Applying game theory to the game Rock, Paper, Scissors, and to other, less important aspects of life.
Chances are you’ve played Rock, Paper, Scissors, but how do you calculate your strategy, if you have one at all?
In Rock, Paper, Scissors: Game Theory in Everyday Life, physicist Len Fisher points out that putting yourself in your opponent’s mindset is a key to success in the game.
It’s all part of game theory, which has to do with everyday strategies and commonplace interactions — and not just those designed for winning at Monopoly or trapping wild elk, as it may sound. Fisher, a visiting research fellow in physics at the University of Bristol and author of several science books for lay audiences, argues that a teaspoon of this sort of thinking can illuminate a range of human behaviors. Not to mention that game theory offers a handy explanation of why all those teaspoons keep disappearing from the communal lunchroom at work. (Individuals think it won’t hurt the collective if they take “just one” spoon, but, voilà, in no time, there are very few, if any, left for the collective to use.)
While I was on vacation I had seen a couple of videos/links about a guy who launched himself with some water rocket of the large soda-bottle variety, and thought that this was the sort of thing Rhett would analyze over at Dot Physics, and as I catch up with my blog reading, I see that it is so: Water Bottle Rocket Guy
“Water bottle rocket guy” is too impersonal and too long to type repeatedly, so I will refer to him as “Mr. Payload”
The thing that screams, “Fake!” the loudest is the video snippet that indicates a cable attached to Mr. Payload’s harness. I notice that he also starts tumbling, as one might expect from a torque from the rockets, but this motion does not continue — something that a guide cable would interrupt. There’s also the trajectory analysis, which doesn’t jibe with expectations.
Rhett does a quick energy analysis of the maximum height, but the analysis assumes all of the energy goes into Mr. Payload and his rocket shell, thus giving an absolute maximum height, and the number he gets isn’t realistic. One must also consider the large amount of energy contained in the expelled water that generates the thrust to get a more realistic limit, as well as the energy used for the forward motion.
Rhett uses 1L of water per bottle , but to me it looks like there is more. I’m going to assume 20L of water but the same energy (i.e. higher pressure) and that Mr. Payload has a mass of 60 kg, which is more than Rhett uses but makes the math easy. Since the water is expelled quickly — it appears to be gone before he’s more than 2m above the dock, so I’m just going to model this as an explosion, with the water getting an impulse and Mr. Payload getting an equal and opposite impulse. Their kinetic energies must add to the total energy of the system, of 27kJ.
We have the sum of the KEs totaling 27 kJ, with \(KE = p^2/2m \) and equal magnitudes of momentum.
Solve for momentum, and I get 900 kg-m/s, or a speed of 15 m/s for Mr. Payload. If launched at ~30º, as in the video, that’s a height of under 3 meters, ignoring the considerable drag. It also means that about 20 kJ of the available energy (i.e. 3/4 of it) went into the expelled water.
One of the comments links to a video which looks real. The launch is at about 3:15
Of all the animals in the world, the lowly spookfish has the oddest eyes — compound mechanisms that bear more than a passing resemblance to rearview mirrors.
The bottom half of its eyes point upwards. The upper half point downwards, and are backed with a layer of reflective guanine crystals that bounce a focused image into the retina.
The titular disclaimer comes from reading this:
Researchers tested the eyes by taking flash photographs from above and below a live spookfish, then dissecting its eyes.
Researchers from Loyola University Health System and other centers compared African American women in metropolitan Chicago with women in rural Nigeria. On average, the Chicago women weighed 184 pounds and the Nigerian women weighed 127 pounds.
Researchers had expected to find that the slimmer Nigerian women would be more physically active. To their surprise, they found no significant difference between the two groups in the amount of calories burned during physical activity.
“Decreased physical activity may not be the primary driver of the obesity epidemic,” said Loyola nutritionist Amy Luke, a member of the study team.
While it may be true that diet, not exercise, causes the obesity, it’s fallacious to conclude that exercise won’t make any difference. It just isn’t a factor in this example. You have two variables that affect weight (Calories in and Calories burned), and only see that one is different here. At the very basic level, it’s conservation of energy.
People burn more calories when they exercise. Thing is, they compensate by eating more, said Richard Cooper, co-author of the study and chairman of the Department of Preventive Medicine and Epidemiology.
“We would love to say that physical activity has a positive effect on weight control, but that does not appear to be the case,” Cooper said.
It’s not clear if this was tested in the study — there’s no mention in the story — so one doesn’t know if it was a crappy experiment or it’s crappy reporting.
Do two football teams meeting in a game, ever, ever like each other? I mean, for years I’ve been hearing variations of These two teams don’t like each other! in the pre-game blather.
Has anyone ever seen a player not make a tackle ot hard hit, or not pick up a fumble, because it turns out they liked the other team?
These screw types have a “+” shaped recess on the head and are driven by a cross-head screwdriver, designed originally for use with mass-production mechanical screwing machines. There are a few other recessed drive screws presented that you also want to be aware.
So, why all the confusion? Why all the damaged screw heads and drivers? Why is this screw and driver thing so awkward? Read on and be amazed while I unravel the mystery of screw drives and present some you may have never seen.
I didn’t learn any of this watching way too much Handy Manny last week.
