In 1638 Galileo Galilei, who is called the Father of Science, published the Square-Cube Law. Frankly, it’s not particularly clever as scientific discoveries go. It’s an observation that big things are bigger than small things. However, the particular way in which objects scale does create a few interesting implications.

I’m going to explain the concept using Jell-o. Alright, so imagine a perfect cube of that fruity lime-flavoured gelatin dessert sitting on a plate. Let’s say the cube is 1 inch in all directions. But, seeing as how there’s always room for Jell-o, you say you want “twice as much”. So, you would be expecting a cube that is two inches tall. Twice as much, right?

Not so! It may be twice as tall, and twice as wide, but the other measurements of size have more than doubled. The surface area has been squared, and the volume has been cubed. (hence Square-Cube Law) So, going by the volume, you actually have eight times more Jell-o in a 2-inch-sized serving as you do in a 1-inch-sized serving. A serving 4 inches across would contain 64 times as much Jell-o!

This exponential growth puts a hard limit on how big your Jell-o serving can get before it overwhelms the structural integrity of gelatin. As the volume increases, so does the weight of all that Jell-o pushing down on the bottom-most layer. (the mass is growing faster than the footprint, so the pressure increases) If you visualize this growing cube on your dinner table, you can picture it begin to bulge and eventually crush itself into a gooey mess.

This same law puts a limit on the size of land animals. It explains why ants can walk around on spindly little legs while lifting 50 times their body weight, compared to elephants with their tree-trunk sized feet who would strain to lift a quarter of their mass.

It also affects more than the size of animals. Elephants are practically naked (compared to most other fuzzy-haired mammals) because they have significantly more inside (volume) relative to their outside (surface area) and have a much harder time cooling down their body temperatures. Maximizing the surface area for cooling also explains the big floppy ears and wrinkly skin, which can expel more heat than a smooth surface.

It also explains why the Nazis failed when trying to build a massive tank, and why our giant friend Robert Wadlow needed leg braces to walk. Oh, and why an elephant might die if it could only jump, while a mouse could safely fall off a building. And lastly, if not to beat a dead horse, it explains why Goliath probably wasn’t ten feet tall.

• Source: Galileo’s Square-Cube Law – DinosaurTheory.com – which is just the introduction to the rather curious problem that huge dinosaurs seem to contradict the law. I’m not done reading the whole theory on that website, but so far it’s quite interesting!

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• What is Light made of?
• The Wide World of Electromagnetic Wavelengths

Last week I was writing about Goliath, the giant of biblical renown. The earliest records mark his height at 6 and a half feet, while later stories (including the Old Testament bible) report him being just shy of ten feet tall.

I had commented that the average height was shorter then, so being over 6 feet might very well be gigantic, relatively speaking. Well, now I’m doing the follow-up to that. Just how tall have humans been throughout history?

As it turns out, the answer is remarkably un-dramatic. Currently, the average height of men worldwide measures in at 5 feet, 9 inches. Turn the clock back 1000 years and the average height then was… [suspenseful organ sound] …5 feet, 8 inches. So in the last 1000 years we’ve grown an inch? Not quite. In around the 1600′s when our health and sanitation hadn’t yet caught up to the size of growing cities, human height was averaging 5 feet, 5 inches.

So we’re looking at a general fluctuation of maybe 5 inches per millennium. Not too exciting. Now let’s talk about some notable exceptions!

The tallest man… ever! Robert Wadlow was measured at 8 feet, 11 inches. He died in 1940, at the age of 22. Being ridiculously tall does seem to affect your lifespan. The average age of people over 8 feet is 43 years. (not counting two gentlemen still towering among us) Biologically, the human body runs into a lot of problems at that size, which seems to cast some doubt on Goliath pushing 10 feet and still being an able-bodied warrior.

Now, I find it rather amusing that there is a speck of physical evidence in support of the biblical height claim… but it comes from our ape ancestors. The Gigantopitecus blacki is an ancient species of ape discovered in southern China. All that has been found is a jaw bone and a few teeth, but they are huge! Some very smart people have been working on this, and by comparing the size of the jaw to its nearest related species the whole ape is speculated to be 10 feet tall. It’s a real-life sasquatch!

There are plenty of other stories of giants. Many claim “hearing about” giant skeletons found around the world, but in every case… every single case… the bones were either A) secreted away by some un-named government organization, or B) mysteriously lost. And for science, frankly, that just won’t do.

• Source: Historically Tall – The Height Site
• Source: Gigantopithecus blacki

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After losing a little belly this summer, I’ve become more aware of my belt. It’s about an inch and a half wide, made with fairly thick “genuine” leather, and a heavy steel buckle. I would estimate it to hold over 200 pounds without any trouble. The phrase “swatting flies with a sledgehammer” comes to mind. Why on earth do I need such a heavy-duty strap for the rather pedestrian duty of cinching my trousers in a bit?

I wanted to figure out how this over-qualified leather belt came to be accepted as the right tool for the job.

From the bronze age right through to the start of the 20th century, belts were almost exclusively tied to military uniforms. While they sometimes came into function as a strap to hold a sword’s scabbard, they were very often employed strictly for fashion. In modern history, from the Crimean war through to Word War II, tight form fitting belts were used as part of the uniform design to emphasize broad shoulders and protruding chests to look more intimidating. (many officers in the Crimean war were said to wear corsets to further shape their figure)

In the civilian world, belts were rarely seen. Suspenders (also known as braces) were the popular choice for keeping your dignity in place. Even cowboys liked their suspenders until Hollywood came along. The whole idea of the large shiny belt buckle first appeared in movies before taking it’s place in real life cowboy culture.

Belts came into favour when “the boys” came home from the war and brought that piece of the uniform with them. Combined with a lowering of the fashionable waistline, the belt took its place on top of the “pants-keeper-upper” podium.

So, it seems there’s absolutely no good reason why I’m wearing such a clunky belt for a job that could be easily accomplished with a length of yarn.

Bonus fact: In my research I also learned about the origin of the questionably fashionable trend of having your pants almost falling off, hanging halfway down your bum, called “sagging”. Turns out, that little fad came from the prison scene where inmates weren’t allowed to have belts for safety reasons. Of course, we all know prison inmates are just the sort of folks we all want to emulate, so it became a hot look.

• Source: Belt – Wikipedia

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I like to think I’m really in tune with my readers, and I know, without you even having to ask, what you really want to learn. You’re probably thinking, “Hey Ryan, if we all get together on this we could probably bring back some words that have been lost to time.”

Well, dear reader, you’re absolutely right. Here’s some dusty old gems to work into your everyday conversation.

Chittyfaced – A gaunt, slim face that might be associated with not getting enough to eat. “You’re positively chittyfaced, my dear! Here, have a meat pie.”

The word derives from a ballad about the monster named Chichevache. (in Olde English, chiche = starving, vache = cow) You see, Chichevache’s diet consisted solely of “patient housewives”, and as such he was constantly starving due to lack of available food.

Rigadoon – A lively dance, particularly referring to the feet. The Scottish variation was Rig-adown-daisy which referred to a dance that, if done in a field, would trample the daisies. “Hold me closer tiny rigadooner.”

This may have been corrupted from the name Rigaud, who might have invented the dance, combined with the Italian donzella for dance.

Further research reveals that in the 1980s there was a line of puppets, no doubt inspired by the Cabbage Patch Kids, called the Rigadoon Gang

Inveigle - To be hoodwinked or blinded, in terms of deception. “Bullwinkle was inveigled by Natasha’s sensual charms.”

The in is not a prefix here (there is no plain viegle) because this is an anglicized French word, aveugler, with the same meaning. It was written as far back as 1547.

So there you go, add a little Olde English flavour to your emails this week.

• Source: “Folk-etymology” on Google Books – circa 1882

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Yesterday as I was writing an overview of Electromagnetic waves (which manifest as radio, heat, light, and more depending on the wavelength) but I left myself with the question of what “stuff” makes up these waves. As I discovered, I can give you two different answers that are, apparently, both correct.

Now, just a quick catch-up for those who missed yesterday’s class: Visible light is but a very small section of the electromagnetic spectrum. The different colours of the rainbow are created by a difference in the wavelength of the electromagnetic wave. Violet is the shortest, while red is the longest wave. These very same electromagnetic waves can get longer to become invisible heat (infrared), or radio waves. On the other side, shorter waves turn into ultraviolet radiation, x-rays, or gamma-rays. It’s all the same stuff, physically, so now I’m trying to figure out what that stuff is.

The original answer defines light strictly as a wave. The wave is created as an electric field interacts with a magnetic field. The wave can travel endlessly through this electro-magnetic field, which exists throughout the universe.

You’re not the only one who thinks that does a pretty poor job of explaining anything. Einstein, Planck and other scientists felt so unfulfilled by that answer that they formulated the whole concept of quantum theory. In that light is not a wave, but rather particles full of energy called photons that can travel at the speed of light. A burning fire would then be emitting photon particles in every direction, and the energy contained in a photon would replace the defining wavelength as the means of determining whether each photon would be the visible orange glow, or the infrared heat.

It’s still not a solid answer to what is the stuff of light, since photon particles have no mass. There’s nothing there, other than “energy”, which could take us on a similarly confusing path to figure out just what energy is. I’ll pass on that one, thanks.

To add insult to injury, there’s a little thing called wave-particle duality, that shows by experimentation (meaning it’s not just some crazy idea, it can be observed) that light is both a wave and a particle. Not that sometimes it’s a wave and sometimes it’s a particle, but in fact that light is both a wave and a particle simultaneously.

At this point, I’m going to simultaneously throw my hands up and give in. It seems I’m not quite ready to understand what light (or any electromagnetic wave) really is in a tactile sense that I can wrap my head around.

To offer a little comfort, I did find this quote from Richard Feynman, who was always very good at explaining things to everyday folks like us:

“We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics.” – Prof. Richard Feynman

• Source: What Is Light? – ThinkQuest
• Regarding wave-particle duality, here’s a good animation explaining the oddness of the “dual slit experiment” (YouTube video)

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• The Shape of the Universe (part 2): Infinity and Beyond
• The Shape of the Universe (part 1): the Hypersphere

Question: What do the following things have in common?

• Hearing an ad for “Armor Hot Dogs” played over the radio.
• Cooking some hot dogs in the microwave oven.
• Roasting hot dogs over a campfire.
• Seeing mustard stains on your shirt from that hot dog you ate.
• Tanning on the beach after going to the hot dog stand.

The answer: They are all the result of Electromagnetic Waves! (oh, were you distracted by the hot dog references?)

Radio waves, Microwaves, Infrared waves (what we feel as heat), Visible Light waves, Ultraviolet waves… plus the mysterious X-ray waves, and Gamma-ray waves. Each and every one is an electromagnetic wave. Though each can do very different things, the only difference between them is the wavelength.

So what is wavelength? Really it’s about as simple as it sounds; it’s the length of a wave. If you think of ocean waves there are high spots (peaks) and low spots (valleys). If you measure from peak to peak you would have the entire length of one wave.

Some example wavelengths:

• AM Radio Station ~ 300 meters
• FM Radio Station ~ 3 meters
• Microwave oven ~ 1 foot
• Radar ~ 5 centimeters
• Body heat ~ 10 micrometres (micrometre = 1 millionth of a meter)
• The colour blue ~ 0.5 micrometres
• Sunburn inducing Ultraviolet ~ 30 nanometres (nanometre = 1 billionth of a meter)
• Gamma rays at the far end of the spectrum go beyond 0.003 nanometres across.

In the same way that a mountain and the beach are made of the same thing, sometimes size does matter.

Now hold on just a minute, buster! I have a question. Waves don’t really exist as a physical thing. It’s just a method of movement. I understand a wave of moving water, but what is a wave of electromagnetism? I mean, what “stuff” is moving?

Well, all electromagnetic waves move at the speed of light. The fact is, they are light. Or more accurately, light is them. So to answer what is an electromagnetic wave, you have to answer what is light?

That’s such an interesting question that I’m going to save it for next time.

• Source: NASA explains Electromagnetic Waves to Kids (or anybody else who wants a basic understanding)

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The story of “David vs. Goliath” has become a popular parable anytime the “little guy” faces off against a giant. The people do love a good David vs. Goliath triumph. However, you may not be so enthusiastic if you get to know the rest of the story.

Let’s start with the famous incident. It’s about 1000 BC. The then homeless Isrealites under King Saul are facing off against the Phillistines. The two fought all the time. In this battle, there was this one big jerk, Goliath, that kept calling out for a one-on-one fight with an Isrealite champion. The fate of battles was thought to be pre-determined, so a single match could reveal the chosen winner allowing everybody to go home early. I think we all know how that turns out. (hint: scrawny little David wins)

Fun fact: the giant Goliath is said to be four cubits and a span in the earliest accounts. That’s about 6 and a half feet tall. Not so great by today’s standards, but if you’ve ever seen suits of armour in a museum it’s obvious that humans are taller than they used to be. In later writings, Goliath came to be 6 cubits, or nearly 10 feet.

David was a favourite of King Saul at this point. He was part of his personal guard, but with David’s new popularity, the King gets jealous. Skipping the details, Sauls sends David away, David teams up with the Phillistines, attacks the Isrealites, and King Saul is killed along with all but one of his sons. Due to his popularity, David is made to be the king of the Isrealites (switching sides again), except that the rightful heir, Saul’s last son, still lives. David simply has him killed to settle the matter. Long live King David!

His ambition is to establish the kingdom of Isreal, which obviously proved succesful, but was not without a few massacres as they traveled up to where the City of David (Jerusalem) was built. The Old Testament bible clearly tells what happened to one of the the tribes along the way:

And he smote Moab, and measured them with a line, casting them down to the ground; even with two lines measured he to put to death, and with one full line to keep alive. And so the Moabites became David’s servants, and brought gifts. (2 Samuel 8:2 – King James)

Yes indeed. Two thirds of a nation were randomly chosen and slaughtered. The same thing happened to the Edomites and Arameans.

Now, being a “fact” blog I feel compelled to point out that there is very little archeological evidence to support this story. Though it seems true that King David did exist, and many of the events did occur, the timeline and characters may be way off. All we have is stories that may have changed with re-tellings. For example, there is a story very reminiscent of David vs. Goliath in the Greek Illiad by Homer, who may have lived a century or two before David.

Generally, it’s best to take these stories as mythology with moral lessons, which brings me back to my point of telling you all this… The morality of David vs. Goliath isn’t so simple. Perhaps you’ll want to consider this next time you relate an under-dog hero to the infamous David.

• Source: After watching a History channel show that dramatized this whole thing, I went hunting for a less made-for-TV version of the story. I started with Goliath – Wikipedia and cobbled together this story from multiple pages there.

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