Fun with numbers for January 30, 2020

Some collected numerical fun I had on twitter since the last post.

Science illustration fail: meteor tails in outer space

Why oh why do these representations always put meteor tails on objects far off the exosphere? That tail extends past 3000 km altitude, with the fireball center at around 1400 km. Little atmosphere there, fellas…

Also, that meteor (assuming it's the darker circle inside the fireball) is well over 300 km in diameter; even losing a big chunk of its mass in the atmosphere, it would reach the ground much larger than the 7 km the article says.

Source: https://www.cnet.com/g00/news/asteroid-that-smashed-earth-2-229-billion-years-ago-may-have-thawed-the-planet/

Star Trek: Picard nonsense: solar panels on/over the Golden Gate Bridge

I got this image, from the new show Star Trek: Picard, requiring unattainable suspension of disbelief — as if there was ever fluid traffic, let alone no traffic, on the GGB.

Oh, and also, solar roadways?! Really?!

I assume the Picard writers are from Hell-A, since anyone from the Bay Area would know that the GGB is fogged-in most days, so putting solar panels on it would be even stupider than on other roads, and that's saying something...

Okay, some have suggested panels are above the road. At 100% efficiency, 4 kWh/(m$^2$ * day) San Francisco insolation, and 75,000 m$^2$ deck area for the GGB, that's a 12.5 MW (average power) generator, and for that we cover one of the best views of the city?! In the 24th Century?!

Anyone who drives East on the Bay Bridge gets the transition from claustrophobic (West of Yerba Buena Island) to open space (East of YBI). Covering the GGB, especially as a pedestrian park, would be a terrible decision, more so for a puny 12.5 MW power rating.

Corona virus causes an epidemic of bad economics

What is it about supply and demand that is difficult to understand for otherwise intelligent people?

Two of many reasons why raising prices in these circumstances is good:

Some of the people who are reminded of the need for N95 masks, hand sanitizer, and disposable gloves during an emergency might realize that they shouldn't be unprepared in the future; if there's no enforced rationing (terrible thing to do, rationing) and the prices don't rise, these people may buy more than they need now, to address their previous failure to prepare. Therefore, raising the price will deal with some of this behavior, making supplies available to more people.

Expedited delivery (to the retailer) costs more than regular delivery. Some of these deliveries were made with an assortment of goods, many of which were high-margin (say bottles of 30-year-old scotch) that absorbed most of the cost of the delivery. Delivering truckloads of low-margin items like sanitizer and N95 masks alone (no expensive items to share the cost of the delivery) means the cost per unit is much higher.

California electrical consumption in nuclear explosions per year

Impressing people who have trouble with division, for emotional responses. (Not me.)

There's a video circulating on Twitter (not linking to it, for reasons that will become obvious) that describes the effect of AGW in terms of nuclear explosions per day. This is an excerpt of a much longer Thunderf00t video, which includes his customary numerical errors and bombast, but more importantly, and worse for a purported scientist, uses the imagery of nuclear destruction to create emotional responses to serious issues that demand cold analysis.

To show how ridiculous the imagery is, I calculated the equivalent of California's 2018 electricity consumption* in nuclear (fission and fusion) explosion units:

The point, which might escape some of the audience for that video, is that energy is energy and power is power; 45 Hiroshima-like nuclear explosions per day is just another way of saying 33 GW. Using such imagery is an appeal to emotion, not something a scientist should do.

Draw your own conclusions.

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* AEMO (Australian Energy Market Operator) has near real-time data, California, land of high-tech, releases information for a given year in late-June the following year.



Live long and prosper.

Fun with numbers for November 15, 2019

How many test rigs for a successful product at scale?

From the last Fun with Numbers:

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."

A rational case for Solar Roadways projects in organizations

The first time I heard of Solar Roadways my response was "so they are putting solar panels flat on the ground and shaded by cars?" My interlocutor correctly interpreted that as "What a thoroughly stupid idea; no point wasting more time on it." *

There are, however, some good reasons to start a Solar Roadways project in some organizations. Really: good, rational reasons, that you can convince an engineer with. Well, some engineers.

Because of the buzz surrounding Solar Roadways, the project might be funded. And a project funded means a number of ways to fund other projects that would not be funded. For example:

1. An overhead charge is applied to all outside grants and funding. For example, an organization might add a fifty-percent surcharge to any expenditure: spend 1000 on your Solar Roadways funded project, contribute an additional 500 to a general fund (from which the projects that aren't sexy or buzz-worthy can be funded).

2. Fund as much personnel as you can get away with from the Solar Roadways money; of course, funding them doesn't mean that they can't work on other things, and in many organizations it's difficult to tell which project a worker is working on without expending a lot of effort. Given its own problems, it's unlikely that Solar Roadways project funders will be too eager to get a serious audit of expenditures.

3. Fund as much infrastructure, capital investment, and current expenses with Solar Roadways project money. Basically same argument as personnel.

4. Use the buzz of having a Solar Roadways project to attract attention and more funding, to get potential donors to come to fund-raisers, to impress upon the alumni (for universities) how "with it" your institution is. Also, you can play the "Solar Freaking Roadways" clip with the Serenity captain over and over again for the nerdiest of your audience, thus distracting them from any inconvenient engineering professor whose pet project isn't being funded.

Obviously these aren't arguments for Solar Roadways as an energy source, but rather examples of why smart and knowledgeable people go along with nonsense like that.

Great video by Crazy Aussie Dave Jones (EEVBlog) on Solar Roadways:

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* Some people start going over the details and quibble over the durability of the panels and the visibility of the lights in them or whether they could really melt snow (hint: no, they can't).

That's like arguing about whether the container cross-bracing ties in a Maersk Triple-E would hold if instead of sailing it over water we attached rocket motors to the hull and sent it to orbit and then deorbited it towards the destination port.

(Yes, get it to orbital speed then deorbit, to make it even stupider than a simple --- though also highly unrealistic --- ballistic trajectory.)

The cross-bracing isn't the problem, the concept itself is demented.