In our final unit of Argument, we learned how to synthesis. In our Internal Investigation, we looked at how people throughout history synthesized in their arguments. For this Action Project, we were asked to investigate the role of a member of the president's cabinet. Then, we had to prove why this position was useful, why the current occupant was a good choice in the eyes of the president, and choose our own nominee for said position.
Sunday, February 26, 2017
Thursday, February 23, 2017
Binary and Hexadecimal Number Systems
In one of my many Workshops at GCE called Math Problem Solving, we were given the freedom to research and follow any challenging math concept we wanted. This workshop was new and very special in the sense that we were given the responsibility to keep track of our own work and go at our own pace. For my topic, I chose to learn about binary and hexadecimal (hex) number systems because I am majoring in computer science next year.
When I first started my research, I chose to learn the basic concepts of binary. This meant learning how the number system is structured, how to convert it to base 10 or hexadecimal, and how to add, subtract, and divide in binary. My most valuable resource was Kahn Academy. They have many videos on binary and hex and different things you can do with them. This video gave me my basic understanding of binary:
Hexadecimal is very easy once you understand the basics of place values in the number system. Another name for hexadecimal is base 16. So, hex uses 16 numbers. However, we are used to the base 10 system where we only have 10 numbers (0,1,2,3,4,5,6,7,8,9). In hex, the numbers we use are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. While this seems confusing, the letters that follow the numbers correspond to numbers that we see in base 10. A=10, B=11, C=12 and so on. Also, since hex operates in powers of 16, the place values are 1s, 16s, 256s, 4096s and so on for infinity. As an example, if we had the number 6A4 in hex, you'd convert it to base 10 as follows: In the 1s place we have 4 so thats 4 ones. In the 16s place we have A so we have eleven 16s. In the 256s place we have 6 so we have six 256s. Add everything together and you get (4x1)+(16x10)+(256x6)=1700. So, 6A4 in base 10 equals 1700.
As for applications of these concepts, I learned in my research that binary is used mostly in computers and are the way that computers carry out their operations. In computer circuits, something is either on or off. Thus, in binary, 1 stands for on and 0 stands for off.
When I first started my research, I chose to learn the basic concepts of binary. This meant learning how the number system is structured, how to convert it to base 10 or hexadecimal, and how to add, subtract, and divide in binary. My most valuable resource was Kahn Academy. They have many videos on binary and hex and different things you can do with them. This video gave me my basic understanding of binary:
Basically, when learning about number systems, the most important thing to look at is place value. If you look at base 10 (what we use), you see that the first place value is 1s, then 10s, then 100s, and so on. It is called base 10 because each place value is a power of ten. The 1s are 10 to the 0th power because that equals 1, the 10s are 10 to the 1st power because that equals 10, the 100s are 10 to the 2nd power because that equals 100, and so on. If we look at the number 251 in base 10. By looking at the place value, you see that we have 2 "100s", 5 "10s", and 1 "1s". Add those together and you get 251.
Both binary and hex are very similar. For binary, the only numbers we can use is 1 or 0. Also, the place value for each place one of those numbers can go changes. Another word for binary is base 2. In base two, each place value is two to the power of a number rather than ten to the power of a number in base ten. So, the first place is still the 1s because 2 to the power of 0 equals 1. But, the next place is the 2s place because 2 to the power of 1 is two. Then, the third place is the 4s place because 2 to the power of 2 is 4. Just like base ten, the places go on and on like this infinitely. Since binary only has the numbers 1 or 0, each place value can only have 1 or none of said value. To look at an example, if we had the number 1011 in binary, you'd covert it to base 10 like so: In the 1s place we have 1 so that is one 1. In the 2s place we have a 1 so that is one 2. In the 4s place we have a 0 so we have zero 4s. In the 8s place we have a 1 so that is one 8. Add that together and you get (1x1)+(1x2)+(0x4)+(1x8)=11. So, 1011 in binary equals 11 in base 10.
As for applications of these concepts, I learned in my research that binary is used mostly in computers and are the way that computers carry out their operations. In computer circuits, something is either on or off. Thus, in binary, 1 stands for on and 0 stands for off.
Designing a Clock
In the third and final unit of Light, Sound, and Time, we learned about Time. Moreover, we studied how gravity affects time and how time and space are related. We also looked at different time telling devices and instruments like pendulums and sundials. For the math section of the unit, we learned how to figure out longitude and latitude, how to calculate arc length, and how to calculate the period of a pendulum. For our Action Project, we were asked to design a time telling device based off of our research we did on ancient clocks.
For my clock, I combined the main ideas from each unit into one device. The clock I designed uses Light and Sound to communicate the Time. In order to tell the time with light, the device starts dim and gradually increases/decreases the brightness as the day goes on. While when the peak of brightness happens is programmable, it would originally be set to noon to mimic the real sun. In order to tell time with sound, a constant sound is emitted throughout the day with a increase/decrease in frequency as the day goes on.
Similar the light aspect of the clock, the sound tells time by increasing/decreasing the frequency and can also be programmed to have the peak happen at different times of the day. The program that the device would be set on when it was first turned on would be to start emitting a sound with a frequency of 150 Hz at 12am. For 12 hours until noon, the sound would increase in frequency at a rate of 0.4861 Hz per minute. Once it hits the peak of 500 Hz it would start to decrease at the same rate until it hit 12am again to repeat the cycle. Also, the volume is adjustable and comes with the option to toggle it on and off so the sound is not bothersome.
Like we learned in unit two, the frequency of the sound wave is tied to the pitch of the sound. The higher the frequency of the wave, the higher the pitch. Also, we used the equation 340.29 m/s (speed of sound)= wavelength x frequency. If we wanted to test this equation, we could look at the lowest frequency of the clock (150 Hz) and find its wavelength by dividing the speed of sound by 150 Hz. So, 340.29/150= 22.686. The wavelength of a wave with a frequency of 150 Hz is 22.686 m.
Primarily this clock was made to be a cool and new way to tell time. However, it also allows people who are either blind or deaf to see or hear time. People who need this device to tell time are more likely to buy it so that is why it was designed with those people in mind. But, there is no limit on who can enjoy the device. Also, because there is the option to program the cycle of the sound and light, the user can make it so they wake up to a soothing dim light and a low but relaxing tone.
The idea of using light to tell time is not new. The most common example of how ancient civilizations practiced this is the sundial. The earliest record of the use of the sundial goes all the way back to ancient Egypt. To tell time, the sundial relies on the sun's change in position in the earth's sky. As time goes by, the shadow casted by gnomon (the part in the middle of the sundial that sticks upward) gets moved around the face of the sundial. To read the time, people just see where the tip of the shadow is casted around the numbers on the face (just like a traditional analog clock). My clock is similar to this old time invention because of its use of light. However, my design is in no way an improvement of this ancient clock. The sundial would be a way more accurate way to tell time than my device would be. However, my device was not made to be a precise way of keeping track of time. It was more for a novelty and to help those who cannot see a normal clock.
The measurements of the clock would be approximately 5in Tall x 10in Long x 3 in Wide. Because of this, the volume would be around 150 in^3.
Citations
n.d. Web. 26 Feb. 2017.
For my clock, I combined the main ideas from each unit into one device. The clock I designed uses Light and Sound to communicate the Time. In order to tell the time with light, the device starts dim and gradually increases/decreases the brightness as the day goes on. While when the peak of brightness happens is programmable, it would originally be set to noon to mimic the real sun. In order to tell time with sound, a constant sound is emitted throughout the day with a increase/decrease in frequency as the day goes on.
Similar the light aspect of the clock, the sound tells time by increasing/decreasing the frequency and can also be programmed to have the peak happen at different times of the day. The program that the device would be set on when it was first turned on would be to start emitting a sound with a frequency of 150 Hz at 12am. For 12 hours until noon, the sound would increase in frequency at a rate of 0.4861 Hz per minute. Once it hits the peak of 500 Hz it would start to decrease at the same rate until it hit 12am again to repeat the cycle. Also, the volume is adjustable and comes with the option to toggle it on and off so the sound is not bothersome.
Like we learned in unit two, the frequency of the sound wave is tied to the pitch of the sound. The higher the frequency of the wave, the higher the pitch. Also, we used the equation 340.29 m/s (speed of sound)= wavelength x frequency. If we wanted to test this equation, we could look at the lowest frequency of the clock (150 Hz) and find its wavelength by dividing the speed of sound by 150 Hz. So, 340.29/150= 22.686. The wavelength of a wave with a frequency of 150 Hz is 22.686 m.
Primarily this clock was made to be a cool and new way to tell time. However, it also allows people who are either blind or deaf to see or hear time. People who need this device to tell time are more likely to buy it so that is why it was designed with those people in mind. But, there is no limit on who can enjoy the device. Also, because there is the option to program the cycle of the sound and light, the user can make it so they wake up to a soothing dim light and a low but relaxing tone.
The idea of using light to tell time is not new. The most common example of how ancient civilizations practiced this is the sundial. The earliest record of the use of the sundial goes all the way back to ancient Egypt. To tell time, the sundial relies on the sun's change in position in the earth's sky. As time goes by, the shadow casted by gnomon (the part in the middle of the sundial that sticks upward) gets moved around the face of the sundial. To read the time, people just see where the tip of the shadow is casted around the numbers on the face (just like a traditional analog clock). My clock is similar to this old time invention because of its use of light. However, my design is in no way an improvement of this ancient clock. The sundial would be a way more accurate way to tell time than my device would be. However, my device was not made to be a precise way of keeping track of time. It was more for a novelty and to help those who cannot see a normal clock.
The measurements of the clock would be approximately 5in Tall x 10in Long x 3 in Wide. Because of this, the volume would be around 150 in^3.
Citations
Marie, Niclas. "When Time Began: The History and Science of Sundials." Time Center. TimeCenter,
Thursday, February 16, 2017
Student Representation
In our second unit of Argument at GCE, we looked at the constitution and how it presented arguments. In our internal investigation, we discussed how the US government works and more importantly, how the different branches of government interact with each other. For our external investigation, we went to a courthouse to watch a trial and visited an Alderman to see how arguments are constructed in court and how elected officials view/use the principals of argument. For this Action Project, we were asked to come up with an amendment for the Code of Conduct. The amendment could change anything that we have the ability to support with logical reasons and solid arguments.
The part of the code I am amending involves who is a part of the disciplinary council. Currently, the person who is supposed to represent the interests of the student is the Director of Counseling. In the Code of Conduct, it says: “The Counselor’s primary role in the Disciplinary Council is to be an advocate for the student and to facilitate conversation between the members of the Disciplinary Council.” There have been reports of unfair treatment and decisions coming out of the council that do not fully take into account the need of the student. Thus, I am proposing an amendment to the Code of Conduct that allows a randomly picked student to be involved in the disciplinary process per student request.
P1: Students have bias to their peers in the decisions made and the opinions put forward.
P2: Students “on trial” has a right to privacy during the disciplinary process.
P3: Having a student on the council would infringe on the student in question’s right to keeping their issues private between them and the staff.
P4: Discipline can only be dispensed by professionals
C: Therefore, students should not have a place on the disciplinary council.
The argument above shows the assumed opinions of the people who originally created the Cod of Conduct. It describes how they would've thought and it helped me to think in their shoes when constructing my argument. In multiple cases, I have heard testimonies from students (former and current) that consistently say that the current student representative/mediator in the disciplinary council does not always represent the perspective of the student. By leaving the student to fend for themselves, they are much less likely to effectively present their side of the story and defend themselves. By adding a student representative, students being processed by the council can now have someone to relate to, feel supported by, and get defended by during the entire process. My changes to the rule are described in the syllogism below:
P1: The student rep does not have to have an empowered position on the council. Only a position that allows the representative to help the student in question explain their side and provide support.
P2: Student privacy and how it’s kept/broken is up to the student in question. It should be up to the student as to whether or not they want a representative and if they should know the details of the situation.
P3: With the point of GCE being a Lab school being constantly brought up, it would be counterintuitive to deny student representation based on the status quo definition of professional.
C: Therefore, students should have a place on the disciplinary council.
With this amendment, students will have more trust in how the staff deals with disciplinary actions. More students would be less resilient of the decisions that come out of the council. A student that supports my amendment by being a co-signer recently said this when discussing the details change: “Having a student on the disciplinary council would broaden the perspectives and make sure all sides of the story is heard and taken into fair account. It would also ensure all decisions made are justified.“ -SG
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| Cartoon jury (2008) bethtgirl
The above image symbolizes my argument because it shows a fair trial by jury and represents the how the disciplinary council could be more fair and just with student representation.
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The part of the code I am amending involves who is a part of the disciplinary council. Currently, the person who is supposed to represent the interests of the student is the Director of Counseling. In the Code of Conduct, it says: “The Counselor’s primary role in the Disciplinary Council is to be an advocate for the student and to facilitate conversation between the members of the Disciplinary Council.” There have been reports of unfair treatment and decisions coming out of the council that do not fully take into account the need of the student. Thus, I am proposing an amendment to the Code of Conduct that allows a randomly picked student to be involved in the disciplinary process per student request.
P1: Students have bias to their peers in the decisions made and the opinions put forward.
P2: Students “on trial” has a right to privacy during the disciplinary process.
P3: Having a student on the council would infringe on the student in question’s right to keeping their issues private between them and the staff.
P4: Discipline can only be dispensed by professionals
C: Therefore, students should not have a place on the disciplinary council.
The argument above shows the assumed opinions of the people who originally created the Cod of Conduct. It describes how they would've thought and it helped me to think in their shoes when constructing my argument. In multiple cases, I have heard testimonies from students (former and current) that consistently say that the current student representative/mediator in the disciplinary council does not always represent the perspective of the student. By leaving the student to fend for themselves, they are much less likely to effectively present their side of the story and defend themselves. By adding a student representative, students being processed by the council can now have someone to relate to, feel supported by, and get defended by during the entire process. My changes to the rule are described in the syllogism below:
P1: The student rep does not have to have an empowered position on the council. Only a position that allows the representative to help the student in question explain their side and provide support.
P2: Student privacy and how it’s kept/broken is up to the student in question. It should be up to the student as to whether or not they want a representative and if they should know the details of the situation.
P3: With the point of GCE being a Lab school being constantly brought up, it would be counterintuitive to deny student representation based on the status quo definition of professional.
C: Therefore, students should have a place on the disciplinary council.
With this amendment, students will have more trust in how the staff deals with disciplinary actions. More students would be less resilient of the decisions that come out of the council. A student that supports my amendment by being a co-signer recently said this when discussing the details change: “Having a student on the disciplinary council would broaden the perspectives and make sure all sides of the story is heard and taken into fair account. It would also ensure all decisions made are justified.“ -SG
Monday, February 6, 2017
Building a Guitar
In the second unit of my STEAM course Light, Sound, and Time, we learned all about sound. By looking sound both in a science perspective and a mathematical perspective, we were able to learn how sound travels and how we can use math to calculate different features of the wave. For our Action Project, we were asked to make a makeshift guitar. By doing this, we could demonstrate both our knowledge of the math behind waves and how sound travels through a guitar.
In our internal investigation, we looked at how sound travels. What we discovered was that sound travels at a speed of ~343 meters per second. We also learned how the amplitude of a sound wave affects the volume and how the frequency and wavelength affect the pitch. In my makeshift guitar, the sound gets created by strumming the sting. Then, the vibrations travel down the length of the string and into the tin can. There, the sound gets amplified and the sound waves go out the open end of the can.
To make my guitar, I used a tin can, a piece of wood, screws, a battery, and a guitar string. The string I used was 0.02 in thick. I first put a hold in my can with a sharp object. Then, I secured the tin can with one screw on each side. To put the string on, I winded the string on one each on each side of the guitar, making sure to pull it tight and run it through the hole in the tin can. You can hear me playing my diddley bow here.
The calculations I did on my guitar were based off of the trapezoid shape that the string makes with the top of the wood. I turned the top half of the trapezoid into a triangle to use trigonometry to find the measurements of some of the angles. The length of the string from he can to the battery was 13.5 in, the length of the wood from the can to the battery was 13 in, the height from the top of the wood to the string by the tin can was 0.5 in, and the height from the top of the wood to the string by the battery was 0.25 in. I used the inverse tangent of angle y to find it's measurement then used that information and my knowledge of triangles to find the rest of the angles. I also found the volume of the tin can by using the formula v=pi*r^2*h and I got 35.5 in^3. Finally, I found the thickness of my string to be 0.02 in.
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| Diddley Bow (2017) LS |
In our internal investigation, we looked at how sound travels. What we discovered was that sound travels at a speed of ~343 meters per second. We also learned how the amplitude of a sound wave affects the volume and how the frequency and wavelength affect the pitch. In my makeshift guitar, the sound gets created by strumming the sting. Then, the vibrations travel down the length of the string and into the tin can. There, the sound gets amplified and the sound waves go out the open end of the can.
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| Harmonics (2017) LS |
To make my guitar, I used a tin can, a piece of wood, screws, a battery, and a guitar string. The string I used was 0.02 in thick. I first put a hold in my can with a sharp object. Then, I secured the tin can with one screw on each side. To put the string on, I winded the string on one each on each side of the guitar, making sure to pull it tight and run it through the hole in the tin can. You can hear me playing my diddley bow here.
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| Diagram (2017) LS |
The calculations I did on my guitar were based off of the trapezoid shape that the string makes with the top of the wood. I turned the top half of the trapezoid into a triangle to use trigonometry to find the measurements of some of the angles. The length of the string from he can to the battery was 13.5 in, the length of the wood from the can to the battery was 13 in, the height from the top of the wood to the string by the tin can was 0.5 in, and the height from the top of the wood to the string by the battery was 0.25 in. I used the inverse tangent of angle y to find it's measurement then used that information and my knowledge of triangles to find the rest of the angles. I also found the volume of the tin can by using the formula v=pi*r^2*h and I got 35.5 in^3. Finally, I found the thickness of my string to be 0.02 in.
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| Calculations (2017) LS |
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