Grasping data through physical models

Is it eas­ier to glean insights from data using a phys­i­cal model? Most of the advances in tech­nol­ogy (data visu­al­iza­tion, chart­ing, inter­ac­tive graph­ics) have made it much eas­ier to get insights using on-​screen imag­ing. By and large they have replaced phys­i­cal con­struc­tion and draw­ing of charts with rulers, com­passes, and inks. But what if we used phys­i­cal mod­els to under­stand data bet­ter? I’ve been read­ing three books recently which make the case for a phys­i­cal, real world mod­els to help understand:

1) How Round isY­our Cir­cle (John Bryant and Chris Sang­win) [web­site] describes ways of phys­i­cally rep­re­sent­ing math­e­mat­i­cal equa­tions. In one exam­ple, they model har­monic series diver­gence using stacks of domi­noes which can be mea­sured to show the proof. A har­monic series is 1+1/2+1/3+1/4+1/5.…

The Book, How round is Your Circle?, explores visualizing mathematical concepts using physical objects like dominoes, pantographs, and wooden models.

The Book, How round is Your Cir­cle?, explores visu­al­iz­ing math­e­mat­i­cal con­cepts using phys­i­cal objects like domi­noes, pan­tographs, and wooden models.

Dominoes can be used to model the divergence of the harmonic series .

Domi­noes can be used to model the diver­gence of the har­monic series .

2) Math­e­mat­i­cal Mod­els (Condy and Rol­lett) was a ground­break­ing book in the early 1950s. Cundy in par­tic­u­lar was instru­men­tal in devel­op­ing the “new math” cur­ricu­lum in Britain in the 1960s. The book is filled with ideas on mod­el­ing math­e­mat­i­cal con­cepts, includ­ing poly­he­dra, wire mod­els, and qua­dratic sur­faces. Bryant and Sang­win acknowl­edge the influ­ence of this book on their work.

Polyhedra, from Cundy and Rollett's Mathematical Models.

Poly­he­dra, from Cundy and Rollett’s Math­e­mat­i­cal Models.

3) Archi­tec­tural Mod­els (Megan Warner) describes mate­ri­als and meth­ods of cre­at­ing archi­tec­tural mod­els. While not strictly data mod­el­ing, the meth­ods can be used to cre­ate mod­els of 3d graphs and charts.

Model Making by Megn Werner gives methods an dmaterials for creating architectural models.

Model Mak­ing by Megn Werner gives meth­ods an dma­te­ri­als for cre­at­ing archi­tec­tural models.

In a later post, I will cre­ate some Venn dia­gram mod­els using both 2d and phys­i­cal mod­els as an experiment.

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