Lecture 2

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1.) Review and revisit last lectures content
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Modeling (heuristics [wiki: are simple, efficient rules, learned or hard-coded by evolutionary processes, that have been proposed to explain how people make decisions, come to judgments, and solve problems typically when facing complex problems or incomplete information], use triangles to build a structure) is intrinsic to the way we think.  
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Show examples from
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'''Value proposition for a University:''' what value do you get and how does that fit into this course?
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1.) Learn critical/analytical thinking.
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2.) Learn content; how to construct a professional argument that data support a scientific model.
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3.) Personal development; “The responsibility for us as teachers is to help our students understand that they must be active participants in the creation of their own character and to insist they do so even in the face of discomfort or adversity.” President of University of Portland. This is a bit like the value proposition of insurance being peace of mind (the value  is not obvious). The value proposition of an education is character development (responsibility, civility, leadership, tolerance, . .). Here you practice this in group work and class discussions.
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http://www.stonybrook.edu/commcms/cas/liberalartseducation.html
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I’ll give examples of each point throughout the semester. First let's consider models, which are the foundation of these goals.
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'''Modeling is intrinsic to the way we think.'''
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Besides scientific models this includes heuristics [wikipedia: are simple, efficient rules, learned or hard-coded by evolutionary processes, that have been proposed to explain how people make decisions, come to judgments, and solve problems typically when facing complex problems or incomplete information], use triangles to build a structure. Show examples from (particularly of heuristics in artificial intelligence)
 
http://c2.com/cgi/wiki?HeuristicRule
 
http://c2.com/cgi/wiki?HeuristicRule
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deciding to eat at restaurant B rather than restaurant A only because B has more cars in its parking lot
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Modeling also involves ways to interpret literature and speech.
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When the level in the fuel tank drops to 1/2 tank or less, always filling up the fuel tank at the very next re-filling station.
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Does your model of the way the world works match the data? Does sacrificing people lead to good weather (Mayan model)? Say you collected data which supported this model and tried to publish the data. Why would it be difficult to get it accepted? There is no scientific model of the universe that explains the results. Therefore people would have trouble believing it. We need a model to justify how the world behaves. For example, the blood vapor contains particulates upon which water condenses to form raindrops.
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Does your model of the way the world works match the data? Does sacrificing people lead to good weather (Mayan model)? Say you collected data which supported this model and tried to publish the data. Why would it be difficult to get it accepted? There is no scientific model of that explains the results. Therefore people would have trouble believing it (they see correlation but no model to cause the effect). We need a model to justify how the world behaves. For example, the blood vapor contains particulates upon which water condenses to form raindrops.
  
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A current controversy involves a propulsion method that doesn’t emit anything. The model is that the group velocity is less on the cone side where reflection leads to a smaller momentum exchange.
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A current controversy involves a propulsion method that doesn’t emit anything. See
 
http://emdrive.com/
 
http://emdrive.com/
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Note the fringe theory warnings on this site
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There used to be “fringe theory” warnings on this site
 
https://en.wikipedia.org/wiki/RF_resonant_cavity_thruster
 
https://en.wikipedia.org/wiki/RF_resonant_cavity_thruster
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Why would this idea have trouble being accepted? It helps if there is a model which explains why something happens rather than simply a correlation without a cause. However, the data may support motion but it seems to violate conservation of momentum since the net force on a body is the time rate of change of the total momentum. Since there is no net force there can be no change in total momentum.
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How do you make an argument that the model is valid? Does that sound like what you would hear in an english class where you are asked to make an argument (both orally and in writing) about an interpretation of a novel.  This type of study is the foundation for critical thinking in a liberal arts college.
  
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Why isn't modelling a familiar topic in what you have studied at Mines? You spend most of your time learning about complicated mathematical models rather than thinking critically about these models. For example, what are the assumptions of the model and when are they valid?
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'''Example; Value Proposition A (critical/analytical thinking):'''
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In all lab expts I expect you to formulate a model and see if the data supports that model.
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How do you make an argument that the model is valid? Does that sound like what you would hear in an english class where you are asked to make an argument about an interpretation of a novel.  Does anyone want to give an example of what they had to do in an English or history class?
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Example:
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You collect data  which is presented in this graph
 
You collect data  which is presented in this graph
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http://wwwold.mpiwg-berlin.mpg.de/projects/DeptII_Sepkoski_Extinction/Extinction.jpg
 
http://wwwold.mpiwg-berlin.mpg.de/projects/DeptII_Sepkoski_Extinction/Extinction.jpg
 
Here is the source of the data
 
Here is the source of the data
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What do you think? What questions do you have?
 
What do you think? What questions do you have?
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By the end of this class I hope that the first question you have is what is the error or mistakes in the data? Maybe it's just noise. How do you check if it’s noise? REPEAT the expt. However, you can’t do that in this case. How do determine the error? Use multiple ways of measuring the data to check it. How well you know the assumptions in each measurement method and their validity will determine your estimation of the error.
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By the end of this class I hope that the first question you have is what is the error in the data? Maybe it's just noise. How do you check if it’s noise? REPEAT the expt. However, you can’t do that in this case. How do determine the error? Use multiple ways of measuring the data to check it. How well you know the assumptions in each measurement method and their validity will determine your estimation of the error.  
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Assume that these extinction events are valid. What model is supported by the data? Periodic volcanic eruptions, asteroids that intersects the Earth's orbit periodically due to a Nemesis star or planet X orbiting every 27 million years, dark matter, etc. Would these models be accepted compared with the sacrifice model?
 
Assume that these extinction events are valid. What model is supported by the data? Periodic volcanic eruptions, asteroids that intersects the Earth's orbit periodically due to a Nemesis star or planet X orbiting every 27 million years, dark matter, etc. Would these models be accepted compared with the sacrifice model?
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Some people think the data is valid but that no model is appropriate because the random events lead to this distribution. Then if you were to repeat the expt it would not look the same. This again focuses on our nature to come up with models of what we observe even if the data is random.
 
Some people think the data is valid but that no model is appropriate because the random events lead to this distribution. Then if you were to repeat the expt it would not look the same. This again focuses on our nature to come up with models of what we observe even if the data is random.
  
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'''Example; Value Proposition A (critical/analytical thinking): RC decay part (a)'''
  
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3.) Error analysis (see section 3.7 of Baird)
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-When asked to set up the circuit you don’t start plugging components into the circuit board. You construct a circuit diagram and critically analyze it first. Someone observing you would conclude that you’re an analytic thinker.
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-In processing your RC data to eliminate 60 Hz noise you integrate the voltage across the capacitor. What complication does that generate?
  
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-Working eqn using e/m as an example.
 
  
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-Add errors in quadrature. Review the focal length example.
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'''Example; Value Proposition A (critical/analytical thinking): RC lab part (b)'''
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The scientific method involves testing if the data support a model. There are two ways to test the model: (1) The model in the RC lab is exponential decay. How would you test only if the decay is exponential without concern for the values of R and C? Semi-log plot.
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(2) How would errors in R can C affect the determination of the time constant? Error in slope = Sqrt[ (partial slope/particle R error R)^2 + (particle slope/particle C error C)^2]. Make a table of 1/RC, error 1/RC, R, error R, C, error C. Make a table of slope calculated (plug in R and C), error in slope calculated (from quadrature),  slope from data, R, error in R, C, error in C. Is the slope calculated the same as the data slope within error? You will learn how to get an estimate of the error in the slope just from the data from a least squares procedure.
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'''Example; Value Proposition C (Personal development): RC lab'''
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You don’t notice that your lab partner sticks a wire on the proto-board shorting the power supply. In diagnosing your circuit the lab instructor find the short. This mistake makes you look like you don’t know much about electronics. How do you react? Does that reaction help the two of you to work together on the final report?
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'''Error analysis (see section 3.7 of Baird) Value Proposition B, Content:'''
  
 
-Do error of the product of two quantities.  Z = xy. Use percent error.
 
-Do error of the product of two quantities.  Z = xy. Use percent error.
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-Do error of the sum Z = x + y
 
-Do error of the sum Z = x + y
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-What’s the error in the mean value of n voltage measurements? Vmean =Sum[Vi,{i,1,n}]/n. This is a sum. How does error in this sum depend on errors in the individual terms of the sum.
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-What’s the error in the mean value of n voltage measurements? Vmean =Sum[Vi,{i,1,n}]/n. This is a sum. How does error in this sum depend on errors in the individual terms of the sum.  
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Use the heuristic that to understand need to simplify the notation: use (V1+V2+V3+  )/n rather than sum notation. Assume dV1 = dV2 = dV3 . . . and the error in dV3/n is just due to dV3 and not n since n is an integer with no error.
 
Use the heuristic that to understand need to simplify the notation: use (V1+V2+V3+  )/n rather than sum notation. Assume dV1 = dV2 = dV3 . . . and the error in dV3/n is just due to dV3 and not n since n is an integer with no error.
  
 
delVmean=Sum[dVmean/dVi delVi, {i,1,n}]/n
 
delVmean=Sum[dVmean/dVi delVi, {i,1,n}]/n
 
where
 
where
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dVmean/dV1 = 1/n,  dVmean/dV2=1/n , etc.  
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dVmean/dV1 = 1/n,  dVmean/dV2=1/n , etc.
 
So, delVmean=Sum[delVi/n, {i,1,n}] . Assume delVi = delV is constant, that is every measurement of Vi has the same error. Adding the errors in quadrature we get   
 
So, delVmean=Sum[delVi/n, {i,1,n}] . Assume delVi = delV is constant, that is every measurement of Vi has the same error. Adding the errors in quadrature we get   
 
delV=Sqrt[Sum[(delV/n)^2, {i,1,n}] but summing identical terms n times give a factor of n so
 
delV=Sqrt[Sum[(delV/n)^2, {i,1,n}] but summing identical terms n times give a factor of n so
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The error in the mean value is the error in an individual measurement divided by the square root of the number of measurements.
 
The error in the mean value is the error in an individual measurement divided by the square root of the number of measurements.
  
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4.) Data visualization
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Mean and stnd dev (see section 2.4 Baird)              
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How do you determine errors in a measurement?
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You want to devise detectors to measure the energy of high energy particles (gamma rays etc).  
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REPEAT the measurement! Voltmeter may give 6 sig figs but only 3 repeat. Don’t take only the first measurement.
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-The first is an ionization device (charged cylindrical cap) which outputs a voltage spike (ac coupled) when a gamma rays creates a spark (avalanche breakdown) in the device. Sketch the device. Would the voltage output be linearly related to the energy of the incident particle? What model might describe the device? Turns out low energy particles are more likely to ionize the inert gas atoms. The spark is a good indicator that a particle has entered the detector but not of its energy.
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-Next you use a material that emits visible light when the particle traverses it. Any idea how this works? This is like the e/m expt where the electron strikes multiple He atoms, each time exciting the atom which then fluoresces. However, in this case the number of photons emitted is related to the energy of the incident particle. A gamma ray gives its energy to an electron via the Compton effect and this electron travels through the material losing energy. How do you measure this flash of light? Use the photoelectric effect. The light free electrons from a surface and these are made to go through a resistor to measure a voltage. The more photons the more electrons the more voltage = IR.
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The other is a  bolometer. It measures the change in resistance when heat is absorbed. The first detector consisted of two strips of platinum covered with black paint. One was the sensor and the other a calibrator. A difference in resistance between these is measured with a bridge circuit. “By 1880, Langley's bolometer was refined enough to detect thermal radiation from a cow a quarter of a mile away,” (detects differences of 0.00001 C) from wikipedia. How would you make that measurement? (move the cow or put up a reflector for the IR).
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The two devices measure high energy particles from the same sources, each of which emits a different energy particle, with the following tabular results for the detector voltage output. Your assignment is to come up with a way to visualize this data. Talk about sig. Figs. in the output not exceeding the error.
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{| class="detector output"
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|-
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! Particle energy
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! Bolometer output (Volts)
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! Scintillator output (Ohms)
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|-
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| 0.5
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| $2.00 <math>\pm</math> 0.2$
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| 3.00 \pm 0.2
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|-
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| R2C1
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| R2C2
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| R2C3
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|}
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If you graph the two outputs vs particle energy on one graph can see the two are similarly calibration. Are the points on this graph within error. If you graph output 1 on the x-axis vs output 2 on the x-axis you would like it to fit within error a line at 45 degrees. If there is a curve upwards then the two outputs are not proportional. Which detector is more likely to be valid? How do you determine the repeatability (reliable)?
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I repeat the measurement of the lifetime of a light bulb 1000 times and get a Gaussian distribution with mean T and stnd dev
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Tsigma. What happens to the distribution if I measure 10^6 bulbs?
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Show the definition of standard deviation here
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https://en.wikipedia.org/wiki/Standard_deviation
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Note that it depends on sqrt[N-1]. Does this mean the standard deviation gets smaller with N?
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Run the animation to show how the stnd dev does not change with samples.
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http://onlinestatbook.com/stat_sim/sampling_dist/index.html
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Critical thinking comments? (do all measurements behave this way? If there is time dependence due to temperature changes or something else then there is NOT a Gaussian distribution.)
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The derivation for the error in the mean does not use a Gaussian distribution nor does it mention the standard deviation of the mean. However the two ideas are related.

Latest revision as of 16:38, 16 September 2017


Value proposition for a University: what value do you get and how does that fit into this course?

1.) Learn critical/analytical thinking.

2.) Learn content; how to construct a professional argument that data support a scientific model.

3.) Personal development; “The responsibility for us as teachers is to help our students understand that they must be active participants in the creation of their own character and to insist they do so even in the face of discomfort or adversity.” President of University of Portland. This is a bit like the value proposition of insurance being peace of mind (the value is not obvious). The value proposition of an education is character development (responsibility, civility, leadership, tolerance, . .). Here you practice this in group work and class discussions.

http://www.stonybrook.edu/commcms/cas/liberalartseducation.html


I’ll give examples of each point throughout the semester. First let's consider models, which are the foundation of these goals.

Modeling is intrinsic to the way we think.

Besides scientific models this includes heuristics [wikipedia: are simple, efficient rules, learned or hard-coded by evolutionary processes, that have been proposed to explain how people make decisions, come to judgments, and solve problems typically when facing complex problems or incomplete information], use triangles to build a structure. Show examples from (particularly of heuristics in artificial intelligence) http://c2.com/cgi/wiki?HeuristicRule Modeling also involves ways to interpret literature and speech.

Does your model of the way the world works match the data? Does sacrificing people lead to good weather (Mayan model)? Say you collected data which supported this model and tried to publish the data. Why would it be difficult to get it accepted? There is no scientific model of that explains the results. Therefore people would have trouble believing it (they see correlation but no model to cause the effect). We need a model to justify how the world behaves. For example, the blood vapor contains particulates upon which water condenses to form raindrops.

A current controversy involves a propulsion method that doesn’t emit anything. See http://emdrive.com/ There used to be “fringe theory” warnings on this site https://en.wikipedia.org/wiki/RF_resonant_cavity_thruster Why would this idea have trouble being accepted? It helps if there is a model which explains why something happens rather than simply a correlation without a cause. However, the data may support motion but it seems to violate conservation of momentum since the net force on a body is the time rate of change of the total momentum. Since there is no net force there can be no change in total momentum. How do you make an argument that the model is valid? Does that sound like what you would hear in an english class where you are asked to make an argument (both orally and in writing) about an interpretation of a novel. This type of study is the foundation for critical thinking in a liberal arts college.

Example; Value Proposition A (critical/analytical thinking): You collect data which is presented in this graph http://wwwold.mpiwg-berlin.mpg.de/projects/DeptII_Sepkoski_Extinction/Extinction.jpg Here is the source of the data https://www.mpiwg-berlin.mpg.de/en/research/projects/deptii_sepkoski_extinction

What do you think? What questions do you have? By the end of this class I hope that the first question you have is what is the error or mistakes in the data? Maybe it's just noise. How do you check if it’s noise? REPEAT the expt. However, you can’t do that in this case. How do determine the error? Use multiple ways of measuring the data to check it. How well you know the assumptions in each measurement method and their validity will determine your estimation of the error.

Assume that these extinction events are valid. What model is supported by the data? Periodic volcanic eruptions, asteroids that intersects the Earth's orbit periodically due to a Nemesis star or planet X orbiting every 27 million years, dark matter, etc. Would these models be accepted compared with the sacrifice model?

Some people think the data is valid but that no model is appropriate because the random events lead to this distribution. Then if you were to repeat the expt it would not look the same. This again focuses on our nature to come up with models of what we observe even if the data is random.

Example; Value Proposition A (critical/analytical thinking): RC decay part (a)

-When asked to set up the circuit you don’t start plugging components into the circuit board. You construct a circuit diagram and critically analyze it first. Someone observing you would conclude that you’re an analytic thinker. -In processing your RC data to eliminate 60 Hz noise you integrate the voltage across the capacitor. What complication does that generate?


Example; Value Proposition A (critical/analytical thinking): RC lab part (b)

The scientific method involves testing if the data support a model. There are two ways to test the model: (1) The model in the RC lab is exponential decay. How would you test only if the decay is exponential without concern for the values of R and C? Semi-log plot. (2) How would errors in R can C affect the determination of the time constant? Error in slope = Sqrt[ (partial slope/particle R error R)^2 + (particle slope/particle C error C)^2]. Make a table of 1/RC, error 1/RC, R, error R, C, error C. Make a table of slope calculated (plug in R and C), error in slope calculated (from quadrature), slope from data, R, error in R, C, error in C. Is the slope calculated the same as the data slope within error? You will learn how to get an estimate of the error in the slope just from the data from a least squares procedure.


Example; Value Proposition C (Personal development): RC lab

You don’t notice that your lab partner sticks a wire on the proto-board shorting the power supply. In diagnosing your circuit the lab instructor find the short. This mistake makes you look like you don’t know much about electronics. How do you react? Does that reaction help the two of you to work together on the final report?


Error analysis (see section 3.7 of Baird) Value Proposition B, Content:

-Do error of the product of two quantities. Z = xy. Use percent error. -Do error of the sum Z = x + y -What’s the error in the mean value of n voltage measurements? Vmean =Sum[Vi,{i,1,n}]/n. This is a sum. How does error in this sum depend on errors in the individual terms of the sum. Use the heuristic that to understand need to simplify the notation: use (V1+V2+V3+ )/n rather than sum notation. Assume dV1 = dV2 = dV3 . . . and the error in dV3/n is just due to dV3 and not n since n is an integer with no error.

delVmean=Sum[dVmean/dVi delVi, {i,1,n}]/n where dVmean/dV1 = 1/n, dVmean/dV2=1/n , etc. So, delVmean=Sum[delVi/n, {i,1,n}] . Assume delVi = delV is constant, that is every measurement of Vi has the same error. Adding the errors in quadrature we get delV=Sqrt[Sum[(delV/n)^2, {i,1,n}] but summing identical terms n times give a factor of n so delV=Sqrt[(delV)^2/n] = delV/Sqrt[n].

The error in the mean value is the error in an individual measurement divided by the square root of the number of measurements.

Mean and stnd dev (see section 2.4 Baird) How do you determine errors in a measurement? REPEAT the measurement! Voltmeter may give 6 sig figs but only 3 repeat. Don’t take only the first measurement.

I repeat the measurement of the lifetime of a light bulb 1000 times and get a Gaussian distribution with mean T and stnd dev Tsigma. What happens to the distribution if I measure 10^6 bulbs? Show the definition of standard deviation here https://en.wikipedia.org/wiki/Standard_deviation Note that it depends on sqrt[N-1]. Does this mean the standard deviation gets smaller with N? Run the animation to show how the stnd dev does not change with samples. http://onlinestatbook.com/stat_sim/sampling_dist/index.html Critical thinking comments? (do all measurements behave this way? If there is time dependence due to temperature changes or something else then there is NOT a Gaussian distribution.) The derivation for the error in the mean does not use a Gaussian distribution nor does it mention the standard deviation of the mean. However the two ideas are related.

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