Nature Abhors a Gradient

Otto von Guerick's experiment 

I recall back to my first days in physics class where I read the quotation “Nature abhors a vacuum”.  The phrase was accompanied by an image of two teams of horses trying to pull two hollow hemispheres apart after the air was pumped out from inside.

These were called Magdeburg hemispheres and the experiment was performed by Otto von Guericke.  I didn’t realize this, but according to Wikipedia it was Aristotle’s theory Horror Vacui that von Guericke was trying to disprove.  This theory suggested that nature hates a vacuum and that the vacuum will suck material in to fill it.  Von Guericke demonstrated that it is not a sucking force, but a pushing force from the outside air.  However, as I recall from the physics text, the presentation was written as if this experiment was a demonstration of this “principle”.  I imagine that this misconception is why you still see the phrase commonly used today.  This is one of the science myths that keeps floating around.

A more accurate viewpoint is that Nature Abhors a Gradient.  It isn’t that there is a vacuum that is holding the hemispheres together.  Nor is it that there is air surrounding the hemispheres that is holding the hemispheres together.  Rather it is that there is an enormous gradient in the air density outside the hemispheres with respect to the inside.  The result of this gradient is a force.

Gradients in potential energy cause forces.

More generally, gradients in any scalar field result in generalized forces.

The gradient of the electric potential is the electric field.  The gradient of the gravitational potential energy is the gravitational force.  Over and over again these ideas reappear.  In physics, we learn them as separate concepts, and then later in the abstract topic of statistical mechanics we are expected to put it all together.  But each of these gradients resides in its own little box in the student’s cortex, and statistical mechanics is in its own little box.  Rarely do these ideas merge to form a unified concept.

Temperature gradients are responsible for our weather. 
Huge temperature gradients are responsible for hurricanes.  The temperature of the extremely warm air at the sea surface in the Gulf of Mexico drops quickly as one rises higher into the atmosphere.  This enormous gradient powers the heat engine known as a hurricane.  Nature abhors gradients, and will do something about them.  The gradients will result in forces that tend to eradicate the gradient.  Watching this NASA video of satellite imagery during the 2005 hurricane season, one can clearly see that hurricanes are designed to cool the sea surface.

Our weather here in Albany is due mainly to cyclonic storms that act to relieve the temperature gradient between the Earth’s equator and the poles.  Forces due to this gradient brings parcels of warm air north from the south and exchanges them with parcels of cold air from the north.  The spinning of the Earth results in the Coriolis force which deflects the northbound warm air eastward and the colder southbound air westward.  This creates a counter-clockwise rotating structure that brings warm air north on the eastern front and cold air south on the western front.  The result is that the extremely warm weather we had a few days ago had to be followed by the extremely cold weather as this cyclonic structure moved over us from the west.

However, the weather is not the only system driven by the Earth’s energy gradients.  Life itself is driven by these forces.  The “purpose” of life is to relieve gradients.  This is why forests are cooler, they are working to dissipate thermal gradients induced by incoming light heating the surface.  During the process of relieving these thermal gradients, the plants grow.  This excess organic matter results in residual chemical potential energy, which again creates a gradient.  The herbivores devour the plant matter to further relieve the chemical potential gradients.  This works up to a point, but again there is a residual chemical potential, of which the carnivores take advantage.  The cycles of life are driven by energy gradients.

But it doesn’t stop here.  There are other scalar fields that have gradients.  Wealth gradients result in generalized forces.  In cites where there are enormous gradients between the wealthy and the poor one sees violence.  Across the southern U.S. border there is another enormous gradient in wealth.  This gradient results in forces that drive Mexican immigrants into this country.  Building a wall won’t help because it doesn’t eliminate the gradient.  The gradient will merely increase until new forces become strong enough to eliminate it. 

How does one solve the problem? 
Eliminate the gradient.
Nature abhors a gradient.

Kevin Knuth
Albany NY

Posted under Biology, Climate, Energy, Evolution, Philosophy, Physics, Social Justice

This post was written by drknuth on November 27, 2007

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Why Intelligent Machines Appear Intelligent (or Not)

I have been working for about 48 hours (straight with intermittent cat naps) on my robotic arm, which is equipped with a point light sensor.  I have re-programmed it to characterize polygons as well as circles.  However, the main purpose of this research project is to develop an inquiry engine that is generally engineered to decide which experiment the robot should perform to obtain the information that it requires.  In this case, an experiment is characterized by the location of potential light measurements.

Here is a link to an older post that references a research paper, a slide presentation, and a video of my talk on this topic.

One thing that has surprised me is just how intelligent the instrument appears.  It selects measurements that are obviously the smart measurements to take.  What is strange, is that I can intrepret these measurements in terms of the techniques that I would employ to solve the problem, such as: “It is trying to find the edge of the polygon” or “It is verifying that the center of the polygon is where it thinks it is” or “It is checking to see if there is a vertex at a given position”. 

The important fact is that the robot is not using heuristics at all, which is what makes this intelligent system a powerful and generic plug-and-play system.  Instead, the robot is maximizing the relevance of the experimental question with respect to the issue that the robot is programmed to resolve (in this case characterizing a white shape on a black background).  The relevance is related to the entropy, and the inquiry engine performs its computations by sampling a posterior probability of models and considering the entropy of the set of predictions that this set of models makes regarding the outcomes of potential measurements.

How can an instrument that simply performs computations with entropy select manuevers which I, who uses heuristics (or general problem-solving strategies), easily recognize as intelligent.  The only reason I can imagine is that my heuristics work!  The heuristics that I employ to solve such problems are excellent approximations to computing relevance via entropy.

An interesting consequence of this is that sometimes the robot chooses a measurement that I cannot interpret as intelligent.  However, when I study the results of the measurement, I always find that these measurements provide a great deal of information; more than the measurement I would have selected.

The system still has some difficulties, which involves two issues.  The first issue is the fact that the current algorithm design requires that the new measurements be analyzed in conjunction with all of the past measurements.  I could get around this with particle filters, but this is an approximation to the complete inference problem, and I’d like to avoid that.  I am working on a solution to this. 

The second issue has to do with the fact that I require a diverse set of probable models to query to perform the entropy calculations.  If the set is not sufficiently diverse, the robot does not consider the wide variety of possible solutions when it is planning the next experiment.  There are easy ways to assure that the set of samples is diverse, but this takes computation time, which I am aiming to avoid.

In the near future, I will have a video of the robot in operation.

Kevin Knuth
Albany NY

Posted under Computation, Exploration, Information, Intelligent Systems, Inventions, Lego, Programming, Research, Robotics, Technology

This post was written by drknuth on November 24, 2007

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Origin of the Word Idiot

I learned today that the word idiot originates from the Greek word idiwtes (idiotes), which refers to a person disinterested in participating in democracy and public life.  These people were viewed as selfish, contemptable and stupid as they were more concerned with their daily personal affairs than they were of the good of the society.  Later in the Middle Ages the word took on additional connotations associated with being stupid, such as being mentally incapable.

So don’t be an idiot… get involved in your democracy.
Freedom isn’t free.  (pay attention, vote, run for office)

Now this definition seems to run counter to Mark Twain’s statement “Suppose you were an idiot. And suppose you were a member of Congress. But I repeat myself.”  However, at this time, most people in Congress are more interested in their careers than they are interested in our democracy.  This is evident by the ease with which they make compromises and give up their powers (our powers, since they are our representatives) so that they don’t have to make the hard decisions that may upset voters.  In the original Greek sense of the word, today’s Congress is full of idiots.

My friend James Kurien once told me a quote that goes

Stop acting like an idiot you moron!” 

What is funny about this is that it is entirely a reasonable thing to say since by today’s definition, a moron (50 < IQ < 69) is slightly more intelligent than an idiot (IQ < 20). 
Apparently morons are the people who vote.

Kevin Knuth
Albany NY

Posted under Blather, General, Social Justice

This post was written by drknuth on November 22, 2007

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Four on the Floor

My sister-in-law Becky posted her answers to a personal survey on her blog.  While I usually focus on science and robots and other cool things that I want to remember here in my Online memory, why not a fun survey?  Just once…

Four jobs I have had in my life (not including my current job):

  • Bus Boy at Bonanza (ugh… I climbed that ladder starting at the bottom rung)
  • Teaching Gifted-and-Talented Kids D&D (seriously, a teenage boy’s dream job) 
  • Computer Programmer at Mercury Marine (programming is fun… as a hobby)
  • NASA Scientist (very high at this point… can barely make out Bonanza!)

Four Films I have watched again and again:

Four Programs I love to watch:

Four Places I have been on vacation:

Four favorite foods:

Four favorite drinks:

Four places I would rather be right now:

Posted under Fun

This post was written by drknuth on November 22, 2007

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Animations

I have made some animated gifs that I am putting on this blog’s Animations page.

This is an animation of a rotating Earth, and was constructed from 48 images generated by Celestia.  These were then stitched together and optimized using Adobe ImageReady.

Please feel free using these on your own website.
Just remember, they are not for sale or re-sale.
And stop back periodically because I will make more.

Enjoy,
Kevin Knuth
Albany NY

Posted under Astronomy, Climate, Fun, Green, Internet

This post was written by drknuth on November 22, 2007

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