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Teachable moments in Boston Harbor

The king tides are back, along with high winds, and they caused some havoc in Boston – leading to a teachable moment by Boston Harbor. A massive ship broke free from dock, and had drifted out – while crewed! They were rescued by tugboats, and the boat is now stationed between Nahant and Winthrop.

This was the perfect opportunity to discuss with students where Boston Harbor was, how tides are created, how to read maps, and maritime geography.

Seaport Boston harbor teaching

As for those King Tides:

It’s that time of the year again. Sure, the holiday season has returned, but so have — this week, at least — the king tides. The astronomically caused ultra-high tides peaked in Boston just before noon Tuesday, according to the National Oceanic and Atmospheric Administration. Reaching more than two feet higher than average daily high tides, the seasonal occurrence produced minor flooding in low-lying areas along the East Coast.

king tides NOAA Lunar orbit

Let’s see how the motion of the moon creates tides:

Tides Spring Neap

News from the Boston National Historical Park Twitter page.

boston NHP King Tides

News story from WCVB


A container ship broke free from a terminal in Boston, the Coast Guard confirmed early Wednesday morning. The 1,065-foot ship “Helsinki Bridge” was at the Paul W. Conley Container Terminal when the 12 lines securing the vessel broke.

Helsinki Bridge container ship floats away

“They notified us very quickly. The ship’s crew was very quick in getting their engine equipment up and running so that they could drop their anchor and not be drifting around,” Coast Guard Lt. Jennifer Sheehy said.

Terminal workers who were on the ship were able to get off, and no injuries were reported. Two tug boats and a pilot helped to escort the runaway ship out to Broad Sound, between Winthrop and Nahant. State police said the ship hit a dock and did some minor damage when it broke free.

Paul W. Conley Container Terminal Boston

“They’ll take a look at all of the equipment.  They’ll talk to the ship’s crew, and a team is at Conley Terminal looking at any damage that might be there,” Sheehy said.

Officials said weather may have played a role in the ship breaking free.  “Winds that we had last night, the strength of those winds and a ship this size has a lot of sail area to push against, so it’s not unheard of for a ship this size to part ways because of the wind strength,” Sheehy said. The ship will eventually be towed back to the terminal.

See our lesson on tides, and Why Is There a Tidal Bulge Opposite the Moon?

Learning Standards

Ocean Literacy Scope and Sequence for Grades K-12


Ocean Literacy Principle #3, The ocean interaction of oceanic and atmospheric processes controls weather and climate by dominating the Earth’s energy, water and carbon systems.

Ocean Literacy Principle #6,

b. The ocean provides foods, medicines, and mineral and energy resources. It supports jobs and national economies, serves as a highway for transportation of goods and people, and plays a role in national security.

f. Much of the worlds population lives in coastal areas. Coastal regions are susceptible to natural hazards (tsunamis, hurricanes, cyclones, sea level change, and storm surges).




Four types of multiverses

Intro tba / Max Tegmark

type 1

type 2

Some people believe that the universe began at the Big Bang, and that our universe is the only one that has ever existed. Others believe that the universe is cyclical, and that universes existed before ours: those universes, it is hypothesized, collapsed and were replaced by later universes.

When Georges Lemaître, a Belgian physicist and Roman Catholic priest, first began to develop the Big Bang Theory (in 1927), many scientists assumed the former (this is the only universe that has ever existed) In this view, it makes no sense to ask “what happened before the Big Bang?” as there was no before.

In more recent years, scientists have studied the possibility of a multi-verse. Our universe may not be the only one that has existed; perhaps others existed before our own, and others may exist after our own. Also, perhaps other universes  – in some way removed from our own – simultaneously exist.  In this view, one indeed may ask “what happened before the Big Bang?” as there was a time before our universe.

We have no direct evidence of other universes, although astronomical and physics evidence, as interpreted through theories like Quantum Mechanics and General Relativity, does suggest that other universes may exist.

As such, some physicists have developed models of how our universe may have been created, perhaps from the destruction of a previous universe, or perhaps ours branched off from some other.

type 3

type 4





Further reading


Learning Standards

2016 Massachusetts Science and Technology Curriculum Framework
Appendix VIII: Value of Crosscutting Concepts and Nature of Science in Curricula

ETS3. Technological Systems.  5.3-5-ETS3-1(MA). Use informational text to provide examples of improvements to existing technologies (innovations) and the development of new technologies (inventions). Recognize that technology is any modification of the natural or designed world done to fulfill human needs or wants.

9. Influence of Engineering, Technology, and Science on Society and the Natural World

In grades 9–12, students can describe how modern civilization depends on major technological systems, such as agriculture, health, water, energy, transportation, manufacturing, construction, and communications. Engineers continuously modify these systems to increase benefits while decreasing costs and risks. New technologies can have deep impacts on society and the environment, including some that were not anticipated.

SAT Subject Test: Physics

Quantum phenomena, such as photons and photoelectric effect

Atomic, such as the Rutherford and Bohr models, atomic energy levels, and atomic spectra. Nuclear and particle physics, such as radioactivity, nuclear reactions, and fundamental particles. Relativity, such as time dilation, length contraction, and mass-energy equivalence.

College Board Standards for College Success: Science

Enduring Understanding 1D: Classica mechanics can not describe all properties of objects.

Warp drive

Most people are familiar with warp drive as a form of FTL (Faster Than Light travel) Its most popular use is in the science-fiction series Star Trek. What is warp drive – and according to the laws of physics, as we know them today, could this potentially be possible?

Enterprise at warp speed Star Trek

Warp drive in science fiction


Warping space in general relativity



Gravity General Relativity warping The Elegant Universe

From “The Elegant Universe”, PBS series NOVA. 2003.

Warp drive in real physics

The Alcubierre drive is a speculative analysis of physics which shows that warp drive may in fact be possible. It is based on a solution of Einstein’s field equations in general relativity.  It was first proposed by Mexican theoretical physicist Miguel Alcubierre. In his analysis, a spacecraft could effectively achieve a kind of FTL travel if a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created.

Alcubierre Warp Drive

From a demo on Wolfram.com by Thomas Mueller.

Rather than exceeding the speed of light within a local reference frame, a spacecraft would traverse distances by contracting space in front of it and expanding space behind it, resulting in effective faster-than-light travel.

In this analysis, objects still cannot accelerate to the speed of light within normal spacetime; therefore it doesn’t violate the laws of General Relativity.

Instead, the Alcubierre drive shifts space around an object so that the object would arrive at its destination faster than light would in normal space.

“Space-time bubble is the closest that modern physics comes to the “warp drive” of science fiction. It can convey a starship at arbitrarily high speeds. Space-time contracts at the front of the bubble, reducing the distance to the destination, and expands at its rear, increasing the distance from the origin (arrows). The ship itself stands still relative to the space immediately around it; crew members do not experience any acceleration. Negative energy (blue) is required on the sides of the bubble.” – Ford and Roman


Lawrence H. Ford and Thomas A. Roman. Sci Am article.



Although the metric proposed by Alcubierre is consistent with the Einstein field equations, it may not be physically meaningful. We are not certain that the mathematical solutions are possible in the real world. If so then this warp drive will not be possible.

Even if it is physically meaningful, that does not necessarily mean that a drive can be constructed. The proposed mechanism of the Alcubierre drive implies a negative energy density and therefore requires exotic matter. So if exotic matter with the correct properties can not exist, then the drive could not be constructed.

Further reading

Negative Energy. Wormholes and Warp Drive. Scientific American Jan 2000

Faster-than-light (FTL) Travel in Science Fiction. Dan Koboldt

Alcubierre warp drive, Wikipedia

Faster Than Light, Wikipedia

Negative Energy, Wormholes and Warp Drive, Scientific American, Jan 2000

By Lawrence H. Ford and Thomas A. Roman

Learning Standards

2016 Massachusetts Science and Technology Curriculum Framework
Appendix VIII: Value of Crosscutting Concepts and Nature of Science in Curricula

ETS3. Technological Systems.  5.3-5-ETS3-1(MA). Use informational text to provide examples of improvements to existing technologies (innovations) and the development of new technologies (inventions). Recognize that technology is any modification of the natural or designed world done to fulfill human needs or wants.

9. Influence of Engineering, Technology, and Science on Society and the Natural World

In grades 9–12, students can describe how modern civilization depends on major technological systems, such as agriculture, health, water, energy, transportation, manufacturing, construction, and communications. Engineers continuously modify these systems to increase benefits while decreasing costs and risks. New technologies can have deep impacts on society and the environment, including some that were not anticipated.

SAT Subject Test: Physics

Quantum phenomena, such as photons and photoelectric effect

Atomic, such as the Rutherford and Bohr models, atomic energy levels, and atomic spectra. Nuclear and particle physics, such as radioactivity, nuclear reactions, and fundamental particles. Relativity, such as time dilation, length contraction, and mass-energy equivalence.

College Board Standards for College Success: Science

Enduring Understanding 1D: Classica mechanics can not describe all properties of objects.

Ampère’s circuital law

I’m caching a copy of www.maxwells-equations.com/ampere/amperes-law.php
This isn’t to negate the copyright of the original website, which I direct people to! I create backups like this on occasion, because even favorite teaching websites sometimes disappear (maybe the owner didn’t pay to renew the domain name.) And I wouldn’t want something so valuable to disappear.


On this page, we’ll explain the meaning of the last of Maxwell’s Equations, Ampere’s Law, which is given in Equation [1]:


Ampere was a scientist experimenting with forces on wires carrying electric current. He was doing these experiments back in the 1820s, about the same time that Farday was working on Faraday’s Law. Ampere and Farday didn’t know that there work would be unified by Maxwell himself, about 4 decades later.

Forces on wires aren’t particularly interesting to me, as I’ve never had occassion to use the very complicated equations in the course of my work (which includes a Ph.D., some stints at a national lab, along with employment in the both defense and the consumer electronics industries). So, I’m going to start by presenting Ampere’s Law, which relates a electric current flowing and a magnetic field wrapping around it:


Equation [2] can be explained: Suppose you have a conductor (wire) carrying a current, I. Then this current produces a Magnetic Field which circles the wire.

The left side of Equation [2] means: If you take any imaginary path that encircles the wire, and you add up the Magnetic Field at each point along that path, then it will numerically equal the amount of current that is encircled by this path (which is why we write encircled current for encircled or enclosed current).

Let’s do an example for fun. Suppose we have a long wire carrying a constant electric current, I[Amps]. What is the magnetic field around the wire, for any distance r [meters] from the wire?

Let’s look at the diagram in Figure 1. We have a long wire carrying a current of I Amps. We want to know what the Magnetic Field is at a distance r from the wire. So we draw an imaginary path around the wire, which is the dotted blue line on the right in Figure 1:


Figure 1. Calculating the Magnetic Field Due to the Current Via Ampere’s Law.

Ampere’s Law [Equation 2] states that if we add up (integrate) the Magnetic Field along this blue path, then numerically this should be equal to the enclosed current I.

Now, due to symmetry, the magnetic field will be uniform (not varying) at a distance r from the wire. The path length of the blue path in Figure 1 is equal to the circumference of a circle of radius r:  2 x Pi x r.

If we are adding up a constant value for the magnetic field (we’ll call it H), then the left side of Equation [2] becomes simple:


Hence, we have figured out what the magnitude of the H field is. And since r was arbitrary, we know what the H-field is everywhere. Equation [3] states that the Magnetic Field decreases in magnitude as you move farther from the wire (due to the 1/r term).

So we’ve used Ampere’s Law (Equation [2]) to find the magnitude of the Magnetic Field around a wire. However, the H field is a Vector Field, which means at every location is has both a magnitude and a direction. The direction of the H-field is everywhere tangential to the imaginary loops, as shown in Figure 2. The right hand rule determines the sense of direction of the magnetic field:


Figure 2. The Magnitude and Direction of the Magnetic Field Around a Wire.

Manipulating the Math for Ampere’s Law

We are going to do the same trick with Stoke’s Theorem that we did when looking at Faraday’s Law. We can rewrite Ampere’s Law in Equation [2]:


On the right side equality in Equation [4], we have used Stokes’ Theorem to change a line integral around a closed loop into the curl of the same field through the surface enclosed by the loop (S).

We can also rewrite the total current (I enclosed, I enc) as the surface integral of the Current Density (J):


So now we have the original Ampere’s Law (Equation [2]) rewritten in terms of surface integrals (Equations [4] and [5]). Hence, we can substitute them together and get a new form for Ampere’s Law:


Now, we have a new form of Ampere’s Law: the curl of the magnetic field is equal to the Electric Current Density. If you are an astute learner, you may notice that Equation [6] is not the final form, which is written in Equation [1]. There is a problem with Equation [6], but it wasn’t until the 1860s that James Clerk Maxwell figured out the problem, and unified electromagnetics with Maxwell’s Equations.


Displacement Current Density

Ampere’s Law was written as in Equation [6] up until Maxwell. So let’s look at what is wrong with it. First, I have to throw out another vector identity – the divergence of the curl of any vector field is always zero:


So let’s take the divergence of Ampere’s Law as written in Equation [6]:

divergence of ampere's law [Equation 8]

So Equation [8] follows from Equations [6] and [7]. But it says that the divergence of the current density J is always zero. Is this true?

If the divergence of J is always zero, this means that the electric current flowing into any region is always equal to the electric current flowing out of the region (no divergence). This seems somewhat reasonable, as electric current in circuits flows in a loop. But let’s look what happens if we put a capacitor in the circuit:

a-c circuit with a capacitorFigure 3. A Voltage Applied to A Capacitor.

Now, we know from electric circuit theory that if the voltage is not constant (for example, any periodic wave, such as the 60 Hz voltage that comes out of your power outlets) then current will flow through the capacitor. That is, we have I not equal to zero in Figure 3.

However, a capacitor is basically two parallel conductive plates separated by air. Hence, there is no conductive path for the current to flow through. This means that no electric current can flow through the air of the capacitor. This is a problem if we think about Equation [8]. To show it more clearly, let’s take a volume that goes through the capacitor, and see if the divergence of J is zero:

divergence not zero when a capacitor is presentFigure 4. The Divergence of J is not Zero.

In Figure 4, we have drawn an imaginary volume in red, and we want to check if the divergence of the current density is zero. The volume we’ve chosen, has one end (labeled side 1) where the current enters the volume via the black wire. The other end of our volume (labeled side 2) splits the capacitor in half.

We know that the current flows in the loop. So current enters through Side 1 of our red volume. However, there is no electric current that exits side 2. No current flows within the air of the capacitor. This means that current enters the volume, but nothing leaves it – so the divergence of J is not zero. We have just violated our Equation [8], which means the theory does not hold. And this was the state of things, until our friend Maxwell came along.

Maxwell knew that the Electric Field (and Electric Flux Density (D) was changing within the capacitor. And he knew that a time-varying magnetic field gave rise to a solenoidal Electric Field (i.e. this is Farday’s Law – the curl of E equals the time derivative of B). So, why is not that a time varying D field would give rise to a solenoidal H field (i.e. gives rise to the curl of H). The universe loves symmetry, so why not introduce this term? And so Maxwell did, and he called this term the displacement current density:

displacement current density [Equation 9]

This term would “fix” the circuit problem we have in Figure 4, and would make Farday’s Law and Ampere’s Law more symmetric. This was Maxwell’s great contribution. And you might think it is a weak contribution. But the existance of this term unified the equations and led to understanding the propagation of electromagnetic waves, and the proof that all waves travel at the same speed (the speed of light)! And it was this unification of the equations that Maxwell presented, that led the collective set to be known as Maxwell’s Equations. So, if we add the displacement current to Ampere’s Law as written in Equation [6], then we have the final form of Ampere’s Law:

final form of Ampere's Law [Equation 10]

And that is how Ampere’s Law came into existance!

Intrepretation of Ampere’s Law

So what does Equation [10] mean? The following are consequences of this law:


  • A flowing electric current (J) gives rise to a Magnetic Field that circles the current
  • A time-changing Electric Flux Density (D) gives rise to a Magnetic Field that circles the D field

    Ampere’s Law with the contribution of Maxwell nailed down the basis for Electromagnetics as we currently understand it. And so we know that a time varying D gives rise to an H field, but from Farday’s Law we know that a varying H field gives rise to an E field…. and so on and so forth and the electromagnetic waves propagate – and that’s cool.


This website is educational. Materials within it are being used in accord with the Fair Use doctrine, as defined by United States law.

§107. Limitations on Exclusive Rights: Fair Use

Notwithstanding the provisions of section 106, the fair use of a copyrighted work, including such use by reproduction in copies or phone records or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use, the factors to be considered shall include:

the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
the nature of the copyrighted work;
the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
the effect of the use upon the potential market for or value of the copyrighted work. (added pub. l 94-553, Title I, 101, Oct 19, 1976, 90 Stat 2546)

Carbon dating


“At an archaeological dig, a piece of wooden tool is unearthed – and the archaeologist finds it to be 5,000 years old. A child mummy is found high in the Andes – and the archaeologist says the child lived more than 2,000 years ago. How do scientists know how old an object or human remains are? What methods do they use and how do these methods work?

Carbon-14 dating is a way of determining the age of archaeological artifacts of a biological origin up to about 50,000 years old. It is used in dating things such as bone, cloth, wood and plant fibers that were created in the relatively recent past by human activities.”

  • How Stuff Works, How Carbon-14 Dating Works, Marshall Brain

“The method was developed by Willard Libby in the late 1940s and soon became a standard tool for archaeologists. Libby received the Nobel Prize in Chemistry for his work in 1960. ” – Wikipedia

How does it work?

Radiocarbon is constantly being created in the atmosphere by the interaction of cosmic rays with atmospheric nitrogen.

matthew2262 Radiocarbon dating

From the matthew2262 wordpress blog.

The resulting radiocarbon combines with atmospheric oxygen to form radioactive carbon dioxide.

That is incorporated into plants by photosynthesis.

Animals then acquire 14 C by eating the plants.

When the animal or plant dies, it stops exchanging carbon with its environment, and from that point onwards the amount of 14 C it contains begins to decrease, as the 14
C undergoes radioactive decay.

Measuring the amount of 14 C in a sample from a dead plant or animal such as a piece of wood or a fragment of bone provides information that can be used to calculate when the animal or plant died.

The older a sample is, the less 14 C there is to be detected, and because the half-life of 14 C (the period of time after which half of a given sample will have decayed) is about 5,730 years.

The oldest dates that can be reliably measured by this process date to around 50,000 years ago, although special preparation methods occasionally permit accurate analysis of older samples.

– Carbon Dating, Wikipedia


As years go by, how much C14 is left?

carbon dating part 1

C12 does not decay and remains constant in a sample, whereas C14 decays at an even, constant rate.

By measuring the ratio of C12 to C14, we can understand how long a sample has been around for.

The half life of C 14 is around 5,730 years. As seen by the second graph, this means that if a sample has half of the C14 it should usually have, it has been around for 5,730 years. A quarter of the amount, double that time, one eight of the original amount, more still.

Carbon dating is only as accurate as the consistency of it’s decay rate, which is unchanging and extremely uniform.

It is almost exclusively used for organic material as all life on earth is carbon based.

There is a misconception that carbon dating is used to date the age of the earth. For longer time scales, other elements are used, based on the same principles.

Graphs from a video by Scientific American that explains carbon dating. Watch the full video here How Does Radiocarbon Dating Work? – Instant Egghead #28: Scientific American

  • text from http://blunt-science.tumblr.com/post/109954909373/a-representation-of-the-age-span-carbon-dating-is


Is radiocarbon dating reliable?

Excerpted from National Center for Science Education, by Christopher Gregory Weber:


Radiocarbon dating can easily establish that humans have been on the earth for over twenty thousand years …. it is one of the most reliable of all the radiometric dating methods.

Question: How does carbon-14 dating work?

carbon dating part 1

Cosmic rays in the upper atmosphere are constantly converting the isotope nitrogen-14 (N-14) into carbon-14 (C-14 or radiocarbon).

Living organisms are constantly incorporating this C-14 into their bodies along with other carbon isotopes.

When the organisms die, they stop incorporating new C-14

The old C-14 starts to decay back into N-14 by emitting beta particles.

The older an organism’s remains are, the less beta radiation it emits because its C-14 is steadily dwindling at a predictable rate.

So, if we measure the rate of beta decay in an organic sample, we can calculate how old the sample is. C-14 decays with a half-life of 5,730 years.


Question: Kieth and Anderson radiocarbon-dated the shell of a living freshwater mussel and obtained an age of over two thousand years. ICR creationists claim that this discredits C-14 dating. How do you reply?

Answer: It does discredit the C-14 dating of freshwater mussels, but that’s about all. Kieth and Anderson show considerable evidence that the mussels acquired much of their carbon from the limestone of the waters they lived in and from some very old humus as well.

Carbon from these sources is very low in C-14 because these sources are so old and have not been mixed with fresh carbon from the air. Thus, a freshly killed mussel has far less C-14 than a freshly killed something else, which is why the C-14 dating method makes freshwater mussels seem older than they really are.

When dating wood there is no such problem because wood gets its carbon straight from the air, complete with a full dose of C-14.


Question: A sample that is more than fifty thousand years old shouldn’t have any measurable C-14. Coal, oil, and natural gas are supposed to be millions of years old; yet creationists say that some of them contain measurable amounts of C-14, enough to give them C-14 ages in the tens of thousands of years. How do you explain this?

Answer: Very simply. Radiocarbon dating doesn’t work well on objects much older than twenty thousand years, because such objects have so little C-14 left that their beta radiation is swamped out by the background radiation of cosmic rays and potassium-40 (K-40) decay.


Younger objects can easily be dated, because they still emit plenty of beta radiation, enough to be measured after the background radiation has been subtracted out of the total beta radiation. However, in either case, the background beta radiation has to be compensated for, and, in the older objects, the amount of C-14 they have left is less than the margin of error in measuring background radiation. As Hurley points out:

Without rather special developmental work, it is not generally practicable to measure ages in excess of about twenty thousand years, because the radioactivity of the carbon becomes so slight that it is difficult to get an accurate measurement above background radiation. (p. 108)

Cosmic rays form beta radiation all the time; this is the radiation that turns N-14 to C-14 in the first place. K-40 decay also forms plenty of beta radiation. Stearns, Carroll, and Clark point out that “. . . this isotope [K-40] accounts for a large part of the normal background radiation that can be detected on the earth’s surface” (p. 84).

This radiation cannot be totally eliminated from the laboratory, so one could probably get a “radiocarbon” date of fifty thousand years from a pure carbon-free piece of tin. However, you now know why this fact doesn’t at all invalidate radiocarbon dates of objects younger than twenty thousand years and is certainly no evidence for the notion that coals and oils might be no older than fifty thousand years.


Question: Creationists such as Cook (1966) claim that cosmic radiation is now forming C-14 in the atmosphere about one and one-third times faster than it is decaying. If we extrapolate backwards in time with the proper equations, we find that the earlier the historical period, the less C-14 the atmosphere had.

If we extrapolate as far back as ten thousand years ago, we find the atmosphere would not have had any C-14 in it at all. If they are right, this means all C-14 ages greater than two or three thousand years need to be lowered drastically and that the earth can be no older than ten thousand years. How do you reply?

Answer: Yes, Cook is right that C-14 is forming today faster than it’s decaying. However, the amount of C-14 has not been rising steadily as Cook maintains; instead, it has fluctuated up and down over the past ten thousand years. How do we know this? From radiocarbon dates taken from bristlecone pines. There are two ways of dating wood from bristlecone pines: one can count rings or one can radiocarbon-date the wood.

Since the tree ring counts have reliably dated some specimens of wood all the way back to 6200 BC, one can check out the C-14 dates against the tree-ring-count dates. Admittedly, this old wood comes from trees that have been dead for hundreds of years, but you don’t have to have an 8,200-year-old bristlecone pine tree alive today to validly determine that sort of date. It is easy to correlate the inner rings of a younger living tree with the outer rings of an older dead tree. The correlation is possible because, in the Southwest region of the United States, the widths of tree rings vary from year to year with the rainfall, and trees all over the Southwest have the same pattern of variations.

When experts compare the tree-ring dates with the C-14 dates, they find that radiocarbon ages before 1000 BC are really too young—not too old as Cook maintains. For example, pieces of wood that date at about 6200 BC by tree-ring counts date at only 5400 BC by regular C-14 dating and 3900 BC by Cook’s creationist revision of C-14 dating (as we see in the article, “Dating, Relative and Absolute,” in the Encyclopaedia Britannica). So, despite claims, C-14 before three thousand years ago was decaying faster than it was being formed and C-14 dating errs on the side of making objects from before 1000 BC look too young, not too old.


Question: But don’t trees sometimes produce more than one growth ring per year? Wouldn’t that spoil the tree-ring count?

Answer: If anything, the tree-ring sequence suffers far more from missing rings than from double rings. This means that the tree-ring dates would be slightly too young, not too old.

Of course, some species of tree tend to produce two or more growth rings per year. But other species produce scarcely any extra rings. Most of the tree-ring sequence is based on the bristlecone pine.  This tree rarely produces even a trace of an extra ring; on the contrary, a typical bristlecone pine has up to 5 percent of its rings missing. Concerning the sequence of rings derived from the bristlecone pine,  Ferguson says:

In certain species of conifers, especially those at lower elevations or in southern latitudes, one season’s growth increment may be composed of two or more flushes of growth, each of which may strongly resemble an annual ring.

Such multiple growth rings are extremely rare in bristlecone pines, however, and they are especially infrequent at the elevation and latitude (37� 20′ N) of the sites being studied. In the growth-ring analyses of approximately one thousand trees in the White Mountains, we have, in fact, found no more than three or four occurrences of even incipient multiple growth layers. (p. 840)

In years of severe drought, a bristlecone pine may fail to grow a complete ring all the way around its perimeter; we may find the ring if we bore into the tree from one angle, but not from another. Hence at least some of the missing rings can be found. Even so, the missing rings are a far more serious problem than any double rings.

Other species of trees corroborate the work that Ferguson did with bristlecone pines.  Before his work, the tree-ring sequence of the sequoias had been worked out back to 1250 BC. The archaeological ring sequence had been worked out back to 59 BC. The limber pine sequence had been worked out back to 25 BC.

The radiocarbon dates and tree-ring dates of these other trees agree with those Ferguson got from the bristlecone pine.  But even if he had had no other trees with which to work except the bristlecone pines, that evidence alone would have allowed him to determine the tree-ring chronology back to 6200 BC. …


Question: Does outside archaeological evidence confirm the C-14 dating method?

Answer: Yes. When we know the age of a sample through archaeology or historical sources, the C-14 method (as corrected by bristlecone pines)  agrees with the age within the known margin of error.

For instance, Egyptian artifacts can be dated both historically and by radiocarbon, and the results agree. At first, archaeologists used to complain that the C-14 method must be wrong, because it conflicted with well-established archaeological dates; but, as Renfrew has detailed, the archaeological dates were often based on false assumptions.

One such assumption was that the megalith builders of western Europe learned the idea of megaliths from the Near-Eastern civilizations. As a result, archaeologists believed that the Western megalith-building cultures had to be younger than the Near Eastern civilizations.

Many archaeologists were skeptical when Ferguson’s calibration with bristlecone pines was first published, because, according to his method, radiocarbon dates of the Western megaliths showed them to be much older than their Near-Eastern counterparts.

However, as Renfrew demonstrated, the similarities between these Eastern and Western cultures are so superficial that the megalith builders of western Europe invented the idea of megaliths independently of the Near East. So, in the end, external evidence reconciles with and often confirms even controversial C-14 dates.

One of the most striking examples of different dating methods confirming each other is Stonehenge. C-14 dates show that Stonehenge was gradually built over the period from 1900 BC to 1500 BC, long before the Druids, who claimed Stonehenge as their creation, came to England.

Astronomer Gerald S. Hawkins calculated with a computer what the heavens were like back in the second millennium BC, accounting for the precession of the equinoxes, and found that Stonehenge had many significant alignments with various extreme positions of the sun and moon (for example, the hellstone marked the point where the sun rose on the first day of summer). Stonehenge fits the heavens as they were almost four thousand years ago, not as they are today, thereby cross-verifying the C-14 dates.


Relative Ages of Rocks: WIkiBooks

(WikiBooks: A project hosted by the Wikimedia Foundation for the creation of free content textbooks)



External links

Willard Libby and Radiocarbon Dating. American Chemical Society

Learning Standards

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012), from the National Research Council of the National Academies.

By the end of grade 12. Radioactive decay lifetimes and isotopic content in rocks provide a way of dating rock formations and thereby fixing the scale of geological time.

College Board Standards for College Success: Science

ES.3 Earth’s History: Relative and Absolute dating. Students understand that various dating methods — relative and absolute — have been used to determine the age of Earth.

Suggested Connections. Between Earth Science and Other Disciplines: Evidence of Common Ancestry and Divergence (LS.1.1); Living Systems and the Physical Environment (LS.3.1); Nuclear Chemistry (C.1.6); Nuclear Interactions and the Conservation of Mass–Energy (P.2.3)

Benchmarks: American Association for the Advancement of Science.

Knowledge of radioactivity helps them understand how rocks can be dated, which helps them appreciate the scale of geologic time… Scientific evidence indicates that some rock layers are several billion years old. 4C/H6** (BSL)

Peptide bonds – How we make proteins

2 amino acids can join to form a peptide.

A very long peptide is known as a protein.

When they join one of the amino acid’s loses an H atom, while the other loses an OH moiety (part of a molecule)  They join together to form H2O (water.) This is a condensation reaction.

peptide bond formation 1

Doc Kaiser’s Microbiology Home Page (Gary E. Kaiser)


Here is another animation of the same process

The CONH link created is called a peptide bond (red)
Water (blue) is removed.

This process can be continued repeatedly to form longer peptides (eventually, when they are over 50 amino acids long, we call them proteins.)

peptide bond formation 2

BioTopics.co.uk by Richard Steane

The monomer here is an amino acid.

The polymer here is a peptide or protein.

These are 20 different types of common amino acids.

Amino acids are bonded together to make peptides, or proteins.

A peptide is just a small protein, less than 50 amino acids (aa) long.

Proteins are much larger, 100 aa, 500 aa, even 1,000 aa.

A chain of amino acids folds up into a shape.

Every protein has its own shape.


If all land ice melted how would coastlines change

Scientists have used evidence to reconstruct sea-level rise around America’s northeast coast over the last 10,000 years.

New Jersey going back 10,000 years in research newly published in the Journal of Quaternary Science. To do this, they collected sediment cores drilled tens of meters below ground from coastal marshes, then examined the sediment back in a lab for microscopic organisms that only exist at specific depths below sea level. Salt marsh grasses also fossilized within the sediment were used to radiocarbon-date the samples.

The 10 maps contained in the GIF below show the movement of sea level at 1,000-year intervals leading up today:


sea rise GIF Influence of tidal-range change and sediment compaction on Holocene relative sea-level change in New Jersey,

HORTON, B. P., ENGELHART, S. E., HILL, D. F., KEMP, A. C., NIKITINA, D., MILLER, K. G. and PELTIER, W. R. (2013), Influence of tidal-range change and sediment compaction on Holocene relative sea-level change in New Jersey, USA. J. Quaternary Sci., 28: 403–411

If This GIF of 10,000 Years of Sea Level Rise Doesn’t Freak You Out, Nothing Wil


Boston underwater: How the rising sea levels will affect the city


What Could Disappear. New York Times Sunday Review.


“If we keep burning fossil fuels indefinitely, global warming will eventually melt all the ice at the poles and on mountaintops, raising sea level by 216 feet. Explore what the world’s new coastlines would look like.

“The maps here show the world as it is now, with only one difference: All the ice on land has melted and drained into the sea, raising it 216 feet and creating new shorelines for our continents and inland seas.

There are more than five million cubic miles of ice on Earth, and some scientists say it would take more than 5,000 years to melt it all. If we continue adding carbon to the atmosphere, we’ll very likely create an ice-free planet, with an average temperature of perhaps 80 degrees Fahrenheit instead of the current 58.”

from National Geographic Magazine, What the World Would Look Like if All the Ice Melted

Map 1

The entire Atlantic seaboard would vanish, along with Florida and the Gulf Coast. In California, San Francisco’s hills would become a cluster of islands and the Central Valley a giant bay. The Gulf of California would stretch north past the latitude of San Diego—not that there’d be a San Diego.

Ice melt north america

Map 2

The Amazon Basin in the north and the Paraguay River Basin in the south would become Atlantic inlets, wiping out Buenos Aires, coastal Uruguay, and most of Paraguay. Mountainous stretches would survive along the Caribbean coast and in Central America.

Ice melt South America

Map 3

London? A memory. Venice? Reclaimed by the Adriatic Sea. Thousands of years from now, in this catastrophic scenario, the Netherlands will have long since surrendered to the sea, and most of Denmark will be gone too. Meanwhile, the Mediterranean’s expanding waters will also have swelled the Black and Caspian Seas.

Ice melt Europe

Map 3

Land now inhabited by 600 million Chinese would flood, as would all of Bangladesh, population 160 million, and much of coastal India. The inundation of the Mekong Delta would leave Cambodia’s Cardamom Mountains stranded as an island.

Ice melt Asia


East Antarctica: The East Antarctica ice sheet is so large—it contains four-fifths of all the ice on Earth—that it might seem unmeltable. It survived earlier warm periods intact. Lately it seems to be thickening slightly—because of global warming. The warmer atmosphere holds more water vapor, which falls as snow on East Antarctica. But even this behemoth is unlikely to survive a return to an Eocene Climate.

West Antarctica: Like the Greenland ice sheet, the West Antarctic one was apparently much smaller during earlier warm periods. It’s vulnerable because most of it sits on bedrock that’s below sea level.The warming ocean is melting the floating ice sheet itself from below, causing it to collapse. Since 1992 it has averaged a net loss of 65 million metric tons of ice a year.

Ice melt Antarctica

All maps by: Jason Treat, Matthew Twombly, Web Barr, Maggie Smith, NGM Staff. Art Kees Veenebos. From Sept. 2013 National Geographic Society

What the World Would Look Like if All the Ice Melted (National Geographic)


Learning Standards