Religion and Ethics Forum
General Category => Science and Technology => Topic started by: Rhiannon on October 15, 2015, 07:51:49 PM
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When IRL is it necessary to add fractions with different denominators?
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When IRL is it necessary to add fractions with different denominators?
Quite often, I should think, but operationally we usually transform the vulgar fraction into a decimal fraction. How about dealing with relative quantities in cooking?
Has this been prompted by a children's homework question?
The purpose of learning mathematics at school is to acquire logical thinking skills ... not just to operate a calculator.
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My eldest's maths teacher has said he can think of no situation IRL when he would need to add together fractions with different denominators, and neither can I. I thought about cooking, but that works more on ratio IME - a 3:1 flour to fat ratio for example, or mostly mince to a little onion. And it isn't something you need do with mathematical precision unless baking a cake to impress Mary Berry.
Incidentally my daughter spent the summer* doing logical thinking problems set by her teacher. She rarely uses a calculator except when instructed to do so to check her work.
* Eta not the whole summer, because that would be weird.
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My eldest's maths teacher has said he can think of no situation IRL when he would need to add together fractions with different denominators, and neither can I. I thought about cooking, but that works more on ratio IME - a 3:1 flour to fat ratio for example, or mostly mince to a little onion. And it isn't something you need do with mathematical precision unless baking a cake to impress Mary Berry.
Incidentally my daughter spent the summer* doing logical thinking problems set by her teacher. She rarely uses a calculator except when instructed to do so to check her work.
* Eta not the whole summer, because that would be weird.
Integration and differentiation, which are used when attempting to discern information from equations, often require the ability to manipulate fractions of differing denominations - calculus like this is quite important to various forms of engineering and statistical analysis. Although purely numerical fractions can normally be rationalised relatively easily, the skills of manipulating them are useful when you start to work with irrational components and variables.
O.
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When IRL is it necessary to add fractions with different denominators?
In maths, frequently, although the denominators are rarely simple numbers.
In the kind of arithmetic most people use in everyday life, not so much, especially now that the imperial system is on its way out at last.
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My eldest's maths teacher has said he can think of no situation IRL when he would need to add together fractions with different denominators, and neither can I. I thought about cooking, but that works more on ratio IME - a 3:1 flour to fat ratio for example, or mostly mince to a little onion. And it isn't something you need do with mathematical precision unless baking a cake to impress Mary Berry.
Incidentally my daughter spent the summer* doing logical thinking problems set by her teacher. She rarely uses a calculator except when instructed to do so to check her work.
* Eta not the whole summer, because that would be weird.
Integration and differentiation, which are used when attempting to discern information from equations, often require the ability to manipulate fractions of differing denominations - calculus like this is quite important to various forms of engineering and statistical analysis. Although purely numerical fractions can normally be rationalised relatively easily, the skills of manipulating them are useful when you start to work with irrational components and variables.
O.
How would you use this in daily life? (Genuine question, really have no idea)
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When IRL is it necessary to add fractions with different denominators?
In maths, frequently, although the denominators are rarely simple numbers.
In the kind of arithmetic most people use in everyday life, not so much, especially now that the imperial system is on its way out at last.
I didn't realise it would apply to Imperial measurements. Otherwise I can't think of anything that couldn't be better served by using percentages or ratio - not that maths is my thing, as you will have gathered.
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Otherwise I can't think of anything that couldn't be better served by using percentages
Multiplying decimals is multiplying fractions. It's just that the fractions are always some power of ten.
or ratio - not that maths is my thing, as you will have gathered.
Not quite sure what you mean by "ratio". In my mind, a ratio is a fraction.
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Otherwise I can't think of anything that couldn't be better served by using percentages
Multiplying decimals is multiplying fractions. It's just that the fractions are always some power of ten.
or ratio - not that maths is my thing, as you will have gathered.
Not quite sure what you mean by "ratio". In my mind, a ratio is a fraction.
It's what I said earlier about cake or pastry making - you know you need twice or three times the amount of flour for every unit of fat. But of course that is sometimes expressed as 'half fat to flour'.
Yes, we get the thing about fractions and decimals being the same. But I think most of the time we'd convert into decimal before adding. Even then I can't think of a reason why the original fractions would have different denominators - not in everyday maths.
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Your last answer, Rhi, has got me thinking.
When we used £sd (old money, real money etc) were we not often provided with different "types" of fraction that we sometimes used concurrently - half a crown, eighteen pence, five guineas and so on?
And when we counted up a column of values involving twelve pence in one shilling and twenty shillings in one pound were we not - in reality (since the total of pennies had to be converted into shillings) - adding fractions?
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How would you use this in daily life? (Genuine question, really have no idea)
Engineering, computer programming, any sort of statistical analysis... it really rather depends on what job you want to do.
Outside of work situations, of course, probably not so much.
O.
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Of course you can always do arithmetic in decimal or rearrange the operations to avoid the fractions or approximate where appropriate.
Using different denominators hmm . consider calculating how long a journey would take if the route involved 57 miles along a road with expected speed 30 mph and 157 miles along a motorway at 70mph:
Total time in hours = 57/30 + 157/70
etc.
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It's what I said earlier about cake or pastry making - you know you need twice or three times the amount of flour for every unit of fat. But of course that is sometimes expressed as 'half fat to flour'.
This is all definitely fractions by another name. If you see a recipe that says 1/2 as much fat as flour but it also says 1/2 pound of flour, you know how much fat and flour you need to put on the scales, yes? Well, that is adding two fractions.
yes, we get the thing about fractions and decimals being the same. But I think most of the time we'd convert into decimal before adding.
Nothing wrong with that. You convert one problem into a different problem that you know how to solve. Mathematicians do that sort of thing all the time.
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I dare say you are right, Jeremy. :)
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Where maths is concerned I pass! Thank goodness for calculators, without mine for even simple sums, I would be completely up the creek without the paddle!
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How can you be sure the calculator is giving you the right answer?
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When IRL is it necessary to add fractions with different denominators?
Quite often, I should think, but operationally we usually transform the vulgar fraction into a decimal fraction. How about dealing with relative quantities in cooking?
Has this been prompted by a children's homework question?
The purpose of learning mathematics at school is to acquire logical thinking skills ... not just to operate a calculator.
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. 😁
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When IRL is it necessary to add fractions with different denominators?
Quite often, I should think, but operationally we usually transform the vulgar fraction into a decimal fraction. How about dealing with relative quantities in cooking?
Has this been prompted by a children's homework question?
The purpose of learning mathematics at school is to acquire logical thinking skills ... not just to operate a calculator.
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. 😁
Calculators do not help with maths, they only help with arithmetic which is not the same thing.
As to whether maths is rubbish or not, clearly it is not because without it, the modern World would look very different. Maths is far more important than any crappy religion, of which yours is one.
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When IRL is it necessary to add fractions with different denominators?
Quite often, I should think, but operationally we usually transform the vulgar fraction into a decimal fraction. How about dealing with relative quantities in cooking?
Has this been prompted by a children's homework question?
The purpose of learning mathematics at school is to acquire logical thinking skills ... not just to operate a calculator.
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. 😁
Calculators do not help with maths, they only help with arithmetic which is not the same thing.
As to whether maths is rubbish or not, clearly it is not because without it, the modern World would look very different. Maths is far more important than any crappy religion, of which yours is one.
What an eloquent and well-worded argument - you ought to be on Question Time!
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What an eloquent and well-worded argument - you ought to be on Question Time!
Thank you. That makes a change from your usual whining.
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What an eloquent and well-worded argument - you ought to be on Question Time!
Thank you. That makes a change from your usual whining.
No, thank you, for replying without a swear word in sight. ;)
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When IRL is it necessary to add fractions with different denominators?
Quite often, I should think, but operationally we usually transform the vulgar fraction into a decimal fraction. How about dealing with relative quantities in cooking?
Has this been prompted by a children's homework question?
The purpose of learning mathematics at school is to acquire logical thinking skills ... not just to operate a calculator.
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. 😁
Calculators do not help with maths, they only help with arithmetic which is not the same thing.
As to whether maths is rubbish or not, clearly it is not because without it, the modern World would look very different. Maths is far more important than any crappy religion, of which yours is one.
Oooo! ::) Of course maths has its uses but for me I think it's rubbish. I just can't get my head round it. I hate calculations. They're for boffs. At school I was always more an English, history and geography person. English I loved especially.
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Of course maths has its uses but for me I think it's rubbish.
No it isn't even for you.
I just can't get my head round it. I hate calculations.
Ah, you aren't any good at math,therefore maths is rubbish. Has it not occurred to you that, actually, it is you that is rubbish (at maths)? Would it be acceptable for me to say "music is rubbish" just because I am completely inept at any musical instrument?
They're for boffs. At school I was always more an English, history and geography person. English I loved especially.
It's interesting that people who are illiterate tend to be highly embarrassed about it, but people who are innumerate seem to wear it as a badge of pride.
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Of course I'm rubbish at maths. My brain just doesn't work that way.
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Oooo! ::) Of course maths has its uses but for me I think it's rubbish. I just can't get my head round it. I hate calculations. They're for boffs. At school I was always more an English, history and geography person. English I loved especially.
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Mathematics is not what you think it is.
All you know is arithmetic ... and, if what you say is correct, you do not even have the skill to know whether the result your calculator shows is correct or not. If you hate calculations then you cannot be aware of all those occasions that shopkeepers have short changed you. How sad.
Mathematics is about thinking and using symbolic logic to solve problems. Mathematics is universal.
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Oooo! ::) Of course maths has its uses but for me I think it's rubbish. I just can't get my head round it. I hate calculations. They're for boffs. At school I was always more an English, history and geography person. English I loved especially.
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Mathematics is not what you think it is.
All you know is arithmetic ... and, if what you say is correct, you do not even have the skill to know whether the result your calculator shows is correct or not. If you hate calculations then you cannot be aware of all those occasions that shopkeepers have short changed you. How sad.
Mathematics is about thinking and using symbolic logic to solve problems. Mathematics is universal.
I know how much change I'm supposed to get, silly. I'm not that dumb. Basic arithmetic (if you must call it that, though I prefer to lump it all together) I'm fine with, though when you get to long division and multiplication then you might as well be speaking Greek. That always got me stumped. If you're talking algebra and stuff like that, then you might as well be speaking Hebrew (though I'd sooner spend the next ten years of my life learning Greek and Hebrew, which I'm not inclined to do, than spending a day trying to get my head round trigonometry, for instance). I'd much rather spend my time playing pool.
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You use maths when playing pool to work out angles and how hard to hit the ball.
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You use maths when playing pool to work out angles and how hard to hit the ball.
I know where the cue ball and object ball are going to go through instinct and because I've played the shot a thousand times. Nothing to do with maths. Maths doesn't move the balls about but skill through hours of practice.
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But it's still maths as used in everyday life - not arithmetic, but mathematics.
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As to whether maths is rubbish or not, clearly it is not because without it, the modern World would look very different. Maths is far more important than any crappy religion, of which yours is one.
What an eloquent and well-worded argument - you ought to be on Question Time!
If you hadn't made that argument on-line - utilising the mathematics inherent in the design, encoding, encryption, decryption, decoding and integration of the programming, machine code and physical components of the keyboard, monitor, network, switching mechanisms, world-wide transmission systems, demodulation, and rendering of the signal you might have had a point.
Oh, wait, my mistake, no you wouldn't.
O.
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It's interesting that people who are illiterate tend to be highly embarrassed about it, but people who are innumerate seem to wear it as a badge of pride.
This.
So, so many times this. The anti-intellectualism of the modern Western world is sickeningly demoralising.
O.
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Basic arithmetic (if you must call it that, though I prefer to lump it all together)
That's like equating spellings with Shakespeare.
I'm fine with, though when you get to long division and multiplication then you might as well be speaking Greek. That always got me stumped. If you're talking algebra and stuff like that, then you might as well be speaking Hebrew (though I'd sooner spend the next ten years of my life learning Greek and Hebrew, which I'm not inclined to do, than spending a day trying to get my head round trigonometry, for instance). I'd much rather spend my time playing pool.
D'Oh!
O.
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You use maths when playing pool to work out angles and how hard to hit the ball.
I know where the cue ball and object ball are going to go through instinct and because I've played the shot a thousand times. Nothing to do with maths. Maths doesn't move the balls about but skill through hours of practice.
You're not that brilliant with language, either.
You do not use "instinct" to play a shot. You use the knowledge you have acquired through practice. You use your stored recollections of forces and angles in order to make the shot. You use a practical application of a combination of Newtonian physics and mathematics.
Were this instinctive then every human on the planet would have the same capability.
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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.
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I'm with ad_o here, he is using maths at an instinctive level , even if developed by practice. He is not doing maths in the sense of doing the equations.
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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.
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I'm with ad_o here, he is using maths at an instinctive level , even if developed by practice. He is not doing maths in the sense of doing the equations.
Whilst I know what you mean, I'd be inclined to use 'intuitive' rather than instinctive. In common use they're pretty much synonyms, but if someone's going to resort to the technical definitions - which has never happened here, of course :) - the 'instinctive' doesn't fit.
O.
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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.
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You use maths when playing pool to work out angles and how hard to hit the ball.
I know where the cue ball and object ball are going to go through instinct and because I've played the shot a thousand times. Nothing to do with maths. Maths doesn't move the balls about but skill through hours of practice.
You're not that brilliant with language, either.
You do not use "instinct" to play a shot. You use the knowledge you have acquired through practice. You use your stored recollections of forces and angles in order to make the shot. You use a practical application of a combination of Newtonian physics and mathematics.
Were this instinctive then every human on the planet would have the same capability.
Tell that to a naturally gifted 12 year old kid who just "knows" how to play a shot and who knows bugger all about Newtonian physics and mathematics. I've seen it plenty of times. Instinct, my old mucker!
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This is not a technical discussion, and I don't see that the marginal difference in meaning contributes anything to the question of whether ad_o is in any sense doing maths.
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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.
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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.
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Tell that to a naturally gifted 12 year old kid who just "knows" how to play a shot and who knows bugger all about Newtonian physics and mathematics. I've seen it plenty of times. Instinct, my old mucker!
No. As has already been explained, the word you should have used is intuitive not instinctive.
An instinct is a hard wired capability which is present in all members of a species. Instinct makes swallows fly south for the winter.
Whether on not you know bugger all about Newtonian physics and mathematics, you are using an understanding of the ways they act acquired by practice or observation in order to engage in a rather simple recreational activity. Since you have not taken the trouble to formally understand their operation, you are using them intuitively.
For someone who earlier claimed "English I loved especially" you are using English in a rather imprecise manner.
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Except here, ad_o seems to be using instinctive as the near synonym it is to intuitive in everyday English covering not conscious thought to describe what he is doing as not being maths. And I think he is correct in the point he is making and that arguing about not using the term in the more technical sense entirely misses that point.
Someone playing pool is not doing maths.
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Except here, ad_o seems to be using instinctive as the near synonym it is to intuitive in everyday English covering not conscious thought to describe what he is doing as not being maths. And I think he is correct in the point he is making and that arguing about not using the term in the more technical sense entirely misses that point.
Someone playing pool is not doing maths.
They are doing trigonometry, which is a branch of maths. They are 'estimating' rather than calculating, so they're approximating rather than doing the arithmetic, but the understanding of reciprocal angles is applied trigonometry. I'd agree it's entirely possible they're doing intuitively rather than because they've formally studied and applied it to that situation, but they're doing mathematics.
O.
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No, to be doing maths there would have to be conscious thought about actually doing maths. It doesn't show any understanding of trig as a discipline. It gives no indication that the person knows anything about trig as a discipline or would have any real chance of understanding it.
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No, to be doing maths there would have to be conscious thought about actually doing maths. It doesn't show any understanding of trig as a discipline. It gives no indication that the person knows anything about trig as a discipline or would have any real chance of understanding it.
And they have learnt trig as a discipline, within that specialised environment: they've learnt about angles, about the incident angles of the path of a ball bouncing off the surface are equal either side of the perpendicular to that plane (which is also a bit of physics - isn't learning wondeful!).
They haven't studied it formally as trigonometry, but they've learned trigonometry.
It's much the same as how we learn our native language organically, but someone who come to it later in life haven't learnt their own language learns it formally - they're still learning English, they're just not thinking of it in those terms because it's not formal education.
O.
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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.
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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.
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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.
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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?
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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.
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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.
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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.
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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.
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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.
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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.
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Good thing the Earth knows all about how to estimate its orbit around the sun then, otherwise we'd really be up the creek!
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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I said ad-o is using maths. That's different from 'doing' maths.
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I am not sure you can use maths without doing it?
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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.
Not just trigonometry, Udayana. Consider a batsman facing a ball on which the bowler has applied spin, and it is swerving as it follows a parabola over the wicket. He is doing some very serious calculus in order to decide how and where to hit the ball.
He deserves his honorary degree.
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I am not sure you can use maths without doing it?
Your internet posting just got encrypted and decrypted - you used maths, albeit hard-coded into your computer and uploaded in the software, but you didn't do any of the maths.
O.
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I am not sure you can use maths without doing it?
Your internet posting just got encrypted and decrypted - you used maths, albeit hard-coded into your computer and uploaded in the software, but you didn't do any of the maths.
O.
Except none of that applies to the distinction that is being made by Rhiannon as regards Ad_o's use vs doing maths.
The context used changes the possible meanings, and it we change use to lean simply the above then we are back at the bird of prey making the same use of maths.
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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.
Not just trigonometry, Udayana. Consider a batsman facing a ball on which the bowler has applied spin, and it is swerving as it follows a parabola over the wicket. He is doing some very serious calculus in order to decide how and where to hit the ball.
He deserves his honorary degree.
Thanks, that explains a lot. Is it why Indians are such good mathematicians - or possibly vice versa, such good cricket players? Anyway we now know who to get on the team in putting together the next Mars shot :)
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I think 'doing' implies a conscious awareness, which 'using' doesn't.
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Agreed. But the very use of "using" is the disagreement here.
A fielder is not "using" calculus to calculate the trajectory of the ball and then catching it in any sense. His/her mind/body are using an entirely different mechanism that can model the same trajectory. There is no encoding for calculus in our cells in the way that there is an encryption/decryption algorithm in networking software.
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You could contrast with some recent work that shows that some biological processes are sensitive to and "use" quantum effects.
https://www.ted.com/talks/jim_al_khalili_how_quantum_biology_might_explain_life_s_biggest_questions
http://www.theguardian.com/science/2014/oct/26/youre-powered-by-quantum-mechanics-biology
i.e. despite the birds having no knowledge or intention to use quantum physics, they are using quantum effects to determine their position/route. It doesn't mean that they are using quantum field theory etc to do any calculations.
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When IRL is it necessary to add fractions with different denominators?
Quite often, I should think, but operationally we usually transform the vulgar fraction into a decimal fraction. How about dealing with relative quantities in cooking?
Has this been prompted by a children's homework question?
The purpose of learning mathematics at school is to acquire logical thinking skills ... not just to operate a calculator.
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. 😁
Calculators do not help with maths, they only help with arithmetic which is not the same thing.
As to whether maths is rubbish or not, clearly it is not because without it, the modern World would look very different. Maths is far more important than any crappy religion, of which yours is one.
What an eloquent and well-worded argument - you ought to be on Question Time!
First it was '' science vs religion''.
Then, not content with looking totally stupid having proposed this piece of nonsense, they have come up with ''maths vs religion''.
What next from Jeremy? Greggs Pies vs Religion?
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Agreed. But the very use of "using" is the disagreement here.
A fielder is not "using" calculus to calculate the trajectory of the ball and then catching it in any sense. His/her mind/body are using an entirely different mechanism that can model the same trajectory. There is no encoding for calculus in our cells in the way that there is an encryption/decryption algorithm in networking software.
I've played pool - not as much as ad-o, but a fair bit. You work out the angles required to successfully pot shots by eye, but it's a mathematical concept. Similarly I work out how to make a cheese sauce using ratio - I don't measure ingredients, I know if I put that much butter in I need this much flour and that much milk.
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Of-course if you play pool then you can choose how to play it. You might look at the layout and guesstimate the angle of attack - a rough maths, ad-o trusts his eye,and experience, I could take my protractor, ruler and calculator.
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It's a trigonometric model
Is it. Do you think that a snooker player unconsciously works out sines and cosines? I'm sceptical on that point.
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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.
That's going in the Best Bits thread
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It's a trigonometric model
Is it. Do you think that a snooker player unconsciously works out sines and cosines? I'm sceptical on that point.
No, I don't, because sin and cosine are arithmetic tools to assist in making trigonometric assessments more accurate.
O.
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It's a trigonometric model
Is it. Do you think that a snooker player unconsciously works out sines and cosines? I'm sceptical on that point.
No, I don't, because sin and cosine are arithmetic tools to assist in making trigonometric assessments more accurate.
I tend to think maths is a bit more than looking at two balls and estimating what a right angle looks like.
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It's a trigonometric model
Is it. Do you think that a snooker player unconsciously works out sines and cosines? I'm sceptical on that point.
No, I don't, because sin and cosine are arithmetic tools to assist in making trigonometric assessments more accurate.
I tend to think maths is a bit more than looking at two balls and estimating what a right angle looks like.
Maths is quite a lot more than that - in exactly the same way that English is more than just looking at the sentence 'See spot run' and noting the lack of capitalisation for the proper noun... but that's part of English, and the assessment of angles in relation to one-another is part of maths, specifically part of trigonometry.
At its simplest it's a visual assessment and an estimate 'This is bigger','this is smaller', 'these are the same'... Then you develop more refined - arithmetic - tools to calculate to greater degrees of precision, or you apply logical principles to determine that certain situations MUST be a certain way without the need to resort to arithmetic.
It's the most basic form of trigonometry, perhaps, but if more people were aware of ideas like that then perhaps fewer people would be afraid of maths and we wouldn't be in a situation where parents see it as some wierd badge of honour to tell each other how their ten year old's maths homework is beyond them.
O.
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Dad: Ready for school tomorrow?
Son: Sure, I've been practicing my maths down at snooker club all evening...
:)