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computer simulation

Are You Living in a Computer Simulation?

This idea might be familiar to fans of The Matrix – and at first glance may seem somewhat unbelievable.  However, Oxford University Professor Nick Bostrom makes an interesting case using both conditional probability and logic as to why it’s more likely than you might think.

The summary of Bostrom’s Computer Simulation argument is the following:

At least one of the following propositions is true: (1) the human species is very likely to go extinct before reaching a “posthuman” stage; (2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof); (3) we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation.

The full paper where he makes his argument is available as a pdf here – and is well worth a read.  Alternatively Bostrom makes this case in a detailed interview:

Taking the argument step by step, firstly when Bostrom talks about a “posthuman” stage he is referring to an advanced civilisation with significantly greater technological capabilities than we have at present.  Such a civilisation would have the ability to run a computer simulation so accurate that it would be indistinguishable from “real life”.

This is a twist on the traditional “Brain in a Vat” thought experiment much loved by philosophers when trying to argue whether we be sure that anything exists outside our own subjective experience:

Based on the same logic, we have no way of genuinely knowing whether we are really “here” or whether we are nothing but a computer model designed to give the impression that we really exist.  Interestingly, the possibility that our individual life, the world around us and indeed everything we know about the universe may be false means that we can never truly claim to have knowledge of anything.

I think that most optimists would think that civilisation has the potential to develop into a “posthuman” phase of advanced technology.  Indeed, you only need to look at the phenomenal growth in computer power (see Moore’s Law) to have confidence that should we stick around long enough, we will have the computational power possible to run such simulations.

So if we optimistically accept that humans will reach a “posthuman” stage, then it’s even easier to accept the second proposition – that if an advanced civilisation is able to run such civilisations they will do.  After all human nature is such that we tend to do things just because we can – and in any case running such ancestor simulations would potentially be very beneficial for real world modelling.

If we do accept both these premises, then this therefore leads to the argument that we are almost certainly living in a computer simulation.  Why?  Well, an advanced civilisation with the computational power to run ancestor simulations would likely run a large number of them – and if there is only one real world, then our experience of a world is likely to be one of these simulations.

As a ToK topic this is a fantastic introduction to epistemological questions about the limits of knowledge and questions of existence, and is a really good example of the power of logic and mathematics to reveal possibilities about the world outside our usual bounds of thinking.

If you enjoyed this post you might also like:

Imagining the 4th Dimension – How mathematics can help us explore the notion that there may be more than 3 spatial dimensions.

Is Maths Invented or Discovered? – A discussion about some of the basic philosophical questions that arise in mathematics.

Essential resources for IB students:

1) Revision Village

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Revision Village has been put together to help IB students with topic revision both for during the course and for the end of Year 12 school exams and Year 13 final exams.  I would strongly recommend students use this as a resource during the course (not just for final revision in Y13!) There are specific resources for HL and SL students for both Analysis and Applications.  

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There is a comprehensive Questionbank takes you to a breakdown of each main subject area (e.g. Algebra, Calculus etc) and then provides a large bank of graded questions.  What I like about this is that you are given a difficulty rating, as well as a mark scheme and also a worked video tutorial.  Really useful!

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The Practice Exams section takes you to a large number of ready made quizzes, exams and predicted papers.   These all have worked solutions and allow you to focus on specific topics or start general revision.  This also has some excellent challenging questions for those students aiming for 6s and 7s.

Each course also has a dedicated video tutorial section which provides 5-15 minute tutorial videos on every single syllabus part – handily sorted into topic categories.

2) Exploration Guides and Paper 3 Resources

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I’ve put together four comprehensive pdf guides to help students prepare for their exploration coursework and Paper 3 investigations. The exploration guides talk through the marking criteria, common student mistakes, excellent ideas for explorations, technology advice, modeling methods and a variety of statistical techniques with detailed explanations. I’ve also made 17 full investigation questions which are also excellent starting points for explorations.  The Exploration Guides can be downloaded here and the Paper 3 Questions can be downloaded here.

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All content on this site has been written by Andrew Chambers (MSc. Mathematics, IB Mathematics Examiner).

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