October 1, 2013
Think3DPrint3D has generously donated 3D printer time and plastic filament to the unusual task of rendering the usually intangible concept of honeybee colour spaces into real, physical, matter!
The first two spaces we printed were chosen by me, in part because I think they are theoretically interesting, and in other part, because unlike some other colour spaces they are finite sized, 3D objects.
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September 25, 2013
Sometimes you need to find a rotation matrix that rotates one vector to face in the direction of another. Here’s some code to do it for vectors of arbitrary dimension. The code is at the bottom of the post.
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August 23, 2013
Why should we care if someone else is being irrational? and in what way can we know that this is actually the case?
The idea of rationality is often thought of as a consistency within a collection of behaviours or beliefs. For example, if I think it is absolutely wrong to eat meat, I should think it is wrong to eat beef. As beef is a meat it would be irrational for me to think it was wrong to meat but also have the belief that it is OK to eat beef. Similarly, it would be irrational to think that eating meat was abolutely wrong, and then eat a plate of steak. To be rational, my behaviour should also match what I think.
How do we know when we are being irrational? Asking about the rationality of other people seems easier at first. When we observe others, we can spot things that they ought not be doing if they were rational. For example, they might claim to be vegetarian whilst eating a steak. According to most people, I would say, what they are doing is inconsistent. But this doesn’t mean that they do not have a perfectly consistent way of thinking that accounts for their actions and it is us, the majority, who have failed to grasp it. How do you know that someone else is being irrational, not you yourself?
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July 4, 2013
The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform. – Ada Lovelace
James recently posted about a Guardian article on “big data”. The article outlines the many roles which algorithms play in our lives, and some of the concerns their prevalence raises. James’ contention, as far as I understand, was with the focus on algorithms, rather than the deeper issues of control, freedom, and agency. These later issues are relevant to all types of automation, from assembly lines to artificial intelligences.
Automation flies in the face of any attempt to give some human activity special merit, whether this is our capability to produce, to create, make choices, procreate, socialise or whatever. It relentlessly challenges our existential foundation: I am not made human by what I make as I can be replaced by a robot, it’s not what I think, I can be replaced by a computer, etc. Each new automation requires us to rethink what we are.
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June 24, 2013
Nothing makes me empathise more with those struggling with probability theory than reading things like this on Wikipedia:
Let (Ω, F, P) be a measure space with P(Ω)=1. Then (Ω, F, P) is a probability space, with sample space Ω, event space F and probability measure P.
This is written so that only the people who already know what it is saying can understand it. The only possible value of this sentence would be to someone who managed to study measure theory without being exposed to it’s most widespread application; in other words: no one! Whilst the attitude this, and soooo many Wikipedia pages displays encourages people to be precise in a way that mathematicians cherrish, it also alienates a lot of perfectly capable, intelligent people who just run out of patience in the face of the relentless influx of oblique statements.
Personally, I think that understanding probability spaces is very important, but for the reasons including those I mention above, most people find the measure theoretic formalisation daunting. Here I have tried to outline the most widely used formalisation, which has turned out to be far more work than I expected…
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June 1, 2013
People always want an explanation of Friston’s Free Energy that doesn’t have any maths. This is quite a challenge, but I hope I have managed to produce something comprehensible.
This is basically a summary of Friston’s Entropy paper (available here). A friend of jellymatter was instrumental in its production, and for this reason I am fairly confident that my summary is going in the right direction, even if I have not emphasised exactly the same things as Friston.
I’ve made a point of writing this without any maths, and I have highlighted what I consider to be the main assumptions of the paper and maked them with a P.
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April 26, 2013
I think it is fairly intuitive that the smiley in the title is upside down. But why is this?
Generally, when we look at a face we look at the eyes first. These days it is pretty easy to track where people look, the equipment is cheap and easily available – one simply uses a camera to look at the pupil and then calculates where the subject is looking. A preference for beginning with the eyes is a widely observed phenomenon (‘eyes are special’).
English readers, like readers in most languages, scan left to right when reading. With reading we constantly train ourselves to prefer moving left to right, something which leads to a phenomenon often called a readers bias (see this). It is not only during reading that the direction from left to right is preferred.
So, it is not surprising that we should think that smilies with eyes on the left are correct: left to right is preferred for reading, and eyes to mouth is preferred for viewing faces.
July 1, 2012
For a while now I have had an interest in information geometry. The maxims that geometry is intuitive maths and information theory is intuitive statistics seem pretty fair to me, so it’s quite surprising to find a lack of easy to understand introductions to information geometry. This is my first attempt, the idea is to get an geometric understanding of the mutual information and to introduce a few select concepts from information geometry.
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March 13, 2012
Not the usual kind of topic, but this needs to go out into the wide world. How to print the annotations that sometimes one might get on a pdf file:
First install or upgrade Adobe Reader to 9.0:
sudo apt-get install acroread
sudo apt-get upgrade acroread
Then back up and open the following file in your home directory: “~/.adobe/Acrobat/9.0/Preferences/reader_prefs”
cp reader_prefs reader_prefs.backup
gedit will complain about the encoding, but ignore it and click “edit anyway” (we have a backup if anything goes badly wrong). Find the bit where it says:
/printCommentPopups [/b false]
and change “false” to “true”. Save the file. So it looks like
/printCommentPopups [/b true]
Now you can just open up your file in adobe reader
and print, making sure to select the “Documents and Markups” option in the “Comments and Forms” combo box in the print dialogue.