Sure, if you'd like to hold off on trig till you've had enough calculus to establish it... traditionally I've seen Euler's equation derived from taylor series... that was how I was introduced to trig and Euler's equation, but it seems to be an unfashionable way of going about it.
Personally, I've always found Eulers theorem far more useful than the pythagorean theorem, but you may know nifty tricks that I don't;)
And there in lies the mistake. Everybody is in such a damn hurry to teach this or that 'practical' application of math that they neglect the underpinings that makes it easy...
Trig should be about a 1 to 2 week topic in school. If instead of having students memorize endless identities you simply teach them 1 (Eulers equation) and show them how to easily derive the rest then it becomes pretty trivial.
All of the trig identities fall out as simply through simple algebraic games when you start with Euler's equation. It also makes looking at the calculus of trig pretty trivial, greatly simplifies the study of waves, etc. I cannot for the life of me understand why everyone doesn't teach it this way.
Since when is a teaching degree considered 'Advanced'? It's generally been well understood for some decades that it's somewhat less work than an English degree, and other than the monopoly guaranteed job field, somewhat less useful.
SWT and RCP are good choices for a cross platform app.
As to cross-platform/cross browser web apps. I've generally found that if you stick to XHTML 1.0 Strict, CSS 1.0, and the DOM 1 core object model for Javascript the web apps I've written just work cross browser 90% of the time, and the 10% of problem is the non-standard behavior of IE that I was going to have a problem with whether I supported the other browsers or not. Or at least that's been my experience doing aggressively cross browser web dev. Oh, and also avoid using tables for layout of non-tabular things. Frankly, what makes cross-browser dev hard is IE. If you live clean (ie standards complaint) your pages will just work in KHTML/Mozilla/Opera out of the box, but about 50% of your time will be spent trying to produce something to work around IEs bugs.
More important even than the collection of tools in your toolbox, is the breadth of approach and understanding of systems that comes from having experience with all of those tools.
Cross skilling is a definite must. Being able to manage the *nix servers, keep the J2EE containers going, manage the network, address security issues, etc, even if only on a decent enough level to be able to assist the *real* experts in those areas in interfacing into your area of expertise is a real plus.
However, I've noticed that almost everyone I know in IT who knows jack about Windows has been made unhappy by that knowledge. Maybe I'm just to far out in enterprise land (where NOTHING important is EVER put on a Windows box), but Windows knowledge leads to having to address all of the stupid annoying issues Windows boxes sprout. I'd far rather spend my time architecting useful solutions to hard problems in the enterprise level stuff than have to fight with the Windows virus dejure (at least on the desktop, network level mitigation can be fun).
If you need to cross skill pick up some background in J2EE containers, or Oracle DBA skills, or go pick up a CCIE and learn somethings about the network. Not only do those add more earning power than Windows skills, but they don't make you want to slit your wrists.
(Proud to have had almost know Windows expertise since 1993:) ).
Let me go over this slowly on home mortgage tax deductions.
On your existing mortgage, under the current system, with the existing mortgage interest deduction you pay 15.3% (payroll taxes) on every dollar before you get to apply it to your mortgage interest, and 15.3% + your income tax on every dollar before you get to apply it to mortgage principle.
Under the FairTax, you pay 0% tax on your dollar before it is applied to either mortgage interest or principle, since the FairTax does not tax loan payments at all.
Which system do you think you do better under? Still attached to your mortgage interest deduction?
No, the FairTax does not require sending in receipts. EVERY household receives a rebate every month for the amount they would have paid in taxes if they spent up to the poverty level for a household of their size.
As to being regressive... here is a comparison of effective tax rates for various household sizes and spending/income levels. If you look at it you will see that every married household does better under the FairTax, and that some single households with low incomes and children do worse (it's very hard to compete with the -24.7% tax rate the Earned Income Tax rate provides).
I still remember being told by an atmospheric scientist when I was an undergrad *not* to go into atmospheric science, because it was almost impossible to do science in that field anymore. If you wanted funding you either took it from the pro or anti global warming people. And if you took money from one crowd and your results DIDN'T support their position, you'd have a very hard time getting funding from them again. This was in 1993. I'm sure it's much worse now.
Basically, anytime the science gets politicized it starts getting questionable. I'll easily trust what comes out of solid state physics, because it has no political import, and the commercial consumers don't *care* what the results are as long as they allow them to do real physical things that are cool. I don't trust atmospheric science because it's SO political at this point.
IBM is cutting those 13,000 jobs in Western Europe for two reasons:
1) Those workers are hugely expensive. 2) The market for their goods and services isn't growing in Western Europe (as Western Europe isn't growing appreciably).
I don't feel threatened because as an American Worker I 1) Am cheaper. 2) Am in a growing market. 3) Am still experiencing strong productivity gains.
Thus these 13k laid off IBM workers are not competing against me, because they aren't competetive with me.
As to offshoring and India... I've worked with offshoring efforts to India, they're great for some things. They are not currently great for what I do. If things reach the point where my value can be replicated at lower cost in India, ship my job offshore, I'll find something else to do.
I love python. It's by far my prefered language for development, but it has one major impediment that makes it very hard to take seriously in many rolls in an enterprise: the GIL (global interpreter lock).
You see Python has quite good support for threads, but there are a number of operations in the interpreter that are hacked into being thread safe by providing a global lock on the whole interpreter. One of them is reference counts on objects. So everytime I do an assignment, I have to queue for the GIL. This effectively means that I only really run one thread at a time, even if I have multiple CPUs in the box (or soon, multiple cores).
As more and more applications start shifting to multicpu (or multicore boxes) this problem becomes a much more noticable issue.
OK... sure, if we add in interest on the debt ($160.2 billion out of a $1880.1 billion in revenue in 2004 according to CBO: http://www.cbo.gov/showdoc.cfm?index=1821&sequence =0 ) you get another 8% or so. Even taking my original 27% number (and I SOOO agree with you about BATF and DEA being things that should be cut) that would only bring us to %35 of revenue at the federal level.
At the state level I pay sales taxes in the neighborhood of 6.25% ( the localities can layer on another 2%, but I'm willing to count that into local fire and police and roads even though I suspect it's paying for other things).
Sure... lets add in the Department of Justice (many parts of which like the DEA, ATF, etc I consider a deteriment, not a service). DEA budget for 2004 can be found here:
http://www.whitehouse.gov/omb/budget/fy2006/just ic e.html
They spent $29 billion in 2004.
Federal courts budget is here:
http://www.uscourts.gov/judiciary2005.html
They got $5.1 billion in 2004. So law enforcement and courts at the federal level cost $34.1 billion in 2004. Out of $1880.1 billion in revenue in 2004 that's almost another 2% of my taxes. So if I spot you all of Justice (which I feel is hugely over generous) and the Federal Courts that brings the total to 27% of my Federal income and payroll taxes paying for an actual service for me.
Education funding varies state to state, but in my state it's almost entirely funded through local property taxes, not my state sales tax. The state moves some of the property tax money 'around' to balance things out, but that still leaves me wondering why I'm paying so much in property taxes.
By my count about 25% of my federal payroll and income taxes, and NONE of my state sales taxes actually go to pay for services I use (or have any intention of using/desire for).
I don't see how NY taxing a TN resident is all that different...
I agree. The only question is where to draw the line. First, I suspect that drawing the line in absolute terms in undesirable, as the cost of money and the inflation rate vary over time, and what you are really seeking to control is the maximum allowable risk premium. Second, I don't think you want to cap the risk premium as low as 4.5%. It would basically make the credit worthy class smaller than the investor class.
Cost of Money right now is about 2.5% (Fed Rate) Expected Inflation is about 3% right now
So if you fix the top rate at 10% then the maximum allowable risk premium is 4.5%. This means you can afford to lend to a pool where maximally 4.3% of the people you lend to default.
Last time I pulled my credit report (you do check your credit report, right) that meant people with credit scores over 700 or so. This basically means that 40-50%+ of Americans would be to risky to lend to.
Don't get me wrong. I do support some form of usury laws because I do believe that some people are such large credit risks they shouldn't be allowed to borrow period (letting them do so is a harm to them and society). But you do have to realize that when you set the max interest rate for your usury laws you are not so much limiting the profit of credit card issuers as you are restricting access to credit to millions of Americans.
The public education system is, IMHO, broken beyond all repair. It is broken for a number of easily identifiable reasons:
1) It is the convolution of public finance of education (which is a good thing) with public provision of education (which doesn't seem to work that well).
2) It separates customers (the student, and by extension the parents) from the providers (teachers, and by extention the schools). If you are a student, your teacher doesn't work for you, she works for the school. You aren't a customer of the school, the state government and the local school board are the customer of the school.
3) It is a system without acceptable feedbacks. Elements of the system may fail for decades without meaningful consequences. A given student can be failed for their entire educational career (k-12) without any substantive corrective action being taken.
My proposed solution:
1) Determine how much per pupil you are going to spend.
2) Send a check for that amount to the student (the customer) in care of their parents (as they're educational guardian) every year.
3) Administer an evaluation exams annually to each student. If the student either doesn't perform up to their age level or doesn't show a year or more improvement since the last assessment, then send the case to a special court to appoint a new educational guardian for the child.
As long as the child can demonstrate skills at or above age level or has made a year or more of progress, I DON'T CARE where the money went.
Public finance, customer control, private provision.
Hmm... when pursuing a BS in Physics as an undergrad I was required to take 30 credit hours out of 124 in liberal arts and foreign language (which I wouldn't mind in general, but the offerings where I was weren't worth the time and effort). I think there must have been some elective credit hours available on top of that, but I think I spent all of them on the math degree:)
Breaking in is always hard to do. If it's any consolation it's a pain finding good entry level people as well. Make sure you document the project you work on independently (and perhaps some of your mathematical interest) on your resume. I can't tell you how many times I've seen people almost loose a job because they almost didn't bother to mention some item of outside work that showed passion and initiative that they thought didn't matter.
It also helps to have opinions that show a depth of understanding. I tend to use two questions in interviews a lot when I think the interviewee can handle them (and they have the right background), I alternate the order I ask them in:
1) Why does Java suck? 2) Why does Java rock?
If you understand the language well enough to field those questions well, it says a lot of positive things about your interest and how much thought you put into the tools use. I also occasionally learn arcane issues or features of Java from interviewees with such a question.
I would tend to agree that many liberal arts degrees compare favorably to junk degrees like communication or marketing. But then, I've seen to many modern liberal arts curricula were you are required to take less foreign language than a science major, and sometimes not significantly more 'hard liberal arts' classes (history, philosophy, serious literature... as opposed to 'soft' blank studies classes) outside your area of focus than a science major has to take.
CS is a special case. To many people with no passion for the subject have gone into CS seeking a paycheck, and to many programs have been willing to cater to the untalented in order to cash their tuition checks.
I'm completely unsurprised that you've done well with a music degree. Music people tend to be highly repurposable for the same reason many hard science people are easily repurposable: it does something strange and useful to the way you think.
Interesting... I've never heard that claim before. I've seen, and heard from many quarters, the claim I made about history majors, but at least in the circles I run in anthropology and sociology are seen as 4 year vacation degrees.
Neither field has much of a reputation that I am aware of for producing much in the way of useful insight.
Please point me to some indication otherwise, I am always willing to entertain the possibility that I am mistaken, if for no other reason than because I've known myself to have been mistaken on so many occasions in the past.
Re:The decline of generalism
on
Who Needs Harvard?
·
· Score: 4, Interesting
Actually, it isn't a decline in generalism, it's a decline in liberal arts degrees. If you really want a generalist, hire a physics major. Most liberal arts majors get almost no meaingful training in mathematics, or science. Mathematics and science background, and more importantly the kind of critical thinking they engender, is crucial today. Liberal arts majors don't have that.
I interview lots of job candidates. While specialization that will make them applicable to the problem their being hired for is a plus, it's not the deciding factor, because I will need to use them on something completely different in 6 months to a year. Adaptability is key. Quick learning is key. The ability to flesh out a hard technical problem and come up with an innovative solution to it is key. I've never seen anyone with a liberal arts degree who could do those things. I see physics, mathematics, biochem, and engineering people do them routinely.
The one kind of liberal arts major I've seen a general use for is history majors. They can pull together large quantities of scattered data and write a coherent explanation of what it all means. That's a niche, but it's a highly useful niche.
Slashdot Mirror
Sure, if you'd like to hold off on trig till you've had enough calculus to establish it... traditionally I've seen Euler's equation derived from taylor series... that was how I was introduced to trig and Euler's equation, but it seems to be an unfashionable way of going about it.
;)
Personally, I've always found Eulers theorem far more useful than the pythagorean theorem, but you may know nifty tricks that I don't
And there in lies the mistake. Everybody is in such a damn hurry to teach this or that 'practical' application of math that they neglect the underpinings that makes it easy...
Trig should be about a 1 to 2 week topic in school. If instead of having students memorize endless identities you simply teach them 1 (Eulers equation) and show them how to easily derive the rest then it becomes pretty trivial.
Euler's equation:
e^(i*x) = cos(x) + i*sin(x)
Need a double angle formula? No problem.
e^(i*2*x) = cos(2*x) + i*sin(2*x)
e^(i*2*x) = (e^(i*x))*(e^(i*x))
= (cos(x) + i*sin(x))*(cos(x) + i*sin(x))
= (cos(x))^2 - (sin(x))^2 + i*2*cos(x)*sin(x)
So you can clearly see that
cos(2*x) = (cos(x))^2 - (sin(x))^2
sin(2*x) = 2*sin(x)*cos(x)
All of the trig identities fall out as simply through simple algebraic games when you start with Euler's equation. It also makes looking at the calculus of trig pretty trivial, greatly simplifies the study of waves, etc. I cannot for the life of me understand why everyone doesn't teach it this way.
Since when is a teaching degree considered 'Advanced'? It's generally been well understood for some decades that it's somewhat less work than an English degree, and other than the monopoly guaranteed job field, somewhat less useful.
SWT and RCP are good choices for a cross platform app.
As to cross-platform/cross browser web apps. I've generally found that if you stick to XHTML 1.0 Strict, CSS 1.0, and the DOM 1 core object model for Javascript the web apps I've written just work cross browser 90% of the time, and the 10% of problem is the non-standard behavior of IE that I was going to have a problem with whether I supported the other browsers or not. Or at least that's been my experience doing aggressively cross browser web dev. Oh, and also avoid using tables for layout of non-tabular things. Frankly, what makes cross-browser dev hard is IE. If you live clean (ie standards complaint) your pages will just work in KHTML/Mozilla/Opera out of the box, but about 50% of your time will be spent trying to produce something to work around IEs bugs.
More important even than the collection of tools in your toolbox, is the breadth of approach and understanding of systems that comes from having experience with all of those tools.
I presume you are going after the routing and switching? Have you passed the written yet?
:)
I wish you good luck
Cross skilling is a definite must. Being able to manage the *nix servers, keep the J2EE containers going, manage the network, address security issues, etc, even if only on a decent enough level to be able to assist the *real* experts in those areas in interfacing into your area of expertise is a real plus.
:) ).
However, I've noticed that almost everyone I know in IT who knows jack about Windows has been made unhappy by that knowledge. Maybe I'm just to far out in enterprise land (where NOTHING important is EVER put on a Windows box), but Windows knowledge leads to having to address all of the stupid annoying issues Windows boxes sprout. I'd far rather spend my time architecting useful solutions to hard problems in the enterprise level stuff than have to fight with the Windows virus dejure (at least on the desktop, network level mitigation can be fun).
If you need to cross skill pick up some background in J2EE containers, or Oracle DBA skills, or go pick up a CCIE and learn somethings about the network. Not only do those add more earning power than Windows skills, but they don't make you want to slit your wrists.
(Proud to have had almost know Windows expertise since 1993
Let me go over this slowly on home mortgage tax deductions.
On your existing mortgage, under the current system, with the existing mortgage interest deduction you pay 15.3% (payroll taxes) on every dollar before you get to apply it to your mortgage interest, and 15.3% + your income tax on every dollar before you get to apply it to mortgage principle.
Under the FairTax, you pay 0% tax on your dollar before it is applied to either mortgage interest or principle, since the FairTax does not tax loan payments at all.
Which system do you think you do better under? Still attached to your mortgage interest deduction?
No, the FairTax does not require sending in receipts. EVERY household receives a rebate every month for the amount they would have paid in taxes if they spent up to the poverty level for a household of their size.
As to being regressive... here
is a comparison of effective tax rates for various household sizes and spending/income levels. If you look at it you will see that every married household does better under the FairTax, and that some single households with low incomes and children do worse (it's very hard to compete with the -24.7% tax rate the Earned Income Tax rate provides).
I still remember being told by an atmospheric scientist when I was an undergrad *not* to go into atmospheric science, because it was almost impossible to do science in that field anymore. If you wanted funding you either took it from the pro or anti global warming people. And if you took money from one crowd and your results DIDN'T support their position, you'd have a very hard time getting funding from them again. This was in 1993. I'm sure it's much worse now.
Basically, anytime the science gets politicized it starts getting questionable. I'll easily trust what comes out of solid state physics, because it has no political import, and the commercial consumers don't *care* what the results are as long as they allow them to do real physical things that are cool. I don't trust atmospheric science because it's SO political at this point.
IBM is cutting those 13,000 jobs in Western Europe for two reasons:
1) Those workers are hugely expensive.
2) The market for their goods and services isn't growing in Western Europe (as Western Europe isn't growing appreciably).
I don't feel threatened because as an American Worker I
1) Am cheaper.
2) Am in a growing market.
3) Am still experiencing strong productivity gains.
Thus these 13k laid off IBM workers are not competing against me, because they aren't competetive with me.
As to offshoring and India... I've worked with offshoring efforts to India, they're great for some things. They are not currently great for what I do. If things reach the point where my value can be replicated at lower cost in India, ship my job offshore, I'll find something else to do.
I love python. It's by far my prefered language for development, but it has one major impediment that makes it very hard to take seriously in many rolls in an enterprise: the GIL (global interpreter lock).
You see Python has quite good support for threads, but there are a number of operations in the interpreter that are hacked into being thread safe by providing a global lock on the whole interpreter. One of them is reference counts on objects. So everytime I do an assignment, I have to queue for the GIL. This effectively means that I only really run one thread at a time, even if I have multiple CPUs in the box (or soon, multiple cores).
As more and more applications start shifting to multicpu (or multicore boxes) this problem becomes a much more noticable issue.
Kill the GIL.
OK... sure, if we add in interest on the debt ($160.2 billion out of a $1880.1 billion in revenue in 2004 according to CBO: http://www.cbo.gov/showdoc.cfm?index=1821&sequence =0 )
you get another 8% or so. Even taking my original 27% number (and I SOOO agree with you about BATF and DEA being things that should be cut) that would only bring us to %35 of revenue at the federal level.
At the state level I pay sales taxes in the neighborhood of 6.25% ( the localities can layer on another 2%, but I'm willing to count that into local fire and police and roads even though I suspect it's paying for other things).
Sure... lets add in the Department of Justice (many parts of which like the DEA, ATF, etc I consider a deteriment, not a service). DEA budget for 2004 can be found here:
t ic e.html
http://www.whitehouse.gov/omb/budget/fy2006/jus
They spent $29 billion in 2004.
Federal courts budget is here:
http://www.uscourts.gov/judiciary2005.html
They got $5.1 billion in 2004. So law enforcement and courts at the federal level cost $34.1 billion in 2004. Out of $1880.1 billion in revenue in 2004 that's almost another 2% of my taxes. So if I spot you all of Justice (which I feel is hugely over generous) and the Federal Courts that brings the total to 27% of my Federal income and payroll taxes paying for an actual service for me.
Education funding varies state to state, but in my state it's almost entirely funded through local property taxes, not my state sales tax. The state moves some of the property tax money 'around' to balance things out, but that still leaves me wondering why I'm paying so much in property taxes.
Look at it this way. The government services I use from the federal government are:
From my state I get:
From my local municipality I get
By my count about 25% of my federal payroll and income taxes, and NONE of my state sales taxes actually go to pay for services I use (or have any intention of using/desire for).
I don't see how NY taxing a TN resident is all that different...
I agree. The only question is where to draw the line. First, I suspect that drawing the line in absolute terms in undesirable, as the cost of money and the inflation rate vary over time, and what you are really seeking to control is the maximum allowable risk premium. Second, I don't think you want to cap the risk premium as low as 4.5%. It would basically make the credit worthy class smaller than the investor class.
You left out the risk premium.
You do realize that all usury laws do is cap who can get credit right?
Credit Card Rate = Cost of Money + Expected Inflation + Risk Premium
Cost of Money right now is about 2.5% (Fed Rate)
Expected Inflation is about 3% right now
So if you fix the top rate at 10% then the maximum allowable risk premium is 4.5%. This means you can afford to lend to a pool where maximally 4.3% of the people you lend to default.
Last time I pulled my credit report (you do check your credit report, right) that meant people with credit scores over 700 or so. This basically means that 40-50%+ of Americans would be to risky to lend to.
Don't get me wrong. I do support some form of usury laws because I do believe that some people are such large credit risks they shouldn't be allowed to borrow period (letting them do so is a harm to them and society). But you do have to realize that when you set the max interest rate for your usury laws you are not so much limiting the profit of credit card issuers as you are restricting access to credit to millions of Americans.
The public education system is, IMHO, broken beyond all repair. It is broken for a number of easily identifiable reasons:
1) It is the convolution of public finance of education (which is a good thing) with public provision of education (which doesn't seem to work that well).
2) It separates customers (the student, and by extension the parents) from the providers (teachers, and by extention the schools). If you are a student, your teacher doesn't work for you, she works for the school. You aren't a customer of the school, the state government and the local school board are the customer of the school.
3) It is a system without acceptable feedbacks. Elements of the system may fail for decades without meaningful consequences. A given student can be failed for their entire educational career (k-12) without any substantive corrective action being taken.
My proposed solution:
1) Determine how much per pupil you are going to spend.
2) Send a check for that amount to the student (the customer) in care of their parents (as they're educational guardian) every year.
3) Administer an evaluation exams annually to each student. If the student either doesn't perform up to their age level or doesn't show a year or more improvement since the last assessment, then send the case to a special court to appoint a new educational guardian for the child.
As long as the child can demonstrate skills at or above age level or has made a year or more of progress, I DON'T CARE where the money went.
Public finance, customer control, private provision.
Hmm... when pursuing a BS in Physics as an undergrad I was required to take 30 credit hours out of 124 in liberal arts and foreign language (which I wouldn't mind in general, but the offerings where I was weren't worth the time and effort). I think there must have been some elective credit hours available on top of that, but I think I spent all of them on the math degree :)
Nope. Don't much care :)
Breaking in is always hard to do. If it's any consolation it's a pain finding good entry level people as well. Make sure you document the project you work on independently (and perhaps some of your mathematical interest) on your resume. I can't tell you how many times I've seen people almost loose a job because they almost didn't bother to mention some item of outside work that showed passion and initiative that they thought didn't matter.
It also helps to have opinions that show a depth of understanding. I tend to use two questions in interviews a lot when I think the interviewee can handle them (and they have the right background), I alternate the order I ask them in:
1) Why does Java suck?
2) Why does Java rock?
If you understand the language well enough to field those questions well, it says a lot of positive things about your interest and how much thought you put into the tools use. I also occasionally learn arcane issues or features of Java from interviewees with such a question.
I would tend to agree that many liberal arts degrees compare favorably to junk degrees like communication or marketing. But then, I've seen to many modern liberal arts curricula were you are required to take less foreign language than a science major, and sometimes not significantly more 'hard liberal arts' classes (history, philosophy, serious literature... as opposed to 'soft' blank studies classes) outside your area of focus than a science major has to take.
CS is a special case. To many people with no passion for the subject have gone into CS seeking a paycheck, and to many programs have been willing to cater to the untalented in order to cash their tuition checks.
I'm completely unsurprised that you've done well with a music degree. Music people tend to be highly repurposable for the same reason many hard science people are easily repurposable: it does something strange and useful to the way you think.
Interesting... I've never heard that claim before. I've seen, and heard from many quarters, the claim I made about history majors, but at least in the circles I run in anthropology and sociology are seen as 4 year vacation degrees.
Neither field has much of a reputation that I am aware of for producing much in the way of useful insight.
Please point me to some indication otherwise, I am always willing to entertain the possibility that I am mistaken, if for no other reason than because I've known myself to have been mistaken on so many occasions in the past.
Actually, it isn't a decline in generalism, it's a decline in liberal arts degrees. If you really want a generalist, hire a physics major. Most liberal arts majors get almost no meaingful training in mathematics, or science. Mathematics and science background, and more importantly the kind of critical thinking they engender, is crucial today. Liberal arts majors don't have that.
I interview lots of job candidates. While specialization that will make them applicable to the problem their being hired for is a plus, it's not the deciding factor, because I will need to use them on something completely different in 6 months to a year. Adaptability is key. Quick learning is key. The ability to flesh out a hard technical problem and come up with an innovative solution to it is key. I've never seen anyone with a liberal arts degree who could do those things. I see physics, mathematics, biochem, and engineering people do them routinely.
The one kind of liberal arts major I've seen a general use for is history majors. They can pull together large quantities of scattered data and write a coherent explanation of what it all means. That's a niche, but it's a highly useful niche.