Maths: Discovered Or Invented?

[naomi24]

”Magic Numbers: Hannah Fry’s Mysterious World of Maths”, a BBC Four documentary series in which Dr Hannah Fry explores the mystery of maths and asks “Is maths invented like a language or is it discovered and part of the fabric of the universe?”

https://www.bbc.co.uk/programmes/b0bn9dth/episodes/player

Your thoughts?

[IJKLM]

Jim
Isn't that kind of thing just awesome?

But that kind of fits with my beer-soaked human construct thing.

Accepting that sqrt(-1) is a valid and useful concept is entirely human. THere's no real-life situation (such as counting apples, or pears) that naturally drives us to think of sqrt(-1) as a part of the commonsense world.

INstead, it takes a leap of imagination and creativity (both utterly human activities) to see that this new way of describing certain aspects of the universe helps us to develop mathematical models that provide insigts into physical phenomena - such as the relationship between current and voltage in a large power generator, for example.

I have to be at a meeting at 8am local time: 7am in the UK, so i'll be off to sleep now, but will continue tomorrow if this continues..

[ToraToraTora]

talbot 21:52, it makes more sense now than reverting to a metric figure. The world of geometry etc would look very different whilst actually not being different, eg if there were say 1000 newdegrees in a circle then the internal angles of a polygon would now add up to (S-2)*500 rather than the now familiar (S-2)*180. So it would be a major upheaval to change in all the text books and school curriculums etc now. The French tried it with time briefly and soon reverted back, though there are 10 hour clocks in a Paris museum.

[Peter Pedant]

// Ad to PP - half the fun of these is to think for oneself.//
yeah but no but ....but not to re-invent the wheel ....

Hey I have thought of a wonderful poem - no one has thought of before
to be or not to be ....yes yes that is the question er er whether it is ...
The idea is to think for oneself ( step aside ABers!) but not laboriously go thro what someone has done much better 1,000 y ago. - or reinvent the vector notation that Mobius did in 1860.....

The History of Maff courses that were brought in post war
MIGHT have been in response to the impasses of the thirties of theoretical physics. Didnt Heisenberg reinvent matrix math to describe his discoveries? And someone stick up their hand and say - this was all done ( the maff side of course) fifty y ago?
Prince de Broglie also did article-wave duality 1926 but likened it to a surfer on a wave.
everyone ( at the solvay conference) saw the idea was right
but the analogy was wrong because the surfer represented the centre of the wave - uh -uh - it doesnt have one - being a wave.

and so it was decided world wide to have English courses ( sort of) (that is history and philosophy of maff) so that the pointy headed intellectuals could describe to us normals what they had written ( discovered, invented or made up ) rather than just wave their hands and comment " this is so....so....ow you say.....difficile!"

The standard of discussion here isnt high - I notice: "imaginary isnt imaginary" is causing some squawking and protesting.....

[Peter Pedant]

// Can I ask TTT why a circle is 360 and not ...say a 1000 or a 100?//
it should be 2-pi for chrissakes

and yeah counting to sixty is babylonian. linking to metric hours ( 10 in a day) is a leap even I would wonder about making

[Khandro]

P.P. The Jeremy Gray video you posted at 17:16 yesterday I've just watched - very good, I hadn't seen it before.
The book I admire and always find stimulating is by Olive Whicher from Rudolf Steiner Press (1971); Projective Geometry, Creative Polarities in Space and Time

[Peter Pedant]

Hi Candee !

the set book for the OU was
Amazon.co.uk User Recommendation

which should be Jeremy Gray Ideas of Space

£13 cheapest on Amazon

He had to fill in teaching us thickos on the Open Uni - I did a few of the courses up to 1985 ( eek but I have a long memory )

I had a lot of respect for those toots who used by day to teach the young Einsteins like Jim by day and instead of seettling down and watching Coronation St would instead roll up their sleeves and try to teach us over thirties. They said they enjoyed it

[vetuste_ennemi]

A long time ago (when Jim was still in short trousers) there was a Listener crossword on quaternions and William Hamilton. (Another one I couldn't do.)

Sure i was in there somewhere. Or am I just imagining it?

[jim360]

Obviously I don't know the Listener, but yeah, there will have been an "i" in there somewhere. Quarternions are numbers built in terms of 1, i, j, k such that i^2 = j^2 = k^2 = ijk = -1, although that's not the same as saying that i = sqrt(-1).

Different (but related) concept.

[Peter Pedant]

yeah oh that one
Hamilton was trying to enlarge complex number into three
using i,j and k
and he couldnt get it to gel
( alot of this around in 1860 - Maxwell couldnt unify the e-m equations without adding a liddle ( j ) term)
and he was walking along the canal in Dublin
and thought ooo I know..... ijk=-1
and it was ! sort of - he got consistency
Nowadays you just look at them ( quaternions ) and think o yeah very interesting
and if you look here
https://en.wikipedia.org/wiki/Quaternion
scroll down to History
and you will see a photie of the plaque on the very bridge on the very canal where the unifying concept struck him!

I think Polya ( how to solve it) has something to say about this

[vascop]

The reason for using 360 must be because it is exactly divisible by so many integers:
2,3,4,5,6,8,9,10,12,15,18,20,24,30 and so on.