John Baez talking to Jason Brown About Applied Category Theory

My comment:

11:41 Applied category theory was invented by Ernst Mach in around 1882, I think. From The Economical Nature of Physical Inquiry "The greatest perfection of mental economy is attained in that science which has reached the highest formal development, and which is widely employed in physical inquiry, namely, in mathematics. Strange as it may sound, the power of mathematics rests upon its evasion of all unnecessary thought and on its wonderful saving of mental operations.... No one will dispute me when I say that the most elementary as well as the highest mathematics are economically-ordered experiences of counting, put in forms ready for use. In algebra we perform, as far as possible, all numerical operations which are identical in form once for all, so that only a remnant of work is left for the individual case. The use of the signs of algebra and analysis, which are merely symbols of operations to be performed, is due to the observation that we can materially disburden the mind in this way and spare its powers for more important and more difficult duties, by imposing all mechanical operations upon the hand." 

Here's his video about negative mass:

I think maybe the problem with negative Newtonian mass is how you empirically measure G. The units of G are area times acceleration per unit mass, so wouldn't you get a negative result if you tried to measure it with positive and negative mass? But maybe you need some sort permittivity / permeability notion to make it stable. Maybe there's something you can learn from all the thought people have put into trying invent the physics of magnetic monopoles. 

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NIST measuring G. See NIST Weighs In on the Mystery of the Gravitational Constant: 

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There is some mystery as to why the NIST result was so different from that of the BIPM experiment it was repeating. See the BIPM page for publications on this. 

See Measurement of the Gravitational Constant Using the Attraction Between Two Freely Falling Discs: a Proposal by Leonid Vitushkin, Peter Wolf and Artyom Vitushkin. 

John Baez talking about duality in logic and physics and dagger-compact categories in 2010:

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For more on negative mass and how it can be observed in the laboratory, see Avshalom Elitzur's talk about the Aharonov-Bohm effect in Physicists Talking About Physics:

Maybe in fifty years or so people will start publishing decent Quantum Mechanics textbooks! See Jorge S. Diaz's Series on the Old Quantum Mechanics.