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Akano's Blog
Equation of the Day #4: Measurement Standards
Posted by
Akano Toa of Electricity
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Math/Physics
Nov 25 2012
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91 views
Standard, Meter, Pendulum
If you're building something and want to tell other people how to build it, it's useful to show the dimensions of said something (how big it is) relative to other things that people are familiar with. However, there are very few things in this world that are exactly the same size as other similar things (e.g. not all apples weigh the same or have the same volume). So, some smart people once upon a time decided to make standards of measurement for various properties of matter (which I think we can all agree was a smart decision). I wanted to talk about one of these today: the meter.
The word meter (or metre for those who live across the pond/in Canada) comes from the word for "measure" in Greek/Latin (e.g. speedometers measure speed, pedometers measure steps, &c.), but the meter I'm talking about is the International System (SI) unit of distance. The original definition of the meter was one ten-millionth of the distance from the Earth's equator to the North Pole at sea level (not through the Earth). The first person to measure the circumference of the Earth was the Greek mathematician/astronomer/geographer Eratosthenes (and he was accurate to within 2% of today's known value) circa 240 B.C., so this value was readily calculable in 1791 when this standard was accepted.
In 1668, an alternative standard for the meter was suggested. The meter was suggested to be the length a pendulum needed to be to have a half-period of one second; in other words, the time it took for the pendulum to sweep its full arc from one side to the other had to be one second. The full period of a pendulum is
So, when L = 1 m and T = 2 sec, we get what the acceleration due to gravity, g, should be in meters per second per second (according to this standard of the meter). It turns out that g = pi2 meters per second per second, which is about 9.8696 m/s2. This is very close to the current value, g = 9.80665 m/s2 which are both fairly close to 10. In fact, for quick approximations, physicists will use a g value of ten to get a close guess as to the order of magnitude of some situation.
So, you may be wondering, why is it different nowadays? Well, among a few other changes in the standard meter including using a platinum-iridium alloy bar, we have a new definition of the meter: the speed of light. Since the speed of light in a vacuum is a universal constant (meaning it is the same no matter where you are in the universe, unlike the acceleration due to gravity at a point in space), they decided to make the distance light travels in one second a set number of meters and adjust the meter accordingly. Since the speed of light is 299,792,458 meters per second exactly, this means that we have defined the meter as the distance light travels in 1/299,792,458th of a second.
This is all nice, but it's not a very intuitive number to work with. After all, we humans like multiples of ten (due to having ten fingers and ten toes), so why not make a length measurement of the distance light travels in one billionth (1/1,000,000,000th) of a second (a.k.a. nanosecond)? That seems a bit more intuitive, don't you think? It turns out that a light-nanosecond is about 11.8 inches, or about 1.6% off of the current definition of a foot. In fact, one physicist, David Mermin, suggests redefining the foot to the "phoot," or one light-nanosecond, since it's based off of a universal constant while the current foot is based off the meter by some odd, nonsensical ratio.
The word meter (or metre for those who live across the pond/in Canada) comes from the word for "measure" in Greek/Latin (e.g. speedometers measure speed, pedometers measure steps, &c.), but the meter I'm talking about is the International System (SI) unit of distance. The original definition of the meter was one ten-millionth of the distance from the Earth's equator to the North Pole at sea level (not through the Earth). The first person to measure the circumference of the Earth was the Greek mathematician/astronomer/geographer Eratosthenes (and he was accurate to within 2% of today's known value) circa 240 B.C., so this value was readily calculable in 1791 when this standard was accepted.
In 1668, an alternative standard for the meter was suggested. The meter was suggested to be the length a pendulum needed to be to have a half-period of one second; in other words, the time it took for the pendulum to sweep its full arc from one side to the other had to be one second. The full period of a pendulum is
So, when L = 1 m and T = 2 sec, we get what the acceleration due to gravity, g, should be in meters per second per second (according to this standard of the meter). It turns out that g = pi2 meters per second per second, which is about 9.8696 m/s2. This is very close to the current value, g = 9.80665 m/s2 which are both fairly close to 10. In fact, for quick approximations, physicists will use a g value of ten to get a close guess as to the order of magnitude of some situation.
So, you may be wondering, why is it different nowadays? Well, among a few other changes in the standard meter including using a platinum-iridium alloy bar, we have a new definition of the meter: the speed of light. Since the speed of light in a vacuum is a universal constant (meaning it is the same no matter where you are in the universe, unlike the acceleration due to gravity at a point in space), they decided to make the distance light travels in one second a set number of meters and adjust the meter accordingly. Since the speed of light is 299,792,458 meters per second exactly, this means that we have defined the meter as the distance light travels in 1/299,792,458th of a second.
This is all nice, but it's not a very intuitive number to work with. After all, we humans like multiples of ten (due to having ten fingers and ten toes), so why not make a length measurement of the distance light travels in one billionth (1/1,000,000,000th) of a second (a.k.a. nanosecond)? That seems a bit more intuitive, don't you think? It turns out that a light-nanosecond is about 11.8 inches, or about 1.6% off of the current definition of a foot. In fact, one physicist, David Mermin, suggests redefining the foot to the "phoot," or one light-nanosecond, since it's based off of a universal constant while the current foot is based off the meter by some odd, nonsensical ratio.
Jackson ≪ Griffiths
Posted by
Akano Toa of Electricity
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Math/Physics,
Life
Nov 16 2012
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94 views
Physics, Education, Rant
I know most of you aren't physicists, but it's very important to me that physics education be designed to effectively teach physics to any and all audiences. After all, if you want people to have some inkling as to what you do, you want to be able to come up with a way to explain the necessities without getting bogged down in all the details. When you do this, it prevents the person you talk to from feeling like a moron and also allows you to talk about yourself and what you do to someone who has no clue what you do.
This is why graduate-level texts frustrate me. The authors always assume that half the stuff they're discussing in their textbook is obvious to the reader/student who has maybe seen the material once before in an undergraduate course. While some of this material should be expected to be known already, you can't just chuck stuff at your reader and say "it is now obvious that" or "the proof is trivial" when neither of these statements is actually true. If you use either of these statements in your textbook, you're not a good teacher. Period.
The title of this entry comes from the fact that I'm comparing two Electromagnetic Theory textbooks, one by D.J. Griffiths and the other by J.D. Jackson. Griffiths' Introduction to Electrodynamics is a witty, conversational, and informative text that helps undergraduates cope with the fact the E&M is really hard and that most of the concepts are foreign to someone who has only ever dealt with classical mechanics. Jackson's Classical Electrodynamics, on the other hand, is a text where the reader can tell that the author really knows his stuff when it comes to E&M, but has no sense of how to convey that knowledge to someone who is not an advanced student of the subject.
For instance, let's say I were teaching the concept of projectile motion to someone who has never delved into the subject. If I were Griffiths, I would say something like, "All objects in free fall on Earth experience a force due to gravity toward the ground. This force causes all objects to accelerate at the same rate, meaning that the rate at which something speeds up/slows down in Earth's gravity is the same for all objects regardless of how heavy they are. Because this acceleration is constant near the ground, objects tend to follow a parabolic trajectory (if we ignore air resistance). The equations that show this follow from Newton's second law, F = m a. If you don't believe this, let's try it, shall we?"
Now wasn't that nice? This explanation is certainly very clear about what projectile motion is and what causes it. Griffiths enjoys taking concepts that may be hard to comprehend and then following through with some equations/proofs to try and clarify the situation, usually speaking to the reader as though he were sitting down with them helping them through a problem.
What about Jackson? He would probably say something along the lines of, "The reason projectiles follow parabolic paths is simple: if you solve the Hamilton-Jacobi equation in a uniform gravitational field, you will find that the path that minimizes the action is that of a parabola. This can be seen by setting the variation of the Lagrangian equal to zero."
Well that was simple, wasn't it? While technically correct, you probably have no idea what the Hamilton-Jacobi equation or Lagrangian are, nor do you probably know what "action" means in physics. Now you may be thinking, "well, these things are part of undergraduate courses, right?" Well, no, actually. I had no idea what the Hamilton-Jacobi equation was until I took graduate level quantum mechanics, and I was expected to have known that from my graduate classical mechanics course (which I didn't take until my second semester of quantum mechanics). Suffice it to say, there was a lot I had to learn on the fly, but you can probably see what I'm getting at. The assumption that students know everything you expect them to know and have it ready to go the minute you throw that curve ball at them is a terrible way to go about teaching and, in my opinion, does not foster good education.
On an unrelated note, I have a problem set out of Jackson due tomorrow which I haven't finished yet. So, how was your day?
This is why graduate-level texts frustrate me. The authors always assume that half the stuff they're discussing in their textbook is obvious to the reader/student who has maybe seen the material once before in an undergraduate course. While some of this material should be expected to be known already, you can't just chuck stuff at your reader and say "it is now obvious that" or "the proof is trivial" when neither of these statements is actually true. If you use either of these statements in your textbook, you're not a good teacher. Period.
The title of this entry comes from the fact that I'm comparing two Electromagnetic Theory textbooks, one by D.J. Griffiths and the other by J.D. Jackson. Griffiths' Introduction to Electrodynamics is a witty, conversational, and informative text that helps undergraduates cope with the fact the E&M is really hard and that most of the concepts are foreign to someone who has only ever dealt with classical mechanics. Jackson's Classical Electrodynamics, on the other hand, is a text where the reader can tell that the author really knows his stuff when it comes to E&M, but has no sense of how to convey that knowledge to someone who is not an advanced student of the subject.
For instance, let's say I were teaching the concept of projectile motion to someone who has never delved into the subject. If I were Griffiths, I would say something like, "All objects in free fall on Earth experience a force due to gravity toward the ground. This force causes all objects to accelerate at the same rate, meaning that the rate at which something speeds up/slows down in Earth's gravity is the same for all objects regardless of how heavy they are. Because this acceleration is constant near the ground, objects tend to follow a parabolic trajectory (if we ignore air resistance). The equations that show this follow from Newton's second law, F = m a. If you don't believe this, let's try it, shall we?"
Now wasn't that nice? This explanation is certainly very clear about what projectile motion is and what causes it. Griffiths enjoys taking concepts that may be hard to comprehend and then following through with some equations/proofs to try and clarify the situation, usually speaking to the reader as though he were sitting down with them helping them through a problem.
What about Jackson? He would probably say something along the lines of, "The reason projectiles follow parabolic paths is simple: if you solve the Hamilton-Jacobi equation in a uniform gravitational field, you will find that the path that minimizes the action is that of a parabola. This can be seen by setting the variation of the Lagrangian equal to zero."
Well that was simple, wasn't it? While technically correct, you probably have no idea what the Hamilton-Jacobi equation or Lagrangian are, nor do you probably know what "action" means in physics. Now you may be thinking, "well, these things are part of undergraduate courses, right?" Well, no, actually. I had no idea what the Hamilton-Jacobi equation was until I took graduate level quantum mechanics, and I was expected to have known that from my graduate classical mechanics course (which I didn't take until my second semester of quantum mechanics). Suffice it to say, there was a lot I had to learn on the fly, but you can probably see what I'm getting at. The assumption that students know everything you expect them to know and have it ready to go the minute you throw that curve ball at them is a terrible way to go about teaching and, in my opinion, does not foster good education.
On an unrelated note, I have a problem set out of Jackson due tomorrow which I haven't finished yet. So, how was your day?
Ponies Premiere
Posted by
Akano Toa of Electricity
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in
My Little Pony
Nov 10 2012
·
96 views
Season 3, Crystal Ponies
These villains are getting less and less backstory development as we go, huh? In terms of development:
That said, though, I enjoyed the episode quite a bit. The songs were okay, but I've only listened to them once, really. However, it was nice for Spike to get a role as Twilight's supporting vocals. Cathy Weseluck amazes me.
I did think Rainbow Dash was a bit over the top, but I enjoyed everyone else.
También, sombra = shadow en espańol, por tu información.
Sombra < Chrysalis < Discord / Nightmare Moon
That said, though, I enjoyed the episode quite a bit. The songs were okay, but I've only listened to them once, really. However, it was nice for Spike to get a role as Twilight's supporting vocals. Cathy Weseluck amazes me.
I did think Rainbow Dash was a bit over the top, but I enjoyed everyone else.
También, sombra = shadow en espańol, por tu información.
So I just laughed uncontrollably for about five minutes...
Posted by
Akano Toa of Electricity
,
in
Life
Nov 09 2012
·
102 views
Laughing, Insane
Griffiths is best textbook author
Posted by
Akano Toa of Electricity
,
in
Math/Physics
Nov 07 2012
·
76 views
College, Physics, Textbook and 1 more...
"The proportionality factor σ (not to be confused with surface charge) is an empirical constant that varies from one material to another; it's called the conductivity of the medium. Actually, the handbooks usually list the reciprocal of σ, called the resistivity: ρ = 1/σ (not to be confused with charge density—I'm sorry, but we're running out of Greek letters, and this is the standard notation)."
This is the man who allegedly can teach physics to gerbils. I wish I could take a class with him simply for his wit and skillz at teaching.
This is the man who allegedly can teach physics to gerbils. I wish I could take a class with him simply for his wit and skillz at teaching.
It's almost like I'm back in Ohio. Except in Ohio it snowed in late October.
Eh, close enough.
Eh, close enough.
Voting and such
Posted by
Akano Toa of Electricity
,
Nov 06 2012
·
58 views
Voting, Election, Bandwagon
You people are all slow; I voted weeks ago (absentee FTW!). Thanks to all who voted, whether it was Democrat, Republican, or Bull Moose. Statisticians really appreciate having a good sample size for such things.
(But seriously, voting is important. Exercise those rights!)
(absentee FTW!). Thanks to all who voted, whether it was Democrat, Republican, or Bull Moose. Statisticians really appreciate having a good sample size for such things. (But seriously, voting is important. Exercise those rights!)
>>
<<
Normal - Togekiss
Fighting - Lucario
Water - Milotic
Grass - Breloom
Fire - Chandelure/Volcarona
Electric - Rotom
Poison - Haunter
Ghost - Shedinja
Psychic - Lugia
Bug - Galvantula
Flying - Zapdos
Dragon - Zekrom
Rock - Tyranitar
Ground - Steelix
Ice - Lapras
Steel - Magnezone
Dark - Zoroark
Gen I: 3 Gen II: 3 Gen III: 3 Gen IV: 4 Gen V: 4/5 (if you count both Chandelure and Volcarona)
I couldn't decide between Chandelure and Volcarona, because they be beastly. I almost put Giratina with Zekrom, but Zekrom has the electric factor going for him, which, if you couldn't tell, I like.
Also, my favorites are very spread among gens. Akano does not play favorites with his generations of Pokémon.
(Gen II all the way!)
<<
Normal - Togekiss
Fighting - Lucario
Water - Milotic
Grass - Breloom
Fire - Chandelure/Volcarona
Electric - Rotom
Poison - Haunter
Ghost - Shedinja
Psychic - Lugia
Bug - Galvantula
Flying - Zapdos
Dragon - Zekrom
Rock - Tyranitar
Ground - Steelix
Ice - Lapras
Steel - Magnezone
Dark - Zoroark
Gen I: 3 Gen II: 3 Gen III: 3 Gen IV: 4 Gen V: 4/5 (if you count both Chandelure and Volcarona)
I couldn't decide between Chandelure and Volcarona, because they be beastly. I almost put Giratina with Zekrom, but Zekrom has the electric factor going for him, which, if you couldn't tell, I like.
Also, my favorites are very spread among gens. Akano does not play favorites with his generations of Pokémon.
(Gen II all the way!
)
Pokémon White 2: Postgame
Posted by
Akano Toa of Electricity
,
in
Life
Nov 02 2012
·
102 views
Pokémon, White 2, Nicknames
While I technically beat the Elite Four on Tuesday, I thought I'd share my team here.
I couldn't nickname Zoroark due to it being N's originally, and Tornadus I just never got around to nicknaming after I got him from Dream Radar. This was actually the first time I've ever raised any of these Pokémon for a team, so it was a very different game experience this time around. I wish Lucario were just a bit bulkier, because he can dole out punishment but can't really take it. I love Zoroark's speed, but man is he frail. Emboar was all right, but I definitely prefer Samurott. Magnezone was pretty awesome, too; his Special Attack is beastly.
I should raise a Chandelure when I replay through White. He looks pretty awesome...
- Anubis (Lucario)
- Tornadus-T
- Vanessa (Emboar)
- Zoroark
- Tesla (Magnezone)
- Golduck - HM slave
I couldn't nickname Zoroark due to it being N's originally, and Tornadus I just never got around to nicknaming after I got him from Dream Radar.
This was actually the first time I've ever raised any of these Pokémon for a team, so it was a very different game experience this time around. I wish Lucario were just a bit bulkier, because he can dole out punishment but can't really take it. I love Zoroark's speed, but man is he frail. Emboar was all right, but I definitely prefer Samurott. Magnezone was pretty awesome, too; his Special Attack is beastly.I should raise a Chandelure when I replay through White. He looks pretty awesome...
About Me
Akano Toa of Electricity
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Name: Akano
Real Name: Forever Shrouded in Mystery
Age: 23
Gender: Male
Likes: Science, Math, LEGO, Bionicle, Ponies, Comics, Yellow, Voice Acting
Notable Facts: One of the few Comic Veterans still around
Has been a LEGO fan since ~1996
Bionicle fan from the beginning
Misses the 90's. A lot.
Twitter: @akanotoe
My Lovely Topics
Hieroglyphs And The Like
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