Of what practical real-world use is a hypotenuse? How many times have you used one since you graduated from high school/college?

It isn't my question Shar. It is the question Henry Winkler asked during an interview. His point was that some if not much of what we provide our kids education-wise is never used in the real world. As a retired Internal  Auditor I never needed an hypotenuse or square root thereof. I did not know you used it in your profession.  Thank you for that information. Mathematicians needs it and I guess builders and architects too. 

It was Henry Winkler who asked that question during an interview Sbf. I thought it was a good one. He was talking about the value of the education we provide our kids. Some of it is useful, some not so much. As a retired Internal Auditor I never needed to use an hypotenuse or square root thereof. If it is something required in the profession you're in of course it's useful. But really how many professions find it useful? Thank you for your reply and Happy Sunday! :)

Well to be honest with you m'dear I heard that question from the lips of Henry Winkler (THE FONZ). He was being interviewed on some show and was talking about the value of the kind of education we are providing to our kids. His point was that a lot of what we learn in school we never use. But math brains of course would find Hypoteni awesome. We're not all math brains. Yes. I am a retired Internal Auditor but I never needed to use a hypotenuse or square root therefore when performing an audit. I thought it was a sensible point that he made and also funny as he**. Thank you for your reply Ele!  :)

An interesting aspect of educational theory, but I wonder if it was originally promulgated by people more concerned with neat filing-systems than actual learning. Your second two paragraphs imply this, with its "they", although without source or context it's hard to see what if any real meaning or significance exists in that definition beyond the bureaucrats' 'Though Shalt Have Seven In Thy List' box-ticking. 

I can see the point about a geometrical law being an example of relationships that may make us look for analogues elsewhere, and mathematics is a world of formal relationships; but whilst I also see and agree with you the value of that ability to seek them, surely we do not realise the entity exists until we are shown it directly, or shown how to search for it?

Unfortunately, defining a "liberal art" in that quoted but anonymous way, is binary. It separates general intellectual ability from technical or professional skills, whereas in real life, those skills require one to have sufficient intellect to learn and apply them.

Consequently, 'liberal art' by that uncited definition could be mis-read as hardly 'liberal' in the social sense, of liberation of thought and imagination anyone can enjoy with help, but as an aloof pursuit for the few. Education needs both abstract and applied, but towards its real purpose, equipping people to lead and enrich their lives; not in a narrow sense hedged by academic subject or trade skill, but in a broad sense - the 'non-liberal' facts but also the 'liberal' analytical ability. 

My argument against the term shows it as a phrase so devoid of real meaning it is desperate to find one; a meaningless slogan of the type beloved by politicians and administrators, but - or so - devoid of genuine value.

All learning is of value; artificial divisions like that mean and achieve nothing.

Mathematics cannot be defined as a 'liberal art' in that way anyway because it encompasses both camps. Is it 'non-liberal'? Dictatorial?

Maths can be, and indeed is, pursued as a 'liberal-arts', abstract, intellectual exercise; but by far the majority of mathematics people are paid to use, at any level of complexity, is not abstract but a "technical or professional skill". Otherwise, Rosie would not have been an auditor, and we would not be able to discuss it like this. We would not even have the electricity to drive the computers that could not exist.


[Edited to replace an incorrect conjunction affecting meaning.] This post was edited by Durdle at September 5, 2017 4:45 PM MDT

I was only commenting from personal experience.  But if mathematics is said to be a universal language, I'm surprised you denigrate it to the status of universal tool.  On the other hand, I did not and do not intend to address educational theory---I have no particular expertise in that area. 

I included a definition of "liberal arts" to minimize misinterpretation and to provide the formal object through which I was commenting on this discussion.

My comments only refer to my own personal experience with learning and "education." Looking at what both knowledge and education has done for me, I find that in retrospect, "liberal arts" is a very useful and logically reasonable term for describing what the effect on me has been.

Perhaps I should have used "it was preferred" instead of "they wanted" so that causation may have been more difficult to infer?

I like this comment about John Henry Newman and The Idea of a University :  "...for Newman, 'the general principles of any study you may learn by books at home; but the detail, the colour, the tone, the air, the life which makes it live in us, you must catch all these from those in whom it lives already.' The university of Newman’s day was a place in which men (and it was then an institution for men only) lived for scholarship, and arranged their lives around the sacrifice that scholarship requires. It was not simply a repository of knowledge. It was a place where work and leisure occurred side by side, shaping each other, and each playing its part in producing the well-formed and graceful personality.

I certainly had no wish to denigrate Mathematics or indeed any other academic field. Yes, it is a "universal language" for its own purposes, in the way music is for its purposes.

Nor did I think you coined the term "liberal arts" but you did imply that its is at least used by some nebulous "they" trying to fit everything into neat databases and bureaucratic channels.

The OP questioned the apparent need for learning particular details; therefore questioning practical application. One could ask that of anything. If you never go to France the obscure tenses of French irregular verbs hardly matter - but they certainly do to literate French people. Accordingly, I answered on the basis of Maths being a tool to do a job of work.

You can pursue mathematics into the higher realms of purity beyond discernible practical use, simply for the love of learning. Equally you can use mathematics for everyday tasks, be that designing an airliner or making a five-barred gate; be it using extremely high-order calculus or Pythagoras' Theorem.

It's possible to apply the general principle to any academic or artistic endeavour. If I was not tone-deaf I might have learnt to play a musical instrument or to sing; as it is I do know a crochet from a quaver, or a symphony from a concerto; but these are merely for my own pleasure even if that skill is vital to the performer's own livelihood.

I take your point about the somewhat bucolic ideal explained by John Henry Newman; but it's an ideal which even if it still applies, holds the trap of ivory-tower'd exclusivity in which learning for the love only of learning becomes an end in itself for an intellectual elite unable to comprehend life outside the hallowed Halls. Some say William Blake's "dark Satanic mills" - tonight was the Last Night of the Proms! - were not directly the factories of his time, but metaphorically the contemporary universities that may have loved education but stifled original thought! Indeed, you could read that quoted paragraph as espousing a life unable to differentiate work from leisure - not broadening the mind but compressing it within the College library book-ends.     

Judging by the people I have known socially or at work over the years, universities now assume a life outside the red bricks or the cloisters; a life of salaried work yes, but also of leisure and social activity far removed from degree-exams and weekly time-sheets.

One former professional mathematician I knew - a Government scientist by profession - quoted, as I recall, Tim Brooke-Taylor, on his accepting an Honorary Doctorate at her university saying that a University education is more than just the degree course itself. This seems to invert what Newman saw, and if so, a good thing too.

It would be interesting to know what the universities of the time he described actually taught; but I suspect these days it would be seen as very limiting by imposition and self; perhaps oppressive. Even without the male chauvinism they espoused in the days when fluency in debased Latin was a necessary entry qualification for some universities.

So whence the charge of "denigrating" an academic subject by using it for a practical purpose? Those antique "scholars" might have used the term, but nowadays? I can't tell if Newman admired those people, or was showing them as a narrow-minded, self-centred mutual-appreciation society making me think of a very clever version of Radio Four's Loose Ends.

I can enjoy learning, and perhaps it's salient to remark I had no idea of the point of Differentiation - let alone how to do it - when trying to learn it from a bad teacher at school. Years later I finally twigged what it is, in one of my hobbies, during a lecture on rivers hosted by my geology club. Learning for the love of learning - but neither for professional use, nor as a be-all and end-all. If anyone debased learning or denigrated a subject, the men Newman described certainly did. This post was edited by Durdle at September 9, 2017 6:00 PM MDT