How Quantum Computers Work

The massive amount of processing power generated by computer manufacturers has not yet been able to quench our thirst for speed and computing capacity. In 1947, American computer engineer Howard Aiken said that just six electronic digital computers would satisfy the computing needs of the United States. Others have made similar errant predictions about the amount of computing power that would support our growing technological needs. Of course, Aiken didn’t count on the large amounts of data generated by scientific research, the proliferation of personal computers or the emergence of the Internet, which have only fueled our need for more, more and more computing power.

Will we ever have the amount of computing power we need or want? If, as Moore’s Law states, the number of transistors on a microprocessor continues to double every 18 months, the year 2020 or 2030 will find the circuits on a microprocessor measured on an atomic scale. And the logical next step will be to create quantum computers, which will harness the power of atoms and molecules to perform memory and processing tasks. Quantum computers have the potential to perform certain calculations significantly faster than any silicon-based computer.

Scientists have already built basic quantum computers that can perform certain calculations; but a practical quantum computer is still years away. In this article, you’ll learn what a quantum computer is and just what it’ll be used for in the next era of computing.

You don’t have to go back too far to find the origins of quantum computing. While computers have been around for the majority of the 20th century, quantum computing was first theorized less than 30 years ago, by a physicist at the Argonne National Laboratory. Paul Benioff is credited with first applying quantum theory to computers in 1981. Benioff theorized about creating a quantum Turing machine. Most digital computers, like the one you are using to read this article, are based on the Turing Theory.

Defining the Quantum Computer

The Turing machine, developed by Alan Turing in the 1930s, is a theoretical device that consists of tape of unlimited length that is divided into little squares. Each square can either hold a symbol (1 or 0) or be left blank. A read-write device reads these symbols and blanks, which gives the machine its instructions to perform a certain program. Does this sound familiar? Well, in a quantum Turing machine, the difference is that the tape exists in a quantum state, as does the read-write head. This means that the symbols on the tape can be either 0 or 1 or a superposition of 0 and 1; in other words the symbols are both 0 and 1 (and all points in between) at the same time. While a normal Turing machine can only perform one calculation at a time, a quantum Turing machine can perform many calculations at once.

Image used under the GNU Free Documentation License 1.2 The Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers.

Today’s computers, like a Turing machine, work by manipulating bits that exist in one of two states: a 0 or a 1. Quantum computers aren’t limited to two states; they encode information as quantum bits, or qubits, which can exist in superposition. Qubits represent atoms, ions, photons or electrons and their respective control devices that are working together to act as computer memory and a processor. Because a quantum computer can contain these multiple states simultaneously, it has the potential to be millions of times more powerful than today’s most powerful supercomputers.

This superposition of qubits is what gives quantum computers their inherent parallelism. According to physicist David Deutsch, this parallelism allows a quantum computer to work on a million computations at once, while your desktop PC works on one. A 30-qubit quantum computer would equal the processing power of a conventional computer that could run at 10 teraflops (trillions of floating-point operations per second). Today’s typical desktop computers run at speeds measured in gigaflops (billions of floating-point operations per second).

Quantum computers also utilize another aspect of quantum mechanics known as entanglement. One problem with the idea of quantum computers is that if you try to look at the subatomic particles, you could bump them, and thereby change their value. If you look at a qubit in superposition to determine its value, the qubit will assume the value of either 0 or 1, but not both (effectively turning your spiffy quantum computer into a mundane digital computer). To make a practical quantum computer, scientists have to devise ways of making measurements indirectly to preserve the system’s integrity. Entanglement provides a potential answer. In quantum physics, if you apply an outside force to two atoms, it can cause them to become entangled, and the second atom can take on the properties of the first atom. So if left alone, an atom will spin in all directions. The instant it is disturbed it chooses one spin, or one value; and at the same time, the second entangled atom will choose an opposite spin, or value. This allows scientists to know the value of the qubits without actually looking at them.

Next, we’ll look at some recent advancements in the field of quantum computing.

Qubit ControlComputer scientists control the microscopic particles that act as qubits in quantum computers by using control devices.

• Ion traps use optical or magnetic fields (or a combination of both) to trap ions.
• Optical traps use light waves to trap and control particles.
• Quantum dots are made of semiconductor material and are used to contain and manipulate electrons.
• Semiconductor impurities contain electrons by using “unwanted” atoms found in semiconductor material.
• Superconducting circuits allow electrons to flow with almost no resistance at very low temperatures.

Can adding iron to the oceans slow global warming?

By: Jennifer Horton.

Enter forward-thinking scientists and companies like Planktos and Climos, who propose adding iron to the world’s oceans to reduce atmospheric carbon dioxide levels and, in turn, to decrease temperatures. The idea of dumping iron in the oceans to lower temperatures has been around since the late 1980s and has been known variously as carbon sinking, ocean seeding or iron fertilization.

Photo courtesy NOAA
Phytoplankton absorb CO2 and sunlight to produce energy in photosynthesis.

The premise is act­ually simple. Iron acts as a fertilizer for many plants, and some, like the phytoplankton that form the base of the marine food web, need it to grow. Adding iron to the water stimulates phytoplankton growth, which in turn gobble up carbon dioxide through photosynthesis. The resulting decrease in carbon dioxide is supposed to help reduce temperatures since carbon dioxide is one of the main gases responsible for trapping ­heat on the earth’s surface through the greenhouse effect.

Numerous iron dumping trials have been conducted since oceanographer John Martin suggested the idea more than 15 years ago . One trial conducted in 2004 indicated that each atom of iron added to the water could draw between 10,000 and 100,000 atoms of carbon out of the atmosphere by encouraging plankton growth . Some scientists theorize that adding iron to the Southern Ocean alone could reduce carbon dioxide levels by 15 percent .

Scientist Oliver Wingenter suggests a more cautious approach, arguing that adding massive amounts of iron to the ocean could cause a major cooling of more than 10 degrees Celsius . He recommends fertilizing just 2 percent of the Southern Ocean to cause a 2 degree Celsius cooling and to set back the tipping point of global warming 10 or more years .

Instead of focusing on cutting carbon dioxide levels, Wingenter’s research concentrated on increasing other gases that result from the phytoplankton blooms, namely dimethyl sulfide, or DMS. DMS is largely responsible for cloud formation in the polar region and could increase cloud reflectivity, which would in turn reduce temperatures. During his iron fertilization experiments, Wingenter found that adding iron increased the concentration of DMS five-fold .

Coffee.

If your morning routine includes a cup or two of coffee, you may know a few things about it. It’s a stimulant drink, it comes from beans that are roasted and ground and, for many of us, it’s a staple of life. But do you know where coffee grows and how it gets to America? How a French roast differs from an Italian roast? What a coffee cherry is? Or how decaffeinated coffee is made?

Photo courtesy CoffeeResearch.org Your morning cup of Joe begins its life on a coffee plantation.

There’s much more to that morning cup o’ Joe than you may realize! In this article, we’ll look at coffee’s origins and how it spread, where it’s grown, how it’s harvested and processed and what roasting is all about. We’ll finish by learning how to make a really great cup of coffee.

Catching the Buzz

Coffee’s story begins with a goat, at least in legends. It’s said that Kaldi, an Ethiopian goatherd, noticed his goats acting very frisky after eating a certain shrub. He took some of the shrub’s berries for himself, caught the buzz and coffee’s future was secured.

Originally, coffee was a food, not a drink. Early East African tribes mixed the coffee berries (the unhulled bean, also called a coffee cherry) with animal fat, forming energy balls — something like primitive Power Bars. Coffee also grew on the Arabian Peninsula, and it was there that it was first developed into a hot drink, sometime around A.D. 1000. By the 13th century, Muslims were drinking coffee fervently. The “whirling dervishes” of early Islam may have been fueled by coffee.

As Islam spread, so did coffee. But the Arabs closely guarded the coffee plants, and no fertile seeds were found outside Arabia (with the exception of the other place where coffee grew naturally, Africa) until the 1600s. Another coffee legend states that an Indian smuggler named Baba Budan left Mecca with fertile seeds strapped to his chest. Soon, coffee plants were growing in India.

As European traders returned from exotic locales such as Turkey, they brought news of and a new-found taste for the black beverage. It was the Dutch who founded the first European coffee estate on the island of Java, then a Dutch colony (now part of Indonesia), in 1616.

Coffee crossed the Atlantic around 1727. Yet another coffee legend: Brazil’s emperor asks a spy, Lt. Col. Palheta, to smuggle seeds into the country. Palheta goes to French Guiana, exudes his considerable charm on the governor’s wife and leaves with a farewell bouquet — spiked with coffee seedlings. Brazil is now the world’s top coffee producer.

Coffee is grown in only one U.S. state, Hawaii. Its famed Kona coffee, grown on Hawaii’s volcanic mountains, is highly desired.

Photo courtesy Kona Coffee/Bay View Farm Coffees Kona coffee beans, drying here in Hawaii, are highly desirable by coffee connoisseurs.

What gives coffee its kick?

Caffeine, of course. Caffeine is trimethylxanthine (C8H10N4O2). It’s an addictive stimulant drug that operates in the brain the same way amphetamines, cocaine and heroin do (although caffeine is much milder than those drugs). Caffeine occurs naturally in a number of plants, including coffee beans. Your average 6-ounce cup of drip-brewed coffee contains 100 mg of caffeine. A 12-ounce cola soft drink contains about 50 mg of caffeine.

The Bean Belt

While you may drink coffee every day, unless you’ve lived in a coffee-producing country you may have no idea what a coffee tree looks like. A coffee tree is a woody perennial evergreen, covered with dark-green, waxy leaves growing opposite each other in pairs. They can grow 30 feet (9 m) high, but in cultivation, coffee trees are kept short for easier harvesting. It takes three or four years after planting for the tree to become productive. The tree produces fragrant white blossoms (some say the blossoms smell like jasmine), and then, nearly a year later, the coffee cherries mature. A coffee tree produces continuously: One plant can be flowering, have immature beans and mature cherries all at the same time. Each tree can produce beans that make between 1 and 1.5 pounds (0.45 and 0.68 kg) of roasted coffee every season.

Source: National Geographic Coffee grows best in an area known as the Bean Belt — the band around the Earth in between the Tropics of Capricorn and Cancer.

A coffee plant prefers rich soil and mild temperatures, with lots of rain and shaded sun. It grows best in a band around the middle of the world, bounded by the Tropics of Capricorn and Cancer, known as the Bean Belt. Soil, climate and altitude affect the flavor of the beans.

Fibonacci Number.

In mathematics, the Fibonacci numbers form a sequence defined by the following recurrence relation:

That is, after two starting values, each number is the sum of the two preceding numbers. The first Fibonacci numbers (sequence A000045 in OEIS), also denoted as F_n, for n = 0, 1, … , are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, …

(Sometimes this sequence is considered to start at F₁ = 1, but in this article it is regarded as beginning with F₀=0.)

The Fibonacci numbers are named after Leonardo of Pisa, known as Fibonacci, although they had been described earlier in India.

Origins

The Fibonacci numbers first appeared, under the name mātrāmeru (mountain of cadence), in the work of the Sanskrit grammarian Pingala (Chandah-shāstra, the Art of Prosody, 450 or 200 BC). Prosody was important in ancient Indian ritual because of an emphasis on the purity of utterance. The Indian mathematician Virahanka (6th century AD) showed how the Fibonacci sequence arose in the analysis of metres with long and short syllables. Subsequently, the Jain philosopher Hemachandra (c.1150) composed a well known text on these. A commentary on Virahanka’s work by Gopāla in the 12th century also revisits the problem in some detail.

Sanskrit vowel sounds can be long (L) or short (S), and Virahanka’s analysis, which came to be known as mātrā-vṛtta, wishes to compute how many metres (mātrās) of a given overall length can be composed of these syllables. If the long syllable is twice as long as the short, the solutions are:

1 mora: S (1 pattern)

2 morae: SS; L (2)

3 morae: SSS, SL; LS (3)

4 morae: SSSS, SSL, SLS; LSS, LL (5)

5 morae: SSSSS, SSSL, SSLS, SLSS, SLL; LSSS, LSL, LLS (8)

6 morae: SSSSSS, SSSSL, SSSLS, SSLSS, SLSSS, LSSSS, SSLL, SLSL, SLLS, LSSL, LSLS, LLSS, LLL (13)

7 morae: SSSSSSS, SSSSSL, SSSSLS, SSSLSS, SSLSSS, SLSSSS, LSSSSS, SSSLL, SSLSL, SLSSL, LSSSL, SSLLS, SLSLS, LSSLS, SLLSS, LSLSS, LLSSS, SLLL, LSLL, LLSL, LLLS (21)

A pattern of length n can be formed by adding S to a pattern of length n−1, or L to a pattern of length n−2; and the prosodicists showed that the number of patterns of length n is the sum of the two previous numbers in the series. Donald Knuth reviews this work in The Art of Computer Programming as equivalent formulations of the bin packing problem for items of lengths 1 and 2.

In the West, the sequence was first studied by Leonardo of Pisa, known as Fibonacci, in his Liber Abaci (1202)^[3]. He considers the growth of an idealised (biologically unrealistic) rabbit population, assuming that:

• in the first month there is just one newly-born pair,
• new-born pairs become fertile from their second month on
• each month every fertile pair begets a new pair, and
• the rabbits never die

Let the population at month n be F(n). At this time, only rabbits who were alive at month n−2 are fertile and produce offspring, so F(n−2) pairs are added to the current population of F(n−1). Thus the total is F(n) = F(n−1) + F(n−2)

The bee ancestry code

Fibonacci numbers also appear in the description of the reproduction of a population of idealized bees, according to the following rules:

• If an egg is laid by an unmated female, it hatches a male.
• If, however, an egg was fertilized by a male, it hatches a female.

Thus, a male bee will always have one parent, and a female bee will have two.

If one traces the ancestry of any male bee (1 bee), he has 1 female parent (1 bee). This female had 2 parents, a male and a female (2 bees). The female had two parents, a male and a female, and the male had one female (3 bees). Those two females each had two parents, and the male had one (5 bees). This sequence of numbers of parents is the Fibonacci sequence.

This is an idealization that does not describe actual bee ancestries. In reality, some ancestors of a particular bee will always be sisters or brothers, thus breaking the lineage of distinct parents.

Relation to the golden ratio

[edit] Golden ratio defined

The golden ratio.

The golden ratio (phi), also written τ (tau), is defined as the ratio that results when a line is divided so that the whole line has the same ratio to the larger segment as the larger segment has to the smaller segment. Expressed algebraically, normalising the larger part to unit length, it is the positive solution of the equation:

or equivalently

which is equal to:

[edit] Closed form expression

Like every sequence defined by linear recurrence, the Fibonacci numbers have a closed-form solution. It has become known as Binet’s formula, even though it was already known by Abraham de Moivre:

where is the golden ratio.

The Fibonacci recursion

is similar to the defining equation of the golden ratio in the form

which is also known as the generating polynomial of the recursion.

Proof (by induction):

Any root of the equation above satisfies and multiplying by shows:

By definition is a root of the equation, and the other root is . Therefore:

and

Now consider the functions:

defined for any real

All these functions satisfy the Fibonacci recursion

Selecting and gives the formula of Binet we started with. It has been shown that this formula satisfies the Fibonacci recursion. Furthermore:

and

establishing the base cases of the induction, proving that

for all

For any two starting values, a combination a,b can be found such that the function is the exact closed formula for the series.

Since for all is the closest integer to For computational purposes, this is expressed using the floor function:

[edit] Limit of consecutive quotients

Johannes Kepler pointed out that the ratio of consecutive Fibonacci numbers converges, stating that “…as 5 is to 8 so is 8 to 13, practically, and as 8 is to 13, so is 13 to 21 almost” and concludes that the limit approaches the golden ratio ^[5]

This convergence does not depend on the starting values chosen, excluding 0, 0.

Proof:

It follows from the explicit formula that for any real :

because and thus

[edit] Matrix form

A 2-dimensional system of linear difference equations that describes the Fibonacci sequence is

or

The eigenvalues of the matrix A are and , and the elements of the eigenvectors of A, and , are in the ratios and .

This matrix has a determinant of −1, and thus it is a 2×2 unimodular matrix. This property can be understood in terms of the continued fraction representation for the golden ratio:

The Fibonacci numbers occur as the ratio of successive convergents of the continued fraction for , and the matrix formed from successive convergents of any continued fraction has a determinant of +1 or −1.

The matrix representation gives the following closed expression for the Fibonacci numbers:

Taking the determinant of both sides of this equation yields Cassini’s identity

Additionally, since AⁿA^m = A^{m + n} for any square matrix A, the following identities can be derived:

[edit] Recognizing Fibonacci numbers

Occasionally, the question may arise whether a positive integer z is a Fibonacci number. Since F(n) is the closest integer to , the most straightforward test is the identity

which is true if and only if z is a Fibonacci number.

A slightly more sophisticated test uses the fact that the convergents of the continued fraction representation of are ratios of successive Fibonacci numbers, that is the inequality

(with coprime positive integers p, q) is true if and only if p and q are successive Fibonacci numbers. From this one derives the criterion that z is a Fibonacci number if and only if the intersection of the closed interval

with the positive integers is not empty.^[6]

[edit] Identities

1. F(n + 1) = F(n) + F(n − 1)
2. F(0) + F(1) + F(2) + … + F(n) = F(n + 2) − 1
3. F(1) + 2 F(2) + 3 F(3) + … + n F(n) = n F(n + 2) − F(n + 3) + 2
4. F(0)² + F(1)² + F(2)² + … + F(n)² = F(n) F(n + 1)

These identities can be proven using many different methods. But, among all, we wish to present an elegant proof for each of them using combinatorial arguments here. In particular, F(n) can be interpreted as the number of ways summing 1’s and 2’s to n − 1, with the convention that F(0) = 0, meaning no sum will add up to −1, and that F(1) = 1, meaning the empty sum will “add up” to 0. Here the order of the summands matters. For example, 1 + 2 and 2 + 1 are considered two different sums and are counted twice.

[edit] Proof of the first identity

Without loss of generality, we may assume n ≥ 1. Then F(n + 1) counts the number of ways summing 1’s and 2’s to n.

When the first summand is 1, there are F(n) ways to complete the counting for n − 1; and when the first summand is 2, there are F(n − 1) ways to complete the counting for n − 2. Thus, in total, there are F(n) + F(n − 1) ways to complete the counting for n.

[edit] Proof of the second identity

We count the number of ways summing 1’s and 2’s to n + 1 such that at least one of the summands is 2.

As before, there are F(n + 2) ways summing 1’s and 2’s to n + 1 when n ≥ 0. Since there is only one sum of n + 1 that does not use any 2, namely 1 + … + 1 (n + 1 terms), we subtract 1 from F(n + 2).

Equivalently, we can consider the first occurrence of 2 as a summand. If, in a sum, the first summand is 2, then there are F(n) ways to the complete the counting for n − 1. If the second summand is 2 but the first is 1, then there are F(n − 1) ways to complete the counting for n − 2. Proceed in this fashion. Eventually we consider the (n + 1)th summand. If it is 2 but all of the previous n summands are 1’s, then there are F(0) ways to complete the counting for 0. If a sum contains 2 as a summand, the first occurrence of such summand must take place in between the first and (n + 1)th position. Thus F(n) + F(n − 1) + … + F(0) gives the desired counting.

[edit] Proof of the third identity

This identity can be established in two stages. First, we count the number of ways summing 1s and 2s to −1, 0, …, or n + 1 such that at least one of the summands is 2.

By our second identity, there are F(n + 2) − 1 ways summing to n + 1; F(n + 1) − 1 ways summing to n; …; and, eventually, F(2) − 1 way summing to 1. As F(1) − 1 = F(0) = 0, we can add up all n + 1 sums and apply the second identity again to obtain

   [F(n + 2) − 1] + [F(n + 1) − 1] + … + [F(2) − 1]

= [F(n + 2) − 1] + [F(n + 1) − 1] + … + [F(2) − 1] + [F(1) − 1] + F(0)

= F(n + 2) + [F(n + 1) + … + F(1) + F(0)] − (n + 2)

= F(n + 2) + F(n + 3) − (n + 2).

On the other hand, we observe from the second identity that there are

• F(0) + F(1) + … + F(n − 1) + F(n) ways summing to n + 1;
• F(0) + F(1) + … + F(n − 1) ways summing to n;

……

• F(0) way summing to −1.

Adding up all n + 1 sums, we see that there are

• (n + 1) F(0) + n F(1) + … + F(n) ways summing to −1, 0, …, or n + 1.

Since the two methods of counting refer to the same number, we have

(n + 1) F(0) + n F(1) + … + F(n) = F(n + 2) + F(n + 3) − (n + 2)

Finally, we complete the proof by subtracting the above identity from n + 1 times the second identity.

[edit] Identity for doubling n

Another identity useful for calculating F_n for large values of n is

for all integers n and k. Dijkstra^[7] points out that doubling identities of this type can be used to calculate F_n using O(log n) arithmetic operations.

(From practical standpoint it should be noticed that the calculation involves manipulation of numbers which length (number of digits) is . Thus the actual performance depends mainly upon efficiency of the implemented long multiplication, and usually is or .)

[edit] Other identities

Other identities include relationships to the Lucas numbers, which have the same recursive properties but start with L₀=2 and L₁=1. These properties include F_2n=F_nL_n.

There are also scaling identities, which take you from F_n and F_n+1 to a variety of things of the form F_an+b; for instance

These can be found experimentally using lattice reduction, and are useful in setting up the special number field sieve, should you wish to factorize a Fibonacci number. Their existence is strongly dependent on the fact that ; Fibonacci-like numbers with a less symmetrical form to the solution of the recurrence relation do not have such identities associated with them.

[edit] Power series

The generating function of the Fibonacci sequence is the power series

This series has a simple and interesting closed-form solution for x < 1/

This solution can be proven by using the Fibonacci recurrence to expand each coefficient in the infinite sum defining s(x):

Solving the equation s(x) = x + xs(x) + x²s(x) for s(x) results in the closed form solution.

In particular, math puzzle-books note the curious value , or more generally

for all integers k > = 0.

Conversely,

[edit] Reciprocal sums

Infinite sums over reciprocal Fibonacci numbers can sometimes be evaluated in terms of theta functions. For example, we can write the sum of every odd-indexed reciprocal Fibonacci number as

and the sum of squared reciprocal Fibonacci numbers as

If we add 1 to each Fibonacci number in the first sum, there is also the closed form

and there is a nice nested sum of squared Fibonacci numbers giving the reciprocal of the golden ratio,

Results such as these make it plausible that a closed formula for the plain sum of reciprocal Fibonacci numbers could be found, but none is yet known. Despite that, the reciprocal Fibonacci constant

has been proved irrational by Richard André-Jeannin.

Right triangles

Starting with 5, every second Fibonacci number is the length of the hypotenuse of a right triangle with integer sides, or in other words, the largest number in a Pythagorean triple. The length of the longer leg of this triangle is equal to the sum of the three sides of the preceding triangle in this series of triangles, and the shorter leg is equal to the difference between the preceding bypassed Fibonacci number and the shorter leg of the preceding triangle.

The first triangle in this series has sides of length 5, 4, and 3. Skipping 8, the next triangle has sides of length 13, 12 (5 + 4 + 3), and 5 (8 − 3). Skipping 21, the next triangle has sides of length 34, 30 (13 + 12 + 5), and 16 (21 − 5). This series continues indefinitely.

[edit] Magnitude of Fibonacci numbers

The number of base b digits of asymptotes to .

[edit] Applications

The Fibonacci numbers are important in the run-time analysis of Euclid’s algorithm to determine the greatest common divisor of two integers: the worst case input for this algorithm is a pair of consecutive Fibonacci numbers.

Yuri Matiyasevich was able to show that the Fibonacci numbers can be defined by a Diophantine equation, which led to his original solution of Hilbert’s tenth problem.

The Fibonacci numbers occur in the sums of “shallow” diagonals in Pascal’s triangle and Lozanić’s triangle (see “Binomial coefficient“).

Every positive integer can be written in a unique way as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers. This is known as Zeckendorf’s theorem, and a sum of Fibonacci numbers that satisfies these conditions is called a Zeckendorf representation.

Fibonacci numbers are used by some pseudorandom number generators.

Fibonacci numbers arise in the analysis of the Fibonacci heap data structure.

A one-dimensional optimization method, called the Fibonacci search technique, uses Fibonacci numbers.^[9]

In music, Fibonacci numbers are sometimes used to determine tunings, and, as in visual art, to determine the length or size of content or formal elements. It is commonly thought that the first movement of Béla Bartók’s Music for Strings, Percussion, and Celesta was structured using Fibonacci numbers.

Since the conversion factor 1.609 for miles to kilometers is close to the golden ratio (denoted φ), the decomposition of distance in miles into a sum of Fibonacci numbers becomes nearly the kilometer sum when the Fibonacci numbers are replaced by their successors. This method amounts to a radix 2 number register in golden ratio base φ being shifted. To convert from kilometers to miles, shift the register down the Fibonacci sequence instead.^[10][11][12]

[edit] Fibonacci numbers in nature

Sunflower head displaying florets in spirals of 34 and 55 around the outside

Fibonacci sequences appear in biological settings,^[13] such as branching in trees, the fruitlets of a pineapple,^[14] an uncurling fern and the arrangement of a pine cone.^[15]. In addition, numerous poorly substantiated claims of Fibonacci numbers or golden sections in nature are found in popular sources, e.g. relating to the breeding of rabbits, the spirals of shells, and the curve of waves^{[citation needed]}.

Przemyslaw Prusinkiewicz advanced the idea that real instances can be in part understood as the expression of certain algebraic constraints on free groups, specifically as certain Lindenmayer grammars.^[16]

A model for the pattern of florets in the head of a sunflower was proposed by H. Vogel in 1979.^[17] This has the form

,

where n is the index number of the floret and c is a constant scaling factor; the florets thus lie on Fermat’s spiral. The divergence angle, approximately 137.51°, is the golden angle, dividing the circle in the golden ratio. Because this ratio is irrational, no floret has a neighbor at exactly the same angle from the center, so the florets pack efficiently. Because the rational approximations to the golden ratio are of the form F(j):F(j+1), the nearest neighbors of floret number n are those at n±F(j) for some index j which depends on r, the distance from the center. It is often said that sunflowers and similar arrangements have 55 spirals in one direction and 89 in the other (or some other pair of adjacent Fibonacci numbers), but this is true only of one range of radii, typically the outermost and thus most conspicuous.

50 years ago, Sputnik changed the world

 

By RICK MONTGOMERY

The Kansas City Star

It happened the night “Leave It to Beaver” first aired across America, 50 years ago this coming Thursday.

Hundreds of miles above the TV antennas, Sputnik made its first beeps.

Just after the sun set on a nation meeting the Cleavers — that impeccable 1950s family played to fantasy proportions — many real-life families stepped outside and gazed up at a dark, disturbing reality: What newspapers called a “baby moon” roamed the skies, and it belonged to the Russians.

The gadget itself, just 184 pounds, did little but beep to ham-radio operators worldwide that the Soviets had launched the first artificial satellite. Its battery soon died. In three months, Sputnik fell into the atmosphere to burn up.

Yet the space around Earth would never be the same, and, in countless ways, neither would life on the ground.

“I remember just as well as it was yesterday,” said Blue Valley West High School biology teacher Ken Bingman, who was 18 then and living in Kansas City, Kan. “You could only see it at dusk or dawn, when the sun reflected off of it.

“As I stood outside my apartment, there came this bright, aluminum-looking ball, traveling across the sky with such … regularity.” No sound, no blinking lights, just a streak.

“It sent chills through me. One has to remember that the Cold War was really raging then. A sign posted on Southwest Trafficway said that in case of enemy attack, this was a one-way street heading south.”

The legacy of Sputnik has at least two distinct sides to it, depending on your age.

Older people recall the edgy, “space race” part of the story — a geopolitical and scientific struggle culminating in Neil Armstrong, an American, stepping onto the moon in 1969.

But for younger populations — including the U.S. majority not yet born when the race began — Sputnik’s legacy lives on in the global reach of their wireless laptops, made possible by the thousands of satellites that followed the first one into orbit.

“That’s something a lot of people take for granted today,” said Ed Thompson, an engineer familiar with satellite technology at Overland Park-based Sprint Nextel Corp.

“Nowadays you have satellites flying overhead all the time, and people don’t even give it a thought. … If you could see all of (the transmissions), it would be overwhelming.”

• • •

In Frontenac, Kan., the feelings that stirred in Jim Spigarelli and his teenage peers that week in 1957 were unmistakable:

“Disbelief that the Russians could put anything up in space before we did.”

Added Spigarelli, who today presides over the Midwest Research Institute in Kansas City: “Hands down, the U.S. and its schools were always thought to be No. 1. So at first, the reaction was shock.

“The other thing I thought? This was cool.”

It was the cool factor, spreading through his small-town high school and classrooms across the nation, that nudged students such as Spigarelli to the science tables — once the domain of the quiet, not-so-popular kids.

He was the varsity quarterback, after all, “and being very competitive, I felt we can’t settle for second place. It was the competitive factor of the space race that pushed me” to pursue science rather than law or teaching. He majored in analytical chemistry in college.

In Sputnik’s wake, Congress passed the National Defense Education Act of 1958, boosting funds for science education and providing scholarships for aspiring chemists, engineers and mathematicians.

Fears that the Soviets could arm their satellites with nuclear weapons slowly gave way to a new understanding that the Cold War would be fought with slide rules (what we used before calculators, kids).

Initially, President Dwight D. Eisenhower dismissed the significance of the Soviet satellite. Sputnik’s clunky appearance — a kind of metallic exercise ball with four javelins sticking out — lacked the scope and grandeur of the futuristic space vehicles and moon stations illustrated earlier that decade in Collier’s magazine.

“That Collier’s vision — big equipment, with lots of people — had fueled most people’s expectations of what space travel would be. But Sputnik changed it,” said Roger Launius, senior curator at the Smithsonian Air and Space Museum’s division of space history.

The first men in space (and, for Russia in 1963, the first woman in space) were thus wedged into tin cans atop rocket boosters.

For U.S. scientists, an ugly and tiny vehicle was the only way to go if they were to come close to meeting President John Kennedy’s pledge of “landing a man on the moon and returning him safely to the earth” by the end of the 1960s.

By far, the biggest challenge in Kennedy’s call was the humans-getting-there part. Soviet unmanned missions were getting there even before Kennedy was elected.

In fact, a Russian spacecraft launched in 1959 had already struck the moon. A month later, another mission provided the Soviets the first pictures of the moon’s back side.

“It’s all about framing the debate. Kennedy framed it in terms of putting a man on the moon,” said Launius. “You could send robots up there, but as someone once said, ‘Nobody does ticker-tape parades for robots.’ ”

• • •

Besides housing the largest collection of Soviet space-travel artifacts outside Moscow, the Kansas Cosmosphere and Space Center in Hutchinson offers a nostalgic ride back in time for visitors: “Jetsons” lunch boxes, early astronaut suits, even replicas of the Apollo capsules and landers — all the offspring of Sputnik.

“The schoolchildren will look at spacecraft from back then and say, ‘That just looks like foil wrapped on the outside.’ Well, that’s pretty much what it is,” said Cosmosphere spokeswoman Jill Ulrich.

“They understand the looks of the space shuttle. This cone-looking stuff is very foreign to them.”

Even at the Olathe headquarters of Garmin International Inc. — makers of Global Positioning System devices that owe their existence to satellite technology — the name “Sputnik” means different things to different people.

“Not a heck a lot of old guys here, so to speak,” said company spokesman Ted Gartner.

“The glory days of manned space flight could be behind us. Whether it has a future, I don’t know. But as for the present, (Sputnik’s legacy) is the satellite technology that we use every day.”

We use it to track hurricanes. We use GPS devices in our cars to find the nearest store. Satellites let us watch live coverage of royal weddings and funerals, even follow the movements of endangered species.

Using mobile towers, Sprint this year signaled satellites to provide cell phone service to emergency workers after a tornado in Greensburg, Kan., ripped that area’s communications infrastructure to pieces.

All told, the U.S. Air Force counts some 6,000 satellites launched into space, at the behest of more than four dozen countries, since Sputnik. About 3,200 of those satellites continue to orbit — including two that deliver XM Satellite Radio.

Their names?

“Rock” and “Roll.”

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By the numbers
5,958 Total man-made satellites — from puppy-toting capsules to the things that beam driving directions to your dashboard — that orbited the planet9,341 Pieces of space junk loitering above the atmosphere

1 in 3 Chances that a satellite or scrap of space junk is American-made

352 Lead in orbiting satellites the former Soviet Union has over the United States

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Spawn of Sputnik
3,204Number of satellites circling Earth today

2,754

Number of objects launched into the sky that have fallen back to Earth — including Skylab, the space shuttles and thousands of satellites you never knew were aloft

Analysis and Identification of Computer Viruses

Analysis and Identification of Computer Viruses

In the past decade, computer and networking technology has seen enormous growth. This growth however, has not come without a price. With the advent of the “Information Highway”, as it’s coined, a new methodology in crime has been created. Electronic crime has been responsible for some of the most financially devastating victimizations in society.

In the recent past, society has seen malicious editing of the Justice Department web page (1), unauthorized access into classified government computer files, phone card and credit card fraud, and electronic embezzlement. All these crimes are committed in the name of “free speech.” These new breed of criminals claim that information should not be suppressed or protected and that the crimes they commit are really not crimes at all. What they choose to deny is that the nature of their actions are slowly consuming the fabric of our country’s moral and ethical trust in the information age.

Federal law enforcement agencies, as well as commercial computer companies, have been scrambling around in an attempt to “educate” the public on how to prevent computer crime from happening to them. They inform us whenever there is an attack, provide us with mostly ineffective anti-virus software, and we are left feeling isolated and vulnerable. I do not feel that this defensive posture is effective because it is not pro-active. Society is still being attacked by highly skilled computer criminals of which we know very little about them, their motives, and their tools of the trade. Therefore, to be effective in defense, we must understand how these attacks take place from a technical stand-point. To some degree, we must learn to become a computer criminal. Then we will be in a better position to defend against these victimizations that affect us on both the financial and emotional level. In this paper, we will explore these areas of which we know so little, and will also see that computers are really extensions of people. An attack on a computer’s vulnerabilities are really an attack on peoples’ vulnerabilities.

Today, computer systems are under attack from a multitude of sources. These range from malicious code, such as viruses and worms, to human threats, such as hackers and phone “phreaks.” These attacks target different characteristics of a system. This leads to the possibility that a particular system is more susceptible to certain kinds of attacks.

Malicious code, such as viruses and worms, attack a system in one of two ways, either internally or externally. Traditionally, the virus has been an internal threat (an attack from within the company), while the worm, to a large extent, has been a threat from an external source (a person attacking from the outside via modem or connecting network).

Human threats are perpetrated by individuals or groups of individuals that attempt to penetrate systems through computer networks, public switched telephone networks or other sources. These attacks generally target known security vulnerabilities of systems. Many of these vulnerabilities are simply due to configuration errors.

Malicious Code

Viruses and worms are related classes of malicious code; as a result they are often confused. Both share the primary objective of replication. However, they are distinctly different with respect to the techniques they use and their host system requirements. This distinction is due to the disjoint sets of host systems they attack. Viruses have been almost exclusively restricted to personal computers, while worms have attacked only multi-user systems.

A careful examination of the histories of viruses and worms can highlight the differences and similarities between these classes of malicious code. The characteristics shown by these histories can be used to explain the differences between the environments in which they are found. Viruses and worms have very different functional requirements; currently no class of systems simultaneously meets the needs of both.

A review of the development of personal computers and multi-tasking workstations will show that the gap in functionality between these classes of systems is narrowing rapidly. In the future, a single system may meet all of the requirements necessary to support both worms and viruses. This implies that worms and viruses may begin to appear in new classes of systems. A knowledge of the histories of viruses and worms may make it possible to predict how malicious code will cause problems in the future.

Basic Definitions

To provide a basis for further discussion, the following definitions will be used throughout the report;

• Trojan Horse – a program which performs a useful function, but also performs an unexpected action as well;

• Virus – a code segment which replicates by attaching copies to existing executables;

• Worm – a program which replicates itself and causes execution of the new copy and

• Network Worm – a worm which copies itself to another system by using common network facilities, and causes execution of the copy on that system.

In essence, a computer program which has been infected by a virus has been converted into a “trojan horse”. The program is expected to perform a useful function, but has the unintended side effect of viral code execution. In addition to performing the unintended task, the virus also performs the function of replication. Upon execution, the virus attempts to replicate and “attach” itself to another program. It is the unexpected and uncontrollable replication that makes viruses so dangerous. As a result, the host or victim computer falls prey to an unlimited amount of damage by the virus, before anyone realizes what has happened.

Viruses are currently designed to attack single platforms. A platform is defined as the combination of hardware and the most prevalent operating system for that hardware. As an example, a virus can be referred to as an IBM-PC virus, referring to the hardware, or a DOS virus, referring to the operating system. “Clones” of systems are also included with the original platform.

History of Viruses

The term “computer virus” was formally defined by Fred Cohen in 1983, while he performed academic experiments on a Digital Equipment Corporation VAX system. Viruses are classified as being one of two types: research or “in the wild.” A research virus is one that has been written for research or study purposes and has received almost no distribution to the public. On the other hand, viruses which have been seen with any regularity are termed “in the wild.” The first computer viruses were developed in the early 1980s. The first viruses found in the wild were Apple II viruses, such as Elk Cloner, which was reported in 1981 [Den90]. Viruses were found on the following platforms:

• Apple II

• IBM PC

• Macintosh

• Atari

• Amiga

These computers made up a large percentage of the computers sold to the public at that time. As a result, many people fell prey to the Elk Cloner and virus’s similar in nature. People suffered losses in data from personal documents to financial business data with little or no protection or recourse.

Viruses have “evolved” over the years due to efforts by their authors to make the code more difficult to detect, disassemble, and eradicate. This evolution has been especially apparent in the IBM PC viruses; since there are more distinct viruses known for the DOS operating system than any other.

The first IBM-PC virus appeared in 1986 [Den90]; this was the Brain virus. Brain was a boot sector virus and remained resident in the computer until “cleaned out”. In 1987, Brain was followed by Alameda (Yale), Cascade, Jerusalem, Lehigh, and Miami (South African Friday the 13th). These viruses expanded the target executables to include COM and EXE files. Cascade was encrypted to deter disassembly and detection. Variable encryption appeared in 1989 with the 1260 virus. Stealth viruses, which employ various techniques to avoid detection, also first appeared in 1989, such as Zero Bug, Dark Avenger and Frodo (4096 or 4K). In 1990, self-modifying viruses, such as Whale were introduced. The year 1991 brought the GP1 virus, which is “network-sensitive” and attempts to steal Novell NetWare passwords. Since their inception, viruses have become increasingly complex and equally destructive.

Is there really a hole in the universe?

In August 2007, scientists from the University of Minnesota published an astonishing finding in the Astrophysical Journal. The universe, they declared, had a hole in it — a hole far bigger than anything scientists have ever seen or expected. This “hole” spans almost one billion light years and is six to 10 billion light years from Earth, in the Eridanus constellation . (For reference, one light year measures about six trillion miles.)

Outer Space Image Gallery

Bill Saxton, NRAO/AUI/NSF, NASA This picture depicts the spread of cosmic microwave background radiation, beginning with the universe just after the big bang (left), spreading through the universe’s many galaxies, clusters and voids (center), and ending with a recent CMB map. In the giant void, the WMAP satellite (top left) detects a cold spot while the VLA radio telescope (bottom left) sees fewer galaxies.

What makes this vast area of the universe a hole? The area shows almost no signs of cosmic matter, meaning no stars, planets, solar systems or clouds of cosmic dust. Researchers couldn’t even find dark matter, which is invisible but measurable by its gravitational pull. There were also no signs of black holes that might have gobbled up the matter once present in the region.

The hole was initially detected by a NASA program studying the spread of radiation emitted from the Big Bang, which scientists believe spawned our universe. It was then further examined using information gleaned from the Very Large Array (VLA) telescope, used in the NRAO VLA Sky Survey Project to study large sections of the visible sky.

One researcher described the find as “not normal,” going against computer simulations and past studies . Other such holes, also known as voids, have been found before, but this find is by far the largest. Other voids amount to around 1/1000th the size of this one, while scientists once observed a void as close as two million light years away — practically down the street in cosmic terms .

Astronomer Brent Tully told the Associated Press that galactic voids in all likelihood develop because regions of space with high mass pull matter from less massive areas . Over billions of years, a region can lose most of its mass to a massive neighbor. In the case of this giant void, further studies may reveal some matter in the region, but it would still be far less than what is found in “normal” parts of space.

Earlier we said that the void was first discovered through a NASA program examining radiation stemming from the Big Bang. On the next page, we’ll take a closer look at that program and how scientists can look far back into the universe’s history — almost to its beginnings — in order to make discoveries like this one.

Mind-Control Microbe

A parasitic infection can give you schizophrenia, make you have a car crash, or determine the sex of your child.

by Kathy A. Svitil

Five years ago, Oxford University zoologists showed that the parasite Toxoplasma gondii alters the brain chemistry of rats so that they are more likely to seek out cats. Infection thus makes a rat more likely to be killed and the parasite more likely to end up in a cat—the only host in which it can complete the reproductive step of its life cycle. The parasite also lives in the brain cells of thousands of species, including about 60 million supposedly symptom-free Americans. Studies over the past few years have suggested that toxoplasmosis infections in humans, too, may cause behavioral changes—from subtle shifts to outright schizophrenia. Two studies this year add even weirder twists.

Toxoplasma gondii, revealed here in a colorized electron micrograph, may exert a spooky influence on the people it infects.

U.S. Geological Survey biologist Kevin Lafferty has linked high rates of toxoplasmosis infection in 39 countries with elevated incidences of neuroticism, suggesting the mind-altering organism may be affecting the cultures of nations.

Stranger still, parasitologist Jaroslav Flegr of Charles University in Prague thinks T. gondii could also be skewing our sex ratios. When he looked at the clinical records of more than 1,800 babies born from 1996 to 2004, he noted a distinct trend: The normal sex ratio is 104 boys born for every 100 girls, but in women with high levels of antibodies against the parasite, the ratio was 260 boys for every 100 girls. Exactly how the parasite might be tipping the odds in favor of males isn’t understood, but Flegr points out that it is known to suppress the immune system of its hosts, and because the maternal immune system sometimes attacks male fetuses in very early pregnancy, the parasite’s ability to inhibit the immune response might protect future boys as well as itself.

“Our present study was rejected by eight journals, usually without any formal review,” says Flegr, who had the same problem publishing an earlier one showing that infection more than doubles the odds of a person having a traffic accident. “People don’t like the possibility that their behavior and life are manipulated by a parasite,” he says.

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If altering our culture and causing car crashes weren’t bad enough, toxoplasma may actually wheedle their genes into our genomes.

There are plenty of other theories about what affects the reproductive sex ratio. Some of them are actually true.

10 unresolved mysteries of the brain

What we know—and don’t know—about how we think.

by David Eagleman
Of all the objects in the universe, the human brain is the most complex: There are as many neurons in the brain as there are stars in the Milky Way galaxy. So it is no surprise that, ­despite the glow from recent advances in the science of the brain and mind, we still find ourselves squinting in the dark somewhat. But we are at least beginning to grasp the crucial mysteries of neuroscience and starting to make headway in addressing them. Even partial answers to these 10 questions could restructure our understanding of the roughly three-pound mass of gray and white matter that defines who we are.

Pyramidal neuron in medial prefrontal cortex of macaque.

Image courtesy of brainmaps.org

1. How is information coded in neural activity?

Neurons, the specialized cells of the brain, can produce brief spikes of voltage in their outer membranes. These electrical pulses travel along specialized extensions called axons to cause the release of chemical signals elsewhere in the brain. The binary, all-or-nothing spikes appear to carry information about the world: What do I see? Am I hungry? Which way should I turn? But what is the code of these millisecond bits of voltage? Spikes may mean different things at different places and times in the brain. In parts of the central nervous system (the brain and spinal cord), the rate of spiking often correlates with clearly definable external features, like the presence of a color or a face. In the peripheral nervous system, more spikes indicates more heat, a louder sound, or a stronger muscle contraction.

As we delve deeper into the brain, however, we find populations of neurons involved in more complex phenomena, like reminiscence, value judgments, simulation of possible futures, the desire for a mate, and so on—and here the signals become difficult to decrypt. The challenge is something like popping the cover off a computer, measuring a few transistors chattering between high and low voltage, and trying to guess the content of the Web page being surfed.

It is likely that mental information is stored not in single cells but in populations of cells and patterns of their activity. However, it is currently not clear how to know which neurons belong to a particular group; worse still, current technologies (like sticking fine electrodes directly into the brain) are not well suited to measuring several thousand neurons at once. Nor is it simple to monitor the connections of even one neuron: A typical neuron in the cortex receives input from some 10,000 other neurons.

Although traveling bursts of voltage can carry signals across the brain quickly, those electrical spikes may not be the only—or even the main—way that information is carried in nervous systems. ­Forward-looking studies are examining other possible information couriers: glial cells (poorly understood brain cells that are 10 times as common as neurons), other kinds of signaling mechanisms between cells (such as newly discovered gases and peptides), and the biochemical cascades that take place inside cells.

2. How are memories stored and retrieved?

When you learn a new fact, like someone’s name, there are physical changes in the structure of your brain. But we don’t yet comprehend exactly what those changes are, how they are orchestrated across vast seas of synapses and neurons, how they embody knowledge, or how they are read out decades later for retrieval.

One complication is that there are many kinds of memories. The brain seems to distinguish short-term memory (remembering a phone number just long enough to dial it) from long-term memory (what you did on your last birthday). Within long-term memory, declarative memories (like names and facts) are distinct from non­declarative memories (riding a bicycle, being affected by a subliminal message), and within these general categories are numerous subtypes. Different brain structures seem to support different kinds of learning and memory; brain damage can lead to the loss of one type without disturbing the others.

Nonetheless, similar molecular mechanisms may be at work in these memory types. Almost all theories of memory propose that memory storage depends on synapses, the tiny connections between brain cells. When two cells are active at the same time, the connection between them strengthens; when they are not active at the same time, the connection weakens. Out of such synaptic changes emerges an association. Experience can, for example, fortify the connections between the smell of coffee, its taste, its color, and the feel of its warmth. Since the populations of neurons connected with each of these sensations are typically activated at the same time, the connections between them can cause all the sensory associations of coffee to be triggered by the smell alone.

But looking only at associations—and strengthened connections between neurons—may not be enough to explain memory. The great secret of memory is that it mostly encodes the relationships between things more than the details of the things themselves. When you memorize a melody, you encode the relationships between the notes, not the notes per se, which is why you can easily sing the song in a different key.

Memory retrieval is even more mysterious than storage. When I ask if you know Alex Ritchie, the answer is immediately obvious to you, and there is no good theory to explain how memory retrieval can happen so quickly. Moreover, the act of retrieval can destabilize the memory. When you recall a past event, the memory becomes temporarily susceptible to erasure. Some intriguing recent experiments show it is possible to chemically block memories from reforming during that window, suggesting new ethical questions that require careful consideration.

3. What does the baseline activity in the brain represent?

Neuroscientists have mostly studied changes in brain activity that correlate with stimuli we can present in the laboratory, such as a picture, a touch, or a sound. But the activity of the brain at rest—its “baseline” activity—may prove to be the most important aspect of our mental lives. The awake, resting brain uses 20 percent of the body’s total oxygen, even though it makes up only 2 percent of the body’s mass. Some of the baseline activity may represent the brain restructuring knowledge in the background, simulating future states and events, or manipulating memories. Most things we care about—reminiscences, emotions, drives, plans, and so on—can occur with no external stimulus and no overt output that can be measured.

One clue about baseline activity comes from neuroimaging experiments, which show that activity decreases in some brain areas just before a person performs a goal-directed task. The areas that decrease are the same regardless of the details of the task, hinting that these areas may run baseline programs during downtime, much as your computer might run a disk-defragmenting program only while the resources are not needed elsewhere.

In the traditional view of perception, information from the outside world pours into the senses, works its way through the brain, and makes itself consciously seen, heard, and felt. But many scientists are coming to think that sensory input may merely revise ongoing internal activity in the brain. Note, for example, that sensory input is superfluous for perception: When your eyes are closed during dreaming, you still enjoy rich visual experience. The awake state may be essentially the same as the dreaming state, only partially anchored by external stimuli. In this view, your conscious life is an awake dream.

The awake state may be essentially the same as the dreaming state. In this view, your conscious life is an awake dream.

4. How do brains simulate the future?

When a fire chief encounters a new blaze, he quickly makes predictions about how to best position his men. Running such simulations of the future—without the risk and expense of actually attempting them—allows “our hypotheses to die in our stead,” as philosopher Karl Popper put it. For this reason, the emulation of possible futures is one of the key businesses that intelligent brains invest in.

Yet we know little about how the brain’s future simulator works because traditional neuroscience technologies are best suited for correlating brain activity with explicit behaviors, not mental emulations. One idea suggests that the brain’s resources are devoted not only to processing stimuli and reacting to them (watching a ball come at you) but also to constructing an internal model of that outside world and extracting rules for how things tend to behave (knowing how balls move through the air). Internal models may play a role not only in motor acts, like catching, but also in perception. For example, vision draws on significant amounts of information in the brain, not just on input from the retina. Many neuroscientists have suggested over the past few decades that perception arises not simply by building up bits of data through a hierarchy but rather by matching incoming sensory data against internally generated expectations.

But how does a system learn to make good predictions about the world? It may be that memory exists only for this purpose. This is not a new idea: Two millennia ago, Aristotle and Galen emphasized memory as a tool in making successful predictions for the future. Even your memories about your life may come to be understood as a special subtype of emulation, one that is pinned down and thus likely to flow in a certain direction.

5. What are emotions?

We often talk about brains as information-processing systems, but any account of the brain that lacks an account of emotions, motivations, fears, and hopes is incomplete. Emotions are measurable physical responses to salient stimuli: the increased heartbeat and perspiration that accompany fear, the freezing response of a rat in the presence of a cat, or the extra muscle tension that accompanies anger. Feelings, on the other hand, are the subjective experiences that sometimes accompany these processes: the sensations of happiness, envy, sadness, and so on. Emotions seem to employ largely unconscious machinery—for example, brain areas involved in emotion will respond to angry faces that are briefly presented and then rapidly masked, even when subjects are unaware of having seen the face. Across cultures the expression of basic emotions is remarkably similar, and as Darwin observed, it is also similar across all mammals. There are even strong similarities in physiological responses among humans, reptiles, and birds when showing fear, anger, or parental love.

Modern views propose that emotions are brain states that quickly assign value to outcomes and provide a simple plan of action. Thus, emotion can be viewed as a type of computation, a rapid, automatic summary that initiates appropriate actions. When a bear is galloping toward you, the rising fear directs your brain to do the right things (determining an escape route) instead of all the other things it could be doing (rounding out your grocery list). When it comes to perception, you can spot an object more quickly if it is, say, a spider rather than a roll of tape. In the realm of memory, emotional events are laid down differently by a parallel memory system involving a brain area called the amygdala.

One goal of emotional neuroscience is to understand the nature of the many disorders of emotion, depression being the most common and costly. Impulsive aggression and violence are also thought to be consequences of faulty emotion regulation.

6. What is intelligence?

Intelligence comes in many forms, but it is not known what intelligence—in any of its guises—means biologically. How do billions of neurons work together to manipulate knowledge, simulate novel situations, and erase inconsequential information? What happens when two concepts “fit” together and you suddenly see a solution to a problem? What happens in your brain when it suddenly dawns on you that the killer in the movie is actually the unsuspected wife? Do intelligent people store knowledge in a way that is more distilled, more varied, or more easily retrievable?

We all grew up with the near-future promise of smart robots, but today we have little better than the Roomba robotic vacuum cleaner. What went wrong? There are two camps for explaining the weak performance of artificial intelligence: Either we do not know enough of the fundamental principles of brain function, or we have not simulated enough neurons working together. If the latter is true, that’s good news: Computation gets cheaper and faster each year, so we should not be far from enjoying life with Asimovian robots who can effectively tend our households. Yet most neuroscientists recognize how distant we are from that dream. Currently, our robots are little more intelligent than sea slugs, and even after decades of clever research, they can barely distinguish figures from a background at the skill level of an infant.

Recent experiments explore the possible relationship of intelligence to the capacity of short-term memory, the ability to quickly resolve cognitive conflict, or the ability to store stronger associations between facts; the results are not yet conclusive. Many other possibilities—better restructuring of stored information, more parallel processing, or superior emulation of possible futures—have not yet been probed by experiments.

Intelligence may not be underpinned by a single mechanism or a single neural area. Whatever intelligence is, it lies at the heart of what is special about Homo sapiens. Other species are hardwired to solve particular problems, while our ability to abstract allows us to solve an open-ended series of problems. This means that studies of intelligence in mice and monkeys may be barking up the wrong family tree.

7. How is time represented in the brain?

Hundred-yard dashes begin with a gunshot rather than a strobe light because your brain can react more quickly to a bang than to a flash. Yet as soon as we get outside the realm of motor reactions and into the realm of perception (what you report that you saw and heard), the story changes. When it comes to awareness, the brain goes through a good deal of trouble to synchronize incoming signals that are processed at very different speeds.

For example, snap your fingers in front of you. Although your auditory system processes information about the snap about 30 milliseconds faster than your visual system, the sight of your fingers and the sound of the snap seem simultaneous. Your brain is employing fancy editing tricks to make simultaneous events in the world feel simultaneous to you, even when the different senses processing the information would individually swear otherwise.

For a simple example of how your brain plays tricks with time, look in the mirror at your left eye. Now shift your gaze to your right eye. Your eye movements take time, of course, but you do not see your eyes move. It is as if the world instantly made the transition from one view to the next. What happened to that little gap in time? For that matter, what happens to the 80 milliseconds of darkness you should see every time you blink your eyes? Bottom line: Your notion of the smooth passage of time is a construction of the brain. Clarifying the picture of how the brain normally solves timing problems should give insight into what happens when temporal calibration goes wrong, as may happen in the brains of people with dyslexia. Sensory inputs that are out of sync also contribute to the risk of falls in elderly patients.

We grew up with the near-future promise of smart robots, but today we have little better than the Roomba robotic vacuum cleaner. What went wrong?

8. Why do brains sleep and dream?

One of the most astonishing aspects of our lives is that we spend a third of our time in the strange world of sleep. Newborn babies spend about twice that. It is inordinately difficult to remain awake for more than a full day-night cycle. In humans, continuous wakefulness of the nervous system results in mental derangement; rats deprived of sleep for 10 days die. All mammals sleep, reptiles and birds sleep, and voluntary breathers like dolphins sleep with one brain hemisphere dormant at a time. The evolutionary trend is clear, but the function of sleep is not.

The universality of sleep, even though it comes at the cost of time and leaves the sleeper relatively defenseless, suggests a deep importance. There is no universally agreed-upon answer, but there are at least three popular (and nonexclusive) guesses. The first is that sleep is restorative, saving and replenishing the body’s energy stores. However, the high neural activity during sleep suggests there is more to the story. A second theory proposes that sleep allows the brain to run simulations of fighting, problem solving, and other key actions before testing them out in the real world. A third theory—the one that enjoys the most evidence—is that sleep plays a critical role in learning and consolidating memories and in forgetting inconsequential details. In other words, sleep allows the brain to store away the important stuff and take out the neural trash.

Recently, the spotlight has focused on REM sleep as the most important phase for locking memories into long-term encoding. In one study, rats were trained to scurry around a track for a food reward. The researchers recorded activity in the neurons known as place cells, which showed distinct patterns of activity depending upon the rats’ location on the track. Later, while the rats dropped off into REM sleep, the recordings continued. During this sleep, the rats’ place cells often repeated the exact same pattern of activity that was seen when the animals ran. The correlation was so close, the researchers claimed, that as the animal “dreamed,” they could reconstruct where it would be on the track if it had been awake—and whether the animal was dreaming of running or standing still. The emerging idea is that information replayed during sleep might determine which events we remember later. Sleep, in this view, is akin to an off-line practice session. In several recent experiments, human subjects performing difficult tasks improved their scores between sessions on consecutive days, but not between sessions on the same day, implicating sleep in the learning process.

Understanding how sleeping and dreaming are changed by ­trauma, drugs, and disease—and how we might modulate our need for sleep—is a rich field to harvest for future clues.

9. How do the specialized systems of the brain integrate with one another?

To the naked eye, no part of the brain’s surface looks terribly different from any other part. But when we measure activity, we find that different types of information lurk in each region of the neural territory. Within vision, for example, separate areas process motion, edges, faces, and colors. The territory of the adult brain is as fractured as a map of the countries of the world.

Now that neuroscientists have a reasonable idea of how that territory is divided, we find ourselves looking at a strange assortment of brain networks involved with smell, hunger, pain, goal setting, temperature, prediction, and hundreds of other tasks. Despite their disparate functions, these systems seem to work together seamlessly. There are almost no good ideas about how this occurs.

Nor is it understood how the brain coordinates its systems so rapidly. The slow speed of spikes (they travel about one foot per second in axons that lack the insulating sheathing called myelin) is one hundred-millionth the speed of signal transmission in digital computers. Yet a human can recognize a friend almost instantaneously, while digital computers are slow—and usually unsuccessful—at face recognition. How can an organ with such slow parts operate so quickly? The usual answer is that the brain is a parallel processor, running many operations at the same time. This is almost certainly true, but what slows down parallel-processing digital computers is the next stage of operations, where results need to be compared and decided upon. Brains are amazingly fast at this. So while the brain’s ability to do parallel processing is impressive, its ability to rapidly synthesize those parallel processes into a single, behavior-guiding output is at least as significant. An animal running must go left or right around a tree; it cannot do both.

There is no special anatomical location in the brain where information from all the different systems converges; rather, the specialized areas all interconnect with one another, forming a network of parallel and recurring links. Somehow, our integrated image of the world emerges from this complex labyrinthine network of brain structures. Surprisingly little study has been done on large, loopy networks like the ones in the brain—probably in part because it is easier to think about brains as tidy assembly lines than as dynamic networks.

10. What is consciousness?

Think back to your first kiss. The experience of it may pop into your head instantly. Where was that memory before you became conscious of it? How was it stored in your brain before and after it came into consciousness? What is the difference between those states

An explanation of consciousness is one of the major unsolved problems of modern science. It may not turn out to be a single phenomenon; nonetheless, by way of a preliminary target, let’s think of it as the thing that flickers on when you wake up in the morning that was not there, in the exact same brain hardware, moments before.

Neuroscientists believe that consciousness emerges from the material stuff of the brain primarily because even very small changes to your brain (say, by drugs or disease) can powerfully alter your subjective experiences. The heart of the problem is that we do not yet know how to engineer pieces and parts such that the resulting machine has the kind of private subjective experience that you and I take for granted. If I give you all the Tinkertoys in the world and tell you to hook them up so that they form a conscious machine, good luck. We don’t have a theory yet of how to do this; we don’t even know what the theory will look like.

One of the traditional challenges to consciousness research is studying it experimentally. It is probable that at any moment some active neuronal processes correlate with consciousness, while others do not. The first challenge is to determine the difference between them. Some clever experiments are making at least a little headway. In one of these, subjects see an image of a house in one eye and, simultaneously, an image of a cow in the other. Instead of perceiving a house-cow mixture, people perceive only one of them. Then, after some random amount of time, they will believe they’re seeing the other, and they will continue to switch slowly back and forth. Yet nothing about the visual stimulus changes; only the conscious experience changes. This test allows investigators to probe which properties of neuronal activity correlate with the changes in subjective experience.

The mechanisms underlying consciousness could reside at any of a variety of physical levels: molecular, cellular, circuit, pathway, or some organizational level not yet described. The mechanisms might also be a product of interactions between these levels. One compelling but still speculative notion is that the massive feedback circuitry of the brain is essential to the production of consciousness.

In the near term, scientists are working to identify the areas of the brain that correlate with consciousness. Then comes the next step: understanding why they correlate. This is the so-called hard problem of neuroscience, and it lies at the outer limit of what material explanations will say about the experience of being human.

Danger from the Belly Button

The navel gives a fetus life, but can bring a newborn death.

by Mark Cohen
The evening pediatric clinic was winding down, and the note on the next chart said, “One week old, belly button problem.” Good, I thought, this case should be straightforward. New parents are usually concerned about one of three things when it comes to their newborn’s belly button: the normal whitish inflammatory material at the base of the cord, which makes it look as if there is an infection; slight bleeding that can happen when the cord falls off; or an unhealed stump of umbilical cord called a granuloma, which must sometimes be treated with a topical chemical that cauterizes the tissue.

I introduced myself to the parents, who looked worried and more than a little tired. With a newborn at home, that was not surprising. The baby, dressed in a pink sleeper, was asleep, but she quickly woke up when her mother began to undo the snaps.

“It looks like her belly button is infected,” the mother said. OK, I thought, anticipating a quick, reassuring talk. But when she lifted up the infant’s undergarment, I stopped short. The baby’s cord had already fallen off, so the parents weren’t worried about the normal discharge around the cord stump. Something else was wrong.

I recalled a baby I’d seen during a stint in the neonatal intensive care unit during my pediatric residency. What had appeared to be a small infection of the umbilicus proved to be a serious infection known as omphalitis. That baby had died.

To small children, the belly button, also known as the navel or umbilicus, is one of the great mysteries of life. My parents told me it was “the knot that the doctor tied in the cord when you were born.” Some cultures endow it with a mystical significance. In Greece, for example, the word for navel, omphalos, is also used to refer to the center of the world. Hawaiians use the word piko for both the umbilical cord and the navel; it is said to be the gate connecting a baby to its ancestors.

That link is literally true—for one generation, at least. The umbilical cord connects the fetus to the placenta, the structure that attaches to the mother’s uterus and funnels nutrients to the fetus. After the baby is born, doctors clamp the cord and cut it, leaving a remnant two to three inches long. The mother delivers the placenta, with the rest of the cord attached, afterward. That is why the placenta is also called the afterbirth.

Over the next few days, the baby’s cord dries out. Protective white blood cells congregate around the base, forming the puslike material that sometimes alarms parents. Enzymes produced by the white cells gradually dissolve the connection at the base of the cord, until one day it just falls off. After a day or so, the small, flat stump that remains is covered by fibrous scar ­tissue. Eventually, skin grows over the area, and it then becomes the belly button we all know. (Most people have an inward, contracted belly button. Those that poke outward are usually related to small defects in the abdominal wall.)

But when I looked at this baby’s ­umbilicus, I saw a small amount of pus around the area where the cord had detached. I swabbed the area with alcohol—and saw something I didn’t expect. In the center of the cord’s pink stump was a small dark opening, about one millimeter across, like a tiny tunnel diving into the middle of the baby’s umbilicus. That was odd. Then I saw something even more disturbing: A drop of thin yellowish-white pus exuded from that little tunnel. This was a sign of a potentially deadly problem.

here is a little-known structure in the developing fetus called the urachus, which is a tube leading from the bladder to the umbilicus. The urachus is derived from a tubelike embryonic structure known as the allantois (Greek for “sausage”), which ­eventually forms the urethra, the urinary bladder, and part of the umbilical cord ­itself. By the time most babies are born, the urachus has collapsed down to a solid cord that connects the bladder with the back of the belly button and is useful only as a landmark for surgeons.

The telltale sign is swelling and redness of the skin around the cord, which often leaks pus. Suddenly, the baby begins to look sick. Those infants, like my patient years ago, can die.

In rare cases, however, part or all of the urachus remains open after a baby is born. When the entire tube is open, the baby will leak small amounts of urine from his belly button. Partial closure can lead to a urachal sinus, a small pocket that remains at the upper end of the urachus and still maintains its connection to the cord. Sometimes that structure can become infected. A simple infected urachal sinus is treated with oral antibiotics and removed surgically after the infection clears. I suspected that was what I was dealing with.

When I described the condition to the pediatric surgeon, she agreed that a urachal sinus was likely and advised me to start antibiotics, order an ultrasound exam of the abdomen—which would detect any cystic dilation of the urachal tract—and schedule the baby for an appointment with her the following week. “And you know what to tell the parents to watch for,” she concluded.

“Right,” I said. “I remember seeing one case of omphalitis when I was a resident. It was ­awful.”

Omphalitis is the most frightening complication of an infected umbilicus or urachal sinus. Bacteria that colonize the cord can sometimes overwhelm the newborn’s immature immune system. Infection in a tiny area can then quickly spread to the loose, soft tissue around the cord and rapidly enter the baby’s bloodstream. The telltale sign is swelling and redness of the skin around the cord, which often leaks pus. Suddenly, the baby begins to look sick. Those infants, like my patient years ago, can die. The condition is extremely rare in the United States, but it has been a common cause of death in the past; it is still a problem in Africa and developing countries.

Fortunately, this child didn’t look sick, and I hadn’t seen any redness around her umbilicus. After talking with the surgeon, I went back and explained the plan to the parents, outlining what they should watch for. “Make sure to bring her in right away if she runs a fever, if she won’t nurse, or if she seems very lethargic or fussy. And ­especially if you see the skin around the belly button turning red,” I said.

The baby’s father pointed to his daughter’s small abdomen. “You mean like that?” he said. Around the umbilicus there was a faint tinge of red, which hadn’t been there just 30 minutes earlier.

This baby wasn’t going home.

I told the hospital’s admitting pediatrician that a newborn with early omphalitis ­needed immediate treatment with intravenous ­antibiotics, along with very careful ­monitoring. Fortunately, we had caught the infection in time, and the baby made a full recovery. I ­shudder to think what might have happened if the ­infection had gone unnoticed just a little bit longer.