One year ago, I posted a fun problem of predicting when we will have the very last total solar eclipse viewable from Earth. It was a fun calculation to do, and the answer seemed to be 700 million years from now, but I have decided to revisit it with an important new feature added: The slow but steady evolution of the sun’s diameter. For educators, you can visit the Desmos module that Luke Henke and I put together for his students.
The apparent lunar diameter during a total solar eclipse depends on whether the moon is at perigee or apogee, or at some intermediate distance from Earth. This is represented by the two red curved lines and the red area in between them. The upper red line is the angular diameter viewed from Earth when the moon is at perigee (closest to Earth) and will have the largest possible diameter. The lower red curve is the moon’s angular diameter at apogee (farthest from Earth) when its apparent diameter will be the smallest possible. As I mentioned in the previous posting, these two curves will slowly drift to smaller values because the Moon is moving away from Earth at about 3cm per year. Using the best current models for lunar orbit evolution, these curves will have the shapes shown in the above graph and can be approxmately modeled by the quadratic equations:
Perigee: Diameter = T2 – 27T +2010 arcseconds
Apogee: Diameter = T2 -23T +1765 arcseconds.
where T is the time since the present in multiples of 100 million years, so a time 300 million years ago is T=-3, and a time 500 million years in the future is T=+5.
The blue region in the graph shows the change in the diameter of the Sun and is bounded above by its apparent diameter at perihelion (Earth closest to Sun) and below by its farthest distance called aphelion. This is a rather narrow band of possible angular sizes, and the one of interest will depend on where Earth is in its orbit around the Sun AND the fact that the elliptical orbit of Earth is slowly rotating within the plane of its orbit so that at the equinoxes when eclipses can occur, the Sun will vary in distance between its perihelion and aphelion distances over the course of 100,000 years or so. We can’t really predict exactly where the Earth will be between these limits so our prediction will be uncertain by at least 100,000 years. With any luck, however, we can estimate the ‘date’ to within a few million years.
Now in previous calculations it was assumed that the physical diameter of the Sun remained constant and only the Earth-Sun distance affected the angular diameter of the Sun. In fact, our Sun is an evolving star whose physical diameter is slowly increasing due to its evolution ‘off the Main Sequence’. Stellar evolution models can determine how the Sun’s radius changes. The figure below comes from the Yonsei-Yale theoretical models by Kim et al. 2002; (Astrophysical Journal Supplement, v.143, p.499) and Yi et al. 2003 (Astrophysical Journal Supplement, v.144, p.259).
The blue line shows that between 1 billion years ago and today, the solar radius has increased by about 5%. We can approximate this angular diameter change using the two linear equations:
Perihelion: Diameter = 18T + 1973 arcseconds.
Aphelion: Diameter = 17T + 1908 arrcseconds.
where T is the time since the present in multiples of 100 million years, so a time 300 million years ago is T=-3, and a time 500 million years in the future is T=+5. When we plot these four equations we get
There are four intersection points of interest. They can be found by setting the lunar and solar equations equal to each other and using the Quadratic Formula to solve for T in each of the four possible cases.:
Case A : T= 456 million years ago. The angular diameter of the Sun and Moon are 1890 arcseconds. At apogee, this is the smallest angular diameter the Moon can have at the time when the Sun has its largest diameter at perihelion. Before this time, you could have total solar eclipses when the Moon is at apogee. After this time the Moon’s diameter is too small for it to block out the large perihelion Sun disk and from this time forward you only have annular eclipses at apogee.
Case B : T = 330 million years ago and the angular diameters are 1852 arcseconds. At this time, the apogee disk of the Moon when the Sun disk is smallest at aphelion just covers the solar disk. Before this time, you could have total solar eclipses even when the Moon was at apogee and the Sun was between its aphelion and perihelion distance. After this time, the lunar disk at apogee was too small to cover even the small aphelion solar disk and you only get annular eclipses from this time forward.
Case C : T = 86 million years from now and the angular diameters are both 1988 arcseconds. At this time the large disk of the perigee Moon covers the large disk of the perihelion Sun and we get a total solar eclipse. However before this time, the perigee lunar disk is much larger than the Sun and although this allows a total solar eclipese to occur, more and more of the corona is covered by the lunar disk until the brightest portions can no longer be seen. After this time, the lunar disk at perigee is smaller than the solar disk between perihelion and aphelion and we get a mixture of total solar eclipses and annular eclipses.
Case D : T = 246 million years from now and the angular diameters are 1950 arcseconds. The largest lunar disk size at perigee is now as big as the solar disk at aphelion, but after this time, the maximum perigee lunar disk becomes smaller than the solar disk and we only get annular eclipses. This is approximately the last epoc when we can get total solar eclipses regardless of whether the Sun is at aphelion or perihelion, or the Moon is at apogee or perigee. The sun has evolved so that its disk is always too large for the moon to ever cover it again even when the Sun is at its farthest distance from Earth.
The answer to our initial question is that the last total solar eclipse is likely to occur about 246 million years from now when we include the slow increase in the solar diameter due to its evolution as a star.
Once again, if you want to use the Desmos interactive math module to exolore this problem, just visit the Solar Eclipses – The Last Total Eclipse? The graphical answers in Desmos will differ from the four above cases due to rounding errors in the Desmos lab, but the results are in close accord with the above analysis solved using quadratic roots.
During a solar eclipse, the lansdcape will slowly dim until it is nearly complete darkness along the path of totality. other observers wil see te landscape dim a bit but then brighten to normal intensity. If you didn;t know that an eclipse was going on you might not even notice the dimming, mistaking it for a cloud passing across the sun. The geometric condition for this dimming have to do with the area of exposed solar surface and how this changes as the disk of the moon passes across it. Below is a simple mathematical model for ambient light dimming that you can put to the test the next time a solar eclipse passes over your geographic location.
I have reanalyzed the geometry and defined it in terms of the center-to-center distance, L, between the sun and moon, and their respective radii Rs and Rm as the figure of the upper half-plane of the intersection shows, with the yellow area on the left representing the disk of the sun and the white area on the right the disk of the moon. This problem was previously considered in 2000 by British astronomer David Hughes who used the distance defined by the segment FE, which he called alpha, but L = 1+M-a. The figure shows the moon overlapping the disk of the sun in a lens-shaped zone whose upper half is represented by the area AFDE.
The basic idea is that we want to compute the area of the lunar arc cap AFD by computing the area of the sector BAF and subtracting the triangle BAE from the sector area. That leaves the area of the cap as the left-over area. We perform the same calculation for the solar sector CAE and subtract the triangle CAD from this. The resulting area of the full lens-shaped overlap region is then
Occulting Area = 2x(AreaAFD + AreaAED).
Because of the geometry, the resulting area should only depend on the center-to-center separation and the radii of the sun and moon. You should not have to specify any angles as part of the final calculation. In the following we will use degree measure for all angles.
The area of the sector of a circle is just A = (Theta/360)piR2 so that gives us the first two relationships:
To simplify the problem, we are only interested in the fraction of the full sun disk that is illuminated. The full sun has an area of pi Rs2, so we divide Am and As by pi Rs2 , and if we define Rs=1.0 and M = Rm/Rs we get:
Although M is fixed by the solar-lunar ratio, we seem to have two angular variables alpha and theta that we also have to specify. We can reduce the number of variables because the geometry gives a relationship between these two angles because they share a common segment length given by h.
so that the EQ-1 for A can be written entirely in terms of the center-to-center distance, L, and moon-to-sun disk ratio M = Rm/Rs. This is different than the equation used by Hughes, which uses the width of the lens (the distance between the lunar and solar limbs) segment FDE=a as the parameter, which is defined as L = 1+M-a.
During a typical total solar eclipse lasting 4 minutes, we can define L as
L = 1900 – 900*(T/240) arcseconds where T is the elapsed time from First Contact in seconds. Since L is in units of the current solar diameter (1900 asec) we have
EQ 3) L = 1 – T/480.
If we program EQ 1, 2, and 3 into an excel spreadsheet we get the following plot for the April 8, 2024 eclipse.
First Contact occurs at 16:40 UT and Fourth Contact occurs at 19:57 UT so the full duration is 197 minutes. During this time L varies from -(1+M) to +(1+M). For the April 8, 2024 eclipse we have the magnitude M = 1.0566, so L varies from -2.0566 (t=0) to +2.0566 (t=197m). As the moon approaches the full 4-minute overlap of the solar disk between L=-0.05 and L=+0.05 (t =97m to t=102m), we reach full eclipse.
We can re-express this in terms of the landscape lighting. The human eye is sensitive to a logarithmic variation in brightness, which astronomers have developed into a ‘scale of magnitudes’. Each magnitude represents the minimum change in brightness that the human eye can discern and is equivalent to a factor change by 2.51-times. The full-disk solar brightness is equal to -26.5m, full moon illumination is -18.0m on this scale. The disk brightness, S, is proportional to the exposed solar disk area, where E is the solar surface emission in watts/m2 due to the Planck distribution for the solar temperature of T=5770 k. This results in the formula:
m = -26.5 – 2.5log10(F)
where F is the fraction of the full disk exposed and is equal to Equation 1. For a sun disk where 90% has been eclipsed, f=0.10 and the dimming is only 2.5log(1/10) = 2.5m. How this translates into how humans perceive ambient lighting is complicated.
The concept of a Just Noticeable Difference is an active research area in psychophysics. In assessing heaviness, for example, the difference between two stimuli of 10 and 11 grams could be detected, but we would not be able to detect the difference between 100 and 101 grams. As the magnitude of the stimuli grow, we need a larger actual difference for detection. The percentage of change remains constant in general. To detect the difference in heaviness, one stimulus would have to be approximately 2 percent heavier than the other; otherwise, we will not be able to spot the difference. Psychologists refer to the percentages that describe the JND as Weber fractions, named after Ernst Weber (1795-1878), a German physiologist whose pioneering research on sensation had a great impact on psychological studies. For example, humans require a 4.8% change in loudness to detect a change; a 7.9% change in brightness is necessary. These values will differ from one person to the next, and from one occasion to the next. However, they do represent generally accurate values.
The minimum perceivable light intensity change is sometimes stated to be 1%, corresponding to +5.0m, but for the Weber Fraction a 7.8% change is required in brightness corresponding to only -2.5log(0.078) = +2.7m. This is compounded by whether the observer is told beforehand that a change is about to happen. If they are not informed, this threshold magnitude dimming could be several magnitudes higher and perhaps closer to the +5.0m value.
Heliophysics is an area of space science, named by NASA, which focuses on the matter and energy of our Sun and its effects on the solar system. It also studies how the Sun varies and how those changes pose a hazard to humans on Earth and in space.
The Heliophysics Big Year is a global celebration of solar science and the Sun’s influence on Earth and the entire solar system.During the Heliophysics Big Year, you will have the opportunity to participate in many solar science events such as watching solar eclipses, experiencing an aurora, participating in citizen science projects, and other fun Sun-related activities. For details, have a look at the NASA video that describes it in more detail [HERE].
This 14-month series for science and math educators focuses on heliophysics topics with related math problems at three levels: elementary, middle, and high school. It is sponsored by NASA’s Heliophysics Education Activation Team.
Each month, I will be hosting a webinar on the theme-of-the-month and also providing some math-oriented activities that go along with he theme. Here is a list of the Webinar viewing dates. When each webinar is completed, you can view a recorded version of it at the link provided. Visit this blog page a day before the scheduled program to register.
HBY Webinar programs:
December 19, 2023 – Citizen Science Projects – Do Auroras Ever Touch Ground?
January 16, 2024 – The Sun Touches Everything – Solar Panel Math and Sunlight Energy.
February 20, 2024 – Fashion – How do color filters work?
March 19, 2024 – Experiencing the Sun – Predicting Solar Storms.
April 16, 2024 – Total Solar Eclipse – The Last Total Solar Eclipse!
May 21, 2024 – Visual Art – Is the Sun Really Yellow?
June 18, 2024 – Performance Art – Do Songs About the Sun Follow the Sunspot Cycle?
July 16, 2024 – Physical and Mental Health – How Old is Sunlight?
August 20, 2024 – Back to School – Can You Accurately Draw the Solar Corona in Under 5 Minutes?
September 17, 2024 – Environment and Sustainability – Interplanetary solar electricity for spacecraft.
October 15, 2024 – Solar Cycle and Solar Max – Predicting the Next Sunspot Cycles and Travel to Mars.
November 19, 2024 – Bonus Science – TBD
December 17, 2024 – Parker’s Perihelion – TBD
To participate in a webinar, held at 7:00pm Eastern Time, you first need to register for it by clicking on the appropriate link below and filling out the registration form. You will then receive via email the link to the live program.
This is my new book for the general public about our sun and its many influences across the solar system. I have already written several books about space weather but not that specifically deal with the sun itself, so this book fills that gap.
We start at the mysterious core of the sun, follow its energies to the surface, then explore how its magnetism creates the beautiful corona, the solar wind and of course all the details of space weather and their nasty effects on humans and our technology.
I have sections that highlight the biggest storms that have upset our technology, and a discussion of the formation and evolution of our sun based on Hubble and Webb images of stars as they are forming. I go into detail about the interior of our sun and how it creates its magnetic fields on the surface. This is the year of the April 2024 total solar eclipse so I cover the shape and origin of the beautful solar corona, too. You will be an expert among your friends when the 2024 eclipse happens.
Unlike all other books, I also have a chapter about how teachers can use this information as part of their standards-based curriculum using the NASA Framework for Heliospheric Education. I even have a section about why our textbooks are typically 10 – 50 years out of date when discussinbg the sun.
For the amateur scientists and hobbyists among you, there is an entire chapter on how to build your own magnetometers for under $50 that will let you monitor how our planet is responsing to solar storms, which will become very common during the next few years.
There hasn’t been a book like this in over a decade, so it is crammed with many new discoveries about our sun during the 21st century. Most books for the general public about the sun have actually been written in a style appropriate to college or even graduate students.
My book is designed to be understandable by my grandmother!
Generally, books on science do not sell very well, so this book is definitely written without much expectation for financial return on the effort. Most authors of popular science books make less than $500 in royalties. For those of you that do decide to get a copy, I think it will be a pleasurable experience in learning some remarkable things about our very own star! Please do remember to give a review of the book on the Amazon page. That would be a big help.
Oh…by the way…. I am a professional astronomer who has been working at NASA doing research, but also education and public outreach for over 20 years. Although I have published a number of books through brick-and-morter publishing houses, I love the immediacy of self-publishing on topics I am excited about, and seeing the result presented to the public within a month or two from the time I get the topic idea. I don’t have to go through the lengthy (month-year) tedium of pitching an idea to several publishers who are generally looking for self-help and murder mysteries. Popular science is NOT a category that publishers want to support, so that leaves me with the self-publishing option.
This page is a supplement to my new book ‘Exploring Space Weather with DIY Magnetometers‘, which is avalable at Amazon by clicking [HERE]. This $8.00 B/W book contains 146 pages and has 116 illustrations and figures that describe six different magnetometers that you can build for under $60.00. I will be posting updates to my magnetometer designs on this page along with new storm data examples as the current sunspot cycle progresses. For convenience, the sections below are tied to updates to the corresponding chapters in the book. In each instance, I have compared my design data for the magnetic D-component (angular deviation from True Geographic North) to the corresponding data from the Fredericksburg Magnetic Observatory (FRD) in Virginia.
What is Space Weather?
Chapter 2: Earth’s Magnetic Field
Chapter 3: Basic Soda Bottle Designs (under $10.00)
Chapter 5: A Dual Hall Sensor Design ($20.00)
Chapter 6: The Smartphone Magnetometer
Chapter 7: The Photocell Comparator ($40.00)
Chapter 8: The Arduino Magnetometer with the RM3100 sensor ($60.00)
This zoomed-in image of Uranus, captured by Webb’s Near-Infrared Camera (NIRCam) Feb. 6, 2023, reveals stunning views of the planet’s rings. The planet displays a blue hue in this representative-color image, made by combining data from two filters (F140M, F300M) at 1.4 and 3.0 microns, which are shown here as blue and orange, respectively.
What a typical Press Release might tell you.
Uranus has eleven known rings that contain dark, boulder-sized particles. Although the rings are nearly-perfect circles, they look like ellipses in some pictures because the planet is tilted as we are viewing it and so the rings appear distorted. They appear compressed in the side-to-side direction but are their normal undistorted distance from Uranus in the top-down direction in this image.
The outermost ‘epsilon’ ring is made up of ice boulders several meters across. The other rings are made up mainly of icy chunks darkened by rocks. The rings are thin ( less than 200 meters), narrow (less than 100 km), and dark compared to the rings of other planets. They are actually so dark they reflect about as much light as charcoal. The rings have a temperature of about 77 Kelvin according to U.C. Berkeley astronomers.
Press Releases and textbook entries depend on scientists interpreting the data they gather to create a better picture of what they are seeing. I am going to show you in this Blog just how some of those numbers and properties are derived from the data astronomers gather. I have created three levels of interpretation and information extraction that pretty nearly match three different education levels and the knowledge about math that goes along with them.
I. Space Cadet (Grades 3-6)
This is the easiest step, and the first one that astronomers use to get a perspective on the sizes of the things they are seeing. In education, it relies on working with simple proportions. The scale bar in the picture tells you how the size of the picture relates to actual physical sizes.
1) Use a millimeter ruler to calculate the diameter of Uranus in kilometers.
2) Place your ruler vertically across the disk of Uranus. Measure the vertical (undistorted) distance from the center of Uranus to the center of the outer ‘Epsilon’ ring. How many kilometers is this ring from the center of Uranus?
3) Compare the size of the Uranus ring system to the orbit of our moon of 385,000 km. Would the moon’s orbit fit inside the ring system or is it bigger?
II. Space Commander (Grades 7-9)
This level of interpretation is a bit more advanced. If you are in Middle School, it works with concepts such as volume, mass, speed and time to extract more information from the data in the image, now that you have completed the previous-level extraction.
1) What is the circumference of the Epsilon ring in kilometers?
2) The rings of Uranus are only about 200 meters thick and no more then 100 km wide, which means their cross-section is that of a skinny rectangle. What is the cross sectional of the area of the Epsilon ring in square-kilometers assuming it is a rectangle with these dimensions?
3) What is the volume of the ring in cubic-kilometers if Volume = Area x Circumference?
4) If the volume of Earth is 1 trillion cubic kilometers, how much volume does the Epsilon ring occupy in units where Earth = 1?
5) With sizes of about7-meters in diameter, what is the average mass of a single boulder if it is made from ‘dirty ice’ with a density of 2000 kg/m^3?
6) Scientists estimate that there could be as many as 25 billion boulders in the Epsilon ring. From your answer to the previous question, what is the total mass of this ring?
7) [Speed and time] The particles in the Epsilon ring travel at a speed of 10.7 km/s in their orbit around Uranus. How many hours does it take for a boulder to complete one orbit?
III. Junior Scientist (College, Graduate school)
This is a very hard level that requires that you understand how to work with algebraic equations, evaluate them for specific values of their constants and variables, and in physics understand Planck’s Black Body formula. You also need to understand how radiation works as you calculate various properties of a body radiating electromagnetic radiation. Undergraduate physics majors work with this formula as Juniors, and by graduate school it is simply assumed that you know how to apply it in the many different guises in which bodies emit radiation.
The Planck black body formula is given in the frequency domain by
where E is the spectral energy density of the surface in units of Watts/meter^2/Steradians/Hertz and the constants are h = 6.63×10^43 Joules Sec; c = 3.0×10^8 meters/sec and k = 1.38 x 10^-23 Joules/k.
If the temperature of the Epsilon ring material is T=77 k, what is E in the 1.4-micron band of the Webb (F140M) and in the 1.3- millimeter band of the Atacama Large Millimeter Array (ALMA) for a single ring particle?
What does your answer to Question 1 tell you about the visibility of the rings seen by the Webb at 1.4-microns?
If the 1.3-millimeter total flux in the Epsilon ring was measured by ALMA to be 112milliJanskies (Table 3), about how many particles are contained in the Epsilon ring if it consists of dirty ice boulders with a 7-meter diameter? Note: 1 Jansky = 10^-26 watts/m^2/Hz. Assume a distance to Uranus of 1 trillion meters.
If the volume of the Epsilon ring is about 6.4×10^6 cubic kilometers, about how far apart are the boulders in the ring?
From your answer to Question 4, if the relative speeds of the ring boulders are about 1 millimeter/sec (see Henrik Latter), how often will these boulders collide?
So, how did you do?
You may not have gotten all of the answers correct, but the important thing is to appreciate just how astronomers extract valuable information about an object from its image at different wavelengths. Other than visiting the object in person, there is no other way to learn about distant objects than to gather data and follow many different series of steps to extract information about them. Some of these series of steps are pretty simple as you experienced at the Space Cadet-level. Others can be very difficult as you saw at the Junior Scientist-level. What is interesting is that, as our theoretical knowledge improves, we can create new series of steps to extract even more information from the data. Comparing the ring brightness at two or more wavelengths, we can deduce if the boulders are made of pure ice or dark rocks. By studying how the thickness of the ring changes along its circumference relative to the locations of nearby moons, we can study gravity and tidal waves in the ring bodies that tell us about how the density of the ring particles change. Astronomy is just another name for Detective Work but where the ‘crime scene’ is out of reach!
I.1 Close to 50,700 km.
I.2 Close to 51,000 km radius 102,000 km diameter.
I.3 The moons orbit radius is 385,000 km. The outer Epsilon ring could easily fit inside our Moon’s orbit.
II.1 Circumference is about 2(pi)R, so with R = 51,000 km, the circumference is 320,000 km.
II.2 The cross-section is 100 km long and 200 meters tall so its area is just A = 0.2 km x 100 km = 20 square km.
II.3 Volume = Area x Circumference = (20 km^2)x (3.2×10^5 km) = 6.4 x 10^6 km^3.
II.5 Mass = volume x density. A single boulder with a radius of 3.5 meters has a volume of 4/3 pi (3.5)^3 = 179 m^3. Then its mass is 179 m^3 x 2000 kg/m^3 = 359000 kg or 359 tons.
II.6 There are 25 billion of these boulders so their total mass is 25 billion x 359 tons = 9.0×10^15 kg or 9 trillion tons. According to calculations in 1989, the mass of the Epsilon ring is estimated to be closer to 1016 kg or 10 trillion tons [Nature].
II.7 51,000 km/(10.7 km/s) = 8.3 hours.
III.1 Working with the Planck equation is always a bit tricky. The units for B will be Watts/m^2/Str/Hertz. First lets evaluate the equation for its constants h, c and k.
For the Webb infrared band of 1.4-microns, its frequency is 3×10^8/1.4×10^-6 or 7.1×10^13 Hertz. For ALMA the frequency is 231 GHz or 2.31×10^11 Hertz. For a temperature of 77 k, we get B(Webb) = (5.26×10^-9)(5.8×10^-20) = 3.0×10^-28 watts/m^2/Hz/str. For ALMA it will be B(ALMA) = (1.8×10^-16)(6.46) = 1.2×10^-15 Watts/m^2/Hz/str.
III.2 The visibility of the ring by its thermal emission cannot be the cause of its brightness in the Webb F140M band because its black body emission at 1.4 microns is vanishingly small due to the huge exponential factor. It must be caused by reflected visible light from the sun.
III.3 In the ALMA 1.3-millimeter band, the flux density from a black body at a temperature of 77 k is 1.2×10^-15 watts/m^2/Hertz/str. One Jansky unit equals 10^-26 watts/m^2/Hz, so the black body emission in the ALMA band can be re-written as 1.2×10^11 Janskies/str. The angular radius of the boulder at the distance of Uranus ( 1 trillion meters) is given in radians by Q = 3.5 meter/1 trillion meters = 3.5×10^-12 radians. The angular area is then AQ = pi Q^2 = 3.9×10^-23 steradians. Then the black body flux density from this boulder is about S=1.2×10^11 Jy/str x 3.9×10^-23 str so S=4.5×10^-12 Janskies. But ALMA detects a total emission from this ring of about 0.112 Janskies, so the number of emitters is just 0.112 Jy/4.5×10^-12 Jy/boulder = 2.5×10^10 boulders or 25 billion boulders.
III.4 The ring volume is 6.4 x 10^6 cubic kilometers, so each boulder occupies a volume in the ring of about 6.4×10^6 km^3/25×10^9 boulders= 256,000 cubic meters/boulder. The average distance between them is L = V^0.333 = 63 meters.
III.5 Time = distance/speed so 63m/0.001 m/sec = 17.5- hours. The Epsilon particle orbit speed is about 8.3 hours (see II.7), so the particles collide about twice every orbit.
In my earlier blogs, I talked about Math Anxiety, about how the brain creates a sense of Now, and various other fun issues in brain research too. Branching off of my long, professional interest in math education, I thought I would look into how ‘doing’ math actually changes your brain in many important ways, especially for children and adolescents. Brain research has come a long way in the last 15 years with the advent of fMRI and sensors that can listen-in to individual neutrons . For a detailed glimpse of modern research have a look at my reference list at the end of this blog.
Here is what we know about how math affects brain structure and maturation. My previous blog on Math Anxiety covered this topic but here are some additional points.
The Basic Anatomy of Math
First of all, let’s put to rest a popular misconception. Its a complete fallacy that we only use 10% of our brain. The misconception probably arose because glial cells that support neurons account for 90% of the cellular matter in the brain, so neurons account for 10% [9,11,10]. The truth is, by the end of each day, your brain has used nearly all of its neurons to facilitate movement, sensory processing, advanced planning, and even day-dreaming!
The architecture of our brains is controlled by about 86 million neurons and the trillions of synaptic connections between them. At the lowest level, our brains are composed of numerous modules that are specialized for specific tasks. Each has its own local knowledge system and ‘data cache’ and can act much faster than the whole-brain, which is the way evolution designed this system to help us respond quickly and not get eaten. We benefit from this ancient architecture because craftsmen, musicians and dancers cannot tell you how they perform their tasks because it is largely unconscious and controlled by specific modules. [6:p45, 198].
Before the age of 2, children use a general knowledge ‘program’ that takes up all of their working memory [2:p151] to interact with the environment. Children require more working memory to do math than adults. Number facts and basic opeations are not yet in long-term memory so they use more of their prefronal cortex (PFC) to keep math in working memory so that they can solve problems [2:p155]. But through training they develope a growing multitude of specialized modules and automatic ‘subroutines’ for specific tasks and skills. [6:p56]. Consciousness occurs when these non-communicating modules begin to share their knowledge across many communities of modules spanning the entire cerebral network. Some of these global communication pathways are highlighted by the so-called brain connectome map. This sharing of multiple representations of similar knowledge leads to problem solving and creativity which now draw inspiration from the experiences of many different modules [6:p58] spanning the entire cortex.
Development of the Brain
At birth, the average baby’s brain is about a quarter of the size of the average adult brain. Incredibly, it doubles in size in the first year. It keeps growing to about 80% of adult size by age 3 and 90% – nearly full grown – by age 5 . Over 1 million new neural connections are created every second among the synapses of the growing population of neurons and dendrites . What then ensues is a process of pruning as seldome-used connections wither and dissappear while others are strengthened .
The growing brain does not start out as a tabla rasa but through genetics and evolution there are already features in place that anticipate the growth of mathematical knowledge.
Number Line Maps
At the most elementary level, neurons already exist at birth that are active for specific numbers. These ‘number neurons’ have been found in both monkeys and in humans. In humans they are mostly found in the lateral prefrontal cortex (l-PFC) and the intraparietal sulcus (IPS). [2:p129], but also the mediotemporal lobe (MTL) [2:p98]
Our brain’s hippocampous has place and grid cells that form a direct map written on its cortex that represents the location of objects in space [7p219]. The posterior cingulate region has neurons tuned to the location of objects in the outside world, and is connected to the parahippocampal gyrus where “place cells’ are found. These neurons fire whenever an animal occupies a specific location in space like the northwest corner of your room. These place cells are so advanced that readout of individual nerve cell firings can be used to tell a researcher where the object is in the subjects visual field of view. This even works when the subject closes their eyes and imagines an animal located there. [4:p149].
A curious feature of how the young brain processes quantities is that it perceives quantities as being located on a mental number line. Called the SNARC Effect, even three-day-old infants will look-right for large quantities and look-left for smaller quantities.[2:236]. That calculation-related activity is being processed like mental movement on a number line was also tested in older subjects by studying neuron activation in the superior parietal lobule (SPL) where information is being manipulated in working memory. They found that eye motion alone predicted the answers to simple addition and subtraction problems [2:239]. So just as the brain uses an internal map in the hippocampus to locate objects in space, it also uses an internal map to locate numbers in space along a line! The number line however is not uniform.
Kindergarten students with no math knowledge see number intervals as quantities mapped out in logarithmic intervals just as many animals do, so that quantities are perceived almost the same way as light brightness or sound volume [2:87]. Large numbers with smaller intervals are crowded together in the right-hand of the mental number line while smaller numbers are more spread out in the left-side of the line.
Meanwhile, the concepts of addition and subtraction are already known to infants as young as nine months[2:196]. Thinking about quantity as symbolic numerals like 1,2,3 etc instead of dots like [.], [..], […] etc at first occupies children up to age 7 who have to use their working memory to keep track of this, but within a few years the relationship between number symbols and dots becomes automatic and unconscious [2:185]. By the way, although algebra looks like a language, algebra is not processed in the brain’s language centers [2:p222] You can think and reason logically without language. In fact, when professional mathematicians are studied and asked to solve advanced problems, their language centers are not activated. Instead, the bilateral frontal, intraparietal and ventrolateral temporal regions were active, which are connected to the regions associated with processing numbers [2:232].
Math Remodels the Brain.
For mathematicians, an interesting recycling of brain areas occurs in order to accommodate advanced mathematics. Afterall, the brain volume is fixed by the volume of the skull, so the only way that new skills are learned and mastered is by appropriating cerebral real estate from other adjacent functions. The inferior temporal gyrus (ITG) is an area where face recognition occurs. For mathematicians, part of this region is invaded by adjacent regions used in number processing [2:191], in some cases making it harder for mathematicians to recognize faces!
Admittedly, this is an extreme result of brain reorganization, but there are other examples that are more relevant to children and young adults and the answer to the question ‘Why do I need to know math?’
Researchers have proposed that math training not only makes us better at math, but also strengthens our ability to moderate our feelings and our social interactions because of the brains proclivity in sharing brain regions for other purposes.
Example 1: In my previous blog on Math Anxiety, I mentioned that the sub-region called the dorsolateral prefrontal cortex helps us keep relevant problem-solving information ‘fresh’ in our working memory. In math it is activated when the individual is keeping track of more than one concept at a time. As it also turns out, this region is also activated as we regulate our emotions. For example, most children learn how to tone-down their glee at winning a game when they see their friends are mortified at having lost. It is also important in suppressing selfish behavior, fostering commitment in relationships, and most importantly inferring the intentions of others, which is called a Theory of Mind.
Example 2: The long-term effect of not continuing math education and problem-solving in adolescents has also been documented. A recent study of adolescents in the UK shows that a lack of math education affects adolescent brain development. In the UK, students can elect to end their math education at age 16. The neurotransmitter called gamma-Aminobutyric acid (GABA) is present in the middle front gyrus (MFG), which is a region involved in reasoning and cognitive learning. GABA levels are a predictor of changes in mathematical reasoning as much as 19 months later. What was found among the older adolescents was that GABA showed a marked reduction. This neurotransmitter is also correlated with brain plasticity and its ability to reconfigure itself by growing new synapses as it learns new skills or knowledge having npothing to do with math .
Example 3: The mediotemporal lobe (MTL) includes the hippocampus, amygdala and parahippocampal regions, and is crucial for episodic and spatial memory. The MTL memory function consists of distinct processes such as encoding, consolidation and retrieval, and supports many functions including emotion, affect, motivation and long-term memory. The MTL also has numerous number neurons [2:p98] and is involved in processing mathematical concepts. Activity in this region represents a short-term memory of the arithmetic rule, whereas the hippocampus may ‘do the math’ and process numbers according to the arithmetic rule at hand.”.
Example 4: Memory-based math problems stimulate a region of the brain called the dorsolateral prefrontal cortex, which has already been linked to depression and anxiety. Studies have found, for example, that higher activity in this area is associated with fewer symptoms of anxiety and depression. A well-established psychological treatment called cognitive behavioral therapy, which teaches individuals how to re-think negative situations, has also been seen to boost activity in the dorsolateral prefrontal cortex. The ability to do more complex math problems might allow you to more readily learn how to think about complex emotional situations in different ways. Greater activity in the dorsolateral prefrontal cortex was also associated with fewer depression and anxiety symptoms. The difference was especially obvious in people who had been through recent life stressors, such as failing a class. Participants with higher dorsolateral prefrontal activity were also less likely to have a mental illness diagnosis.
The bottom line for much of the research on how the brain functions with and without mathematics stimulation is that low numeracy is a bigger problem for the brain than low literacy [2:p307] It affects your economic opportunities in life, handeling personal finances, operating as a savvy consumer, and it even connects with your ability to logically process complex social situations and predict what your best course of action might be in many different circumstances.
Many of the brain regions needed for math performance are still under development between ages of 16 and 26 including most importantly the frontal cortex essential for judgment and anticipating future consequances of actions.
So when a student asks what is math good for, take a step back and walk them through the Big Picture!
Books that are definitely worth the time to read!
 The Tell-Tale Brain, V.S. Ramachandran, 2011, W.W. Norton and Co.
 A Brain for Numbers, Andreas Nieder, 2019, MIT Press
 The Consciousness Instinct, Michael Gazzangia, 2018, Farrar, Straus and Giroux
 Consciousness and the Brain, Stanislaus Dehaene, 2014, Penguin Books.
 Being You: A new science of consciousness, Anil Seth, 2021, Dutton Press
 The Prehistory of the Mind, Stevem Mithen, 1996, Thames and Hudson Publishers.
 The Idea of the Brain, Matthew Cobb, 2020, Basic Books
 The River of Consciousness, Oliver Sacks, 2017, Vintage Books
 Myth: We only use 10% of our brains. Stephen Chew ,2018, https://www.psychologicalscience.org/uncategorized/myth-we-only-use-10-of-our-brains.html
 Unsung brain cells play key role in neurons’ development, 2009, Bruce Goldman, https://med.stanford.edu/news/all-news/2009/09/unsung-brain-cells-play-key-role-in-neurons-development.html#:~:text=Ben%20Barres’%20research%20has%20led,90%20percent%20of%20the%20brain.
I have often wondered how the modern description of the Big Bang could be written as a story that people at different reading levels would be able to understand, so here are some progressively more complete descriptions beginning with Genesis and their reading level determined by Reliability Formulas.
“In the beginning God created the heavens and the earth. Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters. And God said, “Let there be light,” and there was light. God saw that the light was good, and he separated the light from the darkness. God called the light “day,” and the darkness he called “night.” And there was evening, and there was morning–the first day. And God said, “Let there be an expanse between the waters to separate water from water.” So God made the expanse and separated the water under the expanse from the water above it. And it was so. God called the expanse “sky.” And there was evening, and there was morning–the second day. And God said, “Let the water under the sky be gathered to one place, and let dry ground appear.” And it was so. God called the dry ground “land,” and the gathered waters he called “seas.” And God saw that it was good. Then God said, “Let the land produce vegetation: seed-bearing plants and trees on the land that bear fruit with seed in it, according to their various kinds.” And it was so. The land produced vegetation: plants bearing seed according to their kinds and trees bearing fruit with seed in it according to their kinds. And God saw that it was good. And there was evening, and there was morning–the third day. And God said, “Let there be lights in the expanse of the sky to separate the day from the night, and let them serve as signs to mark seasons and days and years, and let them be lights in the expanse of the sky to give light on the earth.” And it was so. God made two great lights–the greater light to govern the day and the lesser light to govern the night. He also made the stars. God set them in the expanse of the sky to give light on the earth, to govern the day and the night, and to separate light from darkness. And God saw that it was good.”
The Flesch Reading ease Score gives this an 87.9 ‘easy to read‘ score. Flesch-Kincaid gives this a grade level of 4.5. The Automated Readability Index gives it an index of 4 which is 8-9 year olds in grades 4-5. Amazingly, the scientific content in this story is completely absent and in fact promotes many known misconceptions appropriate to what children under age-5 know about the world.
Can we do at least as well as this story in a 365-word summary that describes the origin of the universe, the origin of the sun, moon and earth, and the appearance of life? Because the reading level of Genesis is only at most Grade-5, can we describe a scientific treatment using only concepts known by the average Fifth-Grader? According to the Next Generation Science Standards, students know about gravity, and scales of time but ideas about atoms and other forces are for Grade 6 and above. The average adult reader can fully comprehend a text with a reading grade level of eight. So if the text has an eighth grade Flesch Kincaid level, its text should be easy to read and accessible by the average US adult. But according to Wylie Communications, half of all US adults read at or below 8th-grade level. The American Academy of Arts and Sciences survey also shows that US adults know about atoms (51%), that the universe began with a Big Bang (41%) and that Earth orbits the sun (76%) so that US adults rank between 5th and 9th internationally in our basic scientific knowledge.
The genesis story splits itself into three distinct parts: The origin of the universe;The origin of stars and planets; and The origin of life and humanity. Only the middle story has detailed observational evidence at every stage. The first and last stories were one-of events for which exact replication and experimentation is impossible.
Because we are 3000 years beyond the writing of Genesis, let’s allow a 400-word limit for each of these three parts and aim at a reading level and science concept level not higher than 7th grade.
First try (497 words):
Origin of the Universe. Our universe emerged from a timeless and spaceless void. We don’t know what this Void is, only that it had none of the properties we can easily imagine. It had no dimension, or space or time; energy or mass; color or absence of color. Scientists use their mathematics to imagine it as a Pure Nothingness. Not even the known laws of nature existed.
Part of this Void exploded in a burst of light and energy that expanded and created both time and space as it evolved in time. This event also locked into existence what we call the Laws of Nature that describe how many dimensions exist in space, the existence of four fundamental forces, and how these forces operate through space and time.
At first this energy was purely in the form of gravity, but as the universe cooled, some of this energy crystalized into particles of matter. Eventually, the familiar elementary particles such as electrons and quarks emerged and this matter became cold enough that basic elements like hydrogen and helium could form.
But the speed at which the universe was expanding wasn’t steady in time. Instead this expansion doubled in speed so quickly that within a fraction of a second, the space in our universe inflated from a size smaller than a baseball to something many billions of miles across. Today, after 14 billion years of further expansion we see only a small fraction of this expanded space today, and we call it the Observable Universe. But compared to all the space that came out of the Big Bang, our entire Observable Universe is as big as a grain of sand compared to the size of our Earth. The Universe is truly an enormous collection of matter, radiation and energy in its many forms.
Meanwhile, the brilliant ‘fireball’ light from the Big Bang also cooled as the universe expanded so that by one million years after the Big Bang, it was cooler than the light we get from the surface of our own sun. Once this light became this cool, familiar atoms could start to form. As the universe continued to expand and cool, eventually the light from the Big Bang became so cool that it could only be seen as a dull glow of infrared light every where in space. The atoms no longer felt the buffeting forces of this fireball light and had started to congregate under the force of gravity into emmence clouds throughout space. It is from these dark clouds that the first stars would begin to form.
Mixed in with the ordinary matter of hydrogen and helium atoms was a mysterious new kind of matter. Scientists call this dark matter because it is invisible but it still affects normal matter by its gravity. Dark matter in the universe is five times more common than ordinary matter. It prevents galaxies like the Milky Way from flying apart, and clusters of galaxies from dissolving into individual galaxies.
Origin of the Universe. Our universe emerged from a timeless and spaceless void. We don’t know what this Void was. We think it had none of the properties we can easily imagine. It had no dimension, or space or time. It had no energy or mass. There was no color to it either blackness or pure white. Scientists use their mathematics to imagine it as a Pure Nothingness. They are pretty sure that not even the known laws of nature existed within this Void.
Part of this Void exploded in a burst of light and energy. Astronomers call this the Big Bang. It expanded and created both time and space as it evolved in time. This event also locked into existence what we call the Laws of Nature. These Laws describe how many dimensions exist in space. The Laws define the four fundamental forces, and how they operate through space and time.
At first the energy in the Big bang was purely in the form of gravity. But as the universe expanded and cooled, some of this energy crystalized into particles of matter. Eventually, the familiar elementary particles such as electrons and quarks emerged. This matter became cold enough that basic elements like hydrogen and helium could form.
But the speed at which the universe was expanding wasn’t steady in time. Instead this expansion doubled in speed very quickly. Within a fraction of a second, the space in our universe grew from a size smaller than a baseball to something many billions of miles across. After 14 billion years of further expansion we see only a small fraction of this expanded space today. We call it the Observable Universe. But compared to all the space that came out of the Big Bang, our entire Observable Universe is as big as a grain of sand compared to the size of our Earth. The Universe is truly an enormous collection of matter, radiation and energy in its many forms.
Meanwhile, the brilliant ‘fireball’ light from the Big Bang also cooled as the universe expanded. By one million years after the Big Bang, it was cooler than the light we get from the surface of our own sun. Once this light became this cool, familiar atoms could start to form. As the universe continued to expand and cool, eventually the blinding light from the Big Bang faded into a dull glow of infrared light. At this time, a human would see the universe as completely dark. The atoms no longer felt the buffeting forces of this fireball light. They began to congregate under the force of gravity. Within millions of years, immense clouds began to form throughout space. It is from these dark clouds that the first stars would begin to form.
Mixed in with the ordinary matter of hydrogen and helium atoms was a mysterious new kind of matter. Scientists call this dark matter. It is invisible to the most powerful telescopes, but it still affects normal matter by its gravity. Dark matter in the universe is five times more common than the ordinary matter we see in stars. It prevents galaxies like the Milky Way from flying apart. It also prevents clusters of galaxies from dissolving into individual galaxies.
Origin of the Universe. Our universe appeared out of a timeless and spaceless void. We don’t know what this Void was. We can’t describe it by its size, its mass or its color. It wasn’t even ‘dark’ because dark (black) is a color. Scientists think of it as a Pure Nothing.
Part of this Void exploded in a burst of light and energy. We don’t know why. Astronomers call this event the rather funny name of the ‘Big Bang’. It was the birth of our universe. But it wasn’t like a fireworks explosion. Fireworks expand into the sky, which is space that already exists. The Big Bang created space as it went along. There was nothing for it to expand into. The Big Bang also created what we call the Laws of Nature. These Laws describe how forces like gravity and matter affect each other.
As the universe expanded and cooled, some of its energy became particles of matter. This is like raindrops condensing from a cloud when the cloud gets cool enough. Over time, these basic particles formed elements like hydrogen and helium.
The universe continued to expand. Within the blink of an eye, it grew from a size smaller than a baseball to something many billions of miles across. Today, after 14 billion years we see only a small piece of this expanded space today. Compared to all the space that came out of the Big Bang, what we see around us is as big as a grain of sand compared to the size of our Earth. The Universe is truly enormous!
After about one million years the fireball light from the Big Bang became very dim. At this time, a human would see the universe as completely dark. There were, as yet, no stars to light up the sky and the darkness of space. Atoms began to congregate under the force of gravity. Within millions of years, huge clouds the size of our entire Milky Way galaxy began to form throughout space. From these dark clouds, the first stars started to appear.
Mixed in with ordinary matter was a mysterious new kind of matter. Scientists call this dark matter. It is invisible to the most powerful telescopes. But it still affects normal matter by its gravity, and that’s a very good thing! Without dark matter, galaxies like our Milky Way and its billions of stars would fly apart, sending their stars into the dark depths of intergalactic space.
Flesch Reading Ease 73.3. (Fairly easy to read); Flesch-Kincaid Grade: 5.9 (Sixth grade) ; Automated Readability Index: 5.1 (8 – 9 year olds) Fourth to Fifth grade.
The Third Try is about as simple and readable a story as I can conjure up, and it comes in at a reading level close to Fourth grade. Scientifically, it works with terms like energy, space, expansion, matter and gravity, and scales like millions and billions of years. All in all, it is not a bad attempt that reads pretty well, scientifically, and does not mangle some basic ideas. It also has a few ‘gee whiz’ ideas like Nothing, space expansion and dark matter.
The spectacular solar storm we had on April 23, 2023 reminds us that, as the current sunspot cycle continues to progress, we will have many more of these spectacular aurora to look forward to in the next few years. So where are we in the current sunspot cycle?
Sunspot cycles average about 9 to 12 years, with the stronger cycles on the shorter end of this range and weaker cycles on the longer end of this range. The current cycle, Number 25, seems to be exceeding all forecasts for a weaker cycle and may in fact resemble previous ones like Cycle 22 or 23.
The current cycle began in December 2019 and some predictions at that time suggested that it would probably be a very weak cycle perhaps not even exceeding Cycle 24. This is shown by the grey band in the above figure. Some even thought based on solar magnetic field data that we could be heading into another Maunder Minimum with no recognizble sunspots for the next 50 years. Instead, the rapid rise of activity and solar flares since 2020 has demonstrated that we still do not really understand what drives sunspot cycles.
This is rather embarrasing. The sunspot cycle is one of the most glaring features of the sun whose nearly constant period of 11 years begs to be explained. This is like meteorologists still not being able to explain why Earth has its four seasons.
The current sunspot cycle was born with the first spots sighted around April 2018 with spots that had the opposite polarity of those in Cycle 24. It is common for such spots to start appearing several years before the actual cycle commences. But by November 2019 this number had increased to two spots. In May 2020 the first M-class flare erupted, followed by the first X-class flare in July 2020.
Since 2020, the sunsppot counts and flare activity have consistently placed Cycle 25 on the upper tracks of the strong cycle forecasts being nearly 50% more active than the initial predictions year-by-year. Already by January and March 2023 we are seeing 143 and 122 sunspots which compares with the peak of 146 seen for Cycle 24. The red band in the figure below shows the current range of curves based on the most recent data. This places the trend for the maximum somewhere between Cycle 23 and Cycle 24. But the current year 2023 trends will probably give us the definitive predictions. So far, it looks like Cycle 25 will peak around early-2024.
So far, Cycle 25 is 40 months old. During this time we have already experienced 8 X-class flares on (X1) October 2, 2022, (X1.2) January 5, 2023, (X1.3) January 9, 2023, (X1) January 10, 2023, (X1.1) February 11, 2023, (X2.2) February 17, 2023, (X2.1) March 3, 2023, and (X1.2) March 29, 2023. Most of these appeared in 2023 so the pace of these major events is quickening.
Why is this important?
The sunspot cycle is a barometer of what we call space weather. Space weather is a term analogous to Earth weather with a number of parallels. Strong terrestrial winds are equivalent to the solar wind. Solar flares are equivalent to severe lightning storms, and coronal mass ejections are analogous to hurricanes and tornados. Just as severe Earth weather can cause billions of dollars of damage, severe space weather can damage satellites in Earth orbit, produce harmful radiation for astronauts working in space, and cause electric power grid outages. They also produce dramatic aurora!
The most recent examples of what space weather can do is the loss of 40 Starlink satellites on February 3, 2022 costing SpaceX over $100 million.The cause was a space weather event that heated up Earth’s outer atmosphere causing it to expand into space and provide extra drag to the satellites in Low Earth Orbit. The satellites tried to compensate by firing their thrusters but quickly used up all their propellant and burned up in the atmosphere.
Meanwhile, the European Space Agency’s Swarm satellites are having their own problems. Launched in 2013, these satellites measure and map Earth’s magnetic field. By July 2022 the satellites in the three-satellite constellation have been falling by up to 20 km per year from their initial orbit of 450-530 km.
How stormy can it get?
The graph shows how disturbed Earth’s magnetic field is during various years throughout the sunspot cycle. It is based on the average activity from the past three cycles. The black line gives the average number of extreme storms with Kp > 8 that produce aurora seen as far south as southern California or Florida like the recent one on April 23, 2023. The red line is storms stronger tha Kp = 7, and the blue line is storms stronger then Kp=6. These still produce brilliant aurora, but generally only seen in the northern-tier states of the United States and in New England and Alaska.
We are now in Year 4 of the current sunspot cycle with a maximum that may be between Year 5-6 in 2024-2025, so we should expect that most of the aurora activity is still in our future, peaking sometime between Year 7 and 9, which is about 2026-2028. It all depends on how the sunspot numbers play out this year and in 2024, but for aurora lovers, the best is yet to come!
Over the years I have collected a number of online tools that help me keep climate change in perspective. Here are some of my favorites!
Riskfactor.com – Just enter your address and it will use a database from FEMA to give you a forecast of the possible risks your home and property face in the next 30 years. I was not surprised that my Kensington, Maryland has a low risk for fire and heat, but startled that even at my elevation of 200 feet my risk for flooding in the next 30 years was pretty high, mostly from ordinary rain runoff. This is likely because Climate Change predicts more frequent and more severe rain storms that dump more water on my property than what it has faced in the last 50 years. I was also surprised that my Heat risk is elevated from 5 days over 100-degrees F to 20 days over 100-degrees F. This could have health implications for my wife!
Risk by county. What kind of a county do you live in by income or community group? Are you Urban? Rural? Military? How will your county be affected by future hurricanes, tornadoes and floods? The above risk for sea level rise shows the expected risk distribution. My county, Montgomery County, MD has no risk….how about yours??? Other interactive maps at this site give hurricane, tornado, rainfall risks too. The map below shows counties expected to have the greatest heat stress.
Natural Disasters. The map below shows the cumulative federal FEMA payouts for all 50 states due to climate disasters between 1980 and 2020, with most of the expensive ones at more than a billion dollars each, happening since 2010.
“The South, Central and Southeast regions of the U.S., including the Caribbean U.S. territories, have suffered the highest cumulative damage costs, reflecting the severity and widespread vulnerability of those regions to a variety of weather and climate events. In addition to the highest number of billion-dollar disasters experienced, Texas also leads the U.S. in total cumulative costs (~$290 billion) from billion-dollar disasters since 1980. Florida is the second-leading state in total costs since 1980 (~$230 billion), largely the result of destructive hurricane impacts. Louisiana has the 3rd highest total costs (~$205 billion) from billion-dollar disasters, but has a much smaller population and economy than either Texas or Florida. Therefore, the relative cost and impact from extremes in Louisiana is more severe and difficult to recover. ”
Getting back to climate change-related resources…..The practical consequences of increased disasters is your Home Owner’s Insurance. The website HowMuch.net gives the map below of the average annual policy costs by state. My state, Maryland, is half the cost of Texas, but Texas is where everyone wants to live thanks to their excellent marketing over the last 150 years! Everything certainly is BIGGER in Texas!!
An astronomer's point-of-view on matters of space, space travel, general science and consciousness