How Good Is Your Intuition? (Mind-Teaser)

[Geronimo '74]

There will be approx 48 cm or 1.59 ft between the cable and the earth's surface.

(I voted yes before I did the math)

[Geronimo '74]

[jyl]

"yes" is the correct answer.

Two concentric circles, one with circumference equal to the earth, and one with circumference 10 feet longer, you can fit a finger between the circles. The gap is about 1.591 feet. Because, for a circle:

circumference = 2 * pi * radius.

Do the math, prove it for yourself.

Now, same question, this time the inner circle is the same circumference as Jupiter's equator (use 449,197 km).

And same question, this time the inner circle is the same circumference as Jupiter's orbit (we'll agree that is 4.774 x 10^9 km).

What's the answer - yes (can fit a finger) or no (cannot)?

You see where this is going. Even if the inner circle is as large as the universe, adding 10 feet gives you enough room for a finger - indeed, 1.591 feet.

Does this match your intuition? If not, can you explain why your intuition was wrong?

(I confess, when I heard this problem, I didn't use intuition but simply did the math, so I got the right answer. Then I had a hard time understanding why the answer was right, so I failed the real test.)

[wdfifteen]

Originally Posted by jyl

Does this match your intuition? If not, can you explain why your intuition was wrong?

(I confess, when I heard this problem, I didn't use intuition but simply did the math, so I got the right answer. Then I had a hard time understanding why the answer was right, so I failed the real test.)

My intuition said no, but the math said yes, with lots of room to spare. I can't say why my intuition was wrong, probably getting circumference and diameter confused in my visualization.

[island911]

Yeah, it's the visualization of trying to imagine the relatively tiny gap around a HUGE circle, that trips people up. That's why its good to change the thought experiment until you have something that works. The key being knowing when your not clear on the first soln. (aka 'intuition")

Originally Posted by Won

10/(2*pi) ft of gap?

That's the same math that I came up with. ...where "10" is the variable used here (10 feet of extra 'wire' )

[island911]

Originally Posted by Schumi

eeh, When I think of 'wire' I think something that can be bent around. If it has to stay a circle, why not just call it a circle? Oh, I see, it's part of the sensory intuition of the problem...

That cracked me up.

"intuition" . . what does that mean? (to the mere mortals? )

[sammyg2]

Originally Posted by island911

"intuition" . . what does that mean? (to the mere mortals? )

That's what you pay to the college to get edumacated.

[t951]

No, gravity would pull it towards the core.

[jyl]

I think island's visualization made a lot of sense. Here's what tripped me up. I thought, 10 feet is such a miniscule percentage of earth's circumference, it can only make a miniscule difference in diameter - but it is a miniscule percentage difference in diameter, the absolute difference is what counts.

[red-beard]

There are lots of things like this in engineering, which is why we always keep the calculator and the Mark's handbook close by...

[RWebb]

actually, I get 1.592356687898089...

does it match my intuition? No, but it matches many years of geometry...

[70SATMan]

Originally Posted by jyl

There is a wire, whose length is 10 feet longer than the circumference of the earth at the equator. The wire is formed into a circle, slipped over the earth, and placed at the equator. Assume the equator is also circular and smooth (no mountains or oceans). Can you fit your finger between the wire and the earth?

What's the diameter of the wire?

Ohhh, nevermind.

[RWebb]

ok, sports fans....

What diameter of wire (or cable) in the example above will be too thick to fit a finger under? You may assume a finger that is 0.5" thick, just to make it easy...

[tabs]

Does the paper of all the US currency printed weigh more or less than all the trains that pass through Grand Central Station in NYC?

Me thinks I should be checking my safe deposit box about now....

[Erakad]

This is a bunch of BS.....

No worries....I chose poorly as well; I should have asked my son...go figure.

[masraum]

I think the big problem is that we were working with circumference vs diameter/radius which is a linear relationship. If talking about area vs dia/radius the results would likely have been what most of us were expecting because the relationship is exponential, not linear. It gets even worse if we'd been talking about volume.

[Esel Mann]

The answer is it would depend:

Yes if 1/2 the thickness of the wire plus the diameter of the finger is less than or equal to 5/pi;

No if 1/2 the thickness of the wire plus the diameter of the finger is greater than 5/pi.

Cwire = Cearth + 10

pi x 2 x Rwire = pi X 2 x Rearth + 10

Rwire = Rearth + 5/pi


Kind of wild isn't it!

But who cares about fingers. What if the finger was replaced with a swallow.....

[vash]

the maths says, "yes". but my intuition says "no". i would never stick my finger into something that could be a potential trap.

[AirKuhl]

The math above assumes that you simply lift straight up to get a max height value of ~1.59 ft. However, if you are curious about the max height above the surface you can lift the wire, the correct answer is ~5 feet, not ~1.59.

Look at it this way. The wire is already laying there at exactly the same circumference, with no room to get a finger under it. You hold the current tension, cut the wire and splice in 10 more feet. You can now lift that extra amount roughly 5 feet off the surface.

Either way, getting a finger under there is easy.

[304065]

Earth is 40,075.16 km in circumference equatorially =131,480,184 feet

Circ= Pi * D, therefore D = Circ/Pi = 41,851,344.54 feet

Now if you make Circ 131,480,184 + 10, D= 41,851,347.72

3.18 Feet of difference. 1.59 foot on the other side, 1.59 foot on this one.

So I could, but I'm not saying I would. . .