Some people can hear with their eyes. It’s called synesthesia, and it happens when the different sensory systems get crossed. A new app, Sonified, lets you experience it, as the video below demonstrates.
(via The Dish)
Citing this post: Urbano, L., 2012. Hearing Color, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.
That would at least be our address if we were on the “extended” Manhattan Street Grid, according to this website.
The extended Manhattan street Grid.
Just goes to show that everything is relative.
Citing this post: Urbano, L., 2011. Corner of 4911 Avenue and S. 9938 Street, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.
A series of still photographs of a projectile (soccer ball) in motion were used to determine the equation for the height of the ball (h(t) = 4.9 t2 + 14.2 t + 1.25), the initial velocity of the ball (14.2 m), the maximum height of the ball (11.6 m), and the time between each photograph (0.41 s). The problem was solved numerically using MS Excel’s Solver function. There are much easier ways of doing this, which we did not do.
Figure 1. Calculated elevation of the soccer ball after launch.
Figure 2. Animation of the soccer ball projectile.
One of physics lab assignments I gave my students was to see if students could use a camera to capture a sequence of images of a projectile, plot the elevation of the projectile from the photographs, determine the constants in the parabolic equation for the height of the projectile, and, in so doing, determine the velocity at which the projectile was launched.
I offered my old, digital Pentax SLR that can take up to seven pictures in quick sequence and be set to fully manual. A digital video camera with a detailed timestamp would have been ideal, but we did not have one available at the time.
Now the easy way of getting the velocity data would be to estimate the heights (h) of the ball from the image using some sort of known reference (in this case the whiteboard), and determine the time between each photograph (Δt) by photographing a stopwatch using the same shutterspeed settings. After all, the average velocity of the ball between two images would be:
The reference whiteboard is four feet tall (1.22 m) in real life, but 51 pixels tall in the image. Using this ratio (i.e. 1.22 m = 51 px) we can convert the heights of the ball from pixels to meters:
Table 1. Table showing the conversion of the height of the ball in pixels to elevation (in meters).
Unfortunately, I think my students forgot to do the pictures of the stopwatch to get Δt, the time between each photograph. Since the lab reports are due on Monday, and it’s the weekend now I’m curious to see what they come up with.
However, I was wondering if they could use just the elevation data to back out the Δt. So I gave it a try myself. Even the easiest way of solving this problem is not trivial, in fact, I ended up resorting to Excel’s iterative solver to find the answers. While this procedure probably goes a little beyond what I expect from the typical high school physics student, more advanced students who are taking calculus might benefit.
We took the reference whiteboard (1.21 m tall), a soccer ball, and the camera outside. The whiteboard was leant vertically against the post of the soccer goal. The ball was thrown vertically by a student standing next to the whiteboard (see Figure 1) while pictures were taken. The camera’s shutterspeed was 1/250th of a second. The distance from the camera to the person throwing the ball (and to the whiteboard) were not measured.
The procedure was repeated several times, but only one trail was used in this analysis.
The images were loaded onto a computer, and the program GIMP was used to determine the distance, in pixels, from the ground to the projectile. The size of the reference whiteboard, in pixels, was used to calculate the height of the soccer ball in meters.
The elevations measured off the photographs were then used to calculate the release velocity, time between snapshots, and maximum height of the ball.
I started with the fact that once the ball is released, the only force acting on it is the force of gravity. Since the mass of the ball does not change we only have to consider the acceleration due to gravity (-9.8 m/s2). I also neglect air resistance to make things easier.
Start with the fact that, acceleration is the rate of change of velocity with time. You can write it in the differential form:
so we integrate with respect to time to get the equation for velocity as a function of time:
where c is an unknown constant. What we do know though, is that at the beginning, when the ball is just launched, time is zero (t = 0) so cv becomes the initial velocity (v0) at which the ball is thrown:
at t = 0, v(0) = v0:
So our velocity equation becomes:
Now since we know that velocity is the rate of change of distance (in this case height) with time:
so we integrate again to find the height equation:
Similar to what we did with the velocity equation, to find the new constant c we consider what happens at the start time, when the ball is launched, and t = 0 and h(0) = h0;
so:
The constant is equal to the initial height of the ball — the height of the ball when it’s thrown. So we end up with the final equation:
At this point, although we have an equation for the height of the ball, we don’t know the initial velocity (v0), nor do we know the initial height of the ball when it’s released (h0). And we still don’t know the time when the ball is at each position.
With that many unknowns we’d need the same number of independent equations to be able to solve for them all. It may be possible, but instead of analytically solving the equations I opted to take a numerical approach, and use Excel’s Solver function.
I started by setting up the equations to calculate the height of the ball at six different times to correspond with our six height measurements. It was necessary therefore to create a set of variables:
By defining the time between each picture as dt, we can write the time that each picture was taken in terms of the time of the initial picture (t1) and dt. After all the second picture would have been taken dt seconds after the first for a total time of:
similarly for all the pictures:
Table 2. Table of expressions giving the time when each of the six photos were taken.
Now I set up an Excel spreadsheet and gave all the unknown variable values and initial value of 1:
Table 3. Table in Excel for determining the height of a projectile. All of the unknown variables' values are highlighted in green and have been given an initial value of 1.
Now I just had to run Solver and tell it that I wanted the Total Residual, which gives the difference between the h(1) equation’s values for height and the actual, measured values, to be as close to zero as possible. A perfect fit of the equation to the data would have a total residual of one, but that’s not possible when you’re dealing with real data.
Table 4. Parameters set in Solver to determine the values of the unknown constants.
Even so, I had to goose Solver a bit for it to produce reasonable numbers. I put in a few constraints:
I ran the Solver a few times, and had to reset dt to 0.5 at one point when it had become zero, but the final result looked remarkably good: the total difference between the modeled line and the actual data was only 0.113 meters.
Table 5. Solver's solution for the unknown constants in the height equation.
So we found that:
Which makes the height equation:
Using these constants in the height equation, we could see how good fit the height equation was to the data:
Figure 3. Graph comparing the modeled heights (from the h(t) equation) to the actual data.
Finally, the maximum height of the ball can be read off the graph, but it can also be determined using the equation for the height of the ball:
We know that the maximum height is reached when the ball stops moving upward and starts to descend. At that point, the vertical velocity of the ball is zero. Since the velocity of the ball is the rate of change of height (
since we’ve determined that the initial velocity of the ball is 14.2 m/s we get:
when the velocity is zero (v = 0):
which can be solved for t to find that the time the ball reaches it’s maximum height is:
Putting this into the height equation:
gives:
I’m quite happy with the way this project turned out. The fit between the modeled heights (h(t)) and the actual heights was very good.
My primary concern going into the project was that the distortion from the camera lens would make this technique impossible, but that appears not to be a significant problem.
Most of this calculation, including the somewhat tricky numerical solution using Solver could have been avoided if I’d calibrated the camera, simply by pointing it at a stopwatch (using the same shutterspeed as in the experiment) and measuring the time between snapshots. It will therefore be interesting to see if the actual time between shots (dt) is close to the dt of 0.41 seconds calculated by the model.
Finally, as noted above, a video camera with a timestamp would possibly be a more useful technology for this experiment.
It is possible to analyze the projectile path of an object using a series of snapshots, to determine the initial velocity of the projectile, its release height, and the time between snapshots, if you can assume that the time between snapshots is identical. There are, however, much easier methods of solving this problem.
None, but this is where they’d be if I had any.
The Excel spreadsheet where all the calculations were done is here.
Citing this post: Urbano, L., 2011. Projectile Motion, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.
[A]nger … triggers a less systematic and structured approach to the creativity task, and leads to initially higher levels of creativity. … [However] creative performance should decline over time more for angry than for sad people.
– Bass et al (2011): Creative production by angry people peaks early on, decreases over time, and is relatively unstructured
Here are a couple of studies on the interaction between negative emotions and creativity whose implications require some very careful consideration. We want to encourage creativity, but how and at what cost to the student?
Social rejection was associated with greater artistic creativity
– Akinola and Mendes (2011): The Dark Side of Creativity: Biological Vulnerability and Negative Emotions Lead to Greater Artistic Creativity
Anger, it appears, leads to more unstructured thinking, thinking that is more flexible and able to make new connections among different categories of information. However, anger’s creativity boost does not last that long – strong emotions take a toll – and people soon revert back to a more normal baseline.
These results come from an initial study, and there are a lot of unanswered questions. In particular, I wonder just how much anger is useful for this beneficial outcome. I find it hard to believe that too much anger is terrible useful. And, I’m also curious about the negative consequences in terms of group interactions. Brett Ford points out that some studies have found that anger is useful in negotiation, but only when that negotiation is confrontational. Another study found that angry leaders were better at motivating groups of less agreeable people. Conversely, more agreeable people responded better to less angry leaders.
In a scenario study, participants with lower levels of agreeableness responded more favorably to an angry leader, whereas participants with higher levels of agreeableness responded more favorably to a neutral leader.
– Kleef et al. (2010): On Angry Leaders and Agreeable Followers
How Leaders’ Emotions and Followers’ Personalities Shape Motivation and Team Performance
It seems that the ability to project anger may be a useful skill to have in one’s toolbox, given the variety of people we will have to deal with in life.
Modupe Akinola and Wendy Berry Mendes point out that highly creative people tend to introversion, emotional sensitivity and, at the extreme, depression and other mood disorders. Unfortunately:
[M]ood disorders are 8 to 10 times more prevalent in writers and artists than in the general population (Jamison, 1993).
– Akinola and Mendes (2011): The Dark Side of Creativity
On top of the general mood, strong, more transient, activating moods, like anger and happiness, also affect a person’s ability to be creative. Both positive and negative activating moods (the hedonic tone) enhance creativity, but in different ways:
Curiously enough, although creativity is associated with a baseline of sadness and depression, these two are not among the activating moods that can spur the creativity of the moment.
The implications of these studies are complex. I certainly need to think about them a lot more, but it would seem reasonable, or perhaps responsible, to encourage students to carefully monitor their moods and to help them better understand themselves and their behavior. Ultimately, it is probably better if we are able to control how we use our emotions, rather than the other way around.
The pre-frontal lobe, which is responsible for formal thinking, is the part of the brain that can put the brakes on impulsive emotional behavior. It can also, to a degree, modulate how emotions are expressed. As adolescents’ pre-frontal cortex develop, they should be better able to control and use their emotions to their benefit. But to do so, they need to be aware of their emotions and the power of their emotions, which would suggest training in emotional awareness and control.
I’m not aware of any programs or curricula that delve all the way into how to use your emotions proactively, but I’d like to see something that particularly discusses how to use the different activating moods.
Citing this post: Urbano, L., 2011. Creativity, Depression and Anger, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.
Image from the Opte Project.
Andrew Zak Williams asks 30 believers and 30 non-believers why. Their answers do a great job summarizing the major arguments and philosophies of both camps.
Theists assert a number of reasons for their belief: their need for there to be some purpose in the world rather than see the universe as the result of the unguided vagaries of random chance; profound, spiritual experiences in their past; their perception that the beauty of life and the universe must have had some (intelligent) design; and sometimes, an acknowledgment of the need for an element of blind faith.
Atheists, on the other hand, argue the lack of evidence; the often prejudicial, unjust nature of the religions many of them grew up with; and the fact that to recognize one type of religion as correct, often requires its adherents to believe that the others are wrong, leading to the conjecture that none of them are right and they’re all wrong.
Stephen Hawking tries to thread and interesting needle:
I am not claiming there is no God. The scientific account is complete, but it does not predict human behaviour, because there are too many equations to solve.One therefore uses a different model, which can include free will and God.
– Stephen Hawking (2011) in Faith no more (Williams, 2011) in the NewStatesman.
Many adolescents will be encountering these types of questions on their own or through all the bat mitzvah, confirmations and other religious coming-of-age ceremonies adolescents face. Either one of these two articles would be an interesting, if delicate, subject for a Socratic dialogue, especially while studying the history of religions.
[via The Dish]
Citing this post: Urbano, L., 2011. Why I [believe/don't believe] in God, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.
A You are the Ref strip by Paul Trevillion.
Every week, artist Paul Trevillon poses, in text and cartoon form, some truly idiosyncratic situations that might come up in a soccer match in his You are the Ref strip on the Guardian website. Readers get a week to propose their solutions and then referee Keith Hackett give his official answers.
It’s a fascinating series, the subtext of which is that, while there is a lot of minutiae to remember – the actual diameter of a soccer ball is important for one question – the game official is really out there to enforce the spirit of the laws, enabling fair and fluid play to the best of their ability. This is a useful lesson for adolescents who tend toward being extremely literal, and have to work on their abstract thinking skills, especially when they relate to questions of justice. For this reason, I find that when refereeing their games it’s useful to take the time during the game, and afterward in our post-match discussions, to talk about the more controversial calls.
Citing this post: Urbano, L., 2011. The Spirit of the Law, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.
In seeking their identity, adolescents try out a wide variety of different personas. These are often closely associated with changing appearance and style. What I find interesting is how the different styles increasingly cross cultures and other traditional divides (like race). This is evident in Ari Versluis and Ellie Uyttenbroek’s photographic series Exactitudes.
There’s something sad about the loss of local cultural uniqueness to globalization; it’s a bit similar to the feeling you get when you hear about another interesting species becoming extinct. Curiously, however, when Versluis and Uyttenbroek tile together photographs of different people from the same subculture striking identical poses, they not only highlight the similarities between very different people, but also the minute variations that individuals employs to make the subgroup’s “uniform” their own.
26. Preppies - Rotterdam 1999 (from Exactitudes). Girls, "... at Montessori school."
All 128 pictures sets are thought provoking and worth a look. I think they would make useful subjects for students to reflect on (though, warning, there is a little nudity in one of the sets).
(via Brain Pickings)
Citing this post: Urbano, L., 2011. Variations on a Theme, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.
Excerpt from a flow chart on how to have a rational argument by Brandon Scott Gorrell.
Brandon Scott Gorrell has produced a wonderful salvo for our never-ending efforts to promote rational discussion.
Citing this post: Urbano, L., 2011. Lets have a RATIONAL Argument, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.
