Intellectual Betterment

[dan_bo]

I think too many people place too much reliance on fully understanding, which stresses them, and makes them glaze over (not necessarily you). Like I said, I only vaguely 'get it', but I'm happy with that. If I really wanted to know, I'd learn.

Ever since we started inventing or uncovering the meaning of things, there will have been a vast proportion of the population who don't care (and don't need to know!) how things work, just that they do. Maths is one of those things. We can't all know everything.

That said, it's good to learn, but I hate to think of people assuming they are stupid because they don't get something like imaginary numbers - or anyone claiming they are clever just because they do - as Fossyant said, there are some very clever people out there who are barely capable of putting their shoes on the right feet!

Actually you're spot on there Arch. I find it immensely frustrating when I can't expand my knowledge on a subject I wanna grasp beyond the rudimentary.

 

[marinyork]

I hadn't meant it in the sense that because he has qualifications he should *know*, rather in the sense that he's (probably) more intelligent than I am (although sometimes often I do have to wonder ) and he does have to know quite a bit for what he does.

Anything to with Science in general will soon go over his head, not just programmes about maths, whereas I love it, even if I am just a layman.

I didn't mean you, I meant there are people out there and it stops them learning. I take on board Arch's point abuot people stressing about it or yours about dyscalculia or some mind block. I've actually seen stories that reckon people get so stressed out they get mental blocks.

I've known people that are no good with numbers, but understand all the mathematical ideas behind numbers. Also known quite a few people who were pretty good with other areas like Geometry or Algebra. You ever tried reading a popular science book on it like Ian Stewart?

 

[marinyork]

Well, ok, but all you've done there is the equivalent of say what the chap said last night, only slower and louder. If someone has trouble grasping the concept of an imaginary number, that won't help.

Personally, I don't 'understand' the idea of imaginary numbers, but I'm content that some people do, and know how to use them.

It is indeed (deliberately so actually), but there is a reason for that. People really aren't expected to learn things first time round. As DanB has said you can visualise numbers instead of a piece of string that goes on in both directions to a gigantic piece of paper with the everyday numbers on a very thin strip going horizontally and all the complex numbers making up the rest of the sheet. What is perhaps not made clear is that Complex numbers include real numbers. So you really already know loads of loads of complex numbers even if you think you don't, 1,2,3,4,5 are all complex numbers it is just they have zero imaginary component. Just like fractions like 3/3 include whole numbers like 1, complex numbers include all the normal numbers. It's a bit like humans and animals. Humans are animals, but for various reasons people don't go on about us all the time being animals, we're viewed as a special case. Ordinary numbers are a special case they have zero imaginary part, they are stuck on that thin line. Imaginary numbers do have lots of strange things. If you whack in something with an imaginary (rest mass) into Special Relativity you end up with particles that always travel faster than the speed of light.

Another idea that takes longer to explain is that numbers are extensions in terms of equations. Think of numbers as solutions to equations. Start of with x + 6= 3. If we didn't have negative numbers we would have no solution to this equation. We'd only be able to use things like x + 1 = 2. Add in quadratic equations and we have x[sup]2[/sup] -1 = 0 which as we said earlier gets +1, -1. What about x[sup]2[/sup] + 1 = 0? Should be easy right? Not with real numbers. Whatever you do you cannot get a solution. This is because a real number multiplied by itself is always positive. You put in a fiddle to say that a number multipled by itself is negative.

BTW, I've been watching de Sautoy's thing on the History of Maths, on BBC4 and it's pretty much the same info, only without the rather laboured Code theme. I guess some people just won't be interested unless there's a gimmick.

It's not a bad series and it's nice it's repeated every once in a while. Episodes 3 and 4 are pretty good. I would say 4 is actually pretty good as that content has rarely if ever got on tv. Not so keen on 1 and 2, but I think there is more participation in some of those for people. I fully agree about 'the code', but I think a huge section of the population think Maths is a load of made up nonsense with nothing whatsoever to do with the 'real' world and all to do with suffering in classrooms. It is basic. For those that aren't as keen on numbers they may well like next week's programme.

 

[Canrider]

I think too many people place too much reliance on fully understanding, which stresses them, and makes them glaze over (not necessarily you). Like I said, I only vaguely 'get it', but I'm happy with that. If I really wanted to know, I'd learn.

DanB's 'right angles' analogy can be a useful one. It's certainly seeing it explained that way that enabled my younger self to 'get' imaginary numbers.

If (for example) working out how like '2+3i' can even be allowed, you could try telling yourself the 'i' really mostly acts as a kind of 'tag' or 'marker' that serves to keep certain numbers separate from certain other numbers. So you can do maths on the 2 and maths on the 3i, but you're not allowed to combine them together unless the 3i side of things has been multiplied by itself first.

This:

You put in a fiddle to say that a number multipled by itself is negative.

is also another good way of looking at it!

 

[marinyork]

It was a good basis for a programme, but he should have covered less but given us more information - for instance I don't recall any mention of Fibonacci when telling us about the Nautilus, and I would have liked to hear more about that. He gave us facts and details but no explanations - the Nautilus grows at a fixed rate, but why? Prime numbers - why are they so? Pi - why/how does it always work?

As for Fibonacci, there are two books I know that covers some of this stuff - The Divine Proportion by HE Huntley and The Golden Ratio by Mario Livio. You might find the latter one in a library.

 

[Mad Doug Biker]

I take on board Arch's point abuot people stressing about it or yours about dyscalculia or some mind block.

Well, I don't know if it is. I just seem to go a bit astray if doing calculations more than just the basic day to day things and I don't check my working regularly as I am working through it. Even then I don't notice half the time until someone else looks at it and wonders what I've just done

I do seem to have that problem, but also, I wasn't really taught anything remotely challenging at School until near the end, so I never got to know most of it (being the brain damaged kid I was never quick enough to keep up with the rest). I was always more better at English (despite possibly how I write here - I always goode at speelling and righting tings), music and arty things, with my best science subject probably being human biology. I want to learn about Maths and improve my sciences now that I am going back to get better qualifications (highers) in various subjects.

I've actually seen stories that reckon people get so stressed out they get mental blocks.
You ever tried reading a popular science book on it like Ian Stewart?

I have so many different books about things that I'd have to look (I'll look into it though, thanks).

 

[Norm]

Without meaning to detract from MY's excellent posts, I'm currently reading Alex's adventures in numberland and it's a tad more accessible.


Maths is one of the easiest things to get into, imo, because it's everywhere without being noticed. Sudoku, for instance, is a great maths puzzle but few see it as anything other than patterns. But, again as MY posted, that's the thing with maths, it's patterns which uses numbers to communicate in a common language. 2x2=4.

 

[darth vadar]

It all sounds a bit like the 'Emperors New Clothes' to me

 

[marinyork]

Without meaning to detract from MY's excellent posts, I'm currently reading Alex's adventures in numberland and it's a tad more accessible.

I would recommend any number of popular science books. People don't tend to read them though . Some people prefer tv and that's fine. You will probably get a better understanding from a popular science book, but it takes a lot longer than an hour to read. This is what I mean by people aren't expected to understand things first time, you might see it on tv, get into reading a couple of popular science books, have a think about it and then it sinks in.

 

[Norm]

I've read a couple of the earlier passages out loud to my kids, both are now hassling me to finish the book so they can make a grab. But then I knew they would.

IMO, all science is fascinating but some of the delivery methods are better than others. TV is more visual (well, yeah) but tends to be one-shot blink'n'miss it, whereas I've gone back through books several times.

 

[marinyork]

I've read a couple of the earlier passages out loud to my kids, both are now hassling me to finish the book so they can make a grab. But then I knew they would.

IMO, all science is fascinating but some of the delivery methods are better than others. TV is more visual (well, yeah) but tends to be one-shot blink'n'miss it, whereas I've gone back through books several times.

There is a very large bias towards Biology in the media, even for what gets on tv.

I take people's point about explaining on an internet forum, I'm very much better explaining in person having done it at various levels, but even then I don't think I'm the best person at explaining things.

 

[Sh4rkyBloke]

If you want some form of explanation then one probably exists on the Khan Academy website. Truly inspiring stuff and Sal Khan is exceptionally good at explaining stuff. You can then try out problems to do with the subject you've just watched. I'd recommend it to anyone for a whole host of subjects!

 

[Arsen Gere]

I'd like to see him do something on probability, it always kicks me in the nuts.

Things like the monte hall problem ( three door game show host). http://en.wikipedia.org/wiki/Monty_Hall_problem.
Gamblers ruin, prisoners dilema, busses come in three's, monte carlo simulation and so on.

I don't work well with equations I do chunks of work in pictures and then try and work the equations from them. Nothing wrong with not being able to keep all this stuff in your head unless someone wants you to sit for 3 hours and show you can keep it in your head, I can't do that and muck up exams.

I've heard mathematicians talk and their colleagues have problems following their thoughts too, so don't assume they are as smart as you think they are.

 

[marinyork]

Complex Roots from the Quadratic Formula

If you want some form of explanation then one probably exists on the Khan Academy website. Truly inspiring stuff and Sal Khan is exceptionally good at explaining stuff. You can then try out problems to do with the subject you've just watched. I'd recommend it to anyone for a whole host of subjects!

Complex Numbers 1
Complex Numbers 2
Complex Roots from the Quadratic Formula

There are a few other things with complex numbers in there but you'd need to understand them first. Can't quickly find the few topics I'd give to other people.

 

[Sh4rkyBloke]

I'd like to see him do something on probability, it always kicks me in the nuts.

What, like a whole playlist on Probability that he has on there, for example?