More alarming are the university courses in science and accounting that do not include mathematics.

“….mathematical literacy (at whatever level), which carries with it a sense for logical rigour and formal coherence, helps one to better understand and express the rational framework of worldviews.” If this is the central conclusion of this piece (well, it does come at the end) then it’s not really much use. I loved maths when I was studying it and happen to see the world through a kind of mathematical, certainly quantitative, prism. My own scientific research always depended on some basic level of mathematics (but nowhere near that needed in, say, cosmology).

So I have no trouble in accepting that mathematical literacy is a good thing. But Dr Virsik seems to be saying more. He is offering a kind of prescription, or recommendation, which says “if you want to understand things better then become mathematically literate”.

To me that sounds like “if you want to be better at basketball, become taller”. And that’s the problem. Being mathematically literate is the privilege of the few who have either the quantity or the kind of brainpower needed. I’ll leave the detail to the neuroscientists. An elitist view? Of course. Can anyone or everyone become mathematically literate? Of course not. In a place where secondary education is universal (like Australia), how many adults could become mathematically literate if they just tried, but don’t yet realise it? Not many I suspect, but someone might try to find out. A good PhD topic. Till the results come in, I shall view the matter like in the old joke. “Can you play the piano?” “Dunno, never tried”

I would not have started the quoted paragraph with “I even believe that …” if it were meant to be the “central conclusion” of the article. It was a personal view and adding “(at whatever level)” relativised the term “mathematical literacy” (taken from Wilson) so as not to sound “elitist”.

For Tombee; It depends on what level you are imagining. In the old days the South Australian leaving certificate (I forgot its title) was not moderated, so that anyone who wanted a really high score would do double maths, physics and chemistry, where you could, at least in principle, get 400/400 in four subjects. A very high proportion of matriculants did exactly that, which made the science sides of the Adelaide universities very strong. When all subjects were moderated, that was no longer necessary, so the demand for maths and science fell off quite quickly. Howard Gardner argues that given desire, training and encouragement, almost anyone can be highly competent at anything of this kind. I think he's right.

This is just so true.

Today we have B Sc graduates who would have real trouble with high school math B, & would not even understand the questions in a math C paper.

A case study. My daughter signed up to do a combined Bachelor of Science bachelor of Education degree with one of our universities, chosen for it's access from home. Silly girl. All 12 kids doing the course planned on a math/science teaching career.

When she & the 11 others arrived to start they were advised the institution did not have the physics capacity to run the course, & they were transferred to an Environmental science course. [The rumor was a tenured physics professor was drunk too often to teach.] Environmental science would only qualify them to teach biology.

After looking at the course notes, she acquired a set of year 2 notes. We discovered that at the end of the second year of a B Sc at this Goldcoast establishment, the students would be required to be almost, but not quite at the standard required of junior high school kids. This is supposed to be a science degree. Some graduates consider themselves scientists.

She transferred to a "proper" university for the second semester, & had a hell of a job catching up on the math they'd done by then.

In my experience you can't understand anything much more than how to mow the lawn without some math.

It would certainly improve our knowledge of everything if those posing as journalists today were required to have at least senior high math & science. It would certainly make it harder for many conmen to make the news papers & TV broadcasts, with their bull dust.

Good article, i agree with most of it. However, the problem comes in applying mathematics to complex biological systems such as are found in neuroscience. My experience of modellers of even the simplest system is that the model often takes on a life of its own. The difficulty is deciding how accurately the model describes a complex system whose mechanics are unknown. There was a flurry of enthusiasm for maths in the period 1640 to 17something when it was supposed, after Descartes that maths would be the new language that would be able to describe everything. New languages were invented that were as close to the mathematical as possible, even proofs for the existence of God! All of these attempts failed to advance our knowledge either of language or theology. Of course, if you are a theoretical physicist maths are the basis of your work. But the use of mathematics can produce wrong conclusions. For example, mathematically, time looks the same as the three dimensions. This lead to the idea that time was just another dimension in what was called the space-time continuum. But anyone can see that time is totally unlike a physical dimension for obvious reasons.
Peter Sellick

"Of course, on the level of a critical understanding of contemporary theories of the nature of physical reality “exceptional mathematical fluency” is an absolute necessity."

The author wittingly or unwittingly exposes what is apparently lacking in supposed climate scientists who believe in anthropogenic global warming, some of whom have been caught faking 'results' to advance their cause.

Interesting essay.
A pity that he spoilt it by referencing William Demski (a propaganda hack for the "Discovery" Institute) and his absurd attempt to prove the bunkum "intelligent design" thesis using "advanced" mathematical statistics.
Seeing that the usual dim-witted Christians have made some comments
this reference provides a unique understanding of science as an open-ended method of free enquiry as distinct from the now world dominant "religion" of science.
The CD being reviewed also contains a humorous debunking of the "religion of mathematics".
http://global.adidam.org/media/science
This essay provides a unique Understanding of Zero and Infinity
http://beezone.com/AdiDa/Aletheon/zero_point.html
And what is the Unique Potential of Human Beings - are we here just to make toasters, reduce the natural world to a technological waste land while prattling on about "Jesus"?
Or something much more?
http://www.adidam.org/society/beyond_ego/unique_potential_man1.htm

Wilson's views on species extinction rates is highly influential in Green circles and based, as I understand it, almost entirely on mathematical models. I hope his disdain for mathematical competence is not reflected in his own research.

An example from climate science - a well-known sceptic/denier/whatever-you-want-to-call-it, Roy Spencer, has produced work containing mathematical nonsense, see

http://arthur.shumwaysmith.com/life/content/mathematical_analysis_of_roy_spencers_climate_model

It's not just the sciences that require some mathematical knowledge - economics students are often unpleasantly surprised at the amount of mathematics they have to learn.

Most surprisingly mathematics can rear its head in any area of study - even ancient history / religion. A non-mathematician friend recently referred me to a new book in his field, title "Proving History: Bayes's Theorem and the Quest for the Historical Jesus"
by Richard Carrier (for details see http://www.amazon.com/Proving-History-Bayess-Theorem-Historical/dp/1616145595) - apparently he thinks that if it is mathematically sound (and, I suppose, if the mathematics is really relevant) then it's quite a significant work

Sells,

As I put it, it is important to understand what mathematical models can and what they cannot do. I have no experience with biology, but it is probably true that, more than in physics and engineering, one can try to use mathematical models where they - although appripriately reflecting some features of reality - cannot lead to any useful insights or even results.

I do not think this is the case with the Minkowskian model of space-time, since the time coordinate is not interchangeable with the three space coordinates. [Minkowski space is a four-dimensional real vector space equipped with a nondegenerate, symmetric bilinear form with signature (-,+,+,+); here the minus stands for the time coordinate]. So even in this model time does not “look the same”. It “is” not another dimension, it is only represented by a dimension (coordinate) in this particular model of reality.

Raycorn,

As far as I know climate scientist are not concerned with contemporary theories dealing with “understanding the nature of reality”, i.e. they do not discuss whether or not superstring theory, loop quantum gravity, M-theory etc adequately represent physical reality at it basest.

Daffy Duck,

Absurd or not, you cannot debunk a “theory” built on mathematical statistics unless you understand the maths used. Like you cannot debunk any nonsense expressed in Chinese if you do not understand Chinese. Also, the understanding of basic mathematical terms in http://beezone.com/AdiDa/Aletheon/zero_point.html is indeed, politely expressed, “unique”.

jeremy,

I think it is a difference whether you use mathematical models to explain something, or even solve some practical problems, and whether you use mathematical concepts and relations to form a metaphor that helps YOU to understand YOUR preconceived ideas. There is nothing wrong with the other, unless you present it as an explanation binding also for those who do not share your initial position.

george..im just now listening..to alexjones
http://rss.infowars.com/20140117_Fri_Alex.mp3

at around 2;30
anyhow..he is refuting global warming..my point being
he obviously USES MATH..but he hasnt put iT ..into formulation

ie/like ..let C=climate
C=Sun activity..MOON Location..jet steam
NOW WE KNOW ITS NOT CONSTANT..as the sun..needs an..activity
the moon needs a position..and the jet stream needs A velocity..
then..THE SUN..needs a force degree..wITH..a moon modifier..etc

but lets talk..of a more common example
E=mc2..[WHAT HAS C../ie speed of light squared]..TO DO With..MASS

why cant E=M..[to some power of]
say..E=m..]TO the power of 10..[or 10.000...OR WHATEVER.

thing is most of the SCIENCE/stuff..that needs 'math'
has its application..by the formula..[i feel the formula..is the key..more so than the math.][but not everything can be formulated..[probability..is limited by THE UNknown Probables.]

funny how i met a woman/the other day..who was doing math..on her hand
just..covered with numbers..[im still TRYING TO FIGURE..out what was MEANT..by our meeting.]..ANYHOW IM IMPRESSED BY The comments you have generated..

anyhow cheers
[computer problems persist]..
But..that was factored in/..going in.

Maths great in solving problems or predicting outcomes if all the variables are included and given the correct weight.

This is where climate modelling fails dismally. Really complex systems are difficult to express mathematically because we don't know all the variables are,their interactions and degree of influence.

Thank you for this article and its very important implications. As a scientific academic of many years I have witnessed the dumbing down of hardcore disciples (relative to soft science) to such an extent it is possible to be a graduate major in biological science without a working knowledge of statistics and calculus. IMHO such a graduate is unemployable. The present appalling situation almost certainly derives from the desire of so called universities to put bums on seats for funding purposes and from the desire of the Labor/Greens to insist that everybody can have a tertiary education irrespective of whether they have the ability or even want such a degree. It is time to get education reformed from the grass roots up in this nation regardless of what the rest of the world is doing. China could eat us in respect for scholarship without even being aware of it.

Amusing post by Jeremy who links to some one or other who says about Spencer:

"Which seems to go completely against the point I thought he was trying to make, that some sort of internal variability was responsible for decadal climate change."

Internal variability is now being proved to be the dominant cause of climate change.

Later the link, in the comments says:

"More importantly, the central problem with Spencer's argument for PDO (or any other oscillation) driving warming is that he is trying to fit a rising curve to something that oscillates up and down. The only part of the 20th century curve you can really match that way is the part that goes sort of up-and down - the middle 1930 to 1980 bit."

This is wrong; PDO has been shown in many papers be asymmetrical in the intensity of the phases and their duration as this simple graph shows:

http://farm3.static.flickr.com/2702/4503452885_79b5c09c4f_o.jpg

Also in the comments someone more alert than either Jeremy or the author says:

"I thought Spencer's novel claims were about the forcing/feedback distinction, and whether it was appropriate to add upwelling SW and LW at the TOA to derive the TOA forcing when they have different effects at the surface, and he only plugged the data into a noddy model to get a first order estimate of what it meant. He first showed how the conventional feedback diagnosis method applied to the idealised situation with a step-function forcing gives the right answer (saying much the same as you just did), then showed how quasi-random fluctuations in forcing messed this up. Is there much progress to be made in spending a lot of time criticising the noddy estimate, and ignoring what he claims to be the main point?"