Essay #6 May 2016: Accuracy & Simplicity

Knowledge is a trade off between simplicity and accuracy.

This is not the exact title (I am not allowed to print the exact title here). If students are considering this title it is essential that they get the exact title from their teacher.

Students will probably start this essay by considering the definitions of simplicity and accuracy – defining these concepts could be the structure around which the essay is based.

This post is not so much a suggested essay structure for this PT, it’s more a set of inter-related thoughts about the PT.

My starting point for thinking about simplicity and accuracy in terms of ToK is to ask whether accuracy is a form of ‘truth’, and simplicity a form of ‘understanding’ ? This leads on to thoughts about the very purpose of knowledge – this differs according to AoK.

What is simplicity ?
There is often a difference between the lived reality of simplicity, and the understanding once the knowledge framework of an AoK is applied. For example water may have a ‘simple’ taste in comparison to other liquids. However, the complexity of binding hydrogen to oxygen, and then designing a sensing system to produce a taste sensation is far more complex than the lived experience of tasting water may appear. This is just an example, which may not work for you, but I hope that it starts to illustrate the complexity of the word simplicity !

What is accuracy?
Is it measured or is it experienced? Is it predetermined by expectation or objectively analysed? ToK students will immediately recognise the interplay of WoKs and AoKs in this question. Think about the duplicitous conversation : what is said is not what is meant. The accurate representation of knowledge is not the same as the meaning of knowledge that the knower brings to the conversation. The transcript of the conversation is not the same as the lived experience of the conversation.
Hello” has, maybe 3 dictionary definitions, yet has near infinite meanings in the reality of everyday conversation. The knower constructs the meaning (and therefore the PK accuracy) of the word in the context of everyday life.

Reductionism

Students could consider issues of reductionism in knowledge production, especially in the identification of causation. When looking at issues of reductionism students could contrast two Areas of Knowledge, looking at the differences in methodology and concepts in the Knowledge Framework of each AoK. Issues around reductionism could be argued using a number of approaches, for example:

  1. As explanations are reduced in complexity the level of achievable measurement increases to an optimal point, and thereafter reduces.
  2. As explanations are reduced in complexity the very nature of the object of experience changes (“holistic knowledge can be lost”) – consider this for understanding food such as ice cream or cake !
  3. The chicken or the egg ?: Reducing the complexity of understanding could increase problems of causation as the direction of causation becomes less clear.

For example if we look at the causes of artistic appreciation – the two determinants are the artistic subject, and the viewer. In order to understand the direction of causation we could look at the process of development of the subject, the context of the subject, the meaning of the subject etc. We could also look at the predisposition of the viewer, the history of the viewer, the emotional state of the viewer, the motivation of the viewer etc. If we took all of these variables into account we could start to build a model which, maybe, shows the direction of causation. However, if we start to take away variables (in order to simplify the model) it becomes harder to understand the direction of causation – does the subject cause appreciation, or does the viewer create appreciation ? (or, if we accept, a bi-directional approach do we start to undermine processes of causal inference ?)

AoK & WoK specific:

Simplicity and accuracy are both specific to the AoK and WoK under consideration. For example if we consider the differences between Religious Knowledge Systems and Maths as AoK. Simplicity in each AoK of knowledge will be defined, and represented, in very different ways. Simplicity in a RKS maybe seen through the prism of clarity of belief, or the strength in WoK Faith. Accuracy in RKS maybe in the detailed knowledge of the content of the religion. However, in AoK Maths simplicity may be seen in the lack of assumptions inherent to a solution, and accuracy may be seen in the supporting evidence for a solution, or it could be measured by degree of integer etc

This form of analysis could be further developed for any other AoKs.

Occam’s Razor

Occam’s Razor is the idea that the proposal with the fewest assumptions tends to be the most accurate. Citing Occam’s razor would appear to support the premise of the title. Occam’s Razor can be applied to a range of disciplines within the AoKs, e.g. it can be applied in Medicine, Psychiatry, Geology, Mathematics and Ethics. Students could develop their essay by looking at an applied explanation which uses Occam’s Razor, and then evaluating that explanation using contrasting evidence and arguments.

Heisenberg’s Uncertainty Principle.

The Uncertainty Principle was developed in Physics, and states that there is limit to the accuracy of measurement of two related variables. As such, in terms of this essay, it would suggest that accuracy is limited. It could be argued that accuracy is not limited by the simplicity of the knowledge, but limited by natural physical properties. This is an area that students who are particularly interested in Mathematics or Physics could further develop in their essay.

The Observer Effect.

The Observer Effect is the notion that the very act of studying a phenomenon will change that phenomenon in some way. This was first established in the Experimental Sciences, but has also been shown in the Human Sciences (see The Hawthorne Effect, or Reactivity). In terms of this essay it would suggest that accuracy is limited, and to a certain extent dependent upon the Knower’s Perspective. The Observer Effect could be used to extend the counterclaims within essays of students who are particularly interested in the Human or Experimental Sciences.

The PT states that there is always a trade off between simplicity and accuracy. This is a very binary approach to the relationship. Students would be well advised to consider the word ‘always’ in the title. There are numerous examples from which students could develop an argument that simplicity increases accuracy (think of AoKs The Arts, Indigenous Knowledge Systems, and WoKs Sensory Perception, Faith, etc).

Models.

Effective essays could be written around the processes of modelling. AoKs define models in quite specific ways, but most will be developing models in terms of accuracy and simplicity. In Human Sciences models are often described as “ideal type representations of theory”. It could be argued that the model is, therefore, simple but not accurate. However, real world feedback mechanisms which modify the model could lead to increased accuracy. There is a lot of scope for students to explore models in disciplines such as Economics, Biology, Meteorology, Visual Arts, Mathematics etc.

This essay has the potential to be very broad, as such students who are writing this essay should invest significant time identifying their KQs before writing, and planning a focussed argument line for the essay.

Enjoy your ToK writing !

Daniel.

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25 thoughts on “Essay #6 May 2016: Accuracy & Simplicity

    1. Thank you very much for helping me with ToK when my teacher was incapable. Please keep up the good work! My university application is relying on it 🙂

  1. Hello, If I am considering to approach this question using the AoKs of history and mathematics, examining the ways of knowing that could possibly alter the accuracy an AoK (thus compromising simplicity, would it work? Could I also explain that maths is seen as beautiful when it’s presented simply, but history is appreciated more when it’s supported with complex evidence?

    1. Hi, History & Maths make good contrasting AoKs, focus on the various ways in which knowledge is produced in each AoK according to the knowledge frameworks.
      I understand your point about the beauty of simplicity in maths, however in a ToK essay you need to be careful because following this line could lead you into a discussion about the definition of ‘beauty’ – don’t be distracted, just focus on the PT.

  2. Hello, I left a comment a few days ago about accuracy and simplicity in association with Maths and History. Would you please kindly reply to my comment, as I am starting to write very soon? Many thanks

  3. Great post. I am just wondering on your thoughts on contrasting the natural sciences and the arts, do you believe there is lots of space for good developments.

    1. Contrasting Natural Sciences and The Arts is a great way to go with this essay. There’s lots a scope for analysing difference in approach to simplicity and accuracy in each AoK.

  4. Thank you very much for this post. You mentioned that ‘There are numerous examples from which students could develop an argument that simplicity increases accuracy.’ Do you know of any of these examples? I am not able to find any…

    1. It all depends on how you define accuracy within each AoK. Think about the Arts, and the paintings of Lowry, or Rothko. Or maybe time signatures in Music (4/4, 4/2 etc). Think about Dance, and the simplicity of poise. Or maybe you could look at AoK Religious Knowledge Systems, and the simplicity of Faith as a WoK. Or Universalism in AoK Ethics…,
      You just need to explore the problems of defining simplicity and accuracy in different AoK.

    1. It depends on how you define accuracy. For example, if in RKS we defined accuracy of belief as strength of Faith as a WoK then a simple belief could also be an accurate belief. It all comes down to definitions of accuracy in different AoKs.

  5. Dear Mr. Trump, thank you for your enlightening post and happy new year.
    Your inspiration arrives just on time for my Essay.
    – I have chosen Mathematics and Natural Sciences as AoK for evaluating question #6.
    – For the KQ’s I’m using two – the first to elaborate about the connection of Accuracy and Simplicity to Knowledge and the second to discern the mutually exclusiveness between these two with a counterclaim on the ‘always’.

    I’d really appreciate if you could advise me on how you see my choice for AoK and the KQ’s.

    Best regards,
    Abre

  6. Hi, I was wondering what you think would be good points with History and the Arts as AOKS. What WOKS would work? Also are there any circumstances when there ISNT a trade off between accuracy and simplicity? Thanks!

    1. Hi, in relation to History AoK focus on History as a discipline of knowledge production, look at Historical methodology (Historiography) which refers to a wider range of sources in an attempt to be more objective (accurate?), as opposed to a more a subjective historical account. However, in counterclaim – the more individualised historical account could be more accurate in terms of that specific individual’s experience of that event / time. You could use any examples which are pertinent to your interest / experience. Personally, I would use the history of industrialisation in the UK because I grew up in the UK, but you should use examples of the History that you are interested in.
      Let’s move on to the Arts – you have to discuss what accuracy and simplicity means in the arts, and this will very much depend upon the form of arts that you are considering, and maybe the individual artist. For example, if we look at the art work of Joan Miro, many would say that his art work is “simple”, but the process of simplification to create his images was, maybe, very complex. Whether is art work was accurate depends upon how you define accuracy. If you see accuracy as photographic-type reproduction then no his art is not accurate. However, if you define accuracy as the purpose of the art (maybe the purpose is to evoke an emotion, or stimulate an idea) then his art work could be defined, by some people, as highly accurate albeit apparently ‘simple’.

  7. Hello and thanks for this post. What are your thoughts on me using the models in the natural sciences and math as a basis for my essay. In the sense that models are a form of simplified knowledge and are used in both AOKs for predictions, but they are not exactly accurate representations of reality. Thanks!!

  8. First of all thank you very much for the great post. Second, I think about contrasting math and economics in relation to mathematics models and how simplicity draws from their accuracy when applying in real life, mostly regarding economics. Do you think it is a good idea?

  9. Hello, and thank you for your insight!
    I am writing on natural sciences and human sciences and I was wondering what you think would be a good way to organize the essay in order to make sure I don’t start to get onto tangents about Occams Razor and other interesting priniciples. I have had trouble in the past with staying on track to answer the prompt. Also, I need help with taking a stance on this topic. I cannot seem to figure out how to take a strong stance that has the most evidence in its favor because everytime I do so, I end up with no way to provide alternative perspectives. Thank you so much! I can’t wait to hear from you!

    1. Hi Iliana, you seem to have already undertaken lots of good thinking about your essay. I would strongly recommend that you talk to your ToK Teacher. S/He will be able to help you to stay on track, and help you ti use evidence to take a strong stance. Enjoy your ToK writing.

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