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For more fun car efficiency dimensional analysis, see Randall Munroe's take on mpg as an inverse area: what-if.xkcd.com/11/

what-if.xkcd.com

Droppings

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To rant, driving style makes a big difference in efficiency. I commute on a road with timed lights. Some people accelerate and speed on green only to stop at the next red. If I drive the speed limit, every light is green. Stopping and going is an energetic waste. Steady speed maximizes efficiency.

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Steady state resistances (280 N, 63 lbs-f) at my average speed (30 mph) account for a bit less than half the average force exerted by the car. This makes sense as higher speeds have more air resistance, accelerating takes more force, there will be some losses, and the battery also runs the AC.

The car has a drag coefficient of 0.3, a cross-sectional area of 2.5 m^2, and weighs 4500 lbs. With this and some reasonable estimates for the density of air and rolling friction coefficient, at a steady 30 mph air resistance is 80 N (18 lbs-f) and rolling resistance is 200 N (45 lbs-f).

Drag force is 0.5 * (drag coefficient) * (air density) * (cross-sectional area) * (speed squared).

Rolling resistance is (coefficient of rolling resistance, about 0.01 for a car) * (mass) * (gravitational acceleration, 9.8 m/s^2).

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The units of mi/kWh are fun because it's a distance per energy, which is inverse force. Taking the inverse of my average efficiency (3.5 mi/kWh)^-1 gives a force of 640 N or 140 lbs-force. You can interpret this as the average force that the car exerts while it drives.

How does this compare to a gas car? Assuming gasoline density of 0.7 g/cm^3 and heat of combustion of 45 MJ/kg, a Honda Civic (40 mpg) gets 1.2 mi/kWh and a Cadillac Escalade (15 mpg) gets 0.45 mi/kWh. The EV is 2-4.5x more energy efficient than an efficient car and 5.5-12x an inefficient car.

My car's stated efficiency is 2.8 mi/kWh. My average is 3.5 mi/kWh, the worst I've seen is 2.5 mi/kWh (cold, highway driving), and I can get it up to 5.5 mi/kWh (warm, city driving). So the manufacturer gives a low estimate on range and under the right conditions you can do much better.

My electric car measures efficiency in miles per kilowatt-hour, which is a gross mix of imperial and metric. But there are some interesting comparisons and dimensional analysis with that.

@wsuchemistry.bsky.social @waynestatechem.bsky.social · 29/05/2025

Reposted by Alex Albaugh

We are looking forward day 1 of the 55th Midwest Theoretical Chemistry Conference at #wsuchemistry with Keynote speaker Paul Zimmerman! #MWTCC55 #compchem #ChemSky

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Alex Albaugh @alexalbaugh.com · 17/05/2025

In news from my hometown, a GOP mayor candidate was just arrested for DUI. He crashed into a house "to avoid a cat." Told the arresting officer he was drinking vodka 20 minutes prior and mentioned several times he is "going to be the mayor." Election is Tuesday. lebtown.com/2025/05/16/p...

lebtown.com

Palmyra Borough mayoral candidate Kevin Yiengst charged with DUI

Palmyra Borough mayoral candidate Kevin Yiengst was charged with DUI following a Thursday night incident in Palmyra.

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Reposted by Alex Albaugh

James Gleick @around.com · 07/05/2025

There is a developing aviation crisis in the United States. Newark Airport is in shambles, forcing the cancellations of hundreds of flights. Ground-traffic accidents are multiplying. A major disaster is only a matter of time. A functioning government would take emergency action to staff our

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Alex Albaugh @alexalbaugh.com · 05/05/2025

I’m not confident Europe can pick up the torch that the US is dropping. This €500 million over two years sounds good until you realize the NIH budget alone is $50,000 million per year.

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Reposted by Alex Albaugh

Ellyn G. @ellyn57.bsky.social · 04/05/2025

Radical opinion of the day: on-street parking is a bad use of public land. Especially in extremely walkable places like @downtownroyaloak.bsky.social the space should be reserved for 15-minute parking, ride-share pickups, and handicap accessible spots.

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Reposted by Alex Albaugh

Emily St. John Mandel @emilymandel.bsky.social · 30/04/2025

“And I’m like, what do you mean, you ‘do your own research’? You running a double-blind study in your living room, dawg?” - A guy walking ahead of me with his friends on a NYC sidewalk in 2021, also my favorite overheard dialogue of the entire pandemic

NYT headline: “Kennedy Advises New Parents to ‘Do Your Own Research’ on Vaccines”
Subheader:
“In an interview with Dr. Phil, the health secretary offered false information about vaccine oversight and revealed a lack of basic understanding of new drug approvals.”

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Alex Albaugh @alexalbaugh.com · 30/04/2025

Me at the beginning of the semester vs. me at the end of this semester.

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Alex Albaugh @alexalbaugh.com · 21/04/2025

Is there anything in the middle?

Venn diagram of Stefa, Maxwell, and Boltzmann.

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Reposted by Alex Albaugh

@wsuchemistry.bsky.social @waynestatechem.bsky.social · 17/04/2025

Save the date! The 55th Midwest Theoretical Chemistry Conference (#MWTCC55) will take place between May 29 and May 31, 2025, on the campus of Wayne State University in Detroit, MI. We are proud that this is the first time #wsuchemistry will host this event. #compchem #ChemSky

Photo of the campus of Wayne State University

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Disclaimer: There's a lot of simplification here. I'm an expert on chemical physics, but not LLMs and law.

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*Chemical space is continuous and word choices are discrete, so there's a sum on the left and an integral on the right. Boltzmann's constant is on the right to make energy and temperature play nice. We want the maximum activation (xi), but minimum energy (U) so a negative shows up on the right.

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This evidence is from NYT's lawsuit against OpenAI for copyright infringement. Is ChatGPT just regurgitating copyrighted material with some randomness sprinkled on top? Kinda. Like any machine learning model, ChatGPT learns by example and its outputs are going to look like what it has seen before.

Lawsuit filed by the NYT against OpenAI, creators of ChatGPT.

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What happens if you turn the temperature down on ChatGPT? The New York Times found out that it can reproduce their articles word for word. The most likely predictions for certain prompts are just copies of copyrighted material.

Example from NYT lawsuit against OpenAI. Comparison of ChatGPT output (left) and NYT article (right) with identical text marked in red.

Another example from NYT lawsuit against OpenAI. Comparison of ChatGPT output (left) and NYT article (right) with identical text marked in red.

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Temperature works the same in an LLM and a chemical system. At high temperature, more choices or states are likely. At low temperatures you'll usually get the most probable selection. A good LLM needs a balance. Too low and the output is robotic. Too high and it might not make sense at all.

They're the same*! By adjusting an LLM's temperature you adjust how it selects words. A high temperature LLM will select more broadly from the distribution, making stranger choices more likely. A low temperature LLM will usually just select the most likely word.

High temperature LLM makes a wider variety of words more likely.

A low temperature LLM will usually just select the most likely word.

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Converting from activations in the LLM neural network to probabilities for the next word is done with a softmax function. The softmax has a temperature that adjusts the resulting probabilities. Compare the softmax function on the left with the Boltzmann distribution on the right.

Softmax function gives the probability of some word (i) based on the LLM network activations (x_i) and a "temperature" (T).

Boltzmann distribution again. Probability density of a state (x) based on its potential energy (U) and the Boltzmann constant (k_B).

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