Understanding Calculus

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  Table of Contents

  1. Why Study
  2. Numbers
  3. Functions
  4. The Derivative
  5. Differentiation
  6. Applications
  7. Free Falling
  8. Understanding
  9. Derivative
  10. Integration
  11. Understanding
  12. Differentials

  Inverse Functions
  Applications of
  Sine and Cosine
  Sine Function
  Sine Function -
  Differentiation and
  Oscillatory Motion
  Mean Value
  Taylor Series
  More Taylor Series


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Chapter 3 - The Mathematical function and its Graph

Section 3.2 - Nonsense Detection - The UnScientific Method

From "Piled Higher and Deeper" by Jorge Cham - www.phdcomics.com

In a perfect world all scientific research could be trusted at face value. Unfortunately, the world is complex and science is not black or white. There is a lot of grey area where it is difficult to differentiate fact from opinion. Read the words of the Dalai Lama commenting on suicide bombings:

" You know, science or knowledge is just a method. The thing is how to use that. Science itself is wonderful. Sometimes we use that knowledge for destruction. It's not science's mistake, it's our mistake. Similarly, some people manipulate religion in the wrong way. It's not the fault of religion, it is the fault of people and politics. People talk about dirty science. There is also dirty religion and dirty politics. "

The Dalai Lama is saying that science, just like anything else, can be manipulated to prove any point. So how does one distinguish 'dirty science' from 'good science'? Unfortunately, the answer is not a simple one. There are shades of good and bad science in all research. It takes a lot of experience to know how to filter out the nonsense. This article will summarize a few categories most bad science typically falls under. If you see any research that shares elements of these categories then you should be skeptical of the results.

Many conflicting scientific theories explaining the same phenomena

If you see many conflicting theories attempting to explain a scenario, then that should raise a red flag that most of these theories are wrong. Consider Dr. Mehmet Oz, Director of the Columbia University Heart Institute, asking eminent American science writer, Gary Taubes, " Why is it that we can not agree on dietary recommendations? "

" A couple major issues, first of all ... disagreements come about because the science is surprisingly complicated, the human body is incredibly complicated, all people are different, diseases are divergent and different, people and their genetic elements and physiological elements and lifestyle elements.

So when you actually get around to trying to test it, you end up with this morass of confusing and conflicting data out of which people can pick just the elements they want to support their preconceived opinions.

And that sometimes make the particular researcher look very sure that he knows the answer or she knows the answer, but unfortunately that is not how you do good science. "

Lack of complexity implies unattractive conclusion which lack glamor and perceived importance

Consider the excerpt from an article in The New Yorker by eminent surgeon Dr. Atul Gawande. In this excerpt, Dr. Gawande describes how Dr. Pronovost developed simple medical checklists that have proven to save countless lives . Gawande writes, " If a new drug were as effective at saving lives as Peter Pronovost's checklist, there would be a nationwide marketing campaign urging doctors to use it. " As you will read below, his checklists have fallen on deaf ears due to their lack of perceived complexity!

We have the means to make some of the most complex and dangerous work we do in surgery, emergency care, and I.C.U. medicine more effective than we ever thought possible. But the prospect pushes against the traditional culture of medicine, with its central belief that in situations of high risk and complexity what you want is a kind of expert audacity.the right stuff, again. Checklists and standard operating procedures feel like exactly the opposite, and that's what rankles many people.

The still limited response to Pronovost's work may be easy to explain, but it is hard to justify. If someone found a new drug that could wipe out infections with anything remotely like the effectiveness of Pronovost's lists, there would be television ads with Robert Jarvik extolling its virtues, detail men offering free lunches to get doctors to make it part of their practice, government programs to research it, and competitors jumping in to make a newer, better version. That's what happened when manufacturers marketed central-line catheters coated with silver or other antimicrobials; they cost a third more, and reduced infections only slightly.and hospitals have spent tens of millions of dollars on them. But, with the checklist, what we have is Peter Pronovost trying to see if maybe, in the next year or two, hospitals in Rhode Island and New Jersey will give his idea a try.

Pronovost remains, in a way, an odd bird in medical research. He does not have the multimillion-dollar grants that his colleagues in bench science have. He has no swarm of doctoral students and lab animals. He's focused on work that is not normally considered a significant contribution in academic medicine. As a result, few other researchers are venturing to extend his achievements. Yet his work has already saved more lives than that of any laboratory scientist in the past decade.

Furthermore, often times new discoveries are based on very simple incremental improvements to existing ideas. For this reason established scientists find it very easy to ridicule them. They claim how can something so simple replace decades of their research and experience? Society agrees with them since they are conditioned into believing all science is beyond their understanding. Since it is society that ultimately funds scientist work, then without the support of society, the new ideas will never take ground and flourish.

Cause and effect not established

The media often publish health studies that do not demonstrate cause and effect. The typical study goes something like this:

Researchers found that those who:

------ exercised regularly
------ ate fruits and vegetables throughout life were less likely to have contracted xyz disease than those who did not.

One can not make such type of conclusions without first proving there is a relationship between the variables. The conclusions are as absurd as saying "people who drink soda are more likely to contract xyz disease". While the statement may be true for the sample population , it does not establish there is any relationship between soda and xyz disease. The problem is that those who drink a lot of soda probably do or eat other things that are unhealthy, relative to the other group, so any effect noted may be due to the other things.

Using the health study approach, one could argue that bridges made of steel are less likely to break compared to those made of wood. Why? Because historically and statistically steel bridges have a better track record than wooden bridges. However, any decent bridge engineer knows they can build a wooden bridge that is ten times stronger than a steel bridge made of thin and undersized beam sections! This is because they understand the relationship between loads, forces, stresses, and material properties. Detailed mathematics , physics and chemistry can explain what the relationships are.

However, in medicine it seems the health studies often have not identified the association between exercise and heart disease or smoking and lung cancer. They seem content with simply observing that some association may exist which is just as primitive as saying "all bridges made of steel are less likely to break than wooden bridges".

Any theory has at its foundation statements which are accepted as true without being proven. One cannot build a theory starting with nothing. Other sciences seem to be able to dig a lot deeper into the foundations than medicine. One reason is because medicine is perhaps the most complex of all the sciences as it merges elements of all of them. Combine that with billions of years of evolution and you end up with an organism so complex that no simple theory can explain it.

Inability to recognize variability in data

If you recall, the scientific method requires studying how interacting conditions define a situation. The problem is there is variability with each condition. For example, consider a scientist who is studying what causes trees to grow tall. One condition is sunlight. However, sunlight is not a constant. Some years can have more sunlight than others depending on the overall weather conditions. Therefore, sunlight has variability that can effect how much taller trees grow one year relative to other years. It has a tolerance, i.e +/- some amount every year.

This variability of conditions leads to uncertainty in the conclusions of a scientific theory. When you add up all the variability from other interacting conditions, the final result can have almost no meaning. So you have to always question the variability of the conditions and ask the scientist what cumulative effect they have on the uncertainty of their results.

A good scientific experiment must be repeatable. The experiment has to be able to be performed many times and always produce the same result. If repeatability has not been established then you must scrutinize the variability of each condition.

Scientific community seeks maintenance of status quo by rejecting new ideas

There is a famous saying by former US President, Woodrow Wilson, " If you want to make enemies, try to change something ". Human nature does not like change, however, there are good and bad reasons for this. Anytime you have an established convention, the one who comes along and says that it can be done differently, better, faster; that person is seen as the renegade. The scientific community, like any other community, has an unwillingness to accept new ideas often for no other reason than maintaining the status quo.

There are often valid reasons for rejecting change and mantaining status quo. It is not the cost of the new technology, it is the cost of the process of changing to it. Consider something like the complex and expensive black box on an airplane. In today's digital age it would be easy and inexpensive to add a backup system to transmit flight audio and cockpit video via satellite phone and internet technology.

However, once something like the "black box" is in use, it seldom changes unless there is a compelling need. To change it, you have to have meetings, studies, vendor contracts, more studies, more meetings, notices, hearings, training on replacement, etc.

It is the same reason why the on-board Space Shuttle computers are a couple hundred times less powerful than the processors in an iPod: they work, and there is no compelling reason to change them.

On the other hand, some scientists seek to mantain status quo out of pure laziness. Established scientists spend their lifetime mastering a few core ideas. These ideas are their livelihood so any challenge to these ideas directly impacts their livelihood and future. Their job security depends on their ability to show society the value of their work. If new ideas are discovered then society will no longer perceive any value in their obsolete ideas. Consequently, some scientists find it easier to reject those with new discoveries rather than face the humility of admitting the error in their obsolete ideas .

As you can see, there are both good and bad reasons for rejecting new ideas. Often decisions to reject are based on combinations of reasons. A good scientist is one who can prioritize the sensible from the nonsensical reasons!

Focusing on details while ignoring the bigger picture ( Phd's )

While one should have great respect for the work PhD's do, nearly all of them suffer from the 'Ostrich mentality'. Their heads are stuck in the sand so are unable to sense the train coming. Such behavior is fine in the research lab, but in the real world it creates unnecessary red tape to get things done. PhD's are unable to see the big picture. Instead they focus on the tiny flaws of a system to convince people that the entire system is flawed.

It is interesting to note the difference in perspective in the clinical scientist and the engineer. Scientists are interested in 'exactness'; in the minutiae of detail. Engineers are more interested in systems and the dynamics of how things actually work. Clinicians will always argue they are more accurate while failing to understand the problems at hand in the real world.

In conclusion, the world is not only made of one color. Stay open-minded and appreciate all the interacting diversity surrounding you. The best way to avoid the trap of believing bad science is to read from multiple sources to identify common elements and conclusions. When numerous people you respect and trust say the same thing, then you can be more sure you are reading mostly good science.

Keep in mind the real world is not black and white at all. Between pure science and the incorrect interpretation of data, there is a huge gray area, and this is where most research is done.

Unfortunately, as Thomas Edison said, " Opportunity is missed by most people because it is dressed in overalls and looks like work ". This leads to another famous saying, " The less one understands something, the greater one's faith in its capabilities ". It is unfortunate that human nature prefers ignorance and blind faith over hard-work and skepticism.

On the other hand, if you have something worthwhile, people will come. But you better be prepared to show proof. If you have an idea for a machine that flies around with no physical prototype, nobody will care, you can bet on it. Talk is cheap. Demonstrate your machine and the world will beat a path to your door, regardless of what the scientific community has to say.

To end on a humorous note, the following table translates commonly used expressions found in research papers:

Published Translation

" It has long been known...."

I didn't look up the original reference.

" Of great theoretical and practical importance...."

Interesting to me.

" A definite trend is evident...

The data seem practically meaningless

" Three of the examples were chosen for detailed study.."

The others made no sense.

" Typical results are shown..

The best results are shown.

" It is believed that..

I think

" It is generally believed that....

A couple of other guys think so too.

" It is clear that much additional work will be required before a complete understanding of these phenomena is possible..

I don't understand it.

" Correct within an order of magnitude.."


" Statistically oriented projection of the findings..

Wild guess.

" Highly significant area for exploratory study.."

A totally useless topic suggested by my committee.

Source: Unknown

Next section -> Section 3.3 - Dimensions


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