BBC Radio 4, Analysis - Wasted Youth

[dennis]

You don't, you either let the "radar" do it or use tracers and move the gun to hit the plane.

[John Williamson]

Or, to use a slightly different example, how do you know where that car that you're trying to dodge is going to be when you get to its line of travel?

And who's going to program the "radar"? If nobody knows how to solve the problem by hand, then there's nobody who knows how to program the radar in the first place. It's for a similar reason that when you start learning how to navigate a boat or aeroplane, you do it on paper. Then, later on, when the GPS system fails, you can still work out where you are.

Too many people now rely on "the machinery", and this seems to be an attitude encouraged by schools, possibly because a lot of the teachers don't know how to do the job without "the machinery". To get back to my navigation example, how many people know how GPS or satellite navigation actually works, at a basic level? I've met many people who think that the satellites transmit the maps to their satnav unit, and the satnav in turn transmits its location to the satellites.

[jgharston]

That's how it works according to Stephen Fry, and who's going to argue with him?

JGH

[ARWadsworth]

Roger Mellie.

[dennis]

Well you sure don't use "maths" to work it out. You don't usually know the starting conditions to even start working it out.

(I can think of examples where you might use maths for a similar problem but not for driving a car.)

I don't recall doing anything like that for O' level maths and they don't work well anyway as there are too many unknowns like wind speed.

Do you have a GPS system certified for use to navigate a plane?

I do, my daughter does too.

There are units that do that sort of thing, not exactly common due to expense.

[Tim Watts]

She has not done it yet (Year 3) - it's this technique:

Maybe Tim Watts might like to comment as he has two kids that are probably

Certainly I was never taught it. It's an interesting trick but I'm not sure if it's worth the effort over long division...

[Owain]

Mr Fry is a charming man but he is not a scientist.

Owain

[John Williamson]

You do use maths to work it out. To be specific, you use the branch of applied mathematics known as trigonometry. You just don't do it consciously. As for the starting conditions, it's easy to guess the location and velocity of the car shortly after you see it, as well as your own estimated speed, position and direction of travel. The former is done by applying a mathematical transform to the perceived images of the car on your retinas, and the latter by the same, with the addition of feedback based on signals received from your legs and other organs on your body. It's all "maths" and "physics".

There are many, many examples of that sort of use of maths in everyday life that people don't think of as maths.

"Assume a spherical cow..."

By the time I did "O" level maths, I was doing similar problems involving boats, where the vector of the tidal streams had to be taken into account. I will admit that I'm not sure whether that final bit was in the syllabus, but we learned to work it out anyway. For aeroplanes, the figures are different, but the same principles apply.

But my point wasn't about doing it in real life and in real time, my point was about *knowing how* to do it.

No, but if I owned a plane, I would. Compared with the running costs of any 'plane, the cost of a certified GPS system is trivial. Even one which uses differential GPS near the airfield is affordable, if you run a 'plane in situations where it would be useful.

I know peope who have a GPS which will let them dock their boat in the right berth in the dark, in the fog, when the only way they know they've arrived is when they feel the bump of boat on dock. It cost them a couple of hundred quid plus the installation cost.

Congratulations. How basic is that knowledge? Do you start with "The satnav uses satellites to determine its position (Waves hands vaguely)" or "The satellites know exactly where they are and the exact time, which they broadcast" ? If you know exactly *how* the satnav determines its position down to the hardware level in the receiver, you are one of very few indeed.

Yes, having your own dedicated satellites and keeping the mapping data on them up to date isn't exactly cheap. ;-)

On the other hand, the satnav unit I use daily which accesses map data stored on a remote, landbased, server based on its calculated position didn't cost me a penny to buy, as the telco recover the cost of providing it in the data charges. They are as common as muck, as most smartphones now contain them. I use one of them on the evening run from college on some days to keep an eye on the traffic to get the little darlings home earlier. And you wouldn't *believe* the infrastructure requirements to do that little trick.

[Mike Barnes]

I beg to differ. People with no knowledge of mathematics (before mathematics existed) were dodging charging animals, using skills they had developed for themselves. I think I use those same skills to avoid other vehicles. "Dumb" animals do the same. You might call that mathematics, but I wouldn't.

[geoff]

In message , Mike Barnes writes

C'mon then answer this - why do they have schools of dolphins?

[djc]

No you do not use maths in that case. There is a difference between algorithmic methods (ie 'maths') and autonomics. This is the fallacy of hard 'artificial intelligence', as an academic colleague of mine once put it algorithmic methods/AI/logic & maths is how we like to think we think.

[John Williamson]

"Mathematics" doesn't have to be formal and written down. You (Or the antelope) calculate whether you and the car (Or lion) are likely to occupy the same point in space at the same time if things don't change. Then you or the antelope change something if that is likely. If it's not maths (Or, more specifically, trigonometry and vector calculations using estimated data), what is it? Even advanced computers are less intelligent than any complex animal, but maths can be programmed into them to do many jobs. Does your point of view imply that it isn't maths when the silicon based aiming computer on a modern computer controlled gun looks up a table of solutions based on data received, any more than that is the case when you or the antelope do the same to dodge a car or lion. The maths is done, either at the time or previously, and the results cached in memory.

Archers were hitting things with arrows and hunters were hitting things with thrown spears long before others had worked out that arrows and spears fly along a modified parabolic path. Their version of the maths involved many approximations and shortcuts, but it was still maths. What they did was look at the target, then work out (Using an internal look-up table if they were experienced.) how high and in which direction to point the arrow and how hard to pull the string based on the data they received from that look, while taking into account the deviation likely to be caused by the apparent local wind speed as judged by the movement of leaves and branches. Modern archers have sights available for their bows which are an analogue computer programmed with the maths to do this job more accurately and more easily than the human brain, which saves at least one arrow per hit in real life. The computer is using maths explicitly, the human implicitly.

[dennis]

You don't do it at all.

Even animals can catch objects thrown at them and they don't do maths.

It can all be explained by maths and/or physics but they are not required to perform the function. Its all down to experience and learning. If you put a mathematician that can't drive on a track they will crash even if they can do the maths.

That's because it isn't maths. Its a feedback loop with constant corrections.

So you know people who have crashed or are going to crash their boats then? ;-)

I know that the satellites *don't* know where they are at all, they don't need to know. However the receiver does need to know where the satellites are. the receiver works out where the satellites are from the data they download when they listen to the satellites. This data is computed by ground based systems and not by the satellite.

Wouldn't I? Google is cr@p at using traffic information. Tomtom does a far better job at live traffic and routing. Tomtom even takes information from my (and others) satnav to determine what's happening. If they ever get around to releasing the next version of the software it will also download map updates on the fly.

[John Williamson]

If it's not maths, then what is it?

My understanding is that applied mathematics is purely a formalisation of methods we all use to calculate such things autonomically. That doesn't necessarily make it "not maths" when we work such things out without writing it down.

[Grimly Curmudgeon]

Indeed, and when I was at school many of the best teachers were ex-military and couched their questions/instructing in such terms, thereby sparking an interest. Modern History too, has an added piquancy when taught by somebody who was actually there.

[Mike Barnes]

I repeat: you might call that mathematics, but I wouldn't. It is just about possible to stretch the definition of "mathematics" to include an animal's spatial awareness, but I think it's not normally advisable to do so.

mathematics: the abstract deductive science of space, number, quantity, and arrangement, including geometry, arithmetic, algebra, etc., studied in its own right (more fully pure mathematics), or as applied to various branches of physics and other sciences (more fully applied mathematics)

[Grimly Curmudgeon]

Really? There's a fault with the teacher, then.

[Grimly Curmudgeon]

Certainly wouldn't be the first time I've heard Saint Stephen spouting the most outrageous bullshit.

[geoff]

It is not maths, its experience

Maths is a way of explaining e.g. the trajectory of an arrow, the archer isn't using maths to anticipate where the arrow will land, its the product of hours and hours of practice

maths is our way of interpreting the world, thats all

[Tim Watts]

Not necessarily. Whilst a bad teacher can bore an interested student, a lazy unenthusiastic oik is very difficult to engage and if they are being bloody minded, then it's more or less impossible.