OT Math rant, was Re: [sdiy] DSP book recommendation wanted

Fri Sep 25 13:43:48 CEST 2009

I totally agree. I'm polish, and there's only one Polish dictionary,
and it sucks really bad. And we don't even get free polish-english
dictionaries online - if I want to translate a technical term I go to
dict.leo.org which is german-english.

On Fri, Sep 25, 2009 at 12:33 PM, Tom Wiltshire <tom at electricdruid.net> wrote:
> I certainly agree with Cheater that Mathworld is not a place to learn new
> stuff. I've tried, and it's like trying to learn from a dictionary. A Polish
> dictionary.
>
> Lots of math sites make everything *far* more complicated than it needs to
> be and spend a lot of time baffling you with long words, techniques you
> don't know named after dead mathematicians you've never heard of, and write
> the whole thing with obscure symbols that only mathematician's browsers will
> display.
>
> I actually love math, but in recent years I've become extremely frustrated
> by the apparent inability or unwillingness of the academic math world to
> explain things or let anyone else into their little game. I'm beginning to
> suspect that they don't want us to know and would rather we all thought it
> was complicated and impenetrable. I can't forgive that kind of attitude in
> any field (and I see it a lot in computing, which is my own field).
>
> One example; I've been baffled for a long time by the e^jø stuff that I keep
> seeing in filter theory and whathaveyou. Yesterday I found an explanation on
> the dspguide.com. It turns out that it's a alternative way of writing a
> complex number as a vector (e.g. an angle and a magnitude, rather than a x,y
> coord).
> WELL, WHY THE HELL DIDN'T YOU JUST *SAY* SO??!!!
> The actual explanation and math behind the conversion from one form to the
> other is very simple and can easily be described in half a page. However,
> having read no end of stuff on the topic, I'd *never* come across such an
> explanation until yesterday. I doubt you'll find it quickly and easily on
> mathworld.
>
> Ok, rant over.
>
> T.
>
>
> On 25 Sep 2009, at 09:39, cheater cheater wrote:
>
>> Sorry if you felt hurt, Dave!
>>
>> The first point is that reference books are made with being a closed
>> source of information, i.e. any topic mentioned in a book like that
>> can be fully explained by that book, to some specific level.
>>
>> The second point is that references are mostly ordered in a logical
>> order, which makes them great for learning. If you open a reference
>> book at the topic 'sequence', then the next topic will be either
>> 'series' or 'arithmetic progression' or something else that is what
>> you should learn next in order to maximize your learning input.
>>
>> Now if you go here:
>> http://mathworld.wolfram.com/Sequence.html
>> you don't get that benefit. Sure, the 'Series' topic is referred to,
>> but find it in that list:
>>
>> 196-Algorithm, A-Sequence, Alcuin's Sequence, Appell Cross Sequence,
>> Appell Sequence, B2-Sequence, Basic Polynomial Sequence, Beatty
>> Sequence, Binomial-Type Sequence, Carmichael Sequence, Cauchy
>> Sequence, Convergent Sequence, Cross Sequence, Decreasing Sequence,
>> Degree Sequence, Fractal Sequence, Giuga Sequence, Increasing
>> Sequence, Infinitive Sequence, Integer Sequence, Iteration Sequence,
>> List, Nonaveraging Sequence, Polynomial Sequence, Primitive Sequence,
>> Reverse-Then-Add Sequence, Score Sequence, Sequence Density, Series,
>> Sheffer Sequence, Signature Sequence, Sort-Then-Add Sequence,
>> Steffensen Sequence, Ulam Sequence
>>
>> How is someone supposed to learn from that?
>>
>> For this reason authors write themed reference books, for example a
>> reference for students, or a reference for abstract algebra, or
>> topology. Mathworld has everything kludged together in order to be
>> 3-in-1 like head&shoulders.
>>
>> Furthermore, I find that mathworld often has long definition chains.
>> That is, in order to understand definition A you need to understand B,
>> to understand B you need C and D, and to understand each you need E,
>> F, G, H and I and J. This is very often excessive.
>>
>> Reference books are usually written so that those definition chains are
>> minimal.
>>
>> Yet another point is that often the definitions in Mathworld just have
>> way to much in them. For example, imagine I don't know what an
>> integral is, and I want to learn about it as I would learn from a
>> reference book. I would go here:
>>
>> http://mathworld.wolfram.com/Integral.html
>>
>> Now I would have not only been confused by this, since my teacher told
>> me to read about integrals, not 'Riemann integrals', but I'll have
>> also been indoctrinated by 1988 'New Math' quotes, and will have
>> learned nothing.
>>
>> Now let's read on. In a few short lines, they jump from (5) which is
>> usually the first formula that you see in a course on integrals right
>> into (8) which assumes the reader will have started multivariate
>> calculus. This is almost never the case when learning about integrals.
>>
>> Oh, should I learn the identities too? Let's look at 11-16... that
>> might be on the exam - oh boy - better learn em. Put some more garbage
>> in my head that I won't use in the next 3 years or so.
>>
>> Mathworld is a handy reference, but it doesn't stand up compared to
>> CRC in the way as I did, and that is to make it a learning tool. You
>> *might* find Mathworld very useful when you are trying to remember
>> something you've learnt once, but it's definitely not a thing to learn
>> new ideas with.
>>
>> Another point where physical objects win with websites is that they
>> are tangible and invariable. If you learn something, and then forget
>> it, a hazy idea about how the page layout has looked could lead you to
>> the definition. This is not an uncommon way of re-learning things with
>> books. With mathworld, however, the layout will have almost certainly
>> changed, since it depends on the window size, zoom level, browser, and
>> the definition page may have been added to or removed from.
>>
>> Finally, books get worked on by typesetters while mathworld doesn't.
>> It makes them much easier to read and learn from.
>>
>> D.
>>
>>
>> On Fri, Sep 25, 2009 at 7:02 AM, Dave Manley <dlmanley at sonic.net> wrote:
>>>
>>> cheater cheater wrote:
>>>>
>>>> Mathworld doesn't beat CRC in that CRC is an ordered, closed work and
>>>> mathworld is neither.
>>>
>>> You say that like it is a bad thing.  Mathworld is ordered, is
>>> hyperlinked
>>> to related topics and references and is searchable.  Are the editors of
>>> the
>>> CRC references any better than those of Mathworld?  Doesn't Weisstein has
>>> his own massive tome on mathematics published by CRC Press?  Is
>>>
>>> http://www.amazon.com/CRC-Encyclopedia-Mathematics-Third-Set/dp/1420072218/
>>>  somehow better at 4300 pages, 21 lbs, and $398?  Sometimes, I think you
>>> just like to be contrary.  Or have I missed your point?
>>>
>>> -Dave
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>>
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