Dolomite is a Scrabble® word

Definitions for the word, Dolomite
(n.) A mineral consisting of the carbonate of lime and magnesia in varying proportions. It occurs in distinct crystals, and in extensive beds as a compact limestone, often crystalline granular, either white or clouded. It includes much of the common white marble. Also called bitter spar.

Scrabble letter values
A is 1 points
B is 3 points
C is 3 points
D is 2 points
E is 1 points
F is 4 points
G is 2 points
H is 4 points
I is 1 points
J is 8 points
K is 5 points
L is 1 points
M is 3 points
N is 1 points
O is 1 points
P is 3 points
Q is 10 points
R is 1 points
S is 1 points
T is 1 points
U is 1 points
V is 4 points
W is 4 points
X is 8 points
Y is 4 points
Z is 10 points


THE HEATSINK GUIDE: Maximum CPU temperature and maximum CPU power usage

This page is there to answer the common question: "My CPU is running at xx degrees, is it too hot?". Here are the maximum temperatures for the most popular CPUs.

Keep in mind that the onboard measurement facilities are often inaccurate and may report temperatures that are too low. This is especially the case with motherboards that use a thermal sensor below the CPU to "guess" the CPU temperature. The temperature values displayed by the BIOS have usually a correction value added, to compensate for this problem - but in some cases this correction value may be too low, or the sensor might not be in good contact with the CPU.

This means:
If the maximum allowed temperature for your CPU is 95°C, and your motherboard reports a CPU temperature of 90°C, then you are not on the safe side.

However, this doesn't mean that you should start to panic when your Athlon XP CPU reaches 60 degrees celsius, for example. Most people tend to underestimate normal CPU operating temperatures - maybe due to overclockers bragging with their super-low CPU temperatures in forums.

Also, note that these values are for CPUs that are not overclocked. Overclocked CPUs may run unstable even if their temperature is way below the maximal specified temperature.

What happens if the maximum operating temperatures are exceeded?

If your cooler is insufficient and the temperature exceeds the maximum operating temperature, then this does not mean that the CPU is automatically damaged. With AMD CPUs, you will usually encounter crashes if the CPU is overheated; but these go away as soon as the CPU is cooler again. In the long term, running the CPU at a temperature that is too high may reduce the CPU life, since an overheated CPU is more prone to electromigration - even if it runs stable. With P4 CPUs, the CPU will turn its speed down automatically when it overheats. No damage to the CPU is possible, but the system will get slower while it's hot (which, in some cases, users might not even notice).

If you attempt to operate a CPU without heatsink at all, recent AMD CPUs will usually be permanently damaged within seconds, unless special protection circuitry is available on the motherboard. P4 CPUs will run excessively slow without cooler.

The purpose of this page is to give you a quick overview of typical maximum operating temperatures for common CPUs. In the case of Intel CPUs, values vary a bit; if you need precise information for one specific CPU model, please use the datasheets on the CPU manufacturer's website, or visit Chris Hare's Processor Electrical Specifications page - there, you will find more details, and also data for more exotic CPU types than the ones covered here.

Higher is better here

On cooling-related websites, lower temperatures typically correspond to better products. On this particular page, the opposite is true: The higher temperatures a CPU can withstand, the less cooling is required. CPUs with low electrical power, but high temperature rating can be used with more quiet and more compact coolers. An example for such a CPU is the Pentium-M, which dissipates less than 25 watts, but may reach temperatures of up to 100°C. The worst-case example is the Pentium 4 Extreme Edition 3.46GHz, which dissipates over 110 watts, but may only reach a maximum temperature of 66°C. Obviously, you need a large and possibly loud cooler here.

The actual data:

AMD Athlon, Athlon 64, Opteron, Duron and Sempron
All Slot A CPUs (Athlon classic, Athlon Thunderbird) 70°C
Athlon Socket A up to 1 GHz, Duron up to 1.3GHz
Athlon "Thunderbird" Socket A 1.1GHz or more 95°C
Athlon MP 1.33GHz or more 95°C
Athlon XP up to 2100+
Athlon XP 2200+ and faster
Duron "Applebred" 1.4G and faster 85°C
AMD Opteron
69 or 70°C
on model
Athlon 64, 64FX, Sempron
Most models 70°C; 65°C for some Socket 939 Athlon 64 models
Athlon 64 X2 (dual core)

AMD K6 series
All K6 CPUs (166-300MHz) and most K6-2/K6-III CPUs 70°C
K6-2/K6-III CPUs, model name ending with X (e.g. K6-2-450AFX) 65°C
K6-2-400AFQ (uncommon) 60°C (!)
K6-2+, K6-III+, most mobile K6/K6-2 CPUs 85°C
mobile K6/K6-2 model name ending with K (e.g. mobile K6-2-P-400AFK) 80°C

The temperatures specified for AMD CPUs max case surface temperatures. These CPUs do not have an internal diode to measure CPU temperature. The accuracy of the CPU temperature measurement depends on the motherboard; therefore, it is possible that the CPU overheats even though the CPU temperature reported by the motherboard is below the specified maximal temperature.

Intel Pentium III
Pentium III Socket 370 500-866MHz,
Pentium III Slot 1 (first generation, OLGA) 550-600MHz,
Pentium III Slot 1 ('Coppermine') 500-866MHz
80-85°C depending on model
Pentium III Socket 370 and Slot 1, 933MHz 75°C
Pentium III Slot 1 933MHz 60°C (!)
Pentium III Slot 1 1GHz 70°C for newer versions
60°C (!) for older version
Pentium III Slot 1 1.13GHz (first version) 62°C (!)

Pentium III max temperatures are the maximum temperatures reported by the thermal junction inside the CPU.

Intel Celeron / Celeron
Celeron 266-433MHz 85°C (max. CPU case temperature)
Celeron 466-533MHz (0.25µ) 70°C (max. CPU case temperature)
Celeron 533-600MHz ('Coppermine) 90°C
Celeron 633 and 667MHz 82°C
Celeron 700-850 MHz
Celeron 900MHz-1.4GHz
69-70°C depending on model
Celeron 1.7GHz and faster
67-77°C depending on model

Celeron max temperatures are the maximum temperatures reported by the thermal junction inside the CPU, unless otherwise specified.

Intel Pentium II
Pentium II (1st generation, 'Klamath') 72-75°C depending on MHz
Pentium II (2nd generation, 2.0V core), 266-333MHz 65°C
Pentium II (350-400MHz) 75°C
Pentium II (450MHz) 70°C

Pentium II temperatures are the maximum temperatures of the thermal transfer plate (on which the heatsink is installed).

Intel Pentium 4, Pentium 4 Extreme Edition, Pentium M
Pentium 4
Max. temperature depends much on model and clockspeed, but no clear pattern is visible. Consult Intel's tech specs for information on your particular model.
(Lowest: P4 Extreme Edition 3.2GHz with 64°C, highest: P4 Willamette 1.8GHz with 78°C).
64°C - 78°C
Pentium M
100°C (!)

Intel Pentium D (dual core)
Pentium D 820 (2.8GHz) 63°C
Pentium D 830 and 840 (3.0-3.2GHz) 69.8°C

Note: Pentium 4 and Pentium D temperature specifications indicate the maximum cover temperature, which is typically lower than the temperature reported by the internal thermal diode. Therefore, your system may be running fine even if the reported "CPU temperature" in the BIOS is higher than the temperature specified here. This does not mean that you're on the safe side, though.

Intel Pentium Pro
Pentium Pro, 256 or 512K L2 cache 85°C
Pentium Pro, 1MB L2 cache 80°C

Pentium Pro temperatures are maximum surface temperatures.

Typical maximum power usage of common CPUs and overclocked CPUs

Apart from the maximum CPU operating temperature, the maximum power usage under typical worst-case conditions (thermal design power) is also essential for selecting a suitable cooling system. To find out about CPU power usage, please check out Chris Hare's Processor Electrical Specifications page. There, you will find values for unoverclocked CPUs running at their specified voltage.

How can you estimate power usage of an overclocked CPU based on this value?

The theory behind calculating the power usage for an overclocked CPU is very simple: Power usage is proportional to clock speed, and proportional to the square of the core voltage.

Before we express this as a formula, let's intruduce the following variables:

Here is the formula:

A simple example:

We want to calculate the maximum power usage of a Athlon "Thunderbird" 1.33 GHz CPU  overclocked to 1.6GHz using 1,9V voltage. From this page, we find out that:

Also, we know that

Values calculated using this method are not very accurate, since I/O voltage and FSB speed is not taken into account. However, they should be precise enough to help you decide what kind of power supply and cooling you need.

The information here is provided WITHOUT WARRANTY of any kind. If you are designing a system and need to have accurate information on the maximum temperature of a specific CPU, please rely on the information provided by the CPU manufacturer, and not the information here.

Last update: December, 2004. Future CPU models (even if they are marketed under the same name/with the same MHz) as the CPUs mentioned here may have different thermal specifications.

All pages copyright © 1997-2010 Tillmann Steinbrecher
Legal information / Disclaimer / Impressum


Does how you talk about your health affect your health?

Who Am I? Does it change when your sick…?

Let’s talk about the stories we tell our selves. Who am I? is the most important story you can tell yourself. What do our beliefs and stories of what illness and wellness mean do to our healing… When you have an autoimmune, or chronic condition, those stories may be even more complex after being told it’s all in your head, get over it or what’w wrong with you….


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Equilateral Triangles, Midpoints, Midlines, Medians, and Geometric Probability

We are coming close to the end of our 14th season of Mathlete Nation’s discovery of mathematics and its mysteries. While playing with a compass used to draw circles, I discovered that with a single line segment, if I set the compass at that segment’s distance, and draw arcs from each endpoint of the segment, the intersection creates a third point.

Fraction Capture with Cube Dice

After exploring dividing a circle into equal sectors and shading in all equivalent fractions, we are now playing the ultimate fraction game: Fraction Capture.

Golden Angle, Factoring 360, Proper Fraction Shading

Continuing our exploration of the Golden Ratio of 1.618….., the children learned how to use a protractor to measure an obtuse angle of 137.5 degrees. We then discussed the difference between an obtuse angle (between 90 and 180 degrees), an acute angle (between 0 and 90 degrees) and a right angle (90 degrees).

Cognitive Reflection Test -- Math Competition

Daniel Kahneman, as a psychologist, who won an economics Nobel Prize. In Thinking, Fast and Slow, Kahneman wrestles with flawed ideas about decision making.


Motrin Or Advil For Neck Pain

What should you be on the lookout for, how many symptoms constitute a problem, and what can or should you do if you believe there is a problem?
motrin 600 mg over the counter
alternating tylenol motrin for fever
motrin or tylenol for toddler fever
motrin or advil for neck pain
motrin equivalent
for example flaxseed crude oil or possibly sunflower necessary oil In case your looking to gain weight
800 milligram motrin
motrin ib 200mg
motrin ib orange pill
motrin breastfeeding mothers
motrin 3 month old

Sports & Outdoor Recreation


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Pair Correlation Between NZSE and AEX Amsterdam

This module allows you to analyze existing cross correlation between NZSE and AEX Amsterdam. You can compare the effects of market volatilities on NZSE and AEX Amsterdam and check how they will diversify away market risk if combined in the same portfolio for a given time horizon. You can also utilize pair trading strategies of matching a long position in NZSE with a short position of AEX Amsterdam. See also your portfolio center. Please also check ongoing floating volatility patterns of NZSE and AEX Amsterdam.
Investment Horizon     30 Days    Login   to change
 NZSE  vs   AEX Amsterdam
 Performance (%)

Pair Volatility

Assuming 30 trading days horizon, NZSE is expected to generate 0.05 times more return on investment than AEX Amsterdam. However, NZSE is 18.82 times less risky than AEX Amsterdam. It trades about -0.1 of its potential returns per unit of risk. AEX Amsterdam is currently generating about -0.21 per unit of risk. If you would invest  812,955  in NZSE on October 20, 2017 and sell it today you would lose (6,757)  from holding NZSE or give up 0.83% of portfolio value over 30 days.

Correlation Coefficient

Pair Corralation between NZSE and AEX Amsterdam

Time Period1 Month [change]
ValuesDaily Returns

Very poor diversification

Overlapping area represents the amount of risk that can be diversified away by holding NZSE and AEX Amsterdam in the same portfolio assuming nothing else is changed. The correlation between historical prices or returns on AEX Amsterdam and NZSE is a relative statistical measure of the degree to which these equity instruments tend to move together. The correlation coefficient measures the extent to which returns on NZSE are associated (or correlated) with AEX Amsterdam. Values of the correlation coefficient range from -1 to +1, where. The correlation of zero (0) is possible when the price movement of AEX Amsterdam has no effect on the direction of NZSE i.e. NZSE and AEX Amsterdam go up and down completely randomly.

Comparative Volatility

 Predicted Return Density


How Dr. Pasha Alleviated Annie’s & Allie’s Allergies

Home / How Dr. Pasha Alleviated Annie’s & Allie’s Allergies
Blog Image - Annie & Allie

When identical twins, Allergic Annie and Allie, first came to visit Dr. Pasha, their allergies were causing them to be extremely cranky and their mother couldn’t take it any longer. The twins described their most common symptoms as itchy & watery eyes, sneezing and nasal blockage. Dr. Pasha knew that even though the girls were exhibiting the same symptoms, their triggers could be totally different. He decided to start with an allergy test to determine what was behind these nasty allergies. Allergy testing is the first step in allergy management for all of Dr. Pasha’s allergy-ridden patients, and only takes a few minutes. He opted for a prick test, which introduces a series of allergens by gently scratching the forearm. If the twins were allergic to a specific allergen, redness would quickly appear. Although Allergic Annie & Allie had the exact same symptoms, Dr. Pasha quickly learned that what was causing the twins’ allergies wasn’t so similar.

Once the allergy testing was complete, Dr. Pasha, Allergic Annie & Allie, and their mother reviewed the results together. He explained that even though the identical twins had the same symptoms, they had completely different allergy triggers! He determined the best course of treatment for Allergic Annie & Allie would be Sublingual Immunotherapy, or allergy drops. He chose this treatment option because the drops are customizable, painless, and can be done at home- so that means no weekly doctor visits for the twins.

“How do they work?”, Allergic Annie & Allie asked, “If our allergies are different, why are we both taking allergy drops?”. Dr. Pasha explained that Sublingual Immunotherapy allows him to create customized allergy drops for each twin, and will include different allergy triggers that cause Annie’s & Allie’s allergies. Sublingual Immunotherapy is the ideal allergy treatment, since there are no needles or injections involved. Slowly, the number of drops, and the concentration of the allergy trigger will be increased. Eventually, the allergy drops will reach a maintenance level, and the twins will be able to interact with their particular allergy triggers, without having an allergic reaction.

Allergic Annie & Allie have been on their allergy treatment for a few months and are already noticing a difference. Dr. Pasha is hoping they’ll soon be 100% allergy-free! Dr. Pasha has created Sublingual Immunotherapy treatments for many of his allergy patients, who are now also allergy-free. If symptoms persist, there are other allergy treatment options for Dr. Pasha to consider to ensure each patient finds a long-term solution. If you’re ready to breathe freely and become allergy-free make an appointment with Dr. Pasha today!

Are Allergic Annie & Allie not convincing enough for you? Hear it from real patients of Dr. Pasha!


Swimming Without Walls

Just published a short story, my first fiction piece, in the Spring 2017 issue of Razor Literary Magazine, a literary magazine exploring the creative process with support from The Mellon Foundation and the Digital Humanities program at Gustavus Adolphus College. Enjoy!

Dix Field Panorama

Talking to kids about climate change

NASA’s Climate Kids

Scholastic’s “Communicate with your kids about climate change”

Yale Climate Connections: Parenting in an age of climate change

Think Progress: How to talk to a 5-year-old about climate change

NOAA Climate Stewards Education Project

5 Pro Tips for Talking to Kids About Climate Change (Without Freaking Them Out)

Rainforest Alliance Climate Educator Guide

Parent Map: Wisdom for talking to kids about climate change

Archive of EPA’s “A Student’s Guide to Global Climate Change”

Climate 101 from Climate Classroom Kids and the National Wildlife Federation

The Essential Principles of Climate Literacy, by NOAA

Climate Communication: Science and Outreach

SciStarter: Science We Can Do Together

Journey North: Wildlife migration and seasonal change

North Carolina’s Candid Critters

Project FeederWatch

Project BudBurst

If you need a good reason to compost your food waste, Kenneth Weiss provides it an article he wrote for Science magazine in May (Vancouver’s Green Dream, Science 20 May 2016, Vol. 352, Issue 6288, pp. 918-921, DOI: 10.1126/science.352.6288.918).  Weiss describes Vancouver’s efforts to combat climate change, among other environmental initiatives, by capturing methane generated in its landfills with extraction wells. Methane can be 30 times more powerful as a greenhouse gas than is carbon dioxide, so rather than allow methane to escape to the atmosphere, Vancouver burns what it collects to generate useful heat.

Then the city discovered that about 40% of the methane generated in its landfills evaded the extraction wells and escaped to the atmosphere. Extraction wells can only capture so much, so Vancouver decided to do what other cities have begun, barring the food wastes and other compostable garbage that generates methane when buried in a landfill.

That meant convincing the city’s population (over 600,000 within the city limits alone) to keep their food wastes and other compostables out of the regular trash and save it for a separate collection. When that separate collection only happened every other week, compliance lagged, but when the frequency increased to weekly, the city experienced a 40% reduction in garbage while compost collections jumped 60%.

It’s coming, folks. We can’t afford to throw food and other recoverable garbage into landfills which not only tosses valuable nutrients out of reach, but also produces dangerous greenhouse emissions. If your town or city collects food scraps for composting, participate in the program. If they don’t, start your own compost bin. It’s not that difficult, and it will combat climate change.

To do science…

Recently came across this quote from T.S. Eliot’s 1942 poem, Little Gidding, and thought it a wonderful description of the scientific endeavor.

“We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.”

—T.S. Eliot

Hungry Birds

ABC Asteroid XYZ

Spacecraft NEAR Shoemaker executed a soft landing on this asteroid, Eros, in 2000.

In “Asteroids Good and Bad” we touched on NASA’s plans to detect asteroids as well as to eventually land on one and “redirect” a piece of it into orbit around the Moon.

Why the interest in these space rocks?

Asteroids have pounded Earth for billions of years, and they’re not done with their mission, as the Chelyabinsk meteor rudely reminded us over Russia in 2013. With no warning it slammed into Earth’s atmosphere and exploded 28 miles up. Even that far away the relatively small 18-meter diameter asteroid fragment’s 500 kiloton equivalent explosion injured over 1,200 surprised people going about their business below it.

So what are asteroids? They consist of rocks and minerals, and come in three varieties: chondrite (C-class) made of clay and silicate rocks; stony (S-class) made of silicate and nickel-iron rocks; and metallic (M-class) consisting of mostly nickel-iron rock. They’re irregularly shaped, usually pitted or covered with craters.

Size matters, especially if one is headed our way. Most asteroids range from thirty feet to 330 miles in diameter, and none have any atmosphere. They orbit the Sun, rotating or tumbling along. More than half-a-million are known, but millions more are out there – exactly how many is unknown – and size matters.

Most asteroids orbit our Sun between Mars and Jupiter in the main asteroid belt. Between 1 and 2 million asteroids larger than 1 kilometer in diameter may exist in the main belt, yet most are still a million or more kilometers away from their nearest sibling. Just 150 have a companion moon, a few have two moons, and some asteroids occur as a pair of relatively equal-sized bodies. Astronomers have even spotted triple asteroids tumbling along together.

Although most asteroids may remain in the main belt, Jupiter’s massive gravity flings them out across the solar system from time to time. At present, 10,003 are known to approach Earth close enough to be considered potential collision hazards. These asteroids are called “Near-Earth Objects” or NEOs, and 861 NEOs have a diameter of 1 kilometer or more. Thus far scientists have tracked over 1,400 “Earth-crossers” that pose a significant threat. But as the surprise arrival of the asteroid over Chelyabinsk, Russia demonstrated, we’ve not yet located every potential collider.

How often do astronomers expect an asteroid to hit Earth? What evidence do we have that asteroids have hit Earth in the past? Where else can we find most asteroids other than in the main belt? How do asteroids get named, and did you know there’s an asteroid named for a cat called Dr. Spock? That’s weird.

The Ozone Protocol: A Climate Change Precedent

The following letter appeared in the January 1, 2016 edition of the News and Observer, Raleigh, NC

News and Observer Letter

It’s deja vu all over again reading George Will (“Another false ‘turning point’,” N&O, 12/17) and Charles Krauthammer (“Obama’s legacy of fiction,” N&O, 12/18) whine about efforts to address climate change. Neither one considers the science or the history. In this case, it’s history worth repeating, not avoiding.

When the world faced the destruction of stratospheric ozone, 12 countries sat down in 1977 to plan how to negotiate a planet-wide pact. It took 10 years, and the outcome was the Montreal Protocol on Substances that Deplete the Ozone Layer, signed by just 24 countries. It’s strength was flexibility, proven in the eight revisions made since 1987.

Now 197 countries are party to a protocol that includes monitoring, reporting, and critically, sanctions for noncompliance. Most important, it’s working, as the rates of emissions of ozone-depleting chemicals have dropped, and since 2000, the ozone layer has begun its slow process of recovery.

International agreements can succeed in addressing a global environmental crisis. The fits and starts seen in the attempts to address climate change might work faster if those with a monetary or political stake in burning fossil fuels would cease their misinformation campaigns, aided by the head-in-the-sand antics of Will and Krauthammer.

—Denis DuBay

P.S. See this article by Jennifer Morgan and Eliza Northrop,  “Form AND Function: Why the Paris Agreement’s Legal Form Is So Important” for confirmation that the Paris deal holds real promise, not unlike the situation with the Montreal Protocol when it was first signed my just 24 countries. It was published online December 16, 2015 by the World Resources Institute.

Stay tuned.

A referral…

Des Latham explores the evolution of definitions for the term “aviation” from 1934 until 2015, and includes the 1934 meaning of “aviator.” As a bonus you find out why the word “avigation” was invented. A nice end-of-the-year aviation post. Whether you fly for business, fun, or out of necessity, and regardless of where you sit, remember what you’re doing up there!

See Navigation, Avigation, and the Sexless Aviator, by Des Latham.


Val D'Or, Que. (YVO /CYVO )General information and contact details of Val D'Or, Que. in Val d'Or, Québec , Canada

Val d'Or, Québec
IATA code
ICAO code

About Airport

  (819) 825-6963
250 Rue de la Météo, Val-d'Or QC J9P 4N9, Canada
Alliances active
  Public/Civil airport; 1 runway(s), the longest is 10000 × 150 ft (3048 × 45.5 m), paved; elevation: 1107 ft (337 m)

Val-d'Or Airport

Val D'Or, Que. is domestic airport located in Val d'Or, Québec , Canada and serves domestic and rare international flights to 7 different destinations, connecting Val d'Or, Québec with Canada. The most popular destinations to fly to from Airport are Montréal–Pierre Elliott Trudeau International Airport, Montréal–Pierre Elliott Trudeau International Airport and Montréal/Saint-Hubert Airport . The longest flight you can take is to Montréal/Saint-Hubert Airport (1:20 hours) .

Carriers such as Air Canada, Air Creebec and Turkish Airlines have regular flights to and from Airport.

Are you looking for the spotting in Val D'Or, Que.? You will see such planes as Pilatus PC-12, British Aerospace Jetstream 32 or Boeing 737-800 Passenger


Search for extraterrestrial intelligence expands at Lick Observatory

New instrument scans the sky for pulses of infrared light

Astronomers are expanding the search for extraterrestrial intelligence into a new realm with detectors tuned to infrared light at UC's Lick Observatory. A new instrument, called NIROSETI, will soon scour the sky for messages from other worlds.

"Infrared light would be an excellent means of interstellar communication," said Shelley Wright, an assistant professor of physics at UC San Diego who led the development of the new instrument while at the University of Toronto's Dunlap Institute for Astronomy & Astrophysics.

The only downside is that extraterrestrials would need to be transmitting their signals in our direction, Drake said, though he sees this as a positive side to that limitation. "If we get a signal from someone who's aiming for us, it could mean there's altruism in the universe. I like that idea. If they want to be friendly, that's who we will find."

"We had to wait," Wright said. "I spent eight years waiting and watching as new technology emerged."

"This is the first time Earthlings have looked at the universe at infrared wavelengths with nanosecond time scales," said Dan Werthimer, UC Berkeley SETI Project Director. "The instrument could discover new astrophysical phenomena, or perhaps answer the question of whether we are alone."

"Searching for intelligent life in the universe is both thrilling and somewhat unorthodox," said Claire Max, director of UC Observatories and professor of astronomy and astrophysics at UC Santa Cruz. "Lick Observatory has already been the site of several previous SETI searches, so this is a very exciting addition to the current research taking place."


Transitional Skincare

Transitional Skincare by Emily Senoff

The weather is changing. Thankfully, right now it’s a gradual shift, but winter will be here before we know it. As the temperature changes, we need to consider how we should switch up our beauty routines. Lip color is one thing, but what about the products we use to care for our lips and the rest of our skin? It’s no secret that when it gets colder out our skin tends to get dryer. This can be prevented and cared for in a number of ways.

Our skin is changing with the weather so that means exfoliation is key. We want to get rid of dead and dull skin cells that aren’t doing anything just sitting there on the top layer of our skin. Getting rid of these cells will make way for fresh and glowing skin and keeps our pores from getting clogged. Start with a light scrub in the morning and before bed to get your skin used to the movement.

One of the most important steps of skin care is toning. Toning our skin balances out the pH level of our skin. After we wash our face, our skin is probably too acidic. This can cause it to become too dry or produce too much oil. When the seasons are changing, we want our skin’s pH level to stay normal.

Keeping our skin moisturized is also key as the weather changes. We will want to consider switching to a heavier moisturizer. During the summer, the air is full of humidity, so a heavy moisturizer probably wouldn’t be fully absorbed by our pores. Now that the air is becoming more dry, we need to make up for that loss of moisture. Instead of reapplying a light cream every 4 hours, a thicker cream twice a day will make sure our pores are fully moisturized.

Switching up just one detail of our skin care routine can allow for some good results, but all of these tips work together to help our skin adjust correctly.


A couple of cockatiels.

The male cockatiel, right, has more
distinct colors than the female, left.

The easiest way to tell male from female cockatiels is by their coloring. Males will have brighter color in their faces with more pronounced cheek marks, while females will have more of a blended look.

Unfortunately, looking at colors to determine a cockatiel's gender has its faults. For one thing, the coloring may not fully develop until the bird is a little older. Another thing is that in some mutations, such as the Lutino or the Pied, the males and females look almost exactly the same.

Whistling patterns

Another way to determine your birds gender is by how much it whistles. Generally males will whistle more often than females, and they will pick up more tunes. Females generally do not learn to talk either, although there are always exceptions to the rule.

Rembrandt flexing.

Rembrandt, my male cockatiel,
flexes his wings before whistling.

Lastly, males have different habits than females. For one thing, males will sometimes spread their wings a bit to look like they're flexing (especially when whistling).

Males will also bang on the bars of their cages from time to time, presumably to attract females.


Wednesday, May 23, 2012

Review of Constants in Context (Bevans and Schroeder 2004)

Constants in Context: A Theology of Mission for Today is a brilliant fusion of church history and missiology.  It takes it’s place right beside Transforming Mission as the reference book for mission theology. This book offers a panoramic view at how different Christian traditions in historical periods have engaged in mission over the last 2,000 years. In order to explain these developments and point a way forward for mission in the twenty-first Century, Catholic missionary scholars Bevans and Schroeder use three types of theology to show how each type has struggled with issues that have remained constants throughout the history of the church in mission. Answering the questions (the questions themselves are the constants) that every church at all times has struggled to answer amounts to forming a missiology: (1) Who is Jesus Christ and what is his meaning? (2) What is the nature of the Christian church? (3) How does the church regard its eschatological future? (4) What is the nature of the salvation it preaches? (5) How does the church value the human? and (6) What is the value of human culture as the context in which the gospel is preached?” (Kindle Locations 1111-1115).

The three types of theology find their representatives with the early church fathers. “Type A” is represented by Tertullian and is called “law.” Humankind is fallen and only by special revelation can be saved. The mission of the church in Type A is to save souls and start more churches. Type B is represented by Origen and is called “truth.” Human salvation is already realized through the best of human reason. The mission of the church in Type B is to invite others to discover the truth. Type C is represented by Irenaeus and is called “history.” The church is committed to the proclamation and service of Christ’s lordship over all creation. The mission of church in Type C is the liberation and transformation of the world.

One weakness of the book is the caricatures present in the typologies (although I understand the need for simplification). For instance, Type A is unfortunately called “law” simply due to the penal understanding Christ’s death. A much better word to describe Type A would be “revelation” because of the high value placed on God’s initiative in that type. Furthermore, descriptive words for Type B and C could be “exploration” and “transformation,” respectively. I doubt the liberals of Type B would want to be identified with “truth!”

Another weakness is the understanding of mission in the book of Acts. As the authors correctly state, the book of Acts reveals a tension between Jew and Gentile, and how the apostles adapted ministry approaches and even theology as the socio-religious context changed. However, the constants in the book of Acts are the acts of evangelism and church planting. Acts chapter 29 would involve a new ministry approach to church planting in a new context. For the authors, the changing contexts seem to imply that these acts are secondary or optional in mission. “The church only becomes the church as it responds to God's call to mission, and to be in mission means to change continually as the gospel encounters new and diverse contexts” (Kindle Locations 2058-2059).

As an Evangelical, I can see myself in each of the types, although I identify most closely with Types A and C (the Bible is marginalized in Type B). As Catholics, the authors identify mostly with Types C and B. Therefore the book’s proposal of mission as “prophetic dialogue” largely omits Type A’s emphasis on conversion and church planting in mission. I feel that when speaking of the mission of “the church” it is important to make a distinction between the local church and the universal church. The local church seeks to multiply itself (Type A), whereas the universal church works for the transformation of societies (Type C). This could be a helpful corrective to their Catholic missiology. Especially in unreached areas of the world, how can there be any sustainable spiritual power needed for radical culture transformation without discipleship that happens in the context of conversion and church planting?

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Caesarea Philipi Spring

Caesarea Philipi Spring

A peaceful place to stop for reflection and prayer on a busy Holy Land tour, Caesarea Philippi is the location of one of the largest springs feeding fresh water into the Jordan River. Called the Banias in Hebrew, this spring is located at the base of Mount Hermon, adjacent to the site of an ancient Roman city that was called Caesarea Philipi.

Scripture does not describe Jesus entering the city itself, but he was nearby. This is the area where Jesus asked his disciples who they thought he was, and their various answers, including the Confession of Peter, are recorded in the Synoptic Gospels. Another event that took place in the area was the curing of the woman from Paneas, who had been bleeding for 12 years.

Visitors here will marvel at the archaeological remains at the site, including a shrine to the pagan god Pan and the ruins of the ancient Roman city. The spring emerges from a large cave that subsequently became a pagan shrine; sacrifices were thrown into the cave to appease Pan. Near the cave is a rock with inscriptions dedicated to various pagan gods and to those who donated to the shrine.

Many tours here follow the trails from the cave over the Roman bridge and past the Crusader tower, to the only active water-mill in Israel. Walk through the gatehouse into the ruins of the Crusader town to reach the Banias Waterfall. The waterfall is only 10 meters high, but it is one of the most beautiful falls in Israel. From the observation point, the trail continues down to the pool at the bottom, where you can cool off on a hot day.


Reality of Mecca

Mecca is said to be the most sacred place on earth by Islam doctrine. This is the origin of Islam religion. When people speak about religion, people would think of how Mecca is suppose to be like. No one can enter there except Muslims qualified for it. For them, only deserving people can enter the holy place knowing that not all Muslims are called holy. Mecca is a built grand place where there are holy sites and holy belongings of their God.

Haji, pilgrimage to Mecca is a treasure that most Muslims desire to achieve even at least once a lifetime. This is because they believe that whoever sets his foot in Mecca can be guaranteed of a blessing that can not be imagined by an ordinary man.

This may also bring people a name to themselves. If they want to go far, they mean they want to go to Mecca because this may customize the being of a person. While no ordinary men can go there, others are just envious of it?

They too want to know the footstep of Muhammad their prophet when they reach Mecca. The rites and rituals that they do in Mecca originated from ancestral respect for example from Abraham. Actually, they believe that their Ancestor is Ishmael whose mother is Hagar.

They come to conduct the any religious rituals inside the holy sites of Mecca. For example, they intentionally kiss the black stone in the Kaaba, the dwelling place of Allah. Unless they kiss this one, Haji can be considered meaningless.


CSC 161 Grinnell College Spring, 2010
Imperative Problem Solving and Data Structures

Laboratory Exercise on Integer Processing

This laboratory exercise provides practice with

This lab utilizes two programs for processing integer values:

You should read Binary Representation of Integers in C and Java by Christine Wright and Ramuel Rebelsky, with revisions by Marge Coahran and Henry M. Walker.

Integers and Their Representation

Your reading described how positive integers are stored within a computer. This part of the lab asks you to apply your understanding from this reading to both positive and negative integers, as observed on a computer.

The Fixed-Size-Storage Approach for Integers

The first several experiments in this lab utilize a program integer-rep. This program is written in the C programming language. In this language (and in most others), integers are stored using a fixed-size-storage approach, as described in the reading.

  1. Copy ~walker/c/fluency-book/integer-rep.c to your account and compile it. Review the program listing, and write a paragraph describing how the program works.

  2. Run integer-rep, and use the operation "A" to add 1 to the values. Then use "A" again, and again. (When starting with the value 1, the integers will become 2, 3, and 4.)

    Review the binary representation of each integer, and explain why it has the binary representation printed.

  3. Use the "M" option 3 times, each time multiplying the values by 2. The integers will become 8, 16, and 32. Explain why the binary representation of each integer looks as it does.

  4. Use the "I" option to set the values to 5. Explain the binary representation that results.

  5. Use the "I" option to set the values to 32. Then use the "M" option several times to multiply by 2 to obtain the values 64, 128, 256, 512, 1024, 2048, 4096, 8192, and 16384. Explain how the pattern of 0's and 1's obtained changes as you go from one of these numbers to the next.

Now that we have some experience with non-negative integers, we look at a few negative numbers.

  1. Use the "I" option to set the program's values to -1, and describe the binary representation that you see.

  2. Use the "M" option to multiply the program's values by 2 several times to obtain the values -2, -4, -8, -16, ..., -8192, -16384, -32768. Describe a pattern in the 0's and 1's obtained for these numbers.

  3. Use the "I" option to enter several more negative integers and several more positive integers. Explaining the meaning of the initial (leading) bit in the fixed-size-storage approach for integers.

  4. Use the "I" option to enter -32768 again. Then use the "S" option to subtract 1 from -32768. What result do you get with the 16-bit integer form and with the 32-bit integer? Explain why you get each result.

  5. Use the "A" option to add 1 to your result of step 9. What can you conclude about the maximum integer that can be stored in 16 bits (assuming the processing is allowed to handle both negative and positive numbers)?

  6. Use a similar approach to find the maximum integer that can be stored in a 32-bit (signed) integer. Explain your result and how you got it.

  7. What happens if you try to use the "I" option to set integer values higher than this maximum for 32-bit (signed) integers? Describe what happens in at least a few test cases.

  8. Read the news account of the computer-related difficulties that grounded all of Comair's flights on December 25, 2004. The article states, the computer system for Comair "has a hard limit of 32,000 changes in a single month." Other articles confirmed that this problem was due to a field in a database that was designed as a 16-bit integer.

    1. What do you think was the real (not rounded) limit for changes to crews at Comair?

    2. From what you know about the fixed-storage-approach for storing integers, identify one or two ways this problem could have been avoided.

Variable-Size-Storage Approach

While integer-rep.c illustrates how integers usually are stored in computers, a few environments utilize the variable-size-storage approach. The Scheme programming language and environment illustrates this alternative approach. With variable-size-storage, the binary representation does not have a 16-bit or 32-bit form; rather, the binary representation uses as many bits as needed.

  1. Run ~walker/scheme/fluency-book/integer-rep, written in Scheme.
    This program has much the same interface as the C version you used above.
    Check that the operations for entering integers, addition, subtraction, multiplication, and division work as they did with the C version:

    1. Use the "I" option to set the internal integer to 5.
    2. Use the "A" and "S" options to add and subtract 1, respectively.
    3. Use the "M" and "D" options to multiply and divide by 2, respectively.
  2. Use the "I" option to enter very large positive or negative numbers (e.g., over 20 digits). For example, try the values that you used in step 12, and then try even larger numbers. Explain what happens.

  3. With your large integers from step 15, use the "A", "S", "M", and "D" options to determine if simple arithmetic still works for these large values, and describe your results.

  1. Review your experiments with both the fixed-size-approach and the variable-size-approach for storing integers, and write a paragraph summarizing the observations you have made.

Work To Be Turned In

This laboratory exercise coordinates with Chapter 2 of Walker, Henry M., The Tao of Computing: A Down-to-earth Approach to Computer Fluency, Jones and Bartlett, 2005.

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Helpful resources

Whether you're a dancer or the parent of a dancer, these resources have been gathered by the experts at Motions Dance and Fitness Shoppe in order to better assist and equip you with the tools you need. If you ever have any further questions, always feel free to ask by emailing, calling, or stopping by our shop.


Source: PWInsider

- TNA X Division Champion Sanada successfully defended his title at Saturday's Wrestle-1 event in Japan. He defeated Seiki Yoshioka in the show's main event.

- There were rumors going around that TNA released Lei'D Tapa because of her lack of skill and because she was seen as a "ticking time bomb" to management. Tapa confirmed it was TNA's decision to release her but denied those rumors on Twitter. She is already back working for OVW.


International Court of Justice rejects landmark Marshall Islands nuclear case

Judges, with presiding judge Ronny Abraham of France, fifth from left, enter the World Court in The Hague, Netherlands, Wednesday, Oct. 5, 2016. (AP Photo)

The 16-judge bench at the International Court of Justice (ICJ) ruled there was no evidence that Majuro had had a prior dispute with any of the three nuclear giants or sought bilateral negotiations on the issue.

"The court upholds the objection to jurisdiction" raised by each of the countries, presiding judge Ronny Abraham said in separate rulings, and therefore the tribunal "cannot proceed to the merits of the case."

The tiny Pacific island nation was ground zero for a string of devastating nuclear tests on its pristine atolls between 1946-58, carried out by the United States as the Cold War arms race gathered momentum.

After the hearings at the tribunal based in The Hague, the Marshalls said it will now "study the ruling" which is final and without appeal.

"Obviously it's very disappointing," Marshall Islands lawyer Phon van der Biesen told reporters.

Initially in 2014, Majuro had accused nine countries of failing to comply with the 1968 nuclear Non-Proliferation Treaty, which seeks to inhibit the spread of atomic bombs.

The country originally filed cases against all nine nations that have declared or are believed to possess nuclear weapons: The U.S., Russia, Britain, France, China, India, Pakistan, Israel and North Korea. But only the cases against Britain, India and Pakistan got to the preliminary stage of proceedings, as the ICJ already refused to take up cases against the other countries which do not recognize the court's jurisdiction.

Israel has also never formally admitted to having nuclear weapons.

The Marshall Islands had argued that by not stopping the nuclear arms race Britain, India and Pakistan had breached obligations under the treaty -- even if New Delhi and Islamabad have not signed the pact.

The treaty commits all nuclear weapon states "to pursue negotiations in good faith on effective measures relating to cessation of the nuclear arms race at an early date and to nuclear disarmament."

'Islands vaporized'

At a March hearing, Majuro's lawyers painted a vivid picture of the horrors seen after 67 nuclear tests were carried out on Bikini and Enewetak atolls.

"Several islands in my country were vaporized and others are estimated to remain uninhabitable for thousands of years," Tony deBrum, a former Marshall Islands foreign minister, told the court.

The so-called "Operation Castle" tests in March and April 1954 were particularly devastating and resulted in massive contamination because of the nuclear fall-out.

"The entire sky turned blood-red," said deBrum, who witnessed the explosion of the largest-ever US-built nuclear device called "Castle Bravo" as a nine-year-old boy.

Critics have argued however that the ICJ action is a distraction and that the islanders' real fight is with Washington, which carried out the tests in their backyard.

They contend that the case has no relation to the victims' claims for increased compensation, better health care and clean-ups to render the sites habitable again.

Even if the case has no direct impact, the Marshall Islands' residents "perhaps feel that the more the difficulties with nuclear weapons are brought to the public consciousness, the better," said Jens Iverson, assistant professor of Public International Law at Leiden University.

"They may hope that the world may become a safer place," Iverson told AFP.

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Insider Threat Detection in a Borderless World

The wide scale adoption of hybrid data center and cloud IT infrastructures is creating new security gaps, risks and an expanded threat plane. In this borderless world, some cloud solutions are completely outside of IT’s purview: sensitive data is stored globally and is being accessed by increasing numbers of employees, partners and customers.

Traditional approaches to defending the network – like using a firewall to keep threats outs – no longer suffice. Networks are no longer contained within the four walls of the enterprise, but instead extend out to distributed IT infrastructures via the cloud. Meanwhile, detecting insider threats in this new environment also requires a different approach. One that combines securing applications, locking down identities and monitoring how identities use applications.

According to the 2017 Verizon Data Breach Investigations Report (DBIR), the majority of insider attacks involve end-users absconding with data in the hope of converting it to cash somewhere down the line (60%). The second most common activity is employees engaging in unsanctioned snooping (17%). These misuse scenarios are reflected in the types of data compromised. Personal information and medical records (71%) are targeted for financial crimes, such as identity theft or tax return fraud and occasionally just for gossip value.

Securing Applications

Organizations must be able to secure applications in an automated fashion – there are not enough security professionals to monitor all employees, their locations and the myriad of applications they use to access sensitive data. Both the applications and the employees that use them are fragmented. They don’t exist in a single space, use a single device or have a single entity.

Therefore, organizations must be able to track individual identities as well as the applications themselves, to determine when a user is accessing the application or certain data elements, such as payment card information, in an unauthorized fashion.

In addition to these complications, the sheer number of people it would require to adequately monitor threats and the bandwidth necessary to handle all access requests for company data, particularly during peak periods, is manually impossible. This is where user behavior analytics and machine learning can help secure application usage.

Locking Down Identities

Traditional identity frameworks often make it cumbersome to limit appropriate access privileges to individual identities. This often leads to “rubber stamping” cloned profiles when provisioning new identities and providing excess access rights that are often not required for specific roles or job functions.

To limit insider threat risks, identities need to be locked down. The challenge for many organizations is determining not only which identities have access to applications they should not, but also which have privileged access permissions within applications they need to perform their jobs.

One way to address this problem, involves the use of identity analytics (IdA) to monitor all access permissions and activity associated with an identity regardless of the device, application or data to pinpoint excess privileges so they can be revoked. Using IdA reduces the access threat plane that can be exploited by malicious insiders.

Monitoring How Identities Use Applications

According to the Verizon DBIR, 82% of insider and privilege misuse breaches take months and years to detect, rather than weeks or less. By monitoring user behavior using machine learning and analytics, a company can identify anomalous actions which warrant further investigation by human security analysts. So, rather than looking for a code acting in a known malicious way, this approach instead focuses on individual identities and their behaviors.

In some instances, risk scores can determine an automated risk response such as step-up multi-factor authentication, remediating access outliers or issuing a self-audit to the user and manager to leverage their unique context not found within a SOC.

Access to the company’s data needs to be limited to specific, legitimate uses. While someone in marketing have legitimate reasons to access customer purchase history for targeted marketing efforts and to develop more wide-reaching marketing campaigns, the marketing department doesn’t need to have access to the customer’s payment card information. Similarly, the accounting department has a legitimate reason to have access to payment card details, particularly if there’s a disputed payment, but doesn’t need access to other personally identifiable information.

Using automation that relies on machine-based learning to identify user behavior that is outside the norm helps companies identify unknown risks. The model uses Big Data, combining different analytical approaches to identify threats, escalating each as necessary to further analytics and, if needed, to human intervention.

By taking this three-pronged approach, which incorporates new identity and behavioral analytics techniques and machine learning, companies can better protect themselves from insider threats. In contrast, CISOs who limit themselves to more traditional security approaches will leave their companies exposed in today’s borderless world.

What’s Hot on Infosecurity Magazine?


Brandy Hartman / Blog

Raising breast cancer awareness-MARIE 1927-1987

I have created a myspace page in honor of my grandmother, Marie, who died of breast cancer. I want to raise awareness for breast cancer, as well as show people what a wonderful person she was to everyone.

National Fibromyalgia Association (raising awareness)

I was recently diagnosed with this disease and I want to spread the word, Hopefully I will raise awareness, as I have tried with Breast Cancer. Please visit NFA and show your support:

About Fibromyalgia Fibromyalgia (pronounced fy-bro-my-AL-ja) is a common and complex chronic pain disorder that affects people physically, mentally and socially. Fibromyalgia is a syndrome rather than a disease. Unlike a disease, which is a medical condition with a specific cause or causes and recognizable signs and symptoms, a syndrome is a collection of signs, symptoms, and medical problems that tend to occur together but are not related to a specific, identifiable cause. Fibromyalgia, which has also been referred to as fibromyalgia syndrome, fibromyositis andfibrositis, is characterized by chronic widespread pain, multiple tender points, abnormal pain processing, sleep disturbances, fatigue and often psychological distress. For those with severe symptoms, fibromyalgia can be extremely debilitating and interfere with basic daily activities. Whether you have been diagnosed with fibromyalgia or suffer from its symptoms, or have a family member or friend with the disorder, this section is designed to provide you with a better understanding of this chronic pain disorder that affects millions of people worldwide.


Blind Justice

Canaan, a mysterious gunfighter left nearly blind from Civil War combat, roams through Mexico with a baby he has sworn to protect. As he passes through a border town, U.S. Cavalry officers come under attack from bandits. With some reluctance, Canaan steps in to help the soldiers.

DIRECTOR:  Richard Spence

STARRING:   Armand Assante, Elizabeth Shue, Robert Davi, Adam Baldwin, Ian McElhinney, Danny Nucci

PRODUCERS:  David Heyman, Neal Moritz, Rick Nathanson

HBO  1994


Hawaiian Born, Northern raised and Southern fried, Kenny Keawekane has been performing, teaching, and choreographing professionally for the past 8 years.  He comes from a long line of Hawaiian musicians and performers.  Jack of all trades, master of none, he is constantly striving to be a better performer/artist, engulﬁng himself in other types and styles of venues and dance, learning what he can from music editing, videography, costume and prop design, and technical and stage direction.  He loves all forms of art and creativity and loves to collaborate with other artists or styles of art and dance.  Self-taught, he was a closet dancer from ages 10 – 19 learning everything from dance movies, music videos, and YouTube.  He was eventually noticed by a dance crew out of Pennsylvania, House of Gotti, before he moved to Tennessee.  After moving, he decided to take dance a little bit further.  He went to a Jr. Teacher Workshop Program to become a dance assistant and the dance studio made him the Hip Hop Teacher instead.  Since then, he has taught at numerous facilities in Bedford, Rutherford, Coffee, and Franklin Counties. He started doing community theater to build his talent and has choreographed and performed in numerous shows including Hairspray, Addams Family, Peter and The Starcatcher, Rocky Horror Picture Show, All Shook Up, and Gypsy. He is the choreographer of “History Told By Her”, a Michael Jackson tribute, which donates all of the proceeds to a selected charity.  He donates his time to many charities and community projects teaching dance and/or performing.


Wednesday, August 30, 2017

Interesting Geometry problem (6 Rectangles puzzle) - Solved in various ways

I came across this interesting problem and thought to share this with my students...

Students started working on this and after about 5 minutes, one of them was ready with her solution...

I would suggest you to try solving this problem on your own first, and when you are ready with your solution, you can read further to see how these students have 'seen, approached and solved' it....

Vaishnavi's 1st attempt

Her approach was to count all the sides of 6 rectangles (222 x 6) and remove the ones that are not to be counted. So according to her, the answer was 999. I think, you would have figured out the mistake she did.

Yes, she forgot that the overlapping sides need to be removed twice and not just once..

But, I am glad she could quickly think and work out her error after overhearing the final answers of two of her peers, while they were explaining me :)

So this is how she finally presented her solution to the class. Note her work below. See her erased work in the yellowed part. Here, she explained that how the red segments are actually two segments when the rectangles are separated and hence need to be removed twice.

Vaishnavi's 2nd attempt

If you are wondering what her 222 and 111 represents, then this is what she had done..

She has combined the two red breadths and two red lengths (see the 4 sides with vertical strokes) to form one rectangle (222)......what remains is one length (made up of two pieces) and one breadth which is same as half the perimeter i.e. 111

Tanvi's explanation to me

Tanvi's explanation to the class

To explain her approach, let me just make another diagram:

Diagram - to understand Tanvi's approach

Her two 444s represents perimeters of four rectangles..  Now she understands that this sum 'includes' the segments that were not to be included --- the overlapping segments.

From here, she used the same approach as that of Vaishnavi to get 222 and 111. Thus she finally gets 999 - 333 = 666

Siddharth's method
He "traveled along the boundary" of the shape and counted the lengths and breadths of rectangles it included...  He calculated 6 lengths and 6 breadths, thus amounting to thrice the perimeter which leads to 666.

Sahil's method

To understand Sahil's method, let me re-draw the figure again...

Diagram - to understand Sahil's method

I think the above diagram would be self explanatory...

Yes,.... this is how he beautifully saw and made three rectangles out of all the pieces on boundary to get three equivalent rectangles thus amounting to 666.

I thought at least one of the two remaining two students would solve the problem using my method.. However, Rohit's method was same as that of Sahil and Laxmi too had used the same approach as that of Siddharth....

So I asked them if they wanted to know how I solved this problem...

And there was a loud Yes !  :-)

So the perimeter = 6 breadths + 6 lengths = 222 x 3 = 666

They understood the "sliding" that I had done.... But I thought to interrogate them further....

"How can I be sure that when I slide upper block to the left such that pt. D coincides with C, then F too will exactly coincide with E?

Rohit jumped in...

"Sir its obvious..... that x = a...."

"There is nothing obvious in Maths, Rohit... Can you prove this statement ?"

He began...

k = y + a

k = x + y

k = a + b

So, y + a = x + y = a + b

So,  a = x   and  y = b

Two students were absent when we did this problem.. So they solved it the next day... One of them, Jitu, used the same approach as that of Siddharth......

While the other student, Kanchan, gave me a surprise !!

Kanchan just removed the three bricks on the top layer and bottom layer. So according to her. the given shape gets converted into this equivalent shape for finding the perimeter:
Diagram to explain Kanchan's method

So, perimeter of the given shape = 222 x 3 = 666

1) Did you understand her method?

2) How did you solve this problem?

3) How about trying this with your students? Plz do share your classroom experience...

4) Which approach did you like the most? Why?

5) Plz share your views and comments on this article......

Thanks and Regards

Rupesh Gesota

Monday, August 21, 2017

Interesting exploration - Thanks to 18th of August :)

On 8th August, I saw an interesting math post on my fb timeline:

Today's date: August 8

818 is the smallest palindrome that can be expressed as the sum of squares of two prime numbers.  818 = 17^2 + 23^2

As usual, I forwarded this message to many teachers and parents groups... and finally shared this my young group of maths lovers i.e. my students, reading the same message as above, with the only difference being... I did not write the two prime numbers: 17 and 23

So naturally they started working on this problem... This is how they all worked together...

1) Since the last digit of sum is 8, the two addends can end in (1,7), (2,6), (3,5), (4,4), (9,9), (0,8) .... However square numbers cannot end in 7,2,8 and 3. Further, squares of primes cannot end in 4 as well. So the only option is (9,9)

2) The two prime numbers should be less than 30 because 30^2 = 900

3) In fact they should be less than 29, because 29^2 will be more than 818.. When I probed them for the reason, they said that the difference between 29^2 and 30^2 will be 29+30 = 57

4)  Since the squares are ending in 9, so the primes will end in 7 or 3 i.e. both ending in 3, both ending in 7 or one ending in 3 and other in 7

5) So they started with the options that can be easily eliminated like --

(i)   (17, 17) : Since 17^2 < 400, so their sum will be < 800

(ii)   (23,23) : since 23^2 = 529, so sum will be > 1000

(iii)  (13,13) and (13,17) : same reason as that of (i)

(iv)  (23,3) and (23,7) :  sum < 600

(v)   (23,13) :  Digital root of 23^2 + 13^2 = 7 + 7 = 5. But the required digital root is 8 (8+1+8)

If you see the snap, one of them did a mistake here... She multiplied the DRs of the 2 primes instead of adding the DRs of their respective squares... But this was smartly caught by other student while working on the next option i.e. (17,23)

(vi) (17,23)  : They said that since this is the only option left and because my claim is correct, hence (17,23) "has to be" correct.... and we verified this using three ways

a) Estimation: 23^2 = 529 and 225 < 17^2  < 400 .. So their sum is between 850 and 930

b) Digital roots:  23^2 + 17^2 = 7 + 1 = 8 which is same as required DR

c) Actual calculation

When I asked them, as to why they did not use the estimation for (23,13) they said they did not want to add the two big square numbers....(529 + 169)   :-))

How would have you or your students solved this type of problem?

Rupesh Gesota

PS: These students are from marathi-medium government school, class-7 and 8....To know more about the math enrichment program, check the website

Tuesday, August 15, 2017

Celebrating Pythagorean Triplets Day on our Independence Day

I think almost the whole world must be aware, by now, about the interesting fact about 15/08/17 --

I had received this message over whatsapp couple of days before this date itself... Like for anyone, it was a delightful surprise for me too to face & digest this fantastic fact.. And I did not miss this opportunity to share this message with almost everyone in my circle esp. students, teachers and parents on our Independence Day....

While many replied back with the Ooohs and Aaaahs, but there was one guy who did something more.... He is aware of the crazy math experiments that I do with my bunch of government school students... So he asked me "Do your kids know how to manufacture pythagorean triplets (PT) thereby proving that they are infinite in number?"

I replied - "No, I haven't worked on Pythagoras Theorem with them yet... But I am planning to do that today.."

He -- "My son stumbled upon Euclid's proof of 'infinite triplets' in 8th class.. Try to make that happen with your kids (students)"

And while saying this he also shared the link to his blogpost:

I was planning to read this post later, but luckily I clicked on this link - only to get highly motivated.. I now wanted to try this out with my students immediately... I was confident that my students would love to crack this code....

So I scrapped my plan A i.e. to first work on the geometric interpretation and different proofs of Pythagoras theorem....and zoomed into my class with plan B...

After our daily ritual (meditation and mental maths), I shared with them this interesting fact of the date and how it has beautifully coincided with our Independence day this year...

I was little surprised and even disappointed when I could not see much expressions of wonder on their faces as I had expected ! However, I forged ahead, sharing with them the details of ---

1) pythagoras theorem (the right angled triangle, hypotenuse, etc..)
2) with the conventional example of 3,4,5
3) idea of pythagorean triplets -- how (8, 15, 17) is one of those..
4) and finally the story of Euclid - as how he could prove there are infinitely many PTs...

To this, one of my students exclaimed - Yes, there will be infinitely many such triplets because there are infinitely many natural numbers....

True.. But mathematics demands proof ! How can you do so?

They look puzzled to this. So, I asked them -

"Ok, you all seem to believe that there will be infinite PTs... Can you give some more other than (3,4,5) and (8,15,17)?"

Now I could see them trapped.... Some of them started scribbling on their books, while others were still staring at these two sets, probably to get some clue (pattern)...

I could not resist but teased them after 2-3 mins....  "So? Infinite, right?"  :-)

And now I could see couple of them trying to escape my sight..  :-)

And soon, there was a guess -

"Sir, what about 30, 40, 50 ?"

"Are you sure or are you guessing this?"

"I am not sure..."

"How about verifying this?"

And in another moment, the other student reasoned -- "Sir, it will obviously work !!"

I found the other students relieved with this solution...

"Sir, then even 80, 150, 170 will work..."

I wrote this triplet on the board... "More?"

One of them reluctantly guessed -- "How about multiplying 3,4,5 with 2?"

"I am guessing 6,8,10?"

"Okay... Can we all check this case....?"

The class verified this and by now, all of them could figure out the game....

"Sir, we can now multiply 3,4,5 and 8,15,17 with any number and get more PTs...."

"Good.... and how do we represent this fact?"

I wrote on the board what he told me --- (3x, 4x, 5x)

"what is x?"

"any number..."

"So can I put 0?"

He understood what I meant....

"No Sir.... x is a natural number..."

Now, this realization made me share with them about "Primitive Pythagorean Triplet"

For those unaware -- A Pythagorean Triplet (a,b,c) is said to be Primitive Pythagorean Triplet if the GCD of (a,b,c) = 1  means there is no other common factor among them other than 1....

for example: (3,4,5) , (8, 15,17) are PPTs but  (30,40,60) and (6,8,10) are Non-primitive PTs

But you know what?  I did not give this 'explanation' to my students...

I just told them --

"Look... I got to know from you that we can make Infinite PTs from (3,4,5) and (8,15,17).... However, these new sets of triplets formed are not the Primitive Pythagorean Triplets....   But (3,4,5) and (8,15,17) are PPTs....

So can you tell me now, what do I mean by PPT?"

And I was so happy that one of them could say this ---
"the numbers in the triplet should be co-prime!"

So then I asked others - Whats co-prime?  And they responded very well -- "numbers with gcd=1" ... "numbers with only one common factor i.e.1"

They thought that their job was done.... since they could make infinite PTs from the two given PTs...

But soon, I played the Devil......

"Hey wait guys.... what Euclid proved is that there are infinitely many PPTs and not just PTs... So can you give me some more PPTs....?"

And it was worth watching their faces again !!   :-)

There was silence for almost 5 minutes... All engrossed in research.... It was extremely difficult for me to Not give them any hint... But when I saw that some of them were not able to go ahead at all... I thought to intervene,...

I wrote the expression 3^2 + 4^2 = 5^2 on the board.... and asked them...

"What type of numbers are related by this equation?"

 "Natural numbers!" came an instant answer...   :-) :-)

"ohk true.... but are these numbers 9, 16, 25 something more?"

"yes, they are square numbers...."
"Yes, True..... So do we know anything more about square numbers that can help us here?"

I was unaware that Kanchan had already made this observation,... I understood this when she answered to this question instantly....

"Sir, their differences are odd and hence we can now look for....."

Her enthusiasm conveyed to me that she had made that 'million dollar observation' and so I stopped her immediately, so as to not reveal more clue to other students.... I just gave her thumbs up, signaling her to go ahead...., while others were completely puzzled with our exchange of expressions and sign language...

I was pretty sure by now that - not only will kanchan crack this in next few minutes, but even others will pick up the clue to get some breakthrough.... So I waited for 5 more minutes...

I found Kanchan engrossed in her work, while I found others still struggling.... So I decided to write down the list of square numbers on the board....

I asked them -- "Do you remember we had done many observations relating to this list of square numbers?"

"That's all then,.... Its just one of those imp. observations that's going to help you solve this problem at hand..."

Kanchan got in -- "Sir, you have given them a good hint now..."

"True.. Lets see what they do now....."

I found few of them interacting with others after this interaction..... and then, she raised her hand...

"yes kanchan... give me the Pyth Triplet you found..."

" (5, 12, 13) "

"Can others verify this?"

And they agreed for its correctness...

"Can you find one more?"

Silence dominated the class again.... when finally she broke it with her another announcement...

" (7, 24, 25) "

I verified this on the board with the class.... the result surprising other students.

"Kanchan, can you make the formula now, that will give you the list of all the PTs?"

This was the first time when I was not asking my student to explain her thought process before asking her to work on the extension of the problem..... The reason for this change in approach was my awareness that she was on the 'right track' and I just wanted her to leverage on her buzzing flow of thoughts/ strategy... I had decided to interrogate her after her stint on the formula (generalization) part....In case she gets stuck, then I will grab that opportunity to probe her about her thought process...

While she was again engrossed in her book, I decided to throw some more hint to other students...

"Can you notice something in the two triplets she has shared?"

Almost all of them replied -- " two out of three are consecutive numbers...."

Kanchan looked up at me with a smile.... Probably she knew what I was doing....

By this, I found one of them - Rohit - started staring at the chart of first 100 square numbers, that we have pinned up on our board since long....

Its amazing that we all have used this chart so many times till now in various situations... I never knew during my school days, that square numbers are so resourceful...

It was difficult for me to wait... But Patience has always yielded more beautiful results....and this time was no different.....  She approached me with her work after 10 minutes...

Of course, I made her explain/ reason in detail what she had done and how her line of thinking about the previous two pythagorean triplets... and further how she constructed the formula, the terms that she required, etc....

I choose to not share these interesting interactions with you directly... as I first want you to think about this on your own.... (the above hit is anyways there with you now)

But as you see, we realized that the formula has some bug and it does not yield the desired triplet for y=2...   So she went back and started working on this....

Meanwhile, Rohit raised his hand.... He had got this triplet...

"Tell loudly..."

" (9, 40, 41) "

The class verified.... It was correct......

"Good one.... How about one more....? But this time, don't tell the answer aloud... Just write and show it to me....."

Soon he came to me with this ---    (11, 60, 61)

"Hmm.... correct.... So it seems you too have made some observations now...."

He nodded with a smile....

He went and Kanchan came back with the second version of her formula, which she was confident of being correct this time......

The most satisfaction part for me as a maths teacher was when she told me that she could "find out the mistake" she had done in her previous work (formula)...and secondly she could also successfully correct it with the associated reasoning...

While I was congratulating her for this effort, she exclaimed --

"Sir, but this does not give us all the PPTs.... The (8, 15, 17) is left out...."

Isn't this observation worth appreciating again?

"True.... So what will you do now to include even such triplets?"

"Hmmm... May be there will be another formula to include the family of such triplets..."

"May be you are right.... So what do we do?"

"I will work on it....."

"Excellent.... I will wait for your work....."

And meanwhile, Rohit had already queued up.....

"Yes! "

"Have you verified it?"

I asked him for the explanation.... and he too gave a very satisfactory one.... the mathematical thinking was evident....

I called up Kanchan for having a look at this.... and she could quickly infer...

"Its same.... He has just used a = 2x +1 in the representations and I have used the term 2x+1 everywhere...."

"Correct... any advantage?"

"This looks neater.", she smiled & further added that, "he could have also written c = b + 1 instead of writing the whole expression for b again in the equation for c..."

I looked at Rohit.... He agreed....

"So now....?"

" We need to get the other PPT included which are missed out...."

"yes.... may be both of you can work together if you wish...."

After few minutes, Jeetu too was ready with his work --- he directly came up with the formula instead of sharing few PPTs like Rohit and Kanchan....

But while explaining that, he figured out there is some mistake in representation, and corrected it on the spot.... And this was a delight to watch.....!!

I had already told them to take the break and continue after that..... However there were some who did not move at all... and one of them was Sahil...

This is what he came up with.....

What's interesting about his work is --- he arrived at the formula for PPT through the patterns..... and not through logic (like other three)....

So I asked him "what would you have done if you were not given the data of (7,24,25), (9,40,41) ?

"Sir that's when I was not able to do anything with just (3,4,5) and (8,15, 17).... It was possible for me to find the formula only when I got more data...."

"Hmmm.... but then how come your other three peers have constructed the formula for PT.... They did not have the privilege that you had (more data/ pattern observation)..."

He was silent.... I think he was getting what I meant.....

I continued... "They were able to do so, because they have used Logic along with some observations in square numbers..... and not Pattern..."

"Okay Sir.... I will try to find out using the other way now...."

And while going, he further added -- "Sir, even the set (8, 15, 17) does not come out from this formula!"    :-) :-)

Some students had not yet arrived at this....though they had made some observations.... and hence we decided to not discuss this exploration today but in the next session, thus giving them some more time to research at home....

So probably you might hear again from me, on this post :)

1) How about trying this out with your students? Do share your experiences if you do so.. Would love to study...

2) What are your views about the exploration that happened and the way it happened?

3) Could you decipher the rationale behind the approaches of Kanchan/ Rohit and Jeetu?

4) How can you include the missed out PPTs like (8,15,17) ? any change in this formula or new formula?  Will that solve the problem of including all the possible PPTs, or still some might be missed out? How do you know?

5) Any more questions ?  :)

Waiting for your responses/ comments....

Rupesh Gesota

Sunday, August 13, 2017

Mental Math: 9.8 x 2.5

Me - How much is 9.8 x 2.5 ?

Kanchan says,

I will consider the numbers as 98 and 25. Further, lets round up 98 as 100. So now, 25 times 100 gives 2500. But I have taken 2 times 25 more..

So, 98 x 25 = 2500 - 50 = 2450

Now, since I had multiplied each of the two given numbers by 10, the obtained product will be 100 times more than the desired one. Hence the actual answer will be 2450 / 100 = 24.5

Me - Excellent. Any other way?

Rohit says,

I know that 2.5 x 4 = 10 ... So if I am increasing one factor by 4 , then I will have to decrease the other  by 4.... i.e. I need to find 9.8 / 4

Now., I know that 25 x 4 = 100 and so, 24 x 4 = 96.....
Hence 24.5 x 4 = 98
Hence 2.45 x 4 = 9.8  i.e.  9.8 / 4 = 2.45

Now, the problem 9.8 x 2.5 becomes 2.45 x 10 = 24.5

Me - Fantastic. Any other way?

Tanvi says,

Lets ignore the decimal points. So the problem is 98 x 25

Now, 98 x 100 = 9800
So, 98 x 25 = 9800 / 4 = Half of Half of 9800 = Half of 4900 = Half of 4800 + Half of 100 = 2400 + 50 = 2450

Now, with the same reason what Kanchan gave, we will have to decrease the product by factor of 100.

So, 9.8 x 2.5 = 2450 / 100 = 24.5

1) How would you solve this problem mentally?
2) How about your students/ children?
3) What are your views about the approaches used by these students?
4) What are your views about the language used by them to communicate their reasoning?
5) Why do you feel these students were able to solve this problem, this way?

Waiting for your responses...

Rupesh Gesota

PS: These students hail from the marathi medium municipal school in navi-mumbai. To know more about the maths enrichment program being run with them, check the website

Monday, July 31, 2017

Comparison of Confusing Fractions !

Few days back I got to attend the maths teachers' education program, where the facilitator had given us few problems to solve. One of the problems motivated her to encourage the teachers to discuss with their students about the difference and equivalence between the following three expressions.

a /  bc ;   (a/b) / c  ;   a / (b/c)

While my students had already encountered, struggled & tackled these expressions, but I recalled that these experiences were within the context, and in isolation i.e. they had fought with these monsters one at a time and that too on different occasions. So I thought it would interesting to notice what happens when they are made to face these three expressions - all together, without any context and that too without any context.

So the next day itself, I challenged them with this problem..

I asked them,

"Which of the three are equal or not equal?"

They looked at it for a while and soon, one of them said,

"Sir, we have solved such expressions..."

Me: Yes, Lets do it again then.

Couple of them could not resist and they shouted out their answer. I just looked at them; and they understood their mistake (that they had disturbed their peers' thought process)

After a minute or so, I asked one of them to explain

Rohit - "Sir, 2 and 3 cannot be equal.

"Because in (2), a is divided by the quotient b/x  and in (3), a is divided by the product bx.

I looked at the class for their views. And could see everyone agreeing with this. I wanted someone to counter this, but none did. So I had to play devil.

"Are you sure?"

He guessed something fishy it seems and soon exclaimed - ."..except for x=1, when they will be equal"  :-))

We smiled at each other and then I picked up another student--

Sidharth - "(1) and (3) are equal"

He stood up and slowly wrote this on the board -

"Sir, expression (1) is actually a/bx which is same as (3)"

"But how?"

"I multiplied numerator and denominator by x"

"In the numerator, we have b... it is divided by x as well multiplied by x.... So there is no effect of x... Only b remains..... And in the Denominator, we get bx..."

Did you notice the language? your comments?

I was confident that he had understood, but I wanted to take him deeper...

"Ok... So what?"

"Sir, then we can now see that both (1) and (3) are equal...."

"But how do you know that the given expression (1) still remains equal to what you have written? May be you would have changed its value by this manipulation?"

I wanted him to argue with me, but then he remained mum.... and kept staring at the 2 expressions.....

Perhaps, Jeetu could not take this prank I was playing... and he intervened immediately,

"Sir, they are EQUIVALENT FRACTIONS ! So shouldn't they be equal?"

I looked at Sidharth... And found him smiling at all of us :-)

In fact, I could have even probed him further as to why the values of equivalent fractions are equal? and why do you get equivalent fractions by multiplying the Nr and Dr by the same amount? But then, we had worked on these many times earlier... and hence discussing those again now might disturb the flow of the present problem solving process....

I looked around -- "any other views/method?"

Vaishnavi -- "Sir, in (1), we are first dividing a by b, and then the answer is divided by x... So it clearly means that 'a' is divided by the product of b and x..... and hence its equal to a/bx.."

Everyone agreed......

"But then I feel,  if a is divided by b and then by x, then its effectively divided by (b+x).."

And immediately the whole class roared aloud -- "No !! We have already worked on this....."

Let me tell you that this remark made by me now, was the same made by them few months ago.....After working out few examples and even through logical reasoning they had proved that why (a/b)/c is not equal to a/(b+c).... I was happy they still remembered their experience......

"Ok, so can someone tell me what will (2) simplify to?"

Tanvi -- "Sir, (2) will become ax/b"

"Same method as what Sidharth did... "

"So can one of you write the simplified forms of all the three expressions?"

One of them wrote these on the board.....  I forgot to take the snap... but this is what it looked like.....

"So then what's the conclusion?"

This time it was a chorus

"expression (1) and (3) are equal and are not equal to (2)"

I just looked at Rohit again...

"Sir, they all will be equal when x=1"   :-))

I wanted to take them still deeper on this, but I decided to hold for the moment  --- so that we can re-visit this problem after few days, with some flavor...

What do you feel, can there be some more interesting/ important questions? What are those questions?

How did you solve this problem? With understanding or with 'rules and procedure'? :)

How about trying this problem with your students?  Would love to know what happened in your class.....  :)

Rupesh Gesota

PS: These students are from marathi-medium municipal school.... To know more about the math enrichment program, check the website


Title: Separation of gossypol from cottonseed
Researcher: Devesh Kumar
Guide(s): S.S. Sambi and S.K. Sharma
University: Guru Gobind Singh Indraprastha University
Completed Date: 07/2012
Abstract: There is growing need for edible protein and food due to ever increasing newlinepopulation especially in the developing countries. Agriculture land, on the other newlinehand, is on the decrease as a result of rapid urbanization leading to its diversion to newlineresidential / commercial use. Cottonseed is available in large quantity as a newlinebyproduct of cotton can be an important source of protein as it contains both newlineprotein (20-25%) and oil (17-23%). Presently, hexane is being used commercially newlineto extract oil from steam heated cottonseed at 110oC whereby free gossypol newlinepresent in the seed forms a non toxic complex with the protein. After oil extraction newlinethe cottonseed meal is being utilized in regulated quantities as a supplementary newlineprotein to feed animals only as it is not fit for human consumption. The non-edible newlinecottonseed meal can be converted to edible form if gossypol content in it is newlinebrought within the prescribed safe limit of 450 ppm. newlineThis study is aimed at not only to reduce the gossypol content in the newlinecottonseed meal but also to obtain gossypol in concentrated form for its various newlineestablished uses. Ethanol both in pure and acidified form for extraction due to its newlinebetter dissolving power for gossypol. The study involves a two stage extraction newlineprocess where oil is extracted from the cottonseed using hexane and ethanol for newlinegossypol extraction. Experiments were conducted to determine the optimum process conditions like temperature, particle size and solvent to solid ratio (SR). It was found that at 45 degree C maximum extraction of oil occurred for SR:15 for an average particle size (PS) of 0.6 mm. Hexane was used for oil extraction to get defatted meal. In the second stage ethanol (both pure as well acidified) was used to extract newlinegossypol from the defatted meal to the maximum extent. The data obtained indicate that 62% gossypol could be extracted using pure ethanol whereas ethanol acidified with 0.5M Tartaric Acid could extract up to 92.6 % gossypol at 70C, SR:15.
URI: http://hdl.handle.net/10603/110418
Appears in Departments:University School of Chemical Technology


Five better ways to be in 2014: choose empathy over sympathy

Top 'o the morning to you. Let's do this new year thing right. Over the next several days, you'll find me posting five times on better ways to be in 2014. Each of them hinges on the knowledge that "the Lord is here," that the ongoing presence of Jesus in us causes us to live and interact differently with ourselves, with our world and with those closest to us.

Here's #1: let's choose empathy over sympathy in 2014.

Hats off to my friend Beth Hafer who sent along the following video by Brene Brown. It's a fun, accessible way to realize what it means to sit with another in their pain, often without saying anything. What will you choose—empathy or sympathy?

I'll be candid. I've been through enough knocks in 2013 that I simply don't have a lot of tolerance for those who try to apply the sympathy bandage. And I'm thankful for these knocks, because I believe Jesus is trying to continue to shape me into a person of empathy, a person of understanding that represents him well to the broken. I hope I'm never associated with those who try to comfort like the friends of Job in the Bible. Instead, I want to be more like someone who so embodies the Resurrection that I can sit in the pain with grace, knowing that in time all will be well.

As I am formed into the image of Jesus, I hope to choose empathy over sympathy in 2014.

Do you have a memorable experience of someone who showed genuine empathy to you? Do share.


Propel moshing is a skill that only long-haired heavy metal fans can develop properly. To propel mosh is to do a circular motion with your head so that your hair moves like a propeller. It might be a good idea to crouch a bit at the same time and hold your knees / thighs for support so you don't fall over. It is a sight to behold, especially in good heavy concerts where the whole first line of concertgoers are doing it. Or the band. Only a true pro can do it while moving around and jumping at people.


An artist’s impression of the red dwarf planetary system Kepler-444. (Image: Tiago Campante/Peter Devine)

Red dwarfs are the most common type of star in the galaxy. But new research suggests that life within these systems may be limited, due to the stiflingly hot atmospheres on Earth-sized planets that orbit the red dwarfs.

When we look up into the sky at night, we only see a small portion of what’s actually out there. Even though red dwarfs comprise over three-quarters of all stars in the Milky Way, not a single one of them is visible to the naked eye. These stars may be small and dim, but they still feature planets, including many that are Earth-like in terms of size and composition. Given their ubiquity, astrobiologists have speculated that a hefty portion of alien life, should it exist, may reside in red dwarf systems.

Unfortunately for alien-hunting hopefuls, new research published in the Monthly Notices of the Royal Astronomical Society suggests otherwise. Despite the fact that red dwarfs are tiny and dim, many of their planets may still be too hot to be habitable—even those situated within a star system’s habitable zone, i.e. the zone in which rocky planets can sustain liquid water at the surface.

“It was previously assumed that planets with masses similar to Earth would be habitable simply because they were in the ‘habitable zone,’” said Princeton astronomer and study lead author James Owen in a statement. “However, when you consider how these planets evolve over billions of years, this assumption turns out not to be true.”

Here’s the problem: Many of these planets begin with super-thick atmospheres comprised of noxious hydrogen and helium, comprising around one percent of the total planetary mass. That’s a hideously huge amount. By comparison, the Earth’s atmosphere accounts for just a millionth of its mass. Thick atmospheres produce greenhouse gas effects that render the surface far too hot for liquid water, so these planets are not considered habitable—at least not at this early stage in their life cycle.

Prior to this study, scientists had figured that, over time, these thick atmospheres evaporate away owing to the steady bombardment of strong X-ray and ultraviolet radiation from the parent dwarf. But this doesn’t appear to be the case. Computer models show that these thick hydrogen and helium envelopes cannot escape the gravity of planets that are similar in size or larger than Earth. This likely means that Earth-sized planets within red dwarf systems are permanently sterile.

There is some good news, however. Smaller planets, like those the size of Mars and Mercury, lose their oppressive atmospheres over time.

“There are hints from recent exoplanet discoveries that relatively puny planets may be even more common around red dwarfs than Earth mass or larger ones, in which case there may indeed be a bonanza of potentially habitable planets whirling around these cool red stars,” said Imperial college of London and study co-author Subhanjoy Mohanty.

So while discouraging, this finding doesn’t mean we should stop looking for signs of life in red dwarf systems. Given the sheer number of these things, it would be a mistake to do otherwise.

[Monthly Notices of the Royal Astronomical Society]