Hey guys!
As some of you may know, I'm spending the summer doing physics research in Chile. For those of you who don't know, I'm spending the summer doing physics research in Chile. The admin knew I'm fond of writing and asked me to keep a record blog of my time. You can find it at http://scienceinsantiago.blogspot.com/. I'll still be updating here; that's just for Chile related affairs. This is still my main place for nonsensical rambling.
2011-06-17
2011-06-13
Linux
I spent most of yesterday trying to boot Linux on my netbook. To make things interesting, I formatted my hard drive first. All of my old data gone in a flash. Until I got Linux working I wouldn't have a computer. I'd have to use the public one, the one my brother uses to watch the same 'comedy' videos he has the past five years. This was, of course, A Problem. It remained A Problem over 15 hours and five distros. Eventually I pinned it down to a problem in the power management software and got a netbook remix of Fedora working on the comp. Pretty sure I botched a few things on the way. Such is the price of change.
Of course, my job on this blog is to ramble insanely and occasionally talk about physics, not complain about Linux. My thoughts keep coming back to the erasure. Of course I saved the important things. But a sane person would have made sure Linux actually worked before they torched their system. Or they would have had a backup of the old OS, in case they wanted to go back. Hell, why even do Linux? I don't have a major need for it. I can say I wanted to start anew, but then I should have just wiped and replaced Windows.
My family thought I was crazy. And they were right. What I did was possibly the most irresponsible thing I could have done, short of chucking my computer out a window. I knew all of that going in. I knew, I typed in the commands, that there was a good chance I would never get the computer functioning again. And yet I did it anyway. And I have to keep asking myself why.
Okay, I know why. The thoughts make perfect sense in my head. Mostly I was asking myself how to explain it. There are two factors at work here, both drives that most people would call insane or stupid. First of all, I had to erase my hard drive so that I had the risk of it not working. This is difficult to describe. We have to face the consequences of our premeditated actions. But consequences are fickle and unpredictable. We have no way of knowing what will fizzle out and what will go too far. Repercussions blindside us. Mastering the art of response is kinda like trying to shoot by getting randomly pushed into warzones for five minutes at a time. We have to find a way to train ourselves by manufacturing our own potential crises. We can't ignore it, because we engineered it to be unignorable, and we cannot complain, because we knew it would be our own damned fault. All we can do is respond. That's the reason I erased everything first.
So why Linux? Linux is something I cannot use as well as Windows, something I'm completely unfamiliar with, something that would cause me great difficulty if I switched to it. Why not Linux? Comfort leads to complacency leads to stagnation. Better constantly shift my world very slightly, make myself eternally uncomfortable, than risk that. I've always been a person obsessed with flux. In confusion and chaos we find ourselves.
I have no idea how much sense these reasons make to another person. All I know is that these are massive driving forces for me. Switching to Linux isn't going to revolutionize my life, but it will continue to familiarize me with taking these unpleasant and beneficial actions. I guess you could ask are they really beneficial. Who knows? Maybe making chaos more comfortable will itself lead to stagnation, and ten years down the road I'll find new driving forces to combat that.
*G's job is to actually be insightful.
Mathematical Psychics
Mainstream microeconomics assume the "end" of human behaviour is to make oneself as happy as possible. In economics-speak, this is to say consumers want to maximize utility. Utility is the catch-all term for happiness and/or benefits of any kind. The problem of utility maximization naturally leads to the question: how does one measure utility?
Difficulties arise immediately when we consider how we should define utility operationally, i.e. how do we define it in a way that allows it to be measured? But that leads to further questions of what we mean by measure? The following example highlights some of these difficulties.
A friend of mine recently observed that video games cost around $50 and playtime usually lasts over 20 hours, whereas movies cost around $10 and lasts about 2 hours. The cost of "fun per unit time" for video games would be around $2.50, whereas for movies it is around $5. (We just divide the cost by the hours of fun it is estimated to provide). He asked me, if the cost of fun per hour is higher for movies than for video games, then why do movies sell more than video games?
A quick look at the empirics shows that the observations are accurate at least for aggregate figures. Counting movies as $10 per viewing, there are significantly more movie views than game purchases, comparing the highest grossing films and best-selling video games. Of course, we cannot determine how these figures are aggregated and how they handle issues such as exchange rate of foreign currency and inflation in these quick statistics. A more fundamental issue is that friend's argument focuses on the substitution of movies for video games because one is cheaper in terms of fun per hour, whereas the raw number of sales says nothing about each consumer's decision to purchase one or the other. [1] The problem that I want to focus on, however, is that "fun" as derived from video games and "fun" as derived from movies are different notions altogether. By comparing $2.5 video game fun per hour to $5 movie fun per hour, we are assuming that video game fun and movie fun are on equal footing. For most people, they are not.
Despite the fact that different sources of utility like video games and movies are difficult to compare, they are all lumped into the category of utility. And we begin to see how measuring all the different sources of utility, and most importantly, combining them into a single measurement is a very tricky business. Indeed, economists over the years have struggled to operationalize the concept of utility into a measurable quantity, and consequently, the role that utility plays in consumer theory has evolved over time.
During the late 19th century, economists under the influence of utilitarianism were convinced that utility is an absolute physical quantity that can be measured, i.e., phrases like "video games give Mary 3 units of utility" carry a meaning independent of how many units of utility Mary assigns to other forms of consumption. This idea led to works such as Edgeworth's Mathematical Psychics, [2] which attempt to make rigourous how utility can be measured in an absolute sense.
Of course, no amount of mathematics can rectify the fundamentally problematic approach of assigning absolute significance to numbers that simply do not carry any physical meaning by themselves. Utility is similar to ideas like mass and length in physics, which can be defined easily enough as the amount of matter in an object and the distance between two objects, respectively, but is more subtle to operationalize into a measurable quantity. And similar to the physical counterparts, if one says the length of some object is 3, we do not have any idea how long the object is at all! 3 could be in units of feet, meters, Planck lengths or light-years. As soon as we specify units, however, we immediately have an idea of how long the object is.
How units help us is that we have defined what exactly a meter is in terms of a physical object or occurrence. Historically, a prototype meter stick was kept in storage by the International Bureau of Weights and Measures, but to reduce uncertainty, now the meter is fixed relative to the speed of light. Other fundamental quantities like mass and time are similarly either directly defined by some physical standard or is mathematically related to other quantities that are defined by physical standards. Therefore, measurements make sense only inasmuch as they are relative to some established standard.
Later interpretations of utility acknowledge the fact that it is meaningless to speak of x units of utility. Instead the substitution interpretation of utility became the standard. This is an attempt to put preferences of goods relative to each other. Therefore, even though units of video game fun per hour and movie fun per hour do not carry meaning alone, their quotient, video game fun per unit of movie fun does. Economists call this the marginal rate of substitution of video games for movies, which means the minimum number of hours of video game playing a consumer is willing to give up to gain one hour of movie-watching. (the minimum and consumer "willing" requirements together force the consumer to be indifferent before and after this substitution). [3] This is certainly an improvement over measuring absolute utility, for now at least the substitution of goods is observable.
With the solution to one problem, however, arises another. With substitution, we can reasonably say measurements of utility with respect to one consumer is well-defined, as long as the consumer's preferences are "nice". [4] But does substitution provide a well-defined way to compare utility between different consumers, i.e. can we compare one consumer who claims he is willing to give up 1 hour of video games to watch a movie with another consumer who claims she is willing to give up 8 hours for a movie?
I claim that we cannot because the two consumers' values of an hour of movie watching may be inherently different, which is to say the basis with respect to which the two consumers are measuring the value of playing video games may be different, so measurements relative to the two bases cannot be directly compared.
The physics analogy here is say two observers are asked to measure the distance between two points using two different meter sticks. The first meter stick is made slightly longer and the second slightly shorter, so the same physical distance is measured to be longer by the second observer than the first. To each observer, using his/her ruler as the basis of measurement, their measurements are accurate, yet the differences in the meter sticks prevent the two observers' measurements from agreeing.
The fix to the physics case of measuring length is obvious: give everyone a standardized ruler! Unfortunately, this implementation doesn't translate well into economics because the equivalent would be to use a neural-scrambler to set all consumers' values of movies to be exactly equal. Manipulation of preferences to achieve mathematically nice results is really not what economics is about.
Surprisingly, even the physics fix of standardizing the rulers used by the two observers is not enough. One of the consequences of special relativity is that there is no universal rest frame, so there is in fact no physical grounds to believe a single set of measurements should be taken as the absolute standard in physics either! [5] Physicists deal with this problem by exploiting invariant quantities, i.e. quantities that are independent of the observers' state, such as Einstein's postulate that the speed of light is the same in all inertial frames. Along with invariant quantities are transformation rules that give a mathematical connection between quantities made by observers in different states. By applying the correct transformation rules, one can in fact compare observations made by observers in two different locations, traveling at different speeds relative to each other, etc.
Economists cannot emulate the physicists' solution. As far as I know, there are simply no invariant quantities that economists can take advantage of. (Setting everyone's value of movies as the same amounts to arbitrarily setting an economic invariant, but then again, the keyword is arbitrarily). Without an invariant, it is not possible to derive transformation laws that connect consumer A's value of a movie with consumer B's value of a movie, and cross-person substitution rates remain painfully incomparable.
This inherent incomparability is usually silently neglected in economic works. For example, every time that the utility functions of individuals are aggregated to derive the social welfare function (i.e. the well-being/utility of the society as a whole) we are assuming that utilities of different people can be added, which would require that utilities be comparable in the first place!
Perhaps the incomparability is just a philosophical nitpick and doesn't really affect the end result of our work? Examples of carelessly comparing measurements made in different reference frames in physics, and the host of paradoxes they lead to, should convince us otherwise. [6] On the other hand, relativistic effects in physics only become apparent in real life when we deal with objects traveling near the speed of light, so for most phenomena on earth, classical mechanics still holds well enough. Perhaps no difficulties arise in economics currently because we are not dealing with situations that approach some yet-unknown limit.
Economics and utility theory have a "can't live with it; can't live without it" relationship. The shaky foundations of utility measurement is one of the main criticisms toward modern economic theory, and economists are always searching for new ways to make the concept of utility or preference more rigourous. Barring some miraculous invariance relation, the current trend in experimental economics and neuroeconomics essentially boils down to the need to find more systematic ways to characterize preferences. Yet, no matter how we look at preferences, economics cannot do away with utility because "the point" of economics is to allocate scarce resources such that utility, happiness, fun (no matter what word you use for the concept) is maximized. Without considering utility, the enterprise of resource allocation, and hence economics, will be for naught.
----
[1] The aggregate statistics merely give the number of video games versus movies sold, but does not shed any insight on the degree of overlap between the video game and movie market. It is possible that there is great overlap between the two markets, suggesting that consumers actually tend to buy both goods together as opposed to choosing one over the other as friend's claim tacitly assumes. Even if the market overlap is small, the fact that both goods bring in decent numbers is sales suggests that there are probably better reasons for the divide in the markets than the substitution effect. For example, it may be that younger generations play more games, and older generations watch more movies.
[2] No joke, I seriously it said Mathematical Physics when I first happened upon the title.
[3] Below I provide the mathematics behind how utility gives rise to the marginal rate of substitution:
Let x be hours of video game playing and y be hours of movie watching, and U be the utility of the consumer. Assuming a consumer has well-defined utility that is affected by movie watching and video game playing, so the utility U is a function of x and y, i.e., utility is denoted U(x,y). The first-order total differential is
Difficulties arise immediately when we consider how we should define utility operationally, i.e. how do we define it in a way that allows it to be measured? But that leads to further questions of what we mean by measure? The following example highlights some of these difficulties.
A friend of mine recently observed that video games cost around $50 and playtime usually lasts over 20 hours, whereas movies cost around $10 and lasts about 2 hours. The cost of "fun per unit time" for video games would be around $2.50, whereas for movies it is around $5. (We just divide the cost by the hours of fun it is estimated to provide). He asked me, if the cost of fun per hour is higher for movies than for video games, then why do movies sell more than video games?
A quick look at the empirics shows that the observations are accurate at least for aggregate figures. Counting movies as $10 per viewing, there are significantly more movie views than game purchases, comparing the highest grossing films and best-selling video games. Of course, we cannot determine how these figures are aggregated and how they handle issues such as exchange rate of foreign currency and inflation in these quick statistics. A more fundamental issue is that friend's argument focuses on the substitution of movies for video games because one is cheaper in terms of fun per hour, whereas the raw number of sales says nothing about each consumer's decision to purchase one or the other. [1] The problem that I want to focus on, however, is that "fun" as derived from video games and "fun" as derived from movies are different notions altogether. By comparing $2.5 video game fun per hour to $5 movie fun per hour, we are assuming that video game fun and movie fun are on equal footing. For most people, they are not.
Despite the fact that different sources of utility like video games and movies are difficult to compare, they are all lumped into the category of utility. And we begin to see how measuring all the different sources of utility, and most importantly, combining them into a single measurement is a very tricky business. Indeed, economists over the years have struggled to operationalize the concept of utility into a measurable quantity, and consequently, the role that utility plays in consumer theory has evolved over time.
During the late 19th century, economists under the influence of utilitarianism were convinced that utility is an absolute physical quantity that can be measured, i.e., phrases like "video games give Mary 3 units of utility" carry a meaning independent of how many units of utility Mary assigns to other forms of consumption. This idea led to works such as Edgeworth's Mathematical Psychics, [2] which attempt to make rigourous how utility can be measured in an absolute sense.
Of course, no amount of mathematics can rectify the fundamentally problematic approach of assigning absolute significance to numbers that simply do not carry any physical meaning by themselves. Utility is similar to ideas like mass and length in physics, which can be defined easily enough as the amount of matter in an object and the distance between two objects, respectively, but is more subtle to operationalize into a measurable quantity. And similar to the physical counterparts, if one says the length of some object is 3, we do not have any idea how long the object is at all! 3 could be in units of feet, meters, Planck lengths or light-years. As soon as we specify units, however, we immediately have an idea of how long the object is.
How units help us is that we have defined what exactly a meter is in terms of a physical object or occurrence. Historically, a prototype meter stick was kept in storage by the International Bureau of Weights and Measures, but to reduce uncertainty, now the meter is fixed relative to the speed of light. Other fundamental quantities like mass and time are similarly either directly defined by some physical standard or is mathematically related to other quantities that are defined by physical standards. Therefore, measurements make sense only inasmuch as they are relative to some established standard.
Later interpretations of utility acknowledge the fact that it is meaningless to speak of x units of utility. Instead the substitution interpretation of utility became the standard. This is an attempt to put preferences of goods relative to each other. Therefore, even though units of video game fun per hour and movie fun per hour do not carry meaning alone, their quotient, video game fun per unit of movie fun does. Economists call this the marginal rate of substitution of video games for movies, which means the minimum number of hours of video game playing a consumer is willing to give up to gain one hour of movie-watching. (the minimum and consumer "willing" requirements together force the consumer to be indifferent before and after this substitution). [3] This is certainly an improvement over measuring absolute utility, for now at least the substitution of goods is observable.
With the solution to one problem, however, arises another. With substitution, we can reasonably say measurements of utility with respect to one consumer is well-defined, as long as the consumer's preferences are "nice". [4] But does substitution provide a well-defined way to compare utility between different consumers, i.e. can we compare one consumer who claims he is willing to give up 1 hour of video games to watch a movie with another consumer who claims she is willing to give up 8 hours for a movie?
I claim that we cannot because the two consumers' values of an hour of movie watching may be inherently different, which is to say the basis with respect to which the two consumers are measuring the value of playing video games may be different, so measurements relative to the two bases cannot be directly compared.
The physics analogy here is say two observers are asked to measure the distance between two points using two different meter sticks. The first meter stick is made slightly longer and the second slightly shorter, so the same physical distance is measured to be longer by the second observer than the first. To each observer, using his/her ruler as the basis of measurement, their measurements are accurate, yet the differences in the meter sticks prevent the two observers' measurements from agreeing.
The fix to the physics case of measuring length is obvious: give everyone a standardized ruler! Unfortunately, this implementation doesn't translate well into economics because the equivalent would be to use a neural-scrambler to set all consumers' values of movies to be exactly equal. Manipulation of preferences to achieve mathematically nice results is really not what economics is about.
Surprisingly, even the physics fix of standardizing the rulers used by the two observers is not enough. One of the consequences of special relativity is that there is no universal rest frame, so there is in fact no physical grounds to believe a single set of measurements should be taken as the absolute standard in physics either! [5] Physicists deal with this problem by exploiting invariant quantities, i.e. quantities that are independent of the observers' state, such as Einstein's postulate that the speed of light is the same in all inertial frames. Along with invariant quantities are transformation rules that give a mathematical connection between quantities made by observers in different states. By applying the correct transformation rules, one can in fact compare observations made by observers in two different locations, traveling at different speeds relative to each other, etc.
Economists cannot emulate the physicists' solution. As far as I know, there are simply no invariant quantities that economists can take advantage of. (Setting everyone's value of movies as the same amounts to arbitrarily setting an economic invariant, but then again, the keyword is arbitrarily). Without an invariant, it is not possible to derive transformation laws that connect consumer A's value of a movie with consumer B's value of a movie, and cross-person substitution rates remain painfully incomparable.
This inherent incomparability is usually silently neglected in economic works. For example, every time that the utility functions of individuals are aggregated to derive the social welfare function (i.e. the well-being/utility of the society as a whole) we are assuming that utilities of different people can be added, which would require that utilities be comparable in the first place!
Perhaps the incomparability is just a philosophical nitpick and doesn't really affect the end result of our work? Examples of carelessly comparing measurements made in different reference frames in physics, and the host of paradoxes they lead to, should convince us otherwise. [6] On the other hand, relativistic effects in physics only become apparent in real life when we deal with objects traveling near the speed of light, so for most phenomena on earth, classical mechanics still holds well enough. Perhaps no difficulties arise in economics currently because we are not dealing with situations that approach some yet-unknown limit.
Economics and utility theory have a "can't live with it; can't live without it" relationship. The shaky foundations of utility measurement is one of the main criticisms toward modern economic theory, and economists are always searching for new ways to make the concept of utility or preference more rigourous. Barring some miraculous invariance relation, the current trend in experimental economics and neuroeconomics essentially boils down to the need to find more systematic ways to characterize preferences. Yet, no matter how we look at preferences, economics cannot do away with utility because "the point" of economics is to allocate scarce resources such that utility, happiness, fun (no matter what word you use for the concept) is maximized. Without considering utility, the enterprise of resource allocation, and hence economics, will be for naught.
----
[1] The aggregate statistics merely give the number of video games versus movies sold, but does not shed any insight on the degree of overlap between the video game and movie market. It is possible that there is great overlap between the two markets, suggesting that consumers actually tend to buy both goods together as opposed to choosing one over the other as friend's claim tacitly assumes. Even if the market overlap is small, the fact that both goods bring in decent numbers is sales suggests that there are probably better reasons for the divide in the markets than the substitution effect. For example, it may be that younger generations play more games, and older generations watch more movies.
[2] No joke, I seriously it said Mathematical Physics when I first happened upon the title.
[3] Below I provide the mathematics behind how utility gives rise to the marginal rate of substitution:
Let x be hours of video game playing and y be hours of movie watching, and U be the utility of the consumer. Assuming a consumer has well-defined utility that is affected by movie watching and video game playing, so the utility U is a function of x and y, i.e., utility is denoted U(x,y). The first-order total differential is
dU = (∂U/∂x) dx + (∂U/∂y) dy.
Setting dU = 0 and rearranging we get
- dy / dx = (∂U/∂x) / (∂U/∂y)
The right-hand side is the quotient of the marginal utilities of video games and watching movies, which is the ratio of the raw units of utility gained from playing an extra hour of video games and from watching an extra hour of movies. (In this context, U takes on real numbers, but should not be interpreted as an existing, acceptable measurement of utility in the sense that the numbers that U take on have a physical meaning. Instead, one should think of U(x,y) as the image of an order-isomorphism U, between the totally ordered set of the consumers' preferences to the real line). We see this is equal to the left-hand side, which is the hours of movies the consumer is willing to forgo (hence the negative sign) for one hour of video game playing -- the left-hand side is certainly a physical quantity. Since we assumed dU = 0, we know this equality holds when the consumer is indifferent before and after the substitution.
[4] By "nice" consumer preferences, we specifically mean preferences that can be cast into a total ordering, i.e. reflexive, antisymmetric, transitive and complete preferences. Of particular note is that these properties force the non-existence of cycles in preferences, e,g. situations where a consumer prefers x to y, y to z, but z to x.
[5] Special relativity is covered in almost every introductory mechanics or electricity and magnetism text. Kleppner & Kolenkow's An Introduction to Mechanics, and Griffiths' Introduction to Electrodynamics both offer illuminating discussions of the implications of special relativity on measurement.
[6] Length contraction, time dilation are good examples. Of particular note is the relativity of simultaneity, which leads to paradoxes that seem to defy our notion of causality if we do not treat it carefully!
[4] By "nice" consumer preferences, we specifically mean preferences that can be cast into a total ordering, i.e. reflexive, antisymmetric, transitive and complete preferences. Of particular note is that these properties force the non-existence of cycles in preferences, e,g. situations where a consumer prefers x to y, y to z, but z to x.
[5] Special relativity is covered in almost every introductory mechanics or electricity and magnetism text. Kleppner & Kolenkow's An Introduction to Mechanics, and Griffiths' Introduction to Electrodynamics both offer illuminating discussions of the implications of special relativity on measurement.
[6] Length contraction, time dilation are good examples. Of particular note is the relativity of simultaneity, which leads to paradoxes that seem to defy our notion of causality if we do not treat it carefully!
2011-06-01
The Problem of Conceptualism
I have a confession to make, a confession that will probably bar me from theoretical physics forever: I'm a conceptualist. No, not the philosophical kind. Jury's still out on whether universal qualifiers can exist. I'm a physical one. I believe that everything in physics should be understood in terms of physical concepts.
The physical part is important. There are two ways to analyze anything in physics. The first way is with math. If you take the Poynting vector of an oscillating dipole you see that there is energy at infinity. Bam, radiation. But this doesn't tell you why you get radiation. In order to get that you'd have to notice that due to finite propagation time an oscillating dipole creates expanding "kinks" in the electric field. These kinks look like waves. Ergo radiation. This is conceptualizing the problem, recasting it in terms of what the world is actually doing.
Obviously mathematics is important in physics. You can't quantify anything without it, and without quantification you don't know whether your bridge will fall down or explode. What about qualification? Do we need conceptualization? Certainly it helps all physics before 1915 or so. Einstein built special relativity entirely off of gedanken, or conceptualization experiments. Things started getting a little tricky with quantum mechanics, though. It's really goddamned hard to imagine a probability wave, and the uncertainty principle is designed specifically to mess with our heads. Then you get deeper. Cosmology. Particle physics. String theory. The deeper you go the more the qualification becomes math. There is no physical reality happening, just math becoming macroscopics. Do isospin and hypercharge even exist? I have no idea.
I want to believe that conceptualization is still important. Certainly it becomes important in applied physics. If you can't imagine how the physics interacts with your intentions, then you fail as a technologist. I do not know how to rationalize it for pure physics. Surely you can get an understanding of what is going on without caring about it's physicality? But then we're no longer doing physics. We're doing reality math. That does sound pretty cool, but it also seems almost antithetical to the ideas of both reality and math.
There is one possibility to patch it up. We know from special and general relativity that there are things we know are real, but far to complicated for the human mind to comprehend. That's why we represent them entirely mathematically. This bothers me for other reasons that I will not go into now, because it is convention nonetheless. This allows for reality to be happening at the particle level while still requiring that the only qualitative analysis be mathematical. This is probably going to be the way it's going to go.
But what about the skills of conceptualization? Do they simply become useless with the patch? I'd say no, and it's a stance I feel comfortable taking. Conceptualization is simply a manifestation of imagination, and imagination is irrevocably wedded to creativity. And creativity is essential for insight at all levels. Einstein used them all to formulate both relativities. But we're all not Einstein, and we have to show that it also applies to us mere mortals. So let me give an example.
A capacitor is a set of two oppositely charged plates. Obviously they'll attract each other. This gives them potential energy, which for a very long time we've been taught to think of as energy that "balances the checkbook" for conservation. In EM we learned that the energy is in the form of the electric field between them, which carries it's own energy. This was the point where I asked the teacher "so is it field energy or potential energy?" She changed the subject. Later on a friend and I worked out that potential energy was field energy. Any sort of potential energy is actually real energy "trapped" in some kind of field. This has provided a great deal of insight into physics and provided a useful tool for understanding how certain problems interacted with each other. This was a realization that could not have happened without creativity and imagination. Even if you do argue that it could have, you would have to accept that you'd need such creativity to actually do anything with it.
That's my current position on the topic. Creativity in the form of conceptualization may not be necessary to 'get' what's going on in advanced physics, but it's hugely beneficial when you need to create new knowledge and models of reality. It's also necessary to craft the knowledge and models into practical creations for human use. That's why my love of conceptualization keeps me out of theoretical physics. I'd be much much happier doing applied.
The physical part is important. There are two ways to analyze anything in physics. The first way is with math. If you take the Poynting vector of an oscillating dipole you see that there is energy at infinity. Bam, radiation. But this doesn't tell you why you get radiation. In order to get that you'd have to notice that due to finite propagation time an oscillating dipole creates expanding "kinks" in the electric field. These kinks look like waves. Ergo radiation. This is conceptualizing the problem, recasting it in terms of what the world is actually doing.
Obviously mathematics is important in physics. You can't quantify anything without it, and without quantification you don't know whether your bridge will fall down or explode. What about qualification? Do we need conceptualization? Certainly it helps all physics before 1915 or so. Einstein built special relativity entirely off of gedanken, or conceptualization experiments. Things started getting a little tricky with quantum mechanics, though. It's really goddamned hard to imagine a probability wave, and the uncertainty principle is designed specifically to mess with our heads. Then you get deeper. Cosmology. Particle physics. String theory. The deeper you go the more the qualification becomes math. There is no physical reality happening, just math becoming macroscopics. Do isospin and hypercharge even exist? I have no idea.
I want to believe that conceptualization is still important. Certainly it becomes important in applied physics. If you can't imagine how the physics interacts with your intentions, then you fail as a technologist. I do not know how to rationalize it for pure physics. Surely you can get an understanding of what is going on without caring about it's physicality? But then we're no longer doing physics. We're doing reality math. That does sound pretty cool, but it also seems almost antithetical to the ideas of both reality and math.
There is one possibility to patch it up. We know from special and general relativity that there are things we know are real, but far to complicated for the human mind to comprehend. That's why we represent them entirely mathematically. This bothers me for other reasons that I will not go into now, because it is convention nonetheless. This allows for reality to be happening at the particle level while still requiring that the only qualitative analysis be mathematical. This is probably going to be the way it's going to go.
But what about the skills of conceptualization? Do they simply become useless with the patch? I'd say no, and it's a stance I feel comfortable taking. Conceptualization is simply a manifestation of imagination, and imagination is irrevocably wedded to creativity. And creativity is essential for insight at all levels. Einstein used them all to formulate both relativities. But we're all not Einstein, and we have to show that it also applies to us mere mortals. So let me give an example.
A capacitor is a set of two oppositely charged plates. Obviously they'll attract each other. This gives them potential energy, which for a very long time we've been taught to think of as energy that "balances the checkbook" for conservation. In EM we learned that the energy is in the form of the electric field between them, which carries it's own energy. This was the point where I asked the teacher "so is it field energy or potential energy?" She changed the subject. Later on a friend and I worked out that potential energy was field energy. Any sort of potential energy is actually real energy "trapped" in some kind of field. This has provided a great deal of insight into physics and provided a useful tool for understanding how certain problems interacted with each other. This was a realization that could not have happened without creativity and imagination. Even if you do argue that it could have, you would have to accept that you'd need such creativity to actually do anything with it.
That's my current position on the topic. Creativity in the form of conceptualization may not be necessary to 'get' what's going on in advanced physics, but it's hugely beneficial when you need to create new knowledge and models of reality. It's also necessary to craft the knowledge and models into practical creations for human use. That's why my love of conceptualization keeps me out of theoretical physics. I'd be much much happier doing applied.
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