Math Is Fun Forum

Combined Quotes - I

1. Your positive action combined with positive thinking results in success. - Shiv Khera

2. All the armies of Europe, Asia and Africa combined, with all the treasure of the earth (our own excepted) in their military chest; with a Buonaparte for a commander, could not by force, take a drink from the Ohio, or make a track on the Blue Ridge, in a trial of a thousand years. - Abraham Lincoln

3. A multitude of causes unknown to former times are now acting with a combined force to blunt the discriminating powers of the mind, and unfitting it for all voluntary exertion to reduce it to a state of almost savage torpor. - William Wordsworth

4. I always tell people that religious institutions and political institutions should be separate. So while I'm telling people this, I myself continue with them combined. Hypocrisy! - Dalai Lama

5. I love playing ego and insecurity combined. - Jim Carrey

6. Talent and effort, combined with our various backgrounds and life experiences, has always been the lifeblood of our singular American genius. - Michelle Obama

7. Rapid population growth and technological innovation, combined with our lack of understanding about how the natural systems of which we are a part work, have created a mess. - David Suzuki

8. A life of stasis would be population control, combined with energy rationing. That is the stasis world that you live in if you stay. And even with improvements in efficiency, you'll still have to ration energy. That, to me, doesn't sound like a very exciting civilization for our grandchildren's grandchildren to live in. - Jeff Bezos.

X-ray

Gist

An X-ray is a quick, painless test that captures images of the structures inside the body — particularly the bones. X-ray beams pass through the body. These beams are absorbed in different amounts depending on the density of the material they pass through.

The full name for "X-ray" is X-radiation, referring to its nature as a form of high-energy electromagnetic radiation, with the 'X' signifying its unknown nature when first discovered by Wilhelm Conrad Röntgen in 1895.

In many languages, it's also called Röntgen radiation, honoring its discoverer. Through experimentation, he found that the mysterious light would pass through most substances but leave shadows of solid objects. Because he did not know what the rays were, he called them 'X,' meaning 'unknown,' rays.

Summary

An X-ray is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ranging from 10 nanometers to 10 picometers, corresponding to frequencies in the range of 30 petahertz to 30 exahertz (3×{10}^{16} Hz to 3×{10}^{19} Hz) and photon energies in the range of 100 eV to 100 keV, respectively.

X-rays were discovered in 1895 by the German scientist Wilhelm Conrad Röntgen, who named it X-radiation to signify an unknown type of radiation.

X-rays can penetrate many solid substances such as construction materials and living tissue, so X-ray radiography is widely used in medical diagnostics (e.g., checking for broken bones) and materials science (e.g., identification of some chemical elements and detecting weak points in construction materials). However X-rays are ionizing radiation and exposure can be hazardous to health, causing DNA damage, cancer and, at higher intensities, burns and radiation sickness. Their generation and use is strictly controlled by public health authorities.

Details

X-rays are a way for healthcare providers to get pictures of the inside of your body. X-rays use radiation to create black-and-white images that a radiologist reads. Then, they send a report to your provider. X-rays are mostly known for looking at bones and joints. But providers can use them to diagnose other conditions, too.

Overview:

What is an X-ray?

An X-ray is a type of medical imaging that uses radiation to take pictures of the inside of your body. We often think of an X-ray as something that checks for broken bones. But X-ray images can help providers diagnose other injuries and diseases, too.

Many people think of X-rays as black-and-white, two-dimensional images. But modern X-ray technology is often combined with other technologies to make more advanced types of images.

Types of X-rays

Some specific imaging tests that use X-rays are:

* Bone density (DXA) scan: This test captures X-ray images while also checking the strength and mineral content of your bones.
* CT scan (computed tomography): CT scans use X-ray and computers to create 3D images of the inside of your body.
* Dental X-ray: A dental provider takes X-rays of your mouth to look for cavities or issues with your gums.
* Fluoroscopy: This test uses a series of X-rays to show the inside of your body in real time. Providers use it to help diagnose issues with specific body parts. They also use it to help guide certain procedures, like an angiogram.
* Mammogram: This is a special X-ray of your breasts that shows irregularities that could lead to breast cancer.

X-rays can help healthcare providers diagnose various conditions in your body. Some of the most common areas on your body to get an X-ray are:

* Abdominal X-ray: This X-ray helps providers evaluate parts of your digestive system and diagnose conditions like kidney stones and bladder stones.
* Bone X-ray: You might get a bone X-ray if your provider suspects you have a broken bone, dislocated joint or arthritis. Images from bone X-rays can also show signs of bone cancer or infection.
* Chest X-ray: Your provider might order a chest X-ray if you have symptoms like chest pain, shortness of breath or a cough. It can look for signs of infection in your lungs or congestive heart failure.
* Head X-ray: These can help providers see skull fractures from head injuries or conditions that affect how the bones in your skull form, like craniosynostosis.
* Spine X-ray: A provider can use a spine X-ray to look for arthritis and scoliosis.

Test Details:

How do X-rays work?

X-rays work by sending beams of radiation through your body to create images on an X-ray detector nearby. Radiation beams are invisible, and you can’t feel them.

As the beams go through your body, bones, soft tissues and other structures absorb radiation in different ways:

* Solid or dense tissues (like bones and tumors) absorb radiation easily, so they appear bright white on the image.
* Soft tissues (like organs, muscle and fat) don’t absorb radiation as easily, so they appear in shades of gray on the X-ray.

A radiologist interprets the image and writes a report for the physician who ordered the X-ray. They make note of anything that’s abnormal or concerning. Then, your healthcare provider shares the results with you.

How do I prepare?

Preparation for an X-ray depends on the type of X-ray you’re getting. Your provider may ask you to:

* Remove metal objects like jewelry, hairpins or hearing aids (metal can interfere with X-rays and make the results inaccurate)
* Wear comfortable clothing or change into a gown before the X-ray

Tell your healthcare provider about your health history, allergies and any medications you’re taking. Let them know if you’re pregnant or think you could be.

What can I expect during an X-ray?

The exact steps of an X-ray depend on the kind you’re getting. In general, your provider will follow these steps during an X-ray:

* They’ll ask you to sit, stand or lie down on a table. In the past, your provider may have covered you with a lead shield (apron), but new evidence suggests that they aren’t necessary.
* Your provider will position the camera near the body part that they’re getting a picture of.
* Then, they’ll move your body or limbs in different positions and ask you to hold still. They may also ask you to hold your breath for a few seconds so the images aren’t blurry.

Sometimes, children can’t stay still long enough to produce clear images. Your child’s provider may recommend using a restraint during an X-ray. The restraint helps your child stay still and reduces the need for retakes. The restraints don’t hurt and won’t harm your child.

What happens after?

Most of the time, there aren’t any restrictions on what you can do after an X-ray. You can go back to your typical activities.

What are the risks or side effects of X-rays?

X-rays are safe and low risk.

X-rays use a safe and small amount of radiation — not much more than the naturally occurring radiation you get in your daily life. For instance, a dental X-ray exposes you to about the same amount of background radiation you’d get in one day.

X-ray radiation is usually safe for adults. But it can be harmful to a fetus. If you’re pregnant, your provider may choose another imaging test, like ultrasound.

Additional Information:

Overview

An X-ray is a quick, painless test that captures images of the structures inside the body — particularly the bones.

X-ray beams pass through the body. These beams are absorbed in different amounts depending on the density of the material they pass through. Dense materials, such as bone and metal, show up as white on X-rays. The air in the lungs shows up as black. Fat and muscle appear as shades of gray.

For some types of X-ray tests, a contrast medium — such as iodine or barium — is put into the body to get greater detail on the images.

Why it's done:

X-ray technology is used to examine many parts of the body.

Bones and teeth

* Fractures and infections. In most cases, fractures and infections in bones and teeth show up clearly on X-rays.
* Arthritis. X-rays of the joints can show evidence of arthritis. X-rays taken over the years can help your healthcare team tell if your arthritis is worsening.
* Dental decay. Dentists use X-rays to check for cavities in the teeth.
* Osteoporosis. Special types of X-ray tests can measure bone density.
* Bone cancer. X-rays can reveal bone tumors.

Chest

* Lung infections or conditions. Evidence of pneumonia, tuberculosis or lung cancer can show up on chest X-rays.
* Breast cancer. Mammography is a special type of X-ray test used to examine breast tissue.
* Enlarged heart. This sign of congestive heart failure shows up clearly on X-rays.
* Blocked blood vessels. Injecting a contrast material that contains iodine can help highlight sections of the circulatory system so they can be seen easily on X-rays.

Abdomen

* Digestive tract issues. Barium, a contrast medium delivered in a drink or an enema, can help show problems in the digestive system.
* Swallowed items. If a child has swallowed something such as a key or a coin, an X-ray can show the location of that object.

X-ray technology is used to examine many parts of the body.

Risks:

Radiation exposure

Some people worry that X-rays aren't safe. This is because radiation exposure can cause cell changes that may lead to cancer. The amount of radiation you're exposed to during an X-ray depends on the tissue or organ being examined. Sensitivity to the radiation depends on your age, with children being more sensitive than adults.

Generally, however, radiation exposure from an X-ray is low, and the benefits from these tests far outweigh the risks.

However, if you are pregnant or suspect that you may be pregnant, tell your healthcare team before having an X-ray. Though most diagnostic X-rays pose only small risk to an unborn baby, your care team may decide to use another imaging test, such as ultrasound.

Contrast medium

In some people, the injection of a contrast medium can cause side effects such as:

* A feeling of warmth or flushing.
* A metallic taste.
* Lightheadedness.
* Nausea.
* Itching.
* Hives.

Rarely, severe reactions to a contrast medium occur, including:

* Very low blood pressure.
* Difficulty breathing.
* Swelling of the throat or other parts of the body.

How you prepare:

Different types of X-rays require different preparations. Ask your healthcare team to provide you with specific instructions.

What to wear

In general, you undress whatever part of your body needs examination. You may wear a gown during the exam depending on which area is being X-rayed. You also may be asked to remove jewelry, eyeglasses and any metal objects because they can show up on an X-ray.

Contrast material

Before having some types of X-rays, you're given a liquid called contrast medium. Contrast mediums, such as barium and iodine, help outline a specific area of your body on the X-ray image. You may swallow the contrast medium or receive it as an injection or an enema.

What you can expect:

During the X-ray

X-rays are performed at medical offices, dentists' offices, emergency rooms and hospitals — wherever an X-ray machine is available. The machine produces a safe level of radiation that passes through the body and records an image on a specialized plate. You can't feel an X-ray.

A technologist positions your body to get the necessary views. Pillows or sandbags may be used to help you hold the position. During the X-ray exposure, you remain still and sometimes hold your breath to avoid moving so that the image doesn't blur.

An X-ray procedure may take just a few minutes for a simple X-ray or longer for more-involved procedures, such as those using a contrast medium.

Your child's X-ray

If a young child is having an X-ray, restraints or other tools may be used to keep the child still. These won't harm the child and they prevent the need for a repeat procedure, which may be necessary if the child moves during the X-ray exposure.

You may be allowed to remain with your child during the test. If you remain in the room during the X-ray exposure, you'll likely be asked to wear a lead apron to shield you from unnecessary X-ray exposure.

After the X-ray

After an X-ray, you generally can resume usual activities. Routine X-rays usually have no side effects. However, if you're given contrast medium before your X-ray, drink plenty of fluids to help rid your body of the contrast. Call your healthcare team if you have pain, swelling or redness at the injection site. Ask your team about other symptoms to watch for.

Results:

X-rays are saved digitally on computers and can be viewed on-screen within minutes. A radiologist typically views and interprets the results and sends a report to a member of your healthcare team, who then explains the results to you. In an emergency, your X-ray results can be made available in minutes.

Dispersion

Gist

Dispersion of light is the phenomenon where white light splits into its seven constituent colors (VIBGYOR: Violet, Indigo, Blue, Green, Yellow, Orange, Red) as it passes through a transparent medium, like a glass prism or water droplets. This occurs because different colors (wavelengths) of light travel at different speeds in the medium, causing them to bend, or refract, at slightly different angles, creating a spectrum.

In physics, dispersion is the phenomenon where a wave (like light, sound, or water waves) splits into its constituent frequencies or wavelengths, causing them to travel at different speeds, most famously seen as white light separating into a rainbow spectrum (VIBGYOR) when passing through a prism or water droplet. This happens because the refractive index or phase velocity of the medium changes with the wave's frequency, meaning different colors bend or travel at different rates, separating from the original beam. 

Summary

Dispersion, in wave motion, is any phenomenon associated with the propagation of individual waves at velocities that depend on their wavelengths.

Ocean waves in deep water, for example, move at speeds proportional to the square root of their wavelengths; these speeds vary from a few meters per second for ripples to hundreds of kilometers per hour for tsunamis. (When ocean waves come closer to land in shallow water, the waves are nondispersive and move at a constant speed equal to the square root of the acceleration due to gravity times the depth of the water.)

In a vacuum, a wave of light has a defined speed, but in a transparent medium that speed varies inversely with the index of refraction (a measure of the angle by which the direction of a wave is changed as it moves from one medium into another). Any transparent medium—e.g., a glass prism—will cause an incident parallel beam of light to fan out according to the refractive index of the glass for each of the component wavelengths, or colors. This effect also causes rainbows, in which sunlight entering raindrops is spread out into its different wavelengths before it is reflected. This separation of light into colors is called angular dispersion or sometimes chromatic dispersion.

Chromatic dispersion is the change of index of refraction with wavelength. Generally the index decreases as wavelength increases, blue light traveling more slowly in the material than red light. Dispersion is the phenomenon which gives you the separation of colors in a prism. It also gives the generally undesirable chromatic aberration in lenses. Usually the dispersion of a material is characterized by measuring the index at the blue F line of hydrogen (486.1 nm), the yellow sodium D lines (589.3 nm), and the red hydrogen C line (656.3 nm).

Details

Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Sometimes the term chromatic dispersion is used to refer to optics specifically, as opposed to wave propagation in general. A medium having this common property may be termed a dispersive medium.

Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, and in gravity waves (ocean waves). Within optics, dispersion is a property of telecommunication signals along transmission lines (such as microwaves in coaxial cable) or the pulses of light in optical fiber.

In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light, as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses. Design of compound achromatic lenses, in which chromatic aberration is largely cancelled, uses a quantification of a glass's dispersion given by its Abbe number V, where lower Abbe numbers correspond to greater dispersion over the visible spectrum. In some applications such as telecommunications, the absolute phase of a wave is often not important but only the propagation of wave packets or "pulses"; in that case one is interested only in variations of group velocity with frequency, so-called group-velocity dispersion.

All common transmission media also vary in attenuation (normalized to transmission length) as a function of frequency, leading to attenuation distortion; this is not dispersion, although sometimes reflections at closely spaced impedance boundaries (e.g. crimped segments in a cable) can produce signal distortion which further aggravates inconsistent transit time as observed across signal bandwidth.

Examples

Dispersion causes a rainbow's spatial separation of a white light into components of different wavelengths (different colors). However, dispersion also has an effect in many other circumstances: for example, group-velocity dispersion causes pulses to spread in optical fibers, degrading signals over long distances; also, a cancellation between group-velocity dispersion and nonlinear effects leads to soliton waves.

Material and waveguide dispersion

Most often, chromatic dispersion refers to bulk material dispersion, that is, the change in refractive index with optical frequency. However, in a waveguide there is also the phenomenon of waveguide dispersion, in which case a wave's phase velocity in a structure depends on its frequency simply due to the structure's geometry. More generally, "waveguide" dispersion can occur for waves propagating through any inhomogeneous structure (e.g., a photonic crystal), whether or not the waves are confined to some region. In a waveguide, both types of dispersion will generally be present, although they are not strictly additive. For example, in fiber optics the material and waveguide dispersion can effectively cancel each other out to produce a zero-dispersion wavelength, important for fast fiber-optic communication.

Additional Information

A rainbow shining against a gloomy stormy sky is a sight that everyone loves. How does sunshine shining through pure raindrops produce the rainbow of colors observed? A transparent glass prism or a diamond uses the same method to break white light into colors. There are about six colors in a rainbow—red, black, yellow, green, blue, and violet; indigo is often identified as well.

Specific wavelengths of light are correlated with certain colors. Depending on the wavelength, we expect to see only one of the six colors as we absorb pure-wavelength light. Our eye's response to a combination of various wavelengths produces the thousands of other colors we can detect in other conditions. White light, in fact, is a combination of all visible wavelengths that are fairly uniform.

Because of the combination of wavelengths, sunlight, which is known bright, tends to be a little yellow, but it does include all visible wavelengths. The colors in rainbows are in the same order as the colors plotted against wavelength. This means the white light in a rainbow is distributed according to wavelength. This scattering of white light is known as Dispersion. More precisely, dispersion happens if a mechanism changes the direction of light in a wavelength-dependent way. Dispersion can occur with any form of wave and is often associated with wavelength-dependent processes.

What is a White Light?

Sometimes you have noticed that when you face towards the sun and see the sky you see the white light in the sky it is not really a white light it is a mixture of several colors. We can say that white light is the mixture of several colors having different wavelengths and frequency points on the same spot. We can also say that the complete blend of all the wavelengths of the spectrum is known as White Light.

The natural sources of white light are stars and the sun. The source of white light in the solar system is the sun. The artificial white light can be created with the help of LED and fluorescent light bulbs.

What is the Visible Light Spectrum?

Visible light waves are one of the significant forms of electromagnetic waves just like X-rays, infrared radiation, UV-rays, and microwaves.   These waves can be visualized as the colors of the rainbow, with each color possessing a different wavelength. The wavelength of red is the longest, while that of violet is the smallest.

White light is formed when all the waves are seen together. As white light passes through the lens, it splits into the visible light spectrum's colors. The visible light spectrum is a portion of an electromagnetic spectrum which can we can see from our naked eyes. The human eye can only see light with a specific wavelength only, and it ranges between 380 and 740 nm. If we are considering the frequency then the range of frequency varies between 405 and 790 THz.

Dispersion

The phenomenon of splitting of visible light into its component colors is called dispersion. Dispersion of light is caused by the change of speed of light ray (resulting in angle of deviation) of each wavelength by a different amount. 

The dispersion of a light wave by a prism is shown in the diagram. As white light is incident on a glass prism, the emergent light appears to be multicolored (violet, indigo, blue, green, yellow, orange and red). The light that bends the least is red, while the light that bends the most is violet. Dispersion is the process of light breaking into its constituent colors. The continuum of light is the pattern of color components in light.

When light falls on the surface it dispersed into several colors depending on the wavelength of the color or the frequency, as we know that frequency and wavelength are inversely proportional to each other. Each color has its own wavelength and frequency, so we see different colors for the same white light.

Causes of the Dispersion of Light

* The various degrees of refraction produced by different colors of light cause dispersion. In a vacuum, various colors of light travel at the same speed, but in a refracting medium, they travel at different speeds.
* Violet light travels at a much slower speed than red light. As a result, violet light has the highest refractive index of the medium, while red light has the lowest.
* As a result, violet light has the highest refractive index, while red light has the lowest refractive index (in the visible spectrum). As a consequence, violet-colored light refracts or bends the most, while red-colored light refracts the least.
* The dispersion of white light into its constituent colors as it emerges from a prism is caused by the disparity in the degree of bending of various colors of light.

Examples of Dispersion of Light

* Dispersion of white light through a prism: As shown in the figure, when white light falls on the prism a collection of seven colors found to come out from the prism due to the dispersion.
* Dispersion due to Oil on Road: Small amounts of oil are usually present on the road surface e.g. lubricating oil from automobiles, which give rise to bands of beautiful colors when it rains.
* Formation of Rainbow: A rainbow is considered to be one of the most amazing light displays ever seen on the planet. A rainbow is a multicolored arc formed by light striking water droplets. Rainbows are formed during rain by the absorption, refraction, and dispersion of light in water droplets. All of these phenomena provide a light spectrum in the sky, which is known as a rainbow.
* Dispersion in a Diamond: Diamond dispersion is where white light enters a diamond (or any dense object), separates into all the spectral colors of the rainbow, and bounces back to the viewer’s eyes in a wonderful display of colored light, also known as diamond fire.

Rainbow Formation

A Rainbow is formed of seven colors (VIBGYOR) Violet, Indigo, Blue, Green, Yellow, Orange, Red. When rain happens the drops of rain falling on the surface works like a prism and when sunlight falls on the drops of water the rays of the sun scatter into different colors and form a rainbow, and sometimes we may also see multiple rainbows. In this concept drops of water, acts likes a prism and create a rainbow. Drops of water are nothing but the spherical ball containing the water and having the refractive index of water (1.333) which makes the white light to dispersed and forming a beam of light of several called rainbow.

Therefore, the necessary conditions for the formation of the rainbow are: the presence of water droplets or raindrops and the position of Sun must be at the back side of the observer of rainbow. 

Q: Why did the Oreo go to the dentist?
A: Because it lost its filling!
* * *
Q: What does the ginger bread man put on his bed?
A: A cookie sheet.
* * *
Q: What kind of keys do kids like to carry?
A: Cookies!
* * *
Q: What is a monkey's favorite cookie?
A: Chocolate chimp!
* * *
Q: What word backwards can predict the future?
A: Cookies (Seikooc as in psychic of you say it).
* * *

Intelligence Quotient

Gist

An Intelligence Quotient (IQ) is a standardized, numerical score derived from tests designed to measure human cognitive abilities—such as reasoning, logic, memory, and problem-solving—relative to a peer group. Modern IQ scores are calculated using a normal distribution (bell curve) with a mean of 100 and a standard deviation of 15, meaning ~68% of the population scores between 85 and 115.

IQ (Intelligence Quotient) is a score from standardized tests measuring cognitive abilities, originally calculated by dividing a person's mental age (MA) by their chronological age (CA) and multiplying by 100: IQ = (MA / CA) × 100, though modern tests use statistical norms with a mean of 100, says Wikipedia. It assesses logic, memory, problem-solving, and pattern recognition, with average scores around 100, while scores below 70 suggest extremely low intelligence and above 129 indicate giftedness.

Summary

IQ, (from “intelligence quotient”), is a number used to express the relative intelligence of a person. It is one of many intelligence tests.

IQ was originally computed by taking the ratio of mental age to chronological (physical) age and multiplying by 100. Thus, if a 10-year-old child had a mental age of 12 (that is, performed on the test at the level of an average 12-year-old), the child was assigned an IQ of 12/10 × 100, or 120. If the 10-year-old had a mental age of 8, the child’s IQ would be 8/10 × 100, or 80. Based on this calculation, a score of 100—where the mental age equals the chronological age—would be average. Few tests continue to involve the computation of mental ages.

Details

An intelligence quotient (IQ) is a total score derived from a set of standardized tests or subtests designed to assess human intelligence. Originally, IQ was a score obtained by dividing a person's estimated mental age, obtained by administering an intelligence test, by the person's chronological age. The resulting fraction (quotient) was multiplied by 100 to obtain the IQ score. For modern IQ tests, the raw score is transformed to a normal distribution with mean 100 and standard deviation 15. This results in approximately two-thirds of the population scoring between IQ 85 and IQ 115 and about 2 percent each above 130 and below 70.

Scores from intelligence tests are estimates of intelligence. Unlike quantities such as distance and mass, a concrete measure of intelligence cannot be achieved given the abstract nature of the concept of "intelligence". IQ scores have been shown to be associated with factors such as nutrition, parental socioeconomic status, morbidity and mortality, parental social status, and perinatal environment. While the heritability of IQ has been studied for nearly a century, there is still debate over the significance of heritability estimates and the mechanisms of inheritance. The best estimates for heritability range from 40 to 60% of the variance between individuals in IQ being explained by genetics.

IQ scores were used for educational placement, assessment of intellectual ability, and evaluating job applicants. In research contexts, they have been studied as predictors of job performance and income. They are also used to study distributions of psychometric intelligence in populations and the correlations between it and other variables. Raw scores on IQ tests for many populations have been rising at an average rate of three IQ points per decade since the early 20th century, a phenomenon called the Flynn effect. Investigation of different patterns of increases in subtest scores can also inform research on human intelligence.

Historically, many proponents of IQ testing have been eugenicists who used pseudoscience to push later debunked views of racial hierarchy in order to justify segregation and oppose immigration. Such views have been rejected by a strong consensus of mainstream science, though fringe figures continue to promote them in pseudo-scholarship and popular culture.

Additional Information

Earlier this year, 11-year-old Kashmea Wahi of London, England scored 162 on an IQ test. That’s a perfect score. The results were published by Mensa, a group for highly intelligent people. Wahi is the youngest person ever to get a perfect score on that particular test.           

Does her high score mean she will go on to do great things — like Stephen Hawking or Albert Einstein, two of the world’s greatest scientists? Maybe. But maybe not.

IQ, short for intelligence quotient, is a measure of a person’s reasoning ability. In short, it is supposed to gauge how well someone can use information and logic to answer questions or make predictions. IQ tests begin to assess this by measuring short- and long-term memory. They also measure how well people can solve puzzles and recall information they’ve heard — and how quickly.

Every student can learn, no matter how intelligent. But some students struggle in school because of a weakness in one specific area of intelligence. These students often benefit from special education programs. There, they get extra help in the areas where they’re struggling. IQ tests can help teachers figure out which students would benefit from such extra help.

IQ tests also can help identify students who would do well in fast-paced “gifted education” programs. Many colleges and universities also use exams similar to IQ tests to select students. And the U.S. government — including its military — uses IQ tests when choosing who to hire. These tests help predict which people would make good leaders, or be better at certain specific skills.

It’s tempting to read a lot into someone’s IQ score. Most non-experts think intelligence is the reason successful people do so well. Psychologists who study intelligence find this is only partly true. IQ tests can predict how well people will do in particular situations, such as thinking abstractly in science, engineering or art. Or leading teams of people. But there’s more to the story. Extraordinary achievement depends on many things. And those extra categories include ambition, persistence, opportunity, the ability to think clearly — even luck.

Intelligence matters. But not as much as you might think.

Measuring IQ

IQ tests have been around for more than a century. They were originally created in France to help identify students who needed extra help in school.

The U.S. government later used modified versions of these tests during World War I. Leaders in the armed forces knew that letting unqualified people into battle could be dangerous. So they used the tests to help find qualified candidates. The military continues to do that today. The Armed Forces Qualification Test is one of many different IQ tests in use.

IQ tests have many different purposes, notes Joel Schneider. He is a psychologist at Illinois State University in Normal. Some IQ tests have been designed to assess children at specific ages. Some are for adults. And some have been designed for people with particular disabilities.

But any of these tests will tend to work well only for people who share a similar cultural or social upbringing. “In the United States,” for instance, “a person who has no idea who George Washington was probably has lower-than-average intelligence,” Schneider says. “In Japan, not knowing who Washington was reveals very little about the person’s intelligence.”

Questions about important historical figures fall into the “knowledge” category of IQ tests. Knowledge-based questions test what a person knows about the world. For example, they might ask whether people know why it’s important to wash their hands before they eat.

IQ tests also ask harder questions to measure someone’s knowledge. What is abstract art? What does it mean to default on a loan? What is the difference between weather and climate? These types of questions test whether someone knows about things that are valued in their culture, Schneider explains.

Such knowledge-based questions measure what scientists call crystallized intelligence. But some categories of IQ tests don’t deal with knowledge at all.

Some deal with memory. Others measure what’s called fluid intelligence. That’s a person’s ability to use logic and reason to solve a problem. For example, test-takers might have to figure out what a shape would look like if it were rotated. Fluid intelligence is behind “aha” moments — times when you suddenly connect the dots to see the bigger picture.

Aki Nikolaidis is a neuroscientist, someone who studies structures in the brain. He works at the University of Illinois at Urbana-Champaign. And he wanted to know what parts of the brain are active during those “aha” episodes.

In a study published earlier this year, he and his team studied 71 adults. The researchers tested the volunteers’ fluid intelligence with a standard IQ test that had been designed for adults. At the same time, they mapped out which areas of test takers’ brains were working hardest. They did this using a brain scan called magnetic resonance spectroscopy, or MRS. It uses magnets to hunt for particular molecules of interest in the brain.

As brain cells work, they gobble up glucose, a simple sugar, and spit out the leftovers. MRS scans let researchers spy those leftovers. That told them which specific areas of people’s brains were working hard and breaking down more glucose.

People who scored higher on fluid intelligence tended to have more glucose leftovers in certain parts of their brains. These areas are on the left side of the brain and toward the front. They’re involved with planning movements, with spatial visualization and with reasoning. All are key aspects of problem solving.

“It’s important to understand how intelligence is related to brain structure and function,” says Nikolaidis. That, he adds, could help scientists develop better ways to boost fluid intelligence.

Personal intelligence

IQ tests “measure a set of skills that are important to society,” notes Scott Barry Kaufman. He’s a psychologist at the University of Pennsylvania in Philadelphia. But, he adds, such tests don’t tell the full story about someone’s potential. One reason: IQ tests favor people who can think on the spot. It’s a skill plenty of capable people lack.

It’s also something Kaufman appreciates as well as anyone.

As a boy, he needed extra time to process the words he heard. That slowed his learning. His school put him into special education classes, where he stayed until high school. Eventually, an observant teacher suggested he might do well in regular classes. He made the switch and, with hard work, indeed did well.

Kaufman now studies what he calls “personal intelligence.” It’s how people’s interests and natural abilities combine to help them work toward their goals. IQ is one such ability. Self-control is another. Both help people focus their attention when they need to, such as at school.

Psychologists lump together a person’s focused attention, self-control and problem-solving into a skill they call executive function. The brain cells behind executive function are known as the executive control network. This network turns on when someone is taking an IQ test. Many of the same brain areas are involved in fluid intelligence.

But personal intelligence is more than just executive function. It’s tied to personal goals. If people are working toward some goal, they’ll be interested and focused on what they are doing. They might daydream about a project even while not actively working on it. Although daydreaming may seem like a waste of time to outsiders, it can have major benefits for the person doing it.

When engaged in some task, such as learning, people want to keep at it, Kaufman explains. That means they will push forward, long after they might otherwise have been expected to give up. Engagement also lets a person switch between focused attention and mind wandering.

That daydreaming state can be an important part of intelligence. It is often while the mind is “wandering” that sudden insights or hunches emerge about how something works.

While daydreaming, a so-called default mode network within the brain kicks into action. Its nerve cells are active when the brain is at rest. For a long time, psychologists thought the default mode network was active only when the executive control network rested. In other words, you could not focus on an activity and daydream at the same time.

To see if that was really true, last year Kaufman teamed up with researchers at the University of North Carolina in Greensboro and at the University of Graz in Austria. They scanned the brains of volunteers using functional magnetic resonance imaging, or fMRI. This tool uses a strong magnetic field to record brain activity.

As they scanned the brains of 25 college students, the researchers asked the students to think of as many creative uses as they could for everyday objects. And as students were being as creative as possible, parts of both the default mode network and the executive control network lit up. The two systems weren’t at odds with each other. Rather, Kaufman suspects, the two networks work together to make creativity possible.

“Creativity seems to be a unique state of consciousness,” Kaufman now says. And he thinks it is essential for problem-solving.

Turning potential into achievement

Just being intelligent doesn’t mean someone will be successful. And just because someone is less intelligent doesn’t mean that person will fail. That’s one take-home message from the work of people like Angela Duckworth.

She works at the University of Pennsylvania in Philadelphia. Like many other psychologists, Duckworth wondered what makes one person more successful than another. In 2007, she interviewed people from all walks of life. She asked each what they thought made someone successful. Most people believed intelligence and talent were important. But smart people don’t always live up to their potential.

When Duckworth dug deeper, she found that the people who performed best — those who were promoted over and over, or made a lot of money — shared a trait independent of intelligence. They had what she now calls grit. Grit has two parts: passion and perseverance. Passion points to a lasting interest in something. People who persevere work through challenges to finish a project.

Duckworth developed a set of questions to assess passion and perseverance. She calls it her “grit scale.”

In one study of people 25 and older, she found that as people age, they become more likely to stick with a project. She also found that grit increases with education. People who had finished college scored higher on the grit scale than did people who quit before graduation. People who went to graduate school after college scored even higher.

She then did another study with college students. Duckworth wanted to see how intelligence and grit affected performance in school. So she compared scores on college-entrance exams (like the SAT), which estimate IQ, to school grades and someone’s score on the grit scale. Students with higher grades tended to have more grit. That’s not surprising. Getting good grades takes both smarts and hard work. But Duckworth also found that intelligence and grit don’t always go hand in hand. On average, students with higher exam scores tended to be less gritty than those who scored lower.

Students who perform best in the National Spelling Bee are those with grit. Their passion, drive, and persistance pay off and help them succeed against less “gritty” competitors.

But some people counter that this grit may not be all it’s cracked up to be. Among those people is Marcus Credé. He’s a psychologist at Iowa State University in Ames. He recently pooled the results of 88 studies on grit. Together, those studies involved nearly 67,000 people. And grit did not predict success, Credé found.

However, he thinks grit is very similar to conscientiousness. That someone’s ability to set goals, work toward them and think things through before acting. It’s a basic personality trait, Credé notes — not something that can be changed.

“Study habits and skills, test anxiety and class attendance are far more strongly related to performance than grit,” Credé concludes. “We can teach [students] how to study effectively. We can help them with their test anxiety,” he adds. “I’m not sure we can do that with grit.”

In the end, hard work can be just as important to success as IQ. “It’s okay to struggle and go through setbacks,” Kaufman says. It might not be easy. But over the long haul, toughing it out can lead to great accomplishments.