Laboratory one and the density of soap

August 20, 2021

Laboratory one launches the quest to demonstrate that the mathematics not only describes a system but predicts what a system will do. The laboratory opens with my reading of two quotes.

La filosofia è scritta in questo grandissimo libro, che continuamente ci sta aperto innanzi agli occhi (io dico l' Universo'), ma non si può intendere, se prima non il sapere a intender la lingua, e conoscer i caratteri ne quali è scritto. Egli è scritto in lingua matematica,... - Galileo Galilei

which might be translated as:

[Science] is written in that great book which ever lies before our eyes - I mean the universe - but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language,...

and a second quote

For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created... ...equations are quite miraculous in a certain way. I mean, the fact that nature talks mathematics, I find it miraculous. I mean, I spent my early days calculating very, very precisely how electrons ought to behave. Well, then somebody went into the laboratory and the electron knew the answer. The electron somehow knew it had to resonate at that frequency which I calculated. So that, to me, is something at the basic level we don't understand. Why is nature mathematical? But there's no doubt it's true. And, of course, that was the basis of Einstein's faith. I mean, Einstein talked that mathematical language and found out that nature obeyed his equations, too. – Physicist Freeman Dyson

Then I returned to the equation for density from the prior day and introduced mathematical models as shapes on graphs.

To improve access to this material in the course I moved the textbook in Canvas.

The textbook is now embedded in the course available in the Canvas Commons.

I then covered the procedure for the laboratory and suggested that the students work in pairs.

Mercedes enters data directly into Desmos

This laboratory also introduces the Desmos mathematical engine, which I argue changes everything as to how mathematics should be taught.

Marcia and Cynthia recording data and cutting their soap

The push to move towards 1:1 tech to student ratios means that this laboratory no longer needs to adjourn to a computer laboratory to cover how to do the laboratory assignments. The complication this term is that the WiFi has decided to be finicky. The Chromecast logs onto and remains network connected, but attempts to cast to the Chromecast launch and connect, but only for 30 seconds at most, and then the connection is dropped. I then set up a Chromebase to drive the 50" television via HDMI.

But this would prove only a partial solution.

Chrome could not load any pages. Leaf browser, seen above, was able to load pages. Note that the original Leaf browser alpha project was effectively abandoned in 2016, this is the subsequent development work done as a continuation of that project.