Tuesday, February 23, 2010

Comments and Corrections…

I’ve gotten a few comments and corrections from people, so I wanted to take the time to address some of those. First off, thanks to all the people who posted kind words. You made my day. Second, to all the people who like the blog but hate the color scheme, I’m going to try to fix it right after I post this. Also, thanks to all the people who expanded on what I wrote in the comments and/or emailed me related references. I always like hearing how this stuff relates to other things, and I really enjoyed the emails and posts telling me about the Biodome II project, Jules Verne’s Journey to the Center of the Earth, and all of the expanded estimations that people have done. Now on to the (gulp) corrections…

In my first post, I described estimations as being similar to science:

“There’s even peer review. (To anyone who doubts this last point, I suggest you do an estimate and then show your friends. There’s a good chance they’ll be harsher than most referees.)”

In that spirit, it would be in poor taste for me not to admit my slipups, screwups, messups, and other “ups” I can’t mention in a family-friendly blog. That said, here are my responses to some of your comments:

Mount Sinai…don’t you mean Ararat?

hwiersma, just looked it up and you’re absolutely right. Mount Ararat is where Noah is supposed to have landed; Mount Sinai is where Moses is supposed to have gotten the Ten Commandments. The original question from the Skeptically Speaking caller specifically asked for Mount Sinai, and I never bothered to check if it was right. Good eyes and thanks for the correction.

Could you even fit everyone in New York City?

I agree, Mabehr. There’d be very little chance of actually fitting the entire world population into an area the size of NYC unless they pile themselves into the buildings. But if you did stuff them all in buildings, how slow would the traffic be when everyone tried to get out…

Vampire vs. Zombie Hummingbirds

Jennifer, I was going to try to add something to the vampire vs. zombie hummingbird comment, but I don’t think I can. Some things are perfect just the way they are. J

Confessions of Mechanical Pencil User

I admit it. I cheated on the Simon’s Cat problem. I used a mechanical pencil. Phew! It feels so good to get that off my chest. In my defense, it was still an HB #2 pencil, and it made measuring exactly how much graphite I lost way easier than it would have been with a wooden pencil. It’s probably pretty easy to take sharpening into account, but I’m not sure it’s a big source of error. In principle, you’re only shaving off the sides of the pencil so the length should remain the same. (But, obviously, if you leave it in the pencil sharpener too long, the length will shrink.) I suspect the sharper point will lose material more quickly than a dull point, but I haven’t checked this. In regard to Thomas’s comment, I’m not sure why tracing the same line a hundred times should be different than drawing one long straight line. Is it because you change how much friction there is between the paper and the pencil? If so, I’m not sure that’s a significant source of error for an order of magnitude approximation, but it’s good to check just in case.

Giant Basil

I got a Facebook message from a friend saying, “A square foot is a lot of space for 3gm of basil.” I was overestimating a bit. I could make something up about needing extra room to actually go and pick the basil or needing to have extra basil in case some of it died, but in truth, I just wasn't thinking that hard about it. You could probably get by using a tenth of the space.

Passenger Pâté

This seemed to be the estimation that had the most problems. (Who knew cannibalism was such a touchy subject?) As Simkatu and Thomas pointed out, not all of a human body’s mass is made of useful calories. (By the way, Thomas, any day that I get to see an equation that uses “poop” as a variable is a happy one.) I got an email from Dr. Jeremy S. that described this even more precisely:

“First off, you neglect to factor the fraction of body mass that is water. The calories per gram of protein and fat is per dry weight. Approximately 50-70% of body mass is water depending on age and gender. Further, you can estimate fat calories by multiplying average body mass by average fat percentage. As far as total body protein is concerned, my guess is that you can probably sneak by taking the remaining body weight and multipling by calculating by the percentage of weight that is neither fat nor water. (This is probably not a perfect assumption as some organs such as liver and bone marrow* are fatty and other organs are tough to take without significant preparation (I.e. Intestines.) Also, not eating bones is a big mistake. Fat rich marrow is a great source of calories as our frugal recent ancestors knew (ask your grandparents, they probably ate marrow and loved it. My grandma would spread it on toast.)”

Anyway, those are my corrections. I may revisit some of these problems later and go into more detailed corrections, but it’s getting late and I have a background to fix and an estimation contest to post. Until my next set of corrections, remember, these are only order-of-magnitude estimates, and goofy order-of-magnitude estimates at that.

P.S. Thomas, I’ll try to get on the Mercury flywheel problem soon.

1 comment:

  1. I did the Mercury Flywheel problem soon after posting it. The energy stored in Mercury's rotation is about 6.04*10^23 J. Total world energy consumption in 2008 was estimated as 5*10^20 J. If consumption stays constant then Mercury would provide the world with 1209 years of energy. If consumption increases by about 2.5% yearly then Mercury would provide us with 287 years of energy. That's rather attractive. Mercury's pretty useless anyway, right?

    Here's a few more to take your pick from.

    If we built a farm of giant wind turbines in Jupiter's great red spot, how much energy could they provide?

    If we took a cubic meter of the sun and dropped it into the ocean, how much water would it boil away?

    If you took a chunk of styrofoam to the bottom of the ocean and let it go (assume no crushing), how fast would it launch out of the water and how high would it reach into the air?