That's because, as mentioned earlier in this thread, anode and cathode swap positions in a lithium ion cell depending on whether it is being charged or being discharged.
Math, especially once the big formulas come out. I understand the concept, but I just don't know how to start when it comes to applying it. I tend to get hung up on what each variable represents, and what unit to use as often it's not really specified. Ex: if looking at a data sheet.I have a similar problem. Especially when there are formulae with variables in lower and upper case, and Greek characters, which look similar to Latin ones. My hand wring is hard to read and slow, which doesn't help. I just about scraped through mathematics at college.
I couldn't agree more, and being the self-righteous asshole I am, I refuse to call this a brain lock of mine; I blame the math folks, they are just wrong. Mathematical notations, theory, and typical teaching material used would never pass modern day code review process. It's total obfuscation from day one, and especially difficult for people who "think aloud in their heads" like me, when we try to understand a new concept. You can't read out obfuscated formulae where a single letter which is pronounced exactly the same is stylized in three-four different visual ways, to denote completely different things, when all they had to do is to give variables descriptive names.
While I quite often, on this forum and elsewhere, give expert-ish advice on lithium ion batteries, I have to Google every time which of the electrodes is anode and which cathode. It does not help the convention is reversed* compared to electrolytic or ultra capacitors. I just can't come up with a rule of thumb, I have to Google every time.
That's because, as mentioned earlier in this thread, anode and cathode swap positions in a lithium ion cell depending on whether it is being charged or being discharged. When being charged the anode is the positive terminal, and when being discharged the anode is the negative terminal.
The rule of thumb was helpfully provided by Sredni. Conventional current in a circuit enters the anode and leaves the cathode.
IMHO math is like a language you need to learn & understand.
But no one - not the scientific community, not the battery industry - uses such alternating naming; they are not temporary role names; earlier comments on this thread were speculation or opinion how it "could" or "should" be, not a description how it really is. Terms "lithium ion cathode" and "anode" are widely used, well defined fixed names for the two electrodes. The choice which is which is, as far as I know, completely arbitrary. I prefer to call them positive and negative electrode instead, and I know I'm not the only one; even many in the industry do the same. The advantage of calling them positive or negative is that the potential difference (voltage) never changes its sign, even if the current direction reverses.
It's honestly best not to use the words anode and cathode, since depending on context an anode can be either positive or negative, and a cathode can be either negative or positive. Those two words should be stricken from the dictionary as being meaningless without context.
Anyone who wants to communicate accurately should say "positive electrode" and "negative electrode" instead.
IMHO math is like a language you need to learn & understand.
You are right. As such, it's also open to discussion, and one can have opinions about it. In my opinion, it sucks. Also, in my opinion, it doesn't need to be permanently fixed because of some great man made decisions 300 years ago. Even the wheel has improved.
In the end, mathematics is used as a tool all over in the scientific community and engineering. But sometimes I can't avoid the feeling that the tool becomes a master, instead of servant; or some kind of secret club of those who really grok it, and the others who try to cope with it. I feel confident that some modernization of notations and conventions (e.g., multi-character descriptive variable names, and explanations of variables used i.e. comments) would significantly increase the social scope, and decrease the number of engineers who are intelligent per se, but still struggle to use math as their tool to the fullest extent.
IMHO math is like a language you need to learn & understand.
You are right. As such, it's also open to discussion, and one can have opinions about it. In my opinion, it sucks. Also, in my opinion, it doesn't need to be permanently fixed because of some great man made decisions 300 years ago. Even the wheel has improved.
In the end, mathematics is used as a tool all over in the scientific community and engineering. But sometimes I can't avoid the feeling that the tool becomes a master, instead of servant; or some kind of secret club of those who really grok it, and the others who try to cope with it. I feel confident that some modernization of notations and conventions (e.g., multi-character descriptive variable names, and explanations of variables used i.e. comments) would significantly increase the social scope, and decrease the number of engineers who are intelligent per se, but still struggle to use math as their tool to the fullest extent.You seem to be confusing mathematics, and the commonly accepted notations we use for mathematics. The notation is open to discussion. The only discussion about maths itself is whether our understanding is complete and accurate.
IMHO math is like a language you need to learn & understand.
You are right. As such, it's also open to discussion, and one can have opinions about it. In my opinion, it sucks. Also, in my opinion, it doesn't need to be permanently fixed because of some great man made decisions 300 years ago. Even the wheel has improved.
In the end, mathematics is used as a tool all over in the scientific community and engineering. But sometimes I can't avoid the feeling that the tool becomes a master, instead of servant; or some kind of secret club of those who really grok it, and the others who try to cope with it. I feel confident that some modernization of notations and conventions (e.g., multi-character descriptive variable names, and explanations of variables used i.e. comments) would significantly increase the social scope, and decrease the number of engineers who are intelligent per se, but still struggle to use math as their tool to the fullest extent.
IMHO math is like a language you need to learn & understand.
You are right. As such, it's also open to discussion, and one can have opinions about it. In my opinion, it sucks. Also, in my opinion, it doesn't need to be permanently fixed because of some great man made decisions 300 years ago. Even the wheel has improved.
In the end, mathematics is used as a tool all over in the scientific community and engineering. But sometimes I can't avoid the feeling that the tool becomes a master, instead of servant; or some kind of secret club of those who really grok it, and the others who try to cope with it. I feel confident that some modernization of notations and conventions (e.g., multi-character descriptive variable names, and explanations of variables used i.e. comments) would significantly increase the social scope, and decrease the number of engineers who are intelligent per se, but still struggle to use math as their tool to the fullest extent.You seem to be confusing mathematics, and the commonly accepted notations we use for mathematics. The notation is open to discussion. The only discussion about maths itself is whether our understanding is complete and accurate.
Didn't Kurt Godel have something to say about that?
IMHO math is like a language you need to learn & understand.
You are right. As such, it's also open to discussion, and one can have opinions about it. In my opinion, it sucks. Also, in my opinion, it doesn't need to be permanently fixed because of some great man made decisions 300 years ago. Even the wheel has improved.
In the end, mathematics is used as a tool all over in the scientific community and engineering. But sometimes I can't avoid the feeling that the tool becomes a master, instead of servant; or some kind of secret club of those who really grok it, and the others who try to cope with it. I feel confident that some modernization of notations and conventions (e.g., multi-character descriptive variable names, and explanations of variables used i.e. comments) would significantly increase the social scope, and decrease the number of engineers who are intelligent per se, but still struggle to use math as their tool to the fullest extent.You seem to be confusing mathematics, and the commonly accepted notations we use for mathematics. The notation is open to discussion. The only discussion about maths itself is whether our understanding is complete and accurate.
Mathematics happens to be a favorite subject of mine, and I found from childhood that I had a natural aptitude for it. For instance, I could score 100% on a GCSE mock paper without effort when I was 14, and got a grade A in the Further Mathematics A-Level when I was 17.
In fact, people like Einstein and Feynman would invent their own notations to make writing things down easier.
I know this is not necessarily going to help others, but I do think the way mathematics is taught has a lot to blame for this. It's like the analogy of learning music. Do you learn music first by learning musical notation and theory on paper, or do you learn first how to pick up an instrument and make music? Mathematics is like music. If you don't learn as a child how to hear and play the music of mathematics, it will be always harder than it ought to be.
Everybody in my local state school passed maths O-level (Inc calculus) one year early, many went on to do further maths O-level the next year. In the next two years, I and several others passed 3 maths A-levels
Everybody in my local state school passed maths O-level (Inc calculus) one year early, many went on to do further maths O-level the next year. In the next two years, I and several others passed 3 maths A-levels
I remember once at school, finding a stack of old O-level mathematics textbooks buried at the back of a store cupboard. I was surprised to find that they contained an introduction to calculus, and that at one time calculus was on the O-level syllabus. By the time I was doing GCE mathematics after O-levels had been replaced, they had dumbed everything down so much that they didn't even show the derivation of the quadratic formula. It was just, "Here is the formula, trust us, it works, you don't need to know how to derive it, just use it."
How can you properly understand it if you don't know where it came from?
Everybody in my local state school passed maths O-level (Inc calculus) one year early, many went on to do further maths O-level the next year. In the next two years, I and several others passed 3 maths A-levels
I remember once at school, finding a stack of old O-level mathematics textbooks buried at the back of a store cupboard. I was surprised to find that they contained an introduction to calculus, and that at one time calculus was on the O-level syllabus. By the time I was doing GCE mathematics after O-levels had been replaced, they had dumbed everything down so much that they didn't even show the derivation of the quadratic formula. It was just, "Here is the formula, trust us, it works, you don't need to know how to derive it, just use it."
How can you properly understand it if you don't know where it came from?
We used to go through old exam questions, from papers dating back to ~1953. They were hard.
Everybody in my local state school passed maths O-level (Inc calculus) one year early, many went on to do further maths O-level the next year. In the next two years, I and several others passed 3 maths A-levels
I remember once at school, finding a stack of old O-level mathematics textbooks buried at the back of a store cupboard. I was surprised to find that they contained an introduction to calculus, and that at one time calculus was on the O-level syllabus. By the time I was doing GCE mathematics after O-levels had been replaced, they had dumbed everything down so much that they didn't even show the derivation of the quadratic formula. It was just, "Here is the formula, trust us, it works, you don't need to know how to derive it, just use it."
How can you properly understand it if you don't know where it came from?
We used to go through old exam questions, from papers dating back to ~1953. They were hard.At least for the London papers we took, the only real difference between the O-level and A-level maths paper from the late 40s until I took mine in the early 70s was that the O-level had been split into traditional maths and modern maths. The additional maths O-level and A-level syllabus and papers could have been from any year. By the time I took my A-levels in 1973 I had answered every A-level question from 1948 to 1972, and found very little variation in their difficulty. I did quite a few additional maths O-level past papers before my O-levels in 1971, and they were similar. The traditional maths O-level had some basic differentiation and integration. The modern maths O-level had lots of statistics, matrix algebra and other things instead. The additional maths o-level had quite a lot of calculus. When I was at university, mixing with people who had taken various board's papers, people told me London was hard, so if you took other papers things may have varied.
Everything we learned in maths was taught by deriving it from first principles. We were never spoon fed any formulae. Even things like Gaussian distributions were taught from basic principles, although the central limit theorem missed the complexity that distributions without a stable mean can't be munged together to arrive at a Gaussian distribution (e.g. Pareto).
Somewhere I have an SMP maths textbook that I bought in Hay-on-Wye, which states "integration and differentiation of polynomials except 1/x".
When I was at university, mixing with people who had taken various board's papers, people told me London was hard, so if you took other papers things may have varied.
Hmm. I found a Further Mathematics exam from 1981 similar to the one I sat in 1979 (same exam board).
On glancing through it, it would certainly give me a headache now. I would for sure have to review a lot of the material before attempting it.
https://www.slideshare.net/telescoper/a-level-further-mathematics-1981
I know this is not necessarily going to help others, but I do think the way mathematics is taught has a lot to blame for this. It's like the analogy of learning music. Do you learn music first by learning musical notation and theory on paper, or do you learn first how to pick up an instrument and make music? Mathematics is like music. If you don't learn as a child how to hear and play the music of mathematics, it will be always harder than it ought to be.
I know this is not necessarily going to help others, but I do think the way mathematics is taught has a lot to blame for this. It's like the analogy of learning music. Do you learn music first by learning musical notation and theory on paper, or do you learn first how to pick up an instrument and make music? Mathematics is like music. If you don't learn as a child how to hear and play the music of mathematics, it will be always harder than it ought to be.
Yeah. And when I complained above about using the same letter in three or four different styles within a formula, from which CatalinaWOW made a straw man, I was not exaggerating, I was dead serious. I have no issue with dt, especially if it's explained somewhere. But I did have major issues with a formula which contained letter "r" in four and letter "e" in three different meanings, all in different shapes and forms. It just... makes my brain lock. Distinguishing between r, R, r, r, r with ^ on top, R stylized as cursive, all within the same formula, simply wastes time and mental effort. Maybe somebody else just looks at the text and the symbols intuitively enter their brain. When I see such formula for the first time and not understand it, I try to read it out loud in my mind. If it reads out [r r r e x r e r], the things only get worse, and I'm stuck.
I was straight-A full scores in mathematics in high school and until about half of the first year in uni. At some point my motivation started drooping as the pace increased, while the disconnect between engineering-minded courses and math courses widened at the same time. It was clear that to truly understand the math courses, I would have had to invest a lot more time to the matter, finding secondary sources apart from the lectures, official lecture notes, and maybe indeed invent my own notation. It did not happen.
A simple example:
VC(t) = ϵ(1−e−t/τ)
I was straight-A full scores in mathematics in high school