Ulugh Beg
There’s a new docudrama coming out about the life of Ulugh Beg, a medieval astronomer who made Samarkand, now Uzbekistan, a thriving center of culture and science in the 15th century.
Intro adapted from Wikipedia
Mīrzā Muhammad Tāraghay bin Shāhrukh (Chagatay: میرزا محمد طارق بن شاہ رخ, Persian: میرزا محمد تراغای بن شاہ رخ), better known as Ulugh Beg (الغ بیگ) (1394- 1449), was a Timurid ruler as well as an astronomer, mathematician and sultan.
His commonly known name is a moniker, translated as “Great Ruler”
Ulugh Beg was notable for his work in astronomy-related mathematics, such as trigonometry and spherical geometry.
He built the great Ulugh Beg Observatory in Samarkand between 1424 and 1429. It is considered to have been one of the finest observatories in the Islamic world at the time. He built the Ulugh Beg Madrasah (1417–1420) in Samarkand and Bukhara, transforming the cities into cultural centers of learning in Central Asia.
He ruled Uzbekistan, Tajikistan, Turkmenistan, Kyrgyzstan, southern Kazakhstan and most of Afghanistan from 1411 to 1449.

The following is from Gizmodo, The Trailer for The Man Who Unlocked the Universe Is a Gorgeous Mixture of Science and Action, by George Dvorsky
A full 150 years before Galileo gazed at the heavens with his telescope, Ulugh Beg (1394-1449) was building some of the largest astronomical instruments on Earth. Incredibly, he used his observatory to map the stars and create charts that are still considered highly accurate, even by today’s standards.
Beg managed to measure the duration of the year to within 25 seconds of the actual figure, and he even correctly calculated the Earth’s axial tilt at 23.52 degrees. In addition to astronomy, he was a capable mathematician and biologist. He was also a Timurid ruler, transforming the cities of Samarkand and Bukhara into vibrant cultural centers.
A new 38-minute docudrama, titled Ulugh Beg: The Man Who Unlocked the Universe and directed by Bakhodir Yuldashev (Shima, Angel of Death), chronicles the life of the little-known scientist, from his birth as a prince through to his unconventional childhood and eduction, and ending with his untimely death.
Actor Armand Assante (Gotti, American Gangster) portrays Beg, and Vincent Cassel (Black Swan, Shrek) provides the narration. It features some neat CGI, live-action re-enactments of historical events, and interviews with academics and astronauts.
The film will be available for rent or purchase on Amazon starting Friday, June 22.
Bond lengths in molecules
Some people say not to use ice cubes in soda or wine because “it makes flavor molecules contract”, which supposedly makes a drink taste worse. Is this correct?
First note that flavor comes from individual molecules dissolved in solution. These are monomers, not polymers. That’s going to be important.

Let’s break the question down into two parts: Does cooling a drink make flavor molecules contract? Does cooling a drink change how our tongue perceives flavor from such molecules?
(A) Does cooling a drink make flavor molecules contract?
Let’s start with the claim that ice makes flavor molecules contract. Sounds reasonable, after all, in everyday life we see that coldness can shrink materials. For instance, a bimetallic strip consists of two different materials. Each has a different expansion coefficient (way it responds to temperature changes.) When heated, one metal expands more than the other, which forces the metal to bend. These strips are used as switches in some thermostats.

image from hyperphysics.phy-astr.gsu.edu
More commonly, we see large scale materials contract when cooled, like highways. That is why roads over bridges, and in parking lots, need thermal expansion joints. Otherwise the shrinking and expansions would otherwise break the surface.

image from Ontario Ministry of Transportation, Bridge Repairs
Characterization of Typical Potent Odorants in Cola-Flavored Carbonated Beverages
Molecules in Coca Cola (Compound Interest)
Molecules in wine (Compound Interest)
Molecules in whiskey (Compound Interest)
But why do these materials contract when cooled? Has each individual molecule shrunk? No. To understand why we need to think about intermolecular vs intramolecular forces.
Intermolecular forces hold one molecule to another.

image from dynamicscience.com.au
Intramolecular forces hold atoms together within a single molecule. (e.g. chemical bonds, covalent bonds)

The naming comes from Latin roots
inter meaning between or among
intra meaning inside
When we use ice to cool a drink from 75 F down to 45 F, does the size of an individual molecule change in any appreciable way? Well, as we see here, a heated molecule can vibrate faster or slower – but the distance between atoms doesn’t appreciably change: the size of any single molecule is constant.
Nope. First, notice that the temperature in either F or C is misleading. Those temperatures are only measured relative to the freezing point of water. A better comparison is comparing their absolute temperature using the Kelvin scale
75 F = 24 C = 297 K
45 F = 7 C = 280 K
Wow, on an absolute scale this doesn’t change the temperature of the molecules very much.
Now sure, cooling does reduce molecular vibration: this allows intermolecular forces to pull the molecules closer together, which causes shrinking of the material as a whole. Still, this doesn’t change the bond lengths within a molecule.
(B) Does cooling a drink change how our tongue perceives flavor from such molecules?
If flavor change exists then I would think it is because the tongue tastes certain molecules better at certain temperatures.

image from blogs.unimelb.edu.au, The University of Melbourne, Scientific Scribbles, Let’s talk about Taste
images
https://maxfacts.uk/help/oral-food/ttt
discussion
https://www.ncbi.nlm.nih.gov/books/NBK236241/
https://www.ncbi.nlm.nih.gov/pubmedhealth/PMH0072592/
https://www.livescience.com/20286-foods-taste-hot-cold.html
https://academic.oup.com/chemse/article/42/2/153/2547704
https://www.beveragedaily.com/Article/2005/12/19/Food-temperature-affects-taste-reveal-scientists
https://www.quora.com/How-exactly-does-temperature-affect-the-taste-of-food-and-beverages
Learning Standards
Next Generation Science Standards
HS-PS1-3. Plan and conduct an investigation to gather evidence to compare the structure of substances at the bulk scale to infer the strength of electrical forces between particles. The structure and interactions of matter at the bulk scale are determined by electrical forces within and between atoms.
Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS1-3. Cite evidence to relate physical properties of substances at the bulk scale to spatial arrangements, movement, and strength of electrostatic forces among ions, small
molecules, or regions of large molecules in the substances. Make arguments to
account for how compositional and structural differences in molecules result in
different types of intermolecular or intramolecular interactions.
Common Core State Standards Connections:
Sea level rise
Should we be worried about surging Antarctic ice melt and sea level rise?
Dana Nuccitelli, The Guardian, 18 Jun 2018
There’s recently been a spate of sea level rise denial in the conservative media, but in reality, sea level rise is accelerating and melting ice is playing an increasingly large role. In the first half of the 20th Century, average global sea level rose by about 1.4 millimeters per year (mm/yr). Since 1993, that rate has more than doubled to 3.2 mm/yr. And since 2012, it’s jumped to 4.5 mm/yr.

Global mean sea level data from the Colorado University Sea Level Research Group, with 4-to-5-year linear trends shown in black and red. Illustration: Dana Nuccitelli
Thermal expansion (ocean water expanding as it warms) continues to play the biggest role in sea level rise, but its contribution of about 1.3 mm/yr is now responsible for a smaller proportion of total sea level rise (30% in recent years) than its contribution since the 1990s (40% of the total). That’s because of the acceleration in melting ice.
Glacier melt is accelerating, recently contributing about 0.75 mm/yr to sea level rise, up from 0.65 mm/yr since the 1990s. But the biggest jumps have come from ice in Greenland and Antarctica. Greenland had been responsible for about 0.48 mm/yr sea level rise since 1990, but in recent years is up to 0.78 mm/yr. A recent study in Nature Climate Change found that Greenland contributed about 5% to sea level rise in 1993 and 25% in 2014.
Antarctica is a huge question mark with warning signs
A new study published in Nature using data from a range of satellites found that Antarctica’s contribution has tripled from about 0.2 mm/yr since the 1990s to 0.6 mm/yr since 2012, during which time global sea level rise also spiked. Accelerated ice melt from Antarctica, Greenland, and glaciers have all played a role in the faster recent sea level rise. The question is whether it’s a temporary jump, or if we need to worry about a continued acceleration in Antarctic ice loss.
Another recent paper published in Earth’s Future found that rapid losses from Antarctic ice are plausible. The study found that in moderate to high carbon-emission scenarios, an average expected sea level rise of 2 to 2.5 feet by 2100 could actually become 3 to 5 feet once Antarctic ice sheet dynamics are taken into account.
The vast majority of Antarctica’s current ice loss is coming from West Antarctica, where about 75% of the glaciers are located below sea level. In East Antarctica, which has so far remained stable, only about 35% of the glaciers are below sea level. Warming ocean waters are melting the Antarctic ice from below, which is particularly problematic for that low-lying ice in West Antarctica. Research suggests that the collapse of the Western Antarctic ice sheet is already unstoppable.

The amount of ice loss across Antarctica in total (purple), and in West Antarctica (green), East Antarctica (yellow) and the Antarctic Peninsula (red). Illustration: Shepherd et al. (2018), Nature
Should we be worried?
Short term variations in sea level rise do happen. Sea level actually briefly fell in 2010 due to a strong La Niña cycle, which typically results in an increase of rain and snow falling over land. This resulted in a number of epic deluges and flooding across the globe; more water on land temporarily meant less in the ocean.
However, Antarctica and Greenland could potentially cause rapid sea level rise. As James Hansen explains in the video below, there have been periods in the not-so-distant past when sea levels rose at an average rate of 1 meter every 20 years.
In past eras when temperatures and atmospheric carbon dioxide levels were similar to those today and to the Paris climate targets, like in the last interglaciation and the Pliocene, sea levels were about 20 to 80 feet higher. Unless we manage to actually cool global temperatures, we’re certainly due for significantly more sea level rise. The large ice sheets on Greenland and Antarctica will continue to melt for as long as 1,000 years. That’s why sea levels were so much higher in past eras whose climates remained at hot temperatures like today’s for thousands of years.
It takes time for ice to melt. The question is, how fast will it happen? Sea level rise unquestionably poses a long-term threat, but how much of a short-term threat largely depends on just how stable the Antarctic ice sheet turns out to be. The recent acceleration of Antarctic ice loss, while not yet definitive, is certainly cause for concern.
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Dinosaurs
What is a dinosaur?
There’s a big difference between what people think a dinosaur is, and what a dinosaur actually is.
Many people would identify the dimetrodon (left) as a dinosaur and the deinonychus (right) as a non-dinosaur, more specifically they might identify it as a bird.
And yet both would be wrong:
Dimetrodons lived 40 million years before dinosaurs even existed – and they are more closely related to mammals than to dinosaurs.
While the deinonychus, on the right, is a dinosaur.
What about all those other animals that people think of as dinosaurs?
Pterosaurs? Also called pterodactyls. Not a dinosaur. A flying reptile.
Mosasaurs? Not a dinosaur. They are an extinct group of aquatic lizards.
Mosasaur: Apex Predator of the Western Interior Seaway, NPS
Ichthyosaurs? Not a dinosaur. Marine reptile
Plesiosaurs? Not a dinosaur. Mesozoic marine reptiles.
Dimetrodon? Not a dinosaur.
All of the various dimetrodon species became extinct 40 million years before the first appearance of dinosaurs.
They are reptile-like in appearance and physiology, yet nevertheless they are more closely related to mammals than to modern reptiles!
To be clear, they are not a direct ancestor of mammals; they were sort of a cousin branch to the mammals.
Most of those aren’t dinos? How can common beliefs be so incorrect?
People think that dinosaurs are a very specific thing – something related to images from popular movies and children’s books. Yet in reality dinosaurs are just as varied as mammals.
Consider: Which of the following are mammals? All of them!
They’re an incredibly varied class of animals. Yet they all form one clade on the evolutionary tree of life.

from exploringnature.org/db/view/Class-Mammals-4th-Grade-and-up
Turns out that the same is true for dinosaurs: they’re an incredibly varied class of animals – yet at the same they all form one clade on the evolutionary tree of life.
They have some characteristics in common.
Origin of the dinosaurs
Their ancestors were archosaurs, egg-laying reptiles.
They began to develop as a distinct group around 250 MYA (million years ago.)
On a related note see
The Forgotten Archosaurs
The “Dinosaurs” that Weren’t: The [brief] Age of Pseudosuchians
Pseudosuchian archosaurs, National Park Arizona
Archosaurs have two holes (temporal fenestra) in each side of their skulls. These reduce the weight of the skull.
Over time Archosaurs split into several groups: Let’s go through this cladogram carefully. The far past is in the bottom, and as we read upwards we move forward in time.
Let’s look carefully at this family tree: Where are the crocodiles? pterosaurs? Dinosaurs?
Where are the Silesauridae? (They are the sister group of dinosaurs)
What are pterosaurs?
What are crocodilia (crocodilians)?
These include crocodiles, alligators, caimans, and gharials.
What are the actual dinosaurs?
Dinosaurs are the branch descended from archosaurs that have hind limbs held erect beneath the body.
It is their hip structure that most obviously distinguishes dinosaurs from other related groups.
Because of their hips, many dinosaurs could have an upright, bipedal way of walking (like today’s birds.)
Some dinosaurs were quadrupeds (usually walking on all fours) but they were still capable of standing up on their hind legs.
Also see About Sauropod Dinosaurs

See how dinosaurs have hips that allow them to stand? Reptiles can’t do this. Image from Jurassic Park.
Compare this today’s turtles, lizards and crocs – their legs splay out beneath them.
This is clear when we look at the differences between the far left and far right images:

Image from dinosaurjungle.com
Types of dinosaurs
saurischians (‘lizard hipped dinosaurs’) and ornithischians (‘bird hipped dinosaurs’)
For the sake of convenience, the dinosaur family is divided into two main groups.
About 230 million years ago a subgroup of archosaurs split off into two types of dinosaurs, distinguished by the structure of their hip bones.
Saurischian (“lizard-hipped”) dinosaurs went on to include predators like Tyrannosaurus Rex and huge sauropods like Apatosaurus
Ornithischian (“bird-hipped”) dinosaurs consisted of a diverse assortment of other plant eaters, including hadrosaurs, ornithopods and stegosaurs.
Confusingly, we now know that birds descended from “lizard-hipped,” rather than “bird-hipped,” dinosaurs.
Learn more about how are dinosaurs classified here:
What Is the Scientific Definition of a Dinosaur, According to Experts?
What Makes a Dinosaur a Dinosaur? Smithsonian magazine

CC BY-SA 3.0, Wikipedia, Evolution of dinosaurs, Zureks
Possible new way of classifying dinosaurs
Honors level. These details are for students interested in the latest understanding of evolution.
http://www.drneurosaurus.com/2017/03/a-new-dinosaur-family-tree/
Ornithoscelida Rises: A New Family Tree for Dinosaurs, Scientific American
Discussion from Carnivoraforum
How did birds evolve from dinosaurs?
Short version: Almost all branches of the dinosaur family tree died out, except for the branch with small feathered dinosaurs. That branch proliferated and developed into the birds that we know today.

Image by Shawn Gould and Jen Christiansen, from How Dinosaurs Grew So Large—And So Small John R. Horner, Kevin Padian and Armand de RicqlèS Scientific American 293, 56 – 63 (2005)
and

Zina Deretsky, National Science Foundation. Air sac system of birds and of Majungasaurus.
also see The origin of birds evolution.berkeley.edu
How did most dinosaurs become extinct?
Short version: Meteor impact – and perhaps associated Deccan traps volcanic event? See Meteor impacts on Earth
How do we learn about dinosaurs? Fossils
See Dating rocks and fossils
and also Geologic eras
The science of Jurassic Park
Jurassic Park is a 1993 film directed by Steven Spielberg. The first installment of the Jurassic Park franchise, it is based on the 1990 novel of the same name by Michael Crichton. Is there any basis to the science in this movie?
The science of Jurassic Park
Mythology and dinosaurs
How some mythology was inspired by finding fossils
Dinosaurs and their role in mythology
Reptiles are not a true clade
Section TBA
There’s No Such Thing As Reptiles Any More – And Here’s Why
Learning Standards
Next Generation Science Standards
HS-LS4-1. Communicate scientific information that common ancestry and biological evolution are supported by multiple lines of empirical evidence.
HS-LS4-1. Communicate scientific information that common ancestry and biological evolution are supported by multiple lines of empirical evidence.
HS-LS4-2. Construct an explanation based on evidence that the process of evolution primarily results from four factors: (1) the potential for a species to increase in number, (2) the heritable genetic variation of individuals in a species due to mutation and sexual reproduction, (3) competition for limited resources, and (4) the proliferation of those organisms that are better able to survive and reproduce in the environment.
HS-LS4-3. Apply concepts of statistics and probability to support explanations that organisms with an advantageous heritable trait tend to increase in proportion to organisms lacking this trait.
HS-LS4-4. Construct an explanation based on evidence for how natural selection leads to adaptation of populations.
HS-LS4-5. Evaluate the evidence supporting claims that changes in environmental conditions may result in (1) increases in the number of individuals of some species, (2) the emergence of new species over time, and (3) the extinction of other species.
MCAS Open response
Sarah and her biological sister Danielle have some physical characteristics that are the same and some that are different, as shown in the table below.

a. Identify the molecule that stores the hereditary information for these characteristics in the chromosomes of every body cell.
b. Identify the total number of chromosomes that should be in one of Sarah’s body cells and the number of chromosomes that should have been contributed by each biological parent.
c. Explain the roles of meiosis and fertilization in achieving the chromosome numbers you identified in part (b).
d. Explain why Sarah and Danielle have some physical characteristics that are different from each other, even though they have the same biological parents.
See
Ferris wheel physics
A Ferris wheel is a large structure consisting of a rotating upright wheel, with multiple passenger cars.
The cars are attached to the rim in such a way that as the wheel turns, they are kept upright by gravity.

The original Ferris Wheel was designed and constructed by George Washington Gale Ferris Jr. as a landmark for the 1893 World’s Columbian Exposition in Chicago.
The generic term Ferris wheel is now used for all such structures, which have become the most common type of amusement ride at state fairs in the United States.
Forces in the wheel
The wheel keeps its circular shape by the tension of the spokes, pulling upward against the lower half of the framework and downward against the huge axle.
Also see
Classical relativity
This animation shows simultaneous views of a ball tossed up and then caught by a ferris wheel rider –
It shows this from one inertial POV and from two non-inertial POVs.
P. Fraundorf writes
Although Newton’s predictions are easier to track from the inertial point of view, it turns out that they still work locally in accelerated frames and curved spacetime if we consider “geometric accelerations and forces” that act on every ounce of an object’s being and can be made to disappear by a suitable vantage point change.

Created by P. Fraundorf, licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Net work done on you while on the wheel
if you are on a ferris wheel that is rotating, the total work done by all the forces acting on your is zero.
https://www.physicsforums.com/threads/ferris-wheel-work-done-by-net-force.715905/
External resources
https://www.real-world-physics-problems.com/ferris-wheel-physics.html
https://physics.stackexchange.com/questions/205918/centripetal-force-on-a-ferris-wheel
How products are made: http://www.madehow.com/Volume-6/Ferris-Wheel.html
AP Physics problems: Ferris wheels and rotational motion
Build A Big Wheel, by Try Engineering, Lesson plan
AP Physics problem solving
http://faculty.washington.edu/boynton/114AWinter08/LectureNotes/Le8.pdf
PHYSICS IN THE EXPANSE
The Expanse is a series of science fiction novels, novellas and stories by James S. A. Corey – the pen name of authors Daniel Abraham and Ty Franck. The first novel, Leviathan Wakes, was nominated for the Hugo Award for Best Novel in 2012. In 2017 the series as a whole was nominated for the ‘Best Series’ Hugo Award.
These novels are the basis of an American science fiction television series developed by Mark Fergus and Hawk Ostby. The series received positive reviews from critics, who highlighted its visuals, character development, and political narrative. It received a Hugo Award for Best Dramatic Presentation as well as a Saturn Award nomination.
- Wikipedia

https://nerdist.com/getting-the-science-right-makes-the-expanse-a-better-show/
https://www.wired.com/story/the-physics-of-accelerating-spacecraft-in-the-expanse/
https://www.reddit.com/r/TheExpanse/comments/434ihh/what_kind_of_physics_is_the_epstein_drive_based/
LET’S DO THE PHYSICS OF KNOCKING AN ASTEROID INTO THE SUN, Rhett Allain
http://josephshoer.com/blog/2015/06/spaceships-of-the-expanse/
Books
- Leviathan Wakes (June 15, 2011)
- Caliban’s War (June 26, 2012)
- Abaddon’s Gate (June 4, 2013)
- Cibola Burn, (June 5, 2014)
- Nemesis Games (June 2, 2015)
- Babylon’s Ashes (December 6, 2016)
- Persepolis Rising (December 5, 2017)
- Tiamat’s Wrath (December, 2018)
Related works
- “The Butcher of Anderson Station” (The Expanse short story) (2011)
- Gods of Risk (The Expanse novella) (2012)
- “Drive” (The Expanse short story) (2012)
- The Churn (The Expanse novella) (2014)
- The Vital Abyss (The Expanse novella) (2015)
- Strange Dogs (The Expanse novella) (2017)
Television series
tba
Possible rocket engines
from ATOMIC ROCKETSHIPS OF THE SPACE PATROL or “So You Wanna Build A Rocket?” by Winchell D. Chung Jr..
Here is your handy-dandy cheat-sheet of rocket engines. Use this as a jumping-off point, there is no way I can keep this up-to-date. Google is your friend!
I’ll point out a few of the more useful items on the sheet:
-
Aluminum-Oxygen is feeble, but is great for a lunar base (the raw materials are in the dirt).
-
VASIMR is the current favorite among ion-drive fans. Use this with orbit-to-orbit ships that never land on a planet. It can “shift gears” like an automobile.
-
Solar Moth might be a good emergency back-up engine.
-
Nuclear Thermal Solid Core is better than feeble chemical rockets, but not as much as you’d expect.
-
Nuclear Thermal Vapor Core is what you design along the way while learning how to make a gas core atomic rocket.
-
Nuclear Thermal Gas Core Open-Cycle is a full-blown honest-to-Heinlein atomic rocket, spraying glowing radioactive death in its exhaust.
-
Nuclear Thermal Gas Core Closed-Cycle is an attempt to have the advantages of both nuclear solid core and gas core, but often has the disadvantages of both. It has about half the exhaust velocity of an open-cycle atomic rocket.
-
Orion Nuclear Pulse is a rocket driven by detonating hundreds of nuclear bombs. If you can get past freaking out about the “bomb” part, it actually has many advantages. Don’t miss the Medusa variant.
-
Magneto Inertial Fusion This is the best fusion-power rocket design to date.
-
Zubrin’s Nuclear Salt Water This is the most over-the-top rocket. Imagine a continuously detonating Orion drive. There are many scientist who question how the rocket can possibly survive turning the drive on.
…
Cortical homunculus
The cortical homunculus is the part of the brain responsible for processing and integration of motor information (muscles, motion) and tactile information (touch, senses)
The reason for the distorted appearance is that the amount of cortex is proportional to how richly innervated that region is, not to its size.
The resulting image appears as a disfigured human with disproportionately huge hands, lips, and face in comparison to the rest of the body.
Sensory
Cortical

from Wikipedia
Herd immunity
What is herd immunity?
It is a form of indirect protection from infectious disease
It occurs when a sufficient percentage of a population becomes immune to an infection, whether through vaccination or previous infections.
Immune individuals are unlikely to contribute to disease transmission. This slows or stops the spread of disease.
The greater the proportion of immune individuals in a community, the smaller the probability that other people will come into contact with an infectious individual.
Let’s see how this works, with a graphic from the National Institute of Allergy and Infectious Disease (NIAID.)
Top box
Shows an outbreak in a community in which a few people are infected (shown in red) and the rest are healthy but unimmunized (shown in blue); the illness spreads freely through the population.
Middle box
Shows a population where a small number have been immunized (shown in yellow); those not immunized become infected while those immunized do not.
Bottom box
A large proportion of the population have been immunized; this prevents the illness from spreading significantly, including to unimmunized people.
In the first example, most healthy unimmunized people become infected, whereas in the bottom example only one fourth of the healthy unimmunized people become infected.

The National Institute of Allergy and Infectious Disease (NIAID)
Herd immunity is not all or nothing
On her blog, Your Local Epidemiologist, Katelyn Jetelina brings up important points:
-
Is there some known, specific number we have to reach, in order to claim herd immunity?
-
Is mass vaccination useless in stopping the spread of a disease unless we reach this specific percent?
-
Does this specific number stay the same, or does it change over time?
-
How does our behavior affect herd immunity?
In her home city, health officials stated that their county had reached herd immunity against COVID-19. 80% of people in the county had either previously contracted COVID19 and/or had received at least one vaccination.
In response, Katelyn Jetelina writes
This is exciting. Maybe this means there’s light at the end of the long, pandemic tunnel… However, we cannot come to erroneous conclusions once we reach a magical number in our head or on a county dashboard.
***Herd immunity 101***
I think we all know by now that not 100% of our population has to be immune for COVID19 to wither away. We can get to a point where so few people have COVID19 that even those who can’t be protected (like the immunocompromised ) will never have the chance to get sick. An immunity wall will keep any outbreak or transmission from happening.
On a global stage, we’ve only hit herd immunity once. In 1980, the World Health Assembly declared that smallpox was eradicated thanks to a very successful global vaccination campaign. No cases of naturally occurring smallpox have happened since.
In 2000, the CDC also declared that measles was eradicated in the United States as we reached herd immunity. This was a huge achievement given that the measles is incredibly contagious; we needed ~95% herd immunity threshold. Unfortunately, this is not still the case. Because of the antivaxx movement, we continue to dip below the threshold of protection and outbreaks happen all the time. The 2019 measles outbreak at Disneyland is just one example.
***Herd immunity threshold is really complex to measure.***
We don’t even know what the magic number is for COVID19. In the beginning, scientists estimated a 69.6% threshold was needed to reach herd immunity in the United States. This was based on a lot of mathematical models and educated guesses. Importantly, this guess relied heavily on R(0).
But the pandemic is not a fixed. It continuously evolves. Which means this threshold continues to move. The more transmissible the variant (like Delta) the higher the threshold we need.
Our behaviors also impact the threshold. Not wearing masks, not social distancing, etc. will also move our threshold higher. Population density, genetics, environment, and a whole lot of other things can also impact this number.
Thus, herd immunity in the United States can be very different than what is needed in Canada. Because of this, it’s really difficult (in fact I would argue impossible) to forecast an accurate number.
***Even if we knew the number, it’s not a light switch.***
It’s not a finish line. Not a binary decision. Not a static goal post that, once we reach, this nightmare will end and everyone’s risk for COVID19 will be zero.
My friend and colleague, Dr. Malia Jones, explained what it might look like instead:
“(A) receding tide. As more and more people are vaccinated, those who are at highest risk for ending up in the ICU will be protected. We’ll all have growing protection from outbreaks as people who are high transmitters get vaccinated. (Looking right at you, young adults.) Cases will start to ebb overall, but we can expect some ups and downs. There will be more variants, and there will be more surges. We’ll have low enough transmission that we will be able to resume most normal activities.”
***And herd immunity is not a city, county, or even state level metric.***
The 80% threshold that Dallas reached is a pooled estimate. There are still significant pockets within Dallas that remain extremely vulnerable. Even though Dallas reached “herd immunity”, cases continue to rise in Dallas.
But even if there weren’t pockets within, viruses don’t see city lines. We live in a very transient and fluid society. We move between counties, states, and countries.
And it’s dangerous to think that viruses see lines. There’s a very real possibility that people will think they’re protected if we reach a magic number. They may wrongly think this is over, that vaccines aren’t important anymore, and that we can put our guard down. This is a dangerous game to play.
***We may not reach herd immunity. But it isn’t all for nothing.***
We don’t need to reach herd immunity for a pandemic to end; for us to reach some sort of pre-pandemic normality. Herd immunity is not a number we need for cases to all of a sudden plummet. Instead it’s a number we need in order to keep cases down AFTER they are already down. Like Dr. Jones says, it’s a policy goal.
During a Stanford panel, a number of experts agreed that the next phase will be an endemic: “a plateau in infection, with a decrease in prominence over time but continued circulation.” This will be a mild state in which we don’t have exponential swings but, instead, people will get sick on occasion.
***Bottom Line***
There is not going to be a “herd immunity day” where life immediately goes back to normal. We need to start thinking of it as a receding tide rather than a light switch. Yes, we should celebrate vaccine progression. And yes, some are still hopeful that we will eventually reach herd immunity. But it will be slow. It will be quiet. And we will only know we reached it until it’s passed.
About the author: Katelyn Jetelina has a Masters in Public Health and PhD in Epidemiology and Biostatistics. She is an Assistant Professor at a School of Public Health where her research lab resides.
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pH and Equilibrium
from “An Introduction to Chemistry by Mark Bishop”
http://preparatorychemistry.com/Bishop_pH_Equilibrium.htm
According to the Arrhenius theory of acids and bases, when an acid is added to water, it donates an H+ ion to water to form H3O+ (often represented by H+).
The higher the concentration of H3O+ (or H+) in a solution, the more acidic the solution is.
An Arrhenius base is a substance that generates hydroxide ions, OH–, in water. The higher the concentration of OH– in a solution, the more basic the solution is.
Pure water undergoes a reversible reaction in which both H+ and OH– are generated.
H2O(l) H+(aq) + OH–(aq)
The equilibrium constant for this reaction, called the water dissociation constant, Kw, is 1.01 × 10-14 at 25 °C.
Kw = [H+][OH–] = 1.01 × 10-14 at 25 °C
Because every H+ (H3O+) ion that forms is accompanied by the formation of an OH– ion, the concentrations of these ions in pure water are the same and can be calculated from Kw.
Kw = [H+][OH–] = (x)(x) = 1.01 × 10-14
x = [H+] = [OH-] = 1.01 × 10-7 M
(1.005 × 10-7 M before rounding)
The equilibrium constant expression shows that the concentrations of H+ and OH– in water are linked. As one increases, the other must decrease to keep the product of the concentrations equal to 1.01 × 10-14 (at 25 °C).
If an acid, like hydrochloric acid, is added to water, the concentration of the H+ goes up, and the concentration of the OH– goes down, but the product of those concentrations remains the same.
An acidic solution can be defined as a solution in which the [H+] > [OH–].
The example below illustrates this relationship between the concentrations of H+ and OH– in an acidic solution.
EXAMPLE 1 – Determining the Molarity of Acids and Bases in Aqueous Solution: Determine the molarities of H+ and OH– in a 0.025 M HCl solution at 25 °C.
Solution:
Kw = [H+][OH–] = 1.01 × 10-14 at 25 °C
We assume that hydrochloric acid, HCl(aq), like all strong acids, is completely ionized in water. Thus the concentration of H+ is equal to the HCl concentration.
[H+] = 0.025 M H+
We can calculate the concentration of OH– by rearranging the water dissociation constant expression to solve for [OH–] and plugging in 1.01 × 10-14 for Kw and 0.025 for [H+].
Note that the [OH–] is not zero, even in a dilute acid solution.
If a base, such as sodium hydroxide, is added to water, the concentration of hydroxide goes up, and the concentration of hydronium ion goes down. A basic solution can be defined as a solution in which the [OH–] > [H+].
EXAMPLE 2 – Determining the Molarity of Acids and Bases in Aqueous Solution: Determine the molarities of H+ and OH– in a 2.9 × 10-3 M NaOH solution at 30 °C.
Solution:
Kw = [H+][OH–] = 1.47 × 10-14 at 30 °C (From Table)
Sodium hydroxide is a water-soluble ionic compound and a strong electrolyte, so we assume that it is completely ionized in water, making the concentration of OH- equal to the NaOH concentration.
[OH–] = 2.9 × 10-3 M OH–
Note that the [H+] is not zero even in a dilute solution of base.
Typical solutions of dilute acid or base have concentrations of H+ and OH– between 10-14 M and 1 M. The table below shows the relationship between the H+ and OH– concentrations in this range.
Concentrations of H+ and OH– in Dilute Acid and Base Solutions at 25 °C
| [H+] | [OH–] |
| 1.0 M | 1.0 × 10-14 M |
| 1.0 × 10-3 M | 1.0 × 10-11 M |
| 1.0 × 10-7 M | 1.0 × 10-7 M |
| 1.0 × 10-10 M | 1.0 × 10-4 M |
| 1.0 × 10-14 M | 1.0 M |
We could describe the relative strengths of dilute solutions of acids and bases by listing the molarity of H+ for acidic solutions and the molarity of OH– for basic solutions. There are two reasons why we use the pH scale instead.
The first reason is that instead of describing acidic solutions with [H+] and basic solutions with [OH–], chemists prefer to have one scale for describing both acidic and basic solutions. Because the product of the H+ and OH– concentrations in such solutions is always 1.01 × 10-14 at 25 °C, when we give the concentration of H+, we are indirectly also giving the concentration of OH–.
For example, when we say that the concentration of H+ in an acidic solution at 25 °C is 10-3 M, we are indirectly saying that the concentration of OH– in this same solution is 10-11 M.
When we say that the concentration of H+ in a basic solution at 25 °C is 10-10 M, we are indirectly saying that the OH– concentration is 10-4 M.
The pH concept makes use of this relationship to describe both dilute acid and dilute base solutions on a single scale.
The next reason for using the pH scale instead of H+ and OH– concentrations is that in dilute solutions, the concentration of H+ is small, leading to the inconvenience of measurements with many decimal places, such as 0.000001 M H+, or to the potential confusion associated with scientific notation, as with 1 × 10-6 M H+.
In order to avoid such inconvenience and possible confusion, pH is defined as the negative logarithm of the H+ concentration.
pH = -log[H+]
Instead of saying that a solution is 0.0000010 M H+ (or 1.0 × 10-6 M H+) and 0.000000010 M OH– (or 1.0 × 10-8 M OH–), we can indirectly convey the same information by saying that the pH is 6.00.
pH = -log[H+] = -log(1.0 × 10-6) = 6.00
When taking the logarithm of a number, report the same number of decimal positions in the answer as you had significant figures in the original value.
Because 1.0 × 10-6 has two significant figures, we report 6.00 as the pH for a solution with 1.0 × 10-6 M H+.
The table below shows a range of pH values for dilute solutions of acid and base.
pH of Dilute Solutions of Acids and Bases at 25 °C
| [H+] | [OH-] | pH |
| 1.0 | 1.0 × 10-14 | 0.00 |
| 1.0 × 10-1 | 1.0 × 10-13 | 1.00 |
| 1.0 × 10-2 | 1.0 × 10-12 | 2.00 |
| 1.0 × 10-3 | 1.0 × 10-11 | 3.00 |
| 1.0 × 10-4 | 1.0 × 10-10 | 4.00 |
| 1.0 × 10-5 | 1.0 × 10-9 | 5.00 |
| 1.0 × 10-6 | 1.0 × 10-8 | 6.00 |
| 1.0 × 10-7 | 1.0 × 10-7 | 7.00 |
| 1.0 × 10-8 | 1.0 × 10-6 | 8.00 |
| 1.0 × 10-9 | 1.0 × 10-5 | 9.00 |
| 1.0 × 10-10 | 1.0 × 10-4 | 10.00 |
| 1.0 × 10-11 | 1.0 × 10-3 | 11.00 |
| 1.0 × 10-12 | 1.0 × 10-2 | 12.00 |
| 1.0 × 10-13 | 1.0 × 10-1 | 13.00 |
| 1.0 × 10-14 | 1.0 | 14.00 |
This table illustrates several important points about pH. Notice that
- When the solution is acidic ([H+] > [OH–), the pH is less than 7.
- When the solution is basic ([OH–] > [H+]), the pH is greater than 7.
- When the solution is neutral ([H+] = [OH–]), the pH is 7. (Solutions with pH’s between 6 and 8 are often considered essentially neutral.)
Also notice that
- As a solution gets more acidic (as [H+] increases), the pH decreases.
- As a solution gets more basic (higher [OH–]), the pH increases.
- As the pH of a solution decreases by one pH unit, the concentration of H+ increases by ten times.
- As the pH of a solution increases by one pH unit, the concentration of OH– increases by ten times.
- The pH, [H+], and [OH–] of some common solutions are listed in the figure below. Notice that gastric juice in our stomach has a pH of about 1.4, and orange juice has a pH of about 2.8. Thus, gastric juice is more than ten times more concentrated in H+ than orange juice.
The pH difference of about 4 between household ammonia solutions (pH about 11.9) and milk (pH about 6.9) shows that household ammonia has about ten thousand (104) times the hydroxide concentration of milk.
pH of Common Substances Acidic solutions have pH values less than 7, and basic solutions have pH values greater than 7. The more acidic the solution is, the lower its pH. The more basic a solution is, the higher the pH.
The corresponding H+ and OH– concentrations are shown in units of molarity. Notice that a decrease of one pH unit corresponds to a ten-fold increase in [H+], and an increase of one pH unit for a basic solution corresponds to a ten-fold increase in [OH–].
EXAMPLE 3 – pH Calculations: In Example 1, we found that the H+ concentration of a 0.025 M HCl solution was 0.025 M H+. What is its pH?
Solution:
pH = -log[H+] = -log(0.025) = 1.60
EXAMPLE 4 – pH Calculations: In Example 2, we found that the H+ concentration of a 2.9 × 10-3 NaOH solution was 5.1 × 10-12 M H+. What is its pH?
Solution:
pH = -log[H+] = -log(7.5 × 10-12) = 11.29
We can convert from pH to [H+] and [OH–] using the following equations, as demonstrated in Examples 5 and 6.
[H+] = 10-pH
EXAMPLE 5 – pH Calculations: What is the [H+] in a glass of lemon juice with a pH of 2.12?
Solution:
[H+] = 10-pH = 10-2.12 = 7.6 × 10-3 M H+
EXAMPLE 6 – pH Calculations: What is the [OH–] in a container of household ammonia at 25 °C with a pH of 11.900?
Solution:
[H+] = 10-pH = 10-11.900 = 1.26 × 10-12 M H+
Learning Standards
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS1-9 (MA). Relate the strength of an aqueous acidic or basic solution to the extent of an acid or base reacting with water, as measured by the hydronium ion concentration (pH) of the solution. Make arguments about the relative strengths of two acids or bases with similar structure and composition.
Science and Engineering Practices
Mathematical and computational thinking in 9–12 builds on pre-K–8 and experiences and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data.
Benchmarks for Science Literacy, AAAS
Most cells function best within a narrow range of temperature and acidity. At very low temperatures, reaction rates are too slow. High temperatures and/or extremes of acidity can irreversibly change the structure of most protein molecules. Even small changes in acidity can alter the molecules and how they interact. 5C/H7
The temperature and acidity of a solution influence reaction rates. Many substances dissolve in water, which may greatly facilitate reactions between them. 4D/M4
ACS Middle School Chemistry Lessons
From middleschoolchemistry.com, contact staff at ACS. Copyright 2015 American Chemical Society
Online textbook: Chapter 5: Acids Bases and their reactions
http://www.chem4kids.com/files/react_acidbase.html
http://www.chemistryland.com/CHM151S/04-Solutions/acids/AcidsBases151.html













