Math that matters (Part I)

If we want kids/adults to learn math, we might as well make it relevant. Here are a few relevant calculations (that employ nothing more than algebra) which I find very relevant to our future. Imagine these calculations being taught to an 8th grade algebra class! Here is the first installment:

Missing women

Most people are not aware that females were systematically removed from the population during the 20th Century and it is a practice that continues today. How do we know? Well, as Nobel Prize winning economist, Amartya Sen, noted back in the 1990s, if we look at sex ratios of nations, we find several that have ratios that are far from 1:1. Pakistan and China have ratios of 0.94:1 and India has a ratio of 0.93:1 (in 2016) (these numbers are pretty much the same as they were in 1990, though Pakistan has improved slightly from 0.91:1). Given that women live longer than men, nations should have sex ratios above 1–most European nations are above 1.03:1. Given these “small” differences among nations, one might just dismiss the low ratios as “normal” variation. Unfortunately, this would be a huge mistake. Here is the math to determine what a ratio of 0.93:1 means, in comparison to a 1.03:1.

First, let’s define the variables needed:
F = number of females in a population
M= number of males in a population
T = total population = F + M
R = sex ratio = F/M

So the above two equations have 4 variables (F, M, T, & R)…if you know two (and you do, T and R, from Internet sources), you should be able to use simple algebra to compute the other two, F and M.

Again, the equations are: (1) T = F + M and (2) R = F/M

Here is how you solve these two equations:
Solving (2) for M yields (3) M = F/R, substituting (3) into (1) yields, F + F/R = T; this can be rewritten as: F(1+(1/R)) = T
which can be rewritten as
(4) F = T/(1 + 1/R)

So, you can determine how many females are in a population using this equation. This can be considered the Actual Females (Fact).

So, with a population of 1 billion (1,000,000,000; which is smaller than both India’s and China’s current population) and a sex ratio of R=0.94, we use equation (4) to solve for Fact as such:

Fact = 1,000,000,000/(1 + 1/0.94) = 485 million
So, Mact = 1 billion – 485 million = 515 million

Now to determine the Expected Females (Fexp) in a “healthy” society, with F/M = 1.03, we use equation (4) again with this new R value.
Fexp = 1,000,000,000/(1 + 1/1.03)) = 507 million
So, Mexp = 493 million

Now you can determine the “missing females” (Fmiss) using this simple formula:
Missing Females = Fmiss = Expected Females – Actual Females = Fexp – Fact

In our example above (the hypothetical nation of 1 billion people), we find:

Fmiss = 507 million – 485 million = 22 million

Is this a large number? Well, when one considers that between 50-60 million people died in World War II, I’d say it is! Also, this is only for one country (say China or India). If you were to add up all the nations in the world with “missing women,” it comes to close to 100 million! Now that is an abominable figure, isn’t it? Yet, how many of you have heard of this figure before? If you are wondering why women are missing, do some research. It isn’t a pretty story. (I wrote about this issue over 10 years ago and got it published in a local paper’s front page. Sadly, as I recall, it hardly drew any attention.)

Just to put these numbers in perspective it is sometimes valuable to imagine what a sex ratio looks like when you bring it down to a scale that we can see. Let’s say, if you had a party of 100 people and a sex ratio of 0.94, you would have 52 men and 48 women. This would hardly be noticeable, would it? Hence, now we see why we need to do the large-scale calculations to expose something very sinister.


Joe and his wife Alice were poor. Times were very tough and autumn had just begun. Things were so bad that families began rationing food. The stores were bare and all that one had to eat was what they had saved up. And much of that was spoiling by the day. Alice counted 400 portions left (assuming no spoilage) and since she had two children, this meant that there would only be enough food for 100 days. Things looked very bleak. Neither Joe nor Alice, nor any of their neighbors, saw a way out. Economic crashes on this scale had not be seen for several generations and memories of how their ancestors had survived hard times in the past were deeply faded. Understandably, psychological depression set in. The family ate enough each day to stay alive but that was about all.


Mary, the daughter, was looking out a window and noticed that a flock of birds had descended on to this group of weeds that had grown alongside their small abode. They all seemed to be delighting in the eating of the seeds that this plant produced. She wondered, would those seeds nourish humans too? Then, looking more closely, she noticed a grasshopper chewing on the plant’s leaves. It looked like a very healthy grasshopper. Could it be that the leaves would be edible for humans too?

Daniel, the son, simultaneously sitting on the other side of the house, peering out a different window, noticed a squirrel chomping on a green covered tennis ball-sized spherical object. He looked up and saw more of these objects hanging from a tree. Another squirrel appeared to be digging a hole with a sphere nearby. He wasn’t sure why those spheres existed but the squirrels seemed to know something he didn’t. Curious, Dan asked his dad to come check out the scene. Upon arrival at the window, Dan asked his dad, “What’s going on? Why is the squirrel eating the ball? What are those balls for anyway?” Joe wasn’t sure but he vaguely remembered his grandfather talking about how trees come to be and how these balls, if put into the ground, grow into new trees. Daniel, somewhat shocked, wondered if other plants did the same thing.

At dinner that night, the Jamesons were having the norm—a stew of beans with garlic and herbs. Looking down into his bowl, Daniel noticed that the beans looked like diminutive spheres, albeit a bit oblong. He asked his mom, “where did you get these beans?” Alice responded, “oh, they came in a big sack at the Big Box store, 20 lbs for $5. They were one of the last bags they had.” Mary, followed up, asking her dinner mates, “Aren’t they seeds?” Alice responded, “Yes, I guess you are right.” Daniel, followed with, “What are seeds?” Alice said, “Seeds, if planted, result in new plants.” Daniel, flummoxed a bit, “What do you mean? If we put these in the ground, we will get new plants and more seeds?” Joe spoke up, “Sure son. You didn’t know that?” Daniel responded, “Maybe. I guess I just hadn’t thought about it for a while.” Dinner continued, all feeling like the conversation was good despite the monotony of the taste. Ninety-nine more days, Alice thought. Times were tough.

Or were they?

lessons learned in 2016

[Note: some of these lessons were mere reminders but even so they were still noteworthy if only that]

We don’t live in a democracy. Despite our repeated boasts about how we live in the “greatest democracy” of all-time, we must come to terms with the fact that we don’t. Evidence? While too abundant to mention exhaustively in a BLOG, here are a few of the most compelling to me: the Electoral College (ref 1), extensive voter suppression (before election day, on election day, and after election day) (ref 2a, 2b), inability to have a full recount (in several states) (ref 3a, 3b), extensive use of “no paper trail” electronic voting machines (ref 4a, 4b, 4c), exclusive “two-party” Presidential debates (ref 5a, 5b, 5c), and dominant media forms that fail to hold candidates accountable (ref 6a, 6b, 6c).

No country is above electing a racist, sexist, xenophobic, egomaniacal person. Largely because of our failures in democracy, a person with horrific human qualities was given a chance to win/steal a presidential election. According to the Democratic Party’s leadership, a Russian computer hacking or a FBI director’s questionable action had the most to do with Clinton’s loss. However, this take wrongly deflects us from the more significant reasons, many mentioned earlier; this misfocus by a major party isn’t surprising given the little attention they have paid to the other factors (factors, sadly, they seem to accept as “normal”). Add to these, significant miscalculations in strategy (including, saying that many people were “deplorables” and claiming that things are going quite well (as if neoliberalism is good), when they aren’t (and it isn’t)).

Too many continue to spend 90%+ of their political energy focused entirely on the presidential race. This is probably the most vexing to me. I see it in my own community. If only a couple of handfuls of citizens would dedicate themselves to the local political process signficant &*#$ could happen. Hopefully, now that folks see how discombobulated the national election scene is, more will look to act locally.

Misogyny is alive and well! When I first read that White women actually voted more for Drumf than HC, I was shocked (source). I didn’t believe it. When I heard some women easily discounting the blatantly misogynistic statements revealed by Drumf recordings, disregarding it as mere “boy” or “locker room” talk, I was sickened. How could this be? It is clear that the extreme attack on Hillary, one that has lasted more than a decade, has worked. She was built as the devil and enough people came to believe this. (She may not be an ideal candidate but she is no devil.) Also, this attitude is consistent with our generally condoning of violence (physically as well as economic) against women (and people of color) for hundreds of years, examples which have become more easily revealed to us by cell phone videos and texts. Clearly, we all must be more vigilant to expose and censure sexist and racist actions/statements. They are reprehensible and no person who revels in them should ever have the opportunity to be our commander-in-chief. I thought we had made more progress but recent events suggest we still have a long way to go.

Cancer is as debilitating mentally as it is physically. I’ve come toe-to-toe with this disease. It is something that many of us still don’t openly discuss (out of fear?) and yet it affects more and more of us every day. I applaud those that provide care to those who are sick. The doctors, nurses, social workers, and other care givers, often who work exhaustive hours even on holidays, deserve a lot of admiration.

Despite all the fear, hatred, irrationality, and hopelessness that we are fed every day, many good things continue to happen. Every day people are growing TONS of food in Detroit and elsewhere (ref 7), renewable energy is booming almost everywhere (such as the Philippines, ref 8), and volunteerism continues to thrive as well (ref 9). So, as we begin 2017, remember what the great Frederick Douglass said 160 years ago: “If there is no struggle, there is no progress.” (full speech here: ref 10).

Friday is “BND.” Celebrate it!

Based on the increased energy coming from commercials, this Friday purports to be a day of great significance. Every retailer is having a sale and what else is there to do on a Friday but shop. It seems only natural that we would buy (another) large TV or computer, or take advantage of the “incredible” discounts available at most stores. Sadly, there is something quite disturbing about this situation.

Just as we can be lured into pro-war sentiment—remember post-9/11 and the ubiquitous flags—apparently we can be persuaded quite easily to buy more stuff, particularly if we feel we are getting it for a “steal”. So, what could be wrong with this? We are going to buy new things after all, aren’t we? Why does it matter when we do it? And, definitely, we should try to get the most for our dollar, shouldn’t we?

First off, the compulsion to buy things (which we do to make us feel better, notice that the ads make consumers look cool and savvy) is an addiction. Identified by scholars as affluenza (see PBS program on topic, link), this illness is perhaps the greatest challenge we face as a humanity. Overconsumption causes tremendous problems. For every pound of waste that we “see” (for example that old working TV that is going to be put curbside because the new TV is bigger and has better graphics), it is estimated that ~80 pounds are produced upstream (see Annie Leonard’s The Story of Electronics, ref 1). And much of this upstream electronic waste is highly toxic. So, our addiction has grave consequences for the planet.

Second, our addiction is a false solution. Overconsumption doesn’t bring long term happiness. Psychological research has established that the more materialistic one is, the more unhappy he/she/they tends to be (here is a short video that clarify this, link). In this way, buying something for a pick me up is similar to taking an “upper.” At the end of the day, one feels less happy and has more stress caused by financial difficulties driven by spending money one doesn’t have; actually, substance abuse also tends to be higher for materialist people. Ultimately, we must all find more productive ways to deal with our anxieties and unhappiness. According to experts, more social interaction is highly recommended.

There are many resources for those that are looking to fight against consumerism.
Enough (link) is a group in England focused on this. Adbusters is a journal that has lots of material on the subject (link). Buy Nothing Day is this Friday, that sounds a lot better than “Black Friday,” doesn’t it? (link to Adbusters’ BND page!) So, join the anti-consumeristic movement this Friday and feel good about yourself in a way that is powerful, purposeful, and longer lasting. Let others know too, because that is how it will become the new norm. Have a great Thanksgiving everyone!

100 years — father

Since it is Father’s Day, I thought I would discuss something my father has always taught me to admire—longevity. My father, David, has always made a big deal about living a long life. Growing up, I often heard him emphasize the age of “old” people. He also spoke regularly of the importance of taking vitamins and eating lots of protein and nutrients as a means to ensure a long, healthy life. He didn’t just preach, he used to take 10 g of Vitamin C a day (that’s 20-500 mg pills) and a host of other vitamins, probably thirty pills a day; I am not sure of his daily regimen now.

Anyhow, as a result of this “teaching,” I can say that I value longevity. I’ve learned through my scholarship that life expectancy is one of the best indicators of the “well-being” in a country. If people in a country are living long lives, it can be expected that the country also has good quality health care (especially for soon-to-be mothers and children), educational opportunities, and food access for the vast majority of its people; this is in contrast to economic indicators, such as GNP (Gross National Product), which often can mask suffering among its lower classes. I cherish the opportunity to speak to older people as I realize that they have encountered a lot of things that I haven’t lived through—-with experience comes a fair bit of wisdom.

Japan is home to the highest percentage of centenarians (with some 60,000+ of them currently); there is some debate on this, apparently Cuba may have recently surpassed Japan (ref 1). And while I hope to reach the “100” mark (my dad is working towards it to–still running ~14 miles a week at age 72), I realize that a few things working against me. One I am a male. For every male that reaches 100 years, there are 6 females that do. Also, being large (6’4”, 235 lbs) doesn’t help my cause either (ref 2). Yet, given that no statistic is deterministic, I will still eat my “fruits and vegetables” and wish for the best. Better still, I’ll use the time I have on this wonderful planet to make it better for me, my planetary neighbors (of all species), and most of all, on this day, my children!

a “can” or at least a “maybe”

One of the more frustrating things about being a community activist is the number of people that tell you and others what can’t be done or why X is not possible or won’t work. I’m all for a “reality check” and no question I am a bit too optimistic about things sometimes. However, the core of my frustration stems not from people who have taken new ideas seriously but those that either flippantly reject them out of hand or offer none of their own.

From my vantage point, humanity is in a very precarious position. A good number of people in my community don’t disagree with this sentiment. However, where we tend to disagree is how we should go about doing something in response to it. I tend to want to act more than think deeply and others prefer thinking deeply first. I am comfortable with this continuum and actually think diversity of thought is something we should value rather than extinguish. However, diversity of thought doesn’t mean that negativity (or, worse, fatalism) should trump positivity, optimism, or “out of the box” thinking, most of the time.

Einstein is famous for saying many things, but perhaps the most relevant to this conversation are his definition for “insanity”: “doing the same thing over and over again and expecting different results,” and his related insight, “We cannot solve our problems with the same thinking we used when we created them.” We have created lots of problems in the last two centuries and many ecological systems are at their “boiling” point. We have to begin thinking differently and doing things differently.

Spend some time watching how people interact with each other and how often people will “shoot down” someone’s new idea. This mentality is so pervasive we often do it to ourselves as a reflex action. Self-censorship is off the charts. I hear it from my colleagues and friends, who say things like, “it is too risky to say X or Y,” “it might identify me as M or N,” “I might be wrong.” In this cultural environment, isn’t it time to say what we think and feel and be open to honest responses? And, isn’t also time to listen to others more fully, especially those that are trying desperately to make things better before criticizing them or their ideas. Perhaps, a simple, “maybe, that seems plausible” or “perhaps that can work” will be that contribution that keeps us moving where we haven’t been.

Grandpas on Memorial Day

Memorial Day is a great day to reflect on history. Whether it was started by former slaves in Charleston, SC honoring a mass grave of Union soldiers in 1865 (ref 1, ref 2) or Southerners in other cities (ref 3) celebrating the sacrifices of loss Civil War soldiers a year later, we now have a tradition deeply embedded in our culture. Going back to the founding of the US, well over 1 million U.S. servicemen and servicewomen have died fighting wars. And, not to be overlooked, millions of others, many from foreign lands, have died or have sustained significant injuries, physical and mental, as a result of these conflicts.

Both my grandfathers fought in the “Great” wars of the 20th Century, Joseph (in WW I) and Max (in WW II). While Grandpa Joseph sadly passed when I was just a toddler, Grandpa Max and I got to spend ~30 years getting to know each other. Grandpa Max taught me many things, but probably the two most important were: (a) everyone matters and is worth your attention; and, (b) when something is important enough, you must be willing to sacrifice everything to obtain it (in 1945 that was freedom from fascism; he volunteered to serve, and, as a result, fought in France against the Nazis). Despite risking so much and contributing to the “Victory,” Grandpa Max was no fan of war. He openly protested against all other U.S. wars, which he thought were illegitimate on moral grounds (he deemed them imperialistic enterprises). He was a working man, whether it be in the Bowery of New York City, as a diamond setter, or a social worker with schizophrenics later in life. He never made much money but he quietly saved thousands, which he generously gave his five grandchildren at his passing. He was modest and definitely a bit cantankerous (what older men aren’t). I don’t know for sure, but I think his battlefield experiences connected him with humanity in a way few of us ever do. His two sons drew from these lessons as well–both have dedicated their lives to the betterment of humanity.

We definitely have a lot to learn from our soldiers and the experiences they have had; I wish I had had more opportunities to learn from Grandpa Joseph. But given that face-to-face combat is becoming less common (at least among U.S. soldiers) as drones and airstrikes become more popular (both further dehumanizing combat), we must be vigilant not to let war become something that we participate in casually or without exhausting all diplomatic options first. I am sure Grandpa Max and Grandpa Joseph would agree with this.

about me

I, a 40-something environmentalist, who loves to provoke a discussion about important issues, started this blog as a means to: (1) get stuff off my chest and out of my head; (2) share ideas that are often intentionally avoided/ignored by mainstream media; and, (3) learn from others and give them voice at well (so please comment). One never knows where a first step leads, so let’s find out…