A blog devoted to issues in language, epistemology, metaphysics, and mind
Nightline did a feature on our case study, JP, who has acquired synesthesia and savant syndrome
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I've looked around at some of Jason Padgett's work. I don't undertand why his drawings are referred to as fractals. What is it about the drawings that qualifies them as being "of fractals" or in some sense generated fractally?
We don't actually call them 'fractals'. But 'fractal' just means 'self-similar pattern'. So I suppose there is a sense in which some of JP's drawings are fractals.
In mathematics, the word "similar" has a much more specific meaning than the everyday English word: two shapes are similar if one is an exact copy of the other, drawn at a different scale. Consequently, "self-similar" also means something far more specific than what you seem to imply.While the modern definition of fractal does not require strict self-similarity, it is still very precise; besides, this is not the definition you are applying.I see no room for interpretation in the definition of 'fractal' that includes such primitive geometric patterns as Padgett's, which are essentially just circulant graphs.
Hi, yes, I am aware of the stricter definition of 'fractal', which is the main reason we don't use this terminology in our published articles.
Okay, I guess looking closer, this is a grant report and not published work: https://docs.google.com/file/d/0B0GEjtSycjTKNmUzYjgyMjctOWFjNC00N2Q1LThlMzUtNTk0MzM3YzAyODU3/editBut you do refer to his drawings as "fractals" many times in that document, and say things like he's the "first to hand draw a fractal". (A strange claim--I can hand draw a fractal right now, granted I would need to use an eraser at some points in the process. It's trivial, for example, to hand draw the snowflake fractal.)Are you saying that this is language you _used_ to use in professional discussion of Padgett's work, but which you no longer use?Sorry I don't mean to sound so pointed but this has been bothering me for a long time. It's a huge relief to me if a prominent philosopher of mind isn't showing as senseless a set of misunderstandings of her subject matter as I have been thinking you were. Philosophers get a bad enough rap in many circles as it is... And your work with Padgett is positively lampooned among mathematicians (at least, mathematicians who have only read the above article or journalistic summaries of your work) because of this terminological issue.
(BTW I should note that I am the first and third commenter, but not the second commenter. ;))
Whether JP's images are fractals or some other interesting geometrical figures is of no consequence for this project. This is a project in philosophy of mind, not philosophy of mathematics. I will, however, be happy to include a statement about other people's hand-drawn images. So please send me a link to your or some other person's hand-drawn fractals, fractal-like images or other interesting geometrical figures.
I suppose I didn't answer your question. But, yes, we actually don't use this terminology in published work. As nothing hinges on whether or not we use this terminology, I will be happy to change it in the grant report after I finish some pending projects.
It would be excellent if you stopped calling these things fractals. Thanks for listening.As for examples of hand drawn fractals, google "snowflake fractal" and you'll see for yourself how easy it can be to hand draw a fractal, given the use of straightedge, compass and eraser (as I understand the subject of your research uses.)
I googled it but didn't find any sites with hand-drawn fractals or complex geometrical figures. Please send a link, so I can acknowledge it. I don't see any for your name.Though I haven't tried, I suspect it's not going to be easy to do it. Most people don't have the obsession or patience to go on doing it.It's not like anyone ever claimed that it couldn't be done. The claim was that brain injury may lead to changes in brain structure or function.JP certainly wouldn't have even attempted to draw anything prior to the incident.You might be interested in Dehaene's The Number Sense. He argues that the difference between individuals with mathematical savant syndrome and individuals without is simply a difference in obsession.A psychology friend of mine thinks it's a change in personality traits.I will email you a paper on it when I get done with the semester.That's the interesting part. We can all use an algorithm to do, say, calendar calculation (great bar trick!). But it is nonetheless still fascinating when this happens as a result of brain injury.
This is somewhat magic kind of thing, that after getting a brain injury a man turns out to be genius.
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