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Positive & Negative

by rg Sat Mar 22nd, 2008 at 04:03:40 PM EST

A good discussion for a rainy Saturday afternoon indoors... - Promoted by Migeru


Positive and Negative

I am in the process of learning Chemistry.  I find the subject fascinating, but...wow!  For me, it's complicated.

The Basics

So far I have got my brain around the following basic items:

That an atom is made up of smaller particles as follows:

--the nucleus
--electrons

and that the nucleus can be subdivided further into two separate items as follows:

--protons
--neutrons

Building Blocks

Everything around me and including me--my computer, my brain, my hair, the earth's crust, the oceans, the sun, distant galaxies--all are made up of atoms.

Very Complicated Provisos

are what I come to ET (among other places) to learn about.  DoDo pointed me to neutron stars a while back; while Martin gave me a look-see at the latest experiments they are doing on the kinds of things that appear if you smash protons and neutrons into tiny pieces--about these things I know much less than I know about chemistry, and I know very little about chemistry, so...keeping to my simpler model...

Hey, rg, why'd you choose chemistry?

Physics is too difficult (for me, at present.)  I can't do the maths, and without the maths (and maybe even with it--I can't do the maths so I'm guessing), I would be pondering models...that I couldn't understand.

Biology: you start with a cell (the basic building block of life--lots of arguments there, too, intriguing ones but....)--which is made up, when examined, of chemicals such as sulphur, phosphorus, and carbon--and if I don't really understand what sulphur, phosphorus, carbon, etc. are--I have the feeling of...walking into a conversation where everyone knows the various characters they're talking about while I'm going, "Who?"

So...Chemistry

for me sits between "too complicated for me (at present) maths" and "too complicated for me (at present) aggregations".

Talking about positive and negative

Right, here's my hang up--and I want to share it here in order to receive (if possible!) your help in overcoming it.

rg's Hang Up

is with words and their historical associations.  I associate the words "positive" and "negative" as follows:

"positive" = good, more, gain
"negative" = bad, less, loss

Reduction and Oxidation

Also know as "redox" is one of the things you have to know about to pass your Chemistry GCSE [UK exam for sixteen year olds].  Here's wikipedia on the subject.

Redox - Wikipedia, the free encyclopedia

Now, leaving oxidation to one side, reduction is

--a gain in electrons (well, that's a simplification but I'm at that stage in my education...)

So reduction is a gain.  Right, so, following my internal map of positive and negative, a gain must be something positive, right?

Wrong!  A gain in electrons means an increase in negative charge.  So reduction = gain = more negative charge...

I'm stuck in morality!

As a friend said, when I explained my dilemma, "Yes, you have to lose the morality."

"I can do that," I said, "but...negative and positive are not equivalents.  There is a qualitative difference.  My trouble is I can't get my head around the concepts without getting lost in the idea of positive as a gain and negative as a loss."

Cathodes and Anodes

An ion is an atom that has either lost or gained an electron or electrons.  A cation is an atom that is positively charged (it has lost an electron or two or three); and an anion is an atom that is negatively charged (it has gained an extra electron or two or three.)  

Cathodes and anodes are....

Cathode - Wikipedia, the free encyclopedia

A cathode is an electrode through which (positive) electric current flows out of a polarized electrical device. Mnemonic: CCD (Cathode Current Departs).

Anode - Wikipedia, the free encyclopedia

An anode is an electrode through which (positive) electric current flows into a polarized electrical device. Mnemonic: ACID (Anode Current Into Device). Electrons flow in the opposite direction to the positive electric current.

(Ouch my head!)

Positive attracts negative and negative attracts positive

Therefore:

A cathode is giving out electrons--it is a source of electrons (=positive?  No!  It is giving out negative particles--it is losing electrons.)

Positive cations are drawn to the cathode because they lack electrons (lack = negative?  No!  Gaining more electrons is positive?  Well, it's what the positive cations attempt to do--to create electrical balance--)

Yes, thank you.  I understand you perfectly.  (Cough cough cough cough cough!)  So, what is your question?

My question to ETers is:

Can anyone offer me a mental model such that when I see

I don't immediately think, "Ah!  That's the positive sign--two plus two equals five, etc.--so something positive is going on, which means some addition is happening". . .

(An atom becomes positively charged when it loses an electron)

And if I see the following sign:

I don't think "Ah!  Take something away!"

(An atom becomes negatively charged when it gains an electron)

A Brief Deviation (a.k.a. Lovely Symbols)

Why anyone decided to call a "mole" a mole, I don't know.  The guy--Sg. Avogadro--who is associated with the word (more in a sec) was italian, so maybe "mole" could be pronounced "moh leh", of which there is one in Torino:

(It's the big pointy building)

...but what does that have to do with atoms?

NPR: Chemistry Lovers Celebrate Mole Day

A mole is the number 6.02E23 (602000000000000000000000.) It's big, especially in chemistry where most numbers are really small. The mole is used to convert those really small numbers into something chemists can work with.

Check out that number (called Avogadro's number):

6.02 times ten to the power of 23 (which means add twenty three zeros, so):

,000 (3 zeros = thousand)
000,000 (6 zeros = million)
000,000,000
000,000,000,000
000,000,000,000,000 (bear with me!)
000,000,000,000,000,000
000,000,000,000,000,000,000 (that's three six nine twelve, fifteen, eighteen, twenty one zeros)

so...

602,000,000,000,000,000,000,000

(I may be wrong by a couple of zeros!)

= the number of atoms in one "mole" of...anything.

1 gram of hydrogen has 6.02^23 atoms and = 1 mole of hydrogen
12 grams of carbon has 6.02^23 atoms and = 1 mole of carbon
40 grams of calcium has 6.02^23 atoms and = 1 mole of calcium

(If bicycles and cars were atoms, 6.02^23 bicycles would weigh less than 6.02^23 cars)

Putting 6.02^23 into context

I have heard three analogies.

Analogy one:

If one glass of water represents one atom, then one mole of atoms (that's 602,000,000,000,000,000,000,000 individual atoms)contains more atoms than there are glasses of water in all the world's oceans

Analogy two:

If one grain of sand represents one atom, then one mole of atoms contains more atoms than there are grains of sand on all the beaches around the UK

Analogy three:

If a pea is taken to represent one atom (it's round, so I like this analogy!), then one mole of atoms, represented in peas, would cover the entire planet in peas to a depth of twenty kilometres.

(Or maybe it was miles--anyway, that's lots of peas!)

So, imagine the magnification if I want to look at just one atom, and then imagine the magnification if I want to look inside that atom to see the nucleus, which is one ten thousandth the width of the atom, which means if you grabbed that single pea and blew it up to be ten kilometres across (! Huge pea!) the nucleus would be one metre wide--

Did I get that right?

(10,000 metres = 10 kilometres)

So, I hold this imaginary nucleus--one metre across and made up of protons (positive) and neutrons (neutral), and around me fly electons (negative) in their various orbitals (their crazy movements around the positive centre), and those electrons farthest out (up to ten kilometres away), those that can get farthest from the one metre wide nucleus I'm holding, they're the ones that go off and do strange things that we know as chemical reactions--

O + O = O2

2C + O2 = 2CO

and one single CO is Carbon monoxide (Carbon with one oxygen):

And what holds those two atoms together is a reaction between the flying electron clouds, and to understand that, I have to understand the giving, taking, and sharing of electrons, and to do that I need to get my head around this positive and negative business in such a way that:

The qualities I ascribe to positive and negative are such that I find it easy (well, easier) to follow those + and - signs as they appear.

My Current Model

Did I tell you the model my friend suggested?  Here it is:

"The positive is comfortable, it has enough, it can afford to lose an electron or two.  The negative is always after a bit more, it wants to grab an extra electron or two (or even three) if it can."

But isn't it really all about charge?

Charge and forces....I feel complicated mathematical equations bearing down on me.  I mean this kind of thing:

Mental Models

We all hold internal models of the world.  The famous maps described by many, but I'll go with Robert Anton Wilson's version because I can remember where it is on the internet, and because it links into a discussion I had with francois a couple of days ago.

Here's the quote:

Robert Anton Wilson | Cosmic Trigger, Volume I

My own opinion is that belief is the death of intelligence. As soon as one believes a doctrine of any sort, or assumes certitude, one stops thinking about that aspect of existence. The more certitude one assumes, the less there is left to think about, and a person sure of everything would never have any need to think about anything and might be considered clinically dead under current medical standards, where absence of brain activity is taken to mean that life has ended.

My attitude is identical to that of Dr. Gribbin and the majority of physicists today, and is known in physics as "the Copenhagen Interpretation," because it was formulated in Copenhagen by Dr. Niels Bohr and his co-workers c. 1926-28. The Copenhagen Interpretation is sometimes called "model agnosticism" and holds that any grid we use to organize our experience of the world is a model of the world and should not be confused with the world itself. Alfred Korzybski, the semanticist, tried to popularize this outside physics with the slogan, "The map is not the territory." Alan Watts, a talented exegete of Oriental philosophy, restated it more vividly as "The menu is not the meal."

Where our mental models get stuck is when they are no longer effective to understand the realities around us.  I feel that my mental model of positive and negative, when applied to the world of atoms, is not efficient.  I keep making mental assumptions that only serve to confuse me when faced with something like this:

(That's...hmmm...carbon surrounded by four hydrogen atoms, each hydrogen shares its single electron with one of the carbon electrons, so the hydrogen atoms are...er...pulling in more negative energy?

Poof!

If I put my mind to it I could do the chemistry without having the understanding.  I would like to make an immediate analogy to a....to a person....who has beliefs contrary to the way the world works (a 6,000 years ago God made everything creationist, say), who nevertheless can negotiate the world, use chalk, light a fire and burn carbon (+ other things) in oxygen--

Double Boom!

Two explosions, one to my centre right, ahead of me, and then another further to the right and further away.  What can they mean?

With efficient and effective models I'll have a better idea of what's going on.

Display:
I hope that makes some sense!

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Fri Mar 14th, 2008 at 08:54:34 AM EST
Chemistry!!!!!
Alas I don't have time to read through properly right now but will try to soon.

I am often glad I did chemistry following right on through school to uni because these associations of positive, moles etc etc are hardwired into my brain now and I don't need to think about them.  I have often wondered though how it would be to have those associations hard wored elsewhere to then try to absorb the concepts and language of chemistry later in life.

I didn't do physics for the same reason as you, maths is too poor but that said my PhD was in physical chemistry which gives the best of both worlds.

But the stuff they teach you at GCSE about models of atoms, the Bohr model and so on, you get to A-level and they are like, oh no, that's rubbish, it actually works like this.
then you get to uni and they say bollocks, it's all about probability.  But the models are useful for step by step grasping of the concepts.  I see chemistry in my head from building on the foundations those silly models presented to me at 14 and the more I learn, the more amazing it becomes because you realise how little you actually know. Keep us tuned into your journey and I will come back and comment more when I can.

Learn those key equations though and how you move the symbols around because when you can see the algebra fly about in your mind's eye, then you'll really begin to get depth of understanding.

by In Wales (inwales aaat eurotrib.com) on Fri Mar 14th, 2008 at 09:10:56 AM EST
[ Parent ]
Do you actually see positive and negative in some particular way, or does it all depend on the particular relationships?  I get confused when numbers appear around a chemical element (I'm easily confused!)

But all the numbers have something in common: I can add and subtract them, so 6 protons + 1 proton = 7 protons (=nitrogen); 6 - 5 = 4 protons (=boron) etc.

I'd like (maybe it's impossible!) to have a similar way to think about positive and negative, some correlation that I can then apply when I stare at something like:

and those plus and minus symbols mean something to me beyond "the lithium ion has one less electron and the fluorine ion has one more electron"

I mean, maybe there's no single model I can hold onto, and I'm wondering if people (such as yer good self) have some model in mind (e.g.--and this is just to show  what I mean by model i.e. a shorthand--"Ah, well, positive is lighter and negative is heavier"

Sommat like that.

And thanks for the support!  

I have often wondered though how it would be to have those associations hard wired elsewhere to then try to absorb the concepts and language of chemistry later in life.

That's where I'm at!

(OT, in your recent diary: have I got it right, that you can hear all those strange youtube videos I post?  So you're in a similar position but swap Chemistry for Music?)

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Fri Mar 14th, 2008 at 09:29:53 AM EST
[ Parent ]
I have tomato and roasted pepper soup. i will answer bit by bit.

First off, when you think negative or positive think negative CHARGE, positive CHARGE. Charge.  Associate the word charge as a concrete property as something quantitative. You can measure charge.

always associate an electron as -
An electron is negative. Think electron think the symbol -  minus. electron. minus. -

REDOX
reduction. electrons are minus.  more electrons, more minus, more negative. think of numbers. say 2. add a minus. 1. add another minus. 0.  You have reduced the number. add a minus, add an electron, reduction.
(gain electrons, reduce the charge = reduction)

oxidation is just the opposite of reduction. Learn reduction and you can work out oxidation. lose an electron, lose a minus therefore gain a plus.

All of this hinges on the movement of electrons. You are following the electrons. Where they go, they take a minus with them, leaving a plus behind them.

Get this out of your head now,

"The positive is comfortable, it has enough, it can afford to lose an electron or two.  The negative is always after a bit more, it wants to grab an extra electron or two (or even three) if it can."

It is the wrong way around. postive attracts negative. positive is missing electrons and needs electrons to balance itself out. negative has extra electrons and will give them away to balance itself out.

The balance of positive charge and negative charge is neutral, no charge.

Assume you started with a neutral. if you have an ion that is positive, +, it is missing an electron, -.
cations, positive, missing electrons. The minus (electron) went somewhere else and left a plus behind.

if you have an ion that is negative, it has extra electrons, -
anions, negative, has extra electrons

I will do another post to answer more questions.

by In Wales (inwales aaat eurotrib.com) on Fri Mar 14th, 2008 at 09:50:11 AM EST
[ Parent ]
This is just exactly the kind of thing I had in mind!  I look forward to your next installment.

(btw, post as much as you like and can--if you are the funky electron provider, then I am WAY positive!)

(: did I get that right?)

(And also: I am going to re-read yours (and anyone else's!) comments late at night (maybe many times!), after having cleared my mind of clutter (in my own way) and with maximum concentration--and slowly! So more please!  And I promise to pay you back with music, only if you'd like, though!)

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Fri Mar 14th, 2008 at 10:08:09 AM EST
[ Parent ]
If I'm providing the electrons, you'll be gaining them... follow the minus.
by In Wales (inwales aaat eurotrib.com) on Fri Mar 14th, 2008 at 10:20:36 AM EST
[ Parent ]
I'm lacking in electrons so I'll be positive for quite a while.

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Fri Mar 14th, 2008 at 07:20:04 PM EST
[ Parent ]
They're just complementary qualities. You could call them red and blue, day, night, zombo and fruvious.

(In fact quarks are divided up into 'colours' which are just another example of complementary qualities, grouped in threes instead of twos, and don't imply actual colour.)

It works like this - things behave in a certain way, and you have to label them with something. So historically scientists pick a word that sort of fits - often not very well, and sometimes out of context - and leave it at that. The people who do the exploring get to choose the words. If their exploring is good, everyone else copies them. If the words are not so good - too bad, everyone is stuck with them.

But you've illustrated a point I've tried to make before about the difference between scientific and creative types.

Creative types view the world through their feelings, and feeling is a moral process. So if they're excited about something - that's good. It's positive! If they're not excited about it - and feeling negative - that's bad.

Scientific types just describe what happens. There's no moral imperative, and while they do excited about things, getting excited - or not - isn't the main point of the exercise. The main point is describing what happens accurately, precisely, and reliably.

So with charge what matters is that opposing charges attract, and identical charges repel. You can put some numbers in and calculate exactly how much this happens.

E.g. to make an old-style cathode ray TV or monitor, you need to flick a beam of electrons around to paint the picture. Because you know the charge, it's easy to calculate how much flicking is needed, and how to build something that does it.

And - this would still be true if you went through the whole of physics and swapped the negative and positive signs around.

The current (sorry...) convention is actually rather stupid, because in a battery electrons flow from the negative terminal to the positive one. So if you think of it in terms of water flowing - which is sometimes useful for electricity - there's a flow from negative to positive.

This makes no sense at all, and it's really just an accident of history that the labelling is as it is.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Fri Mar 14th, 2008 at 10:48:25 AM EST
[ Parent ]
Great comment, thanks!

If the words are not so good - too bad, everyone is stuck with them.

Ah!  You have felt my pain.

this would still be true if you went through the whole of physics and swapped the negative and positive signs around.

I read an example where they used green and red balls--precisely to remove the associations with the words "positive" and "negative", but then the red balls and the green balls did different things (the red balls clumped together and the green balls flew around them, I think), so there was some essential difference between a red ball and a green ball; you could change the colours but that difference was still there.  I'm looking for a model where I can assign some concept to "red ball" (apart from redness) such that the behaviour of the red ball can be (at least partly) anticipated by my associating my model...."Those red balls are like...diamonds, hard to the touch and expensive; those green balls are like....cars; always around and needing roads...."

Creative types view the world through their feelings, and feeling is a moral process. So if they're excited about something - that's good. It's positive! If they're not excited about it - and feeling negative - that's bad.

Scientific types just describe what happens. There's no moral imperative, and while they do excited about things, getting excited - or not - isn't the main point of the exercise. The main point is describing what happens accurately, precisely, and reliably.

Would the two words "qualitative" and "quantitative" apply here?  I mean, I can do both but I need the "qualitative" so that I can keep my "quantitative"...in some human context...I can see a synthesis whereby the scientific description (accurate, precise, reliable) can only be brought into human action (lives....I dunno ....into the realm of human....something) when effective models are in place for us to relate the numbers to something less abstract (as is happening at the moment--for me--with the great discussions here and across the internet about economics); and vice versa those that can simply feel something need to be able to turn these feelings into something quantitative so that one person's experience can be spread out across humans (human society...something like that.)

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Fri Mar 14th, 2008 at 11:26:04 AM EST
[ Parent ]
IEEE - IEEE History Center: FAQS
In the 18th century a number of people made investigations of static electricity. Charles Dufay distinguished between vitreous electricity (the sort created when glass or rock crystal was rubbed) and resinous electricity (the sort created when resin or a wax rod was rubbed). Dufay proposed a two-fluid theory of electricity, the two fluids corresponding to the two types of electricity. Benjamin Franklin proposed a one-fluid theory, hypothesizing that the two apparent types of electricity were, in fact, occurrences of excesses and deficiencies of a single electrical fluid. Franklin introduced the terminology 'positive' and 'negative' to denote, respectively, an excess of electrical fluid and a deficiency of electrical fluid. It was on the basis of certain charging and discharging phenomena that Franklin assigned the designations 'positive' and 'negative', and in the 19th century the terminals of electric batteries were labeled 'plus' and 'minus'. Early in the 20th century it became clear that in most instances of the transfer of electric charge, it is electrons (negative charge carriers) that move, but by then the labeling conventions were firmly established.


Any idiot can face a crisis - it's day to day living that wears you out.
by ceebs (ceebs (at) eurotrib (dot) com) on Fri Mar 14th, 2008 at 11:46:54 AM EST
[ Parent ]
I think qualitative and quantitative happen later. The key point is really that it's about how you feel, and creative types tend to use their feelings as a guide for making sense of reality.

In my experience creative types approach a problem by asking themselves how they feel and making connections between things, and it's the process of finding things that look like other things and assuming they're connected that keeps them interested.

Scientific types systematise. They like numbers and abstractions, and algorithms to glue them all together.

It's very hard to do both at the same time, and individually both are partial and incomplete.

If you just do the algorithms you can lose the plot and spend time building a system that either doesn't work or doesn't answer the question that really matters to people. If you just do the intuitive feeling stuff you can mistake feeling for understanding - because feeling isn't really a useful model or system, it's a fleeting experience.

What makes science and maths hard is that sooner or later you have to stop relying on trying to experience what you're trying to understand. When the maths gets really hard, you can't do that any more. You start from somewhere familiar, blunder around a maze of twisty little equations bumping into things and feeling blind, and - ideally - fall out the other end into somewhere that makes sense again.

I've always had problems at that point. I suffered through maths A Level making very little sense of mechanics because the teacher hadn't bothered to make a simple connection to things I'd learned earlier. Once I got that, it became easier.

The more advanced the science, the harder it is to be physically intuitive about it. Some rare people seem to have a kind of mathematical intution which is a substitute, kinda sorta.

But I don't, and a lot of professional scientists don't seem to either.

And therefore - hard. Sometimes hard maths is abstracted to make it simpler and more intuitive to work with again.

But you can still end up with:

Which is not necessarily intuitive to most people. ;)

by ThatBritGuy (thatbritguy (at) googlemail.com) on Fri Mar 14th, 2008 at 12:16:08 PM EST
[ Parent ]
but then the red balls and the green balls did different things (the red balls clumped together and the green balls flew around them, I think), so there was some essential difference between a red ball and a green ball; you could change the colours but that difference was still there.

That, at least partly, is because the model you're using is so simplified.  It can't hope to explain why the protons stick together, because they shouldn't.  They're all positively charged and so should repel each other and fly apart.

(Don't worry yet about why they stick together.  Just accept that it gets more complicated later on.)

The terms positive and negative were applied consistently to charge before the discovery of the electron.  Unfortunately this turned out to be the wrong way round for easy visualisation.

A rather value-loaded metaphor I think I've just made up is that when you're positive, you attract what you need, and when you're negative, you lose.

But, really, I visualise electrons a bit like little packets of negative charge.  And because I know electricity is a flow of electrons, it's therefore logical that it flows from maximum to minimum, ie the negative to the positive electrode.

If an ion is negative, it's because it's got an extra packet of negative charge...

And...read this slowly...you already know that two minuses make a plus.  Minus "minus one" is one...if an ion is lacking an electron, it will be minus one unit of negative charge.  Therefore it will be positive.

I hope this makes sense...  :)

by Sassafras on Sat Mar 22nd, 2008 at 05:03:12 PM EST
[ Parent ]
It can't hope to explain why the protons stick together, because they shouldn't.  They're all positively charged and so should repel each other and fly apart.

They don't. Two protons can never form a nucleus. That's what you have neutrons for (or rather, that's what neutrons do, if we want to avoid the pitfall of anthropocentrism). If you want a toy model that'll serve you well enough and remain useful pretty far into your studies (if not forever, depending on your line of enquiry), you can think about neutrons as a kind of glue that holds the positively charged protons together.

And by the time that model is no longer adequate, protons, neutrons and electrons should be such familiar mental constructs that they have long transcended the initial toy model.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Mar 24th, 2008 at 11:15:45 AM EST
[ Parent ]
always associate an electron as -
An electron is negative. Think electron think the symbol -  minus. electron. minus. -

Ah!  I hope I get this right:

where I see a - sign, it means "electrons".  If I see a + sign and a - sign, I can imagine a line running from the plus to the minus: the electrons are over at the - end because - means 'electron(s)'.

A + atom has less electrons than when it was neutral--it's proton to electron balance is skewed.  There are more protons than electrons (in a single atom)

A - atom has extra electrons.  There are more electrons than protons.

In a pair, with either ionic or covalent bonding, + and - tell me which atom in the pair has the most electrons  above its natural (pure element) count.

So I need to have the electron counts memorised for each atom--the valence electrons--or the bonding electrons...

But...the + and the - are the answer: the atom with the minus has more electrons than normal when compared to the atom with the plus.  (Or: the atom with the plus has less electrons than normal when compared to the atom with the minus)

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Fri Mar 14th, 2008 at 07:18:41 PM EST
[ Parent ]
In here, you are jumping ahead of yourself and getting muddled.

a few steps you need to go through include learning about electron levels/shells and the number of electrons in each level.  Look at the periodic table and the number of electrons in the outer shell - which is the key thing that determines it's chemical properties.

Let's take lithium and fluorine since you put them in above.

The lithium atom has 3 electrons. 2 fill the core shell (first level has a maximum of 2 electrons).  This means there is one electron in it's outer shell.  To get the full compliment of electrons in the outer shell it would need to pick up 7 electrons which in energy terms would be HUGE and so completely not happening.  So the easiest thing for it to do is lose that spare electron to another atom that wants to fill it's own shell.

Lithium can completely give it's electron away to say fluorine which needs one electron to fill it's outer shell with. Because Li completely transfers it's electron over to F - they become ions. Li+ and F-
The anion (F-) is attracted to the cation (Li+) and so they hang about together through ionic bonding.  But F- now 'owns' that electron.

Now atomic mass is not always directly equated to the number of electrons because you can have isotopes which have extra neutrons, the particles with no charge.  But protons and electrons will be the same number of each in an atom.

Elsewhere in the periodic table we have atoms that need a number of electrons but instead of completely giving or taking electrons, they share them. Covalent bonding.

Some atoms have a greater affinity for electrons.  oxygen is one of those. but tricky because it has lone pairs and can form multiple bonds which i will only confuse you with at this point.

So let's take your methane molecule in the main post.
Carbon has it's snug pair of electrons in the core shell. They are happy. But, carbon needs 4 electrons for it's outer shell to gain the full compliment and thus be energetically stable.  It is not energetically favourable to give away or receive 4 electrons in the sense that Li can give away one and F can gain one.

So Carbon shares.  Each H atom only has one electron and needs 2 to fill it's shell and be energetically stable.  

So an H shares it's one electron and C shares one of it's electrons to pair up. So they cheat a little bit in filling their shells.  

4 H atoms share with one C atom so that C 'borrows' 4 to fill it's outer shell and each H 'borrows' one to fill it's outer shell.  In reality, these electrons whizz around all over the place, so the H electron can be found anywhere over the molecule, not just around the H atom, the all mix in together to form an electron cloud that holds the molecule together. But that is another model.

Will it help if I tell you the kind of music I like so that you can dig out other stuff for me to try listening to?

by In Wales (inwales aaat eurotrib.com) on Fri Mar 14th, 2008 at 10:18:25 AM EST
[ Parent ]
I'm about at the stage where I know that the 4s orbital fills prior to the 3d orbitals, and I am about at the point where I can make sense of larger molecule diagrams (not quite there, but closer than I was.)  (And all those transition elements filling in the d orbitals...that's my next area of focus)

(I have a feeling I'll be asking for one of those 3D molecule kits for my next birthday (or maybe buy myself one prior) as three dimensionality is one of the keys (for me, in understanding--that these molecules have height, depth, and breadth--that the extend outwards in various directions based on the electrical charges--120 degrees, tetrahedrons--hey, I had to sit down and ponder the beastie with four sides, all of which were triangles)...

So I've moved ahead, but I realised that this issue of plus and minus was getting in the way.  From your other post I'm thinking that I can relate it to a number line

(You know all this of course, but I like the way you can catch my mistakes so...)

,

I can imagine (this could be my model) that positive and negative are at opposite ends such that electrons are at the negative (-) end, and the protons are at the positive (+) end, and they're...tugging towards each other (trying to reach their beloved zero point of no charge and so no more crazy attractions) such that 'negative' means: 'towards the electron end' and 'positive' means 'towards the proton end' and so a gain in electrons means a movement towards the electron (-) end, while a loss of electrons means a movement towards the proton (+) end, and thusly positive and negative and gain and loss come together again--at least in my head!

Does that sound about right?

Will it help if I tell you the kind of music I like

Just a few disjointed adjectives are fine--ya know...just some flavours, no need to use too many words (ah, the joys of music!  Oh, no naming names!  You might love a band and I hold some bizarre prejudice against them because my best friend's sister once went out with the bass player and it all finished badly...etc.)  My experience is that most musical fields will have something comparable so I can go and hunt up some examples and see how they match.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Fri Mar 14th, 2008 at 10:45:13 AM EST
[ Parent ]
so a gain in electrons means a movement towards the electron (-) end, while a loss of electrons means a movement towards the proton (+) end

Yeah that works.

And you may still be jumping ahead with the s,p,d,f orbital stuff unless you have grasped ionic and covalent bonding through use of the Bohr model (circles of shells around the atoms).  But the cool thing about the s,p... orbitals is that they have shapes and this then leads to understanding the shapes of molecules and it is where lone pairs come in too.

Oooh.

You can use plasticine and chopped up straws until you get a modelling kit.

I don't think I know how to describe music in adjectives yet.  Sometimes ambient stuff for chilling out to when the mood suits, I like the way the music can focus me or just be a background.

And other times I like the energy that music gives me.  Sometimes I like stuff to get my teeth into. Not massively into classical by itself. Too much very high pitch hurts. bass that makes my heart beat to follow is good. or when music seems to have some humour to it. Now I am going.

by In Wales (inwales aaat eurotrib.com) on Fri Mar 14th, 2008 at 11:06:53 AM EST
[ Parent ]
I'll post something next week for ya!

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Fri Mar 14th, 2008 at 11:13:31 AM EST
[ Parent ]
That's almost it.

The easiest way to understand this is to get some magnets. It's actually the same force (more or less, ignoring complications about something called spin), but you can pick up a magnet and play with it, which is hard to with an electron.

More electrons -> bigger magnet-type effect.

North/South are another historical accident. +/- and N/S are more or less interchangeable in this context. So if it helps you can think of electrons as being the North half of a magnet and protons as being the South half. (Or vice versa - as long as they're complementary.)

That's not the 'proper' explanation, but it's not a bad guide to how they act.

The only other complication is that when you build your 3D models, keep in mind that everything is moving. The connections are more like springs than rigid links, and you can make them twang in different ways, or spin the model as a whole, or make and break links between molecules, and all of these will be happening all of the time, in differing amounts.

In a solid the links will be stiff, although they'll still be vibrating slightly. In a liquid they'll be forming and breaking continuously, which is what makes liquids flow. In a gas - pffft - not much linking happening at all.

This also applies to the connections between the protons and neutrons in the nucleus. You can make the nucleus ring like a bell by kicking it with a vibrating magnetic field. It will 'sing' at some frequencies, and this creates a signature 'sound' you can use to identify it.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Fri Mar 14th, 2008 at 11:25:03 AM EST
[ Parent ]
I'll repeat to you what I wrote to In Wales:

I am going to re-read yours (and anyone else's!) comments late at night (maybe many times!), after having cleared my mind of clutter (in my own way) and with maximum concentration--and slowly! So more please!  And I promise to pay you back with...

A lovely cup of tea, minimum!

Really really very much appreciated, thanks!

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Fri Mar 14th, 2008 at 11:29:17 AM EST
[ Parent ]
But one thing to remember when playing with magnets is that with protons and electrons, it's possible to have only a + or only a -. That doesn't happen with magnets: They always have both a North and a South pole. That means that while everything you can do with (static) magnets can in principle be duplicated with (static) electrons and protons, electrons and protons can do a lot of interesting things that magnets can't.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Mar 24th, 2008 at 11:33:19 AM EST
[ Parent ]
Ah, I must go now. Won't be back til sunday. If you have more questions, draw my attention to them and I'll answer when I'm back. Happy learning!
by In Wales (inwales aaat eurotrib.com) on Fri Mar 14th, 2008 at 10:44:27 AM EST
[ Parent ]
I just love the "happy" pair of  electrons... :-) You should write a book with drawings for children, "The charm of the spinning quark" !!!!

I used to think that electrons were like salmons, getting back up the river to fray :-)

"What can I do, What can I write, Against the fall of Night". A.E. Housman

by margouillat (hemidactylus(dot)frenatus(at)wanadoo(dot)fr) on Fri Mar 14th, 2008 at 01:54:28 PM EST
[ Parent ]
Redox

Don't leave oxidation to one side, because it's the easier one to get your head around.

The root of the word oxidation is that you've got to imagine your atom reacting with...oxygen.

You know that oxygen is an electron-snatcher (the playground bully), so, like a meek child with their dinner money, your atom is going to lose electrons.

(The reaction doesn't have to be with oxygen, of course.  It's the transfer of electrons that counts.)

Reduction is the opposite of oxidation...  ;)

However, if you're going to be picky...

With reduction, your imaginary reaction is with hydrogen.  This is insistently, whiningly desperate to give up its electron.  (Be..ee my friend.  I'll give you a sweet!).  So, your atom gains an electron.

(The historical root of the term reduction is the fact that many metals were discovered by having their salts/ores treated with hydrogen.  The hydrogen (the whiny kid that doesn't do alone) would react with the non-metallic bit of the salt (Oh, don't play with hi...im, play with me.  I'll give you a sweet!), thereby subtracting the rubbish and reducing the salt to pure metal.)

Of course, just to give it a nasty twist, oxygen is generally reduced and hydrogen oxidised.  I hope I've explained it well enough that you can see why....

by Sassafras on Sat Mar 22nd, 2008 at 08:02:27 PM EST
[ Parent ]
Very nice, thanks ;)

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Sat Mar 22nd, 2008 at 08:17:02 PM EST
[ Parent ]
The mental picture I usually use is that oxidation makes stuff positive, because it's named after oxygen which likes to steal electrons, as described above.

The number of positive charges associated with the oxidised atom in the covalent bond is then the oxidation level - i.e. the degree to which it's been oxidised.

And reduction is then simply a reduction of the oxidation level. Then both words suddenly make sense (to me, at least).

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Mar 24th, 2008 at 11:38:16 AM EST
[ Parent ]
Brilliant.

And clearly part of the ongoing ET Guide to the Galaxy....now, where's my towel...

"The future is already here -- it's just not very evenly distributed" William Gibson

by ChrisCook (cojockathotmaildotcom) on Fri Mar 14th, 2008 at 09:55:03 AM EST
When it comes to airborn ions, the negatives are the good guys, and the postives are bad - the free radicals (Is that us? Are the Free Radicals bad?)

That wonderful feeling by the shore of breaking waves is negative ions. Electronic equipment gives off positive ions - they make you sleepy and innattentive. That is why the cactus Cerus Peruvaneus has been placed in some bourses - ti absorbs positive ions.

Perhaps our present financial troubles are due to an excess of positive ions, and a meagre deployment of cactii. The only thing i know is that solutions are never obvious.

You can't be me, I'm taken

by Sven Triloqvist on Fri Mar 14th, 2008 at 05:05:21 PM EST
The goodies letting off electrons and the baddies, like cactus balls, rolling around, picking up all the electrons on their spikes--grabbing them off other innocent--just passing!--atoms if they can.

The free radicals need food!  Come into my orbit, sweet electron...

(I think TBG had it spot on, except that in my case I think where he  says "feeling" my natural term would be "narrative"--another one of his.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Fri Mar 14th, 2008 at 07:53:22 PM EST
[ Parent ]
Actually, free radicals need not be positive, or even charged at all. Atomic oxygen and atomic hydrogen are both potent free radicals - which is why you don't generally find atomic O and H. Rather, you'll find O_2 and H_2.

And free radicals aren't uniformly Bad Guys In Pointy Hats either, but I think that I'll refrain from drawing parallels between politics and the rather arbitrary naming conventions of the natural sciences...

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Mar 24th, 2008 at 11:45:44 AM EST
[ Parent ]
You might want to find a copy of Linus Pauling's introductory chemistry book, which covers this stuff in a readable but comprehensive fashion.
http://www.amazon.com/General-Chemistry-Linus-Pauling/dp/0486656225
by asdf on Sat Mar 15th, 2008 at 12:53:22 AM EST

I find it interesting that you chose to learn chemistry in a logical, bottom-up way rather that in the (standard) pedagogical way which tends to parallel the historical development of the subject. For instance: you start with the Rutherford model of the atom and the first kind of chemical reaction you talk about is redox, no less!
The Rutherford model or planetary model was a model of the atom devised by Ernest Rutherford. Rutherford directed the famous Geiger-Marsden experiment in (1909), which suggested to Rutherford's analysis (1911) that the Plum pudding model (of J. J. Thomson) of the atom was incorrect. Rutherford's new model for the atom, based on the experimental results, had a number of essential modern features, including a relatively high central charge concentrated into a very small volume in comparison to the rest of the atom.


It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Sat Mar 22nd, 2008 at 02:03:24 PM EST
I read about the four elements, the alchemists, the discoveries of the elements, the weighing of air, more elements...then I came to chemical reactions and they only make sense when considering electrons.  I don't know why but I find electrons are the connective element--there they are in the deepest physics; there they are in chemistry, and there they are in biology.

I got that sodium gives an electron to chlorine, I got that carbon shares electrons with four hydrogen, I could get that there was giving and receiving (receiving = minus; giving = plus.)

Actually, I think the answer is that I decided to read a GCSE revision text, see how far I got, and when I hit redox I couldn't move the ideas around in my head.  I tried an A level book--and hit the same point.

I think TBG captured it just right, except that I'd say "narrative" rather than "feeling"--I need stories to follow so I can connect A to B to C.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Sat Mar 22nd, 2008 at 05:17:57 PM EST
[ Parent ]
I don't know why but I find electrons are the connective element--there they are in the deepest physics; there they are in chemistry, and there they are in biology.

What I mean is, I have a sense that it's worth spending my time getting to understand electrons and charge because if I can really get them clear (ignoring the complicated business about wave/particle...at least for now!) then...I can use them as the base upon which to build...heh....if only things were that simple!

btw, have you (or has anyone?) read Oxygen: The Molecule that Made the World?

A great book, which looks closely at free radicals--oxygen stripping electrons from molecules, charging them and then creating chains of ripping--that's what I mean when I say electrons are in biology--ach!

How do you envisage electrons?

Heh....for my own strange reasons I need to know enough Chemistry to be comfortable with all elements to GCSE level.  The more I delve into valence electrons--the more I get my head round them the easier the rest becomes.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Sat Mar 22nd, 2008 at 05:30:33 PM EST
[ Parent ]
You covered it earlier - chemistry is electron sharing. There's not a lot else going on.

'Proper' chemistry needs the wave/particle stuff because it explains why electrons in atoms do what they do - e.g. why is there are a pattern in the maximum number of electrons in the outer shell of each element?

But you can do all of GCSE chemistry without worrying about that, and just counting the number of available electrons and how they're being shared.

I have a rather metaphysical approach to the wave particle stuff which not everyone shares, and which could be completely wrong - no one really knows what's really happening under the wave particle, so there are all kinds of interpretations.

The traditional old-physics approach is to think of electrons like very, very small billiard balls which happen to have an electric charge.

The more metaphysical approach is to think of electrons as areas in space in which something might happen, and which - randomly - does.

This is for a hydrogen atom. The red and blue areas show where electron-like things are most likely to happen as the electrons hold more energy.

This is useful because if you think in terms of fields - they're called orbitals in chemistry - you don't just get the basic electron counting chemistry of

2H20 -> 2H2 + O2

but also tells you what shapes atoms are going to make as they join up. With the wave/particle stuff you can calculate the geometry, size and shape of molecules. E.g. for water:

As I said, this is not needed for GCSE. But for physics it seems to be more useful to ask what things do and how they behave than what they are.

No one knows what an electron is. It may turn out to be a kind of vibrating membrane, like a small and very weirdly shaped bell in space which rings when certain things happen to it.

Or it could be something else entirely.

Because we don't know, all we can do is look at how electrons behave. And because what electrons do seems to spread out in a way that small billiard balls don't, understanding how the spreading works is useful.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Sat Mar 22nd, 2008 at 06:44:22 PM EST
[ Parent ]
ThatBritGuy:
But for physics it seems to be more useful to ask what things do and how they behave than what they are.
Maybe this is a hint that ontology is just a load of humanure.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 08:12:47 AM EST
[ Parent ]
Not if it gets you asking interesting questions.

There's a difference between unknown and unknowable. It's unscientific to assume that ontology is unknowable unless that can be proved rigorously.

Until that happens, we're left with unknown - and some interesting open questions.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Sun Mar 23rd, 2008 at 11:18:49 AM EST
[ Parent ]
Oh boy.. physics do not address the question of what things are... just how apparently behave...Nailed.

I like your phrasing..."physics seems to be more useful..." one of my physics teacher said to me.. "ei.. no doubt about it, the question of "what things are" is very interesting , that's why it should be discussed in the bar as any other interesting stuff and not in the lab".

We belong to the same subsect of the same sect. Electrons are nothing.. they behave as something (and we created the name and the concept becasue it is useful and relevant to explain the world)...either this or one believes that matehmatical entities exist in reality (which some friends of mine do).

A pleasure

I therefore claim to show, not how men think in myths, but how myths operate in men's minds without their being aware of the fact. Levi-Strauss, Claude

by kcurie on Sun Mar 23rd, 2008 at 08:37:37 AM EST
[ Parent ]
European Tribune - Positive & Negative
My question to ETers is:

Can anyone offer me a mental model such that when I see

+

I don't immediately think, "Ah!  That's the positive sign--two plus two equals five, etc.--so something positive is going on, which means some addition is happening". . .

(An atom becomes positively charged when it loses an electron)

And if I see the following sign:

-

I don't think "Ah!  Take something away!"

(An atom becomes negatively charged when it gains an electron)

Like your friend said, your problem is that you need to eliminate any moral associations from the operation of addition. Maybe the history of the concept of Electric charge might help?
One of the foremost experts on electricity in the 18th century was Benjamin Franklin, who argued in favour of a one-fluid theory of electricity. Franklin imagined electricity as being a type of invisible fluid present in all matter; for example he believed that it was the glass in a Leyden jar that held the accumulated charge. He posited that rubbing insulating surfaces together caused this fluid to change location, and that a flow of this fluid constitutes an electric current. He also posited that when matter contained too little of the fluid it was "negatively" charged, and when it had an excess it was "positively" charged. Arbitrarily (or for a reason that was not recorded) he identified the term "positive" with vitreous electricity and "negative" with resinous electricity. William Watson arrived at the same explanation at about the same time.

We now know that the Franklin/Watson model was fundamentally correct. There is only one kind of electrical charge, and only one variable is required to keep track of the amount of charge.[2] On the other hand, just knowing the charge is not a complete description of the situation. Matter is composed of several kinds of electrically charged particles, and these particles have many properties, not just charge.

The problem was that Franklin made the wrong choice of sign: ordinary moving charges are negative charges, so when there is electrical current going in one direction the actual charge carriers are moving in the opposite direction... In fact, the only way to determine the sign of the fundamental moving charge is the Hall effect
The Hall effect refers to the potential difference (Hall voltage) on the opposite sides of an electrical conductor through which an electric current is flowing, created by a magnetic field applied perpendicular to the current. Edwin Hall discovered this effect in 1879.[1]
Of course, life is never that simple and there are some substances in which the elementary charge carriers are positive (the conductor then displays an anomalous Hall effect). In fact, electric current is not carried by particles at all, but by quasiparticles.
In physics, a quasiparticle refers to a particle-like entity arising in certain systems of interacting particles. It can be thought of as a single particle moving through the system, surrounded by a cloud of other particles that are being pushed out of the way or dragged along by its motion, so that the entire entity moves along somewhat like a free particle. The quasiparticle concept is one of the most important in condensed matter physics, because it is one of the few known ways of simplifying the quantum mechanical many-body problem, and is applicable to an extremely wide range of many-body systems.
The again, I think your psychological hangup is with the aritmetical operation of addition, and with negative numbers. So leave 20th century chemistry aside for a while and let's consider why you have a problem with renaissance-time negative numbers. Given that you want to do things in a logical as opposed to historical way, maybe we need to do Galois theory for dummies to eliminate the psychological hangup about negativity.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Sat Mar 22nd, 2008 at 02:19:13 PM EST
I gave Galois theory a quick google and....it looks way out of my league, but if you can create a dummies version--I'm all for it!

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Sat Mar 22nd, 2008 at 05:22:00 PM EST
[ Parent ]
At the moment your comment is the only text containing the string "quantum" -- and in a quotation, at that. Enough with the negatives, let's move on to the imaginaries!

Words and ideas I offer here may be used freely and without attribution.
by technopolitical on Sun Mar 23rd, 2008 at 01:33:14 AM EST
[ Parent ]
Actually, you can do a lot of quantum mechanics in an arbitrary Rig (Ring without negatives). And a lot of graph theory and statistical mechanics and is also quantum mechanics in a Rig.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 08:14:53 AM EST
[ Parent ]
Ack. Semirings. Yet another bunch of algebras I didn't know about (as such). Now you've made me curious:
  • "A lot of quantum mechanics" omits what?
  • An "arbitrary rig", not non-negative reals? (Is this all about counting states, not describing them or their transitions?)
  • Do you intend that "a lot of graph theory and statistical mechanics and is also quantum mechanics in a Rig" be read as saying that "a lot of graph theory...is also quantum mechanics"?
  • Are complex numbers uniquely necessary for quantum mechanics, or just a convenience?
  • Why do I keep reading about so many mathematical structures that I can't remotely claim to understand?
  • How can anyone (other than a Republican) still support the Clinton candidacy?
I see that Baez has (of course) touched on some of the earlier questions in this list.

Words and ideas I offer here may be used freely and without attribution.
by technopolitical on Sun Mar 23rd, 2008 at 03:12:24 PM EST
[ Parent ]
Well, where do you think I got this stuff from? You think I invented it?
  • "A lot of quantum mechanics" omits squaring the result to get a probability.
  • There are more Rigs that just the nonnegative reals, basically subsets (closed under addition and multiplication) of matrices with nonnegative real entries.
  • No, I intend to say that the mathematical structure of flow in networks, of minimal paths in networks, of statistical mechanics at finite and zero temperature, and quantum mechanics, is that of combinatorics on Rigs.
  • I have no idea whether complex numbers are necessary for quantum mechanics, but given their algebraic completeness once you have characteristic zero you might as well assume your Rig consists of matrices with complex entries. I guess, for convenience.
  • Where do you keep reading about mathematical structures you can't remotely claim to understand?
  • There will always be people who identify with her over the other candidates.
BTW, did you get my e-mail?


It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 03:25:34 PM EST
[ Parent ]
After reading a bit on the web, I assumed that you had invented this stuff at a time when you were incredibly young, but gotten no credit. The sufferings of genius.

  • "'A lot of quantum mechanics' omits squaring the result to get a probability." Fair enough, but with a chemical mindset in this diary, one would miss having wavefunctions and amplitudes. On the other hand, given the vast amount of quantum mechanics, I suppose that omitting lot leaves a lot that is not omitted. Just not the sort of QM that I crunch on this machine.

  • "There are more Rigs than just the nonnegative reals..." Indeed, and some of them are, well, cheesy. (To speak non-technically for a moment.) At the bottom of the barrel, "The simplest example of a semiring which is not a ring is the commutative semiring B formed by the two-element Boolean algebra," and nearby are other lame Rigs mentioned in Wikipedia

  • "Where do you keep reading..."? TWF, of course, for starters!

  • "No, I intend to say..." What you say is, I expect, entirely correct and, in principle, enlightening.

Re. your e-mail: Did you get my response? After the conversation I promised, she suggested considering citizen sector options, and minimizing the gap, on strategic/marketing grounds.

Words and ideas I offer here may be used freely and without attribution.
by technopolitical on Tue Mar 25th, 2008 at 02:46:22 AM EST
[ Parent ]
  • You still get "diffusion of states" and "probability densities", just not wave propagation (you need i for that, I think).
  • What can I say, mathematicians tend to use lame examples when asked to make arcane structures concrete. I think matrices or nonnegative reals are a better meta-example, with the advantage of being universal.
  • TWF? I can't be held responsible for that.
  • "You expect" and "in principle"? Ask some questions!
I replied to your e-mail.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Tue Mar 25th, 2008 at 09:32:58 AM EST
[ Parent ]
Technically, you could do away with i entirely in QM and not lose generality. But then you'd be stuck with 4th order differential equations. At least that's what one of our Optics profs claimed. I never checked myself, because you do not want to do 4th order PDEs anyway, unless you're a mathmatician or some (other) kind of masochist.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Tue Mar 25th, 2008 at 02:41:11 PM EST
[ Parent ]
Well, a complex differential equation can always be written as a real differential equation of twice the order.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Wed Mar 26th, 2008 at 03:07:01 AM EST
[ Parent ]
maybe we need to do Galois theory for dummies to eliminate the psychological hangup about negativity.

I was thinking more along the lines of a short course of Jungian analysis  ;)

by Sassafras on Sun Mar 23rd, 2008 at 04:02:11 PM EST
[ Parent ]
As most people said already here, physics advances comes with the creations of narratives and concepts that explain a particular behavior (which allows for more narratives and more beahvior to be uncovered with mroe experiments that cen be better understood with theprevious narratives and symbols).

So why oh why did physicist chose the terms positive and negative instead of good and evil directly or black and white for the two complementary elements you need in the lectromagnetic force?

I have not the foggiest idea. My suggestion is that you make a feeling map. Some thing like.. now posstive and negative are not clear cut things. Sometimes positive stuff gives bad results, sometimes negative stuff produces good results in the log term. So basically you can construct a history for each of the different possible chemichal reactions.

A pleasure


I therefore claim to show, not how men think in myths, but how myths operate in men's minds without their being aware of the fact. Levi-Strauss, Claude

by kcurie on Sun Mar 23rd, 2008 at 08:42:57 AM EST
That's clear: the model is (signed) numbers because charge is something that can be added and subtracted, and of which there can be an excess or a deficit.

One problem is that the same words positive/negative, used in a different domain have moral implications, and rg cannot seem to separate the different domains.

The other problem is that charge is signed but not ordered, unlike signed numbers which in addition to sign have a linear order (greater than/lesser than).

So, actually, modelling charge as signed numbers is a bad thing to do.

Technically, one can say that the irreducible representations of U(1) are isomorphic to the signed integers Z, but that is incorrect. The are isomorphic to the additive group of the integers, forgetting multiplication. If you don't have multiplication you have no way to distinguish +1 and -1.

So one possible solution is to write 1 for +1 and 1 for -1, so that

1 + 1 = 2
1 + 1 = 2
1 + 1 = 0

and there is no operation of subtraction and no negative (or positive) numbers.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris

by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 08:54:32 AM EST
[ Parent ]
So, actually, modelling charge as signed numbers is a bad thing to do.

How do you view charge--what is the model you use?  I think I'm missing some simple and fundamental point about the attraction / repulsion of equal/opposite charges.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Sun Mar 23rd, 2008 at 10:24:23 AM EST
[ Parent ]
The key is to separate the various meanings of symbols. '-' has a number of different meanings. In algebra, it can be a unary or a binary operator.

As a unary operator, '-' represents the operation of "opposite": -x is the opposite of x.

As a binary operator, '-' represents the operation of "subtraction": x - y is the operation of subtracting y from x.

There is no value attached to "opposite".

You seem to have a value attached to addition and subtraction: addition:good, subtraction:bad. I can't help you there, you have to learn to separate domains by, every time you catch yourself making the association, consciously telling yourself that's not right. Eventually you just won't make the association.

One way to think about positive and negative charge is that they are related to clockwise and counter-clockwise rotation. But notice that if you look at a rotating disk from the other side, clockwise and counter-clockwise trade places. So there is not a preferred sense of rotation: there are just two opposite senses of rotation. You can choose to associate the words "positive", "clockwise" and "right-handed" to one of them and "negative", "counterclockwise" and "left-handed" to the other.

Now, if you accept as a given that net charge has energy, then you will see that putting together two similar charges will have more energy than putting together two dissimilar charges. That is: n + m or n + m have more energy than n + m. Mechanical forces tend to go towards lower energy states, so it follows that similar charges don't like to be together (more energy) and dissimilar charges do like to be together (less energy).

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris

by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 10:48:21 AM EST
[ Parent ]
putting together two similar charges will have more energy than putting together two dissimilar charges.

Okay...but...(I have a horrible feeling I'm about to fall into the deep end)...

net charge has energy

single charge = energy.  Two charges interact and the result (the net) = energy (maybe reduced or amplified--more or less energy)

Opposite charges cancel out (less energy); same charges amplify...

...so it's not that two similar charges (two negative charges, say) repulse each other--it's that they generate more energy, energy which seeks to dissipate into the anti-itself sink of either nothingness (escape into emptiness of space > move away > e.g. heat radiation?  Ach...surely not) or--even better--to fly towards that which will suck energy out of it--

So 'negative' energy (or A energy) finds energy is sucked out of it by 'positive' energy (B energy) and vice versa, such that A + A is more energy, more instability, more energy needs to escape, while A + B means less energy, somehow the energy cancels out, A can absorb B energy and B can absorb A energy--

?

(I'm still missing something.)

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Sun Mar 23rd, 2008 at 11:01:18 AM EST
[ Parent ]
Okay, assume that the energy of a charge inside a small volume goes as the square of the charge.

Then, 2 = 1 + 1 has an energy of 4, and 2 = 1 + 1 has an energy of 4 as well. But 0 = 1 + 1 has an energy of 0.

The energy of 1 or 1 is 1. If two unit charges are very widely spatially separated, than their joint energy is 1 + 1 = 2, regardless of the signs.

But if the two charges are together, the energy can be 4 if they are similarly charged or 0 is they are oppositely charged.

So, similar charges will increase their energy if brought together, and opposite charges will decrease their energy if brought together. Mechanics then dictates that opposite charges attract and similar charges repel.

Note how I avoided the use of the '-' sign by recourse to underlining.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris

by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 11:09:21 AM EST
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