Extreme Geekery: Giant Sun Birthday Cake

sun_birthday_cakeHappy Birthday to me! Today I turn 41. Luckily, I’ll probably have a single candle on my cake (or two candles: a four shaped one and one shaped like the number one). I won’t have to deal with blowing out forty-one candles. Still, I began to wonder exactly how bright you could get with candles. Let’s suppose that the Sun was a giant birthday cake. How many candles would it need to keep outputting as much light as it currently does. (Since this is a thought experiment, we’ll ignore such mundane details as "How do the candles burn without an atmosphere" and "How do the candles not melt down with time".)

The Sun outputs about 6.84 x 1027 lumens. Written out, this is 6,840,000,000,000,000,000,000,000,000. That’s a LOT of lumens.  The best reference I could find for a candle’s output was 12.56 lumens. Of course, the birthday candles I use tend to be smaller and so likely generate less lumans than other candles. Let’s round down to 10 lumens for a birthday candle. (Plus, this makes the math easier.)

If each candle is providing 10 lumans of light, we would need 684,000,000,000,000,000,000,000,000 candles. That’s 684 trillion trillion candles!  I wonder if the warehouse stores carry ultra-mega packs of candles.

So we’ve got our candles and are ready to light them… Wait, first we need to put them in the cake.  So we make a HUGE spherical cake and place the candles all around it. How big of a cake do we need? Well, if each candle has about 1 square centimeter of space around it (we’re packing them in), the cake would need a surface area of 684,000,000,000,000,000,000,000,000 square centimeters or 68,400,000,000,000,000 square kilometers. (That’s over 26,000,000,000,000,000 square miles.)  The Sun itself has a surface area of 6.09 x 1012 square km.  That’s a big cake!

How much bigger, you ask? Stand back, I’m going to use Math!

Now the surface area of a sphere can be calculated by pi*d2.  Let’s say that the cake’s diameter is d1 and the Sun’s is d2. This gives us:

68,400,000,000,000,000 = pi*d12

6,090,000,000,000 = pi*d22

Obviously, the cake is some number, N, times bigger than the Sun so we can say:

d1 = N * d2

Plugging this into the first equation we get:

68,400,000,000,000,000 = pi*(N*d2)2


68,400,000,000,000,000 = pi*N2*d22

Now the second equation can also be written as:

d2 = square root(6,090,000,000,000/pi)

Plugging this into our calculations, we get:

68,400,000,000,000,000 = pi*N2*(square root(6,090,000,000,000/pi))2


68,400,000,000,000,000 = pi*N2*6,090,000,000,000/pi

The Pi’s cancel out and we can divide each side by 6,090,000,000,000 to get:

N2 = 1,123.15

This means that N is about 33.5.

Our birthday cake would need to be almost 34 times the size of the Sun just to be as bright as it is.

I think I’m going to need more frosting!

NOTE: The Sun Birthday Cake image above was made by combining Decorative Sun by ivak and Chocolate Birthday Cake(brown) by version2. Both images are available from OpenClipArt.org.

Extreme Geekery: Travel Times At Spaceship Speeds

15-011a-NewHorizons-PlutoFlyby-ArtistConcept-14July2015-20150115Today, New Horizons will make its closest approach to Pluto.  It has already sent us some fantastic views from the dwarf-planet-formally-known-as-the-ninth-planet and it will likely send back many more.  We’ll learn a lot from the information that New Horizons sends us.  I would be remiss to pass up this opportunity to geek out.  My first instinct would be to take the distance between Earth and Pluto and figure out how long it would take to get there via various “normal transportation” means.  Before I do that, though, it turns out that Adam Frank from NPR already did this.  As much as I’d love to do the math again, let’s flip it around.  Instead of figuring out how long it would take to drive to Pluto, let’s imagine you could get in a car that travels at 32,400 miles per hour – the speed New Horizons is moving at.  Let’s suppose you could use this car to make various journeys.  How quick would those travels be?

First, some ground rules.  We’re going to assume that there is no traffic – no sense in having a car that can go 32,400 miles per hour when there’s a line of cars stopped ahead of it.  We’re also going to assume that our can can take a straight line path without crashing.  Personally, I’ve driven at 80 miles per hour and felt like I was beginning to lose control.  I couldn’t imagine how out of control 32,400 would feel.  Not crashing also means being able to go from 32,400 mph to a full stop without any occupants being injured in any way.

Going To New York City

I’ll often get invites to events in New York City.  Sadly, I need to turn many of them down simply because it takes three hours to drive to the city from where I live.  If I had a New Horizons Car, though, I’d be able to get to New York City in under twenty seconds.  At that travel time, I could order a pizza from a New York City pizzeria and get there before they even began preparing my order.  Maybe we need something a bit father away to drive to.

Disney World

It’s no secret that I’m a Disney fan.  I’ve been in love with Disney World since B and I went there on our honeymoon I’ve loved it even more when we went there with the kids.  Obviously, living in Upstate New York means that I can’t just stop by the Magic Kingdom.  What if I had a New Horizons Car, though.  Rounding up to the nearest 50 miles, it’s 1,250 miles to Disney World for me.  With our space-age car, I could get the family to see Mickey in two minutes and twenty seconds.   With that travel time, we wouldn’t even need the boys to bring any books to keep themselves occupied.

Los Angeles

We have some family on the opposite coast that we rarely get the chance to see.  We’d love to see them more often, but cross-country flights are expensive.  Driving cross-country would be out totally, but now we have a bright, shiny New Horizons car in the driveway.  At about 2,850 miles to Los Angeles (rounding up to the nearest 50 again), it would take less than five and a half minutes to get to LA.

Hong Kong

Let’s push the limits a bit more.  Since the continental United States seems so small for New Horizons Car, what about something on a bit more global a scale.  How long would it take to drive to Hong Kong?  (We’ll assume we can somehow drive on water while maintaining the speed.)  Hong Kong is about 7,950 miles away which would mean New Horizons Car could get there in under fifteen minutes.  Yes, I could travel from my house to Hong Kong and back in the time it takes for a half hour television show (including commercials) to air.

Back To New York City

Let’s do one more trip:  To New York City.  Yes, I know, we’ve done this already, but this time we’re going to take the “scenic route.”  To be specific, we would travel west around the entire world until we came back around to New York City.  Essentially, this would be circumnavigating the world so I’d need to know the circumference of the Earth at New York City’s latitude.  Luckily, this website lists all of these so it was trivial to find out that I would need to travel 30,741.789 kilometers or 19,102 miles.  At New Horizon speeds, this would take just over 35 minutes.

Given how mind-bogglingly big space is, it’s easy to forget how fast these craft are traveling at.  Were we to apply these speeds to our daily modes of travel, our world would shrink dramatically.  We would be able to go anywhere on the globe in a matter of seconds.  While I might not have a car that could take me to Disney World before a microwave meal completes, I will enjoy all of the images that New Horizons sends back as it passes Pluto on its journey deep into space.

NOTE: The New Horizons image above is comes from NASA via Wikipedia and is in the public domain.

Extreme Geekery: Wrecking Havoc on Society with Instant Transportation

TeleporterIn my Extreme Geekery series, I often focus on some scenario that requires science and math to solve. Given my love for science fiction, though, I also love imagining scenarios when science and technology ARE the problem and society needs to figure out the solution.  When the telephone gained popularity, there was a shift in communication abilities.  No longer did you need to wait for weeks for a letter to arrive at its destination.  Conversations across great distances could be accomplished in real-time instead of over months.  With the Internet, this was greatly amplified.  Now, someone in the United States could communicate with someone next door just the same as if they were half a world away.  Businesses could also sell to people even if those people didn’t live anywhere near the shop.  In fact, the Internet revolution had such an impact, that many stores don’t even have a physical shop.  While there was an equivalent pre-Internet in catalog sales, the Internet took this phenomenon to the next level.  Societal shifts of this nature can create many more opportunities for people and businesses, but they can also destroy the old ways.

My question now is: What would happen if we developed instant transportation.

For the sake of this thought experiment, we won’t bother with the "how" of the teleportation.  Let’s just assume that there is a new smartphone application that can teleport you (and your family/luggage) from where you currently are to any place you want to go.  You select where you want to go on a map, click a button, and there you are.  We’ll assume that the transportation method is safe, effective, easy for anyone to use without incident (i.e. not so hard that someone selects "the mall" and winds up 100 feet above the mall plummeting to their death), and inexpensive enough so that pretty much everyone can teleport.  What would happen with society?  Would this be a boon or the beginning of the end?

"Snail Mail" Travel

The obvious casualty of this technology would be the transportation industry.  Why would you get on an airplane – dealing with security, baggage fees, cramped seats, and tiny bags of peanuts – when you could just click and be at your destination?  Airlines and trains would go out of business as people teleported to their destination the same way that people sent less letters via snail mail once e-mail was widely used.  Obviously, there would be some people who still used the slow mode of transport.  Perhaps they liked the trip or perhaps they didn’t trust the new technology.  In any event, the companies might not go completely out of business, but they would need to radically change their service.  Perhaps the availability of instant travel would usher the return of 1950’s style airplane rides.  When it came to shipping goods, companies like FedEx might ditch the fleet of planes and trucks.  Instead, a carrier would pick up your package, zap himself to your house to drop it off, and then zap back for the next package.  Ordering online could mean getting your items in a matter of hours instead of days.

Going On Vacation

With instantaneous teleportation, tourism would increase dramatically.  Want to vacation in Disney World?  Just zap yourself there.  Get the urge to spend an evening in Hawaii?  You’re there.  Get the urge to visit Australia?  Urge satisfied.  You might think that, despite the increased travel, hotels would suffer.  After all, why stay someone else when you could just zap yourself home and sleep in your own bed?  Then again, at home there might be dirty dishes in the sink, a rug that needs vacuuming, sheets that need cleaning, and garbage that needs to be taken out.  If you are going to have some vacation time, why not get away from those chores and let the hotel staff take care of the room for you?  Vacations might wind up taking two forms.  For the quick pop out – for example to have lunch in a nice little restaurant in Italy before getting back to work in New York – you wouldn’t book a hotel stay.  However, if you were planning to get away from it all for awhile, a hotel would definitely get your business.  (Though, forgetting something at home would just mean a quick teleport home to retrieve it.)

A Walk On The Shady Side

While instant travel would make many people’s lives easier, it would have a dark side as well.  Right now, borders are more or less controlled.  If you want to enter or leave a country, you need a passport and you need to pass through the country’s security checks.  With instant travel, a person could just zap themselves deep within the country for whatever reason good or bad.  Criminals sent to jail could have a conspirator on the outsize teleport in, grab them, and teleport back out with them.  Imprisoning lawbreakers would quickly become an ineffective means of punishment.  For that matter, criminals could teleport into a house, grab whatever they want, and then teleport away.  Far, far away.  Burglaries would be impossible to prevent.

Finally, though perhaps least serious, charging admission fees would become obsolete.  Take Walt Disney World for example.  Suppose you want to visit the Small World ride in the Magic Kingdom.  First, you need to purchase an admission ticket.  This ticket is checked before you get into the park.  Once inside, you can go on rides like Small World.  With instant teleportation, though, you could just appear inside the gates, go on the ride, and then teleport back home.  No ticket required.

All of this would quickly mean that laws would be passed requiring teleportation blocks of some kind.  Disney World might block teleportation within their parks from outside the parks.  So you could teleport from Small World to Space Mountain, but not from the parking lot to Big Thunder Mountain.  Furthermore, laws might be passed to limit teleportation liabilities.  Right now, if someone falls in a building, the building’s owner might be sued.  What would happen, though, if you teleported to the top of the Castle in the Magic Kingdom and wound up falling to the bottom?  Would your family be able to sue Disney for not limiting teleportation enough?  Or would lawsuit-shy executives make sure that there were only preset teleportation points for people to use?

Instant teleportation would also be a huge pain for celebrities. Paparazzi wouldn’t need to stalk outside of a celebrity’s compound, but could teleport right inside to take photos of them in their most private moments. Furthermore, overenthusiastic fans would be able to see their favorite celebrities at any moment. If the hotel room that a popular band was staying in was leaked on social media, it would suddenly become packed with screaming teenagers.  For that matter, non-celebrities might find themselves beset by intruders.  Does that guy you’ve told you don’t want to see anymore keep knocking on your door?  Bad news, he can now teleport through it.  Does that ex-girlfriend not get the hint that you’re over?  Unfortunately, she can teleport herself into your bedroom any time she wants to.

Overall Reaction

Given the downsides – both to entrenched businesses and to people/businesses wishing to avoid criminal activities, the development of teleportation capabilities would likely be strictly regulated if not banned outright.  However, technology bans never seem to last in the long run.  Eventually, the technology to teleport would leak out.  For better or worse, teleportation would get out and – like with any other technology – society would need to adapt.  Children would grow up knowing only a world with teleportation.  Elders would remember the "good old days" before people could teleport, but would eventually be replaced in positions of power by people who accepted teleportation as a fact of life.  Before long, mankind wouldn’t be able to conceive of not teleporting the same way that people nowadays can’t imagine not being able to drive where they want to go.

NOTE: The "Teleporter" image above is by qubodup and is available via OpenClipArt.org.

Extreme Geekery: Water, Water, Everywhere, How Much Is There To Drink?

water-dropRecently, I read an article stating that California – in an attempt to alleviate their water shortage – was instituting "toilet to tap" procedures.  That is to say that water flushed from people’s toilets would be treated and put back into the system for use as drinking water.  While the immediate reaction tends to be a big "Yuck!", this isn’t actually too bad.  Water from toilets, showers, and other sources of waste aren’t routed straight to the tap, of course.  First, it is treated, filtered, purified, and otherwise made totally safe for human consumption.

In fact, we’ve been engaging in a large version of "toilet to tap" for quite some time.  Waste water doesn’t simply vanish.  Waste products are consumed by bacteria and other organisms.  The water passes through soil and gravel, is evaporated and precipitated, and winds a long path back into our drinking supply.  This is simply taking a short cut using technology.

This led me to wonder, though.  Suppose we dumped all of the water we used into some secure container marked "Do Not Drink – EVER".  Instead, we provided every human being with new water to drink every day.  For the purposes of this discussion, we’ll ignore all other uses for water.  Only drinking is allowed.  No watering crops,  showering, or washing your car.  Just drink the water and dump it when our bodies are done with it.  We’re also going to assume that the human population remains constant.  No big spikes or drops in the number of humans on this planet.

First, some facts:  The world has 326 million cubic miles of water.  This equals 1.36 x 1021 liters.  There are 7.125 billion people on the Earth now.  The average human needs 75 to 150 ounces of water a day.  Obviously, each person would need a different amount of water depending on age, gender, the climate they lived in, etc., but let’s take the average of that daily water requirement and say that each human would need 97.5 ounces per day.  That’s 2.9 liters of water per person per day.

If you work out the math, this results in 65.8 billion days worth of water or 1.8 billion years.  That’s quite a lot of time until we run out of water.  Around 1.8 billion years ago, the first multi-cellular life was forming.  Even if humans somehow survived for the next nearly two billion years, I doubt we’d look the same as we do today.

There’s one little flaw in my math, though.  Of that 326 million cubic miles of water, only a small fraction can actually be drank.   Only 4% of the Earth’s water is fresh water.  Of that, 31% isn’t locked away in glaciers and icebergs.  Yes, we could desalinate sea water or melt icebergs, but that adds difficulty and expense.  So let’s just take the remaining fresh water and use up that before going after the rest.  That means we have 1.69 x 1019 liters.  That amount of water would last us 816 million days or 2.2 million years.  No, it’s not the billions of years before, but it spans a time from around the first use of stone tools to the present day.

Getting back (slightly) to real world situations, what if we didn’t simply limit water use to drinking.  Let’s let everyone bathe (thank goodness!), clean dishes, flush toilets, etc.  The average person uses between 80 and 100 gallons of water per day.  If we assume 90 gallons (340.7 liters) of water per day then, using just the fresh water again, there would be enough water to last for just under 7 million days or 19,000 years.  This might still seem like forever – after all it is the difference between the era of cave paintings and the era of smartphones, but it’s a blink in the geologic sense.

NOTE: The "water drop" image above is by Keistutis and is available via OpenClipArt.org.

Extreme Geekery: Give Me A Lever Long Enough…

LeverArchimedes once said "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world."  He was waxing poetic about the power of the lever.  The lever is one of several simple machines along with the wheel and axle, the pulley, the inclined plane, the wedge, and the screw.  These machines can help to perform feats that a man acting alone using only his own strength couldn’t hope to achieve.  They can also be combined to increase the machines’ abilities.  Of course, I don’t think Archimedes really meant that one could set up a lever and move the entire Earth.

But could you do this?  How long would the lever need to be?

Obviously, there are some stumbling blocks to our plan.  First of all, there’s no ground in space to position the lever’s fulcrum.  Even if we made a giant lever and somehow put it against the Earth , pushing down on one side would cause the entire contraption to drift through space.  There’s also the problems that gravity would cause – the gravity on the lever close to the Earth would be more than the gravity further away.  What’s more, unlike a lever on Earth, we’ll be battling against the gravity of the Earth orbiting the Sun, not an object resting on the Earth.


All of this could, at least, seriously mess up the calculations for how long our lever would need to be or, at worst, make the whole affair pointless.  Since there’s no such thing as "pointless" when it comes to Extreme Geekery, .  Let’s simplify things, by making two assumptions.  First will be some "ground" and Earthlike gravity.  Our fulcrum will rest on the "ground" and will push up against the Earth attempting to lift it as if it were just an extremely large rock.  The second assumption is that there isn’t any other source of gravity to mess things up.  We’re ignoring the Sun, other planets, the Moon.  Everything.

So, how long would a lever need to be to move the world?  The formula for this is quite simple:

F1 * D1 = F2 * D2

In other words, the force applied down (F1) times the length (distance) of the "pushed down" portion of the lever (D1) is equal to the force upward on the other side of the lever (F2) times the length of that side of the lever (D2).  We’ll position the lever and fulcrum so that the "Earth side" is under half of the planet.  Initially, you might think that this means that the Earth side of the lever is the radius of the Earth.  Don’t worry.  I did too.  I figured out all of my calculations before realizing the truth.  (The good news is that I had to do more math.  This is always good news to a math geek.)


The radius of the Earth at the equator is 6,378 km.  The radius from center to pole is 6,360 km.  The rest depends on how inclined the lever is, but let’s say it’s raised so that the it is up 25% of the center-to-pole radius.  We need to figure out what side C is.  Easy enough.  Using the formula A2 + B2 = C2 gives us a result of about 6,573 km.

The weight of the Earth is easily Googled: 5.972 x 1024 kg.  This only leaves us the force pushing down on the other side.  Given that Archimedes said he could do it, I’m going to say that only one person should attempt it.  No cheating and gathering an army or pushing on it with rocket thrusters.  We’ll do this see-saw style and sit the person on the other end of the lever.  We’ll have the person be 100kg – perhaps slightly overweight but not unrealistically so.

Now how long is the "pushed down" side of the lever?  Well, we have:

D1 * 100 kg * 9.8 m/s2 = 5.972 * 1024 * 9.8 m/s2 * 6,573 km

(Side note: In case you’re wondering where those 9.8s came from, force equals mass times acceleration.  F = ma.  This means that the forces we need for each side of our lever equation are really the weight of our objects times the acceleration – our faked Earth gravity down.  Also, yes I know they cancel each other out, but I’m including them in there for completeness.)

Simplified, this gives us a lever distance of 3.93 * 1026 km.  That seems pretty long, but how long is it really?

Light is the fastest substance known.  The speed it travels at can’t be matched by anything we know of.  That’s why we measure distances in light years – or the distance that light travels in a year.  One light year is 9.46 * 1012 km.  This means our side of the lever would need to be about 4.15 * 1013 (or 41.5 trillion) light years long.  How long is this?  Well, it’s certainly longer than the Milky Way.  That’s 100,000 light years across.  It’s even bigger than the diameter of our local supercluster of galaxies.  That’s 110 million light years.  In fact, our observable Universe is only 45.7 billion light years so our lever would need to be over 908 times the length of the known Universe.

That’s one big lever.

Ok, so one person probably couldn’t do it alone – even by Extreme Geekery standards.  But what about the power of teamwork?  If every human on Earth got together and sat down on the lever, how long would it need to be to move the Earth?

All humans together weigh 632 billion pounds or 286.67 billion kg.  Plugging this into our formula above means that our lever would need to be 1.37 * 1017 km or about 14,474 light years.  This distance is much more reasonable.  Yay teamwork!  Still, maybe we could improve the results.

All of the biomass on Earth (except bacteria – those guys claim to have lost their invitations) hopped onto our galactic see-saw now.


Totaled up, Earth’s biomass weighs 560 billion tonnes or 560 trillion kg.  This translates into a lever of 7 * 1015 km or about 741 light years.  Even better still.

Of course, even a "mere" 741 light years is a long distance for a lever.  As much of a genius that Archimedes was, he might have overestimated himself when it came to levers.  Unless…


NOTE: The Earth image I used is by stevepetmonkey and is available via OpenClipArt.org.

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