Wikipedia:Reference desk/Archives/Science/2007 November 11

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November 11

Physics and Ancient Greece

I remember my grade school science teacher once telling us that Ancient Greece not only knew the world was round, but more amazingly they also knew its rough diameter. The ancient experiment took place on a wide and very flat plain; on it, two towers spread miles apart. The towers would signal each other in daylight and then quickly measure how long the shadows of each tower fell on the plain. That was all they needed to roughly measure the size of the world. I liked this science teacher quite alot and so I almost hate to ask: is an ancient experiment of this kind roughly possible? A lesser question: without too much research, is there any historical corrobaration for the rough diameter of the world being published more than two thousand years ago? Sappysap 00:16, 11 November 2007 (UTC)

Eratosthenes is the first known to have calculated the circumfrance of the earth. He did conduct an experiment very similar to what you describe to estimate the curvature of the Earth. His estimate was probably a bit off but pretty good for a first shot! You can look at History of geodesy for more discussion of his method and later methods. --24.147.86.187 00:26, 11 November 2007 (UTC)

Yep - the numbers that these techniques could come up with would be very approximate - but they could certainly prove that the earth is round simply by noting that the further North you went, the longer the noon-time shadow is - but the length of the shadow doesn't change when you go East/West. I don't think they used two towers that could see each other though. What I thought they did was to measure the length of the shadow at noon for two locations hundreds of miles apart on the same day. Because they knew (roughly) the North/South distance between those locations, they could do the calculation without requiring communications between the towers. They knew that at noon the shadow was at it's shortest - so precise timekeeping was not needed. Not requiring the two towers to be able to see each other means that they can be a lot further apart - which makes the whole calculation much more accurate. But the observation that the length of the day is more variable at higher latitudes is theoretically enough to allow an observant person to deduce that the earth must be round. SteveBaker 00:42, 11 November 2007 (UTC)

According to the Eratosthenes article: "The exact size of the stadion he used is argued by those who suppose he got it right; but the common Attic stadion was about 185 m, which implies a circumference of 46620 km, i.e. 16.3% too large."

I would consider an accuracy of 1/7 very impressive for someone who did this calculation over 2000 years ago.

Eratosthenes decided to use two cities instead of two towers. The Sun shined directly down a well in one city on the noon of every summer solstice, it was at the zenith at these times. In the other city, he measured the noon sun's elevation during another summer solstice. This would give the cities' latitude difference, and the Earth's circumference can easily be computed if the distance between the cities is known. --Bowlhover 07:24, 11 November 2007 (UTC)

That can't be exactly true. The sun only shines "directly" down a well when you are near the equator. Greece is at roughly 38 degrees north - the earth's axial tilt is 24 degrees - so even at mid-day on the summer solstice, sunlight would shine down the well at an angle of roughly 14 degrees to the vertical. In the end, the problem boils down to the precision with which you can measure the angle of the sun (or the length of a shadow or the depth to which sunlight penetrates a well - all of which amount to the same thing) - and the precision with which you can measure the north/south distance between your two points. Picking two cities far apart makes accurate measurement of the distance between them tough - but reduces your dependence on the accuracy of sun's elevation. Picking two points closer together gives you better precision on the distance between them - but the precision with which you measure the angle of the sun becomes vastly more critical. SteveBaker 14:27, 11 November 2007 (UTC)

Minor correction - you don't have to be exactly on the equator for the sun to be at the zenith at noon on certain days of the year - you only have to be between the Tropic of Cancer and the Tropic of Capricorn. One of the end-points of Eratosthenes baseline was Syene or modern-day Aswan, which is slightly north of the Tropic of Cancer. Our article says:

The latitude of Aswan – 24° 5′ 23″– was an object of great interest to the ancient geographers. They believed that it was seated immediately under the tropic, and that on the day of the summer solstice a vertical staff cast no shadow, and the sun's disc was reflected in a well at noonday. This statement is only approximately correct; the ancients were not acquainted with the exact tropic: yet at the summer-solstice the length of the shadow, or 1/400th of the staff, could scarcely be discerned, and the northern limb of the sun's disc would be nearly vertical.

Eratosthenes presumably knew this bit of "folklore" about Syene, and he took his home town of Alexandria as the other end of his baseline, so he could estimate the size of the Earth from measurements made in his own garden. Gandalf61 16:54, 11 November 2007 (UTC)

Yes, Aswan is in Egypt and not Greece. Using Aswan was logical because if the sunlight illuminated the bottom of a deep well, the Sun's altitude could accurately be determined as 90 degrees. If an accurate data point exists, why not use it? --Bowlhover 17:49, 11 November 2007 (UTC)

One more point: the Earth's axial inclination is not exactly constant, owing to tidal effects. In the time of Eratosthenes, it was a little larger and therefore the Tropic of Cancer was farther north, at 23°43'. Syene still wasn't exactly on it, but it was closer than would be the case today. --Anon, 06:33 UTC, November 12, 2007.

The funny part is that Posidonius repeated Eratosthenes calculation, via slightly different means, and came up with essentially the same result -- and a fairly accurate one at that -- but then revised his calculations such that the circumference was about a third to small. And this figure got incorporated into Ptolemy's Geographia which, along with medieval calculations by Islamic geographers that tended to support the smaller figure, greatly influenced Christopher Columbus's theory of Asia being located approximately where the Americas are. History is funny. Pfly 07:34, 11 November 2007 (UTC)

The bottom line: Eratosthenes and other greeks know perfectly how to estimate a sphere's diameter. The problem for them was that the instruments they had at their disposal were some dracmas and a man's footsteps. But apart from those minor details, they made perfect scientists. --Pallida Mors 76 22:51, 11 November 2007 (UTC)

One point often omitted in connection with Eratosthenes's estimate of the size of the Earth is that the calculation is only correct if the Sun is known to be at a great distance. Say A is Alexandria, B is Syene, S is the Sun, and C is the center of the Earth; at the time of measuring, SBC is known to be a straight line, so points SAC make a triangle with point B on side AC. The angle of 7.2° between the Sun and the vertical, as directly measured at Alexandria, is the supplement of angle SAC. When we say that AB forms an arc of 1/50 of the Earth's circumference, we are assuming that angle ACB is also 7.2°!

But in fact angle ACB = ACS = 180° - SAC - ASC = 180° - SAC - ASB = (supplement of angle SAC) - ASB = 7.2° - ASB. However, since the Sun is 93,000,000 miles away, angle ASB is only about 0.0003° and it is safe to treat ACB as having been measured as 7.2° also. If we believed that the Sun was only 25,000 miles away (and therefore about 230 miles in diameter), then angle ASB would be about 1.1°; we would then compute ACB as 6.1°, producing an estimated figure of 29,500 miles for the Earth's circumference. You could also get a 7.2° change of Sun angle over 500 miles if the Earth was flat and the Sun was about 4,000 miles up!

Fortunately, Eratosthenes did believe that the Sun was at a great distance, although it's not clear exactly how great, so his calculation went the right way on this. (Perhaps someone could work some of this into the article on him; I don't have time now.)

Moving onward from the way Eratosthenes actually did it, let's talk about the situation the original poster remembers the teacher describing: two tall towers in sighting distance across a level plain, with the length of each one's shadow observed at the same time, using light signals to synchronize their observations.

The first point is that towers in ancient times weren't built all that high. The biggest Egyptian pyramids were a few hundred feet. Even if a tower 500 feet high was available, the horizon would be only 28 miles away. Therefore even if we imagine that two towers of that height were used, they would have to be no more than 56 miles apart. This means that the important angle formed between the two towers and the center of the Earth would be about 0.8° instead of 7.2°, and therefore a good deal harder to measure with sufficient precision. If we imagine lower buildings,

Further, the story referred to using the shadow of the tower itself. In ancient times nobody was building vertical-sided buildings anywhere near that high. If a building is a pyramid, or in general any shape without vertical sides, you can't measure the length of its shadow by just starting at the base of one wall; you have to measure from a point below the highest part of the tower, presumably well inside the building. So this would introduce additional error. I don't know what the maximum height for a vertical-sided building was in ancient times, but if it was say 100 feet, then the maximum distance between two such buildings would be about 25 miles, requiring an angle of 0.4° to be measured.

Further, the story refers to a signal passed between the buildings using light, and this would have to be done in the daytime, so lighting a fire wouldn't serve. It is difficult to imagine what could be done fast enough to serve as a good signal that could be plainly seen 25 or 50 miles away without such a thing as a telescope. A mirror reflecting the Sun ought to be visible at that distance, but impossible to aim accurately so it could be seen at the other tower. Perhaps a big sheet of cloth like a sail could be hung over the tower and then let fall, but I don't think it would be practical to make one big enough, which would also have to contrast with the tower. At 25 miles a cloth 100 feet square would appear only 1/10 the width of the full Moon. And if the towers are at the maximum distance for sighting each other, then only the top bit of each tower is visible from the other.

--Anonymous, 06:33 UTC, November 12, 2007.

The OP's story sounds like a strange mix of Eratosthenes, the use of Theodolites in the Principal Triangulation of Great Britain (and of India, which doesn't seem to have a page), and Semaphores... or something. Pfly 09:13, 12 November 2007 (UTC)

Are you looking for Great Trigonometric Survey? —Steve Summit (talk) 14:58, 12 November 2007 (UTC)

Ah ha, yes that's it. If I recall right, the project sometimes involved the building of towers in sight of one another, upon which theodolites were placed to survey via triangulation methods. And interestingly enough, that page says the project was was responsible for the first accurate measurement of a section of an arc of longitude, which relates back, sort of, to the circumference of the Earth. Not quite Ancient Greece though. Pfly 16:37, 12 November 2007 (UTC)

That's quite the overstatement -- I daresay Jean Delambre and Pierre Méchain would have something to say about it! I mean, the Indian survey may well have been more accurate than their earlier work, but still! --Okay, fixed now. (See also "The Measure of All Things" by Ken Alder, and if you read French, fr:Figure de la Terre et méridienne de Delambre et Méchain.) --Anonymous, 06:14 UTC, November 13, 2007.

does inhibition of PKC-β activity decrease pigmentation in vivo?

how? is it permanent? —Preceding unsigned comment added by 81.99.212.22 (talk) 01:03, 11 November 2007 (UTC)

According to this article, PKC-β phosphorylates and activates tyrosinase and "topical application of a selective PKC inhibitor reduces pigmentation and blocks UV-induced tanning in guinea-pig skin". They also discuss regulation at the level of transcription. --JWSchmidt 01:17, 11 November 2007 (UTC)

Feces - taste like what?

I've always wondered what human feces (faeces) taste like.

I'm aware that this might be a strange question. I also realize that I could easily provide my own answer, but I'd prefer to leave it to someone with an interest in coprophagy. —Preceding unsigned comment added by 222.155.51.145 (talk) 07:40, 11 November 2007 (UTC)

Most of the taste sensation is due to the smell. SO I think you could imagine the experience. But you would have the texture and tongue taste as well. The average 1 year old probably can remember the experiencem(but not me)! Graeme Bartlett 10:10, 11 November 2007 (UTC)

Without having performed any OR on the matter, I can nevertheless confidently assert that they taste like shit. —Steve Summit (talk) 14:23, 11 November 2007 (UTC)

After digestion, very little that stimulates taste receptors should remain. Probably the only recognizable taste would be salt, but no saltier than blood. 66.218.55.142 14:40, 11 November 2007 (UTC)

I was under the impression that it had a spongey texture, although I cannot remember where I encountered this gem of information. [1] will perhaps help you on your enquiry. (Really, don't follow that link unless you have a strong stomach). Lanfear's Bane | t 15:08, 11 November 2007 (UTC)

For your sake and for mine, let us hope that that is peanut butter. Can I wash my eyes now? --Russoc4 16:47, 11 November 2007 (UTC)

Knowing the right term might help you: Coprophagia --Mdwyer 20:43, 13 November 2007 (UTC)

Actually Mdwyer, coprophagy and coprophagia are synonomous. Re my original qestion about the taste of feces, it's been most interesting to pose a query that nobody can (or cares to)answer.

Oops. I missed that in your question. In that light, my statement made me look not nice. Sorry about that. It wasn't supposed to be snarky. I did get you a link, though! --Mdwyer 20:43, 15 November 2007 (UTC)

commercial radioisotope

What is a commercial radioisotope? —Preceding unsigned comment added by 144.137.98.219 (talk) 10:17, 11 November 2007 (UTC)

It is a radioactive isotope that you can purchase as a standard product, such as ¹³¹Iodine —Preceding unsigned comment added by Graeme Bartlett (talk • contribs) 10:52, 11 November 2007 (UTC) or tritium. Graeme Bartlett

asteroid belt

if some spaceship tries to cross the asteroid belt, then instead of by passing through it, can it go above it and cross the belt?SidSam 10:34, 11 November 2007 (UTC)

A spaceship could go above or below, but asteroids occasionally will orbit at an inclined angle and stray into that space too. The belt is actually very thin and the chances are that a spaceship will fly through and not be impacted. The problem is that more fuel is needed to go outside the eccliptic plane, and then back into it. Space ships always scrape by on the minimum fuel, so such maneuvers are unlikely unless there is a reason to go up and out there. Graeme Bartlett 10:56, 11 November 2007 (UTC)

I heard it's so widely spaced that if you were at one asteroid, you wouldn't even be able to see another asteroid with naked eyes. So passing right through it seems pretty safe. 64.236.121.129 15:08, 12 November 2007 (UTC)

Tbe asteroid belt is more like a flat ring around the sun - like one of Saturns rings - so you could certainly go around it. But the rocks within it are widely spaced - so it's pretty safe to travel through it as though it wasn't there. SteveBaker 14:04, 11 November 2007 (UTC)

The scatter-graphs at asteroid family may suggest how much like Saturn's rings the asteroid belt is not. —Tamfang 22:46, 12 November 2007 (UTC)

Aldol

In the aldol condensation of acetone, mesityl oxide is created. What then, if anything, prevents a further acetone molecule from adding on to the other side of the product, resulting in an endless chain of carbonyls? Or, what prevents the mesityl oxide from adding onto another molecule of acetone, creating a symmetric compound with another isobutene group? What about endless Michael reactions at the double bond? Could't you theoretically just keep making one infinitely larger compound, as long as there are alpha-hydrogens and/or alpha-beta double bonds? --Russoc4 14:56, 11 November 2007 (UTC)

Yes, that's called polymerization. Apparently it can be a serious problem when you don't want to make polymers, because it deactivates the catalyst.[2] [3] That second one says "The active sites for aldol condensation are the same as the active sites for polymer production.". There are even patented methods to inhibit the polymerization.[4] —Keenan Pepper 17:13, 11 November 2007 (UTC)

So then, disregarding any Michael reactions, these [5] would be the possible aldol condensation products? What do you think would happen if I added acetone to a concentrated NaOH solution and heated it? Would that polymer be a likely outcome? --Russoc4 18:01, 11 November 2007 (UTC)

But if you read the page on mesityl oxide, it points out that further condensation yields isophorone, which is a cyclic product. Six-membered rings like that of isophorone are pretty stable and will ressit further attack. Delmlsfan 02:02, 12 November 2007 (UTC)

Heisenberg t-shirt

I am pretty sure I have seen an image containing the Heisenberg uncertainty principle ($\Delta x\Delta p\geq \hbar /2$) and the text "free will". I thought it was a t-shirt or sticker from either xkcd or ThinkGeek, but can't find it. Does anyone know where I might have seen it? —Bromskloss 20:38, 11 November 2007 (UTC)

Not sure, but I'd like a shirt with that inequality and the text "mathematical consequence of a probability theory in the complex field" or maybe "If you get the math, it's obvious". SamuelRiv 22:06, 11 November 2007 (UTC)

Well, it's a trivial consequence of the canonical commutation relation, but is it obvious that the CCR must hold? Algebraist 22:46, 11 November 2007 (UTC)

In the plain math, it comes from the Fourier transform of a waveform, where you find position and momentum space have fundamental uncertainty in deriving one knowing the other. SamuelRiv 22:59, 11 November 2007 (UTC)

So you're claiming it's mathematically obvious that systems are described by wavefunctions? Algebraist 23:16, 11 November 2007 (UTC)

I'm almost positve you can cross XKCD off of the list. As far as I know, they have made a joke of everything nerdy except for the Heisenberg uncertainty priniciple. However, I did find another Heisenberg shirt. Paragon12321 00:16, 12 November 2007 (UTC)

It seems I'm out of luck here. Anyway, you have heard this one, haven't you?:

Police officer: "Have you any idea how FAST you were going back there?"
Werner Heisenberg: "Nope, but I knew EXACTLY where I was!"

:P —Bromskloss 08:26, 12 November 2007 (UTC)

I don't know about a tee-shirt, but as for comics, see Casey and Andy strip 128, and stripts 247 to 249. Related are 89, 67. – b_jonas 11:48, 13 November 2007 (UTC)

Try cafepress and search for Heisenberg; they have a few t-shirts that might be what you are looking for. --— Gadget850 (Ed) ^talk - 13:35, 17 November 2007 (UTC)