The Universe of Discourse


Wed, 30 Sep 2015

A message to the aliens, part 16/23 (vital statistics)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents) Page 4 (algebra) Page 5 (geometry) Page 6 (chemistry) Page 7 (mass) Page 8 (time and space) Page 9 (physical units) Page 10 (temperature) Page 11 (solar system) Page 12 (Earth-Moon system) Page 13 (days, months, and years) Page 14 (terrain) Page 15 (human anatomy)

This is page 16 of the Cosmic Call message. An explanation follows.

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This page, about human vital statistics and senses, is in three sections. The text in the top left explains the population of the Earth: around 6,000,000,000 people at the time the message was sent. The three following lines give the life expectancy (70 years), mass (80 kg), and body temperature (311K) of humans. In each case it is stated explicitly that the value for men and for women is the same, which is not really true.
The glyph used for life expectancy is the same one used to denote the age of the Earth back on page 13 even though the two notions are not really the same. And why 311K when the commonly-accepted value is 310K?

The diagram at right attempts to explain the human sense of hearing, showing a high-frequency wave at top and a low frequency one at bottom, annotated with the glyph for frequency and the upper and lower frequency limits of human hearing, 20,000 Hz and 20 Hz respectively. I found this extremely puzzling the first time I deciphered the message, so much so that it was one of the few parts of the document that left me completely mystified, even with the advantage of knowing already what humans are like. A significant part of the problem here is that the illustration is just flat out wrong. It depicts transverse waves:

but sound waves are not transverse, they are compression waves. The aliens are going to think we don't understand compression waves. (To see the difference, think of water waves, which are transverse: the water molecules move up and down—think of a bobbing cork—but the wave itself travels in a perpendicular direction, not vertically but toward the shore, where it eventually crashes on the beach. Sound waves are not like this. The air molecules move back and forth, parallel to the direction the sound is moving.)

I'm not sure what would be better; I tried generating some random compression waves to fit in the same space. (I also tried doing a cartoon of a non-random, neatly periodic compression wave, but I couldn't get anything I thought looked good.) I think the compression waves are better in some ways, but perhaps very confusing:

On the one hand, I think they express the intended meaning more clearly; on the other hand, I think they're too easy to confuse with glyphs, since they happen to be on almost the same scale. I think the message might be clearer if a little more space were allotted for them. Also, they could be annotated with the glyph for pressure , maybe something like this:

This also gets rid of the meaningless double-headed arrow. I'm not sure I buy the argument that the aliens won't know about arrows; they may not have arrows but it's hard to imagine they don't know about any sort of pointy projectile, and of course the whole purpose of a pointy projectile (the whole point, one might say) is that the point is on the front end. But the arrows here don't communicate motion or direction or anything like that; even as a human I'm not sure what they are supposed to communicate.

The bottom third of the diagram is more sensible. It is a diagram showing the wavelengths of light to which the human visual system is most sensitive. The x-axis is labeled with “wavelength” and the y-axis with a range from 0 to 1. The three peaks have their centers at 295 nm (blue), 535 nm (green), and 565 nm (often called “red”, but actually yellow). These correspond to the three types of cone cells in the retina, and the existence of three different types is why we perceive the color space as being three-dimensional. (I discussed this at greater length a few years ago.) Isn't it interesting that the “red” and green sensitivities are so close together? This is why we have red-green color blindness.

The next article will discuss page 17, shown at right. (Click to enlarge.) Try to figure it out before then.


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Mon, 28 Sep 2015

A message to the aliens, part 15/23 (human anatomy)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents) Page 4 (algebra) Page 5 (geometry) Page 6 (chemistry) Page 7 (mass) Page 8 (time and space) Page 9 (physical units) Page 10 (temperature) Page 11 (solar system) Page 12 (Earth-Moon system) Page 13 (days, months, and years) Page 14 (terrain)

This is page 15 of the Cosmic Call message. An explanation follows.

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This page starts a new section of the document, each page headed with the glyph for “biology” . The illustration is adapted from the Pioneer plaque; the relevant portion is shown below.

Copies of the plaque were placed on the 1972 and 1973 Pioneer spacecraft. The Pioneer image has been widely discussed and criticized; see the Wikipedia article for some of the history here. The illustration suffers considerably from its translation to a low-resolution bitmap. The original picture omits the woman's vulva; the senders have not seen fit to correct this bit of prudery.

The man and the woman are labeled with the glyphs and , respectively. The glyph for “people” , which identified the stick figures on the previous page, is inexplicably omitted here.

The ruler on the right somewhat puzzlingly goes from a bit above the man's toe to a bit below the top of the woman's head; it does not measure either of the two figures. It is labeled 1.8 meters, a typical height for men. The original Pioneer plaque spanned the woman exactly and gave her height as 168 cm, which is conveniently an integer multiple of the basic measuring unit (21 cm) defined on the plaque.

To prevent the recipients from getting confused about which end of the body is the top, a parabolic figure (shown here at left), annotated with the glyph for “acceleration”, shows the direction of gravitational acceleration as on the previous page.

The next article will discuss page 16, shown at right. (Click to enlarge.) Try to figure it out before then.


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Fri, 25 Sep 2015

A message to the aliens, part 14/23 (terrain)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents) Page 4 (algebra) Page 5 (geometry) Page 6 (chemistry) Page 7 (mass) Page 8 (time and space) Page 9 (physical units) Page 10 (temperature) Page 11 (solar system) Page 12 (Earth-Moon system) Page 13 (days, months, and years)

This is page 14 of the Cosmic Call message. An explanation follows.

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This is my favorite page: there is a lot of varied information and the illustration is ingenious. The page heading says to match up with the corresponding labels on the previous three pages. The page depicts the overall terrain of the Earth. The main feature is a large illustration of some mountains (yellow in my highlighted illustration below) plunging into the sea (blue).

The land part is labeled , the air part , and the water part . Over on the left of the land part are little stick figures, labeled people . This is to show that people live on the land part of the Earth, not under water or in the air. The stick figures may not be clear to the recipients, but they are explained in more detail on the next page.

Each of the three main divisions is annotated with its general chemical composition, with compounds listed in order of prevalence., All the chemical element symbols were introduced earlier, on pages 6 and 7:

The lithosphere : silicon dioxide (SiO2) ; aluminium oxide (Al2O3) ; iron(III) oxide (Fe2O3) ; iron(II) oxide (FeO) . Wikipedia and other sources dispute this listing, giving instead: SiO2, MgO, FeO, Al2O3, CaO, Na2O, Fe2O3 in that order.

The atmosphere : nitrogen gas (N2) ; oxygen gas (O2) ; argon (Ar) ; carbon dioxide (CO2) .

The hydrosphere : water (H2O) ; sodium (Na) ; chlorine (Cl) .

There are rulers extending upward from the surface of the water to the height of top of the mountain and downward to the bottom of the ocean. The height ruler is labeled 8838 meters, which is the height the peak of Mount Everest, the point highest above sea level. The depth ruler is labeled 11000 meters, which is the depth of the Challenger Deep in the Mariana Trench, the deepest part of the ocean. The two rulers have the correct sizes relative to one another. The human figures at left are not to scale (they would be about 1.7 miles high), but the next page will explain how big they really are.

I don't think the message contains anything to tell the recipients the temperature of the Earth, so it may not be clear that the hydrosphere is liquid water. But perhaps the wavy line here will suggest that. The practice of measuring the height of the mountains and depth of the ocean from the surface may also be suggestive of a liquid ocean, since it would not otherwise have a flat surface to provide a global standard.

There is a potential problem with this picture: how will the recipients know which edge is the top? What if they hold it upside-down, and think the human figures are pointing down into the earth, heads downwards?

This problem is solved in a clever way: the dots at the right of the page depict an object accelerating under the influence of gravity, falling in a characteristic parabolic path. To make the point clear, the dots are labeled with the glyph for acceleration.

Finally, the lower left of the page states the acceleration due to gravity at the Earth's surface, 9.7978 m/s2. The recipients can calculate this value from the mass and radius of the Earth given earlier. Linked with the other appearance of acceleration on the page, this should suggest that the dots depict an object falling under the influence of gravity toward the bottom of the page.


The next article will discuss page 15, shown at right. (Click to enlarge.) Try to figure it out before then.


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Wed, 23 Sep 2015

A message to the aliens, part 13/23 (days, months, and years)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents) Page 4 (algebra) Page 5 (geometry) Page 6 (chemistry) Page 7 (mass) Page 8 (time and space) Page 9 (physical units) Page 10 (temperature) Page 11 (solar system) Page 12 (Earth-Moon system)

This is page 13 of the Cosmic Call message. An explanation follows.

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There are three diagrams on this page, each depicting something going around. Although the direction is ambiguous (unless you understand arrows) it should at least should be clear that all three rotations are in the same direction. This is all you can reasonably say anyhow, because the rotations would all appear to be going the other way if you looked at them from the other side.

The upper left diagram depicts the Earth going around the Sun and underneath is a note that says that the time is equal to 315569268 seconds, and is also equal to one year . This defines the year.


The upper-right diagram depicts the Moon going around the Earth ; the notation says that this takes 2360591 seconds, or around 27⅓ days. This is not the 29½ days that one might naïvely expect, because it is the sidereal month rather than the synodic month. Suppose the phase of the Moon is new, so that the Moon lies exactly between the Earth and the Sun. 27⅓ days later the Moon has made a complete trip around the Earth, but because the Earth has moved, the Moon is not yet again on the line between the Earth and the Sun; the line is in a different direction. The Earth has moved about !!\frac1{13}!! of the way around the sun, so it takes about another !!\frac1{12}\cdot 27\frac13!! days before the moon is again between Earth and Sun and so a total of about 29½ days between new moons.

The lower-right diagram depicts the rotation of the Earth, giving a time of 86163 seconds for the day. Again, this is not the 86400 seconds one would expect, because it is the sidereal day rather than the solar day; the issue is the same as in the previous paragraph.

None of the three circles appears to be circular. The first one is nearly circular, but it looks worse than it is because the Sun has been placed off-center. The curve representing the Moon's orbit is decidedly noncircular. This is reasonable, because the Moon's orbit is elliptical to approximately the same degree. In the third diagram, the curve is intended to represent the surface of the Earth, so its eccentricity is indefensible. The ellipse is not the same as the one used for the Moon's orbit, so it wasn't just a copying mistake.

The last two lines state that the ages of the Sun and the Earth are each 4550000000 years. This is the first appearance of the glyph for “age”.

The next article will discuss page 14, shown at right. (Click to enlarge.) Try to figure it out before then.


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Mon, 21 Sep 2015

A message to the aliens, part 12/23 (earth-moon system)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents) Page 4 (algebra) Page 5 (geometry) Page 6 (chemistry) Page 7 (mass) Page 8 (time and space) Page 9 (physical units) Page 10 (temperature) Page 11 (solar system)

This is page 12 of the Cosmic Call message. An explanation follows.

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Page 12, begins a new section of the document, with pages headed with the glyph “Earth”, describing the Earth and its environs. This will help the recipients locate our planet, should they come to visit.

The top of the page has a diagram of the Earth -Moon system and a ruler labeled with the distance between them, !!3844\cdot 10^5!! meters. Since the distance between Earth and Moon varies (the orbit is elliptical) an average value is given.

The glyph used here for distance, , is different from the one defined on page 9 . Neither appears elsewhere in the message, so this is probably a mistake.

The following five lines give the mass and radius of the Moon and the Earth, and also the distance from the Earth to the Sun. The latter would have been better on the previous page, which discussed the solar system, but was omitted from there for some reason.

The next article will discuss page 13, shown at right. (Click to enlarge.) Try to figure it out before then.


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Fri, 18 Sep 2015

A message to the aliens, part 11/23 (solar system)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents) Page 4 (algebra) Page 5 (geometry) Page 6 (chemistry) Page 7 (mass) Page 8 (time and space) Page 9 (physical units) Page 10 (temperature)

This is page 11 of the Cosmic Call message. An explanation follows.

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Page 11, headed with the glyph for “physics” is evidently a chart of the solar system, with the Sun at left. The Earth is also labeled, as is Jupiter , the planet most likely to be visible to the recipients. The “Jupiter” glyph does not appear again. Pluto is included, as it was still considered a planet in 1999. (Pluto's status as only one of many similar trans-Neptunian objects was not well appreciated in 1999 when the message was composed, the second TNO having only been discovered in 1992.) To the extent permitted by the low resolution of the image, The diameters of the planets and the Sun are to scale, but not their relative positions; the page is much too small for that. Saturn's rings are not shown, as they are in the Pioneer plaque; by this time it was appreciated that ring systems may be common around large planets.

The masses and radii of Jupiter and the Sun are given, Jupiter above the illustration and the Sun below. The (external) temperature of the Sun is also given, 5763 kelvins. This should be visible to the aliens because the Sun is a blackbody emitter and the spectrum of blackbody radiation is a clear indicator of its temperature. This data should allow the aliens to locate us, should they be so inclined: they know which way the message came from, and can look for a star with the right size and temperature in that direction. When they get closer, Jupiter and the sizes of the planets will provide a confirmation that they are in the right place. Later pages explain that we live on the Earth, so the aliens will know where to point their fusion cannon in order to obliterate our planet.

The next article will discuss page 12, shown at right. (Click to enlarge.) Try to figure it out before then.


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Wed, 16 Sep 2015

A message to the aliens, part 10/23 (temperature)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents) Page 4 (algebra) Page 5 (geometry) Page 6 (chemistry) Page 7 (mass) Page 8 (time and space) Page 9 (physical units)

This is page 10 of the Cosmic Call message. An explanation follows.

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The top half of this page is a table of melting points (on the left) and boiling points (on the right) for various substances: hydrogen , carbon , sulfur , zinc , silver , and gold . The temperatures are given in kelvins .

The boiling points depend on pressure, so there is a notation at the bottom of the list that the pressure should be 101300 pascals . This is one standard atmosphere, so it may tell the aliens a little more about our planet.

To help calibrate the kelvins, the bottom of the page is a chart of the temperature increase of water , showing how the temperature stops increasing at the melting point (273K) and the boiling point (373K). This introduces the glyph for temperature , which will recur later.

There are two regrettable things about this chart. One is that the horizontal axis is labeled “time” . Why is the temperature of the water increasing with time? It should be energy.

But a more serious complaint, I think, it that this is the wrong chart. It depends crucially on the (Earth-)standard atmospheric pressure, with which the recipients may not be familiar. And the kelvin is not defined in terms of standard pressure anyway. It is defined in terms of the triple point of water, the unique, universal temperature and pressure at which all three states of water can coexist. Why not a temperature and pressure chart with the triple point labeled? This is something one might more reasonably expect the aliens to have studied.

The next article will discuss page 11, shown at right. (Click to enlarge.) Try to figure it out before then.


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Mon, 14 Sep 2015

A message to the aliens, part 9/23 (physical units)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents) Page 4 (algebra) Page 5 (geometry) Page 6 (chemistry) Page 7 (mass) Page 8 (time and space)

This is page 9 of the Cosmic Call message. An explanation follows.

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The previous two pages defined fundamental units of mass, distance, and time. This page adds some derived notions: force, energy, pressure, and power; velocity and acceleration.

The first four lines are in two parts each. The left part defines an abstract quantity like force or energy; the right part defines a unit of that quantity like newtons or joules. For example, the second line defines energy and units of energy. The left side says that energy is equal to mass times distance squared divided by time squared. (This is the first appearance of the glyphs for distance and time.) The right side says that a joule of energy is !!1\frac{\mathrm{kg}\,\mathrm{m}^2}{\mathrm{s}^2}!!.

The two following lines define the abstract concepts of velocity (which has appeared before in connection with the speed of light) and acceleration (which is new). There are no units given for these.

Concept
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energy

pressure

power

velocity

acceleration
Unit
newton

joule

pascal

watt
(none) (none)

The newton and the joule won't appear again. Force won't appear again except on the last page, which asks “force WTF?”.

The final part of the page is the most interesting. It mentions the Planck constant !!h!! (not the related !!\hbar!!) which is !!6.6260755\cdot 10^{{}^-34}!! joule-seconds and the universal gravitation constant !!G!! which is !!6.67259\cdot 10^{{}^-11}\; \mathrm{m}^3\; \mathrm{kg}^{{}^-1}\; \mathrm{s}^{{}^-2}!!.

It's quite possible that the recipients won't recognize the gravitational constant, which is tricky to measure directly. Newton's law of universal gravitation was known on Earth for hundreds of years before the value of !!G!! was worked out. But if the recipients don't know it, they will be able to work it out from the later statements about the mass and radius of the Earth and the gravitational force at its surface, This would in turn allow them to calculate the mass of their own planet.

Note that on this page some inverse units are written with a division sign and some with a negative exponent. Will this inconsistency puzzle the aliens? My coworker Jeff Ober suggests that it communicates the important personal information that humans are confused and inconsistent.

The next article will discuss page 10, shown at right. (Click to enlarge.) Try to figure it out before then.


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Fri, 11 Sep 2015

A message to the aliens, part 8/23 (time and space)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents) Page 4 (algebra) Page 5 (geometry) Page 6 (chemistry) Page 7 (mass)

This is page 8 of the Cosmic Call message. An explanation follows.

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The main feature of this page is a diagram of the electron energy levels for a hydrogen atom, annotated at the top with the glyph for hydrogen and at the bottom with the glyph for energy . The four lowest levels are shown, with the lowest level (the ground state) at the bottom. Above these is a thicker bar representing the way the higher energy levels all pile up into a smear. If the bottom level is at 0 and the smear is at 1, then the three intermediate levels are shown at approximately their exact values of !!\frac34, \frac89, !! and !!\frac{15}{16}!!; these are given by the Rydberg formula.

The aliens should be familiar with hydrogen. Normally a hydrogen atom's sole electron is in the ground state. If a photon couples with the electron, say because starlight is falling on the atom, or someone has applied an electric current to it, the electron may jump up to a higher quantum state. (This is the only correct use of the phrase "quantum leap".) When it drops back down, it will emit a photon. But the energy of the emitted photon must be one of a few particular values, corresponding to the difference between the old and the new energy level; the electron never drops down partway to the next level. An incandescent cloud of hydrogen gas will not typically glow in every possible color; it will emit light in only a few particular, characteristic wavelengths, and these colors can be separated with a spectroscope. The wavelengths of these characteristic colors of light, visible everywhere the message is likely to reach, provide a basis for defining the meter.

For example, the second pair of numbers labels the transition from the !!n=3!! to the !!n=2!! state, and an electron transiting between these two states will always emit a photon with a wavelength of 656.2852 nanometers and a frequency of 456.8021 terahertz, and these are the two numbers in the pair. The product of the two numbers in each pair is a constant, which should further confirm to the recipients that they have the right interpretation. The constant product is close to 299792458, which is the speed of light in meters per second. This defines four glyphs, for wavelength and frequency, and meters and hertz.


wavelength

frequency

meters

hertz

seconds

The following item

defines the second as the inverse of the hertz (written as !!\mathrm{Hz}^{{}^-1}!! and as !!1\div\mathrm{Hz}!!).

Finally, the speed of light is given, first theoretically, as the product of wavelength and frequency and then numerically, as 299792458 meters per second .

The next article will discuss page 9, shown at right. (Click to enlarge.)
Try to figure it out before then.


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Wed, 09 Sep 2015

A message to the aliens, part 7/23 (mass)

Earlier articles: Introduction Common features Page 1 (numerals) Page 2 (arithmetic) Page 3 (exponents) Page 4 (algebra) Page 5 (geometry) Page 6 (chemistry)

This is page 7 of the Cosmic Call message. An explanation follows.

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Page 7 discusses mass and defines the kilogram.

The top section of the page continues the table of chemical elements from the previous page, giving the number of protons and neutrons. For example, gold is described as having 79 protons and 117 neutrons .


Sulfur

Zinc

Argon

Silver

Gold

Uranium

Copernicium

Copernicium, element 112, had been discovered but not named at the time the document was written.

There is a major error here. Uranium is given as having 92 protons and 116 neutrons. There is no such substance. It should have said 146 neutrons.

I sometimes imagine the aliens, having received the message, come to visit us. “We weren't going to bother,” they say, “but we had to know about the uranium-208.” And then we will have to tell them that we messed up. Ouch. (It could be an error for lead-208 or bismuth-208 instead; one can't be sure because the glyph does not appear elsewhere in the document.)

I'd been planning to write that paragraph about uranium-208 for more than ten years, but it wasn't until just now that I realized there is a much more serious mistake two lines down, so that the uranium is no longer the most serious error that I know of in the entire document. The line after the table of elements says that the mass of a carbon atom is the mass of six protons plus the mass of six neutrons plus “energy”, , by which I think they mean the binding energy in the nucleus. This is the first appearance of the glyph for energy, which will recur later. And then the following line commits a really horrible boner, one that has the potential to spoil the whole message.

With the mass of the carbon nucleus pinned down, the authors want to define the kilogram : the document says that 12 kilograms is the mass of !!6022137\cdot 10^{19} !! carbon-12 atoms. That !!6022137\cdot 10^{19} !! is Avogadro's number. Except it's not. Avogadro's number is usually given as !!6.022137\cdot 10^{23} !!, and this number is 100 times that big. But it should be 1000 times that big.

Normally, one would say that !!6.022137\cdot 10^{23} !! carbon atoms mass 12 grams, but there are two confusing factors here. One is that the authors have written !!6022137!! instead of !!6.022137!! and the other is that they are defining 12 kilograms instead of 12 grams. But it should be that !!6.022137\cdot 10^{23} = 6022137\cdot 10^{17}!! atoms is 12 grams so that !!6022137\cdot 10^{20}!! atoms is 12 kilograms, and the number written is instead !!6022137 10^{19}!! atoms, making the kilogram 90% smaller than it should have been.

It's possible that the aliens can figure this out, because it is detectably inconsistent with the following statements about the masses of the fundamental particles in kilograms. But it may not be clear to the recipients which of the two definitions of the kilogram is the correct one. Especially given the—I really hate to report this—the typo in the second statement.

The three following lines give the masses of the proton, neutron, and electron in kilograms. These are all more or less correct (although the book values have changed since the message were written) and I think the value for the neutron has a typo; it says !!1.6739286\cdot 10^{{}^-34}!! kg but it probably should have been !!1.67{\mathit 4}9286\cdot 10^{{}^-34}!! kg which would agree with the current book value of !!1.674927351\cdot 10^{{}^-34}!! kg.

Since we're going over the errors on this page, here is yet another oddity. The number of neutrons in a gold atom is given at the top of the page as 117. Unlike uranium-208., the isotope gold-196 actually exists. But it is radioactive, breaking down into platinum or mercury after about a week. One would expect the listing to be for gold-197 instead, which is the only stable isotope and so is the only isotope occurring in naturally-found gold. (Thanks to Peter Annema for bringing this to my attention.) A similar oddity occurs in the listing for zinc : zinc-65 is given instead of the stable zinc-64 or zinc-66. The other isotopes listed here (sulfur-32, argon-40, silver-107) are more plausible.

The next article will discuss page 8, shown at right. (Click to enlarge.) Try to figure it out before then.


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