Pi

Tom Kando 

My previous post began a discussion of some interesting mathematical problems which I want to share with you. I am fully aware that I am a novice in this field. Last time, I wrote about prime numbers. Today, I want to talk about another fascinating topic, namely Pi (π). 

You have heard of the expression “squaring the circle,” right? It means doing (or trying to do) the impossible. 

In order to construct a square with the same area as a given circle, you must first determine the area of the circle, using the following steps: 

1. measure the circle’s circumference. 

2. measure the diameter, that is the distance across the circle between the two halfway points of the circumference. 

3. determine the radius, which is half the diameter. 

4. Square the radius and multiply this number by 3.14 (π). 

In other words A (Area) = π x r 2 (r is radius) 

Then, you simply compute the square root of the circle’s area. This gives you the length of the square’s side. 

Example. You want to square a circle which has a circumference of 1,000 meters. 

Using the π approximation of 3.14, The circle’s diameter is therefore about 318.5 meters, and the radius is half of that - 159.25 meters. The circle’s area is therefore 3.14 x 159.25 2 = 79,582 square meters. The square’s side is the square root of this (√79,582) i.e. approximately 282.1 meters. 

For practical purposes, this procedure will do. However, the problem is that π is a transcendental number. 

Transcendental numbers are non-algebraic and irrational: They are NOT the solution of an algebraic equation. They cannot be expressed as the ratio of two numbers. They have a non-terminating decimal.

22/7 is often used as an approximation of π. It is about 3.14. Since it is a fraction, it is a rational number. Like π,, it has an infinite, non-terminating number of decimals. 

However,UNLIKE π,, the decimals consist of a six-digit repetend. . For example, if you divide 22 by 7 to 24 decimals, you get 3,142857 142857 142857 142857. “142857" is called a “repetend,” and it repeats ad infinitum. Read more...

SOME INTERESTING MATHEMATICAL TOPICS

Tom Kando

Most of my recent posts have been negative. There are so many wrong things these days. The third year of Covid, 5th month of war in Ukraine, the Supreme Court abolishing our constitutional rights, the proliferation of weapons and therefore of mass murder, no progress on the environmental front, the rightward political drift toward fascism in many countries, etc. 

So how about something not depressing, for once? 

A field which has long piqued my curiosity is mathematics, if only because I am not well versed in that area. Incidentally, some of my ancestors were eminent mathematicians and scientists. They include my great-grandfather Beke Mano, who was a pioneer in differential equations and my grand-uncle 

Kalman Kando who invented the phase converter. 

My secondary school education was stellar on the humanities side, but mediocre on the quantitative side: At the gymnasium, we had six years of six languages - Dutch, English, French, German, Latin and Greek! However, our quantitative training did not go beyond algebra, trigonometry, analytic geometry and stereometry. Later, obtaining my PhD at the University of Minnesota required a strong quantitative component in the form of advanced statistics. However, most of my quantitative skills, limited to begin with, have atrophied. I remain fascinated by fields about which I know little, wondering sometimes if I might chose the direction of the exact sciences if I were to do things all over again. 

Take prime numbers, for instance. You can check out a previous post of mine about this: 

Prime Numbers, Large Numbers 

A prime number is a whole number that can only be divided by 1 and by itself. Or put differently, prime numbers cannot be divided by any other whole number without leaving a fraction. The smallest twenty-five prime numbers (those under 100) are: 

Read more...

Ranked Choice Voting

by Madeleine Kando

 

leave comment here

Read more...

Thank God for the Vaccine (From my Coronavirus Diary)

By Madeleine Kando

Day 1

What a wonderful time we had in San Francisco. Aside from the joy of being with my 10 year old grandson, there was the city with its parks, its architecture and its museums. Even without any of that, it would have felt like a get out of jail free card after so much time being cooped up in our own universe, back in Boston. For almost two years, we steered clear of the claws of this ruthless monster called Covid. We didn’t go to restaurants, we had friends over one at a time, no parties, no movies, no nothing. 

Now, it is time to fly back home. Squeezed in the window seat, my glasses fogging up above a n95 mask, I am ready to zone out and pretend I am somewhere else for the next 6 hours. Long gone are the days when I fully enjoyed flying cross-country. The window shade is partially open, symbolic of my ambivalence about an experience that I used to find absolutely thrilling. Most of us think nothing of propelling ourselves at 500 miles an hour, at an altitude that only two bird species on earth are known to reach, but I was born two years before the first transatlantic commercial flights began, and there is still this sense of wonder in me. I open the window shade and endure the dirty looks from my co-passengers who are trying to sleep. I cannot get myself to be completely indifferent to this wonder of aviation.

That evening I collapse on my king-size bed and realize how exhausted I am. My throat doesn’t feel good, but I don’t give it a second thought. Home sweet home…

Day 2

The next day, my throat is painful. I can barely swallow. I have intense body aches and a great desire to stay in bed. I test myself for Covid, but I am negative. I go outside to inspect the vegetable garden and notice that little bites have been taken out of all the seedlings. Cukes, beans, peas, all rendered inedible. ‘Oh I forgot to tell you about the groundhogs, mom’, my daughter says. 

We install chicken wire around everything that we assume would go on a groundhog menu: Marigolds, nasturtiums, pansies.. I sprinkle ‘deer repellant’ around the raised beds, which is a terrible mistake. Its odor is so repulsive, that even I cannot go in the garden.

I crawl back in bed. An hour later, I look through our French doors and see a fat groundhog, probably the mother, blissfully eating away at a clover patch. She stares straight at me, her jaws working a mile a minute. A smaller version has materialized and follows in her footsteps. Like two efficient lawnmowers, they quickly decimate half of the clover patch.

Day 3

My symptoms are worse. The lozenges are pretty much all I can tolerate. Having the flu is no picnic. 

Read more...

Guns and Murders

Tom Kando

My previous post's title was: It's the Guns, Stupid. 

I subsequently thought: There is a simple way to prove this: Just draw up a list of places, list two variables for each place, namely (1) per capita gun ownership and (2) per capita murders, and see if there is a correlation between the two. For example, one could use a list of our 50 states for this or a list of the world's roughly 200 countries.

There is anecdotal and journalistic  evidence that states and countries with high rates of gun ownership also have high murder rates (e.g. Texas vs. Massachusetts, or the US vs, Holland). But I can't think of any  systematic attempt to correlate the two variables, using a list of states or countries. So I did it myself. It was quite simple. I chose to list countries rather than US states. To make it easier on myself I reduced the population to 45 Aimportant@ countries. I then listed each country's  rate of gun ownership and its murder rate.  This produced a bi-variate 2x2 table, on which I did a Chi Square significance test. My data are from  countries ranked by gun ownership rates  and countries ranked by murder rates

Of the 45 countries in my sample, 25 were Ahigh gun ownership@ and 20 were Alow gun ownership@ Of the same 45 countries, 17 were Ahigh murder rate@ and 28 were Alow murder rate. The table below gives the distribution of the 45 countries into 4 cells, as indicated:

                                                               Table I: The relationship between guns and murders

		MURDERS
		MANY	FEW	TOTAL
GUNS	MANY	#1) 12	#2) 13	25
	FEW	#3) 5	#4) 15	20
	TOTAL	17	28	45

 

Cell 1: High rates of gun ownership and therefore high murder rates: US, Pakistan, Venezuela, Honduras, Mexico, Russia, El Salvador, Puerto Rico, Columbia, South Africa, Jamaica, Brazil.

Cell 2: High rates of gun ownership and yet low murder rates: Canada, Finland, Austria, Norway, Switzerland, Sweden, France, Germany, Thailand, Australia, Italy, Belgium, Hungary. Read more...

A Twin’s Perspective on Friendship

By Madeleine Kando

It is difficult to define friendship, but like many other indefinable things in life, ‘you know it when it’s there’. It is more like beauty or art, something that you value for its own sake. As soon as you try to exploit it for personal gain, it vanishes. It’s like trying to catch your own shadow.

I am not talking about the Facebook kind of ‘friend’. I am talking about the bond that is created between two people who decide to devote their time and energy to a mutually agreed upon relationship that is completely voluntary. Unlike other types of relationships like family ties, romantic ties or business ties, where you have some kind of ‘obligation’ to each other, friendship survives on the complete absence of rules. It is literally the stuff of dreams. A friendship is like a dream that you have with another person. And just like a dream, friendship is fragile.

The root word for friend is fréon (to love), which is connected to freo (not in bondage, acting of one's own will). It describes friendship to a T. It is one of the most democratic arrangements in social interactions. And just like a Democratic arrangement, if you don’t work at maintaining a friendship, it just disappears, without complaining or throwing a tantrum.

One factor that has influenced my view of friendship, is the fact that I am a twin. My sister is actually not at all like me. She is uninhibited and blunt and she acts out her frustrations by lashing out. I am self-conscious, reserved and eat up all my anger. But we were never really ‘alone’. There was always this other you that wasn’t you.

We were close growing up, since people couldn’t tell us apart, but for years, we were compelled to create conflict to prove that we were really two people. Especially after my father left and we had to vie for our only parent’s attention.

We have come full circle, however. With the help of distance and time (my twin in Spain, me in the States), we are finally able to meet each other as equals, like two branches on an old tree with a common base. We can talk to each other, accept each other and let bygones be bygones.

I had several friends, on my way to old age, most of them women. There was Marijke in high school, back in Holland. She lived in a beautiful, old style Dutch house with a thatched roof and a large garden with cherry trees. Why we were friends, I don’t remember. She actually decided that we should be, not me. Then, there was Barbara. Beautiful, tall, intoxicating Barbara. We were friends too, to the point of embarking on a secret correspondence based on a semi-pornographic series of teenage books called ‘the thousand and one nights’. Barbara sometimes gave me a ride home on her bike. I sat on the rack behind her, holding her narrow waist, her long skirts brushing against my legs. Her long pony tail reminded me of a beautiful, shiny race horse.

Read more...

POWER!

by Madeleine Kando

The information in this essay is based on Bertrand Russell’s: Power, A New Social Analysis, published in 1938. The book is very much a product of its time; a time when war with Germany was about to begin. The Western world was divided between democracies and countries led by successful revolutionary dictators. Similar to what is happening now.

What is power? Is it good or bad? Or is it neutral, like a hammer when you need to put a nail in a wall? The origin of the word ‘power’ comes from the Latin word ‘potere’, which means ‘to be able’. In French the word ‘pouvoir’, both means ‘power’ and ‘to be able to’.

Let’s face it, without power, nothing would get done. My husband needs muscle power to mow the lawn. I need fine-motor power to move my fingers on the keyboard.

But that kind of power is self-contained, it’s neutral. The problem starts when someone wants to have power over other things or beings. Power over humans, non-humans, land etc. There is a difference between the amount of power you need to have enough to eat and pay for a roof over your head, and the kind of power that has caused problems for our species ever since we grew frontal lobes.

There are people who crave power more than others. I myself want power over my cat. I won’t let her pee wherever she likes and when I was a young mother, I had power over my children. I told them when to go to bed, what time to get up, etc. My husband was a CFO and had decision making power over a small staff. We all have some degree of power, if only to control our own thoughts.

But that kind of power is barely worth the name. It is the power of men that lead nations that we should be talking about. Good and bad leaders alike: Mahatma Gandhi, Hitler, Putin and George Washington, to name a few.

Marx had an economic explanation for what drives human behavior, and Freud said it was all about sex. But according to famous philosopher Bertrand Russell, the pursuit of power is fundamental to understanding human nature. ‘Power is a fundamental concept in Social Science, in the same sense in which Energy is the fundamental concept in physics’. (From: Power, A New Social Analysis, by Bertrand Russell)

In other words, power stems from an infinite desire for something that will never be satisfied. ‘The Boa constrictor, when he has had his meal, sleeps until appetite revives’. He is content until he is hungry again. But with Man it is different. ‘Imagination is the goad that forces human beings into restless exertion after their primary needs have been satisfied.’

Read more...

The War in Ukraine Could Affect the Whole World

Tom Kando 

I just listened to a fascinating interview of  Yuval Noah Harari. He is the Israeli historian who wrote the brilliant Sapiens: a Brief History of Humankind, among others.

The professor’s first and obvious point is that this war should stop ASAP. The longer it goes on, the more EVERYONE will suffer, not just the Ukrainians, even if there is no global conflagration. The longer the war lasts, the worse the situation becomes. The more hatred is created among the Ukrainians. And no one wants this war, not the Russian people, not the Russian oligarchs. 

Unfortunately, it’s been over a month since this interview took place, and things are going in the wrong direction. I see no imminent peace on the horizon. 

The interview occurred when the Russian peaceniks were still marching in Moscow and Saint Petersburg. By now, Putin’s brainwashing machine has done a superb job in rallying a majority of Russians to supporting the war enthusiastically. Dictatorships are often very efficient at creating Orwellian group think within their borders. In Hitler’s Germany, Tojo’s Japan and elsewhere, large majorities continued to happily kill and die for their governments to the bitter end. 

Harari explains that Putin’s attack on Ukraine is not based on a coherent ideology, as for example the Soviet Union was. Instead, it is based on Putin’s own fantasy, not on facts. It is based on Putin’s single-minded desire to re-establish the Russian empire. It is based on the erroneous belief that the Ukrainians are Russians, that they want to be part of Russia. They do not. Ukraine has a thousand-year old history of national identity. Kyiv was a major cultural metropolis long before Moscow. President Zelensky’s and the Ukrainian people’s heroic resistance can be an inspiration to the world.

No war since 1945 has been as much of a threat to the entire world as the current conflict in Ukraine. For the past seventy-seven years, the world has been largely at peace. Authors such as Steven Pinker (The Better Angels of Our Nature) (https://stevenpinker.com/publications/better-angels-our-nature) have documented the decline of war. Since 1945, there have been no wars aimed at obliterating entire countries from the map. By and large, borders have been sacred (or at least the product of negotiations). Countries have ceased ANNEXING each other. No superpower has gone to war in order to aggrandize its empire.  Read more...

The Unraveling of the World

Tom Kando 

The Russian attack on Ukraine is presenting us with a terrible dilemma. We are subject to two impulses that are difficult to reconcile: 

1. We feel deep outrage over Russia’s savage and unjustified attack on its innocent and peaceful neighbor. The barbaric, indiscriminate bombing of civilians, children, pregnant women, schools and hospitals. There are no words to describe Putin’s cruelty. 

2. We fear that this conflict could escalate into global nuclear Armageddon. 

In other words, there is widespread moral agreement, but disagreement about how to respond. 

What Can the Civilized World Do? 

Generally agreed upon are: Strong expressions of moral outrage, solidarity with the Ukrainian people, the provision of humanitarian assistance, exposure of Russian lies, hospitality and assistance to the millions of victims and refugees, economic and military aid to Ukraine short of direct NATO-Russia confrontation. 

The next step is where divergence arises: 

The two key elements of risk assessment are (1) the probability of a risk occurring, and (2) the magnitude of the risk. The greater the magnitude, the lower the probability should be. The probability of humanity committing nuclear suicide is such a risk. This is not a gamble we want to take, no matter how low its probability is. 

Beating back the Russian war machine would require more than speaking out and providing hospitality to refugees. It would require waging war against Russia, with possible escalation to nuclear World War Three. 
There are hawks and doves. Neo-liberals tend to be more hawkish: They are willing to take more risks than the doves. A dovish example is the FiveThirtyEight podcast of an interview of James M. Acton by Galen Duke. Acton is the co-director of the Nuclear Policy Program at the Carnegie Endowment for International Peace: “Russia, Ukraine and the Risk of Nuclear War.”https://fivethirtyeight.com/videos/russia-ukraine-and-the-risk-of-nuclear-war/ 

Acton presents a game-theoretical metaphor: Think of a chess game, where both sides have a button underneath the chess board, which, if pressed, blows up everything including both contestants. The most desirable outcome of a chess game is one where the winner’s victory is not so overwhelming as to lead either side to press the blow-up button. 

Few wars end with one side’s complete annihilation (the US Civil War and the Punic Wars were exceptions). Most wars are won by one side in such a way as to allow the losing side to survive and to recover. And a key to this outcome is that it is based on negotiations.  Read more...

To the Leaders of the Free World

by Madeleine Kando

I am old, 6 years past the average life expectancy of most countries in the World. My life spans from the end of World War 2 to the present year of 2022. Like most old people, I am not aware of how old I am. Until now, that is.

The War in Ukraine that started in February 2022, made me realize that my life was spent during a time when the Western world, my world, was protected from the worst that can happen to human society. It was a time of relative peace and stability. Yes, during that time (which now spans almost a century), there were wars, conflicts, terrorist attacks and injustices done in many parts of the world.

But the rule of law and other basic principles on which the world order was built, protected us from what we now realize has metastasized into the most dangerous and lethal attacks on a way of life that I took for granted. All of that might soon be a thing of the past.

There is a concerted attempt to destroy that which made my life worth living. It was not without personal and social conflict. I am one of those ‘liberal intellectuals’ that many of you out there have a problem with. I am sorry for that. I am not a politician. Just an ordinary wife, mother and grandmother who now weeps when she watches the atrocities taking place in Ukraine. I am sorry that I have been hiding under a rock, suffering from the general delusion that what matters in life is happiness and peace.

The truth is that complacency and a sense of entitlement has brought Armageddon to the doorsteps of the Western World. We just didn’t pay ATTENTION! Is it too late? Do we have to keep whining about higher gas prices? Do we not understand that what is coming down the road is a tornado, gas prices be damned?

If memory serves, it happened before. The Roman Empire destroyed itself as much as it was destroyed by the invading Huns, Goths and Visigoths. It was weak, corrupt, unstable. It had lost its edge, so to speak. Did it deserve its own fate?

Read more...