How many test rigs for a successful product at scale?
This is a general comment on how new technologies are presented in the media: usually something that is either a laboratory test rig or at best a proof-of-concept technology demonstration is hailed as a revolutionary product ready to take the world and be deployed at scale.
Consider how many is "a lot of," as a function of success probabilities at each stage:
Yep, notwithstanding all good intentions in the world, there's a lot of work to be done behind the scenes before a test rig becomes a product at scale, and many of the candidates are eliminated along the way.
Recreational math: statistics of the maximum draw of N random variables
At the end of a day of mathematical coding, and since Rstudio was already open (it almost always is), I decided to check whether running 1000 iterations versus 10000 iterations of simulated maxima (drawing N samples from a standard distribution and computing the maximum, repeated either 1000 times or 10000 times) makes a difference. (Yes, an elaboration on the third part of this blog post.)
Turns out, not a lot of difference:
Workflow: BBEdit (IMNSHO the best editor for coding) --> RStudio --> Numbers (for pretty tables) --> Keynote (for layout); yes, I'm sure there's an R package that does layouts, but this workflow is WYSIWYG.
The R code is basically two nested for-loops, the built-in functions max and rnorm doing all the heavy lifting.
Added later: since I already had the program parameterized, I decided to run a 100,000 iteration simulation to see what happens. Turns out, almost nothing worth noting:
Adding a couple of extra lines of code, we can iterate over the number of iterations, so for now here's a summary of the preliminary results (to be continued later, possibly):
And a couple of even longer simulations (all for the maximum of 10,000 draws):
Just for fun, the probability (theoretical) of the maximum for a variety of $N$ (powers of ten in this example) is greater than some given $x$ is:
More fun with Solar Roadways
Via EEVblog on twitter, the gift that keeps on giving:
This Solar Roadways installation is in Sandpoint, ID (48°N). Solar Roadways claims its panels can be used to clear the roads by melting the snow… so let's do a little recreational numerical thermodynamics, like one does.
Average solar radiation level for Idaho in November: 3.48 kWh per m$^2$ per day or 145 W/m$^2$ average power. (This is solar radiation, not electrical output. But we'll assume that Solar Roadways has perfectly efficient solar panels, for now.)
Density of fallen snow (lowest estimate, much lower than fresh powder): 50 kg/m$^3$ via the University of British Columbia.
Energy needed to melt 1 cm of snowfall (per m$^2$): 50 [kg/m^3] $\times$ 0.01 [m/cm] $\times$ 334 [kJ/kg] (enthalpy of fusion for water) = 167 kJ/m$^2$ ignoring the energy necessary to raise the temperature, as it's usually much lower than the enthalpy of fusion (at 1 atmosphere and 0°C, the enthalpy of fusion of water is equal to the energy needed to raise the temperature of the resulting liquid water to approximately 80°C).
So, with perfect solar panels and perfect heating elements, in fact with no energy loss anywhere whatsoever, Solar Roadways could deal with a snowfall of 3.1 cm per hour (= 145 $\times$ 3600 / 167,000) as long as the panel and surroundings (and snow) were at 0°C.
Just multiply that 3.1 cm/hr by the efficiency coefficient to get more realistic estimates. Remember that the snow, the panels, and the surroundings have to be at 0°C for these numbers to work. Colder doesn't just make it harder; small changes can make it impossible (because the energy doesn't go into the snow, goes into the surrounding area).
Another week, another Rotten Tomatoes vignette
This time for the movie Midway (the 2019 movie, not the 1972 classic Midway):
Critics and audience are 411,408,053,038,500,000 (411 quadrillion) times more likely to use opposite criteria than same criteria.
Recap of model: each individual has a probability $\theta_i$ of liking the movie/show; we simplify by having only two possible cases, critics and audience using the same $\theta_0$ or critics using a $\theta_1$ and audience using a $\theta_A = 1-\theta_1$. We estimate both cases using the four numbers above (percentages and number of critics and audience members), then compute a likelihood ratio of the probability of those ratings under $\theta_0$ and $\theta_1$. That's where the 411 quadrillion times comes from: the probability of a model using $\theta_1$ generating those four numbers is 411 quadrillion times the probability of a model using $\theta_0$ generating those four numbers. (Numerical note: for accuracy, the computations are made in log-space.)
Google gets fined and YouTubers get new rules
Via EEVBlog's EEVblab #67, we learn that due to non-compliance with COPPA, YouTube got fined 170 million dollars and had to change some rules for content (having to do with children-targeted videos):
Backgrounder from The Verge here; or directly from the FTC: "Google and YouTube Will Pay Record $170 Million for Alleged Violations of Children’s Privacy Law." (Yes, technically it's Alphabet now, but like Boaty McBoatface, the name everyone knows is Google. Even the FTC uses it.)
According to Statista: "In the most recently reported fiscal year, Google's revenue amounted to 136.22 billion US dollars. Google's revenue is largely made up by advertising revenue, which amounted to 116 billion US dollars in 2018."
170 MM / 136,220 MM = 0.125 %
2018 had 31,536,000 seconds, so that 170 MM corresponds to 10 hours, 57 minutes of revenue for Google.
Here's a handy visualization:
Still not as egregious as Facebook's toy fine for its part in the Cambridge Analytica data mining snafu:
Engineering, the key to success in sporting activities
Bowling 2.0 (some might call it cheating, I call it winning via superior technology) via Mark Rober:
I'd like a tool wall like his but it doesn't go with minimalism.
No numbers: recommendation success but product design fail.
Nerdy, pro-engineering products are a good choice for Amazon to recommend to me, but unfortunately many of them suffer from a visual form of "The Igon Value Problem."
