Suppose someone asks you the number of bits of data on a typical musical compact
Disc. In response, it is not generally expected that you would provide the
Exact number but rather an estimate, which may be expressed in scientific notation.
An order of magnitude of a number is determined as follows:
1. Express the number in scientific notation, with the multiplier of the power of
ten between 1 and 10 and a unit.
2. If the multiplier is less than 3.162 (the square root of ten), the order of magnitude
of the number is the power of ten in the scientific notation. If the
multiplier is greater than 3.162, the order of magnitude is one larger than
the power of ten in the scientific notation.
We use the symbol _ for “is on the order of.” Use the procedure above to verify
the orders of magnitude for the following lengths:
0.008 6 m ~ 102 m 0.002 1 m ~103 m 720 m ~103 m
Usually, when an order-of-magnitude estimate is made, the results are reliable to
Within about a factor of 10. If a quantity increases in value by three orders of magnitude,
Its value increases by a factor of about 103 _ 1 000.
Inaccuracies caused by guessing too low for one number are often canceled by
Other guesses that are too high. You will find that with practice your guesstimates
Become better and better. Estimation problems can be fun to work because you
Freely drop digits, venture reasonable approximations for unknown numbers,
Make simplifying assumptions, and turn the question around into something you
Can answer in your head or with minimal mathematical manipulation on paper.
Because of the simplicity of these types of calculations, they can be performed on
a small scrap of paper and are often called “back-of-the-envelope calculations.”
Our body’s neural information system is complexity built from simplicity. Its building
blocks are neurons, or nerve cells. Sensory neurons carry messages from the body’s
tissues and sensory organs inward to the brain and spinal cord, for processing. The
brain and spinal cord then send instructions out to the body’s tissues via the motor
neurons. Between the sensory input and motor output, information is processed in
the brain’s internal communication system via its interneurons. Our complexity resides
mostly in our interneuron systems. Our nervous system has a few million sensory
neurons, a few million motor neurons, and billions and billions of interneurons.
All are variations on the same theme (FIGURE 2.2). Each consists of a cell body and its
branching fibers. The bushy dendrite fibers receive information and conduct it toward
the cell body. From there, the cell’s axon passes the message along to other neurons
or to muscles or glands. Axons speak. Dendrites listen.
Unlike the short dendrites, axons are sometimes very long, projecting several feet
through the body. A motor neuron carrying orders to a leg muscle, for example, has a
cell body and axon roughly on the scale of a basketball attached to a rope 4 miles
long. Much as home electrical wire is insulated, so a layer of fatty tissue, called the
myelin sheath, insulates the axons of some neurons and helps speed their impulses.
As myelin is laid down up to about age 25, neural efficiency, judgment, and selfcontrol
grows (Fields, 2008). If the myelin sheath degenerates, multiple sclerosis results:
Communication to muscles slows, with eventual loss of muscle control.
Depending on the type of fiber, a neural impulse travels at speeds ranging from a
sluggish 2 miles per hour to a breakneck 200 or more miles per hour. But even this
top speed is 3 million times slower than that of electricity through a wire. We measure
brain activity in milliseconds (thousandths of a second) and computer activity
in nanoseconds (billionths of a second). Thus, unlike the nearly instantaneous reactions
of a high-speed computer, your reaction to a sudden event, such as a child darting
in front of your car, may take a quarter-second or more. Your brain is vastly more
complex than a computer, but slower at executing simple responses.
Neurons transmit messages when stimulated by signals from our senses or when
triggered by chemical signals from neighboring neurons. At such times, a neuron fires
an impulse, called the action potential—a brief electrical charge that travels down
Taken from different books from different authors. Proper refernce will be available there !