Thursday, 26 January 2012

The Great Anti-Pode Conspiracy

I'll bet you all think I'm too lazy to write a proper blogpost?
Well, you're wrong, so wrong wrong wrong. Truth is I write dozens, hundreds, dozdreds even, that never get posted. "But how can that be?" I hear you ask, wonderingly.
Well, it's just that I write them in my head in the shower, in the kitchen, whilst driving to work, whilst at work etc. And of course, in bed, whilst not sleeping.
What happens to them?
Bzzzzzt! gone.
They exist for a short while, then get overwritten by my memory, or just fade away. Either way, when I do get to the keyboard I stare at it blankly and can't remember the extremely clever things I wrote in my head a few hours before. Anyway, the Red Dirt Girl has chastised me for not writing, whilst leaving blogpost sized comments elsewhere. That's part of it... I'm better when triggered by somebody else's topic. That's of no importance today, because we are going to reveal the antipodean heresy.

Anti = Opposing
Podes = Feet

It's all about where is the opposite side of the planet. Any kid in England, knows, (KNOWS!) that if you dig a hole straight down and keep digging long enough, you'll find kangaroos, because directly below our feet, through the centre of the earth, is Australia. Any American kid will tell you that if you dig deep enough, you'll come out in China.
And these beliefs follow us toward  adulthood. I, of course, being inquisitive, questioned my geography teacher, who told me it would be New Zealand.

"Yonde in Ethiopia ben the Antipodes, men that haue theyr fete ayenst our fete." ["De Proprietatibus Rerum Bartholomeus Anglicus," translated by John of Trevisa, 1398]

Bartolomeus Anglicus, "Bartholomew of England", as translated by John of Trevisa was an early conspirator in the whole antipodean thing. Back in the thirteenth century, the luxury of google earth was not available to learned scholars, possibly because there was no electricity to run their laptops.

Also, there was not really a great set of world maps, or even globes, being that:

  1. Although some people had figured out that the world was indeed round, it was somewhat unwise to say this, as most people, especially the ones who could have you beheaded, or boiled in oil, believed otherwise.
  2. Most of the putatively globe-shaped earth was as yet unknown (to those in europe, where Bartolomeus was writing). I suppose the people living in the "undiscovered" bits had no great difficulty in believing they existed.
  3. Not a lot of people felt the need for maps, as they weren't going to go beyond the horizon during their entire lifetime.
  4. Most of the maps then existent were pretty much based on guesswork anyway.
So, it's no wonder that Bart gets it wrong when he thinks that on the opposite side of the globe to his feet are the Ethiopian's. Bartolomeus was english, though he wrote his book at Magdeburg, in Saxony. 

But no matter. Not even if you take on board the concept that Ethiopia was not, to a mediaeval person, the country it now is, in north east africa, oh no. Ethiopia was the whole dark mysterious continent we now call Africa.

Thing is, if you dig from Magdeburg, you don't come out anywhere near africa.

But that's the point. If you dig from America, you won't come out anywhere near China.
Nor does will any English kid ever meet kangaroos tumbling into the tunnel.
Nor Kiwis.

The truth is, both kids, if kids could really dig for 7,296 miles through the earth, through rock, magma, molten iron, all of that, both would drown instantly as their shovels pierced the seabed above their heads.
Have you ever thought of the logistics? How your little sister would have to haul each bucket of earth on the world's longest rope, and tip the bucket out before lowering it for the next shovelful?

So, how can you know where are your antipodes?
I puzzled about it whilst brushing my teeth, and dental floss gave me the answer. If you have enough dental floss, and know the earth's circumference....
Well, if you have a globe, and enough dental floss to circle it at the equator, then halve the resultant piece, then, if you stretch that floss tight, holding one end at a spot equivalent to your current location, the other end is at exactly the opposite spot on the sphere. To do this in full scale you'll need half of 24,901 miles, or 12,450.5 miles.
(But you might need to adjust for mountains...)

It gets more difficult.. The earth is not a perfect sphere. It's more of an oblate spheroid, but not even precisely one of those. In fact, there is only one word that gets it perfectly right, it's a geoid.
Nobody can argue with that because the definition of geoid is 'earth-shaped'.
I like that. Perfect... "What shape is the earth?"  "It's earth-shaped!".

Oh. And if you did have a hole all the way through the planet, clear and unobstructed, and filled with only a vacuum,  (no friction) and you stepping into into it, in your space-suit with air supply and ipod, how long do you think it would take you to free-fall to terminal velocity, and rise, decelerating until you arrive at your antipodal point?

Answer in the comments.
(in a vacuum, you'd rise to the opposite of your start position, then return, if there was no friction, you'd do this forever, a perfect pendulum... What do we remember about pendulums? (pendula) Ah. Equal time per arc.
(The earth's spin, and all forces other than the earth's gravity, are imagined to have no effect on your straight-line path.)

no, I don't expect you to calculate it, I certainly couldn't and I'm not expecting that any of my readers will be physicists and rocket-scientists.
But I'm told that there is a calculated result and it's nowhere near what I'd have guessed.

Is that enough? my poor typing finger hurts.


  1. Replies
    1. 42 minutes ?? nahh .... can't be. I say ummm .... errrr ... 21 minutes and 37 seconds. That's my final answer and I'm sticking to it. Love the antipodal map link. I was able to locate myself on the map, precisely .... and found I would end up dead center in the Indian Ocean. How cool is that ??? All the curried sushi I could eat. I'm sort of bummed about not ending up in China, though. I really really believed that I would pop up in the middle of some village and everybody would be upside down wearing those great big hats.


  2. Having a bit of difficulty trying to open the mouse. Will keep trying though.

    1. I found that mice open easily with a sharp knife. That's what we used in the school biology lab, anyway

  3. Infinity. You'd be stuck in the middle. You might yo-yo a bit but I can't see how you'd rise on the other side.

    1. I kinda thought that too. I was wondering also how gravity changes as you go deeper. I'd suspect it lessens, to some extent, as the mass exerting gravity would be all around you, above and on every side, as opposed to all beneath you.
      And I'm not totally convinced that there's anybody who could really say for sure what the conditions would be. But the decay, in the distance travelled, of a pendulum, is all due to frictional losses, I seem to recall.

  4. If you got to the other side you would drown as the Pacific ocean would fill the hole you made anyway.

  5. no no no.... the pacific ocean would all drain away and reappear in england as a huge salt-water fountain, flooding farms and villages so people would retreat toward high ground. All of a sudden, the scottish highlands would become valuable real-estate. Meanwhile, you could clamber out of "the plughole of the Pacific", and start trudging, past all the stranded crabs, toward New Zealand.

  6. Enough of this gravity and your auntie pode. I don't think you would fall all the way through, either. I don't think you would fall. I don't think. Reminds me, oddly enough, of Poe's Pit and the Pendulum. Can't quite put my finger on it, frictionally speaking. Just to be safe, I'm going to agree with A.

    Thank you for trying. You did good.

  7. Oy! OK, I am a rocket scientist (really!) and I'm not going to try to calculate this. I'm not saying it couldn't be calculated, but the way the problem is worded is misleading to begin with. Truthfully, I don't have the data to do it and I'm not sure anyone else does either (but they might just more than I have on this).

    If we thought of mass as a point place at the center of the earth (i.e. assumed the center of gravity did all the pulling with the rest of the mass in the earth twiddling its thumbs uselessly) and we somehow borrowed a Romulan space miner to laze a whole through our geoidic world in such a way that we sealed the sides against the incredible heat and pressure using some liner beyond our technology and pulled a vacuum to preclude friction, I can use basic Newtonian physics with a distance of 11741773 m (NEVER try to do physics with standard units; your brain with start killing itself off in disgust), I get a distance to go halfway of 25.8 minutes with an acceleration of 9.8 m/s^2 to get to the center and, of course, the time would be the same to reach the other side when one would bob back for a total of 51.6 minutes

    The difference between my calcs and the ones you quote involve the red herring in the question: terminal velocity. Yes, terminal velocity does preclude one from reaching the highest speeds with free falling in air, but (a) it depends on body size, mass and position and (b) doesn't apply in a vacuum at all because it's air friction vs. gravitational forces. No air, no friction, no terminal velocity.

    The problem with really calculating this theoretical problem is that the mass of earth (which behaves like a point mass at the center as we crawl over it's surface) isn't a point mass. The gravitational pull is not identical everywhere on it's uneven surface and, as one falls down a hole, if it's deep enough, one is also affected by the mass above one as well as below. For the short distances we've been able to dig down, the differences are unlikely to even register on our measurement devices, but then we haven't even broken through the crust to the mantle.

    If we start using realistic physics and properties, the question becomes far too complicated and requires factors I don't know. I do know that, though we have space suits that could go the distance and take the time to make more than one swing of the pendulum, they sure as heck couldn't take the kind of heat you're dealing with.

    And that nickel-iron magnetic core would probably really screw up your ipod.

    1. And: glad you agree with me about the variations in gravity as you cease to be above the mass, and become surrounded by it. I think the deepest hole ever bored is the Kola Superdeep, which reached 12,220 metres below the surface, barely a pinprick in the crust.
      By that depth, they were shearing and losing drill and liners, it was the limit to what our technology could achieve, yet we were not even through the crust, still within the peel of the orange.

  8. Wonderful!

    Now, I never thought the Rocket Scientist would turn up here and read this, but I'm glad she did, to add an extra thought or two to the mix. And almost a ten minute difference to the one I'd found elsewhere. It is, of course, such a screwed-up question, full of things we don't know, that I don't think there is any way to come up with or prove any answer.
    It's the sort of thing that sci-fi writers of the fifties would have played with, I could just see Arthur C Clarke jotting notes and calculations on the back of a menu, wondering if we should allow for the planet's spin...
    It's slower, but easier to take scheduled flights and then charter a boat.

  9. Damn, I meant to comment on "Back in the thirteenth century, the luxury of google earth was not available to learned scholars, possibly because there was no electricity to run their laptops." with something witty, like "I remember when we had to use foot pedals to run our laptops," but the truth is I remember when home computers were pipe dreams spun by geeks no one would ever take seriously. I can remember when, instead of hard drives, you used cassette tapes to store stuff on your TRS-80.

    So now I feel unbearably old.


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