While this web site is a ".com" it's not very commercial. I do consult, teach, and write, and you can find this mentioned somewhere. Mostly this site is a collection of essays on various topics that I have written over a period of several years for different purposes. Think of it as a hobby; I'm a blogger. I have a few general things to say here, but first, please send a note to michael@scienceisart.com if you:

• have a question concerning any of the essays
• see something that is incorrect
• have something to add, know a reference, or link to related material
• just like the essay (scientists have egos too)

Regards, Michael Konrad


The boat is here because I like boats.

If you do too, look at a local boatworks that makes boats like this.


Units and measurements
Scientific (exponential) notation
The scientific literature

Units and measurements

Most of these essays contain references to physical quantities, e.g. length, mass, time, etc. I generally use metric, also called SI, units because:

• the metric system is used by most of the world
• the metric system is used by all scientists
• the metric system is easier to use for very small and very large values in contrast to the British Imperial (BI) system, (still used by many Americans)

The basic quantities needed to describe the physical world are mass, length, and time. The table below gives these basic units for metric and BI systems (more confusion).

mass length time
metric kilogram (kg) meter (m) second (s)
BI pound (lb) yard (yd) second (s)
1 kg = 2.2 lbs 1 m = 1.1 yds
However, the important difference in the two systems is not the different basic units. No one really cares if the unit of length is a meter or a yard. The important characteristic of the metric system is that only one basic unit is defined for each fundamental quantity. Larger and smaller units are multiplies of ten from the basic unit, and are so named, using standard prefixes. The metric system is not completely rational, but it's much better than the BI system.
unit multiplier
kilometer 1000
meter 1
centimeter 0.01
millimeter 0.001
micrometer 0.000001
nanometer 0.000000001
As an example, the table on the right gives some common metric length units. As you can see, all the units are factors of ten apart. Each unit is a prefix, which indicates the multiplier, followed by the modified unit.

The great thing about the metric system is that the same prefixes are used for other physical quantities; a microgram is 0.000001 gram.

Metric areas and volumes are also mostly rational. The metric area unit closest to the BI acre is the hectare. The prefix hect- means 100, and -are means area; thus an area 100 by 100 meters, (about 2.5 BI acres). In contrast, the BI acre is 4,840 square yards or 43,560 square feet.

The metric volume closest to the BI quart is the liter (about 1.1 quarts), which is exactly 0.01 cubic meters. The BI quart isn't a cubic inch, or cubic foot, or cubic anything else. Conveniently, one liter of water weighs almost exactly one kilogram (OK, an US pint of water is close to a pound). I could go on and on, but I'm sure you get the point.

Derived units

You only need units of length, mass, and time in order to derive all other units (ignoring electric current, temperature, etc.). However, these other units have special names. Here are a few important ones.

Force is defined by Newton's fundamental law: F = m a
where m = mass in kg
and a = acceleration as change in velocity, m / s2
thus the units of force are: kg m / s2 , called

Energy (or work) is force time distance: E = F d
thus the units of energy are: kg m2 / s2, called

Power is energy per unit time: P = E / t
thus the units of energy are: kg m2 / s3, called

a chain of fools: one of the best Aretha Franklin songs
The capstan is used to transfer the forces exerted by sailors on bars inserted into the holes in the head to a rope coiled around the barrel.
The BI system uses the same unit name, e.g. the pound, to describe mass, force, and weight. This is bound to confuse because the three are very different things. The mass of an object is the amount of stuff in that object, and is a constant property of the object. The weight of an object is the force that gravity exerts on the object. That force depends on both the strength of gravity and the mass of the object, and thus is not a constant property of the object.

Fw = g m

where Fw is the weight (a force),
and g is the value of gravity at that location, m is the mass of the object. The value of g varies from the equator to the poles, from the tops of mountains to the surface of oceans, etc., but the average is about 9.8 newtons / kg.
thus a kg weighs about 9.8 newtons.

Do not confuse g with the Newtonian gravitational constant G (which is a universal constant with a value of about 6.7 x 10-11 m3 / kg s2). The defining equation for G, which expresses the force of gravity between two objects is:

F = G m1 m2 / r2

where the two m's are the masses and r is the distance between them. We can use this equation to find the approximate mass of the earth, knowing that the radius of the earth is about 6,400 km. Thus F is 9.8 newtons when m1 is 1 kg, r is 6.4 x 106 m and, m2 the mass of the earth:

m2 = F r2 / G m1 = (9.8) (6.4 x 106)2 / 6.7 x 10-11 = 6 x 1024 kg

The crane hook is used to lift objects against the force of gravity (weight).
Another feature of the BI system is that fractions of quantities are given as factors of 2, e.g. 1/2, 1/4, 1/16, ... Thus, rulers calibrated in inches use these fractions, which have historical importance. In the dawn of the Industrial Age it was easy to divide a length into one half, and then that half into another half, etc. Thus, all rulers, drills, and other tools were calibrated in this way. The trouble with this system is that our number system has a base of ten (because we have ten fingers). It's a big pain in the ass to go from a 10 based number system to a 2 based tool system. The metric system is 10 based. Actually, surveyors rebelled from the 2 based system, and thus their tapes are 10 based (even if they are in feet etc.).

Scientific (exponential) notation

As you see from the above sections, scientists often need to use very large and very small numbers. In order to avoid large numbers of zeros in the representation of the numbers, which take up space and are prone to errors (try to count 24 zeros), the exponential notation was invented. It is very simple. The number is expressed as a number (usually in the form n.nnn) times ten raised to an exponent (or power). The exponent tells you the number of zeros you need to add behind the decimal point, or in front of the decimal point if the exponent is negative. A few examples make the principle clear:

100 = 1.0 x 102

1,000,000 = 1.0 x 106

1,235 = 1.235 x 103

0.00076 = 7.6 x 10-4

(note that to multiply two numbers in exponential notation you multiply the numbers and add the exponents)

The scientific literature

There are several scientific magazines intended for non-scientific readers (or as we in the priesthood call them, lay people). Perhaps one of the best is Scientific American. Most public libraries have it.

Then there are hybrid journals, the best known are Science and Nature. These contain news, comment, gossip, reviews, and finally research articles. At least half of the content can be understood by anyone that can understand the material in Scientific American. The remainder are real research articles in a variety of fields, from physics to medicine. Science [sciencemag] is a US journal (Thomas Edison was one of the founders), and is available in many US public libraries and all university libraries. They allow anyone free Internet access to the Table of Contents and Abstracts of all articles. If the article is more than a year old you can download the entire text.

Nature [nature-index.html] is published in England (Charles Darwin was one of the founders), and is very similar to Science. As far as I can see however, they don't have the same policy of allowing free access to abstracts or articles older than one year.

Finally there are "real" scientific journals, thousands of them. Here I will single out The Proceedings of the National Academy of Science (US) [pnas], not because it is published in the US, but because it carries such a wide variety of scientific articles, many of them are important, and it has an enlightened Internet policy. Not only can you read the abstracts and, for articles older than one year read the entire article, but for $10 US you can access all articles for a week.

In the last year (2005) there has been a great deal of pressure applied to journals to allow free Internet access. The pressure has had some success, but many journals feel their "business plan" would be compromised by free access. This is a force in progress, so the situation may be different when you read this.

The National Library of Medicine [nih] is an entry into Medline, a data base of all Journals that have anything to do with medicine (and it's interpreted in the broadest sense). Medline gives you abstracts of most journal articles, and it can be searched by subject. Al Gore was pilloried for his reference to "inventing the Internet", but actually he did good work. As an example, he made Medline public. Before Gore, you had to pay to access Medline.

A Google search will get you an immense amount of information, even about the most obscure (you thought) subject. This is because many University professors post class notes on the Internet, and a great deal of research material is also on the Internet.

Finally, you can go to Amazon.com and search for a book on a subject. If you are lucky you will find what you want and you will be able to afford it. Otherwise, get the title and author and ask your local public library to get it for you on Inter-library loan. This is an incredible resource. I have obtained $400 books this way, and other books that just can not be purchased (even as a used book through Amazon).

Happy hunting!

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