Philosophical Society of Washington

Minutes of the 2036th Meeting

Speaker: Helaman Ferguson, Sculptor/Mathematician, and Claire Ferguson, Author
Topic: “Mathematics in Stone and Bronze”

The President, Ms. Enig, called the 2036th meeting to order at 8:28 p.m. on December 16, 1994. The Recording Secretary read the minutes of the 2035th meeting and they were approved. The President introduced Helaman and Claire Ferguson.

The presentation “Mathematics in Stone and Bronze” began with a video report prepared by WUSA TV describing Mr. Ferguson's work. Ms. Claire Ferguson then read passages from her book describing the sculptures and how they were constructed [1]. The Fergusons believe that while art has traditionally been created from the spiritual and political ideas of its particular time and place, mathematical ideas can also serve as an inspiration and source for art. Mr. Ferguson has sought to create sculptures in stone and bronze by translating mathematical theorems, closed three-dimensional surfaces that represent various laws of topology, analytic and fractal geometry, into tangible form.

Two large, mounted sculptures were presented and described: Umbilic Torus NC, in silicon bronze (op. cit., pages 6-7,73) and Umbilic Torus NIST, also in silicon bronze (op. cit., pages 26-27,73). These sculptures illustrated a type of trefoil cross-section Moebius toroid. The surface of the larger work, Umbilic Torus NC, was textured with a raised, fractal, toroid surface-filling curve commonly but incorrectly known as Hilbert's curve.

Among the smaller sculptures that were described were Torus with Cross-Cap, in silicon bronze (op. cit., pages 14-15,72), Figureight Knot Complement V in Kodachrome flats alabaster (similar to op. cit., pages 42-43,68), and Hyperbolic Quilt of Right Angled Pentagons and Bronze Orbifold. Mr. Ferguson described his representation of the fractal solids, termed wild sphere and wild torus, with paired horns that do not touch but approach each other with decreasingly smaller sets of horns. He encourages viewers to handle his works so that they can better appreciate the configurations of the mathematical curves and textures of the surfaces, and so that the works themselves will have a “socially achieved patina”.

This work would not have been possible 10 years ago because of the innovative computer technology he uses in this creative work. In a cooperative research and development agreement with the National Institute of Standards and Technology he has developed new stone-carving techniques that use three point suspended, computer driven cutters and chisels. This system employs virtual reality techniques to plan the execution of the work, and permits duplicate works to be produced.

[This was a largely visual and tactile presentation of sculptures that, although inspired by a few lines of mathematics, might not be adequately reproduced, as the well-known oriental adage would have it, in thousands of words.]

[1] Claire Ferguson, “Helaman Ferguson: Mathematics in Stone and Bronze”, Meridian Creative Group, Erie, Pennsylvania, 1994.

The President thanked the speakers on behalf of the Society. The Membership Chairman and President elect, Mr. Olmacher, presented the names of two new members. The President announced the speaker for the next meeting, made the parking announcement, adjourned the 2036th meeting at 9:42 p.m. and called the 124th annual general meeting to order.


Respectfully submitted,
John S. Garavelli
Recording Secretary

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