In understanding drugs and how they work, it can be helpful to think of the body and its atoms as a giant set of Lego® bricks[1]. A child can use Lego® bricks to make buildings, space ships, cars, etc; and the body can use its atoms to build muscles, bones, signaling molecules, etc. Moreover, just as the child can disassemble her building and then use the bricks to make a car, the body can disassemble its muscle and build bone. Of course, the car requires special bricks (e.g. wheels) which aren’t needed to make a building, and bone needs special atoms (e.g. calcium) which aren’t needed to make a muscle: the number of cars the child can make is limited by the number of wheels she has, and the amount of bone the body can make is limited by the amount of calcium available.
This last point is important. It means that if we want to regulate the number of cars that the child makes, we only need to regulate the number of wheels we allow her to use. We might do this because we have too many cars, and don’t want any more, or we might do so because we don’t have enough buildings (or space ships, or bridges) and want to conserve our bricks to make those instead of cars.
In the body, if we want to regulate the amount of bone we make, we can regulate the amount of calcium there is to make it with. We might do this because we have too much bone, and don’t want any more, or we might do so because we don’t have enough of something else, and want to conserve building materials to make, say, muscle.
Pharmacology (the science of drugs) manipulates the body by interfering with the way it uses its atoms. Continuing with the Lego analogy, drugs are the equivalent of another person adding or removing bricks to the buildings, cars, space ships, etc as they’re being built or after they’re finished; or adding or removing bricks from the box of unused bricks.
[1] Lego® is a registered trademark of the LEGO® Group of companies, which does not sponsor, authorise, or endorse this site
Saturday, January 18, 2014
Saturday, September 7, 2013
Math Symbols
The SAT likes to include a math few problems with unusual symbols, such as ◊, or ♠. For some exam takers, this is a signal to panic, since they have no idea what ◊ or ♠ mean, but really, these are simple replacement questions, similar to the f(x) questions I addressed in an earlier post.
Really, no one knows what what ◊ or ♠ mean. The College Board (the writers of the exam) make up a meaning for the symbols as they write the question. In each case they give you the definition of the symbol, then ask you to apply that definition.
For example:
a ♣ b = a + (b x 2)
3 ♣ 7 = ?
The first line defines the symbol ♣. We'll use that definition as a template for answering the question on the second line.
Note that in the definition, a appears before the ♣. And in the question, 3 appears before the ♣. The test makers have replaced a with 3 in the left half of the equation; we just need to make the same replacements in the right side of the equation:
a ♣ b = a + (b x 2)
3 ♣ 7 = 3 + (b x 2)
We still have to account for b, though. In the left side of the equation, the test maker replaced b with 7, so now we need to make the same replacement on the right:
a ♣ b = a + (b x 2)
3 ♣ 7 = 3 + (7 x 2)
At this point, we have an equation that we can easily solve. Following the usual order of operations (PEMDAS), we get:
3 ♣ 7 = 3 + (7 x 2)
= 3 + 14
= 17
Really, no one knows what what ◊ or ♠ mean. The College Board (the writers of the exam) make up a meaning for the symbols as they write the question. In each case they give you the definition of the symbol, then ask you to apply that definition.
For example:
a ♣ b = a + (b x 2)
3 ♣ 7 = ?
The first line defines the symbol ♣. We'll use that definition as a template for answering the question on the second line.
Note that in the definition, a appears before the ♣. And in the question, 3 appears before the ♣. The test makers have replaced a with 3 in the left half of the equation; we just need to make the same replacements in the right side of the equation:
a ♣ b = a + (b x 2)
3 ♣ 7 = 3 + (b x 2)
We still have to account for b, though. In the left side of the equation, the test maker replaced b with 7, so now we need to make the same replacement on the right:
a ♣ b = a + (b x 2)
3 ♣ 7 = 3 + (7 x 2)
At this point, we have an equation that we can easily solve. Following the usual order of operations (PEMDAS), we get:
3 ♣ 7 = 3 + (7 x 2)
= 3 + 14
= 17
Friday, September 6, 2013
MCAT Math
The MCAT does not allow calculators, (source: MCAT Essentials (will download as pdf)) a fact that leaves many test-takers in something of a panic. With proper preparation, however, there should be no difficulty in completing MCAT math.
First, recognize that since the test takers aren't allowed to use calculators, the test makers can't include math that requires a calculator. This means that the math on the exam has to be relatively basic, and the numbers used have to be easy to manipulate. Note that sometimes manipulation includes simplification: the acceleration due to gravity on earth is 9.8 m/s^2, but on exam day we typically simplify that number to 10; a sample with a mass of 5.1 grams may be simplified to 5 grams; etc.
Second, keep in mind that as a multiple-choice test, the MCAT has to actually give you the answer - all you have to do is separate out the correct answer from the incorrect answers. It doesn't matter how you do it. Eliminating all of the wrong answers gives you just as much credit as crunching the numbers to arrive at the correct answer. Skilled test-takers work at questions from both ends, eliminating patently absurd answer choices and only then bothering to really grapple with the problem. If they're given answer choices such as 51 J, 51 V, 53 J, and 53 V, their first step will probably be to determine what units the correct answer will have, since doing so will eliminate 67% of the wrong answers. Only then will they bother with the math.
Third, realize that since you're not taking the exam today, you have a chance to improve your math skills. And the best way to do that is to use those skills: between now and exam day, every time you need to do math, do it by hand. Check your work with a calculator if you want, but do it by hand first. And make use of every opportunity, too; when you buy items at a store, estimate or calculate the pre-tax total before you get to the register. Then do the total with tax. Calculate fifteen and twenty percent tips at restaurants. When you're at the gas station, estimate how many gallons you'd get for $20, then crunch the numbers and see how close you were. Balance your check book every night.
Keep these points in mind, and make use of every opportunity to practice, and MCAT math will be a breeze.
Saturday, September 26, 2009
Immune system animations
The immune system is a vast collection of tissues and cells that work together to keep the body free of infection. In doing so, the system has to balance between hypoactivity, which allows infection to reign, and hyperactivity, which causes allergies and autoimmune conditions. A complex system of local and long-distance signals allow for the system to respond appropriately. Long distance signals place the body and the immune system on alert. Local signals tell arriving immune cells that they are entering the war zone, and to draw their weapons (keeping the weapons holstered until they arrive at the battle field reduces friendly-fire incidents)
There is also the problem of recognition - immune cells are worthless if they don't know what to attack, since they ignore pathogens (bacteria, etc) and attack host cells (self). The system by which immune cells are schooled requires specialized environments and signaling processes.
This site shows animations that explain many of the intricacies of the immune process. It's much more than you need for the MCAT, but very useful for those of you already into med school.
There is also the problem of recognition - immune cells are worthless if they don't know what to attack, since they ignore pathogens (bacteria, etc) and attack host cells (self). The system by which immune cells are schooled requires specialized environments and signaling processes.
This site shows animations that explain many of the intricacies of the immune process. It's much more than you need for the MCAT, but very useful for those of you already into med school.
Thursday, September 24, 2009
The War of 1812 and the US Navy
I'm going to give you a hypothetical situation to think about: what if an Iranian frigate took - destroyed - a U.S. frigate?
Now, I'm aware of the attack on the U.S. Cole several years ago - and this is not what I'm driving at. Some crewmen died in that attack, but the Cole survived, was repaired, and returned to service in the U.S. Navy. As shocking as the attack was, the Cole wasn't destroyed, and she wasn't taken. But what if an Iranian frigate took a U.S. one?
In 1812, the United States of America declared war on England. The reasons for this are long and complex (as is so often the case on war) and are beyond the point of this post, but the outcome of the war arguably marked the entrance of the U.S. onto the world stage.
Before the war, the U.S. was merely a loose group of former colonies - a third-rate nation at best. They possessed little in the way of a navy, with 19 vessels, of which 16 were actually in service. Seven of these were frigates, with the remainder being smaller vessels such as brigs and sloops. England's navy (the Royal Navy) possessed over 600 in-service vessels, of which about 175 were ships of the line - a class of ships that would eventually come be known as battleships, and which were larger and heavier than the frigates that formed the largest ships in the American navy. So on paper, there was no contest: the American navy would be lucky to capture a few British merchantmen before being captured itself, or at best bottled up by Royal Navy blockade.(1)
The course of history also seemed to be against the Americans. For the past 20 years, the Royal Navy had routinely routed every enemy it had faced. Nelson's victory at Trafalgar(2) had been notable only for the scale of the victory; the Royal Navy simply won and won, even when outmanned and outgunned. It was a foregone conclusion that the war at sea would be swiftly over, with England victorious.
It was with supreme confidence, therefore, that Captain Dacres of the HMS Guerriere met the USS Constitution (Captain Hull) on August 19th, 1812. He addressed his men, saying that he exepcted them to beat the Constitution in 30 minutes, and that he would be "offended with them if they did not do their business in that time." Dacres was not too far off in the length of the battle (Constitution ceased firing less than 25 minutes after she opened fire at 6:05pm) but he was wrong in his prediction of its outcome: Constitution destroyed the Guerriere, so badly shattering her that she was worthless as a prize and had to be burned so as not to be a menace to navigation. Besides their frigate, the British lost 23 killed, plus another 56 wounded. American casualties were seven killed, and seven wounded.
Let me pause here to see if I can put this in modern terms. England no longer rules the waves - if anyone does, I suppose it is America. So again, what would we think if, say, an Iranian frigate engaged a U.S. frigate - and destroyed her in less than half an hour?
Of course, this only begins to approach the reality of what happened in the War of 1812, because the U.S. Navy hasn't spent twenty years defeating every other armed nation on earth. If the U.S. Navy were to tomorrow take on, say, the combined English and German navies, I don't know who would win. And, of course, not only did the Constitution take the Guerriere on August 19th, but a little over two months later the USS United States took the HMS Macedonian. And then on December 29th, Constitution met and took the HMS Java. The United States, an infant nation with an insignificant navy, met and smashed the forces of the most powerful international force in the world. The world took notice.
[EDIT, 1 OCTOBER 2009: A friend of mine recently pointed out that if Iran were to successfully attack an American warship in any meaningful way, their joy would be short-lived: "I think Iran would regret their victory. The 19th century Royal Navy, for all its immense power had nothing like a B-52 or, heaven forbid, the U.S.S. Tennessee." I think he's correct, and that's part of my point, since England in 1812 felt similarly confident about any naval clash they had with the U.S. So my point is this: England in late 1812 was shocked by the American successes, as shocked as America would now be if its navy repeatedly lost to the Iranians.]
(1) This disparity is lessened by the fact that England was then also embroiled in the Napoleanic wars, which placed great demands on her navy, but the fact remains that the Royal Navy was much more powerful than the U.S. Navy, with larger, heavier ships and greater reserves of men and materiel.
(2) Nelson, with 27 ships of the line, trounced a combined Franco-Spanish fleet of 33 ships of the line, sinking one and capturing 17 while losing none of his own.
Sources:
* Battle of Trafalgar: Grant, R. G. Battle at Sea: 3,000 Years of Naval Warfare. DK Publishing, New York. 2008 @ pp 188-189.
* War of 1812:
- relative strength of the Royal and American Navies: Toll, Ian W. Six Frigates: The Epic History of the Founding of the U.S. Navy. Norton, New York. 2006. @ pp 331-333.
- Constitution:Guerriere engagement: Toll (ibid) @ pp 347-354.
- Constitution:Java engagement: Toll (ibid) @ pp 375-380.
- United States:Macedonian engagement: Toll (ibid) @ pp 360-365.
Cross-posted on main page
Now, I'm aware of the attack on the U.S. Cole several years ago - and this is not what I'm driving at. Some crewmen died in that attack, but the Cole survived, was repaired, and returned to service in the U.S. Navy. As shocking as the attack was, the Cole wasn't destroyed, and she wasn't taken. But what if an Iranian frigate took a U.S. one?
In 1812, the United States of America declared war on England. The reasons for this are long and complex (as is so often the case on war) and are beyond the point of this post, but the outcome of the war arguably marked the entrance of the U.S. onto the world stage.
Before the war, the U.S. was merely a loose group of former colonies - a third-rate nation at best. They possessed little in the way of a navy, with 19 vessels, of which 16 were actually in service. Seven of these were frigates, with the remainder being smaller vessels such as brigs and sloops. England's navy (the Royal Navy) possessed over 600 in-service vessels, of which about 175 were ships of the line - a class of ships that would eventually come be known as battleships, and which were larger and heavier than the frigates that formed the largest ships in the American navy. So on paper, there was no contest: the American navy would be lucky to capture a few British merchantmen before being captured itself, or at best bottled up by Royal Navy blockade.(1)
The course of history also seemed to be against the Americans. For the past 20 years, the Royal Navy had routinely routed every enemy it had faced. Nelson's victory at Trafalgar(2) had been notable only for the scale of the victory; the Royal Navy simply won and won, even when outmanned and outgunned. It was a foregone conclusion that the war at sea would be swiftly over, with England victorious.
It was with supreme confidence, therefore, that Captain Dacres of the HMS Guerriere met the USS Constitution (Captain Hull) on August 19th, 1812. He addressed his men, saying that he exepcted them to beat the Constitution in 30 minutes, and that he would be "offended with them if they did not do their business in that time." Dacres was not too far off in the length of the battle (Constitution ceased firing less than 25 minutes after she opened fire at 6:05pm) but he was wrong in his prediction of its outcome: Constitution destroyed the Guerriere, so badly shattering her that she was worthless as a prize and had to be burned so as not to be a menace to navigation. Besides their frigate, the British lost 23 killed, plus another 56 wounded. American casualties were seven killed, and seven wounded.
Let me pause here to see if I can put this in modern terms. England no longer rules the waves - if anyone does, I suppose it is America. So again, what would we think if, say, an Iranian frigate engaged a U.S. frigate - and destroyed her in less than half an hour?
Of course, this only begins to approach the reality of what happened in the War of 1812, because the U.S. Navy hasn't spent twenty years defeating every other armed nation on earth. If the U.S. Navy were to tomorrow take on, say, the combined English and German navies, I don't know who would win. And, of course, not only did the Constitution take the Guerriere on August 19th, but a little over two months later the USS United States took the HMS Macedonian. And then on December 29th, Constitution met and took the HMS Java. The United States, an infant nation with an insignificant navy, met and smashed the forces of the most powerful international force in the world. The world took notice.
[EDIT, 1 OCTOBER 2009: A friend of mine recently pointed out that if Iran were to successfully attack an American warship in any meaningful way, their joy would be short-lived: "I think Iran would regret their victory. The 19th century Royal Navy, for all its immense power had nothing like a B-52 or, heaven forbid, the U.S.S. Tennessee." I think he's correct, and that's part of my point, since England in 1812 felt similarly confident about any naval clash they had with the U.S. So my point is this: England in late 1812 was shocked by the American successes, as shocked as America would now be if its navy repeatedly lost to the Iranians.]
(1) This disparity is lessened by the fact that England was then also embroiled in the Napoleanic wars, which placed great demands on her navy, but the fact remains that the Royal Navy was much more powerful than the U.S. Navy, with larger, heavier ships and greater reserves of men and materiel.
(2) Nelson, with 27 ships of the line, trounced a combined Franco-Spanish fleet of 33 ships of the line, sinking one and capturing 17 while losing none of his own.
Sources:
* Battle of Trafalgar: Grant, R. G. Battle at Sea: 3,000 Years of Naval Warfare. DK Publishing, New York. 2008 @ pp 188-189.
* War of 1812:
- relative strength of the Royal and American Navies: Toll, Ian W. Six Frigates: The Epic History of the Founding of the U.S. Navy. Norton, New York. 2006. @ pp 331-333.
- Constitution:Guerriere engagement: Toll (ibid) @ pp 347-354.
- Constitution:Java engagement: Toll (ibid) @ pp 375-380.
- United States:Macedonian engagement: Toll (ibid) @ pp 360-365.
Cross-posted on main page
Monday, September 21, 2009
Essays: keep your eyes on the prize
NOTE: The MCAT no longer includes an essay.
I once had an SAT student who wrote a brilliant essay in which she evaluated both sides of an issue before deciding that there was merit to both sides, and that we could determine which side to go with based on a particular criterion, which she listed and discussed. As I said, it was brilliant, and it was better than many of the essays I receive from MCAT students. Unfortunately, she failed to adequately address the question that had been asked of her, so I couldn't give her a good grade.
When you're asked to write an essay, the first step is to be sure that you understand what you're assignment is. the second step is to be sure that you actually write to address that assignment. Both steps are important.
The first step doesn't take much: you just have to take the time to read the assignment and make sure that you understand it. Try to paraphrase the assignment question (put it into your own words) to be sure that you understand it. If you taking an exam where you're allowed to do so, and you're uncertain about the assignment, ask your instructor.
The second can be trickier, since it can be tempting to use the assignment as a jumping-off point for an essay that ultimately charges off into other territories, or to only answer part of a more complex assignment. Once we're writing, our thoughts may focus on the what's in front of us - is this fact correct, is my grammar ok - and we can lose sight of where we're actually supposed to be going.
The solution to keeping on track is to plan out the essay before writing it. Take a few minutes to sketch out the points you want to make, with their examples and/or reasoning. Look at the completed sketch to make sure that it actually matches the assignment. And then write the essay, keeping to the sketched-out plan: if a new example comes to us as we write, don't add it unless there is the time to go back and rework the original plan to include it (in other words, it's okay to add examples to a take-home assignment, but not for an in-class exam).
When you're asked to write an essay, the first step is to be sure that you understand what you're assignment is. the second step is to be sure that you actually write to address that assignment. Both steps are important.
The first step doesn't take much: you just have to take the time to read the assignment and make sure that you understand it. Try to paraphrase the assignment question (put it into your own words) to be sure that you understand it. If you taking an exam where you're allowed to do so, and you're uncertain about the assignment, ask your instructor.
The second can be trickier, since it can be tempting to use the assignment as a jumping-off point for an essay that ultimately charges off into other territories, or to only answer part of a more complex assignment. Once we're writing, our thoughts may focus on the what's in front of us - is this fact correct, is my grammar ok - and we can lose sight of where we're actually supposed to be going.
The solution to keeping on track is to plan out the essay before writing it. Take a few minutes to sketch out the points you want to make, with their examples and/or reasoning. Look at the completed sketch to make sure that it actually matches the assignment. And then write the essay, keeping to the sketched-out plan: if a new example comes to us as we write, don't add it unless there is the time to go back and rework the original plan to include it (in other words, it's okay to add examples to a take-home assignment, but not for an in-class exam).
If f (x) = 3x + 4
Function problems, like f (x), g (x), h (x), etc, leave a lot of students confused. This is unfortunate, because function problems are nothing more than substitution problems. I'll give you an example:
f (x) = 3x + 4
f (2) = ?
We note that in left half of the question, 2 has been plugged in where x was. To solve the problem, then, all we need to do is substitute (plug in) 2 for x in the right half of the equation:
f (2) = 3(2) + 4 = 6 + 4 = 10
Similarly,
f (3) = 3(3) + 4 = 9 + 4 = 13
f (4) = 3(4) + 4 = 12 + 4 = 16
f (5) = 3(5) + 4 = 15 + 4 = 19
f (6) = 3(6) + 4 = 18 + 4 = 22
f (7) = 3(7) + 4 = 21 + 4 = 25
f (8) = 3(8) + 4 = 24 + 4 = 28
f (9) = 3(9) + 4 = 27 + 4 = 31
f (10) = 3(10) + 4 = 30 + 4 = 34
f (y) = 3(y) + 4 = 3y + 4
f (z) = 3(z) + 4 = 3z + 4
etc.
Sometimes, we might find multiple functions used together. When this is the case, we just follow the usual rules of math to untangle the question:
if f (x) = 3x + 4, and g(x) = 5x - 7
f (4) - g (2) = ?
As before, we merely substitute in. Let's work with each function separately, then put them together, being sure to keep straight that 4 was given to us for the f function and 2 was given to us for the g function:
f (4) = 3(4) + 4 = 12 + 4 = 16
g (2) = 5(2) - 7 = 10 - 7 = 3
Taking the original equation and then substituting in these values, we have:
f (4) - g (2) = ?
16 - 3 = ?
and of course that equals 13.
We may also find cases where functions are nested within parentheses:
if f (x) = 3x + 4, and g(x) = 5x - 7
f (g (10)) = ?
Note that I've defined a new function for g. These are solved in the same way: by following the usual rules of math. g (10) is found inside a set of parentheses, so we start with that:
g (10) = 5(10) - 7 = 50 - 7 = 43
We then substitute this value in for g (10):
f (g (10)) = f (43)
And then we solve f (43):
f (43) = 3(43) + 4 = 129 + 4 = 134
PS: If you had to reach for your calculator to do any of that math, then you're relying on your calculator too much.
f (x) = 3x + 4
f (2) = ?
We note that in left half of the question, 2 has been plugged in where x was. To solve the problem, then, all we need to do is substitute (plug in) 2 for x in the right half of the equation:
f (2) = 3(2) + 4 = 6 + 4 = 10
Similarly,
f (3) = 3(3) + 4 = 9 + 4 = 13
f (4) = 3(4) + 4 = 12 + 4 = 16
f (5) = 3(5) + 4 = 15 + 4 = 19
f (6) = 3(6) + 4 = 18 + 4 = 22
f (7) = 3(7) + 4 = 21 + 4 = 25
f (8) = 3(8) + 4 = 24 + 4 = 28
f (9) = 3(9) + 4 = 27 + 4 = 31
f (10) = 3(10) + 4 = 30 + 4 = 34
f (y) = 3(y) + 4 = 3y + 4
f (z) = 3(z) + 4 = 3z + 4
etc.
Sometimes, we might find multiple functions used together. When this is the case, we just follow the usual rules of math to untangle the question:
if f (x) = 3x + 4, and g(x) = 5x - 7
f (4) - g (2) = ?
As before, we merely substitute in. Let's work with each function separately, then put them together, being sure to keep straight that 4 was given to us for the f function and 2 was given to us for the g function:
f (4) = 3(4) + 4 = 12 + 4 = 16
g (2) = 5(2) - 7 = 10 - 7 = 3
Taking the original equation and then substituting in these values, we have:
f (4) - g (2) = ?
16 - 3 = ?
and of course that equals 13.
We may also find cases where functions are nested within parentheses:
if f (x) = 3x + 4, and g(x) = 5x - 7
f (g (10)) = ?
Note that I've defined a new function for g. These are solved in the same way: by following the usual rules of math. g (10) is found inside a set of parentheses, so we start with that:
g (10) = 5(10) - 7 = 50 - 7 = 43
We then substitute this value in for g (10):
f (g (10)) = f (43)
And then we solve f (43):
f (43) = 3(43) + 4 = 129 + 4 = 134
PS: If you had to reach for your calculator to do any of that math, then you're relying on your calculator too much.
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