Knowledge vs Education: Who Should be Labeled as Educated?

[JoeDawg]

Maths may not correspond 100% to reality but it can be 99.999...% in particle physics. When I say do the analyse correctly, I mean within an agreed upon error with experiment.

I'm sitting in a chair.

That's english, it corresponds to %100 of reality.

You're a snob.

 

[baywax]

I'm sitting in a chair.

That's english, it corresponds to %100 of reality.

You're a snob.

Math is a language used to describe a person's experience of life. It isn't snobbery and it isn't anything more than a language. It has its uses and its unique qualities that come in handy in many different situations in life... like if your building a skyscraper or a recycling plant or a wind-power generator. I'd say that, (with a growing population of humans and the demands it creates on the environment and everyone's experience of life), the maths are a useful and sometimes crucial bit of knowledge and education to have.

 

[Smurf]

My situation is not as black and white as you have described. I have taken some good philosophy subjects, especially the ones that are more distant from science like morality and nature of natural language. I find Wittgenstein's views always genuine and learned a lot of new and interestings things from his work. The philosophy of science is also interesting but am convinced that scientists would be able to think about these principles themselves without the help of philosophers.

But I am more from an economics background. Offcourse one of the big things you learn in economics is that productivity is the underlying driver for growth in society and the way for the future. How does productivity increase? The answer is in science. So its as if economists are saying another discipline is 'the way' forward. Normally that dosen't happen as self promotion is usually the case. So when the former happens, heed the advice and act quick smart. Again its a bit black and white but it depends on the person as well. Some people are a humanitites type and can't do science others vice versa. Although its easier for the science types to be better at humanities than vice versa.

I switched out of a commerce degree into science in second year. However I didn't know much about science other than I loved maths. I took philosophy as well at that time as I realized that making money wasn't the whole purpose of life as I had thought previously. I even thought of doing a combined science/arts degree but didn't. Now I am nearly completing my undergrad degree in science with only one semester left and seem to think that science and maths are more important, powerful and enjoyable then ever. Although my previous mythtical view about them is gone (ironically maybe my philosophy training has helped in this). And see the difference between them and the humanitites more and more.

I see, you haven't really answered what I was looking for though, so let me ask some more detailed questions: What year are you now? How much of each of these fields (various philosophies, economics, science)? Have you taken upper level classes (3rd + 4th year) or lower level classes (1st and second year)? Do you have any graduate studies experience? In what? That kind of thing. The reason this is important is because the experience of a first year philosophy course and a fourth year philosophy course is tremendous. Most lower level SS/Hum courses are extremely broad, boring, and completely lacking in detail. In Philosophy this is particularly the case, purely because of the odd way philosophy is structured (which is why I've decided not to pursue a degree in it myself). You're very much jumping into a conversation in progress and it's almost like you have to learn the entire history of philosophy before you can even begin to comprehend most modern philosophy. This is less so for newer sub-disciplines such as the philosophy of science, but still true none the less.

On what you've said though, I can see a few problems in your thinking. Not logical problems per se but problems in the way you write your thoughts that make it difficult for other people to respond to you, for example above when you say "How does productivity increase? The answer is in science." This is a problem because you fail to define science and you fail to define productivity. What this sentence conveys is that science is equivalent to anything that increases productivity. If I were to make the argument that economics increases productivity as well, that would be easy to back up, you could easily say that, well, that's because Economics is very scientific and is based on empirical evidence and mathematics. And that's all true and very good, but it doesn't add anything, and eventually becomes a tautology.

Another problem is that you seem to be confused about what exactly Humanities are. I've never known a University to consider Economics a humanity, that's a social science. As is political science, sociology, etc,. I'm a social science student, not a humanities student. Philosophy, Languages, History, etc,. are all Humanities and are not social sciences.

If I might infer, these kinds of mistakes are the kind that you study in the Humanities. Critical Arguing and Critical thinking. And from my own personal experience, for whatever that's worth to you, most pure natural science students are quite incapable of making critical arguments or studying language in any degree.

Are you thinking of switching to a science degree though? Do you like maths?

Oh no, I completely belong in social sciences. I do like math, and all sciences. I find them more difficult though, probably because I spend so little time in them compared to poli sci and such. And it seems to me that increasingly, the aggregate of human knowledge is becoming dependant on increasingly complex mathematics. Perhaps Asimov's psychohistory is the future.

Just my thoughts.

 

[AsianSensationK]

In high school, everyone who did well in maths and sciences also did well in the humanities. The reverse genearally wasn't true. However the top people in the humanities were often not maths and science people although one did but his dad was a scientist. He got the dux in English and briefly challenged me in my maths class.

This may be true, but come on. Highschool doesn't count for much. I will say that I kind of agree with you, and maybe for the same reason.

I used to be a dual concentrator in English Literature and Philosophy at one point in my college career (end of my third year). After taking a 400 level course in restoration literature, I couldn't stand the subject and switched to pure mathematics and philosophy. It's a choice I'll never regret. I'll finish with my degree at the end of the summer.

English Literature is pretty ridiculous, because the whole concentration is about reading books and critiquing them. You're not really learning how to do anything new in these courses, but you are wasting a ton of money for something that you could do on your own time.

I don't think you could level the same claim across all non-quantitative subjects though.

 

[JoeDawg]

English Literature is pretty ridiculous, because the whole concentration is about reading books and critiquing them.

There is a bit more to it than that. Studying literature is really multi-disciplinary study... to do it correctly you not only have to the read the book, but read about the history or the period it was written in, the specific author, the things that influenced him/her, you have to know a bit about sociology, politics, philosophy and psychology. Even the sciences can come into play, depending on what you are reading. Its also about learning how to communicate ideas, like in other humanities, which is why studying english can lead to careers in technical writing, marketing etc...

Reading and critiquing may be all you got out of it, but like anything, you tend to get out what you put in.

 

[AsianSensationK]

There is a bit more to it than that. Studying literature is really multi-disciplinary study... to do it correctly you not only have to the read the book, but read about the history or the period it was written in, the specific author, the things that influenced him/her, you have to know a bit about sociology, politics, philosophy and psychology. Even the sciences can come into play, depending on what you are reading. Its also about learning how to communicate ideas, like in other humanities, which is why studying english can lead to careers in technical writing, marketing etc...

Reading and critiquing may be all you got out of it, but like anything, you tend to get out what you put in.

It is true. There is quite a bit of psychology, philosophy, politics, history etc discussed in english literature, but I learned nothing new from doing it (maybe a couple of methods used in literary critique, bit that's it). I definitely recognized that it was a mish-mash of things you could study more formally.

You can say that there's more that can be taken away from a study of English literature, but is it really better than what you could take away from actually studying those other subjects?

Also, there's always better preparation for careers in marketing and technical writing and the like. A concentration in english literature isn't really about preparing anyone for careers. But I'm not willing to qualify the study of the humanities as inferior to anything like pivoxa15, so I should probably get back on track.

@pivoxa15: I'd like to bring up the study of music. It is a part of the humanities, and is often overlooked. Can you really compare studying mathematics to studying music in any significant way? How could you characterize music as being "inferior" to mathematics and still make any sense? If you haven't studied any music, I suggest you try it.

In my experience most people who are terrific at math and physics wind up being too stiff when they start studying music and learning instruments. This is especially true with some of the more modern stuff like blues and rock.

 

[JoeDawg]

You can say that there's more that can be taken away from a study of English literature, but is it really better than what you could take away from actually studying those other subjects?

If you studied all of them, you would be better off. Most people don't have the time to get six degrees though. Instead, Literature gives you a small bit of each and allows you to focus on the areas that interest you. Will studying history directly make you a better historian, probably, but that's missing the point. A more broadbased education has benefits too. It really depends on what you want from your education, what you want to do with it. Reading science fiction for instance, can give exposure to science concepts etc... to people who are not scientists, and don't want to be scientists.

Also, there's always better preparation for careers in marketing and technical writing and the like. A concentration in english literature isn't really about preparing anyone for careers.

The first part I agree with, the second, no so much, any sort of broadbased education, while it doesn't prepare you to directly enter a specific field, can provide wealth of knowledge that can be useful in many types of careers.

And heck, a buddy of mine graduated with a math degree and now he is going back to school for accounting. You never know where you are going to end up.

In my experience most people who are terrific at math and physics wind up being too stiff when they start studying music and learning instruments. This is especially true with some of the more modern stuff like blues and rock.

Music is a wonderful mix of disciplines also. Not only do you require a certain manual dexterity... timing.. etc.. which is generally more used in the trades, but it also combines that with having to understand often complex musical notation, and also creativity, which can be enhanced by both realworld experience and good research skills.

 

[pivoxa15]

I'm sitting in a chair.

That's english, it corresponds to %100 of reality.

You're a snob.

You are trying to model a physical state by answering the question 'what am I doing'? hence using English as the model. If I was to use maths to describe the physical state of that same exact moment you just described in English, I might produce gazzillion pages of equations describing the quantum states of every particle in the system. I am likewise trying to model a physical state but using a different language hence gaining different information.

Using my model, I can test how well my theory matches with the physcial state in the universe via experiment in a quantitative way hence very objective. However you cannot test the validity of your statement quantitavely other than maybe use a survey or poll to ask the opinion of others whehter you are correct or not. Once again there is a high level of subjectiveness in this although with this specific example, things may be very obvious but in interesting cases they will generally not.

 

[JoeDawg]

Using my model, I can test how well my theory matches with the physcial state in the universe via experiment in a quantitative way hence very objective. However you cannot test the validity of your statement quantitavely other than maybe use a survey or poll to ask the opinion of others whehter you are correct or not.

All you are saying here is that English is not Math. Nothing more.

You can write an infinite series of equations, and I could write an endless book on what its like for me sitting in a chair. Both could be entirely accurate with regards to what me sitting in a chair is like. You sitting in a different chair will involve differences in both the book and in math, since you will not be in the same location and you are not me. In both cases we could generalize about what its like 'to sit in chairs'. This would reduce the mathematical level of accuracy and the descriptive english level of accuracy with regards to instances of chair sitting. Which you use, depends on what you are trying to achieve.

All of those will be abstractions, until you verify via observation, and see if they resemble reality.

But that's the last I have to say on this, since I'm repeating myself already.

 

[pivoxa15]

I see, you haven't really answered what I was looking for though, so let me ask some more detailed questions: What year are you now? How much of each of these fields (various philosophies, economics, science)? Have you taken upper level classes (3rd + 4th year) or lower level classes (1st and second year)? Do you have any graduate studies experience? In what? That kind of thing. The reason this is important is because the experience of a first year philosophy course and a fourth year philosophy course is tremendous. Most lower level SS/Hum courses are extremely broad, boring, and completely lacking in detail. In Philosophy this is particularly the case, purely because of the odd way philosophy is structured (which is why I've decided not to pursue a degree in it myself). You're very much jumping into a conversation in progress and it's almost like you have to learn the entire history of philosophy before you can even begin to comprehend most modern philosophy. This is less so for newer sub-disciplines such as the philosophy of science, but still true none the less.

On what you've said though, I can see a few problems in your thinking. Not logical problems per se but problems in the way you write your thoughts that make it difficult for other people to respond to you, for example above when you say "How does productivity increase? The answer is in science." This is a problem because you fail to define science and you fail to define productivity. What this sentence conveys is that science is equivalent to anything that increases productivity. If I were to make the argument that economics increases productivity as well, that would be easy to back up, you could easily say that, well, that's because Economics is very scientific and is based on empirical evidence and mathematics. And that's all true and very good, but it doesn't add anything, and eventually becomes a tautology.

Another problem is that you seem to be confused about what exactly Humanities are. I've never known a University to consider Economics a humanity, that's a social science. As is political science, sociology, etc,. I'm a social science student, not a humanities student. Philosophy, Languages, History, etc,. are all Humanities and are not social sciences.

If I might infer, these kinds of mistakes are the kind that you study in the Humanities. Critical Arguing and Critical thinking. And from my own personal experience, for whatever that's worth to you, most pure natural science students are quite incapable of making critical arguments or studying language in any degree.


Oh no, I completely belong in social sciences. I do like math, and all sciences. I find them more difficult though, probably because I spend so little time in them compared to poli sci and such. And it seems to me that increasingly, the aggregate of human knowledge is becoming dependant on increasingly complex mathematics. Perhaps Asimov's psychohistory is the future.

Just my thoughts.

I am in 4th year uni. 1st year economics, 2nd/3rd year philosophy. In my uni 2nd and 3rd year philosophy are together. No graduate school experience at all.

My posts are non rigorous and not excellent with english. The point was that science is the main driver of productivity. I have problems with calling economics a science. It is a social science but the word social is important because I wouldn't want to confuse economics with the natural sciences which are often denoted by science.

I haven't looked into the definition of humanities actually. In high school all subjects were grouped as either humantities or science. So that is what I went by all these years. Thanks for raising this point.

Natural science students are incapable only because they haven't done a course in critical thinking. However given two people both without having done the course but one is a scientist than you can bet your life who will be better at critical thinking. The main point is that a science student will be able to pick up the contents in a critical thinking course faster than a non science student.

 

[pivoxa15]

All you are saying here is that English is not Math. Nothing more.

You can write an infinite series of equations, and I could write an endless book on what its like for me sitting in a chair. Both could be entirely accurate with regards to what me sitting in a chair is like. You sitting in a different chair will involve differences in both the book and in math, since you will not be in the same location and you are not me. In both cases we could generalize about what its like 'to sit in chairs'. This would reduce the mathematical level of accuracy and the descriptive english level of accuracy with regards to instances of chair sitting. Which you use, depends on what you are trying to achieve.

All of those will be abstractions, until you verify via observation, and see if they resemble reality.

But that's the last I have to say on this, since I'm repeating myself already.

I am also saying maths is more precise than English. And should be the tool of choice if you want some precise, objective results that are indisputable. i.e. HUman language is frequently ambiguous: a given statement can often have many possible meanings. Moreover, the definition of words are themselves inprecise with words defined in terms of other words that uses the orginal to define them. In other words circular reasoning but we often get over that and understand somone else because as Wittgenstein would put it we play and are good at the language game we are brought up with.

I don't like the word infinite if you are trying to describe something that happens in reality.

 

[pivoxa15]

It is true. There is quite a bit of psychology, philosophy, politics, history etc discussed in english literature, but I learned nothing new from doing it (maybe a couple of methods used in literary critique, bit that's it). I definitely recognized that it was a mish-mash of things you could study more formally.

You can say that there's more that can be taken away from a study of English literature, but is it really better than what you could take away from actually studying those other subjects?

Also, there's always better preparation for careers in marketing and technical writing and the like. A concentration in english literature isn't really about preparing anyone for careers. But I'm not willing to qualify the study of the humanities as inferior to anything like pivoxa15, so I should probably get back on track.

@pivoxa15: I'd like to bring up the study of music. It is a part of the humanities, and is often overlooked. Can you really compare studying mathematics to studying music in any significant way? How could you characterize music as being "inferior" to mathematics and still make any sense? If you haven't studied any music, I suggest you try it.

In my experience most people who are terrific at math and physics wind up being too stiff when they start studying music and learning instruments. This is especially true with some of the more modern stuff like blues and rock.

I've done some high school literature. If that counts than I think that it is enjoyable and distinctly different to science or philosophy. It allows one to be human in a way, to express one's emotions via language poetically. And allows one to analyse somone else's work of the same nature. In this way it is more like art or music. I have nothing against them as they let people be more human. Science takes away this component to an extent and that is why they seem so odd and don't fit into society that well.

How much of physics have you studied? It could be that the more you study physics and other sciences the more inferior the humanities become. You will realize that all these emotions, created by music, poetry are just manifestations of physical processes hence physics. However, music and the like has nothing to say about physics.

 

[pivoxa15]

When you're driving to Montana and your tire blows out but you don't know how to repair it or change your tire you are missing some important education and knowledge. When motorists drive by and you don't know how or are too embarassed to wave them down and ask for help, here again you are missing some important knowledge and education. Knowing the inverse squared root of the tire pressure isn't going to help all that much. I notice also that all the rocket scientists in the world can't keep insulation from dislodging and eventually causing disaster for some very cool astronauts.

Education and knowledge is endless and no one can know everything. My point was that science and maths is so important because it allows people to learn new things much more quickly and be better problem solvers and thinkers. Alhtough with your specific situation, I'd fancy a scientist having a better chance at fixing the car than a non scientist.

There was an anecdote of the great theorist and experimentalist physicist Enrico Fermi (some say not since Newton have we had somone so good at both aspects of physics) "During one of his early lecture trips to the United States, a car that he had purchased became diabled, and he pulled into a nearby gas station. After Fermi repaired the car with ease, the station owner offered him a job on the spot."

Being too embarrased to call for help is not really due to lack of education of knowledge and education but your own arrogance. Or maybe just a bit too shy.

 

[baywax]

Education and knowledge is endless and no one can know everything. My point was that science and maths is so important because it allows people to learn new things much more quickly and be better problem solvers and thinkers. Alhtough with your specific situation, I'd fancy a scientist having a better chance at fixing the car than a non scientist.

There was an anecdote of the great theorist and experimentalist physicist Enrico Fermi (some say not since Newton have we had somone so good at both aspects of physics) "During one of his early lecture trips to the United States, a car that he had purchased became diabled, and he pulled into a nearby gas station. After Fermi repaired the car with ease, the station owner offered him a job on the spot."

Being too embarrased to call for help is not really due to lack of education of knowledge and education but your own arrogance. Or maybe just a bit too shy.

Define "scientist"! I know plenty of them and most of them are socially inept and mechanically challenged. (Read: very little education or knowledge of interaction with other human beings shy,embarassed, overly arrogant... always had a lab tech to do the mechanicals and very little or no practical knowledge or education.) Because you have one example of a scientist who can apply his/her knowledge to enabling a "disabled" car is inconsequencial.

Don't get me wrong, some of my best friends are scientists... I love scientists... just keep them stuffed in their own little biodome and we'll all get along. When they are eating their own genetically modified beef, pork, corn, peas, wheat etc... and drinking the "pure" water they've filtered out of a human waste treatment plant and when they take the pharmaceuticals they keep coming up with for psychosomatic illnesses ... then I'll know they're on to something. Madam Curie, the Nobel Laureate for Physics never once had a dose of radiation deliberately administered into one of her body parts... but she did suffer greatly from radiation poisoning coming up with what she thought was a cure. Overall survival rates of cancer patients receiving radiation therapy show that radiation is no cure. Its another complication.

 

[radou]

How much of physics have you studied? It could be that the more you study physics and other sciences the more inferior the humanities become. You will realize that all these emotions, created by music, poetry are just manifestations of physical processes hence physics. However, music and the like has nothing to say about physics.

Please, give me a break.

 

[pivoxa15]

Please, give me a break.

The fact that this is the philosophy forum suggets I am giving people including myself a break. There is nothing specific in my coment. But is not false. The theme of the thread has always been knowledge and education of the general population. Especially the ones who has finished high school and maybe an undergrad degree. The point was that an educated person should have at least the equivalent of senior high school science education so they understand the principles of science and the power of it.

 

[Smurf]

The fact that this is the philosophy forum suggets I am giving people including myself a break. There is nothing specific in my coment. But is not false. The theme of the thread has always been knowledge and education of the general population. Especially the ones who has finished high school and maybe an undergrad degree. The point was that an educated person should have at least the equivalent of senior high school science education so they understand the principles of science and the power of it.

I think your second sentence here nails it right on the head. You haven't said anything really specific this entire thread. It seems like every time you post something you change the topic slightly. The "Theme" of the thread has been on knowledge and education, but your arguments certainly haven't been:

But the thing is with the knowledge of the sciences, maths and logic, one can literally learn anything else with confidence.

Biased being only capable of thinking from the human experience or a humanistic thought which naturally arises from using human languages like English.

For a physics student to learn the pure humanities, they may not be able to apply the physical principles directly so it would take hard work. But they are logical thinkers and good detector of patterns which would help in learning any humanity subject as well. At least there would be less irrational thoughts by someone without any science training but also learning the same humanities subject.

Well if you use maths to analyse something than your own emotions won't affect the conclusion as much ... as if you use English to analyse something. With the latter your own emotions on the day may alter the results but you can't say it is wrong if someone else got a different conclusion. So using English is more subjective.

I am also saying maths is more precise than English. And should be the tool of choice if you want some precise, objective results that are indisputable. i.e. HUman language is frequently ambiguous:

It could be that the more you study physics and other sciences the more inferior the humanities become.

The only thing all your arguments have in common is that in some vague and general way, sciences are superior to humanities.

Here's your original post:

When people speak about getting an education, I think of science, maths, logic as the key foundations to an education. However there are many who supposeddly have an education but may not have done any science beyond year 10 and are very ignorant about maths. Should these people be labeled as educated and or knowledgeable? If they are than they are certainly missing on some very important and useful knowledge.

What exactly do you want to figure out with these questions? Are we discussing the idea of 'education' and what kind of knowledge is essential or beneficial to the average human being? It seems to me your more interested in discussing whether humanities university students are smarter than science university students, or which kind of knowledge is more useful, or which one better reflects reality. These are all completely separate questions.

An extremely important part of any intellectual discussion is defining exactly what you want to discuss, and sticking within that definition. I think your inexperience with the humanities shows by your disregard for his and other basic practices in debate. Granted, you had a hard time from most of the other posters here, who didn't make it easy on you, but let me tell you something: You know when your watching a politician get interviewed on the telly, and the politician ignores the questions he's asked and answers almost completely different ones? There's a very very good reason why they do that (and they're all coached by experts on how to do this), it's because interviewers ask really really bad questions, and if they tried to answer them they'd look horribly confused. So they stick with the message they want to get out.

Have you ever heard the saying, that half of philosophy is asking the right questions? I think you need to spend a lot more time on your questions. But hey, if you want there's plenty of people here to help. Finding good questions is most of the fun sometimes. What happened here is everybody got frustrated and antagonized by each other. Gotta stop that happening if you want a constructive discussion.

 

[radou]

(applaudes, and then bows to Smurf)

 

[baywax]

(applaudes, and then bows to Smurf)

The best education is the "well rounded" education. Concentration in one field will always lead to deficiencies in many other, "useful" fields. The synergy created when diverse educational subjects interact is invaluable as a means to better the human experience.

Diversity rules. That's the way its been for a number of billions of years.

 

[pivoxa15]

I think your second sentence here nails it right on the head. You haven't said anything really specific this entire thread. It seems like every time you post something you change the topic slightly. The "Theme" of the thread has been on knowledge and education, but your arguments certainly haven't been:

I am not a professional in education nor have I finished by undergrad degree so as Von Neumann puts it 'its better to be vaguely right than precisely wrong.'

 

[pivoxa15]

The best education is the "well rounded" education. Concentration in one field will always lead to deficiencies in many other, "useful" fields. The synergy created when diverse educational subjects interact is invaluable as a means to better the human experience.

Diversity rules. That's the way its been for a number of billions of years.

One of my main points is that students learn all subjects but come away with the impression that the sciences are more 'powerful' and appreciate it not just as a technical subject but also its influence on society and the history and philosophy of it.

 

[Moonbear]

I am not a professional in education nor have I finished by undergrad degree so as Von Neumann puts it 'its better to be vaguely right than precisely wrong.'

If your premise is that a scientific education should be more highly valued than other forms of education, then this statement would be a direct contradiction of that premise. In science, it is better to be precisely wrong than vaguely right. Vagueness gets one nowhere; it cannot be tested. Something precisely wrong can be shown to be wrong, and leads to progress. Better to be clearly disproven in order to move forward than to have an entirely untestable claim because it is overly vague.

One of my main points is that students learn all subjects but come away with the impression that the sciences are more 'powerful' and appreciate it not just as a technical subject but also its influence on society and the history and philosophy of it.

When you say this is one of your main points, do you mean that is what you desire to happen, or something you have observed among your acquaintances, or are you asking if this is true on a broader scale?

Going back to the original post here, the two primary qualities of one's education are generally described as breadth and depth of knowledge. And there is a challenge in assessing this. I think each field has a pretty good handle on the criteria that need to be met to consider one's depth of knowledge in that field sufficient to call it an area of specialization, and the level to which one has specialized (undergraduate major, or Ph.D.), but breadth of knowledge is much harder to define. How much depth of knowledge do you need in fields outside your area of specialization in order to consider your breadth of knowledge adequate? The original question seems to be essentially asking this...how much education on science and math does a history major, for example, require in order to consider themselves to have an adequately broad education in subjects outside their field of history? One can turn around the question as well to be: "How much education on history or literature does a science or math major require to be considered to have a sufficiently broad education?"

I think the only way to even begin to answer that question is to look at how one will use their specialization, and how much impact the lack of breadth of knowledge would have on what they will do with their lives. For example, if a political science major is going to be influential in decisions that affect science policy, they better know enough about science to at least understand what the experts are telling them about the pros and cons of a particular policy, even if they are not able to study the field in depth.

Nobody can study all subjects in great depth. That's the assumption I'm going to start out with here. Which means the focus of an education, and one's knowledge base outside their own field cannot be to provide a sampling of every subject out there; there is simply not enough time to do that and still devote adequate time to your specialization. Rather, I argue that the focus of education is to learn how to learn independently, to know how to pick up a textbook, use the index, and know how to read for facts in a way that you acquire an accurate understanding of what you read without a teacher there to guide you. (I think many do not succeed in this area.) One should learn how to cross-check facts and references, how to use a library, to be aware that books can be wrong or quickly outdated, and to inquire into the most current information, or even how to locate experts to ask. Taking courses in a sampling of subjects outside of your field will allow you to see how to apply these skills in fields outside your own. If you can do that, and have a curiosity to continue learning throughout life, you will have succeeded in your education, and can always continue to acquire knowledge.