Admit your Brain lock

[Siwastaja]

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.

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.

[coppice]

Viterbi decoding gets me every time. Its far from the most complex thing I've ever dealt with, and its not hard to understand how it works and takes you closer to the Shannon limit. Still I go around in circles implementing it every time I come back to dealing with it.

[nctnico]

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.

That reminds me... last week I was in a building names after this guy: https://nl.wikipedia.org/wiki/Hans_Freudenthal According to you he should have done a better job.

IMHO math is like a language you need to learn & understand. Just like trying to make sense of the ever more abstract paintings by Picasso.

[tggzzz]

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.

Er, no.

The anode has the more positive voltage, the cathode the more negative. That doesn't change between charging and discharging.

The rule of thumb was helpfully provided by Sredni. Conventional current in a circuit enters the anode and leaves the cathode.

Yes, but it is not a rule of thumb, it is a convention. Other things follow from that convention, e.g. power dissipation.

The power dissipated in a circuit element is I*V, where I is the (conventional) current going into the more +ve terminal, and P=VI where V is the voltage across the element.

For a cell, the more positive terminal is the anode, and thus current flowing into the cell's anode causes a positive power dissipation in the cell.
For a cell, the more positive terminal is the anode, and thus current flowing out of the cell's anode causes a negative power dissipation in the cell.

[Siwastaja]

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.

[IanB]

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 seems we are of like mind. Which is why I wrote something similar above:

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.

As for a lithium ion cell, I think the industry designation of anode and cathode follows the convention of the cell being treated as a source (the reason it exists), rather than as a sink. You don't construct lithium ion batteries to consume electricity, you construct them to supply electricity--hence the positive terminal becomes the cathode.

[coppice]

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.

[tggzzz]

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?

[CatalinaWOW]

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.

I am not ready to pooh-pooh this comment without seeing a complete development of your ideas.  It certainly runs counter to my instincts.  Replacing dt with Differential_Time_Increment and like substitutions elsewhere would make almost all equations multi-line and many multi-page, with little or no improvement in understanding.  The usage of comments for definitions is fine, and is already widely used, albeit with two major styles, and omissions just as there are in the software environment.  Your approved software environment uses compact symbols with complex meanings.  They are usually called operators, and cause little confusion to anyone when they overlap with widely used conventions.  Examples being + and -.  * for multiplication already violates the grade school convention of X, and things get really confusing for non-experts when casting and piping operators come into play.

In one sense you are right.  The math notation is a domain specific language designed to convey concepts quickly and compactly to those who understand the language and what it represents (grok it).  Perhaps your ire should be reserved for your math teachers that failed to convey those concepts to you, rather than those who codified the language used.  Teaching is always a difficult job, and one size does not fit all.  Some teachers do not recognize this, or do not use alternate teaching paths.  Sometimes due to incapacity, sometimes laziness, and sometimes due to constraints placed on them by the school administration.

[CatalinaWOW]

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?

All Godel said was that no mathematics could be complete without some unproveable axioms. 

A sublety of almost no relevance when applying math to science and engineering.  In engineering the only concern is if the mathematics correlates to some physical problem.  The same is often true in science, though one corner of science concerns itself with whether the math is exactly representative of the universe, or just a damn good approximation.  The question is important because in some cases the math has preceded the observations and then subsequently phenomena (particles, reactions and the like) discovered which matched the mathematics.  But in other cases observations the math has been proved wrong.  Leading to the question:  Have we found the one true mathematics, or is it yet to be discovered, or is there no such thing.  it is not clear to me whether Godel's proof has any relevance to this question.

[IanB]

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.

One thing I have observed is that when I see people struggling with mathematics, I see them trying to manipulate symbols and notation, and applying rules to rearrange symbols to get a desired result.

I find this is not how I comprehend mathematics. For me, my comprehension consists of concepts and visualizations in my mind of abstract ideas, like painting with thought. 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.

[tggzzz]

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.

Mine too.

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

In fact, people like Einstein and Feynman would invent their own notations to make writing things down easier.

Yes, but so did Newton and Leibnitz - and many others

Maths progresses by introducing new notations, e.g. "0", "=" , etc.

It helps if the new notations obeys the arithmetic conventions for addition, subtraction, multiplication, and preferably division

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.

My school had two 6th form maths teachers. One had created a new method of generating Pythagorean triads; his lessons were almost (but not quite) incomprehensible. The other had got his maths degree and realised he wasn't going any further; his lessons were superb.

By superb, I mean teaching differentiation from first principles in 3 hours. Later repeated with integration. Younger maths teachers don't believe it, but I have one of the textbooks to wave under their nose (Limited to polynomials except 1/x; that was an A-level topic!)

[IanB]

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?

[tggzzz]

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.

But back then... "We choose to go to the Moon in this decade and do the other things, not because they are easy, but because they are hard; ..."

[coppice]

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).

[tggzzz]

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.

<goes and looks at the 2" high line printer output> University of London "363 Maths syll D". June '72, so I was 15.

I remember being told by the maths teacher that they chose to do this in preference to another syllabus, but I have no recollection of what might have been in those.

Somewhere I have an SMP maths textbook that I bought in Hay-on-Wye, which states "integration and differentiation of polynomials except 1/x".

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).

I missed stats, and thermodynamics for that matter. I do remember we had to point out to the teacher that, with about a month to go, we hadn't been taught complex numbers. Quickly rectified

They did bring in a guest teacher for a few lessons, and he introduced us to aleph-null (ℵ0) and transfinite numbers, even though it wasn't on the syllabus.

I also remember my junior school teacher introducing me to very simple algebra.

[coppice]

Somewhere I have an SMP maths textbook that I bought in Hay-on-Wye, which states "integration and differentiation of polynomials except 1/x".

SMP was the School Mathematics Project, the basis for the London board's modern maths O-level. I think London may have had another modern maths options, but I know other exam boards around the UK did. It was a weird time. Some schools found the modern maths syllabus to be hard for the less able, so only the most able streams took it. Other schools felt the modern maths stuff was easier, so only used it for the less able streams. So, the top kids from one school were competing against the less able from others in weird ways. If you were the sort that wanted to cover the greatest ground the SMP O-level plus the additional maths O-level covered a lot of ground. If you did traditional + additional you covered quite a bit of ground twice, just answering harder questions about similar material in the additional course.

[IanB]

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.

I remember being told that at my school. They picked London for every subject except mathematics, where they picked Cambridge instead.

[IanB]

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

[pcprogrammer]

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

Same here. At school I was very good at it and scored nines and tens on tests, but not having used more than basic calculus in my working days it got lost. With the brain fog I now often have it is hard to concentrate on learning again. Even working on my projects is cumbersome and takes way longer than it used to. When I work on a project I get tired and need to walk away from it or take a nap.

Guess it is both my illness and getting older.

[BradC]

Perl. Always has looked more like line noise to me.

[Siwastaja]

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.

[Zero999]

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:
V_C(t) = ϵ(1−e^−t/τ)

[IanB]

A simple example:
V_C(t) = ϵ(1−e^−t/τ)

There may be a kind of analogy here with natural language. When I read and write, I don't see words as a group of letters, I seem them as pictures. Hence I quickly sense if a word is spelled incorrectly because when I see it the picture looks wrong.

When I look at the equation above, I also don't see a formula, I see pictures. I see voltage as a function of time, and I see that being a small number scaling a first order rise with a given time constant.

(If ϵ does not actually represent a small number, then that would be a poor choice of symbol in the equation.)

[coppice]

I was straight-A full scores in mathematics in high school

I find it amusing when younger people say this. When I was at school I never got above 93% in maths. All answers correct. All workings shown. That got me 93% consistently. 70% would get you an A, as the questions were tough enough that this restricted those As to less than 10% of students. I find the expectation that anyone but a genius on a good day would get 100% on an exam an indictment of that exam. A well formed exam should be able to separate even the top 1% of student's performances in that exam.