Archive for the ‘Fried Science’ category

Getting Mathematical on Weeds.

May 31, 2011

Dandelions amaze me.

We tend to take them for granted.

“Huh.  They’re just stupid weeds. ” , many of us might say.

But if you look closer, they’re actually quite beautiful.

And if you zoom in REALLY close, you’ll find something even more amazing.

Notice, there’s definitely a spiral pattern there.

If you connect the dots, you can definitely count 13 curves in the clockwise direction.

But if you connect the dots in a counter-clockwise direction, you get 21 curves.

Now, remember those numbers, (13 and 21), while I digress for a bit.

Consider this mathematical sequence of numbers.

0,  1,  1,  2,  3,  5,  8,  13,  21,  34,  55,  89….

For those of you who don’t recognize this,   these are Fibonacci numbers, where any given number is the sum of the previous two.

It’s quite simple:

0 + 1 = 1

1 + 1 = 2

1 + 2 = 3

2+ 3 = 5…and so on.

Now, if you draw a series of squares,  based on the Fibonacci sequence, and you get something like this:

And if you draw a continuous arc though each square,  it forms a spiral seashell pattern, like this:

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This is called the Fibonacci Spiral

Now, let’s take my 13 clockwise red-curves:

And if I take them, one by one, and superimpose them on the Fibonacci Spiral, I get this:

Kinda fits, doesn’t it?

Same thing if I take the 21 counterclockwise curves…

Again, each curve also seems to fit, when superimposed  on the counter-clockwise Fibonacci spiral:

Now, let’s just recap:

I zoomed in on a photo or a dandelion, connected dots and generated some rough curves.

And the shape of these curves fit a spiral based on the Fibonacci sequence.

Not to mention, the number of clockwise and counter-clockwise spirals are 13 and 21.
Which are Fibonacci numbers themselves.

What’s going on here?   Is this magic?   Or  a fluke?

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Actually, this is no accident.

You see, Nature tends to like Fibonacci numbers.   For example, you rarely see flowers with 4 or 6 petals.  But you see many with 3, 5 or 8.

Flowers seed pods are also arranged this way.  The number of spirals are always Fibonacci numbers…one clockwise, one counter-clockwise.

In this case, with my dandelion,  it was 13 and 21.  With larger flowers (like Sunflowers), you’ll find numbers 34 and 55.

But why Fibonacci numbers?

Basically, it has to do with Nature trying to optimize itself.  With flowers, if seeds are arranged in Fibonacci spirals, you can fit more of them onto the plant,  and you get more bang for your buck.    There’s a good interactive exercise that demonstrates this.

I won’t get into the whole mathematical explanation.   But you can find some good discussions here and here.

It’s not just dandelions.  You’ll also find Fibonacci sequences with pine cones, pineapples and asparagus and seashells.       Plant leaves are arranged in Fibonnacci spirals, to optimize the sunlight they recieve.

Fibonacci numbers are everywher in Nature   More examples are shown here.

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It’s pretty amazing, when you think about it.

Take an abstract concept.   A sequence of pure, unadulterated numbers:

0, 1,  1,  2,   3,  5,  8,  13,  21,  34….

And it’s architecture upon which much of Creation is built.

It’s staring at us, in our face.

The miracle of Pure Math, combined with Mother Nature.

Even with a lowly dandelion.

..and THAT’s why they amaze me.

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Perfessor Friar finds his True North

April 21, 2010

Polaris, known as the “north star”, or “pole star“, isn’t a particularly bright star in the sky.   In fact, in terms of brilliance,  you can consider it a “B-lister”.   But it’s one of the most important stars in our heavens, because it happens to be aligned the axis of the Earth’s rotation.

This means Polaris stays virtually motionless in the night sky while all the other stars appear to rotate around it.   And Polaris always points North.

(Well, not exactly, but to within 0.5 degrees, which is close enough for most of us.)

People all over the planet have recognized this for hundreds of years.    Which makes Polaris a pretty handy celestial guide to help us find our way around.

The angle Polaris makes above the horizon corresponds to your latitude.    If you were at the North Pole,  at 90 degrees north, Polaris would be directly overhead, and the stars would circle around you in a counter-clockwise manner, neither rising or setting.

The further south you went, the lower Polaris would be in the sky, until you got to the Equator at zero degrees north.   Here, Polaris would lie on the northern horizon, with the stars rising and setting from East to West.

The early explorers who first crossed the oceans knew this.  They’d measure the angle Polaris made above the horizon to figure out their latitude.    This was usually done at dawn or dusk, when both the horizon and stars would be visible a the same time.

(Unfortunately, there’s no simple way to measure longitude.   That came much later, but that’s another story…)

Constellations that are close to Polaris are always present in the night sky…they just circle around the North Celestial Pole, neither rising nor setting.   These are known as “circumpolar” constellations.   The further north you are, the higher in the sky these circumpolar constellations are.

In the Northern Hemisphere, examples of circumpolar constellations are Cassiopeia (the “W” you see in the sky) and the famous Big Dipper, which forms part of Ursa Major, the Great Bear.

(By the way, the Greek word for Bear is “Arktos”.   Hence the origin of the word “Arctic”,  referring to the part of the planet where the Great Bear is more prevalent in the sky.  And conversely, “Antarctic” refers to the opposite part of the globe in the southern Hemisphere).

As I mentioned earlier, at the Equator, Polaris would be located just on the horizon.   As you’d proceed further south, Polaris would disappear below the horizon, as would the northern constellations.   However, the South Celestial Pole would become visible and rise higher in the sky, as would the southern constellations.

One of the more famous southern constellations is the Southern Cross.   You can’t see it in Canada or the States, except perhaps glimpses of it in Florida.   But don’t feel bad.   Those who have seen it say the Big Dipper is more impressive.  And I tend to agree.

As for the South Pole, unfortunately, there isn’t really an equivalent “South Star” to guide us.  The closest star would be Sigma Octantis, but it’s quite dim and unremarkable.   It’s nowhere near as prominent as Polaris. is.

Getting back to Polaris: it’s aligned with the axis of the Earth’s rotation, or the Geographic North Pole.   Let’s not confuse this with the  North Magnetic Pole, which is where the Earths’ magnetic field intersects the Earths’ surface.

The Geographic North Pole is at 90 degrees latitude.   Right now the North Magnetic Pole is at about 82 degrees latitude (about 850 kilometers away), but its location is changes by tens of kilometers a year.

A compass will point to the North Magnetic Pole.  From where we are, thousand of miles away, a compass reading is close enough to help us find the true, geographic North. (It’s like San Francisco and LA being about the same direction from New York).

But at higher latitudes,  the compass readings will be off, and will no longer be practical for navigation.   At that point, we would need to refer to Polaris to find the “True North” (That is, we you don’t have a GPS.)

If you think, however, that we can always rely on good ol’ dependable Polaris, guess again.

The Earth’s axis of rotation, as measured against the stars, slowly changes directions, similar to a wobbly spinning top.    Though this it takes a while….the cycle takes 26,000 years to complete, and is known as the procession of the equinoxes.

What this means is that the North Pole will point to different parts of the sky over time, and it’s constantly changing.

Right now, we happen to be alive at a time when Polaris happens to be the Pole Star.

In 3000 BC, the Pole Star was Thuban (a star in the constellation of Draco).   In 14,000 years, the Pole Star will be near Vega, wich is one of the brightest stars in the sky.

And in 27800 AD, it will be Polaris again.

Just goes to show, what goes around, comes around.

Even with the North Celestial Pole.

Science that I’m Ungrateful For

July 3, 2009

The Large Hadron Colider
When they got this thing up and running, some people were worried it would smash together subatomic particles with such force that it would create a black hole,  which could eventually swallow the entire earth.

AWESOME!!!   …How cool is THAT?

But as it turns out, this bajillion-dollar gizmo ran for about week, then glitched.  Now it’s been shut down for almost a year.

Borrrrr-ring …..Thanks for coming out.

….NEXT.

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The Triple Point of Water
Solid, liquid and gas.  All present at the same time.

Hmph.   NOT the best time to be outdoors.

If you don’t believe me, just go to the top of Mt. Trembant, Quebec, in January.

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Dark Energy
This mysterious force is pushing our universe apart.  We still dont’ know what it is.

But if things keep up the way they are,  eventually all the galaxy clusters will spread out and never see each other again.   Stars will die off, and the Universe will ultimately become a cold, dark lonely place.

Forever.

Boy.  Talk about a Buzz-Kill.

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String Theory
According to some Egg-heads, everything we see is made up of tiny 10-dimensional vibrating strings.   Only they’re curled up inside sub-atomic particles, and are so small, that we can’t see them.

Yeahhhh, right.

Hey, I got a theory too.    Neutrinos have little Vikings inside them that like to have sword fights.   Every time their weapons clash, a photon is emitted.

Prove to me that my idea isn’t’ just as valid…..

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Friction
Friction, you’re the reason I scrape my knee when I fall.

You’re why I need to change the oil in my car.

And why we can never have perpetual-motion toys.

Jerk.

But then again, if you didnt’ exist, I woudlnt’ be able to sit down my chair right now and type this.

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Jupiter’s Rings
Bet you forgot . But Jupiter has rings.

But they’re so lame-ass,  only the best telescopes can see them.   In fact, they didn’t even get discovered until 1979 by the Voyageur I space probe.

Hey, Jupiter, nice ANNULUS.

What did you do?   Borrow Saturn’s hand-me-downs?

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Astatine
This is one of the rarest naturally-occurring elements.  Less than one ounce is present in the entire earths’ crust.

Sorry, but in MY books, that doesn’t consist of a real element….ASS-tatine!

Same thing applies for you, Francium.  Not to mention all those other short-lived trans-uranic elements with half-lives in the microseconds.

Why don’ you guys just get the hell off the Periodical Table, and make room for elements that DESERVE to be there.

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Nano-Kelvins
Perfect Absolute Zero is impossible to obtain.

But in the lab, they did manage to come within 0.0000000001 degrees of it.

But…um…what’s with that “1”, after all those “0”‘s?

Just WHO does he think he IS?

I don’t care what anyone says, I’m calling this one ZERO.

(Close enough, for crying out loud!)

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Singularities
You know which singularies I’m talking about:

The ones you find in the middle of  black hole, where the gravity is so strong,  whatever mass there is collapses into zero volume.

I’m sorry, but that’s just WRONG.

(It just messes with my head!)

Singularities, nobody likes you!

Especially quantum physicists.

Perfessor Friar Applies the Brakes

April 13, 2009

Every once in a while,  I’ve heard people ask the following question, something along the lines of:

“Why don’t’ they stick a windmill on top of our cars?  Then when we drive at 60 mph, it would cause the blades to spin, which we could hook up to a generator.   This could make electricity, which we could store in a battery, to power the car.”

Ummm….that would be called a Perpetual Motion Machine, and those only exist in Lah-Lah Land.

Remember as kid, how difficult it was to pedal your bike when it was hooked up to one of those cheezy night-light generators?    Suddenly, it’s a lot more work.

Same thing would apply to your car.  Spinning a windmill takes work.  It would slow you down, acting as a big brake.   You’d end up burning far more energy in gasoline than whatever you’d gain back from any electricity you’d made.

But what if you had a special high-efficiency windmill blades?   What if you had almost perfectly frictionless windmill bearings?

Nope.   Still wouldn’t work.

Even under the most ideal conditions, you wouldn’t even break even.    You’d ALWAYS burn more gasoline with a windmill-generator, than without.

Nature says there’s no such thing as a Free Lunch.

Thank the 2nd Law of Thermodynamics for that.

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Let’s continue the discussion on cars and braking.

What if, instead of a windmill on your roof,  your wheels were connected to an electric generator, that only turned on when you applied the brakes?

This is a whole different story.

When you braked,  the kinetic energy from your car’s mass and speed would now be converted to making the generators spin and make electricity.    This would slow down your car (just like the windmill on your roof would), and THEN you could store this energy in a battery for later use.

Don’t worry, though.   This doesn’t violate any Laws of Thermodynamics.    Remember, there’s no such thing as a Free Lunch.

When you’re cruising on the highway, you’re burning the same amount of gas, regardless.   But it’s HOW the braking is applied, that makes the difference.

With conventional braking,  ALL your kinetic energy is converted into friction on the brake pads and is lost as heat.    All that speed you had, all that gas you burned to get there…Pffft!    Gone! …Never to be re-used again.   And now the atmosphere is slightly warmer.  (Al Gore is crying, as we speak.)

But with electrical-generator braking, the one big difference is that you’d at least recover SOME of your kinetic energy back as electrical energy.   You wouldn’t be creating any more energy, you’d just be wasting LESS.

Which is a huge improvement from before.

This is what’s known as  regenerative braking.

Hybrid cars use this technology.

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Perfessor Friar’s Random Bits of Science Trivia

April 5, 2009

In 2005, we landed a probe on the surface of Titan, which is one of Saturn’s Moons.

Just think of what this involves, for a moment.

Saturn is almost a billion miles away. When you look at it in the sky, it’s an orange dot of light.

And somewhere around that dot of light, is a SMALLER dot of light orbiting around it, that we can’t even see with the naked eye.

Now, imagine firing a gun at 10 times the speed of a bullet, almost 7 years in advance, to try to hit that moving dot around the dot.   Because that’s basically what they did when they launched the Huygens space probe.

Only imagine firing the gun from the surface of a rotating sphere (Earth), which itself moves around the sun. So does Saturn, at a different speed. And Titan moves around Saturn.

Yet NASA managed to compute the right trajectories, and apply the right braking with retro-rockets, so that the probe not only achieved a soft landing on Titan, but managed to send back pictures.

When our grandparents were born, computers didn’t’ even exist, and rockets couldn’t even travel more than a few miles, let alone go into space.

That’s pretty amazing, when you think about it.

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The coldest temperature in the deepest nether-regions of intergalactic space is about 3 degrees Kelvin (-270C).

That’s three degrees above absolute zero (which is as cold as anything can ever get).

But why 3 deg K? Why doesn’t it get colder than that?

Because the 3 degrees is the fossil remnant of the Big Bang:   the huge explosion that was believed to have created the Universe at the Beginning of Time.

The fireball from the Big Bang was intensely hot at first.  But over billions of years, the Universe expanded, and everything cooled off, to the point of where we are today.

But there’s still that remaining 3K of heat left over, that’s present throughout the entire fabric of the Universe.  This is what’s know as “background radiation“.

Though in the laboratory, we’ve managed to get temperatures colder than this, approaching Absolute Zero to within 0.0000000001 of a degree.

So basically, here on earth, we puny humans, with our tiny, insignificant experiments, have created what is the coldest known temperature in the entire Universe.

Not bad, eh? …for hairless apes who only learned to write 6000 years ago!

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By the way, it’s impossible to reach Absolute Zero, exactly.  You can come close to it, but you’ll never quite get there.

It’s not like we eventually can, if we develop technology and design a better way to freeze things.

Nope.  It’s just impossible.

The Laws of Thermodynamics imply that at Absolute Zero, all atoms stop vibrating.   There is zero motion, all particles are in fixed positions.

This violates the Heisenberg Uncertainty Princicple.  The laws of Quantum Mechanics do not allow us to simultaneously know where a particle is and how fast it’s moving (or not moving).

If it sounds complicated, it IS.  I wont’ bore you with all the details.

But just remember, that Absolute Zero is impossible.

Because that’s just the way the Laws of the Universe work.

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It’s fasciniating the way things are quantized at the sub-atomic level, where events take place in discrete steps.

Take electrons orbiting around an atomic nucleus, for example.

Say an electron absorbs some energy. This might kick it up to the next higher orbit around the atom. If this electron loses energy, it would drop back down to the lower orbit from where it came.

But the thing is… the electron can only jump from one orbit to the other. It’s Either-Or. There is no going in-between the orbits.

That would be like the equivalent of someone trying to push you up hill in a wagon.

Imagine if the wagon could only be in two places: at the top, or at the bottom. There would be no such thing as half-way up the hill, or 7/8th up the hill, etc…

Fortunately, things dont’ work this way in our everyday life.

On the human scale, any quantum effects are so incredibly tiny that everything appears to take place smoothly and continuously.

Perfessor Friar rambles about cars, fuel cells and saving the planet.

March 29, 2009

 All this talk about hydrogen fuel-cell powered cars.     Well, what about them?

Remember your high-school science class, when the teacher applied electricty to water with two electrodes?     It would cause electrolysis of the water. The electrical energy would cause the H2O to to dissociate into hydrogen gas and oxygen:

2 H2O + energy = 2H2 + O2

Hydrogen fuel cells work in reverse (I won’t go into the details here).   They combine oxygen and hydrogen gas to form water, and create energy.  

2H2 + O2 = 2H20 + energy

Hydrogen is everywhere on our planet.   Fuel cells don’t generate any CO2 or greenhouse gases,  just water vapor and heat.     Sounds great, doesn’t it?   Wouldn’t it be wonderful if we could run our cars on hydrogen instead of gasoline? 

Well, let’s think of this for a moment.

One way to get hydrogen is from steam reforming, where H2 is extracted from hydrocarbons, mostly from natural gas 

However this process still takes energy, and still generates some  greenhouse gases.   So you’re basically still using hydrocarbons to indirectly power your car.    There is some debate that this is a short-term solution.   It still dosen’t remove us from our dependency from fossil fuels.

Another way to get hydrogen is to electrolyze water.   But the problem is,  the H’s and O’s like to be together in the form of H2O.   It takes a certain amount of coaxing to get them apart.   To do that, we need energy.  (Just like your chemistry teacher had to use a small battery for the hydrogen/water experiment). 

So where would we get that electrical energy to break down water into hydrogen?   From our power-generating stations, naturally, which are based on coal, natural gas, nuclear or hydroelectricity.

Now, what if it happens that your electricity happens to comes from a coal-burning plant? 

Well, then that defeats the WHOLE purpose of your fuel-cell car.     

You’d basically be burning coal…to make electricity… to make hydrogen…to power your car.   The net effect is you’d basically be burning COAL to run your car, which isn’t  exactly the most environmentally-friendly source of fuel.  

Sure, your car might not pollute the local neighborhood where you live, but it most definitely would, indirectly, near the coal-buring plant hundreds of miles away.   

So much for zero emissions.

The only truly zero-emission way to power your hydrogen-fuel cell car would be to generate hydrogen from nuclear or hydroelectric power plants.

Well, lots of people oppose the building of hydro dams.   Besides, there’s only so much hydroelectric  power available (we’ve pretty much dammned up every significant river in North America already).    

The most plausible answer seems to be to build more nuke plants to make more electricity.   Which again,  many people are opposed to.   

So what’s  the right choice?   (Things are never as easy as they seem, are they?)

I”m not saying hydrogen-powered vehicles dont’ have a huge potential.   Yes, we can have zero-emission vehicles that don’t depend on oil or gas.  

We just need to be aware of where this hydrogen will come from, and what price we’re willing to pay to cover the associated costs of getting it to our cars.

Calorie Counting with Perfesser Friar

January 13, 2009

Now that New Years is here, and the big Holiday pig-out is over, lots of us are making resolutions to lose weight.  And we’ll say it’s time to start  “counting calories”.    But how many of us really understand what a calorie actually is?

A calorie is  a unit of energy.   Energy is the ability to do work (applying a  force to move something).  Or the ability to generate heat.    With the exception of nuclear reactions (which I wont’ get into here) that’s pretty much how all the energy is used in this Universe.  Energy goes into work, or is dissipated as heat.

By the official definition (in the thermodynamic sense):    

1 calorie = the energy required to raise one gram of water by 1 degree Celsius.

And that’s actually NOT a lot of energy.   One gram of water is one cubic centimeter.  That’s smaller than the dice you play Monopoly with.   And a change of one degree Celsius is barely something you’d be able to notice by touch.

In fact, if you rubbed your hands together, there you go!  You probably burned several calories’ worth.  The warmth your palms generated could easily heat a dice-sized cube of water by several degrees.

Now, what about FOOD calories?  (The numbers you see in cookbooks or on the food packages).    Those calories are same thing, right?

Well, er…not exactly.

You see, a FOOD calorie is a thousand times larger than a thermodynamic calorie.

(Yeah, I know it’s confusing.)  But don’t blame me.  (Go yell at the science-geeks who made up these names!)

To get back to that definition:

1 food calorie = 1000 thermodynamic calories = 1 kilo-calorie (or 1 kcal).

In the more recent literature, they often talk about food in kilo-calories (kcals) to try to avoid this confusion.

Depending on their size,  a typical adult requires approximately 2000-2500 food calories (or kilo-calories) every day.   And of course, we get this energy from food, that our body burns and metabolizes.   But exactly how does this work?

Think of a log burning in the fireplace.    The log is plant material.  The complex molecules in the wood (cellulose, lignin, resins) react with the oxygen in the air and break down into simpler compounds (carbon dioxide, water, and waste (i.e. ashes).   This combustion process release energy.

The exact same thing happens when you eat an apple, or a piece of bread, or a Big Mac.   Our body converts the complex molecules of proteins, sugars and fats, and breaks them down into simpler molecules  (carbon dioxide, water and waste).  This is also a combustion process, and it also  that releases energy.

Except the food doesn’t burn quickly all at once in a burst of flames.   The process happens happens more slowly, through the biochemical reactions within our cells, spread out over several hours.   But it’s a similar reaction.  Food (i.e. plant and animal material) plus oxygen go in.    Heat, water, carbon dioxide and waste goes out.

In fact, that’s how they measure the caloric value of food. They actually BURN samples of food in specially-devised instruments called “calorimeters”  and measure the heat given off.   The laws of physics don’t care whether the food is burned in a fire place, a calorimeter, or in the mitochondria of our cells.    For a given chemical reactions, the net release of energy remains the same.   And our body takes this energy, and converts it into heat and work.

The heat part, we can easily relate to.   Hold your hand in front of your mouth when you exhale, and feel the warmth of each breath…that’s the heat of your body burning your food.  Anything alive has a metabolic rate and generates heat.

But what do we mean by”work”?

Work, from a physical sense, is defined as (Force x Distance).

Basically, work means pushing something (with a force) to make it move.   We do that all the time with our muscles, when we walk, run, open doors, play with our kids, open the cork on wine bottles.   In fact, right now, I’m using a bit of force with my fingers to make the keyboard move, so I’m doing “work”, in a physical sense.

Anyway, getting back to the 2500-odd kilo-calories you use up every day.   That’s equal to 2.5 million thermodynamic calories, which is quite an impressive number, when you come to think of it.   I wont’ bore you with the calculations, but if you do the math, that’s  enough energy to bring 4 liters of water (just under a gallon) from room temperature to the boiling point.

No way!”, some of you might say.   “Boiling a gallon of water?  That’s way too much!  Surely I don’t get all that energy, just from the food I eat?

Well,  “Yes way!”   You DO burn off that much.   There’s a lot of energy packed into the food you eat. (Have you ever seen a bacon grease fire?) .   Imagine half a pound of buring bacon grease…that’s approximately 2500 calories.  You could probably heat a lot of water with that.

But thankfully, the energy you burn is spread out over the whole day.   Lucky it doesn’t burn all at once, like the grease fire, our you’d have steam coming out of your ears.

Just think how much energy it takes to keep that big hunk of meat you call your body at a  temperature 98.6 F.   In fact, if you do nothing else but breathe and EXIST, it takes a minimum of about ~ 1200 kilo-calories to sustain life.   The remaining 800-1300 kilo-calories are used up moving around, and doing the things you call living.

Now, here’s an interesting fact:  each person gives off about as much energy as a 100-watt light bulb.

Makes sense, if you do that math.    2500 kilo-calories a day = 2,500,000 thermodynamic calories.

Divide this by the 86400 seconds there are in a 24-hour day, and you get (2,500,000) / (86400) =  29 calories per second.

Again, I won’t bore you with the unit conversion.  But 29 calories per second  works out to about 120 watts of power.   Which is close enough to a 100-watts.

So next time your’e in a crowded auditorium wih no air conditioning, you’ll know why to room seems so stuffy and hot.   It’s because each person is giving off as much heat as  a bright lamp.  Ten people give off as much heat as one blow-dryer on “high”.

Now, how does this tie into the FOOD we eat?  Howcome we can scarf down a Big Mac in 2 minutes, but it takes hours to burn it off?

Good question.   That’s because of the way the laws of physics are designed.   Physical work (moving things) dosen’t burn off that much energy.   Not when compared to all the chemical energy stored in food.

But that’s a topic that will be covered in the next Perfesser Friar Science post.