Monthly Archives: July 2017

Part II: Mass of the Death Star in Episode IV

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This is the second in a two part post where I calculate the size and mass respectively of the Death Star in Episode IV (DS1).  Estimating the mass will inform discussion about the power source of the station and other energy considerations.

Part II: Mass of DS1

As argued in Part I, I assert that the diameter of DS1 is approximately 60 km based on a self-consistent scale analysis of the station plan schematics as shown during the briefing prior to the Battle of Yavin.

A “realistic” upper limit for the mass is set if the 60 km volume of DS1 was filled with the densest (real, stable) element currently known.  This is osmium with a mass density of 2.2E4 kilograms per cubic meter.  This places the mass at 2.5E18 kg with a surface gravity of 0.05g.  A filling fraction of 10% would then place a “realistic” estimate of the upper limit at 2.5E17 kg.  Other analyses have made similar assessments using futuristic materials with some volume filling-fraction, also putting the mass somewhere around 10^18 kg assuming a radius of 160 km.

In this mass analysis, using information from the available footage from the Battle of Yavin, I find a DS1 mass of roughly 2.8E23 kg, about million times the mass of a “realistic” approximation  Any supporting superstructure would be a small perturbation on this number.  This implies a surface gravity of an astounding 448g.  To account for this, my conclusion is that DS1 has a 40 m radius sphere of (contained) quark-gluon plasma or a 55 m radius quantity of neutronium at its core.  Such materials, if converted to useful energy with an efficiency of 0.1%, would be ample to 1) provide the 2.21E32 J/shot of energy required to destroy a planet as well as 2) serve as a power source for sub-light propulsion.

Details

The approach here uses the information available in the schematics shown during the briefing.  The briefing displays a simulation of the battle along the trench to the exhaust port.  Again, as shown in Part I of this post, the simulation scale is self-consistent with other scales in both the schematic and the actual battle footage.  As shown in Figure 1, the proton torpedo is launched into projectile motion only under the influence of gravity.  It appears to be at rest with respect to the x-wing as it climbs at an angle of about 25 degrees.

Figure 1

Figure 2

From the previous scale analysis in Part I, the distance from the port, d, and height, h, above the the port can be estimated.  They are approximately equal, h = d = 21 meters. The length of the x-wing is L = 12.5 m.  After deployment, the trajectory slightly rises and then falls into the exhaust port as shown in Figure 2.  A straightforward projectile motion calculation gives the formula for the necessary downward acceleration to follow the trajectory of an object under these conditions

a=\frac{2 V_{0}^2}{d}(\frac{h}{d}+\tan{\theta})\cos^2{\theta}\ \ \ \ (1)&s=3

Where t is the launch angle and Vo is the initial horizontal velocity of the projectile.  If we assume for simplicity that the angle \theta = 0 degrees and h = d, the formula simplifies to

a=\frac{2 V_{0}^2}{d}\ \ \ \ (2)&s=3.

From the surface gravity, the mass of can be obtained, assuming Newtonian gravity,

M=\frac{a R^2}{G}\ \ \ \ (3)&s=3.

Here G = 1.67E-11 Nm/kg, the gravitational constant.  For a bombing run, let’s assume the initial speed of the projectile to be the speed of the x-wing coming down the trench.  To estimate the speed, v, of the x-wing, information from the on-board battle computers is used.  In Part I, the length of the trench leading to the exhaust port was estimated to be about x = 4.7 kilometers.  On the battle computers, the number display coincidentally starts counting down from the range of about 47000 (units not displayed).  However, from this connection I will assume that the battle computers are measuring the distance to the launch point in decimeters.  From three battle computer approach edits, shown in Clip 1 below, and using the real time length of the different edits, the speed of an x-wing along the trench is estimated to be about 214 meters/second (481 miles/hour).  This is close to the cruising speed of a typical airliner — exceptionally fast given the operating conditions, but not unphysical.  This gives a realistic 22 seconds for an x-wing to travel down the trench on a bombing run.

Using this speed and the other information, this places the surface gravity of DS1 at about 448 g (where g is the acceleration due to gravity on the surface of the earth).  DS1 would have to have a corresponding mass of 2.4E23 kg to be consistent with this.

However, it is clear that considerable liberty was taken in the above analysis and perhaps too much credibility was given to the battle simulation alone, which does not entirely match the dynamics show in the footage of the battle. Upon inspection of the footage, the proton torpedoes are clearly launched with thrust of their own at a speed greater than that of the x-wing.  A reasonable estimate might put v (torpedo) to be roughly twice the cruising speed of the x-wing.  Moreover, the torpedoes are obviously not launched a mere d = 21 meters from the port (although h = 21 is plausible), rather sufficiently far such that the port is just out of sight in the clip.  Finally, the torpedoes enter the port at an awkward angle and appear to be “sucked in.”  One might argue that there could be a heat seeking capability in the torpedo.  However, this seems unlikely.  If this were the case, then it greatly dilutes the narrative of the battle, which strongly indicates not only that the shot was very difficult but that it required the power of the Force to really be successful.  Clearly, “heat seeking missiles along with the power of the Force” is a less satisfying message.  Indeed, some have speculated that the shot could only have been made by Space Wizards.  These scenarios, and other realistic permutations, are in tension with the simulation shown in the briefing.  Based on different adjustments of the parameters v (torpedo), h, d, and th, one can tune the value of the surface gravity and mass to be just about anything.

However, if we attempt to be consistent with the battle footage, we might assume again that t=0 degrees while d = 210 m, and v (torpedo) = 2 v (x-wing) for propulsion.  The speed of the x-wing can remain the same as before at 214 m/s.  Even with this, the surface gravity will be 18g.  This still leads to a mass over 10000 times larger than the mass of a realistic superstructure.  In this case, a ball of neutronium 18 m in radius could still be contained in the center to account for this mass.

Nevertheless, my analysis is based on the following premise: the simulation indicates that the rebel analysts at least believed, based on the best information available, that a dead drop of a proton torpedo into the port, only under the influence of DS1’s gravity, was at least possible at d = h = 21 meters at the cruising speed of an x-wing flying along the trench under fire nap-of-the-earth.  Any dynamics that occurred in real time under battle conditions would ultimately need to be consistent with this.

The large intrinsic surface acceleration may seem problematic (consider tidal forces or other substantial technological complications).  However, as demonstrated repeatedly in the Star Wars universe, there already exists exquisite technology to manipulate gravity and create the appropriate artificial gravity conditions to accommodate human activities (e.g. within DS1, the x-wings, etc.) under a very wide range of activities (e.g. acceleration to hyperspace, rapid maneuvering of spacecraft, artificial gravity within spacecraft at arbitrary angles, etc.).

 

Implications for such a large mass.  

One hypothesis that would explain such a large mass would be to assume DS1 had, at its core, a substantial quantity of localized neutrinoium or quark-gluon plasma contained as an energy source.  Such a source with high energy density could be used for the purposes of powering a weapon capable of destroying a planet, as an energy source for propulsion, and other support activities.  For example, the destiny of neutronium is about 4E17 kilograms per cubic meter and a quark-gluon plasma is about 1E18 kilograms per cubic meter.  Specifically, a contained sphere of neutronium at the center of the death star of radius 55 meters would account for the calculated mass and surface gravity of DS1.

It has been estimated that approximately 2.4E32 joules of energy would be required to destroy an earth-sized planet.  If 6.7 cubic meters of neutronium (e.g. a sphere of radius 1.88 m) could be converted to useful energy with an efficiency of 0.1%, this would be sufficient to destroy a planet (assuming the supporting technology was in place).  This is using the formula

\Delta E=\epsilon\Delta m c^2\ \ \ \ (4)&s=3

where \Delta E is the useful energy extracted from a mass \Delta m with efficiency \epsilon.  The mass is converted to a volume using the density of the material.

By using the work-energy theorem, the energy required to accelerate DS1 to an arbitrary speed can be estimated.  Assuming the possibility for relativistic motion, it can be shown (left as an exerise for the reader) that the volume V of fuel of density \rho required to accelerate an object of mass M to a light-speed fraction \beta at efficiency \epsilon is given by

V=\frac{1}{\sqrt{1-\beta^2}}\left(\frac{M}{\epsilon\rho}\right)\ \ \ \ (5)&s=3.

This does not account for the loss of mass as the fuel is used, so represents an upper limit.  For example, to accelerate DS1 with M = 2.4E23 kg from rest to 0.1% the speed of light (0.001 c) would require about 296 cubic meters of neutronium (a sphere of radius 4.1 m).

From this, one concludes that the propulsion system may be the largest energy consideration rather than the primary weapon.  For example, consider DS1 enters our solar system from hyperspace (whose energetics are not considered here) and found itself near the orbit of mars.  It would take two days for it to travel to earth at 0.001 c.

 

Part I: Size of the Death Star in Episode IV

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This is the first in a two part post where I calculate the size and mass respectively of the Death Star in Episode IV (DS1).  At the end of Part II I will discuss thoughts about the energy source of DS1.

Part I: Size of DS1

Conventional wisdom from multiple sources places the size of DS1 to about 100-160 km in diameter.  Based on an analysis of the station’s plans acquired by the Rebels, I estimate that the diameter of DS1 is 60 kilometers, not 100 km to 160 km.  To bolster the case, this scale is compared to other scales for self-consistency, such as the width of the trench leading to the exhaust port in the Battle of Yavin. Part II of the post will focus on the mass of DS1 using related methods.

To estimate the size of DS1, I will begin with the given length scale of the exhaust port w = 2 m.  This information was provided in the briefing prior to the Battle of Yavin where the battle strategy and DS1 schematics are presented.  This scale, when applied to Figure 1, is consistent with the accepted length of an x-wing L = 12.5 m.  I assume that the x-wing has an equal wingspan (there does not seem to be consistent values available).  I am also assuming that the “small, one-man fighter” referred to in the briefing is an x-wing, not a y-wing.  The x-wing is a smaller, newer model than the y-wing and it is natural to take that as the template.  The self-consistent length scales of w and L will establish the length calibration for the rest of the analysis.

Figure 1: A close up view of the exhaust port chamber during final phase of the bombing run.  The port width is given as w = 2 m.  The length of the x-wing is L = 12.5 m.  The forward hole, of length l, is then determined to be about 10 m.

From this, I extract the length of the smaller forward hole in Figure 1 to be approximately l = 10 m.

Figure 2: As the plans zoom out, a larger view of the exhaust port chamber of width t = 186 m.  The first hole is shown with width l = 10 m.  The scale of width l was determined based on information in Figure 1.  The width of t was determined based on the scale of l.

Using l as a calibration, this establishes the exhaust port chamber in Figure 2 to be approximately t = 186 m.

In Figure 3a and Figure 3b, circles of different radii were overlaid on the battle plans until a good match for the radius was established.  Care was taken to have the sphere’s osculate the given curvature and to center the radial line down the exhaust conduit.  From here, the size of the exhaust port chamber, of width t, was used as a calibration to approximate the diameter of DS1 as D = 60 km (red).  Several other circles are show in Figure 3 to demonstrate that this estimation is sensible: 160 km (purple), 100 km (black), and 30 km (blue).  It is clear that a diameter of 160 km is definitely not consistent with station’s schematics.  A diameter of 100 km is not wildly off, but is clearly systematically large across the range over the given arc length.  30 km is clearly too small.

While a diameter of 60 km may seem modest in comparison to the previously estimated 100 km to 160 km range, an appropriately scaled image of New York City is overlaid in Figure 4 to illustrate the magnitude of this systems in real-world terms; even a sphere of 60 km (red) is an obscenely large space station, considering this is only the diameter — more than adequate to remain consistentwith existing canon.  The size of the main ring of the LHC (8.6 km) is overlaid in light blue, also for scale.

Figure 3a (to the right of the exhaust port chamber): As the plans zoom out further, the exhaust port chamber of width t = 186 m is shown with the curvature of DS1 (the square blob is the proton torpedo that has entered the port).  The scale of t was determined based on information in Figure 2.  Several circles with calibrated diameters based on the scales set in Figures 1 and 2 are shown.  The 60 km diameter circle in red is arguably the best match to the curvature.  Care was taken to match the point of contact of the circles to a common central location along the radial port.

Figure 3b (to the left of the exhaust port chamber): The same idea as Figure 3a.  The 60 km diameter is still arguably the best match, although is a little shy on this side. The 100 km diameter, the next best candidate, is shooting higher than the 60 km is shooting low. Since an exact mathematical fit wasn’t performed, the expected radius is probably a bit higher than 60 km, but significantly lower than 100 km.

 

 

Figure 4: A 60 km diameter circle in red (with yellow diameter indicator) shown overlaid on a Google Earth image of the greater New York City region.  The blue ring is an overlay of the scale of the Large Hadron Collider at CERN (about 8.5 km in diameter) — note the blue ring is not a scaled representation of the main weapon!  The main message here is that a 60 km station, although smaller than the accepted 100-150 km, is still freakin’ HUGE.  At this scale, there is only a rather modest indication of the massive urban infrastructure associated with New York City.

As another check on self-consistency, the diameter D is then used to calibrate the successive zooms on the station schematics, as shown in Figures 5 and 6.  The length B = 10 km is the width of the zoom patch from Figure 5, X = 4.7 km is the length of the trench run, and b = 134 m is the width of one trench sector. From Figure 6, the width of the trench is estimated to be b’ = 60 m, able to accommodate roughly five x-wing fighters lined wingtip-to-wingtip.  This indicates that the zoom factor is about 1000x in the briefing.

Figure 7 is a busy plot.  It overlays several accurately scaled images over the 60 m trench, shown with two parallel red lines, to reinforce plausibility.  Starting from the top: an airport runway with a 737 ready for takeoff (wingspan 34 m); a 100 m-wide yellow calibration line; a 60 m-wide yellow calibration line; the widths of an x-wing (green, Wx = 12.5 m, where I’ve assumed the wingspan is about the same as the length — there does not seem to be a consensus online; I’ve seen the value quoted to be 10.9 m, but it isn’t well-sourced) and tie fighter (red, 6.34 m); and a scaled image from footage of two x-wings flying in formation, with a yellow 60 m calibration line as well as a calibrated green arrow placed over the nearer one to indicate 12.5 m.  As predicted, about five x-wings could fit across based on the still image.  Also from this, the depth of the trench is estimated to also be 60 m.  The scales are all quite reasonable and consistent. It is worth noting that if the station were 100 km, the next possible sensible fit to the arc length in Figure 3, the width of the trench would be about 100 m, twice the current scale.  This would not be consistent with either the visuals from the battle footage or the airport runway scales.

In short, while there is certainly worthy critique of this work, I argue that, after a reasonably careful analysis of the stolen plans for DS1, all scales paint a self-consistent picture that the diameter of DS1 is very close to 60 km.

Figure 5: A zoom-out of DS1 in the briefing based on the stolen battle plans.  D = 60 km is the diameter and B = 10 km is the width of the patch in the region of interest near the exhaust port.

Figure 6: A zoom in in the region of interest patch near the exhaust port channel (see Figure 5) with B = 10 km.  the channel itself is about X = 4.7 km long.  The width of the channel is about b = 134 m.  Inset is a further zoom of the insertion point along the channel.  Width of the channel itself is about b’ = 60 m.

Figure 7: A zoom of the insertion point along the channel for the bombing run.  Several elements are overplayed for a sense of scale and for consistency comparisons.  The red parallel lines represent the left and right edges of the channel.  From the top of the figure is a 737 with a wing span of 34 m.  The 737 is on a runway (at SFO).  Down from the 737 is a  yellow line that represents 100 m.  This would be the width of the channel if D = 100 km, which is clearly much too large based on the battle plans.  The next horizontal yellow arrow is the 60 m width based on the scales assumed with D = 60 m.  Next down, embedded in the vertical lines of the runway: a green block representing the width of an x-wing and a red block representing the width of a tie fighter.  Finally, at the bottom is a shot from the battle footage.  It has been scaled so the edges of the walls match the width of the channel (shown as a horizontal yellow arrow).  The width of the near x-wing is shown with a green horizontal arrow, which matches the expected scale of an x-wing.

 

How Do I Learn New Things?

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As an educator, I confront the two questions daily in the context of higher education:

  • how do students learn?
  • what is the role of teachers in the learning process?

There is a vast literature on this and entire academic fields of study devoted to these two questions.

Putting aside this ocean of work done by trained professionals, here I’d like to reflect on how I believe I learn new things.  It is an ongoing project for me to apply this to my own teaching.  However, this isn’t about my teaching style, but a meditation on my own internal modes of learning.

The main bullet points would be:

  • I have to want to learn and be engaged
  • I have to have a simple conceptual foothold to get me started
  • I need to see lots of examples, practice them myself, and obtain rapid feedback
  • I need to have some modest stress
  • I need to apply the learning repeatedly over long periods
  • I need to accept that sustained learning requires multiple exposures
  • I have to memorize key ideas and concepts
  • I need to develop an internal model

I have to want to learn a topic.

Learning a new thing I want to learn can be challenging.  However, it is perhaps not surprising that learning a new thing I don’t want to learn is really, really hard.  My strategy: If there is a topic that I’m being “forced” to learn (e.g. some kind of required training), I pretend I want to learn it.  Like many undergraduates, I had to take many classes (usually General Education courses) that I really didn’t want to take.  But once enrolled and attending, I made every effort to try and learn the new topic as if I wanted to learn it.  This shift in attitude made all the difference in my enjoyment of the course and my ability to learn the content.  Eventually, the sentiment becomes genuine and one really does want to learn the new topic.  This happened to me during an American History class in my senior year of college.  I ended up having to take it based on the GE options available.  But I kicked into this mode I described and really ended up enjoying it.  Another more recent example are these State-mandated sexual harassment sensitivity trainings we must do every couple years.  They aren’t exactly convenient to do and can be much longer to take than you expect.  It is natural to start resenting them.  However, by popping into my “pretend like I want to learn this” mode, they actually become quite interesting and informative.

I have to be engaged in the learning process.

Engagement strategies come in several forms for me:

  • Paying attention
  • Taking copious notes and drawing pictures
  • Making connections between ideas and to things I already know
  • Asking questions
  • Reviewing and repeating the content
  • Memorizing key elements

Here’s one strategy I use.  I don’t just asking questions as they come up, but actually actively think of questions to ask.  That is, even if I don’t think I have questions I still think of some to ask and write them all down in my notes with a “Q*” (circled) in the margin.  By doing this, with feedback, I learn what a “good” question is for a given topic and what a “silly” question is.  The idea that “there is no such thing as a bad question” is simply incorrect.  There are “good” questions and “bad” questions.  However, part of learning a new topic is to learn what the good and bad questions are.  This means asking lots of bad questions.  A better way of turning around that education trope would be “you will ask bad questions when you are learning something new, and that’s ok, even encouraged.”  To a point.  There is a pivot where asking lots questions becomes an attention-seeking exercise and wastes other people’s time, particularly in a classroom setting.  So there is a balance.  Sometimes just writing the question down and seeing if the education process answers it naturally is the best thing.

In contrast to some common active learning activities in modern pedagogy, I don’t usually benefit from talking to others who are also learning the topic (e.g. peer instruction, think-pair-share, etc.).  That activity is helpful for morale (e.g. realizing others are confused too), but it doesn’t seem to help with my learning.  What tends to happen is that we reinforce each others’ misconceptions and walk away thinking we know more than we do.  It can also reinforce a sense that “we are all confused, so the instructor must be screwing up.”  Talking with an instructor directly is a different matter and that can be very helpful.

I have to find an intellectual or conceptual foothold in the topic.

I have to get an early confidence boost by feeling like I understand one little, tiny thing then building on it.  My own strategy is finding analogies with things I already understand, but this has to be done delicately.  One bad analogy can set the learning process back.  This tiny thing is often a weird, special case of some concept.   What works as a foothold for me isn’t always easy to anticipate.   Frequently, it is an example that an expert would almost feel bad presenting because it doesn’t portray the entire picture and is too simplified.  It might even be something an instructor would regard as so self-evident as to not even be worth mentioning.  It can be a vapor-thin analogy or some very simple way to appreciate some concept.  It can sometimes be in the form of understanding the cultural landscape of a topic: “experts think of this idea in this way,” providing a heuristic, bird’s eye view of the concept.  Connecting back to the memorization and repetition theme above, it can mean simply knowing what some new vocabulary word means and how to use it in a sentence!  Yes, that basic!

With a foothold, even if somewhat trivial, the seeds of understanding start to bloom. Note: One can’t stick to the simple, heuristic version forever, but a foothold is essential for me to start.

I have to see a lot of examples then be able to try it myself with rapid feedback.

Coupled to the foothold is the well-crafted example.  My strategy is to seek such examples.  A few completely worked examples that build in complexity are really important to me as I learn new things.  It can take a rather abstract idea and solidify it very quickly.  Yes, the understanding gleaned from an example may be superficial by the standards of an expert, but for me-as-the-student these baby steps are super important.  After seeing a few examples, I need to try it myself then get instant feedback about how I did.  This procedure of seeing a well-crafted example, trying it myself, then getting feedback basically needs to be repeated in some form or another.

I have to have a learning context that has the right balance between stress and leisure.

If my motivation to learn is entirely carefree and leisurely, I’ve found my ability to learn is softened quite a bit.  I might be entertained, but I won’t really learn anything.  My strategy is to come up with a reason to learn something.  Sometimes this isn’t hard because I legitimately have to learn something.  However, even just having a certain personal drive to learn something new can be sufficient to motivate — but there has to be some intensity to the experience, even if internally (“artificially”) generated.  But too much stress is a serious problem.  If I feel that I “must” learn it, feel like I’m having to cram for some reason, or that a lot is at stake for some reason, my own thinking gets very clouded and the whole learning process gets damped.

I have to repeat and practice the modest skills I’ve built over a long period of time.

I can’t really learn something on first exposure. For me, sustainable learning and mastery is iterative.  I pretty much have to apply any new knowledge I learn on a regular basis to retain it.  The old “use it or lose it” platitude is basically true.  This isn’t really a surprise.  As a younger student, the half life of knowledge was longer.  However, I think the fact remains that having to use what I learn allows me to retain the “I learned this” status.

Of course, the motivation for learning something new might not be to use it indefinitely.  Having learned something, even in the short term, as a form of entertainment, can be rewarding.  However, having learned something once, just reviewing it can be easy and lets me get back in the groove. Going back to the intellectual foothold point above: these footholds can serve as reentry points.  They are like those little mnemonic boxes people use in their minds;  they are little pointers to topics, rather than the topics themselves.  With a simple conceptual trigger, a wide infrastructure of the original learning can reopen.

I have to (gasp) memorize stuff.

This is considered blasphemy in my field, but to learn something new I have to memorize a lot of patterns and repeatedly use them until I don’t have to think about them.  This is so certain words and patterns become integrated with my thinking and are no longer some external thing I have to keep looking up, which slows things down.  Even if I understand the concepts, having to stop and lookup/review “what does this symbol mean again?”  is very distracting and bogs down ongoing mastery.  This might include formulas, constants, vocabulary, graphics, sounds, etc.  The memorization need not be active, but it might need to be at first.  Yes, I can understand the concept of something without memorizing anything.  But, sadly, just understanding the concept isn’t usually good enough to actually apply something I’m trying to learn.  This flies in the face of the basic philosophy of my own field of study!  Concepts rein supreme!  In fact, it may even fly in the face of actual studies.  But I have a hard time giving this up.  I’m not saying that memorizing is the same as deep learning or “true understanding.” But it is essential for me if I want want to make progress and apply newfound knowledge.

I understand the concept of chess pretty intuitively, but could I really play it competently without knowing (without hesitation!) how the pieces move at a glance?  No way.  But make no mistake, just knowing how the pieces move isn’t mastery either.  However, it is a necessary condition for mastery.

Without memorizing stuff, the learning process can evaporate quickly.  As topics become more advanced beyond just the inspirational introduction, the information builds on itself.  Without simply knowing what the words mean, it all becomes a firehose of vocabulary.  If you want to think like an expert in that field, you have to know what the words and ideas actually are without hesitation.

It is easy to dismiss memorization and repetition as a pathetic crutch for the intellectually weak — this is easy to say if you already have the important things memorized!  But if you are just learning something new, having a few key ideas memorized and internalized (ideas that you might not yet understand) can make the learning go so much faster.

Memorization isn’t understanding, but it can make the process of understanding so much easier!

I have to build an internal model.

This is really the culmination of all of the above.  Eventually, the processes above align with my brain and I reach a certain level of mastery and learning.  I have attained an internal way of thinking of it that maps directly onto the reality of the topic.  It is difficult to describe an “internal model.”  It is neurological.  Internally, it is qualitative and part of my qualia.  Some set of ideas, words, concepts, applications, etc. that seemed unfamiliar are now familiar and can be applied to new things.  It is a curious effect.  The words and symbols that meant nothing last week now have some internal substance that can be manipulated in a meaningful way.  It is quite satisfying.  My ultimate test to see if I’ve learned a topic is to see if I can apply it to something new.  More frequently than not, I’m disappointed in my inability to do so at a level I would like.  It is humbling, but a nice check.  Learning and mastery are ongoing experiences, usually lifelong, and it should be no surprise that innovations and creative problem solving don’t come quickly.

So, that’s a very rough outline about how I tend to learn things.  I’ve certainly forgot many other factors.  Also, I’ve probably overstated and understated some of the ones above.  In any case, hopefully I’ve left you with some food for thought: how do YOU learn new things?