QI: Archimedes & Card Shuffles

by Pratyush

One of my guilty pleasures, and a great encourager of thoughtless procrastination, is the wonderfully diabolical show QI. It takes the most eclectic sets of historical or scientific facts and gives them a bit of flavor, via featured comedic personas. I watched two episodes recently, and each had a unique moment that I won’t be forgetting too soon.

A Quantum Shift

Archimedes: “Give me a place to stand, and I shall move the Earth.”

If Archimedes weighed 100kg and he placed his fulcrum 1km away from the bottom of the Earth, in order to balance the planet, he’d need a lever 6.5 billion light-years long. If he moved said lever 1m on his end, the Earth would move less than a diameter of a single proton.

The more you know, via QI. You can find the relevant clip at 39m40s:

 

Something that Stephen Fry didn’t mention, and I tried figuring out (so you might want to double-check), is that the difference in time from when Archimedes would shift his end of the lever to the moment the Earth would move (assuming the lever was made from Oak), would exceed 5×10^14 years, which is roughly 36,000 times the age of our universe. That’s because pressure waves travel at set speeds too, and a pressure wave through Oak wood travels at 3850m/s, more than 10 times the speed of sound (also a pressure wave) in air at sea level. Why mention that?

In undergraduate Physics courses, one of the more common thought experiments posed by students is the idea that a long enough lever, or ruler, or anything solid, could conceivably violate Einstein’s postulate that light is the fastest thing in the universe. For if a ruler placed further than a few light seconds away from something was pushed at one end, wouldn’t the ruler’s opposite end immediately move as well, making the “push” faster than light? Well, no. The pressure wave generated by the push would take significantly longer to reach the other end. In the humdrum of everyday occurrences, we don’t notice that pressure waves even exist (perhaps with the exception of sound). When I push a table, the other end immediately shifts away from me as well, or so it seems. In reality, the pressure wave I’ve started by putting force on the particles at one end is traveling at a certain speed; 3850m/s for Oak tables, as it turns out. Faster than we can notice, but almost 80,000 times slower than the speed of light.

A question I don’t have the answer to is whether it makes a difference pushing the lever from the side or the top. Would directional changes matter? Don’t worry, the next astonishing fact is within the realms of sanity.

Shuffling Through Improbability

Ever wanted to accomplish something that no one’s ever been able to before? Why not shuffle a deck of cards?

Some obvious but jarring mathematics at 39m30s:

 

I’ll note that the term “fact” as used by Fry is synonymous with fact as defined by science. But the mathematical result of such a simple action is a maddeningly cool thing to consider.

To reiterate, if every star in our galaxy had a trillion planets – that’s 1,000,000,000,000 celestial rocks of some magnitude – each planet with a trillion inhabitants shuffling a trillion packs of cards, at once, 1,000 times a second (keeping up?), and they’d been doing that since the Big Bang, they’d only now be getting around to repeating the orders of the cards.

I know it’s probabilities we’re talking about here, but reality itself is a statement of an amalgamation of a countless set of probabilities. And if card shuffling is how one begins to grasp that… well, all I can say is that it’s a lot easier than quantum mechanics.

About these ads