Electronics > Beginners

Exponents

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ebastler:

--- Quote from: tggzzz on April 11, 2019, 12:16:18 pm ---If they don't do that then there's nothing to prevent "I'm going to get a cup of coffee" meaning "You're going to drive the car" :)

--- End quote ---

But "I'm going to have a few beers now" does indeed mean "You're going to drive the car" :)

Buriedcode:
I'm still unsure why this thread has so many replies (I'm aware I'm adding to this!).  Precedence is indeed important and despite what nominal animal suggested, I'm pretty sure almost all "mathematicians" could state the order, perhaps with the acronyms BODMAS or PEDMAS.  Especially as it is so fundamental to even basic algebra. 

Whilst the average Joe who was taught this in basic mathematics has probably forgotten because most simply do not need to use this, I am willing to bet Engineers will be more likely to know this.

If the OP struggles with where to use parenthesis (I'm not suggesting he does, I don't know) then playing around with Excel can be handy, as that is quite strict in its use of them.  Even when they are correctly closed moving them about will give different answers, and breaking up an equation - so you can see the output of each part in its own cell - is a good way of seeing whats happening.  Algebra is just one of those things that tends to "click", and once basic rules are known/realized, can be a powerful tool.

Nominal Animal:

--- Quote from: tggzzz on April 11, 2019, 12:16:18 pm ---The point is that there has to be some commonly understood and shared meaning, otherwise communication cannot happen. If a person chooses new meanings that are different to the standard meanings, then it is up to that person to state what they mean.

--- End quote ---
No, I mean that us "users" must verify we agree what the rules/meanings/precedences are, and not just assume they are some standard ones, because they do vary.

Just because the PEMDAS infix notation is the only one you have been taught, does not mean it is the only one used.  It is the only one you've ever used, perhaps... but the rest of us have used RPN and others, especially when using practical tools to solve practical problems.  (Conversion between infix and postfix notation, using the shunting yard algoritm, is a very common exercise in computer science.)

For example, if you show
$$ y = c_i x^i $$
to a mathematician, they probably think it is an odd way to specify a monomial whose degree depends on some constant named \$ i \$; but physicists know this is just shorthand, Einstein notation (as having the constant factor name depend on the degree of the monomial makes no sense!), equivalent to
$$ y = \sum_i c_i x^i $$

In quantum mechanics you have Dirac or bra-ket notation, \$ \left\lt\varphi\right\rvert \$ and \$ \left\lvert\theta\right\gt \$, that follow the rules of linear algebra, and actually represent matrices; but because of their properties, they are rarely if ever expanded to their actual matrix representations.  For example, the superposition of wave functions \$\varphi\$ and \$\theta\$ is \$ \left\lt\varphi\right\rvert\left.\theta\right\gt = \int \left\lt\varphi\right\rvert\left. x \right\gt \left\lt x \right \rvert \left . \theta \right \gt dx = \int \overline{\varphi(x)} \theta(x) dx\$, where \$ \overline{\varphi(x)} \$ is the complex conjugate of the wave function \$\varphi(x)\$, \$\left\lvert \varphi \right\gt\$ is the state (column) vector for the wave function \$\varphi\$, and \$\left\lt \theta \right\rvert\$ is the Hermitian conjugate of the state vector for the wave function \$\theta\$.
Here, you don't just need to know the notation, you need to know the domain-specific rules that apply to this notation, to save yourself a fuckton of extra work.

(Stuff like Gaussian error functions, elliptic integrals, and so on, being already implemented in many programming languages and math libraries is what typical programmers might not know, and instead open-code inferior/approximate versions of.  And that some languages/applications use a different order of arithmetic and unary/binary/boolean operators than you might expect.)

Notation rules are not universal, they do vary.  The more complex the application domain is, the more likely it is they use their own notation and rules to simplify it.


--- Quote from: tggzzz on April 11, 2019, 12:16:18 pm ---Hence, in the original question, it is reasonable to ask where the parentheses are, and reasonable to answer "no parentheses, normal laws of arithmetic", or "no parentheses, in Excel spreadsheets".
--- End quote ---
Fully agreed; and the core of what I am trying to say too.

tggzzz:

--- Quote from: Buriedcode on April 11, 2019, 01:52:11 pm ---I'm still unsure why this thread has so many replies (I'm aware I'm adding to this!).  Precedence is indeed important and despite what nominal animal suggested, I'm pretty sure almost all "mathematicians" could state the order, perhaps with the acronyms BODMAS or PEDMAS.  Especially as it is so fundamental to even basic algebra. 

Whilst the average Joe who was taught this in basic mathematics has probably forgotten because most simply do not need to use this, I am willing to bet Engineers will be more likely to know this.

--- End quote ---

Engineers ought to. I wouldn't bet on UK primary school teachers knowing though :(


--- Quote ---If the OP struggles with where to use parenthesis (I'm not suggesting he does, I don't know) then playing around with Excel can be handy, as that is quite strict in its use of them. 

--- End quote ---

It may be strict, but it is wrong (except within its own self-contained world). Shades of "Through the Looking Glass":


--- Quote ---Humpty Dumpty took the book, and looked at it carefully. ‘That seems to be done right —’ he began.

‘You’re holding it upside down!’ Alice interrupted.

‘To be sure I was!’ Humpty Dumpty said gaily, as she turned it round for him. ‘I thought it looked a little queer. As I was saying, that seems to be done right — though I haven’t time to look it over thoroughly just now — and that shows that there are three hundred and sixty-four days when you might get un-birthday presents —’

‘Certainly,’ said Alice.

‘And only one for birthday presents, you know. There’s glory for you!’

‘I don’t know what you mean by “glory,”’ Alice said.

Humpty Dumpty smiled contemptuously. ‘Of course you don’t — till I tell you. I meant “there’s a nice knock-down argument for you!”’

‘But “glory” doesn’t mean “a nice knock-down argument,”’ Alice objected.

‘When I use a word,’ Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’

‘The question is,’ said Alice, ‘whether you can make words mean so many different things.’

‘The question is,’ said Humpty Dumpty, ‘which is to be master — that’s all.’
--- End quote ---

tggzzz:

--- Quote from: Nominal Animal on April 11, 2019, 02:09:23 pm ---
--- Quote from: tggzzz on April 11, 2019, 12:16:18 pm ---The point is that there has to be some commonly understood and shared meaning, otherwise communication cannot happen. If a person chooses new meanings that are different to the standard meanings, then it is up to that person to state what they mean.

--- End quote ---
No, I mean that us "users" must verify we agree what the rules/meanings/precedences are, and not just assume they are some standard ones, because they do vary.

--- End quote ---

See the "Through the Looking Glass" quote in my previous message.


--- Quote ---Notation rules are not universal, they do vary.  The more complex the application domain is, the more likely it is they use their own notation and rules to simplify it.


--- Quote from: tggzzz on April 11, 2019, 12:16:18 pm ---Hence, in the original question, it is reasonable to ask where the parentheses are, and reasonable to answer "no parentheses, normal laws of arithmetic", or "no parentheses, in Excel spreadsheets".
--- End quote ---
Fully agreed; and the core of what I am trying to say too.

--- End quote ---

Ah, but which is it more likely that people should know:

* something that has been invariant for hundreds of years across all civilisations, and they were taught in school
* one specific computer program created a few decades ago, that was then copied by other programsThe latter makes me wince, and I think it is unreasonable.

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