. Interests have — following an insightful discussion with Narcis Pares in Barcelona — been moved to the design process instead.

Subjectivity in Mathematics – Implications of Richard Buckminster Fuller’s Energetic Geometry

This is an essay I have written as part of a Philosophy of Science course with Blay Whitby in Summer 2016.


I compare Euclidean and Energetic Geometry to show how there is a set of mathematical languages, which are subjected to interpretation. This theoretical exercise provides deeper insights into the agendas and world views mathematical concepts carry and deconstruct the presumed ‘neutral’ or ‘objective’ stance that is largely attributed to them.

The Point of Euclidean Geometry

There is a large desire in human society to order the world it exist in, because “[b]eing able to see connections confirms our hope that our world is under- standable and not just a bunch of senseless accidents” [Meyer, 2006, p.5]. Consequently, around 300 BCE Euclid attempted to structure space by formally defining Elements [Euclid and Joyce, 1996].
There is just one problem. “(…) [T]here seems to be nothing in nature that is absolutely straight enough to be a “true” line segment” [Meyer, 2006, p.7]. Hence, Euclid’s geometry has to produce a symbolic system that is tightly cou- pled to rigorous rules of precision. Otherwise the geometry cannot function as an abstraction beyond a visual depiction (ibid.). This means that the underlying axioms of which formulae are deduced have to be both strict and generally applicable at the same time.
It is all the more surprising then that Euclidean geometry does not give strong definitions for its pre-axiomatic building blocks such as the point and subsequently also lines and planes [Meyer, 2006, p.22]. Rather, they remain undefined. Considering that Euclid’s geometry demands rigour and proof through axioms, it appears inconsistent that when it comes to the core parts of these axioms, Euclid relies on ’common’ knowledge of what constitutes a point. Through this, Euclid offers a subjective gateway into geometry. It becomes then situ- ated within the tools that are used to work with them (e.g., pen and paper vs. computational construction) and depends on context, that, for the sake of comparability gets abstracted away to defend the objectivity of a system, whose grammatical base has not been properly specified.
Following this, Euclidean geometry constructs meaning through the formulae and abstractions of the world, which is limited by the axiomatic space it provides. We will see how this defines discursive limits and how representations of the world contain ideological and subjective points of view.

Fuller’s Critique

During the first half of the 20th century, Richard Buckminster Fuller – alongside being a well-received architect – publicly criticised the construction of the Euclidean right angle. Fuller points out, that it relies on the opportunities and limitations provided by the instrument used. Next to the already often cited ones (ruler, compass and pen), Fuller adds another important agent into this set: the flat surface on which a right angle is constructed on [Fuller, 1999a, p.175]. This pre-axiomatic critique of Euclidean geometry can also be seen as a critical approach to the prevalent world view at the time as it shows itself by the methods and spaces spanned open by geometry as a way to measure the world.
To Fuller, mathematics as a discipline and geometry as a part of that discipline is full of ”inconsumerable ratios and a barrel full of clumsy constants” [Fuller, 1999a, p.178]. Constants such as π or e are difficult to conceive. This shows how not only the instruments, but also the creations they produce are lost in the resulting complexity. ”Whatever happens in the depths of matter, disappears behind ever larger apparatuses, which we cannot look inside and even if we could, we would not see anything and even if we saw, we wouldn’t understand it, since the quantal world doesn’t bother to shape itself in our form of sensual experience. In one word: the constructive mediatedness of our perception is in theoretical and practical aspects so overwhelming, that it becomes understandable, that some physicists don’t really know what their matter actually is.” [Mutschler, 1998, p.33, translated from German]. To Fuller, this is not acceptable. His ontology requires a world that has an image that is as easily perceivable as the world itself (Heidegger might agree, see Heidegger [1926/1967]).
Euclidean geometry and mathematical constants put a layer on the world, which does its elegance no justice [Fuller, 1999a, p.178]. Its abstractions fail to simplify the direct world, but rather construct purely nonphysical constructs such as straight lines [Fuller, 1999a, p.173]. Those who practise Euclidean geometry agree (cf. Meyer [2006, p.5]). The three dimensional space became more and more of a problem. ”The leitmotif of the 19th century, which con- nected maths, physics and philosophy, the >space problem< emerged: How can the natural space be described mathematically." [Mehrtens, 1990, p.44, translated from German]. Energetic Geometry

With the feeling ”(…) that the whole universe must be the starting point for his enquiry (…)” [Morrell, 1986, p.613], Richard Buckminster Fuller understood mathematics as a generalised form of learning which – in his opinion – should be oriented on patterns found in nature (ibid.). While I personally am not inclined to distinguish between nurture and nature, this perspectives make sense within the then contemporary major scientific paradigm.
Because Euclidean geometry is insufficient for Fuller, he developed an alter- native geometry, which he claims to be intuitive and supporting human creativity. This is especially important to him. It is interesting though, how – despite the thousands of years of the history of humankind full of innovation and archi- tecture – he claims to have developed a more fitting system that is supposed to be better for exactly what has been already achieved with an old out-dated one: the creatively built and inspiring environment in which he thinks.
To Fuller, every physical force (such as warmth, electricity and magnetism) can be described in energetic terms. A geometry delivering a more intuitive image of the world, should, hence, follow this, which is why he calls his approach Energetic Geometry. He starts with new basics, in order to follow a more strict construction of his postulates [Fuller, 1999a, p.178]. For this, he first defines his tools with the goal of an explicit mention of the inscription of tools in the the- ory they are being used by. This does neglect, that the implicit assumptions of Euclidean Geometry are not effectively circumvented, but rather made explicit.
”[T]he apparently simple and unproblematic idea of a »point« had to be rethought, and »the phenomena accommodated by the packaged word point will always prove to be a focal center of differentiating events.« For Fuller, geometry did
not describe a timeless space of pure Cartesian form, but rather a universe where lines »cannot go through the same point at the same time.«” [Nye, 2009, p.88]. Fuller tries to abstract from the undefined grounds of Euclidean geometry and defines his core elements as events and vectors connecting those. This equivalency to points and lines is being presented by Fuller himself in Fuller [1999b]. Geometrical deliberations are especially suitable for equivalent theories due to their strictly axiomatic build up. ”(…) Equivalence of axiomatic theories is given ipso facto, since every mathematical system of axioms can be described differently achieving the same. Whether something is an axiom or a theorem depends on its place in a network of mathematical relations, which can be differently arranged while accomplishing the same thing.” [Mutschler, 1998, p.29, translated from German]. Energetic geometry, hence, provides a different way of expressing the same things as Euclidean geometry.

Geometry as Construct

While Fuller is by far not the first who voices issues with Euclidean geometry (see, e.g. the concept of spherical geometry Katz and Imhausen [2007, S.4]), he does provide a unique ’solution’ to the spatial problem. He does not base his work on the right angle, but rather on the rigid construct of triangular bodies and derivations thereof. Polyhedra are especially fascinating to him and also provide a way to illustrate how geometry is constructed by the language and the implicit ideologies roaming through it. Buckminster Fuller describes polyhedra as such:

(…) Every vector (line) leads from one center of a sphere to an- other and therefore represents the operational effect of melting two forces. Every vector (line) consists of two halves, each of them be- longing to one of the spheres and each half of the line represents the radius of each tangential sphere, which all are in a right angle to the identical tangent point and construct a continuous straight line: Through that it is defined that a unit (represented by the inter nuclear vector-module) necessarily holds double the value, which means: unity is inherently two, since it represents the unity of at least two centers of energy. [Fuller, 1999b, S.183, translated from German]

In comparison, the definition of a polyhedron from a Euclidean perspective:

A polyhedron is a three-dimensional solid bounded by a finite number of polygons called faces. Points where three or more faces meet are called vertices. Line segments where exactly two faces meet at an angle are called edges. The vertices and edges of a polyhedron make a graph called the graph of the polyhedron. [Meyer, 2006, S.418]

It should be mentioned, thought, that rigid polyhedra are rare to find and often constructed by humans. “There were only a few polyhedra to be found in nature or the man-made world at that time in history: rooms of buildings, which are basically rectangular parallelopipeds; the pyramids of Egypt; and perhaps a few other examples.” [Meyer, 2006, S.432]. Therefore, polyhedra are more of a thought experiment in other versions of geometry.
Interestingly enough, although Fuller attacks the straight line with a passion only two years earlier [Fuller, 1999a], he now re-establishes it. He also just renames points and calls them centres of spheres. Hence, it is not necessarily the mathematical consistency, he attacks in Euclidean geometry. His agenda is a different one.
The difference between the two definitions can be seen especially in the lines (or vectors). Fuller’s centres of energy are loaded with meaning while Euclidean geometry tries desperately to keep all meaning out, which necessarily fails. The basis from which we construct, analyse and depict the world around us, is, hence constructed in and off itself only providing another tool to express what we perceive.
Another example for a different dialect within geometry is Hilbert’s. ”(…) [Y]ou can extract the graphic model of Euclidean geometry from the abstraction of Hilbert geometry.” [Mutschler, 1998, p.35, translated from German]. Since one geometrical system can be translated in another, we can understand it as a language system. In that context, we can see mathematics as one language and different versions of it as dialects.
However, then geometry cannot be what it claims it is: an accurate depiction of the perceivable world. ”If it depends on the phrasing of a theory on whether a space is Euclidean or not, whether reality consists of particles or fields, then we cannot naively understand the theoretical concepts as portrayal of a world being for itself.” [Mutschler, 1998, S. 35, translated from German]. Fuller’s energetic geometry, hence, shows how mathematical systems are subject to interpretation and are con- structed through their perception every time. The societal agreement on how to ’properly’ construct the meaning given by Euclidean geometry is fairly rigorous in the western world; that doesn’t necessitate only one way to understand it, though.


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