Should students study from the Principia?
A lot of students, including myself, get confused when their teachers try and explain a particular something, maybe a method or theorem because they can't see how the logic is assimilated from one line to the next. There are huge gaps in their understanding and when exam time comes around, they fail to answer even the most basic question.
So maybe we should break down the logic to its fundamental level through studying Philosophiæ Naturalis Principia Mathematica, which is a huge mathematical dictionary proving logical arguments and setting the foundation for mathematics to exist.
I think this would benefit students a lot because often, what's written in text books only shows one type of example and method, when there are many others ways to answer the question.
If students should struggle to understand the principia then they aren't mentally equipped for academia and I think these kinds of students are represented by the C/D and E grades at A level. You could also say that because only very few people understand 'real mathematics of the Principia' then there will be less people gaining worthless degrees, which will increase the value of a degree to a place where it was 50 years ago.
So maybe we should break down the logic to its fundamental level through studying Philosophiæ Naturalis Principia Mathematica, which is a huge mathematical dictionary proving logical arguments and setting the foundation for mathematics to exist.
I think this would benefit students a lot because often, what's written in text books only shows one type of example and method, when there are many others ways to answer the question.
If students should struggle to understand the principia then they aren't mentally equipped for academia and I think these kinds of students are represented by the C/D and E grades at A level. You could also say that because only very few people understand 'real mathematics of the Principia' then there will be less people gaining worthless degrees, which will increase the value of a degree to a place where it was 50 years ago.
(edited 10 years ago)
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it is a good idea if possible..But in many cases thoroughly understanding the logic and method requires way more than students of that age are expected to know.
Original post by Gondur
If students should struggle to understand the principia then they aren't mentally equipped for academia and I think these kinds of students are represented by the C/D and E grades at A level.
That's a bit harsh. Also, isn't it written in Latin?
Original post by Gondur
A lot of students, including myself, get confused when their teachers try and explain a particular something, maybe a method or theorem because they can't see how the logic is assimilated from one line to the next. There are huge gaps in their understanding and when exam time comes around, they fail to answer even the most basic question.
As for your lack of understanding, why don't you just ask your teacher how they proceeded in their working? Surely just sitting there isn't the best way to understand what is actually going on.
(edited 10 years ago)
Original post by Khallil
That's a bit harsh. Also, isn't it written in Latin?
As for your lack of understanding, why don't you just ask your teacher how they proceeded in their working? Surely just sitting there isn't the best way to understand what is actually going on.
As for your lack of understanding, why don't you just ask your teacher how they proceeded in their working? Surely just sitting there isn't the best way to understand what is actually going on.
Yes it is written in Latin but I think an English translation exists, or can easily exist.
Do you mean the book that Newton wrote?
"If students should struggle to understand the principia then they aren't mentally equipped for academia"
So if i don't understand something written in one certain book, then I'm not equipped for a degree in mathematics??
"If students should struggle to understand the principia then they aren't mentally equipped for academia"
So if i don't understand something written in one certain book, then I'm not equipped for a degree in mathematics??
Original post by hassassin04
it is a good idea if possible..But in many cases thoroughly understanding the logic and method requires way more than students of that age are expected to know.
Age does not make a difference. Your ability to 'learn' does, which depends on your IQ and amount of grey matter in your brain.
Answer:
No
It's written in Latin, it won't include new discoveries and some of the mathematical proofs were written almost "verbally" rather than mathematically.
Pretty sure your ability to learn is also linked to neuron structure which does change as you grow, and in fact grey matter changes throughout your life too.
No
It's written in Latin, it won't include new discoveries and some of the mathematical proofs were written almost "verbally" rather than mathematically.
Original post by Gondur
Age does not make a difference. Your ability to 'learn' does, which depends on your IQ and amount of grey matter in your brain.
Pretty sure your ability to learn is also linked to neuron structure which does change as you grow, and in fact grey matter changes throughout your life too.
(edited 10 years ago)
Original post by Khallil
That's a bit harsh. Also, isn't it written in Latin?
As for your lack of understanding, why don't you just ask your teacher how they proceeded in their working? Surely just sitting there isn't the best way to understand what is actually going on.
As for your lack of understanding, why don't you just ask your teacher how they proceeded in their working? Surely just sitting there isn't the best way to understand what is actually going on.
Nothing wrong with doing a bit of Latin upfront (I just wish I'd had some formal lessons in it!).
This could lead to all sorts of problems if students took up this suggestion - imagine the humiliation as thousands of teachers are forced to admit that they have no idea how the thing they've just "taught" actually works!
Original post by Gondur
Age does not make a difference. Your ability to 'learn' does, which depends on your IQ and amount of grey matter in your brain.
You must have a foundation to be able to grasp fundamental concepts. i think it is not that wrong to teach the techniques of differentiation for example first then the theory behind it. Another reason is that some people might not need all the theory behind it , only applications.
It is like wanting to learn a programming language without even being able to turn on the computer / create a folder / rename a file etc..
Original post by yo radical one
Answer:
No
It's written in Latin, it won't include new discoveries and some of the mathematical proofs were written almost "verbally" rather than mathematically.
Pretty sure your ability to learn is also linked to neuron structure which does change as you grow, and in fact grey matter changes throughout your life too.
No
It's written in Latin, it won't include new discoveries and some of the mathematical proofs were written almost "verbally" rather than mathematically.
Pretty sure your ability to learn is also linked to neuron structure which does change as you grow, and in fact grey matter changes throughout your life too.
Two English translations exist. I could be wrong when I say this, but new discoveries are irrelevant given that the A level curriculum uses mathematics Newton discovered.
Often students don't understand something because of the method used by the teacher - there are often several ways to approach problems even at low (GCSE) levels, some are easier to understand than others. The teacher will teach what s/he learned or finds easiest which of course isn't going to be a 100% match for all their students. A good teacher will teach more than one method and encourage students to use the one they are most comfortable with. There are also teachers who are ineffective at communicating the material and in those cases only the brightest students with the ability to work everything out themselves will appear to succeed.
Original post by Gondur
Two English translations exist. I could be wrong when I saw this, but new discoveries are irrelevant given that the A level curriculum uses mathematics Newton discovered.
Secondly do you mean Newton's book or Russell and Whiteheads?
(not even trying to namedrop)
Which Principia Mathematica do you mean? The one written by Isaac Newton, or the one by Bertrand Russell? The name matches up with the former but the description seems to match up more with the latter.
Either way, neither is a good idea as they are both far too complicated for an elementary level. Pretty much everyone would struggle with them; not just the C/D/E kids.
In terms of Russell, it is highly technical; nearly 400 pages until it is shown that 1+1=2. This kind of thing is not helpful for students and the length of time it takes to show even the simplest things would leave students even worse equipped with the mathematics they need in everyday life.
If you are referring to Newton, then it's a bad idea for slightly different reasons. Firstly is that the book does not cover what could be considered a sufficiently wide curriculum for school, and already assumes fairly sophisticated mathematical knowledge anyway. Then, a lot of Newtons work is fairly complicated geometrical proofs of his claims, which whilst very interesting in their own right are at too high a level for students, and many of his proofs have simpler analogues using more modern techniques.
(One of my Maths lecturers at Cambridge was actually telling us about Newtons Principia and this is where I get this information from as I have not read it personally.)
Either way, neither is a good idea as they are both far too complicated for an elementary level. Pretty much everyone would struggle with them; not just the C/D/E kids.
In terms of Russell, it is highly technical; nearly 400 pages until it is shown that 1+1=2. This kind of thing is not helpful for students and the length of time it takes to show even the simplest things would leave students even worse equipped with the mathematics they need in everyday life.
If you are referring to Newton, then it's a bad idea for slightly different reasons. Firstly is that the book does not cover what could be considered a sufficiently wide curriculum for school, and already assumes fairly sophisticated mathematical knowledge anyway. Then, a lot of Newtons work is fairly complicated geometrical proofs of his claims, which whilst very interesting in their own right are at too high a level for students, and many of his proofs have simpler analogues using more modern techniques.
(One of my Maths lecturers at Cambridge was actually telling us about Newtons Principia and this is where I get this information from as I have not read it personally.)
Original post by davros
Nothing wrong with doing a bit of Latin upfront (I just wish I'd had some formal lessons in it!).
Latin is a dying language. I really wouldn't want to learn it, but if I had the spare time and sufficient interest it wouldn't hurt. (This is all assuming I won't struggle with it horrendously!)
This could lead to all sorts of problems if students took up this suggestion - imagine the humiliation as thousands of teachers are forced to admit that they have no idea how the thing they've just "taught" actually works!
How ... can they not know why what they're teaching works?Original post by Gondur
A lot of students, including myself, get confused when their teachers try and explain a particular something, maybe a method or theorem because they can't see how the logic is assimilated from one line to the next. There are huge gaps in their understanding and when exam time comes around, they fail to answer even the most basic question.
So maybe we should break down the logic to its fundamental level through studying Philosophiæ Naturalis Principia Mathematica, which is a huge mathematical dictionary proving logical arguments and setting the foundation for mathematics to exist.
I think this would benefit students a lot because often, what's written in text books only shows one type of example and method, when there are many others ways to answer the question.
If students should struggle to understand the principia then they aren't mentally equipped for academia and I think these kinds of students are represented by the C/D and E grades at A level. You could also say that because only very few people understand 'real mathematics of the Principia' then there will be less people gaining worthless degrees, which will increase the value of a degree to a place where it was 50 years ago.
So maybe we should break down the logic to its fundamental level through studying Philosophiæ Naturalis Principia Mathematica, which is a huge mathematical dictionary proving logical arguments and setting the foundation for mathematics to exist.
I think this would benefit students a lot because often, what's written in text books only shows one type of example and method, when there are many others ways to answer the question.
If students should struggle to understand the principia then they aren't mentally equipped for academia and I think these kinds of students are represented by the C/D and E grades at A level. You could also say that because only very few people understand 'real mathematics of the Principia' then there will be less people gaining worthless degrees, which will increase the value of a degree to a place where it was 50 years ago.
You mean Bertrand Russell's Principia Mathematica, right? If students were to study it, I think they should also study Godels Theorems.
So maybe we should break down the logic to its fundamental level through studying Philosophiæ Naturalis Principia Mathematica, which is a huge mathematical dictionary proving logical arguments and setting the foundation for mathematics to exist.
The trouble is that mathematics is not all mindless proof. It's all well and good if you can read the Principia and a month later be able to churn out every formula just as Newton did it, but that's not how mathematics and science progress. You need imagination for that, and attempting to learn logic by rote is not the way to cultivate an imaginative mind.
...when there are many others ways to answer the question.
Again, it's great if you know the endless ways of solving a particular problem, but only one or two of those methods are going to count in an exam. In Newton's time when only a tiny percentage of the population went to school and university, you could pretty much learn whatever you wanted and do whatever you personally wanted to do to achieve a degree, because the exams were written by your teachers and tailored to you. Nowadays with compulsory education until age 18, there has to be standardised tests and students have to learn certain things to pass those tests.
Yes, many people do not have the mental capability to understand the Principia, but that does not make them bad or worthless mathematicians/scientists/members of society. It just means that they're better at another area.
Lastly your question does come across as a little arrogant... it almost seems like you're saying "Look at me! I understand the Principia! I must be one of the best A Level mathematicians out there!" Unfortunately those two things don't necessarily correlate. When you get to university you'll realise you're just a small fish in a very large pond. In 1st year the 2nd years know more than you. When you're on your Master's, the PhD students still outrank you. Even when you get your PhD there are hundreds of people around the world with twenty years' research in your field under their belt. Learning the Principia will not change this.
Original post by davros
This could lead to all sorts of problems if students took up this suggestion - imagine the humiliation as thousands of teachers are forced to admit that they have no idea how the thing they've just "taught" actually works!
PRSOM
Original post by DJMayes
Which Principia Mathematica do you mean? The one written by Isaac Newton, or the one by Bertrand Russell? The name matches up with the former but the description seems to match up more with the latter.
I accidentally suggested it - I meant Russell, but OP has taken it to be Newton.
Original post by DJMayes
Which Principia Mathematica do you mean? The one written by Isaac Newton, or the one by Bertrand Russell? The name matches up with the former but the description seems to match up more with the latter.
Either way, neither is a good idea as they are both far too complicated for an elementary level. Pretty much everyone would struggle with them; not just the C/D/E kids.
In terms of Russell, it is highly technical; nearly 400 pages until it is shown that 1+1=2. This kind of thing is not helpful for students and the length of time it takes to show even the simplest things would leave students even worse equipped with the mathematics they need in everyday life.
If you are referring to Newton, then it's a bad idea for slightly different reasons. Firstly is that the book does not cover what could be considered a sufficiently wide curriculum for school, and already assumes fairly sophisticated mathematical knowledge anyway. Then, a lot of Newtons work is fairly complicated geometrical proofs of his claims, which whilst very interesting in their own right are at too high a level for students, and many of his proofs have simpler analogues using more modern techniques.
(One of my Maths lecturers at Cambridge was actually telling us about Newtons Principia and this is where I get this information from as I have not read it personally.)
Either way, neither is a good idea as they are both far too complicated for an elementary level. Pretty much everyone would struggle with them; not just the C/D/E kids.
In terms of Russell, it is highly technical; nearly 400 pages until it is shown that 1+1=2. This kind of thing is not helpful for students and the length of time it takes to show even the simplest things would leave students even worse equipped with the mathematics they need in everyday life.
If you are referring to Newton, then it's a bad idea for slightly different reasons. Firstly is that the book does not cover what could be considered a sufficiently wide curriculum for school, and already assumes fairly sophisticated mathematical knowledge anyway. Then, a lot of Newtons work is fairly complicated geometrical proofs of his claims, which whilst very interesting in their own right are at too high a level for students, and many of his proofs have simpler analogues using more modern techniques.
(One of my Maths lecturers at Cambridge was actually telling us about Newtons Principia and this is where I get this information from as I have not read it personally.)
Glad I'm not the only one who thought this
Original post by Khallil
Latin is a dying language. I really wouldn't want to learn it, but if I had the spare time and sufficient interest it wouldn't hurt. (This is all assuming I won't struggle with it horrendously!)
How ... can they not know why what they're teaching works?
How ... can they not know why what they're teaching works?It's not a "dying" language - it's a "dead" one. That said, I can think of good reasons for giving it a go:
it encourages mental discipline
it gets you used to the constraints of a grammar that isn't fluctuating (this is especially useful if you work in computer languages as they operate with fixed expectations of how things are structured, unlike "modern languages" which evolve over time)
it underpins not just part of English but many romance languages too
it gives you freedom to read old-fashioned texts by yourself if you come across them - I read a Cambridge maths history a while back that was written in the 1880s and frustratingly the author slipped in Latin passages every so often without translation!
My comment about teaching wasn't entirely facetious - if you believe the media reports, there are teachers knocking about who couldn't handle last year's infamous C3 paper. This gives you an idea of why many students now struggle!
Original post by davros
It's not a "dying" language - it's a "dead" one. That said, I can think of good reasons for giving it a go:
I'll append "it's really fun and it appeals to the crossword-solving part of my brain" - every so often I have a little revelation like:
Huh, "tolerate" literally means "bear", as in "fero ferre tuli latus" the principal parts of "to bear" - and it's the same as "qui tollis peccata mundi" from the Church liturgy.
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