When you run every day, that means you run wherever you are. For this stretch that’s covered Washington, Idaho, California, and Cork, Ireland. Here’s a recap.

Washington: The joy of running in the Pacific Northwest in the fall and winter can be summed up in three words: cold, wet, wind. For full effect I also include ‘dark’ on a regular basis, having started runs at 12:30 a.m. and after 11 p.m. Things are unusually dry here for the past month, so the main hurdle has been the cold, frequently in the 30′s. Recently I’ve noticed that if I run right after waking up, I’m still warm enough from being in bed that I don’t notice the cold so much. Or I’m not conscious enough to figure it out. 

Idaho:  We managed a 500 mile drive to Boise one day. The next day I ran in the community race and then watched our son’s cross country team in the Nike Regional meet followed by a quick a 500 mile drive back home. Those drives were accompanied by tumbleweeds occasionally tumbling into the car in the high winds.

This 5k run features two laps  that each include a short but brutally steep hill, strategically positioned shortly after a stretch of very sandy beach to maximize pain. The beach (the light patch in the course picture HERE) seemed much longer on the 2nd lap. I wasn’t last and even managed to finish in the top 15 in the men’s group, which is as high as I may ever finish. Unless the next run has only 14 men.

California: A few days of running in Silicon Valley means, almost inevitably, that you will have to run through a Cisco campus at some point. My runs started with a half mile through the campus near the 880 / 237 intersection, and then on the road over to the Coyote Creek Trail, and back along a short stretch of the 237.

The California Loop in Milpitas - Cisco on the right side

Cork, Ireland: International travel can wreak havoc on an everyday running schedule, and requires a little careful planning what with the time changes and the long hours in the air. In this case I was able to run at home on Sunday afternoon, then fly to and arrive at the hotel in Cork on Monday night about 9 p.m. and hit the streets. Halloween night.

Cork - Running off to the upper right

Fortunately an Irish colleague had been visiting the U.S. the previous week, so he was able to give a recommended route so I could avoid a sufficient amount of the hazardous reveling. My route around the town took me past the occasional batch of costumed lads, and I was also surprised to find an Occupy Cork group along the way by the bank street. They had their small collection of tents – rumored to be only partly filled – and a sentry out front. Or maybe he was just renting space in the open tents. A few days later I took this longer run up Blackrock Road and back by some water (click for a close up). You may notice that this one goes right by the stadium where I saw a hurling match on a previous trip.

The Cork Run

Marathons: Well accomplishment is mostly about deciding what we can claim is an accomplishment, and I applied some creative thinking toward that on one of these runs. I estimate that I averaged close to 3 miles/run over the 100 days (going between 2 and 6), certainly at least 2.62 miles on average. And that happens to be one-tenth of a marathon distance. So, with careful use of bold and small fonts, I can say that for those 100 days, I ran a marathon [worth of miles] every week and a half. Now that is impressive (sounding). Fame and glory is just a statistical extrapolation away if you word things right (and use fonts carefully).

The Streak: Now that I’m in the post-100 days, there are two conflicting things pestering me. I’ve discovered the Running Streak list of those who have run at least a mile every day for a year. If you follow that link, you’ll see that there are currently 6 people who have done this for at least 40 years. And I’m only 260 or so days away from the one-year mark right now. That Running Streak site has two lists, for those still going on their streaks and those who stopped. You can imagine some human interest stories for some of the folks on both lists — such as one Geza Feld of Farmingdale NY, who at 78 has been running for over 35 years, but took off for four days in July 2007. So he’ll never improve on that 30 year streak, unless he keeps this up until he’s well past 105 years old.

I’m entertaining the thought of getting on that list.

But on the other hand, since somewhere before day 70 of my shorter streak, my right leg began trying to withdraw from being part of this experiment. It’s still hurting – various muscles in the upper leg – but I’m continuing my therapeutic technique of just-keep-running anyway. The last few days I’ve dropped down to one mile runs at a slow pace (by my slow standards) to aid healing, and I’m also letting a physical therapist give exercises to provide additional torture. I think I’ll know in another week or two if I’ll be able to continue.

If I do, then on any longer travel, such as another trip to India, I’m going to have to plot how to do a run during the midway layover at the airport. That will be fun. Or not. If you have an exercise feat like this, let me know.

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Running maps traced from mapmyrun.com. Another good mapper is the daftlogic site.

This bad habit started on a lark after reading an article about a guy who’s run at least a mile daily, for 40 years. That kind of achievement takes a certain obsession. As one of the handful of folks in the 40 year club puts it, “What we’re doing is not a mark of intelligence.”

Run #50 was a 5k run on the course where my son had just finished his cross country season. I ran and won the self-declared “open race” at the end of the day. No one else got the message, which is why I won (I led “wire to wire”). Unfortunately I fell 6 seconds short of my target, finishing in 25:05. Now I can spend a long time agonizing about how I could have picked up a few seconds here and there.

Here’s a short photo-highlights of my running journey, as seen through the eyes of my shoes. The runs usually start with this rather sharp uphill, which I always walk.

Once that’s over, the run begins. The number of routes available keeps increasing. But most of them take me past a retirement home, which posts daily advertisements. Another sign boasts that this place (off to the right of the photo) has the best food in town. Well, among retirement homes.

Sometimes I treat myself to the Lake Hills Connector — currently the longest uphill on any of my routes. The location in the next picture occurs after a steady uphill, which turns to this despairing view. But don’t worry, around the corner to the right up at the top … is more uphill! The upside, of course, is that what goes up gets to then run down. For the survivors.

Finally, here’s another fun hill on a different route. In addition to the rough terrain on the narrow path, there is that barrier to avoid bumping into while working around the occasional creeping blackberry plant crossing the path. And the sudden drop-offs that open up occasionally, a couple feet to the left of the path. There’s a major cross-country freeway just off to the right of the photo.

Well, every day on this streak is a new personal world record for those of us who set easy-to-achieve personal records and then make them sound dramatic. I don’t know if I can handle much more of that drama. Maybe 50 is enough?

The male passenger pigeon

I’ve been pondering a rather remarkable fact lately, since learning that passenger pigeons — extinct for about 100 years now — used to number in the several billions. The remarkable thing is that they used to fly around in flocks which were estimated at more than a billion, perhaps over three billion. ‘Flock’ may be too small of a term for that size group.

The bird’s name comes from the French word passager, to pass by. Which these birds could do at a blazing 60 mph.

Here’s an entertaining essay that describes the scene in the U.S. a couple hundred years ago (LINK). Try to imagine being outside one day when a billion birds fly over. For hours and hours. I think it’d be fascinating, and I’d be tempted to lie down on the grass and watch. But it wouldn’t take long to decide that it’s wiser to watch from under some protection, like a tree.

Here’s a curious observation about passenger pigeons that helped lead to their demise once hunting limited their population: “This was a highly gregarious species—the flock could initiate courtship and reproduction only when they were gathered in large numbers; it was realized only too late that smaller groups of Passenger Pigeons could not breed successfully, and the surviving numbers proved too few to re-establish the species.” [a],[b]

In other words, this species took the concept of group-dating to a whole new level (or, to new heights). And it raises an interesting variation on the chicken-or-egg problem: Which came first, 1 billion passenger pigeons or a billion eggs? These critters didn’t seem inclined to populate from small numbers.

Billions

All this got me to wondering: how often, if ever, do I encounter things that number into the billions? There are several billion people on the planet, but on a normal day I probably encounter a thousand or less. Going to an event like a ball game or concert could push that up to tens of thousands.

If you want to find a billion of something one day, it needs to be small sized. It’s easy enough to be around billions of molecules, although they’re a bit hard to see. Grains of sand is a good choice. I estimate that in a moderate sized sandy beach, there are probably more than a trillion grains of sand, and about a billion of them lying on the surface so in a sense you can more or less see them all at once. (For the curious, see calculations below.)

Tree leaves are a candidate for encountering a billion in a day. I live on a greenbelt and so I spent some time estimating leaf count per tree. This varies widely with tree type and size, of course. I estimated perhaps 5,000 to 10,000 per moderate sized tree, and maybe 10 – 20 times more, up to 200,000 on the big trees. Here’s a panoramic shot out back, with the world curving the wrong way due to the panorama stitching effect.

There are a lot of trees in this greenbelt, as shown in the satellite picture of the area, below. It would take more than 10,000 trees at these (wild) estimates to make the billion — might be possible. So a day of strolling through such forested areas should put one in the presence of a billion leaves. Not bad for finding a billion of something that big.

Rule of thumb: People, Ants, Stars

Critter wise, there are a lot more ants on the earth than there were ever passenger pigeons — many quadrillions, but you’re not going to find a billion in one day (hopefully). But here’s a very handy rule of thumb. With about 7 billion people on earth, something in the vicinity of 100 quadrillion ants, and something in the (very large) ballpark of 70 sextillion stars (70,000,000,000,000,000,000,000) in the universe, a handy (and very approximate) way to relate these is:

For every person on earth, there are about 10 million ants.
For every ant, there are about 10 million stars.

It’s simple to remember: just imagine each person covered by 10 million ants, and then each ant associated with 10 million stars.

Estimates: Red tree, 5000 leaves. Big tree, 150,000 leaves.

By the way: remember that Carl Sagan, famous for the phrase “billions and billions” didn’t actually use this phrase (link). This reminds me of a time when Logitech discovered, through customer surveys, that they were thought to be #2 or #3 in the world in keyboards, before they had actually entered that market. This is a good strategy — whenever possible, dominate a market before entering it.

Also, this post is dealing with the “true” billion, the one with 9 zeros (1,000,000,000). Some of the Europeans have developed a bad habit of sneaking in a few extra zeros for a billion (1,000,000,000,000) — see this article (which also includes the important misinformation about Sagan’s billions and billions phrase). Maybe this has something to do with the debt crises there.

Have a favorite thing that you encounter in the billions? Leave a note so we can go looking for more billions and billions.

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Calculations: Taking an average sand grain as having diameter = 1 mm. On a beach that’s about 100 yd (or meters) by 25 yards by 8 inches deep with sand:

# grains of sand total = Volume of beach / Volume of sand grain = (100 * 25 * 0.2 m³ * 10⁹ mm³/m³) / ((4*pi/3)*(0.5mm)³) = approx 1 trillion.

# grains on beach surface = Area of beach / Area of grain = (100 * 25 m² * 10⁶ mm²/m²) / ((pi * 0.5mm)²) = 3 billion

About a year ago Shirlee’s grandson, whom I knew, died tragically, starting my leisurely (or let’s say deliberate instead of slow) journey to write a poem. At that time I managed to get all the way through the title. Shirlee’s passing has motivated a completed Haiku version as a preliminary release; the final poem rendition, that’s a deep and touching thing of beauty, is scheduled for the very distant future.

The nice thing about creating a Haiku poem, as I practice it (using 5 – 7 – 5 syllables in three lines), is that you’re never more than 17 syllables from the end. Some Haiku-ists are not so adamant about the syllable count in English Haiku, seeings as the form developed in the Japanese language.

Anyway, here it is, a teensy-tiny glimpse of the transition to glory that’s ingrained in the Christian view of reality.

The Final Dawn

Eyes close one last time
Winter yields to sudden Spring
Wake to endless light

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* The actual odds are not quite 1 in (365)² since there are not equal chances of being born or dying on each day. But it’s close, since there are fewer deaths in the summer, but more births in the summer. Maybe something to look at in a future post.

The controversy involves some people’s favorite number, pi. That’s the 3.14 etc etc number that’s also written as π. This number is featured in one of the possibly three most famous equations known to the masses (note that it’s good to have something “squared” if you want to invent a famous equation):

1. E = mc² (Einstein’s big winner about energy, mass, and the speed of light)
2. a² + b² = c² (Pythagorean theorem for right triangles)
3. A = πr² (Area of a circle in terms of its radius)

Some upstart folks have starting lobbying that it’s better to talk about a number “tau” (written as τ) instead of our lifelong friend π. All this for a number that is simply equal to 2*pi. That’s it. So tau is about 6.28 while pi is about 3.14. These upstarts want to replace π in equations with τ (well, with τ/2 to keep things accurate).

This might not be a captivating matter to all readers. And that’s OK because this post is actually about a number better than either π or τ. So hang on a moment.

First of all, the tau advocates are passionate that circle size (circumference) should be thought about in terms of its radius (C=τr) instead of its diameter (C=πd). And they claim that this also makes some equations a little simpler. Their full case can be read at this LINK. Take some tranquilizers before reading that so you won’t get too worked up about suggestions that we relegate π to second class citizen status. This is almost as unthinkable as deciding that Pluto is no longer to be considered a planet. As with Pluto, it will never happen. In any case, a rebuttal to the τ manifesto can be found HERE.

Ending the pain: e-volve

Enough of that. It’s time to end all that numerical saber rattling by moving those two numbers aside for the number that actually deserves top honors. It’s known as ‘e’, and like π it’s value is written by an endless string of decimal place numbers that doesn’t repeat: 2.718281828459 … and so on forever.

This number is at the heart of an exponential equation that has the following curious characteristic: at any point, the value of the equation is equal to the rate at which the equation is changing. Yes I know, that’s profound and at least 75% life-changing. The rather simple equation is: y = e^x, as shown in the picture.

So here are approximately 3*e (8) reasons to go with ‘e’ over its competitors.

1. It’s used in equations relating to exponential growth or decay, such as population growth or compound interest. People do not use pi when analyzing how bacteria can multiply to take over the world, or how many years it will be after they’ve died before they can actually afford to retire. It can even be used solving ‘derangements‘ which is obviously a cool word even though we don’t know what it means.

2. We are living in exponential times, the theme of this video, and e is all about exponential. We are not living in pi or tau times.

3. Its name has a nice history, involving other letters.

While the concept of e has existed in the universe from way back (since the times when people could count to almost 3), it only started to be used and written down in the 1600′s. An early reference comes from work of one John Napier. He forgot to name it, and later in the century Jacob Bernoulli ‘discovered’ the constant explicitly and it was named ‘b’ for a while.

But in 1727 or 1728, the 21-year old Leonhard Euler came along and figured out a number of important properties about e. But mainly he started calling it ‘e’ in an act of extreme humbleness. There are reports that it was also briefly called ‘c.’

4. As a number, e is both irrational and transcendental. Like most of our bosses. Admittedly, π and τ also have these properties, but who’s counting. And transcendental is another nice sounding word that we don’t understand but will use freely.

5. e is involved in two of the easiest possible math questions that can make you look smart even if you aren’t. Here’s a tidbit from calculus: It turns out that the derivative of e^x is e^x, and also the integral of e^x is e^x (ignoring the inevitable constant that comes along with integration). So if someone asks what the derivative or integral of e^x is, you don’t have to remember the details, just confidently mimic back the answer: e^x (pronounced “e to the x”).

Let’s see π or τ be such an easy answer to a complicated sounding question.

6. Because of the previous point, e is involved in an excellent gimmick that a math teacher can play on students.

Teacher: What’s the derivative of e^x?

Student: e^x?

Teacher: Yes, that’s what I’m asking, e^x. What’s the derivative of e^x?

Student: e^x

Teacher: Are you deaf?? Yes, I want the derivative of e^x. Now tell me the answer!

Student (emphatically): e^x!

Teacher: All right, if you’re not going to answer, let’s try a different one: What’s the integral of e^x? Ignore the constant in the answer.

Student: e^x

Teacher: Yes I’d like you to tell me the integral of e^x.

Student: e^x

Teacher: [etc. etc.]

After a while, the teacher expresses exasperation, rolls eyes, and says with resigned drama: OK, let’s switch gears. What’s the 4th derivative of sine of x?

Student: sine of x

Teacher: Yes, tell me its 4th derivative

Student: sine of x

Etc.

7. Google’s IPO in 2004 sought to earn e-billion dollars, or $2,718,281,828 (and some change). If Google likes e, it must be good. I verified that with Bing.

8. Smaller is bigger

While 2.718… is smaller than 3.14… which in turn is smaller than 6.28…, this discussion on ranking allows us to accurately but paradoxically write,

e > π > τ

This is illustrated vertically in the figure above. Click on that figure to see how e feels about that.

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Teaser for future post: an easy way to quickly remember and recite more digits of e than even 99.9% of mathematicians can recite. Can’t wait.

As I am closely related to some people who trace their fairly recent ancestry to North Korea, I do not question the truthiness of this claim. You cannot seriously doubt any such story coming from the country of the second happiest people in the world, as discovered in a survey originating from same said second happiest country.

But I need to warn them of some things to watch out for in future sports training, because I fear headlines like these:

I’m sure the North Korean team was the second happiest team in the world to find themselves being hit by lightning.

When is nothing stronger than something?

Well, one answer is: when the nothing is something that isn’t there any more.

Consider for example something that is nearly nothing: Air. Imagine the amount of air in a decent sized balloon. It’s hard to appreciate how powerful that air is until you take it away. Thanks to gravity (that fundamental force that’s always getting us down) pulling on the little invisible air molecules, the Earth’s atmosphere weighs in at about 11 trillion-trillion pounds. At the surface, that’s about 14.7 pounds per square inch. That adds up, so that an open newspaper has a few tons of air pushing down on it.

Fortunately this air pressure pushes on things in all directions, so we don’t notice it so much until it gets removed. Suck the air out of a pop can and it would collapse from the surrounding pressure. But if you make a strong enough container that won’t collapse, you can earn a small place in the history books.

In the 1650′s the mayor of the German city of Magdeburg, one Otto von Guericke, figured out how to make a vacuum pump. With the flair of a modern-day infomercial producer, he sought a demonstration to dazzle the crowds with the power of the nothingness that his pump could produce.

He fashioned two bronze balloon-sized hollow hemispheres (about 1.5 ft across). When placed together, they could be easily separated. But with the air between them pumped out, the resulting vacuum held the two hemispheres tightly. So tightly that in various showings he was able to take 8 to 30 horses, split into two teams pulling the resulting sphere in opposite directions, without separation. Once the air was let back in, the hemispheres fell apart.

And so nothing proved to be stronger than at least several horses.

Nothing like Search Trivia

As you may know, searching in Google or Bing using “double quotes” forces the search engine to find the exact phrase, instead of variations that change the word order or may use less than all of the words. Before this post was posted, if you searched for “nothing is stronger than something” with those double quotes, Google gave only one hit (here) and Bing found zero matches. In the modern world, this is nearly impossible and means that this phrase must be Special. If you don’t use the double quotes, you’ll get hits for things like ‘nothing is stronger than love’ and other non-Special things like that.

Should we conclude that Bing has figured out the power of the vacuum since it had zero hits? Maybe. And if you know other cases of strong nothingness, please comment.

Half-full, half-empty, or ... ???

We could tackle the easy questions like why anything exists, or how one could know there is a God, but today we’re going all out. It’s time to solve the haunting dilemma: Is the glass half full or half empty???

I will offer you a set of choices.

Half full: the glass is half-way full of the liquid.

Half empty: the top half has no liquid, it’s empty up there.

Full (#1): The glass is full, half way with water and half way with air.

Empty (nearly): In either the liquid or the air, consider the molecules and atoms that make up the contents. The atoms are made up of sub-atomic  particles such as protons, electrons, and neutrons. The size of these, in the particle sense at least, makes up only a teensy tiny fraction of the space. The protons and neutrons are tightly packed at the atoms’ cores, with the much smaller electrons buzzing around in the vast emptyness of the remainder of the territory that comprises the atoms. These account for such a small volume that the atoms (and hence the glass) is about 99.9999999999999% empty. (OK, maybe that last digit was supposed to be an 8, I’m not sure.) And that’s 0.0000000000001% full for you incurable optimists.

Emptier than that: Most of the volume of the atom’s particles is found in the nucleus. But the protons and neutrons in the nucleus are made up of 3 quarks each, and the quarks are extremely tiny themselves, so that the protons and neutrons could be thought of as mostly empty space. In a sense.

Emptier yet? Maybe. This emptiness may continue “all the way down.” Here’s a discussion of trying to look into quarks: click here.

Full of fields

Full (#2): The glass is full of fields. There are electric, magnetic, gravity fields and waves everywhere inside that glass. Just lower a compass inside either the air or the water to realize this.

Not recommended: lowering your iPhone in to see if its built-in compass works under water. But if you do safely float your phone inside the glass, you’ll find that you can call it, thanks to the electromagnetic waves that make their way through the glass, liquid, and air.

Full (#3): The sub-atomic particles, according to quantum theories, are constantly exchanging things like photons and “bosons”. Because they like to. Kind of like playing catch, in a very small and quantumy sense.

Empty and Full: Hold onto your brain. The quantum world knows of virtual particles, which come in pairs (like electrons and positrons). These tiny something-or-other pairs  pop into existence and then re-combine lickety-split and go back out of existence. That keeps the quantum accountants happy. It’s worth noting that these are virtual particles in the sense that they’re not real particles, but as it turns out they’re real, too (click). Ouch.

If we consider any bit of the glass contents for a very short time, we can’t be sure there aren’t some virtual particles there, making a temporary existence (and generally partying it up for a billionth of a trillionth of a second). As one physicist puts it, referring to an ‘empty’ box, it’s “… both empty and full of all manner of particles, at the same time.” That’s due to a gift from the superposition notion of quantum physics. Here’s a quote worth committing to memory and sharing with your friends:

“In quantum physics, even a perfect vacuum is a constant storm of activity, with “virtual particles“ popping  into existence for a fleeting moment, thanks to zero-point energy, then disappearing again.”

This is one of those comments that would be funny if the physicists weren’t so confident that it’s been verified to high precision.

And just in time, you can get yourself a T-shirt appropriate to the topic.

Any other views on the glass? Let us know. We (obviously) need help.

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Sources: For emptiness of the atom, see Frank Close’s Nothing: A Very Short Introduction pg. 26.

For the physicist quotes, see Chad Orzel’s How to Teach Physics to Your Dog, the Virtual Particles chapter.