This is a repository of pictures I have been drawing to further my understanding of low dimensional topology. Some are finished; some will never be.  I do most of my drawings with SketchUp, Xfig, or good ol’ chalk on a blackboard.  Lately I’ve been doing some work with the pre-beta Rhino OS X port of Rhino 3D.

And in case you’re wondering who I am:
I am Kenneth Baker.

38 Responses to “About”

  1. lol and behold!

  2. Nice blog, but can you put an RSS subscription link in on the side navigation? Find it in the wordpress dashboard somewhere

  3. penrose diagrams
    global hyperbolicity and cauchy hypersufaces

    Click to access time.pdf

  4. Hello Baron Baker. Wonderful pictures. Do you guard them closely, or would you be happy for me to post one or two on my website (with full credit and a link, of course)?

  5. By all means, post and link all you like.

  6. Dear Ken,
    I am writing from the American Mathematical Society (AMS) to request permission for the use of one of your graphics in literature to be published for the annual Joint Mathematics meeting in January 2009. You can view information about the meeting at: http://www.ams.org/amsmtgs/2110_intro.html
    I would very much appreciate it if you could contact me at your earliest convenience.

    Best regards

  7. Dear Ken,
    The Mathematics Department at Rice University will be having Ian Agol as our annual Wolfe Lecturer this year. We try to put an interesting graphic on the poster announcing the talk and Dr. Agol suggested using one of yours. May we (with full attribution, of course). Thanks.

  8. Great pictures!

  9. Very interesting – so if understand well you studied law, went into politics and now you are a hobby mathematician?

  10. OK, I think you are making fun of us. Above on this page you say your are Kenneth Baker, the politician, then you are Kenny Baker, the actor…
    Well, I am really http://www.mathoman.com and http://film.tunes.org
    (no fun)

    • Of course I’m only joking around. Why not? If one truly cares, there is information enough within this blog to determine who I really am.

  11. KB, you didn’t need to link to Wikipedia. Everyone already knew you were the Baron of Dorking. Sry we didn’t talk much at Davis – at least I get to see your interesting pictures and comments.

  12. Great visualizations.

  13. nice blog you own! greetings sven


  14. Hello, I was wondering if you know anything about Bing’s house with two rooms? I understand the proof that it’s contractible, but I’ve been struggling for months to actually see the deformation retraction. Not to mention, I’ve been struggling to understand why it should be so difficult to see! Any light you can shed on this would be greatly appreciated. It would be truly amazing to see a clear visualization of a homotopy from the identity map on Bing’s house to a constant map. Great blog.

    • It’s actually a somewhat subtle thing to explicitly see the deformation retraction of Bing’s house. Good suggestion. I’ll have to figure out how to suitably draw it clearly.

  15. […] something much more subtle. Bing’s house actually deformation retracts to a point. Franciscus asked about this, and perhaps it’s what was meant to be asked on MathOverflow. But it’ll take […]

  16. This may be a bit of a tall order, but what are the chances of you doing some pieces describing the topology of magnetic reconnection? It’s what happens on the surface of the sun when mass ejections of waves get aimed at points in space, including our planet?


    “In an electrically conductive plasma, magnetic field lines are grouped into ‘domains’ – bundles of field lines that connect from a particular place to another particular place, and that are topologically distinct from other field lines nearby. This topology is approximately preserved even when the magnetic field itself is strongly distorted by the presence of variable currents or motion of magnetic sources, because effects that might otherwise change the magnetic topology instead induce eddy currents in the plasma; the eddy currents have the effect of canceling out the topological change.”

    –w’pedia article on magnetic reconnection

    I’m an artist myself, not a mathematician. But science is about the only thing besides naked chicks that makes me want to draw. Unfortunately, visualizing science is another matter entirely, and I greatly admire the graphics you have produced. I regard them as being on par with the time-consuming drawings of my favorite artist, Zak Smith. I spend hours looking at his drawings, trying to figure out how he does what he does, hat’s about the highest comment I can give.

    • I’ll chew on it… Not quite sure what I would illustrate about magnetic reconnection. Though from a glance at the wiki article perhaps something about stability vs. critical points would be related.

      Thanks for your interest! Keep drawing!

  17. Not sure if you’ve seen this yourself, but I’ve been reading this blog for a while and absolutely loved it so I thought I’d send it along. A friend of mine stumbled across this: Mathematically Correct Breakfast which is a bagel cut into two mobius strips through a single cut. Thought I’d pass it along.


  18. Hello Ken,

    Can you model DNA loops of a specific topology, too?

  19. Great!!!!! I am interested in the Holiday Junction conformation. It is a 4 stranded DNA structure… I do not know if it is possible to attach pictures here, but I could email you some slides and papers that explain what I am interested in.

  20. Dear Ken,

    I am writing from the University of Hong Kong to request permission for the use of your graphics for science education propose. We would like to include them in our publications. We will give full credit to you.
    I would very much appreciate it if you could allow us to do so.

    Best Regards,
    Sze-leung Cheung
    Faculty of Science
    University of Hong Kong

  21. What an amazing site! I was wondering: what are the licensing terms of your images?

    More concretely, what is the policy to use a particular sketch of yours for commercial purposes, or as a company logo, etc?


    • Thanks.

      For you and others who may have the same question:

      Licensing? Hmm. Well I have the copyright to all the images. People are free to use them for personal and educational purposes, though I’d appreciate a line or two dropped here to let me know how they’re being used. In particular if they’re wanted to be used in print or as a logo for educational purposes, ask here and I’ll get in touch.

      I’m reluctant to let them be used for commercial purposes. But drop a line here and we can talk about it.

  22. Dear Ken,
    This is a terrific, wonderful collection of images and explanations. Thank you! I wondered if you might post something explaining this question: I can easily visualise how to map a square lattice onto the surface of a torus, by identifying the opposite edges of the square as in a Pacman game board. Recently I learned that a sphere will result from identifying the edges of a square, but in a different way (I’m sure you know the way I mean). My problem is, try as I might, I cannot figure out how the inside of the square, not just the edges, would get mapped to a sphere’s surface. And I haven’t found any good pictures to help me imagine this. Would it be easy to make such a picture, showing how a regular grid of perpendicular lines on a flat square would get mapped onto the surface of a sphere under the fundamental polygon mapping, and what the resulting deformed grid would look like on the surface of the sphere?
    Whether or not you can do this, thanks again for a great collection of clearly explained, beautifully illustrated examples. Best, Edwin.

    • Well, maybe it’s just as well for me to suggest that you start by stretching the square to “flatten” a corner so that a pair of adjacent edges looks like a single edge. Then do the same to the opposite corner. Now you’ve got a shape somewhat like a lens with two curved edges and two corners. Billow out the interior while you zip up the two edges like you’re making a pouch. Voila.

  23. Asking permission to use one of your images (with accreditation) on my Web site. I’m a freelance writer and photographer so technically, I suppose, it’s a commercial application. But only as commercial as one person with a camera can be. Thanks.

    • Sorry for the delay in reply. Thanks for your interest. In general, I’m not so keen on these being used commercially.

  24. Hi,

    I have an old 4 min video made in 1992 called “Pivoted lines and the Mobius Band” by IBM Research, and turned into an MPEG from a tape supplied by them. It was designed by me and some stills can be seen at


    I would like to get it updated to modern standards, as shown by your graphics. I wonder if you would be interested?

    I think the screenplay of showing how rotations are modelled by the projective plane, seen as an identification of a Mobius Band with a disc, is not available elsewhere, and I use it to illustrate the Dirac String trick for popular lectures. I know the video “Air on the Dirac strings” which is very good, but it does not actually explain.

    Ronnie Brown

    • Nice. Thanks for the suggestion. That would be a great topic to cover here. I’ll have to toy around with it one of these days. Sorry for the long delay in reply.

  25. Your work here is amazing.

  26. Dear Ken,
    I am writing an essay on sutured manifolds and would like to use your picture as part of the front cover.
    Is that all right?
    Thanks a million!

  27. Hi! Very cool pictures! I’m working on a poster for a workshop and was wondering if I could use some of your images? This is the event in question: http://www.floer.rub.de/activities/floerlectures2015.html

  28. Hi! I invented interesting from.
    Please have a look at below URL.


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