Maths question

[BeRational]

Maths is far more important than any crappy religion, of which yours is one.

That is one attitude that I would have to disagree with.  One without the other is dead.

No. Even if you're a believer, you can still be non-religious but see the wonder, beauty and utility of maths.

As it is I'm not a believer, and therefore definitely not religious, but maths is amazing, and has changed the world more, and faster, than any religion you can name.

O.

Be kind enough to illustrate how that is.

Planes, trains, automobiles, telephones, television, computers, electronics, firearms, medicine, banking, CNC machining, meteorology...

Pick any one of them, they're all applied mathematics.

O.

But all materialistic, and not all exclusively beneficial to Man.  However:

"All religions, arts and sciences are branches of the same tree. All these aspirations are directed toward ennobling man's life, lifting it from the sphere of mere physical existence and leading the individual towards freedom." - Einstein.

Also:  “I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.”   - Einstein, again.   That is what guides the world towards a better life and understanding, not the puerile notion of imagination that Floo has;  nor your total lack of it.

You do know that Einstein did NOT believe in a personal god don't you?

[BashfulAnthony]

Maths is far more important than any crappy religion, of which yours is one.

That is one attitude that I would have to disagree with.  One without the other is dead.

No. Even if you're a believer, you can still be non-religious but see the wonder, beauty and utility of maths.

As it is I'm not a believer, and therefore definitely not religious, but maths is amazing, and has changed the world more, and faster, than any religion you can name.

O.

Be kind enough to illustrate how that is.

Planes, trains, automobiles, telephones, television, computers, electronics, firearms, medicine, banking, CNC machining, meteorology...

Pick any one of them, they're all applied mathematics.

O.

But all materialistic, and not all exclusively beneficial to Man.  However:

"All religions, arts and sciences are branches of the same tree. All these aspirations are directed toward ennobling man's life, lifting it from the sphere of mere physical existence and leading the individual towards freedom." - Einstein.

Also:  “I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.”   - Einstein, again.   That is what guides the world towards a better life and understanding, not the puerile notion of imagination that Floo has;  nor your total lack of it.

You do know that Einstein did NOT believe in a personal god don't you?

I'm not discussing his religious beliefs, but his philosophy.

[Outrider]

But all materialistic

So? You have a problem with the things we have evidence for? How do you apply mathematics to things that you can't show actually exist - how can you quantify the unmeasurable?

and not all exclusively beneficial to Man.

Not that this was specified as a requirement, I simply suggested it had had more effect and quicker than any given religion - not that those religions have been exclusively beneficial either, of course.

However:

"All religions, arts and sciences are branches of the same tree. All these aspirations are directed toward ennobling man's life, lifting it from the sphere of mere physical existence and leading the individual towards freedom." - Einstein.

Also:  “I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.”   - Einstein, again.   That is what guides the world towards a better life and understanding, not the puerile notion of imagination that Floo has;  nor your total lack of it.

You're presuming because I keep my imagination grounded that it's non-existent - again with the ad hominem. I temper my imagination with evidence, with acquired knowledge, with the preserved wisdom of humanity so far as I can find it.

O.

[Udayana]

The analogy doesn't work. Learning English is actually doing English, it doesn't really work as an abstract discipline. There is a gap between playing pool and doing trig as a discipline which does not arise in the difference between learning a language initially and later.

Grammar doesn't work as an abstract concept? Language doesn't work as an abstract concept?

Talking is the application of that concept, writing is the application of that concept.

Playing pool includes doing trigonometry, whether you choose to think of it like that or not, in exactly the same way as it includes understanding the physical concepts of restitution and friction - you might not have the formal background to articulate them, but you can apply them.

That's why it's an intuitive understanding, but it's still an understanding.

O.

If you consider, say, a bird of prey using thermals to rise higher, swooping down to catch prey and so forth, it certainly seems incorrect to say it is performing maths or physics in any way. It's brain and nervous system just do not calculate it's path mathematically. Its instinctual control over its muscles are enhanced by  the patterns stored in its brain and nervous system built up by experience. We can understand the statistics that result in the collection of these patterns, but the bird is no statistician and has no understanding of stats or the maths underlying its maneuvers.

[Outrider]

The analogy doesn't work. Learning English is actually doing English, it doesn't really work as an abstract discipline. There is a gap between playing pool and doing trig as a discipline which does not arise in the difference between learning a language initially and later.

Grammar doesn't work as an abstract concept? Language doesn't work as an abstract concept?

Talking is the application of that concept, writing is the application of that concept.

Playing pool includes doing trigonometry, whether you choose to think of it like that or not, in exactly the same way as it includes understanding the physical concepts of restitution and friction - you might not have the formal background to articulate them, but you can apply them.

That's why it's an intuitive understanding, but it's still an understanding.

O.

If you consider, say, a bird of prey using thermals to rise higher, swooping down to catch prey and so forth, it certainly seems incorrect to say it is performing maths or physics in any way. It's brain and nervous system just do not calculate it's path mathematically. Its instinctual control over its muscles are enhanced by  the patterns stored in its brain and nervous system built up by experience. We can understand the statistics that result in the collection of these patterns, but the bird is no statistician and has no understanding of stats or the maths underlying its maneuvers.

And that's why the distinction between instinct and intuitive is important. Intuitive is still learnt, but it's not formally studied. Birds flight is instinctive - walking for humans is instinctive. Trigonometry isn't.

O.

[Udayana]

Yes, but my point was a bit more than that- the brain doesn't work mathematically - if it had to calculate everything it needed for us to to walk along- it would just not be fast enough, and we would fall over, possibly even before the first step.

Maths is something we have developed in order to be able talk about and understand the world. It doesn't exist out there in some Platonic ideal world.

[Outrider]

Yes, but my point was a bit more than that- the brain doesn't work mathematically - if it had to calculate everything it needed for us to to walk along- it would just not be fast enough, and we would fall over, possibly even before the first step.

You don't need to do the calculation to be doing the trigonometry - even if you're estimating you're using the notions of the relationships between angles in a given space, which is trigonometry.

O.

[Udayana]

Good thing the Earth knows all about how to estimate its orbit around the sun then, otherwise we'd really be up the creek!

[Nearly Sane]

Birds learn how to catch prey just as much as we might learn to play pool in terms of the angles. That their desire to catch prey is fully instinctive does not mean that the attempt to do it is not improved by the intuitive.

[jeremyp]

The calculator is one of the bestest inventions ever. Why do it in your head when you can use a calculator? Never liked maths. It's rubbish. 😁

But we still need to know that we have got the answer to the right power of 10. 

I had a slide rule when I was at school.  This gave answers that were stripped of powers of 10.  One had to estimate an answer in order to know where the decimal point lay.

I do two things when checking a calculation.

1. Make a rough estimate so I know what the magnitude should be.

2. Do the calculation using only the last digit so I know if there are rounding errors.

[jeremyp]

Maths is far more important than any crappy religion, of which yours is one.

That is one attitude that I would have to disagree with.  One without the other is dead.

Wrong. Maths does not depend on anything in the real World whether it is true or not. In fact, maths alone cannot tell you anything about the real World or its religions. This is why you also need observations and experiment.

[Outrider]

Good thing the Earth knows all about how to estimate its orbit around the sun then, otherwise we'd really be up the creek!

The earth isn't doing anything, it's just letting gravity influence it.

O.

[jeremyp]

No, to be doing maths there would have to be conscious thought about actually doing maths.

Would there?

It doesn't show any understanding of trig as a discipline.

Not withstanding my question above, I think I agree with you. I think what is actually happening is that you observe the effects of hitting the balls at various different angles and using different amounts of spin and you (or your subconscious) builds a model of how the balls are going to react in various circumstances. The model is then updated with every shot you play. This is more like doing science than doing mathematics.

[Outrider]

No, to be doing maths there would have to be conscious thought about actually doing maths.

Would there?

It doesn't show any understanding of trig as a discipline.

Not withstanding my question above, I think I agree with you. I think what is actually happening is that you observe the effects of hitting the balls at various different angles and using different amounts of spin and you (or your subconscious) builds a model of how the balls are going to react in various circumstances. The model is then updated with every shot you play. This is more like doing science than doing mathematics.

I'd say physics... which is applied maths...

O.

[jeremyp]

I'd say physics... which is applied maths...

It's maths applied to the real World, which I consider to be science - not maths. Also, I don't know if I would describe the model that a snooker player builds of how his balls behave is a mathematical model. It is a model, but not, I think, mathematical.

[Outrider]

I'd say physics... which is applied maths...

It's maths applied to the real World, which I consider to be science - not maths. Also, I don't know if I would describe the model that a snooker player builds of how his balls behave is a mathematical model. It is a model, but not, I think, mathematical.

It's a trigonometric model - that's classically considered part of mathematics, but that's a rather arbitrary classification. If I said it was a 'spacial reasoning' task, you'd accept that I suspect.

The language changes, but the toolkit is the same - it's about a grasp of angles and their relationships.

O.

[Nearly Sane]

The toolkit doesn't seem to be the same at all though. Taking ad_o as the example , he isn't using the same type of understanding that doing nonapplied trig does. It seems to be a different approach.

[Outrider]

The toolkit doesn't seem to be the same at all though. Taking ad_o as the example , he isn't using the same type of understanding that doing nonapplied trig does. It seems to be a different approach.

He's not calculating, he's estimating, so he's building a mental model rather than an arithmetic model - he's still modelling the relationship between various angles.

O.

[ad_orientem]

The toolkit doesn't seem to be the same at all though. Taking ad_o as the example , he isn't using the same type of understanding that doing nonapplied trig does. It seems to be a different approach.

What I do is form an image in my mind of what I want to do and then do it. It either works or fails.

[Outrider]

The toolkit doesn't seem to be the same at all though. Taking ad_o as the example , he isn't using the same type of understanding that doing nonapplied trig does. It seems to be a different approach.

What I do is form an image in my mind of what I want to do and then do it. It either works or fails.

I'm not  regular player, but I know the process, the sensation, the idea. It's another form of model, and it's trigonometric - maths is not just about numbers.

O.

[Udayana]

You mean .. like visualize the end effect and let everything else fall into place to achieve it - muscle memory.

If that is trigonometry .. it would explain all the sportsmen with honorary maths degrees.

[Nearly Sane]

It's not purely muscle memory though, that is part of the overall activity. There is a genuine and immensely complex calculation going on each shot but it doesn't seem to me to relate to how we would do the equivalent maths calculation. It may get to an equivalent result in theory but the methods seem entirely different.

[Udayana]

Yes, we can write and use a mathematical description of what happens, but the neurons themselves use a different method to get to the same point- one that we will also (eventually) describe mathematically.

[Rhiannon]

I said ad-o is using maths. That's different from 'doing' maths.

[Nearly Sane]

I am not sure you can use maths without doing it?