### A biologist seeks to dumb down science

This fascinating call to dumb down science by E.O. Wilson not only demonstrates my point about the relative lack of intelligence and intellectual rigor on the part of biologists, but is particularly untimely given the recent relevations concerning the economic work of some famous, and apparently similarly limited economists, Carmen Reinhart and Kenneth Rogoff.

For many young people who aspire to be scientists, the great bugbear is mathematics. Without advanced math, how can you do serious work in the sciences? Well, I have a professional secret to share: Many of the most successful scientists in the world today are mathematically no more than semiliterate.

Many of the most successful scientists in the world today are mathematically no more than semiliterate.

During my decades of teaching biology at Harvard, I watched sadly as bright undergraduates turned away from the possibility of a scientific career, fearing that, without strong math skills, they would fail. This mistaken assumption has deprived science of an immeasurable amount of sorely needed talent. It has created a hemorrhage of brain power we need to stanch.

## 183 Comments:

I have a homeschooled kid of junior high school age who is already more mathematically advanced than one of the most famous scientific advocates of TE(p)NS was when he was in his thirties and a tenured professor at Harvard.You could have just said "I have a homeschooled kid of junior high school age."

I hate to bring up the debate.. but when I was writing the response to the response you haven't posted yet... I was going over some standard Keynesian equations and reading some various sites on Keynesian theory and such. While doing so I realized... some of these people don't even know basic algebra. They set up make believe equations and then they would try to manipulate them to solve for this variable or that... and they would literally do it incorrectly. This is like 6th grade math people! X*Y=Z*A... and they move it around to Y= X(Z*A) What? What property of mathematics is that? The "Just move stuff around" property? I wasn't taught that one.

And this was found on the home page of a rather large university's economics department... written by a tenured professor.

I agree with Wilson, to a certain extent. In fields that are not as hard-core mathy as, say, Physics, there are hard-working, intelligent scientists who do good research, but who don't have highly-advanced mathematical skills. Often, there are competent mathematicians and statisticians available with whom they can collaborate when those disciplines are required. This system works when coupled with scientific integrity (the lack of which is a bigger problem, imo).

What's the baseline for mathematical literacy? Post calculus?

I speak from experience when I tell you that baby boomers want to dumb down everything that is hard and not super fun!! And there's always the pathological desire to appear to want to embrace third-world savages of the darkest type possible. For that you have to make hard things damn near disappear altogether.

I don't entirely disagree with Wilson. People in my field (theoretical biology) obviously need strong math skills (note: everyone in my lab actually comes from a physics background, not a biology one, as is somewhat common for the field). However, there are many fields of biology where a weak math background simply is not a severe impediment, as long as biologists (e.g.) understand the basics and know when not to use certain statistical tests.

What's the baseline for mathematical literacy? Post calculus?Basic mathematical literacy is algebra and statistics. Advanced mathematical literacy is geometry, trig, and calculus. Remember, having successfully taken a class in it doesn't mean you actually know how to do it. I did very well in my Japanese classes at university and don't have a single credit in Italian or French. But I speak a lot more Italian and French than I do Japanese.

As Nate noted, there are no shortage of PhDs who can't even manage the algebra. Or in some cases I have seen, the multiplication and the percentages.

However, there are many fields of biology where a weak math background simply is not a severe impediment, as long as biologists (e.g.) understand the basics and know when not to use certain statistical tests.Well, sure, you don't need any math beyond addition for most butterfly collecting.

(note: everyone in my lab actually comes from a physics background, not a biology one, as is somewhat common for the field)That would appear to explain your remarkable ability to discuss potential flaws in TENS without frothing at the mouth. Why so many with a physics background? Is it some sort of fallback for failed physicists or something?

I don't mean that in any critical sense, you understand, but a practical one. Studying physics seems to be a strange way to go about pursuing work in biology.

Every science--even the soft sciences (in fact, most especially the soft sciences) need much more literate mathematicians. If every scientist of even the softest of soft sciences (history, political science, gender studies (snicker), etc.) had an even basic grounding in statistics, academia would be a much better place.

It's true that some sciences are not math heavy. And scientists don't need to worry about math that isn't relevent to their field. But there is almost no field of inquiry in academia (maybe literature, or art history, I guess, but even then I'd be skeptical) that wouldn't be improved if its practitioners understood some basic statistics so they weren't so easily mislead by outliers that they believe to be significant. But which aren't.

Advanced mathematical literacy is geometry, trig, and calculus.Proficiency in differential equations is absolutely necessary in undergraduate physics, and should be a requirement for biology, as well. For one thing, how can anyone understand exponential growth/decay without understanding diff eq?

One would think that the very high failure rate would cause Wilson to at least consider the possibility that the conceptual framework is false, but then, as we can reasonably surmise, logic is not his strong point.It isn't a matter of logic, or math, it is a matter of faith. No faith is worse than the one that is denied. He doesn't know and doesn't care, so long as everyone in his control believes are acts the part. The value of his whole miserably useless overpaid underworked existence depends on the truth that doesn't exist. Of course you won't be able to help him. God couldn't help that man unless he asked for it. He is too invested in a lie and will only dig deeper. He is like a drug addict.

Full out libertines are easier to help. They eventually tire, age, become infirm in ways they can see. This guy? He surrounds himself with fellow believers, and doesn't even dig too much there because they all believe, or pretend to believe, a different form of the lie.

As I suggested in a recent post, I believe they realized they couldn't find truth without God, so decided to aim at everything but the truth in order not to miss the target. And, well, they hit exactly what they aim at, everything but the truth. Addicted to be sure.

Biology majors? Differential equations? Bahahahahahaa

I just demonstrated they can't even handle algebra 1.

why would we need to stanch a hemorrhage of demonstrably inferior brains?Because they are female.

Wilson himself notes that the "annals of theoretical biology are clogged with mathematical models that either can be safely ignored or, when tested, fail." The same is true of economicsAnd "climate science"...

Greg Cochran recently ripped into Wilson's math skills over at "West Hunter", as well.

http://westhunt.wordpress.com/2013/04/09/math-is-hard/

Proficiency in differential equations is absolutely necessary in undergraduate physics, and should be a requirement for biology, as well. For one thing, how can anyone understand exponential growth/decay without understanding diff eq?My experience is that the "standard advanced math toolkit" is pretty much the college intro calc sequence, which is usually something like Calc 1, Calc 2, Multidimensional/Vector Calc, and DiffEq. People with more sophisticated mathematical needs might want complex analysis as well. Those are all you need to prepare you for just about anything that doesn't invovle being an actual mathematician. Of course depending on what you're doing you might be interested in some special topics, which you could teach yourself from this foundation.

Basic probability theory should definitely be a part of mathematical competency, or are you subsuming that into statistics?

Basic mathematical literacy is algebra and statistics. Advanced mathematical literacy is geometry, trig, and calculus.So Wilson is arguing that they don't even need algebra and statistics? Sweet Darwin.

How can one even be granted a BS without at least first year calculus is beyond me.

Wilson's headline is proven wrong by his own words.

He would not be considered competent, let alone "great," if he didn't collaborate w/ good mathematicians and statiticians. So his cliche inequality is proven wrong, he needed good math, he just couldn't provide it.

In fact, one might argue, from his own description, that he was simply a tech gathering data, and it was his collaborators who did the science.

At any rate, it's another biologist who is throwing logic out the window.

Basic probability theory should definitely be a part of mathematical competency, or are you subsuming that into statistics?It's part of statistics.

How can one even be granted a BS without at least first year calculus is beyond me.Yes, although perhaps Wilson got a BA. I can see fine arts grads w/o calculus, but not many others. But it was U [sic] Alabama. Standards are low.

I would add that college students are there for the "college experience" and to get that piece of paper in order to get a job. It is easier to be lazy, avoid the "hard subjects," fraternize, and still get that piece of paper. Math is not hard if you apply yourself. Unlike a lot of the sciences, with math you will get an answer in the end. You may take different paths to get there, shortcuts, alternative solving methods, but if x = k, you will always get k in the end if you do it properly. That's too much work for many, many students. I would say the potential science majors don't go that route because they don't want to mentally sweat too much.

It has created a hemorrhage of brain power we need to stanch.I'm wondering if he is truly ignorant of supply and demand in his field or if he is aware of it but pretends not be because he wants to protect his livelihood and the livelihoods of his friends. Tuition and textbook sales have to keep flowing.

How can you combat willful ignorance on the most important issue conceivable?

One would think that the very high failure rate would cause Wilson to at least consider the possibility that the conceptual framework is falseVDTrueBelievers. Ego Identity.

Economics has driven people out of science, not the math requirements. If you are very good at math there are far more lucrative fields like finance.

"Why so many with a physics background? Is it some sort of fallback for failed physicists or something?".

Bills have to be paid. Kids need to be fed. It's a lot easier for a Phsyics person to muscle into a Biologist's seat than the other way around.

An alternative is to be an "Industrial Physicist" aka "engineer"; however, private industry engineers police their ranks a'la MDs in that regard and tend to blackball pure physics folks.

By the way, the lack of drive and intellectual curiosity in our youth is disheartening, to say the least.

I topped out at vector calculus. But probably should have taken differential equations instead. Whoopsies.

A working understanding of statistics and probability is much more important (especially understanding which statistical test is appropriate) than vector calculus to the average cell biology researcher.

However... any time you are dealing with modeling a phenomenon (e.g. enzyme or receptor kinetics), you'd better have your math right. Anyone who, like E.O. Wilson, wants to decrease the rigor of biology can go sodomize himself with a pinecone.

Considering how much biology research seems to rely on statistics, this is a hilarious fact-free assertion. How on earth can you be a scientist without a basic grasp of probability and statistics? If you can't hack that, you might be better off flipping burgers.

For one thing, how can anyone understand exponential growth/decay without understanding diff eq?Let's not get carried away. Calculus 1 and 2 are perfectly adequate to demonstrate that d/dx exp(x) = exp(x), and the conceptual understanding is usually within easy grasp by the end of the latter course. Usually multivariate calc is required for undergraduate biology, and even that's a little overboard.

Most fields would benefit from fewer requirements, not more. It's an opportunity cost thing. Expanding general education requirements is IMHO the best way to ensure general ignorance.

How on earth can you be a scientist without a basic grasp of probability and statistics? If you can't hack that, you might be better off flipping burgers.Some of us can hack that and better, and yet flip burgers X-P.

I have a homeschooled kid of junior high school age who is already more mathematically advanced than one of the most famous scientific advocates of TE(p)NS was when he was in his thirties and a tenured professor at Harvard.

-- VD

But...but...

socialization!!Math is introduction to abstraction. You can't do science without abstractions.

I still remember a pretty stupid student to whom I tried to explain a basic algebraic equation. He literally yelled at me: "What is 'a'. I can't think about this without knowing what 'a' is.". His head exploded once I told him that 'a' is 'Apple'. Good times.

How important is math to economics? I've seen economics books that didn't have any math in them, and I've also seen ones that had a lot of equations.

By the way, the lack of drive and intellectual curiosity in our youth is disheartening, to say the least.Every generation has had that complaint about their succeeding generation since forever.

How important is math to economics?It's very important to those schools of economics that want economics to be considered a real science like physics.

I still remember a pretty stupid student to whom I tried to explain a basic algebraic equation. He literally yelled at me: "What is 'a'. I can't think about this without knowing what 'a' is.". His head exploded once I told him that 'a' is 'Apple'. Good times.I thought the answer to that was give him basic story problems and have him write out the full words to the equations as he solves them.

Won't take too long before he figures out the benefits of using symbols and shortened expressions.

I noticed that when when I got out of school and faced problems in my fields of endeavor I found mathematical formulas that I needed.

For instance, I found that saving money only required knowing some arithmetic. In architecture and later in outdoor advertising I had to know the square footage of shapes other than rectangles. This required some geometry but it was all I needed.

Of course, when we have to work on the broad frontiers of reseach, that is a different story. Various Mensa tests claim that they measure reasoning ability only, Since I would need a refresher course in math, I wonder if I would pass the test today.

I've forgotten my math, but I'm wiser with age. That could be a subjective opinion only.

Wilson's article is particularly amusing in light of Mike Williamson's claim of the intellectual inferiority of "creationtards". I have a homeschooled kid of junior high school age who is already more mathematically advanced than one of the most famous scientific advocates of TE(p)NS was when he was in his thirties and a tenured professor at Harvard.VD, I don't think that the "creationtards" slur is directed towards, essentially, +1 SD intelligence folks. I would wager that in your homeschooling environment, your pupils have successfully mastered the entire penumbra of what is believed by the mainstream, what your view of the evidence is, what the weaknesses and strengths are, etc. There may even be maths in there somewhere.

This is not the view of what a "creationtards" is, according to those who use the slur. The perception is that there are kids, living on a religious compound, who are given a copy of the bible, and read Genesis, and that's it. There entire biology education.

And for sure, there are some of those rare cases. But I would wager the former is an order of a magnitude more common the later.

Speaking of science, this is too funny not to mention:

It Seems That NASA Has Drawn a Giant Penis on the Surface of Mars

Economics has driven people out of science, not the math requirements. If you are very good at math there are far more lucrative fields like finance.Yup. This is it. The non-productive fields - like finance - are sucking up the brain power. The demand is there, and the money is there, and that's all there is to it.

The same thing is true in software engineering. It's sort of disturbing to see people used to doing production work leaving that field and going into trying to win the App lottery with some inane non-productive app or game or whatever.

I took this course at UW with the math very heavy but it was taught by a scary young Russian non-tenured professor and he hammered us using multivariate calculus. The number of dropped students within the first 2 weeks was astonishing. haha

I submit that part of the problem is the way math is presented to the student.

I'm another with homeschooled kids. By the time my daughters were 20 they were managing their own successful (fast food) franchise stores, had bought their own cars and houses. Hard working, not dumb at all where business math and accounting is concerned.

Deciding to move on from there and get into the medical field, they ran headlong into college algebra. Their main complaint is that it is of no use in the real world, and that the teachers don't seem inclined to explain things in a way that breaks down the logic of what they are trying to do in a 'why' fashion instead of tossing it out as 'math is wonderful and this is the simple stuff'. Someone who can analyze past store traffic, weather predictions and upcoming local special events to put together a weekly supply order doesn't care to be talked down to that way.

Given the number of college graduates I've seen over the years without the ability to do anything useful or practical, I'd suggest a foundation of practical and business oriented math, geometry and trig in an applied fashion, practical statistics and the equations involved, then followed by the algebraic theory and equation solving in a pure form. Finally, make that division of those who have the mental bent for pure math and those who want/need 'engineering' math.

Biology majors typically aren't required to have even as much math as engineering and physics majors are, which is still not all that much. Most of the rigor has already been removed from the math that STEM majors learn, so the curriculum has already been dumbed down a great deal.

But hey, if students want to go into $100k of debt to learn stamp collecting, that's fine by me.

I take that back. It was the "Advanced Treatment" course, the Econ312 version and it was damn brutal. There is a special track at UW for Econ with a mathematical emphasis. Too bad that's not the general track.

You can choose the easy way or challenging way. I really think most students prefer not to be challenged.

Let's not get carried away. Calculus 1 and 2 are perfectly adequate to demonstrate that d/dx exp(x) = exp(x), and the conceptual understanding is usually within easy grasp by the end of the latter course. Usually multivariate calc is required for undergraduate biology, and even that's a little overboard.Meh, fair enough. Though, in my experience, students at this level often lack the conceptual understanding.

How do they know penises don't grow just from watching porn and hooking up to a penile plethysmograph? They need nonsmoker data for comparison. And they want us to take dick science seriously!

Math literacy at least at the algebra and statistics level is fundamental to any science field. But it is more than that. People who aren't math literate will not be able to make sense of reams of data. They will not be clear-headed enough, logical enough, to find their own errors and the errors of others. I realize I'm repeating a fair amount of what you already stated in your article. However, I'm not certain intelligence has as much to do with it as a willingness to reason and focus. These are learned skills. A student who is not willing to dedicate himself to mathematics will be too lazy to reason and focus. I'm astonished at the people who pull out their IQ cards on the first day I meet them (I attend a techie university, but this happened at the liberal arts college I attended, too), but are essentially lazy when it comes to logic. They won't focus!! Focus is one of my only skills, and I can't understand why others can't do it!! I can understand, though. They are mentally lazy, as are most people. The educated world is not immune to mental laziness.

Meh, fair enough. Though, in my experience, students at this level often lack the conceptual understanding.True, but the ones who've read their books (the horror!) and done their homework will understand.

Jill,

Even as a very generous estimate, college-level calculus

requiresan above-average IQ.The same is true of economics, and it is a direct result of insufficient intelligence - or more ominously, insufficient integrity - being used in the construction and testing of those models.Interesting word there, integrity. Math has this annoying tendency of generating demonstrably "right" and "wrong" answers. If you try to use a wrong answer, nothing works and sooner or later it's clear that you're answer is incorrect and needs to be abandoned. When you've got a field full of "scientists" (or economists) who've made their careers on 1 + 2 = 347, they're understandably not too keen on math.

Proficiency in differential equations...This made me realize it's been a decade or more since I've solved a diff eq. I'm rusty. I think I'll give myself a refresher course.

WHAT?

Biology NEEDS Mathematics, human beings understand how nature works with mathematics and statistical studies are the very basics of how to get data out of biological phenomena.

Without Mathematics, Biologists are pretty much making shit up.

Is he a moron or something? I knew that tenure tends to rot the brain, but this is impressive.

"Even as a very generous estimate, college-level calculus requires an above-average IQ."

I don't agree. Calculus has a reputation for difficulty. Yet it's the most basic level of math where all degrees start (in the science and tech world).

Jack Amok,

Free DEQ books: http://www.e-booksdirectory.com/listing.php?category=93

Can't vouch for 'em, but the Chasnov one is from 2010.

Ah, I didn't quite finish my point--most people working toward undergrad degrees don't have above average IQs.

Has anyone else had the experience of learning something completely new and then finding it hard to imagine that you didn't always know it? Happens to me sometimes and it's a strange feeling.

RACE-MEMORY

(By a dazed Darwinian)

I remember, I remember

Long before I was born,

The tree-tops where my racial self

Went dancing round at morn.

Green wavering archipelagos,

Great gusty bursts of blue,

In my race-memory I recall

(Or I am told I do).

In that green-turreted Monkeyville

(So I have often heard)

It seemed as if a Blue Baboon

Might soar like a Blue Bird.

Low crawling Fundamentalists

Glared up through the green mist,

I hung upon my tail in heaven

A Firmamentalist.

* * *

I am too fat to climb a tree,

There are no trees to climb;

Instead, the factory chimneys rise,

Unscaleable, sublime.

The past was bestial ignorance:

But I feel a little funky,

To think I’m further off from heaven

Than when I was a monkey.

~G.K. Chesterton (1925)

Don't mistake the following terseness for hostility. You came to VP with an intellectually honest attitude, as far as I can tell, and this exchange is going to sharpen you.

I don't agree. Calculus has a reputation for difficulty. Yet it's the most basic level of math where all degrees start (in the science and tech world).Irrelevant.

Ah, I didn't quite finish my point--most people working toward undergrad degrees don't have above average IQs.Incorrect. The average IQ score of an undergraduate is usually estimated to be 110-115 (see chapter 1 of "The Bell Curve") and seems to be rising, although they don't seem to be learning anything or capable of independent thought.

"most people working toward undergrad degrees don't have above average IQs."

Exactly.

And this is a big part of the problem.

"Incorrect. The average IQ score of an undergraduate is usually estimated to be 110-115 (see chapter 1 of "The Bell Curve")"

When was the Bell Curve written again?

Yeah thanks for playing.

@Noah B.

Yes, one time I used a Fluke meter rated at 600VAC to check a circuit rated at 4600VAC. Indeed, it's a strange feeling.

"Yes, one time I used a Fluke meter rated at 600VAC to check a circuit rated at 4600VAC. Indeed, it's a strange feeling."

I note you say you only did it the one time.

1992.

Here's 2012 data based on the SATs (naively, as it is now an achievement test rather than an aptitude test). Even with this caveat, and the observation that more students are choosing elementary education over electrical engineering, it is still clear that average undergrad IQ is above 100.

I'm as cynical as they come, Nate, but you could at least peek at WORDSUM.

http://www.statisticbrain.com/iq-estimates-by-intended-college-major/

"The average IQ score of an undergraduate is usually estimated to be 110-115 (see chapter 1 of "The Bell Curve") and seems to be rising, although they don't seem to be learning anything or capable of independent thought."

Yes, I'm already aware of this. Your last statement is why it's all down the rabbit hole for me. And, honestly, if you don't approach calculus with a priori assumptions, it's not that difficult.

Jill,

Also irrelevant. Would you admit that learning calculus requires some small intelligence (perhaps estimated at a score of 100 IQ), aside from the right teaching method and good study habits?

"I'm as cynical as they come, Nate, but you could at least peek at WORDSUM."

Sure. I just don't buy it. Mostly because I know that we're paying for kids with c averages in high school to go... and I know how colleges are complaining about all the remedial classes they have to create because of the idiots coming through the doors.

I will allow though... idiot is a hard thing for me to grasp... as generally 110 and 90 look the same to me.

"I speak from experience when I tell you that baby boomers want to dumb down everything that is hard and not super fun!!" -Fisk Ellington Rutledge III

I suspect you mean Ivory towered tenured communist Boomers and their dimwitted counterparts in education. Right? All of the people my age that I know helped and encouraged their kids in Calculus while in HS plus teaching them who invented it and why.

Sure. I just don't buy it. Mostly because I know that we're paying for kids with c averages in high school to go... and I know how colleges are complaining about all the remedial classes they have to create because of the idiots coming through the doors.The potter complaining about bad clay...I've seen this before...

" if you don't approach calculus with a priori assumptions, it's not that difficult."

I don't think you realize just how dumb someone with an IQ of 90 really is.

"The potter complaining about bad clay...I've seen this before..."

Remember back in the 1980s when C students were encouraged to go to college?

Oh wait.

That didn't happen.

@Nate. I offer no excuse but utter lack of conscientiousness on my part. Making matters worse it wasn't my first time to troubleshoot this particular cabinet. The importance of following the "Lock Out-Tag Out" procedures can not be overstated. So to answer you question, yes, only once.

Yeah, a good potter can make a decent product with bad clay, but he doesn't buy bad clay in the first place. Bad clay will never be much for calculus.

Whoo! Full circle!

In conclusion, colleges have nothing to do with education...and everyone here knew that already.

"Also irrelevant. Would you admit that learning calculus requires some small intelligence (perhaps estimated at a score of 100 IQ), aside from the right teaching method and good study habits?"

Okay, you may find it irrelevant, but I find IQ to be irrelevant (in spite of the fact that you just dropped or allowed for the necessary IQ to be 100). Yes, some people aren't wired to do calculus. Some people don't want to. Some people aren't intelligent enough to get it. While intelligence has some effect on math results, an average intelligence with the right kind of personality/brain wiring AND an ability to focus and work hard are more important than IQ.

Just to set that stage that I know what I am talking .. Calc I, II, III, Diff Eq, Advanced Eng Math, Vector Analysis, Statistics and Probability, Random Signals, Transform Analysis I and II. 25+ year engineer in very high tech field.

I think the fundamental point he is making is correct -- and applied not just to science but engineering as well. The reality is that most of the math you learn in an engineering program will never be used in your professional engineering life -- you tend to use very simple calculus of functions limited to that can exist in real - sin, cos, exp, ln .. x^2 --- you almost never by hand anything past 2nd order systems. And many of the problems that were really really hard to solve and had no close form solutions can now be solved with FEA, CFD, matlab etc . I have meet many an young engineer who made it through school based on their strong math skills who were piss poor engineers --- there is a lot more required to be a good engineer than the math.

I would say math is a good indicator of basic intelligence/IQ but maybe not so good for predictor for success in actual applied science and engineering fields.

"I don't think you realize just how dumb someone with an IQ of 90 really is."

I have an IQ of about 95. Either those five points make a world of difference in me understanding them, or IQ isn't all it's cracked up to be.

I don't think you realize just how dumb someone with an IQ of 90 really is.Really? I routinely test into the mid-90's. There are certainly topics I can't grasp, effectively or not all. And many many that take me months or years longer than people in the median or +1 SD range to master.

What's a good working definition of dumb?

have an IQ of about 95. Either those five points make a world of difference in me understanding them, or IQ isn't all it's cracked up to be.It's sort of hard to contemplate that you are average, or half a deviation below, average. But there it is. You are. Welcome to the club. It doesn't make you a bad person.

"Dumber than me."

clk,

I would say math is a good indicator of basic intelligence/IQ but maybe not so good for predictor for success in actual applied science and engineering fields.You'll want chapter 2 of "The Bell Curve".

"Stupid is as stupid does." Intellect is much more complicated than IQ tests developed in 1916 can measure. If you think just because you scored 145 on the Stanford-Benet that you can rebuild a Chevy or make a woman wet just by talking to her you are sadly mistaken.

For those studying math as a supplement to another field, they don't need to understand the theory, just how to use the math. Recognizing how and when to use certain equations or methods doesn't need a high IQ and applying those equations and methods doesn't either. Just as a construction worker doesn't have to understand the full physics theory behind mass, force, acceleration, etc, he can still use a hammer (the tool) to get his job done. When I tutor people who just need the basics for moving forward in their degree field, I just teach them how to use the formulas and how to recognize the when and where of applicability. The rest is a waste of my breath, regardless of how excited I get when trying to point out connections between different areas of study and previous topics learned and any potential future topics. Beating my head against that wall enough times made me stop.

what's a good working definition of dumb?Voting for liberals.

Voting for liberals.Ahh, but we know that the converse isn't true, so it's probably not a good definition.

Wow...sorry for that crass reference (especially to my sisters on the blog) but I like to make certain that my points stick and I am especially passionate about the simplistic approach to intellect and wisdom.

Regarding calculus, I think an IQ in the 115+ range is probably necessary. As to what the average IQ of college students is, I dunno, but most of them aren't taking calc.

Dh, "a" definition, rather than "the" definition.

Regarding calculus, I think an IQ in the 115+ range is probably necessary. As to what the average IQ of college students is, I dunno, but most of them aren't taking calc.Struggled with it in college, but did well in a moderately rigorous program. Practical applications used almost daily, and the routine calculations are just that. I few friends I had who were likely in the 140's never broke a sweat.

E.O. Wilson's comments made me wonder were the drive is in these brilliant students? Where is the desire to respond to a challenge? Mathematics is very building block oriented, at least to the Calculus 1 level. It may take a person some time to build up to that level, but I think those of average intelligence could get there if they wanted to do so.

I worked with students from several majors when I was an undergraduate. I was always impressed by those outside of the physics and mathematics bunch that would work, and often work hard, to get over the basic physics and calculus 1 hurdles. But the driven ones always made it no matter how much they struggled, the others just faded away. It is more about mind set than raw ability. How many really intelligent people have you seen that utterly failed at life and never even really tapped into their potential?

Average height is what... 5'9? 5'10? Put someone of average height in a room full of NBA players and average suddenly looks awful short.

Its still average though.

"When I tutor people who just need the basics for moving forward in their degree field, I just teach them how to use the formulas and how to recognize the when and where of applicability." LL

Wise. I told both of my sons when they hit college not to waste a single cell on anything besides acquiring the degree. 99% of the learning I have done has been outside of the classroom. Strive to be a Polymath. But then we are Vox-1SD so we have to try harder.

Best comment on the thread:

"This goes a long way to explain the agreement among scientists about the science of global climate change and what is causing it."

LOL.

"Average height is what... 5'9? 5'10? Put someone of average height in a room full of NBA players and average suddenly looks awful short.

Its still average though." - Nate

Right but when you see a guy that is 5'9" dunk...it is a thing of beauty.

"For consider your calling, brethren, that there were not many wise according to the flesh, not many mighty, not many noble; but God has chosen the foolish things of the world to shame the wise, and God has chosen the weak things of the world to shame the things which are strong," I Cor 1:26,27

@OG, I once audited a class that was required for a degree in elementary education. Now, I personally enjoyed it, my favorite part being the proofs on irrationality, such as for sqrt 2. But I felt that the professor who taught the class didn't fully grasp that elementary school teachers are not going to use proofs and theory to explain long division to 3rd graders. But the difference between myself and my fellow students is that I truly enjoy math and the theory and understanding behind the how and why of it all. The other students were practically homicidal by the end of the class and I can understand why. The professor was not a good fit for the particular goal of the class. I think that is reflected throughout every college and university in our country. Hell, even in the high schools. It's unfortunate and a waste of time, energy, and resources.

OG

No one here has ever claimed a high IQ to be a universal good. We've often written about how many problems it causes.

as generally 110 and 90 look the same to me.Yeah, hopelessly out of reach.

"How many really intelligent people have you seen that utterly failed at life and never even really tapped into their potential?" - John Wilson

Yea John...I must agree. How many? Most I think. We have to keep reaching though.

OG

No one here has ever claimed a high IQ to be a universal good. We've often written about how many problems it causes. - Nate

I know and it was not directed toward you or the Ilk at all....Just a pet peeve of mine that because a person scored a 145 once and/or has a Phd after their name they believe they have arrived.

Ugh. Does anybody have any stats to back up the necessity of having an above average IQ to excel at calculus? It sounds like the sort of nonsense that intellectual elites regularly regurgitate. I am able to excel at math because of the way my brain is wired to function, and not because of my (low) IQ. Frustration. I'd like to say "if I can do it anybody can" but I also know that's Disneyesque nonsense. I'm so tired of IQ. Anyway, I have things to do, such as math(s). If you add an "s" you're smarter than the average bear (because everything's better in Anglophilia).

Like an asshole Psychiatrist asked me one time when I suggested a change in dosage for a patient..."What Medical School did you go to?"

I told him I went to F*ck U.

We have to keep reaching though.Living a happy life means knowing your limits.

There is a really interesting movie, a bit older now, that covered intelligence and potential. I can't remember what it was called, but there was a scene where the bad future government servant said something along the lines that stated potential cannot be exceeded, if you appear to have exceeded your potential, it was merely incorrectly measured in the first place.

This is of course true. I believe it was the dramatic foil of the story, where a genetically inferior person won out over a genetically superior person, through harder work.

In the real world, this doesn't happen, on average. Depending on the degree difference from the elite to the average, it may not even be physically possible.

Basketball was a nice analogy. The 5'10" person dunking is a sight to behold, but move down another SD, and tell me how interesting it is to see a 5'6" person dunking. Okay, fine, now move down another SD, and tell me how interesting it is to see a 5'1" person dunking in game conditions. Move down another half-deviation, and tell me again.

There is nothing that makes you a bad person being average or even below average. Many of us live perfectly happy, contented lives, doing our business and making a living and having a nice existence, privileged to be in America.

But we also don't catch butterflies and then try to tell ourselves we're real scientists, either.

How important is math to economics? I've seen economics books that didn't have any math in them, and I've also seen ones that had a lot of equations.Actual economics--as done by economists--is basically just a field of applied statistics. It's nothing

butmath.@dh

That sounds nice and all but the commenters on this blog aren't the ones selling the student debt scam.

@VD:

That would appear to explain your remarkable ability to discuss potential flaws in TENS without frothing at the mouth. Why so many with a physics background? Is it some sort of fallback for failed physicists or something?Maybe we think the biologists have been doing some of the modeling wrong.

I can't speak for all of my colleagues, but among the handful of physicists-turned-biologists whose backgrounds I do know, one got into evolutionary biology after using genetic algorithms and wanting to better understand how the parameter space affects the optimality of solutions. Another two got into evolutionary biology by studying protein dynamics. Pretty much all of us think the standard population genetic toolbox (neutral theory, accounting for linkage by rescaling the effective population size, etc.) is inappropriate for studying organisms in which clonal dynamics are important, like facultative outcrossers and ones that adapt rapidly (e.g., HIV). So some new models, away from the neutral theory, are required.

"Ugh. Does anybody have any stats to back up the necessity of having an above average IQ to excel at calculus? It sounds like the sort of nonsense that intellectual elites regularly regurgitate. I am able to excel at math because of the way my brain is wired to function, and not because of my (low) IQ." - Jill

Savant Syndrome like Autism is expressed as a continuum from moderate to acute. Intellect is expressed in a spectrum of areas and just because a person scores average on an antiquated IQ Test...does not make them an average person.

@Nate:

Biology majors? Differential equations? BahahahahahaaActually, even in my undergrad ecology course a basic knowledge of diffy q was required (Lotka-Volterra), albeit at a conceptual level.

EO Wilson 2013:"If your level of mathematical competence is low, plan to raise it, but meanwhile, know that you can do outstanding scientific work with what you have."

"Far more important throughout the rest of science is the ability to form concepts, during which the researcher conjures images and processes by intuition."

EO Wilson 1999:"The physicists succeeded magnificently, but in doing so they revealed the limitations of intuition unaided by mathematics; an understanding of Nature, they discovered, comes very hard."

"Still, because of its effectiveness in the natural sciences, mathematics seems to point arrowlike towards the ultimate goal of objective truth."

I'd add to the above comment: if you want to do work in biology that has any kind of computational or theoretical bent to it, it's easier to learn the quantitative stuff first and the biology later than vice-versa.

why would we need to stanch a hemorrhage of demonstrably inferior brains?Why did the Waffen SS have a division of swarthy Muslims?

They need the numbers. I think they know that they can't win based on data, hypothesis, and research, they need a legion of priests and priestesses to apply for grant money to convert the unbelievers.

There's an open sourced statistical package out on the net called "R". There's a lot of support for it, universities with download mirrors, 3rd party modules that can do things unimaginable with numbers, etc. There's over a dozen US mirrors alone, but the one that consistently has the most current everything is a cancer research center in Seattle. I'm sure those are guys doing science, benefiting mankind.

I've also seen physics majors function as competent mechanical engineers. They understand the math, the kinematics, and have a solid understanding of motors, and electrical power. Throw in a little hands on skills and some experience turning a wrench, and there's a lot a physics major is capable of. They seem to me to have curiosity, a desire to learn and no fear of math.

I think the driving force here is universities looking at profits from bio departments and trying to cut attrition in customers.

"Basketball was a nice analogy. The 5'10" person dunking is a sight to behold, but move down another SD, and tell me how interesting it is to see a 5'6" person dunking. Okay, fine, now move down another SD, and tell me how interesting it is to see a 5'1" person dunking in game conditions. Move down another half-deviation, and tell me again." - dh

Thank you dh the analogy is not perfect and as you aptly pointed out breaks down rather quickly. A person 5'5" should probably not count on a career in the NBA but could play in some College and perhaps many HS venues. Likewise a person 2SD from the top should probably not plan on Harvard or Yale. In addition, Phoenix University has evening classes.

;-)

@Jill

I would personally opine that IQ has little to do with it (other than very low would really struggle). I think it is the level of instruction that determines how well someone grasps calculus. If a teacher is heavy in theory and focusing on the delta so intrinsic to the proof, it's not so easy to work backwards from theory to application. If a prof shows how to solve based upon the previous years of math, ie algebra, a student could grasp calculus and solving integration and differentiation pretty easily. One thing I see over and over is that people let the notation overwhelm them (this holds true in stats also). They see the alphas, betas, and deltas and brain lock.

Separate area, but...I find the state of the debate on anthropogenic global warming to be pitiful. And I've come to realize it's largely due to math illiteracy.

Proponents of AGW, including some of the scientists who form the backbone of the so called "consensus", can't seem to perform basic arithmetic when discussing possible solutions. They just chant "solar...wind...conservation" without the slightest clue about the amount of energy involved or the logistics of transitioning to other sources. When you actually hit them with numbers, they look like deer in the headlights, then proceed to chant some more.

Why, again, should I trust these people and their climate models when they are challenged by simple logistics?

Our politicians are no better. Basic math could be used to demonstrate that the Waxman-Markey bill was logistically and financially impossible, yet our president and the Democrats in Congress tried to pass it.

How, precisely, is a democracy of people who can't perform basic arithmetic supposed to function again?

Getting back to the topic, the strongest objections to abiogenesis and TE(p)NS are rooted in mathematics. Which is why biologists continue to believe in both. If you can't understand the objection...

"Basketball was a nice analogy. The 5'10" person dunking is a sight to behold, but move down another SD, and tell me how interesting it is to see a 5'6" person dunking. Okay, fine, now move down another SD, and tell me how interesting it is to see a 5'1" person dunking in game conditions. Move down another half-deviation, and tell me again." - dh

The analogy works in a couple different ways. You have both height (IQ) and the force multiplier... one's ability to leap (this could be lots of things, work ethic for example). The shorter one is (the lower the IQ) the higher one has to jump to dunk. Its not really impressive to see Shaq dunk. And what's really impressive about Lebron is that he's huge... AND he has insane leaping ability as well. Its the combination.

We don't like the blog because Vox is smart. We like the blog because he's smart and he's working at applying himself.

So integration was an attempt to reverse the slippery slope? (This is one of the few places where people will understand).

I had a surreal experience. I am not an EE but understand and build circuits. Electronics is harder than software because electrons actually have to move, generate magnetic fields, have resistance, so you have to worry about skin-effect, cross-talk, and a bunch of other magical things and can't just cut and paste circuits.

I had to review something from a Chinese engineering team. I pointed out they had a 300mA fuse going into a boost power supply that was supposed to work down to 6v, but produce 20v at 150mA, which is 3 watts. When I pointed out that 3W = 500mA @ 6V, I got a response that showed they did not understand so I tried to explain it again.

So for biology and geology, maybe math isn't as needed (though they should know statistics to know if their sample size is sufficient). But electrical engineering? (We will find out both how good their civil engineers are and how corrupt their cement and iron suppliers at the next earthquake of sufficient magnitude).

Software though is mostly applied mathematics. One problem with "software patents" is that most things are obvious to 3SDs but not to the USPTO.

" Likewise a person 2SD from the top should probably not plan on Harvard or Yale. In addition, Phoenix University has evening classes."

We get your point but your scale is off. 2 SD from the top in terms of IQ is very.. very high.

if you want to do work in biology that has any kind of computational or theoretical bent to it, it's easier to learn the quantitative stuff first and the biology later than vice-versa.Yep. Feynman explained that the library has a map of a cat tucked away somewhere.

I don't think you need an exceptional IQ to understand calculus or other mathematics, but it helps the way it is taught. Calculus, algebra, statistics, and the rest are all around you in the world and everyday life. If you can grasp what is going on, it is easy to put an equation on it. If you have the equations but can't see how they apply to electrical fields, or your car accelerating or decelerating it will be useless.

The baseline for any real science is one or two courses past differential equations. Most things cannot be adequately modeled without a basic level of understanding the concepts of laplace and other transforms and diffy Q's. Physics and chemistry take several courses past diffy Q's. All real engineering majors take at least one past diffy q's. If you can't understand the math, you are just playin.

BTW, biology isn't a science--where does it use the scientific method? Lots of untestable hypotheses, no real science after basic genetics which left biology long ago.

...

On the very same blog were we discuss the fact that most people are incapable of dialect, and must rely on rhetoric, you guys are seriously going to suggest that someone of average IQ should be able to grasp calculus without a problem?

...

smh

You can't say, "MPAI" and then say "Calculus is no big deal to most people" when most people clearly cannot hack calculus!

Jill,

Okay, you may find it irrelevant, but I find IQ to be irrelevant (in spite of the fact that you just dropped or allowed for the necessary IQ to be 100).I think I found our critical point of contention. Were you aware that IQ tests are normed such that 100 is the average score?

"We don't like the blog because Vox is smart. We like the blog because he's smart and he's working at applying himself." - Nate

Right? Encourages me to be a Renaissance man like him. Shoot... I have been dragged kicking and screaming into learning economics, the dialectic as applied to the blogosphere, and even an analytical approach to game. I used to think Gamma was just the letter between ἄλφα and ðelta.

Furthermore, you claim that your IQ is 95 and you understand calculus. If that is true, it would be strong evidence against my claim that 100 is an effective lower limit to understanding. To that end, two questions:

1) Where did you get your IQ score?

2a) In your own words, what does d/dx mean?

(If you prefer calculus skills to theoretical understanding, answer this question instead...)

2b) What is the limit of the following function as x approaches infinity? f(x) = (x + 1) / (x^2 - 1)

"Josh April 24, 2013 11:18 AM

By the way, the lack of drive and intellectual curiosity in our youth is disheartening, to say the least.

Every generation has had that complaint about their succeeding generation since forever."

I understand what you're getting at but there is evidence for this that goes beyond old folks complaining about young people's propensity for play rather than work.

To borrow a word from Fred Reed, they've been enstupidated by the school system, on purpose.

Nate, again, I contend that you can teach someone to use a tool without them having to understand the underlying proof or theory behind that tool. Math is really just a series of steps, one-by-one, moving things around, substitutions, until you get the answer. You can teach the steps and "basic" reasoning behind why you are doing them, and a person could replicate that over and over again, never understanding the proof that makes it so. That has little to do with IQ other than IQ has to be of a minimum level to follow instructions and recognizing symbols and patterns and determining how to apply a process. People do this every day in their lives without being high IQ.

Since Chemistry, Biology, Physic aren't very valuable undergrad degrees, I don't know why they aren't converted to 5 year master's degrees where you spend 2 years learning statistical probability, differential equations, set theory, and other useful tools of data analysis. Could probably get it done in 4 years if they would strip out the worthless indoctrination classes you have to take.

"On the very same blog were we discuss the fact that most people are incapable of dialect, and must rely on rhetoric, you guys are seriously going to suggest that someone of average IQ should be able to grasp calculus without a problem?" - Nate

Most people are not "incapable of dialect" they haven't learned it. Like Calculus the Dialectic method is learned...""Plato, particularly in his middle and late dialogues, uses it to describe “the total process of enlightenment, whereby the philosopher is educated so as to achieve knowledge of the supreme good, the Form of the Good” (Blackburn 1996, 104)."

A process ...taught and caught.

A high IQ would only indicate the speed at which a person has the ability to grasp a thing and that given that the standard measure of IQ is in fact a comprehensive measure of all facets of intellect, which it isn't.

"Nate, again, I contend that you can teach someone to use a tool without them having to understand the underlying proof or theory behind that tool."

and I contend that if you don't understand what the math represents... you're not actually doing the math.

If you can't explain what an integer does... what good does it do you to be able to use one to calculate? You don't know what you're calculating!

Since Chemistry, Biology, Physic aren't very valuable undergrad degrees, I don't know why they aren't converted to 5 year master's degrees where you spend 2 years learning statistical probability, differential equations, set theory, and other useful tools of data analysis. Could probably get it done in 4 years if they would strip out the worthless indoctrination classes you have to take.Depends on what you mean by "valuable". There are decent opportunities to be chem lab techs (and even bio majors get such positions). Smart people can advance here.

As for what you describe, it's similar to what a friend of mine said the way it was done at the Mexican university one of his friends attended.

"Most people are not "incapable of dialect" they haven't learned it. Like Calculus the Dialectic method is learned..."

Like calculus.. most folks are incapable of understanding it.

Where did you get your IQ score?

"At the gettin' place" - No Country for Old Men

2a) In your own words, what does d/dx mean?

It means d forward slash dx

(If you prefer calculus skills to theoretical understanding, answer this question instead...)

2b) What is the limit of the following function as x approaches infinity? f(x) = (x + 1) / (x^2 - 1)

The limit of 1/x as x approaches Infinity is 0

I don't know Calculus but I can Google like a MF.

I've never put much stock into IQ (for the record, my score is 135). I think what is most important is how your brain is wired -- you can be a very intelligent person but be limited in math, while you can also be very good in math but limited in nearly every other area (as many mathematicians seem to be). I'm not naturally bad at math, but I'm mathematically illiterate through a combination of shockingly bad math teachers in high school and laziness on my part.

I regret not taking math seriously and therefore never learning how to do it, though I can't say this intellectual deficiency has significantly harmed me. I think it would help otherwise intelligent students if math teachers would focus more on the practical applications of what they teach.

Nate, you cannot get to the level of calculus without the preceding maths such as algebra. I could explain how to figure out the limit to that problem above by Aeoli Pera using just the level of algebra taught in most high schools and definitely at the college level without having to use the formal theory of f(a+h) and tiny changes and all that happy horseshit that I had to deal with in advanced calc where it was all theory and proofs. I am pretty sure that those of average IQ and no calculus would be able to follow along.

"Most people are not "incapable of dialect" they haven't learned it. Like Calculus the Dialectic method is learned..."

Like calculus.. most folks are incapable of understanding it. - Nate

Maybe but we could sure make "most" head toward "many" if the students are properly taught and motivated. If you said only people who pass Calculus can have sex ... you would see a serious increase in Walmart's bottom line. They sell "Calculus for Dummies" for $12.08 plus tax and shipping.

I also don't put a huge amount of stock in IQ. I do well in the areas that IQ tests measure, but these tests don't address many complex abilities like artistic and musical abilities. I can't, for example, draw freehand or carry a tune, and I'm always a bit amazed by people who can do these things.

Shucks...should have read.

Maybe but we could sure make "MANY" head toward "MOST" if the students are properly taught and motivated.

Drain Bamage.

" LL April 24, 2013 2:56 PM

Nate, again, I contend that you can teach someone to use a tool without them having to understand the underlying proof or theory behind that tool. Math is really just a series of steps, one-by-one, moving things around, substitutions, until you get the answer. You can teach the steps and "basic" reasoning behind why you are doing them, and a person could replicate that over and over again, never understanding the proof that makes it so. That has little to do with IQ other than IQ has to be of a minimum level to follow instructions and recognizing symbols and patterns and determining how to apply a process. People do this every day in their lives without being high IQ."

You just described my relationship with algebra. It's likely I can't write a proof to save my life but I can solve an equation.

I regret not taking math seriously and therefore never learning how to do it...No time like the present.

Athor, and that is why I said what I said. I have tutored many people from very bright, to not so bright, from working towards a serious degree where higher math is going to be needed to the minimum requirements. In all the years I've done this, I have not run across anyone who could not be taught at least how to solve the problems, even if it was step-by-step rote solving. It can be done and does not need higher understanding to do it, although deeper knowledge and understanding helps to see greater connections within the field of math (and/or applications to other fields).

You just described my relationship with algebra. It's likely I can't write a proof to save my life but I can solve an equation.I don't know, this is what a lot of inferior programmers come to thinking. "Well, I am not strong on my math BUT"

And then I give them a go, and find silly things all over their code that is related to the fact they have "clever" ways to do things that in fact require no cleverness and no hoops. I am not dead set against clever tricks, but at this point in the evolution of the art, it's sort of dumb.

For example, many of the original computer scientists struggled with creating graphics that had a smooth spline calculated (a nicely rounded edge). Calculating the floating point operation that does this is, it turns out, very expensive for earlier CPUs to muster. And so, stuff with rounded edges becomes quite difficult on antique hardware. (Link: http://www.folklore.org/StoryView.py?story=Round_Rects_Are_Everywhere.txt)

So, this was very clever in 1981. If one of my developers came to me now, with a loop and addition to determine the root of a value, I would not think it was clever. I would think it's a waste of time, of effort, of creativity, and I would nasty.

I see it all the time. I *do not* understand the more advanced functions and algorithms that people who work for me develop. I just don't. But, I still make them document and explain them to me. I have a passing knowledge of how heuristic regressions help detect abnormalities in data-sets, and I know how this applies to detection of standardized testing fraud, but can I write the code to implement it? Absolutely not.

And I am still on top of it enough to know when I've got a non-hacker on my hands.

"It can be done and does not need higher understanding to do it, although deeper knowledge and understanding helps to see greater connections within the field of math (and/or applications to other fields)." LL

Right LL I had Algebra since I was in the eighth grade but it was not till I took it again in College that I applied my reasoning skills to understand it. Sounds silly but I guess my brain was just not ready to apply what I was learning but one day ...it was like a light turned on and I said "Hey!" Since then my linear reasoning abilities have jumped up. I was always a non-linear ADD type...intuitive but not analytical. It took a while for my brain to build the neural pathways enabling me to truly understand it.

Studying physics seems to be a strange way to go about pursuing work in biology.VoxIt's called physiology, although the biophysicists get upset when you point this out.

For one thing, how can anyone understand exponential growth/decay without understanding diff eq?StickwickChance would be a fine thing. Why understand it when you can just deploy the terms and remember "63% reduction"?

hey vox, can you show me some evidence that dawkins sucks at math? would be awesome thanks.

OG, I'm a rare girl that needs to SEE things, so after tough classes up in Madison, I'd come see my math mentor and he'd pull out the whiteboard, draw me a picture and BINGO, I'd get it. That's why I try several different methods when tutoring. If I see someone doesn't get it, I'll draw a picture. Or try verbally explaining using real life analogies. Most college professors fail in the understanding that people learn differently and I think that is why a lot of people just don't do well in higher math classes. You have a PhD in math from MIT who sees the "obvious" and they don't get to the level of "oh shit, what is THIS and what do I do with it??" that most students work at. *sigh*

"Savant Syndrome like Autism is expressed as a continuum from moderate to acute. Intellect is expressed in a spectrum of areas and just because a person scores average on an antiquated IQ Test...does not make them an average person."

Nobody has called me an idiot savant before, at least not to my face. Obviously, I overreached with my contrariness. I'm neither brilliant nor special in any way. Simply put, I believe IQ is not a good indicator of a) ability or b) what somebody will accomplish. I'm currently working at an ME degree. I have a history as a straight A student (at the uni level), but only God knows whether I will ultimately be successful.

Simply put, d/dx is the derivative w/ respect to x. Do I understand it on a more theoretical level? Maybe. However, the short answer is that it isn't d/dy. Isn't that not clever of me?

2a) In your own words, what does d/dx mean?

2b) What is the limit of the following function as x approaches infinity? f(x) = (x + 1) / (x^2 - 1)

I can't seriously think of these two questions as equivalent. The first one is a bit tricky, as definitions of mathematical concepts in freshman calculus classes are usually not emphasized, and even if they are taught, they are not given in a rigorous manner.

On the other hand, the limit question here doesn't even require a much of genuine understanding of math to solve. My immediate reaction within 5 seconds: Input infinity. Get infinity over infinity. Apply L'Hopital's rule: i.e. differentiate both the numerator and denominator. Get 1/2x. Input infinity. Get zero. We're done.

And the majority of problems in calculus classes are of this sort, where you can just rely on your memory of several rules. Calc 1, 2, even 3, ultimately doesn't require much understanding of math - they're basically computational classes (which makes me wonder how the hell Wilson could have gotten Cs in them). I am bewildered that you might even imagine it as needing an IQ threshold (other than not severely below average). What is your own IQ again?

My immediate reaction within 5 seconds: Input infinity. Get infinity over infinity. Apply L'Hopital's rule: i.e. differentiate both the numerator and denominator. Get 1/2x. Input infinity. Get zero. We're done.I would go even more basic and say that the expression can be simplified to 1/x to observe behavior approaching inf because the -1 and +1 in it don't mean much at that point, and ask what happens to your fraction as the bottom number gets bigger? The fraction gets smaller. What happens at "giant" numbers? It gets damn close to zero, so the limit.... That does not need theory, L'Hopital's rule, and those who have passed algebra could follow the simplification and everyone pretty much understands what happens with a fraction when the denominator increases.

See, Nate? Doesn't take an intellectual giant to follow that reasoning.

E.O. Wilson is the guy with the ants, right? I'unno, he's a pretty old dude, and he's had to put up with a lot of political horseshit in his life, so maybe he's just being cranky and provocative.

He IS supposed to be pretty impressive when it comes to ants, but maybe we'd be better off calling him a "natural historian" rather than a scientist. I was under the impression that his claim to fame was having looked very carefully at ants, and then telling you what he saw, and that his "scientific" theoretical work takes a back seat to his careful observation of fascinating critters. Maybe he should have held the Yogi Berra Chair of You Can Observe A Lot Just By Looking. But, maybe I'm wrong.

"During my decades of teaching biology at Harvard, I watched sadly as bright undergraduates turned away from the possibility of a scientific career, fearing that, without strong math skills, they would fail."If true, I wonder how this all played out. Did these "bright undergraduates" personally come to Wilson, express regret about their math skills, and tell him of their decision to forgo science? Did he observe a sort of group lamentation about lack of math skills in classrooms and labs and then watch those drop out of the program? Was this more of a situation where younger undergrads showed low interest in science and who, when questioned, made generalizations about the mathematics and other aspects of science being too difficult?

"they're basically computational classes (which makes me wonder how the hell Wilson could have gotten Cs in them"

There are a lot of smart people in the world who can do math if they're forced to, it's just that they really don't like it, and they begin to organize their lives in such a way that they can avoid it whenever they can -- even in, say, a math class.

(x+1)/(x^2-1) = 1/(x-1)

There's a reason that algebra is first. It's to avoid the hard stuff.

I would go even more basic and say that the expression can be simplified to 1/x,Yes, I missed that in my reaction, I think due to the fraction being spelled out to the side (and we're talking about a <5 second reaction here). And taking derivatives of polynomials has become a process faster to me than even factorization, which I learned in eighth grade.

I'm neither brilliant nor special in any way...I have a history as a straight A student (at the uni level), but only God knows whether I will ultimately be successful.The picture I'm getting is that you're a very, very hard worker. As in 95th percentile or better. That's pretty special.

Obviously, I overreached with my contrariness.Only in that you couldn't back up your opinion. That happens, and owning up to it is a good habit. So is learning to back up your opinions.

That said, your own case throws doubt on my statement. To that end...

Simply put, d/dx is the derivative w/ respect to x. Do I understand it on a more theoretical level? Maybe. However, the short answer is that it isn't d/dy. Isn't that not clever of me?Good enough for undergrad work, I suppose. In order to determine the truth of my assertion (IQ must be 100 or higher to understand calculus) I still need an answer to question 1. And try your hand at 2b.

I can't seriously think of these two questions as equivalent.They aren't. One appeals to the philosophical folks and the other appeals to the visual folks.

What is your own IQ again?I don't know. I can only say with a reasonable degree of certainty that it's above 130.

"Nobody has called me an idiot savant before, at least not to my face. Obviously, I overreached with my contrariness. I'm neither brilliant nor special in any way." - Jill

No no no no. I said Savant Syndrome...NOT Idiot Savant. Idiot Savant is an arcane description of an extreme condition described in 1887 where drooling idiots could do long division to seven decimal places in their heads. That was 120+ years ago and things have changed a little since then. Savant syndrome ranges from the extreme to just trace. You are not an idiot...and not necessarily a genius either. Your math ability may just outstrip your MEASURED IQ enough to be statistically significant. This stuff is so new that it is not even described in the current DSM-IV.

BTW...For future reference...I try never to insult anyone that has not viciously insulted me first and more than once.

It isn't too hard to come up with a Fermi estimate of how difficult calculus is. I would consider basic competence to be equivalent to a 5 on the BC exam (at my institution, 5 on BC exam ~ B+ in intro engineering/science calculus class). This is achieved by about 50,000 students per year in a birth cohort of say 4 million. If you assume that maybe twice as many individuals later take calculus in college and understand it, one finds that it is a somewhat select group.

http://apcentral.collegeboard.com/apc/public/repository/ap12_calculus_BC_ScoringDist.pdf

There is also interesting data here correlating other achievement tests to SAT performance:

(the mean physics achievement taker scores 700 on the SAT-M).

http://media.collegeboard.com/digitalServices/pdf/research/TotalGroup-2012.pdf

Math is easy. People talk themselves into believing it's hard.

Given that as far as I can tell none of you bothered to talk about the area under a curve... I'm going to guess that a lot of you don't understand calculus as well as you think you do.

I can't seriously think of these two questions as equivalent.

They aren't. One appeals to the philosophical folks and the other appeals to the visual folks.

Well, since you turn out to be satisfied with the answer that d/dx is simply the derivative with respect to x, they're now closer together in terms of difficulty.

none of you bothered to talk about the area under a curveI don't think anyone has brought up integration yet.

"I don't think anyone has brought up integration yet."

sure.. because what's that got to do with calculus right?

What do you want to talk about in terms of integration, Nate? If you get differentiation, which is taught first, you get integration because it is the "reverse" process. Do you want to talk about meaning, process and difficulty, if someone needs a "high IQ" to understand the way to solve them?

" If you get differentiation, which is taught first, you get integration because it is the "reverse" process. Do you want to talk about meaning, process and difficulty, if someone needs a "high IQ" to understand the way to solve them?"

IQ is a measurment of the ability to think in the abstract. Infinity is an abstract concept.

Employing calculus to calculate the area under a curve... in clearly abstract as well. The steps are not abstract.

But again... simply regurgitating the steps with no understanding does not rise to the level of being proficient in math.

Proficiency requires understanding.

If you can't grok the proofs... you have no business pretending to play the game.

Also... if it takes you "months" to get something... you're to dumb for it. You may eventually get it... but you're clearly swimming in water that's way to deep for you.

in any kind of group learning setting... you're going to drive everyone else insane.

I think you are confusing application versus theory. Application is fine for those who don't use it other than to analyze data. Like I said, it is moving things around until you get an answer. For theory, it is why, how, what makes them all fit together. For application it is put the numbers in, get the numbers out. Now interpretation, that's a whole 'nother argument because as has been quoted before in reference to statistics which is probably the most used form of data in, data out, There are three kinds of lies: lies, damned lies and statistics."

VD: Wilson doesn't understand supply and demand in his own fieldNot knowing the man, is he presently a biology professor? If so, he knows more about supply and demand than you give him credit for. The article is basically a recruiting ad for customers- err, undergrads afterall. Undergrads pay for those tea-sipping furloughs/visiting prof trips abroad, don't ya know.

" Application is fine for those who don't use it other than to analyze data. "

You can't apply something if you don't know how it applies. You can go through the steps.. but if you don't know what the end result represents (for example the area under a curve) how are you supposed to know what to do with your answer?

But again... simply regurgitating the steps with no understanding does not rise to the level of being proficient in math.

Proficiency requires understanding.

That depends on what you mean by proficiency. I didn't really understand calculus when it was first taught in 10th grade. I simply regurgitated steps - yet I always managed to score high grades. The reason is that calculus classes, at least nowadays, are taught and examined as simply mechanical mathematics - basically plug-and-chug. I only gradually gained a better understanding of what it is when I started taking calculus-based physics courses which actually used the equations.

Understanding what it represents, ie what information you are analyzing for, is again different from theory and why it works. SAS math software doesn't care about the theory, but you can input data points and get out information. Now, when you use the software, in econometrics or statistical analysis, you have to understand what variables you are taking into consideration, but you don't need to know the theory or proof behind why it works. See my example of the hammer and physics.

I'm off to bed. I do appreciate where you are coming from and as a person who loves mathematics, I totally have that hunger to know WHY, but most people who do application mathematics don't need the theory. Compounded daily interest vs continuously compounded interest, you don't need to understand the theory, only that when you calculate one and calculate the other, one number is higher so you get an account using the continuously. It is what it is and I don't think people need a high IQ to say, "hmmm, I'd get more with continuously compounded interest." They just know it's more. ;-)

Mathematics is a tool, like a saw. Application of a tool is how work is done, like sawing a board in half. Theory is taking the time to PROVE that the limit of the number of boards approaches 2 as distance from the saw to the bottom of the board approaches zero. Which is to say, while theory has its place, most of that place involves proving the working formulas engineers had developed decades beforehand. Also, Gabriel's Horn.

Well, since you turn out to be satisfied with the answer that d/dx is simply the derivative with respect to x, they're now closer together in terms of difficulty.This, from the guy who used L'Hopital's rule on problem 2b.

Here's another assertion: You're deliberately missing the point of my entire exchange with Jill so you can jerk off to your own IQ.

Feel free to submit any evidence to the contrary. Or to hop away like the intelligence-worshipping coward you are.

The logic is quite sound! - If its difficult, make it easy! Problem solve!

If she's so hard to get, turn her into a slut! Now I can get into her pants! YAY!!

Hmmmm... what else is difficult? So that we can make them easy as well!

Salvation is hard! Make it easy!

The logic is quite sound! - If its difficult, make it easy! Problem solve!Salvation is hard! Make it easy!Of course it is. You can solve lim x->inf of f(x)=1/x by applying all possible x and hope that one day you'll find a solution. But that would be pretty stupid if you want to build a bridge over a river.

Because salvation is hard, make everything else hard too? Now, that's logic!

@OG:

If you think just because you scored 145 on the Stanford-Benet that you can rebuild a Chevy or make a woman wet just by talking to her you are sadly mistaken.I think anyone who scores 145 could learn to rebuilt a Chevy very quickly, if they have some motivation to learn.

Making a woman wet, on the other hand...you're absolutely right. The question is, is the world a better place or a worse place because IQ and wetness are so uncorrelated?

Feel free to submit any evidence to the contrary. Or to hop away like the intelligence-worshipping coward you are.I retract this as a huge overreaction. I was drunk, and I apologize for the rudeness.

Dear Vox, for me to evaluate your pontifications about biologists, I would like to know what are your achievements and experiences in that branch of science. (Not credentials, just experience and achievements). Siring a smart kid would not be one of them.

Dear Vox, for me to evaluate your pontifications about biologists, I would like to know what are your achievements and experiences in that branch of science.Since when do you need to be Picasso to point out that someone is not able to draw a stickman?

Dear Mr. Garstig, I would like to hear Vox's ruminations on the subject. Thank you for your concern, however.

Dear Vox, for me to evaluate your pontifications about biologists, I would like to know what are your achievements and experiences in that branch of science.Sadly, I don't care about your evaluation. Also, you are logically incorrect. The validity of my pontifications about biologists do not, in any way, depend upon my achievements and experiences in that branch of science.

One need not demonstrate an ability to do calculus to point out that 2+2!=37.

Well, VD, you present yourself as smarter about biology than a well known biologist so I wondered if you actually know anything about the subject or are just blowing smoke. I think I see smoke.

While one does not need to know calculus to know the sum of 2+2, one ought to demonstrate a bit of awareness about what biologists do before pontificating about how they need to study higher mathematics.

I am, by the way, a mechanical engineer and have studied and used calculus my entire career, so I am in no way opposed to teaching it to those who need it to do their jobs.

Well, VD, you present yourself as smarter about biology than a well known biologist so I wondered if you actually know anything about the subject or are just blowing smoke. I think I see smoke. While one does not need to know calculus to know the sum of 2+2, one ought to demonstrate a bit of awareness about what biologists do before pontificating about how they need to study higher mathematics.I am considerably smarter, period, than that well-known biologist. Who, by the way, reportedly got some very simple addition wrong in his Gay Uncle theory. About which more anon.

Furthermore, while you were smelling smoke, you completely missed the point. It's not about any need to study higher mathematics to do what biologists do, it's about the need to require ability to handle higher mathematics in order to have smarter biologists.

Do you need me to explain the concept of "proxy" to you or can you look it up on your own?

So higher learning math stimulates clearer reasoning? What proportion of university math teachers voted for Obama?

I've been proseletizing =without success-that we work with 3 brains, and 2 of them compete with each other.

Since the Reptilian Brain has millions of years of development and runs all systems in the body, it can be a savant at math, but don't expect it to charm anybody. That's a role for the Reasoning brain.

There is compensation in letting the Reptilian brain dominate. It doesn't get bored by complexity and it never needs a vacation. Sir Isaac Newton is an example of such autism. For more practical every-day matters, I would let my Reasoning brain dominate.

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