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."

Fun with numbers for November 1, 2019

Fast-charging batteries

From the web site that hangs off of the brand equity of the very prestigious journal Science: "New charging technique could power an electric car battery in 10 minutes" 

Congratulations to the team improving battery technology. But:

I. According to the news, this is a technology demonstration, though that might be inaccurate (the original report makes it a testing rig, which is one step farther back from a final product). There's a lot of work to do (and many avenues for failure) before this becomes a deployable product, much less at scale.

II. Charging a 75 kWh battery (AFAIK, the smallest battery in a Tesla car) in 10 minutes requires a charging power of 450 kW. Even using 480 V as the charging voltage, that's still a 937.5 A current; those cables will need some serious heft, and any impurities in the contacts will be a serious fire hazard.

III. A typical gas pump moves about 3 l of gasoline per second. Gasoline has around 34 MJ/l energy density, so that pump has a power rating of 102 MW, 227 times higher energy throughput than the new battery. Even if the distance/energy efficiency of internal combustion engines is lower than electric motors, that's a big difference. Also, you can buy Reese's peanut butter cups at gas stations.

More fun with Rotten Tomatoes

Watchmen (HBO series) shows that sometimes when data changes, the conclusions change.

Despite the caterwauling of many in the comic-book nerd community (not that I would know, as I don't belong… okay, I occasionally might take a look, but I'm not a comic book nerd… not since the early 70s…), data show that it's much more likely that the critics and the audience are using similar criteria for their evaluation of Joker than opposite criteria.

How much more likely? Glad you asked:

210,565,169,600,721,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 times more likely.

Ah, the power of parameterized models: you set them once, you can nerd out on them till the end of time. (I haven't watched either the show or the movie. Maybe when they get to Netflix or Amazon Prime.)

Added Nov 3: Haven't watched it yet, but Rotten Tomatoes data shows that critics are 1,361,188 times more likely to be using the same criteria as the audience than opposite criteria to evaluate "For All Mankind."

Some progress in nuclear fusion?

Some simple physics:

1 kg mass = 9E16 J of energy ($E = mc^2$)
Coal has 30 MJ/kg specific energy
10E6 kg coal have 3E14 J (assuming Bloomberg meant using combustion)

Fusion is to have 1/300 efficiency relative to pure mass-energy conversion?

Kudos. Now, get to it!

Shredded Sports Science eats an apple

Shredded Sports Science has a video making fun of people who know even less about fitness and nutrition than the "experts" in those "sciences," where he takes a bite of an apple and says "one rep," another bite, "two reps," the joke being on Chris Heria of Thenx.

Huh, the quant says, I wonder how the numbers will go…

Let's say a warm-up set of 100 kg squats and the total vertical path is 1 m. How much energy does one rep use, just for the mechanical work?

Naïve physics neophyte: huh, zero, the rep starts and ends at the same point.

No. The mechanics of the rep are different on the way down and on the way up: assuming that the weight moves at constant speed most of the time, the down movement requires the body provide work to counteract acceleration, so we can approximate the total work by 2 * 100 * 9.8 * 1 = 1960 J.

Note that this is just the mechanical part. Muscles have less than 100% efficiency and that efficiency changes as fatigue increases, hence the heat (heat, and to a smaller degree, changes to the mix of waste products of muscle contraction, represent losses in efficiency).

The other side of the coin is the chemical energy in that apple, which is measured by the magic ['delusion' or 'deception' also work here] of mistaking the simple process of combustion for the very complex processes of digestion and respiration. But let's pretend…

Apples are basically 1/3 sugar and 2/3 water, with some esters and ester aldehydes for taste and aroma, so for a small bite let's say 15g of apple we get 5 g of sugar; that's 20 kCal or ~ 84,000 J.

Shredded Sport Science's little joke would point to a combined digestion, respiration, and muscle contraction efficiency of 2.33%.

Evolution would have selected this biochemical parameterization right out of the gene pool.

Fun with energy

Talk about counting calories in a way that matters. (From the BP energy stats 2019; and yes, their tables are in MtOE, not calories, but unit changes are trivial, except maybe for gymbros.)

Bay Area versus Europe

With the return of Silicon Valley on HBO, there's a lot of hating on the Bay Area going around, so here's a thought in numbers…

How many tangerines fit in this room?

How a person answers simple questions can tell a lot about what type of thinker they are.

It's not that you need to know a lot of math to answer this question (it's basic geometry and arithmetic), but rather that people who think quantitatively as part of their day-to-day life can be identified by their attitude towards this question.

There's a big difference between someone who thinks like a quant and someone who can do math on demand, so to speak. Thinking like a quant means that you generally look at the world through the prism of math; that when you're solving a work problem, you're not just applying knowledge from your education, but also something you practice every day. And that practice makes a difference.

 It's like the difference between an athlete (even if amateur) and someone who goes to gym class.

To illustrate, consider your typical "lone inventor can upset entire industry" story, in particular this one that was in the last Fun With Numbers.

I didn't read the article, but from the photo [which is deceptive, in the article the 1500-mile battery is bigger, though still small enough to make the result non-credible] we can see that the '1500-mile battery' volume is about 2 liters, so a little bit of arithmetic ensued: 

1. 1500 miles w/ better-than-current vehicles [a google search shows that they're all over 250 Wh/mi], say 200 Wh/mi: 300 kWh (1.08 GJ)
2. Volume of battery, from article photo [estimated by eye], let's say 2 l, so energy density = 504 MJ/l
3. Current Li-Ion battery energy density [google search] ~2.5 MJ/l to  5 MJ/l (experimental) 

Home inventor creates something 100 to 200 times more dense than
current technology (and about 15 times more energy-dense than gasoline)?! Not credible.

Are we to believe that the journalists can't do the simple search and arithmetic needed to raise the concerns we can see? Or that they expect none of their audience to? (This second question assuming that the journalists know that the battery can't work, but are willing to write these clickbait headlines because they assume their credibility is not going to be questioned by innumerate audiences.)

Back to the tangerines, and a tale of three people.

Person one gets confused by the question, takes a while to think in qualitative terms (sometimes verbalizing those), then eventually realizes it's a geometry question and with more or less celerity solves it. Person one can do math "on demand," but doesn't think like a quant.

Person two grasps the geometric nature of the problem immediately, estimates the size of the room and of an average tangerine, reaches for a calculator, and gives an estimate. Person two "groks" the problem and is a quant thinker.

Person three sketches out the same calculation as person two, but then adds a twist: instead of a calculator, person three reaches for a spreadsheet, to create a model where the parameters can be varied to allow for sensitivity analysis. Person three is an advanced version of a quant thinker, a model-based thinker.

Fun with numbers for October 19, 2019

(Yes, yet another tweet-recycling post. When I unfroze the blog the reason was that I was tweetstorming blog posts, so now I'm refactoring ideas from twitter, with — one hopes — improvements.)

Negative [effect on carbon capture]

Via Thunderf00t, who manages to find the occasional bad product gem amongst the many non-bad products he "busts!" by not understanding engineering (or pretending not to), we learn of Negative, a captured-carbon bracelet.*

Enter basic math, illusion exits stage left.

Say Bay Area Bob commutes from San Francisco to Palo Alto (100 mi roundtrip), 5 days/week (500 mi/week) on a 25 MPG car; that's 20 gallons of gasoline burned per week.

Gasoline is a complicated mixture, but let's simplify by treating it as 100% iso-octane (2-2-4-trimethylpentane), C8H18; let's simplify further by assuming perfect stoichiometric burn, so 1 kg of iso-octane generates 3.1 kg of CO2.

Gasoline has a density of 0.7489 kg/l or 2.835 kg/gal; this generates 8.75 kg(CO2)/gal(gasoline), so a weekly commute creates 175 kg of CO2.

Say that bracelet is 25 g of pure carbon. That corresponds to 1/1910th of the carbon in a single one-week commute for Bob. (175 kg of CO2 contain 47.7 kg of carbon.)

I'm sure every Bay Area Bob will be sporting one of these Negative bracelets.

What about other hydrocarbons? Given the small mass differences between alkanes, alkenes, and alkynes, we can take a look at the CO2 per kg(hydrocarbon) with a simple calculation:

Note that the maximum CO2 per kg is when the fuel is pure carbon, at 3.67 kg (CO2)per kg (C). So the approximation above (for Bob) isn't too bad.

-- -- -- --

*Another annoying habit of TF is to gloss over the math, usually to the point where his approximations accumulate into nonsensical territory and occasionally even significant technical errors.

Much ado about Ruby Rose's petite physique.

One of the criticisms of Batwoman that might have some merit is that a petite person like Ruby Rose is not credible as an action hero; that a punch from her not-very-muscular arms would not knock out a 250-lb henchman. To which I reply: as opposed to not-exactly-Schwarzenegger Ben Affleck or Christian Bale throwing said 250-lb henchman clear across a parking lot with a single arm? Pah!

This scene, where Batwoman gets shot by a pistol led to some comments on how she would have been thrown in the air, backwards. Because "momentum," say the people who love science but can't do math (or actually bother to learn the science they profess to "love").

The batsuit is bulletproof (has been all along); assuming that it completely distributes the pressure of the impact over the 1/4 square meter of her torso front, there's little effect, as can be seen from the delta speed for the system:

Say Batwoman (Ruby Rose + suit) = 50 kg, bullet (looks like a .45 ACP) is 15g at a muzzle velocity of 250 m/s, so conservation of momentum shows the after-impact speed to be (0.015 * 250)/(50.015) = 0.075 m/s or less than 0.3 km/h, a very small change in velocity to Batwoman that can be easily countered by a braced position.

An alternative way to see the limited effect:

Consider that the bullet is stopped by the suit and loses all its velocity while pushing back 5cm. Assuming constant force, it takes t = 2 s/v = 2 (0.05)/250 = 0.0004 s to stop, for an acceleration of a = v/t = 625000 m/s^2 and a force F = 9375 Newton (almost 975 kgf, but just for 400 microseconds), which spread over 1/4 square meter of her torso is a pressure of 0.38 kgf/cm^2, which is the pressure of a light finger poke (again, for 400 microseconds).

And a tip of the hat to old-style scifi machinery (no labels on buttons or indicators):

Flexagons. Not the hexa ones.

A late entry: more battery nonsense.

Via eevblog, we learn of yet another life-changing momentous innovation by a lone inventor squashed by the Big Industry Conformance Bureau:

I didn't read the article, but from the photo we can see that the '1500-mile battery' volume is about 2 liters, so a little bit of arithmetic ensued:

1500 miles w/ better-than-current vehicles (say 200 Wh/mi): 300 kWh (1.08 GJ)
Volume of battery, from article photo let's say 2 l) so energy density = 504 MJ/l
Current Li-Ion battery energy density ~2.5 MJ/l to  5 MJ/l (experimental)

Home inventor creates something something 100 to 200 times more dense than
current technology (and about 15 times more energy-dense than gasoline)?!

Nope, not credible.

(Note: apparently the photo is deceptive, and the actual "1500 mile battery" is larger, only 9 times more energy-dense than current technology. Which is as non-credible, especially the idea that car manufacturers would be able to stop small electronics makers from adopting a technology that would allow for smaller batteries in laptops and longer times between charge in cell phones. Added Oct 21.)

Fun with numbers for October 9, 2019

Rotten Tomatoes and Batwoman

The day after the pilot, a familiar pattern emerges:

Using the same math as these two previous posts, it's 198,134,550 (almost 200 million) times more likely that the critics are using the opposite criteria to those of the audience than they both using the same criteria.

A couple of days later, more data is available:

This data makes the case even more stark: it's now 2,924,953,580,108 (almost three trillion!) times more likely that the critics are using the opposite criteria to those of the audience than they both using the same criteria.

And today (with a tip of the Homburg to local vlogging nerd Nerdrotics), it's even worse:

With this data (ah, the joys of reusable models, even if "model" is a bit of a stretch for something so simple, relatively speaking) we get that it's now 11,028,450,795,963,200 (eleven quadrillion!) times more likely that the critics are using the opposite criteria to those of the audience than they both using the same criteria.

For what it's worth, I liked the pilot, despite my nit-picking it on twitter:

Aerobics: The Paper that Started The Craze.

Here are three explanations that all match the data:

I. The official story: running develops cardiovascular endurance. This is the story that led to the aerobics explosion, to jogging, and to all sorts of "cardio" nonsense. Note that this story is isomorphic to "playing basketball makes people taller."

II. The selection effect story: people with good cardiovascular systems can run faster than those without. This is the "tall people are better at basketball than short people" version of the story.

III. The athletes are better at both story: people who have athletic builds (strong muscles, large thoracic capacity, low body fat) are better at both running and cardiovascular fitness because of that athleticism.

Most likely the result is a combination of these three effects, or in expensive words, the three variables (cardiovascular fitness, muscular development, and running ability) are jointly endogenous. Note also the big excerpt from Body By Science at the end of this post.

Let's take  a closer look at that table:

Not that I'm questioning Cooper's data (okay, I am), but isn't it strange that there are no cases when, say a runner with a distance of 1.27 mi had VO2max of 33.6? That the discrete categories on one side map into non-overlapping categories on the other? No boundary errors? That's an unlikely scenario.

Also, no data about the distribution of the 115 research subjects over the five categories. That would be interesting to know, since the bins for the distance categories are clearly selected at fixed distance intervals, not as representatives of the distribution of subjects. (It would be extremely suspicious if the same number of subjects happened to fall into each category. But if they don't, that's informative and important to the interpretation of the data.)

I know this was the 60s; on the other hand, the 60s were the first real golden age of large-scale data processing (with those "computer" things) and a market research explosion.

One of the factors that confounds these "cardio" results is that training for a specific test makes you better at that test. Another is that strengthening the muscles that are used in a specific motion makes that motion less demanding and therefore puts less strain on the cardiovascular system.

This excerpt from Body By Science illustrates both of these confounds:

Grant Sanderson (3 Blue 1 Brown) on prime number spirals

A late addition: Elon Musk promises PowerPacks for CA

Which brings up two thoughts:

a. Is "just waiting on permits" the new "funding secured"?

 

b. Each powerpack has 210 kWh capacity, so one charges ~3 Teslas, assuming they're low on charge but not zero. (Typical tank truck ~ 11,000 gal tops-up 733 x 15 gal gas tanks. Just FYI)

Fun with numbers for October 4, 2019

It's flu season, let's talk product diffusion

One of the classic marketing models people learn in innovation classes is basically a SIR(1) model without the R part: the Bass model of product diffusion.

The idea is that some fraction $a$ of the consumers are "innovators" who adopt a product without social pressure, while another fraction $b$ are "imitators" who adopt a product when they see others with it. The fraction $x$ of the market that has adopted the product at a given time is given by the following differential equation

$\dot x = (a  + b x)(1-x)$, 

and the behavior looks like a traditional product life-cycle curve (an S-shaped curve):

The process for a viral infection is similar: some people get the virus from the environment (those would be the $a$ fraction), some get it from contact with other people (those would be the $b$); the infection process has a third element, recovery, which we ignored here.

Growth confusion and punditry, part 1

Pundits throwing around growth numbers seem to be unaware that there are significant differences even with very small growth numbers.

Growth confusion and punditry, part 2

A pundit: "it's important to get the economics high-growth first, so that the slower growth starts from a higher number." (Paraphrased.)

Me: Gah! Multiplication is transitive. The order doesn't matter, what matters is that the high-growth period be the longer period.

Consider two periods, with $t_1$ and $t_2$, with associated growth rates $r_1$ and $r_2$. Starting from some value $x_0$, the result of period 1 before period 2 is:

$\left( x_0 \, e^{r_1 t_1} \right) \, e^{r_2 t_2}$,

and the result of period 2 before period 1 is

$\left( x_0 \, e^{r_2 t_2} \right) \, e^{r_1 t_1}$,

in other words, the same result.

These pundits get paid to go on television and say these things and to write them in Op-Eds. And influential people take them seriously. The innumeracy is staggering.

Having some fun with Tesla data

Downloaded some historical data from Yahoo Finance (yes, I have other better sources, but this one is public and can be shared) and played around with smoothing. Here's a nice view of the TSLA closing price for the last year using the same triangular smoothing I did for my bodyweight (in other words, a second-order moving average of (5,5)):

Throughout the first half of 2019 Tesla boosters on Twitter were fully convinced that this would be the year that heralded the end of the internal combustion engine car. In reality, this seems to be the year in which Tesla's financial shenanigans are likely to bring its valuation to a more appropriate level.

CYA statement: I have no personal position on Tesla and will not initiate one in the next 72 hours. This is not intended as financial advice and represents my personal views (of making fun of Tesla boosters) not those of my employer or our clients.

Also:

(Yes, it's sarcastic.Very, very sarcastic.)

Yet another infrastructure photo

Fun with numbers for Sep 1, 2019

Apple declines to burn 17 billion, Tesla boosters disappointed.

Ross Gerber, a Tesla booster who provides endless entertainment on TSLA twitter, had an interesting idea (the same idea he's had for the last 4-5 years), that Apple should burn 17 billion dollars instead of giving them to people who hold AAPL stock.

The first Tesla car that was targeted at the general public (as opposed to tech billionaires and centi-millionnaires who wanted to be thought as forward-thinking) was the Model S, introduced in 2012. So we'll use 2012 as the beginning of Tesla as a real car company.

As I write this it's Sunday, September 1st, 2019 and the last TSLA close was on Friday, August 31st at 225.61. We'll compare this number with the stock closing price for the closest date for all years 2012-2018 and compute the annualized growth. Then we use that growth to forecast the evolution of an hypothetical Apple stake of 17 billion.

Using a 5-year growth rate for that tweet was basically the textbook default, but looking at that table, the last two columns really tell an interesting story… didn't Ross suggest Apple buy Tesla in late 2017 and in late 2018? Because the numbers in that table say something about financial acumen.

Calories, calories, calories... What a bunch of nonsense!

This marvel of mechanical engineering is the Siemens STG5-9000HL gas turbine. Running in single-cycle mode at nominal power it takes in almost 59,000 kg of LNG per hour or around 900 MW (Calories in: 755 million kCal/hour) and delivers around 400 MW of spinning power to a generator, for about 360 MWe (Calories out: 310 million kCal/hour) of electrical power.

Wait, what? Isn’t it Calories-In-Calories-Out? Is the turbine getting fatter or something?

No. Running in single-cycle mode the system loses around 60% of its power to unrecovered heat.

This is the real problem with CICO and 'Just Get a Caloric Deficit' recommendations: because no one measures the energy lost in radiated, conducted, and convected heat, or the energy content of urine, feces, and ‘outgassing,’ and because those show large variation across people (and across different situations for the same person, including changes in diet), the whole thing is nothing more than pretend science: like astrology made with computers, adding the trappings of science to a flawed foundation yields nothing valuable.

Well, of no real value, but monetizable; and there’s also the moral posturing afforded by telling others that being fat is proof of their lack of willpower or moral failings. (And, of course, since it doesn’t work, leads to continuing supply of clients.)

Thermodynamics is not a magical incantation. But some people use as if it were.

(I'd be willing to bet that 90% of the people who invoke 'thermodynamics' as a magical incantation to ward off the evil spirits of low-carb diets couldn't have made the junior-high Physics computations in that first paragraph.)

More infrastructure

"How can you take photos of those ugly things when there are all these flowers and rocks?"

Me: because when you understand what these things are, you marvel at the detail, at the functionality, and at the fact that they work to begin with. Also, I photograph nature too.

Fun with numbers - August 28, 2019

Air conditioning FTW!

Part of what I do is training people, under the fancy name of "executive education," and to match the fancy name we tend to get nice AV equipment, color handouts, markers that work, fancy chairs, and climate-controlled rooms.

The least remarkable of those is also probably the most important. The air conditioning, not the markers.

For a large-ish event with around 60 people in a comfortably large room, with about 50% of heat losses to the exterior, the temperature would increase by almost 15 °C in a 90-minute session:

Okay, there's a lot of approximations in that calculation, but even 10 °C increase means that either it was too cold at the beginning or too warm at the end. So hurrah for air conditioning.

Seriously, how can people fall for this?

Today The Tesla Promotion Network Electrek, posted a news item about batteries. Apparently "[a] startup that spun out of Cambridge University claims a battery breakthrough that can charge an electric car in just six minutes."

That phrasing is unclear: how much charge? Even the slowest chargers in my neighborhood (6 kW) will give any electric car battery some charge in 6 minutes (0.6 kWh). Most people will read that to mean they could give a full charge to, say, a Tesla Model 3 in six minutes.

Say the Tesla has a 80 kWh battery; charging it in 6 minutes requires an average power of 800 kW; even using 480 V, that would mean the current would be almost 1700 A. That would be a really interesting current to see in a lithium-ion battery, or as the fire department calls it, "the initiating event of the fire."

For comparison, a typical gas pump can pump 3 l/s of gasoline, which at 34 MJ/l means that the gas pump can transfer energy at a rate of over 100 MW or around 125 times the rate of that fictional battery.



Not math: some infrastructure