Disinfotainment

I recently got some new batteries. My favorite new gadget is a lithium-ion battery about the size of a cell phone with some jumper cables to start your car. It was only $27, cheap.

Sometimes my car battery runs down in cold weather and my car won’t start. Fortunately, the engine starts easily once I get it to turn over. This little jump starter has just enough juice to start my tiny Honda 4 cylinder engine.

I could not get it to work the first time. I emailed tech support, the design had changed, the instructions neglected to mention a hidden ON button. Then I suddenly realized, I was talking to tech support for a battery. The next time, the jumpstart worked perfectly.

I thought this was such a useful feature, why don’t all cars have Li-ion batteries as a reserve, built right in? Then I thought about it. The standard lead-acid battery is the reserve power. You could have a Li-ion battery as the reserve to the reserve. At this point, you might as well run the whole car on electric batteries, and you’ve got a Tesla.

I was also surprised to get a battery replacement for my 2 year old iPhone 6s. Apple didn’t just replace the battery, they gave me a brand new iPhone for free.

My iPhone wasn’t holding much of a charge lately, so I tested it and it only had 54% capacity! I called Apple Support and my iPhone was covered under an extended replacement program. I was eligible for a free replacement battery. I had a new iPhone on my desk FedEx overnight about 12 hours after I called. I set it up and checked its battery capacity: 103%.

People often complain that their iPhone batteries don’t last very long. That’s because they use their iPhone all the time.

I bought a new photo gadget that totally revolutionized some old photo gadgets I already owned. Here is the entire rig:

On the left is a Manfrotto Super Clamp, I bought it decades ago. It had a brass stud and mini ball head to attach a camera, but I lost them somehow. I also recently bought a Glif, the bracket on the right end. It’s a clip to mount an iPhone to a tripod. I tested it but it didn’t work very well, using a tiny phone camera on my tripod made for large format cameras. Maybe the Glif would work better with the Super Clamp, if only I hadn’t lost the parts.

I looked online for replacements and instead, I found this interesting Manfrotto Heavy Duty Flex Arm. It has a hex stud to mount in the Super Clamp at one end, 20 inches of flexible extension arm, and a 1/4″ tripod head at the end.

Now all I really need is a mini ball head to make it easier to swivel the Glif and iPhone camera into position. A cheap one will do, I bought this for $7. It’s not a very good swivel head but the matching Manfrotto 494 is $65, this will have to do.

It’s really easy to clamp this anywhere and bend the arm into place. I clamped it on my old photo enlarger and it makes a great copy stand. The 20″ extension puts the camera out in the middle of my work table so I can copy huge originals, like a tabloid 11×17 double spread. Here is a pic of the rig clamped to my kitchen cabinet, I used a paper towel to avoid clamp marks. Oh no this looks like a setup for coffee demo videos.

After I got this rig and used it a while, I discovered it had another uniquely useful function. I clamped it to my bed’s headboard, to hold up my iPhone so I can watch video in bed.

Today I noticed an New York Times obituary for mathematician Raymond Smullyan. I was immediately drawn in by the photo of Smullyan demonstrating some very basic algebra.

Smullyan was a college dropout and autodidact. I was amused to read an account of his academic history.

One of Smullyan’s teachers at the University of Chicago…Rudolf Carnap…recommended Smullyan for a mathematics post at Dartmouth College.. Smullyan had no formal qualifications at this time but was already working on mathematical research for future publications. He taught at Dartmouth College from 1954 until 1956, being awarded his B.S. from the University of Chicago in 1955. He had never completed sufficient courses to merit the award, but to make up the number Chicago credited him with a calculus course which he had never taken but was teaching.

The NY Times published a quiz of Smullyan’s math puzzles, but I was terribly disappointed at one question, presented as a logic puzzle. Here it is, with a correct solution reached by an incorrect procedure.

That is utterly ridiculous. Any high school senior will immediately recognize this as a basic algebra question, not a logic question at all. It is hardly worthy of Smullyan’s legacy. Here is the proper method of solution, with nice graphics produced by Wolfram Alpha.

Edit: I decided the solution needs more explanation. We are told the price of a large bird (represented as x) equals the price of two small birds (2y). So we get (x = 2y). Then we found the price of five large birds (5x) and three small (3y) is (5x + 3y), the same as three large and five small, plus 20.  Since 3x + 5y is 20 less than 5x + 3y we add 20 to make them equal as (3x + 5y + 20). We could simplify that equation to (x = y + 10) but the Wolfram solver is just as happy to work with our original, unsimplified equations.

Result: {x = 2y, 5x + 3y = 3x + 5y + 20}

The two equations represented by lines will intersect at only one point, which is a solution that works for both equations.

This is a simple solution of two simultaneous linear equations. It may look complex, but it’s basic Algebra 1. It is merely a literal translation of the problem into equations. It could be solved without plotting by substitution, but graphs are always fun (especially if I don’t have to plot them myself).

I was expecting a spark of genius, and ended up back in high school. But perhaps that is not so bad. I was recently employed as a mathematician, one of my colleagues gave me this XKCD cartoon. I understand it completely.