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

[cheater cheater]

Seriously, though: the whole rigidness of people who want to pretend
maths are something holy is very annoying. There is no end to snobism
in mathematics, physics, finance, and nowadays even engineering.

Maybe it comes from the fact that most people can't grasp the terms
well enough that they can explain them in their own words, and instead
have to recite lines from books people have written before them.

Maybe it comes from the fact that people don't actually know any sort
of way to *use* what they are teaching, so they can't let you know of
those ways. You're learning topology. OK. So what? What uses are there
of topology? Can someone answer me that question? I'm not doubting
that there are many. I have learned many myself. Most people at
university that I asked couldn't answer the questions though, past the
point of saying 'you'll need that in the course you'll take in a
year'. Are people teaching and learning maths for no purpose other
than to teach and learn maths later on? That doesn't go anywhere.

Some people, lecturers, scientists, just barely know enough to let you
know what they were told 30 years ago. It's sort of like the middle
ages where monks were rewriting books without actually grasping what
they had meant. And if a mistake crept in, no one knew better to
correct it. Are mathematics really so holy that you have to teach it
in a rigid way?

Then again there's the point of having a 'well rounded course' that
makes note of all the additional stuff that you could learn about
things. But some courses are so swamped with this that you only get
half the time to study the important stuff. As they say, everything is
a compromise. Often the compromise is chosen wrong.

Then you get literally flooded by the amount of pointless, shitty
publications. Someone mentioned here or on AH that people post crappy,
pointless synth videos on youtube showing off another microkorg van
halen cover. Spamming. The same happens in the world of maths books.
You need so and so many publications to get a PhD or a tenure. So,
just write something. Anything. Your students will have to buy it,
because otherwise you can fail them - and put it on amazon while
you're at it, why don't you? It's not like there's a maths book
police.

And then you get this:

> 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??!!!

Good books always lay out in the introduction what sort of level of
scientific and mathematical tools they require, and many good books
even add a supplement, or an introductory chapter, that you can skip
if you know everything you need already. But in a world of shitty
books I'm not surprised Tom was lead to buy a crappy one that didn't
do that. Or did he? Maybe he didn't even buy those books, and just
looked at web pages. Don't take me wrong, I make websites for a
living. I love them. But there's a lateral problem displayed by
people's more and more willing behavior of using websites over books..

In Poland there are many good mathematicians. Nobody will argue that.
So are there in Russia. What's the difference you might ask. The
society isn't that different between Poland and the UK. I'd even say
that the UK allows you more time to study and do other related things
with ease, unlike Poland, where earnings are massively lower and
living expenses are almost the same. The genetics aren't that
different either. USA was set up by europeans. Same genes. The UK has
a lot of polish migrants, the east end of London has probably got more
polish genes floating around than of any other nationality.

However, in Poland you can buy the 20th revision of a maths book
written by Kuratowski for 2 British pounds. In the UK you can buy a
crappy, unrevised course book by John Doe from University of Wisconsin
for 100 pounds. That's the first, very important, difference. You
literally cannot be a mathematician nowadays without immediate access
to a big library of books, at least a rack of 50 at a bare minimum.
This is really, really required for proper mathematical and scientific
work. Sure, you can do treks to the library, IF you're lucky enough to
be within even remote vicinity of one that has a good selection of
maths books, and IF you have access to it through connections to a
university or a mathematical society of some sort. You don't get that
in most places. And then, a visit to the library is probably 2 hours.
And if you can't find the book you're looking for, you'll have to
request a different one, which will ask additional time of you to
understand that book. And then by the time you're out of the door
you'll have forgot that brilliant idea you had. Thesis: most flashes
of genius have to be addressed by feeding them additional information
within 1 minute.



And then you have the prohibitive cost of studying at universities.
Not only a cost in money, but also a cost in life, time, health, and
societal rejection. The society of extortion is terrible here in the
UK. One time I went to a graduate job fair just to find out what's
going on. The guy there was trying to 'hire' me (I was hired in a
different place already, which he hadn't known). He said I would find
it impossible to get hired for more than the 12k GBP he was trying to
slave me for. I was earning multiple times that during that year. He
assumed I knew nothing and - if I hadn't known better - I could have
believed him.
So being that kid with a prospect of:
- going to university,
- not learning much because:
--- he has to read books written by his lecturer who has no shame to
admit that Rudin did it better,
--- and because that same lecturer is more occupied with working for
British Telecom than teaching them
- and then getting into huge debt that he won't be able to repay
because he'll only be earning 12000 GBP for the rest of his life

...would you, as that kid, be inspired to do great things in the world
of science, mathematics, finance, and engineering?

And if you went that way, would you be doing inspiring things after
you have finished university? Or would you be working for Rackspace,
making UTP-8 cables, earning an extortionately low salary, wasting
away the most productive years of your life doing nothing to
contribute to the society and future generations?

And in the light of all this, how is a pure subject like mathematics
supposed to be studied and taught in a healthy manner?

D.

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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