Rolle Rant

[TheGlimmerMan]

Rolle's Theorem.
http://en.wikipedia.org/wiki/Rolle's_theorem

Something I first came across at university 40 years ago.
It really pissed me off, and still does.
Isn't it so totally, utterly obvious that it does not need proving?
A bit like claiming that given two numbers, x and x where x<y any number
greater than x and less than y will be between x and y?

Are you trying to read between the lines or write or append between the
lines?

 

[Dirk Bruere at NeoPax]

Are you trying to read between the lines or write or append between the
lines?

I'm just surprised nobody mentioned the typo

 

[ehsjr]

I'm just surprised nobody mentioned the typo

You were just on such a great roll(e) with your rant that nobody
wanted to interrupt it with "x marks the spot" or similar.

Ed

 

[Dirk Bruere at NeoPax]

You were just on such a great roll(e) with your rant that nobody
wanted to interrupt it with "x marks the spot" or similar.

Ed

But would the theorem still work if it was done in pictures instead of
Roman/Greek letters? Answer that if you're so smart!

 

[Dirk Bruere at NeoPax]

Trolle's Theorem: people will rant about the most ridiculous things.

Yes, but this is more intellectual than most.
It would be wasted in most NGs

 

[Nobody]

So it's obviously very plausible, but isn't certain till it's proven.

The problem with intuition is that it doesn't get you very far once you
move away from familiar territory (integers, reals) and, worse, can
lead you astray. E.g. applying the rules of real arithmetic to complex
numbers, assuming Euclidean geometry, etc.

 

[Dirk Bruere at NeoPax]

Russell & Whitehead's "Principia Mathematica" goes through more than 500
very dense pages before getting to the point of proving that 1+1=2.

So it's obviously very plausible, but isn't certain till it's proven.
Rolle's theorem is part of the scaffolding for the theory of continuous
functions (and therefore of calculus), so it's pretty important. There
have been some pretty counterintuitive theorems proven in that field,
e.g. Fourier's theorem!

Well, if you want to go that far, what is a proof?
What does "a proof exists" actually mean?
Does a proof exist independent of someone proving it?
Does it only exist after someone proves it?

 

[Tim Williams]

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

Well, if you want to go that far, what is a proof?
What does "a proof exists" actually mean?
Does a proof exist independent of someone proving it?

Yes, Erdos
http://en.wikipedia.org/wiki/Paul_Erdős
believed that there exists a Big Book, containing all the most elegant
proofs which God does not want us to know (i.e., good proofs are hard to
create). Kind of a Prometheus thing.

When he would read a particularly excellent proof, he would exclaim, "This
one's from the Book!"

I'm supposing Rolle's isn't in said book.

Tim

 

[Dirk Bruere at NeoPax]

2 is the most complicated number I've nearly got too.
Physically, 1+1=2 cannot be proven, example:

1 Apple + 1 Apple =2 Apples

rewitten as the first Apple A(1) and the 2nd being A(2) requires,

A(1) = A(2),

needs to be proved.
(Electronics guys might use electrons, if Uncertainty Principle
didn't cause a hassle).

Hence 1+1 =2 is assumed as precision of the equality of Apples
tends to infinity, is a reasonable approximation.
(That's my 2 cents)
Ken

But that's just "experimental maths", something rather looked down upon.

 

[[email protected]]

2 is the most complicated number I've nearly got too.

Two can be as bad as one
It's the loneliest number since the number one

<...>

 

[Dirk Bruere at NeoPax]

Yes, Erdos
http://en.wikipedia.org/wiki/Paul_Erdős
believed that there exists a Big Book, containing all the most elegant
proofs which God does not want us to know (i.e., good proofs are hard to
create). Kind of a Prometheus thing.

When he would read a particularly excellent proof, he would exclaim, "This
one's from the Book!"

I'm supposing Rolle's isn't in said book.

Platonism leads to even stranger places.
Such as "what is a calculation", given that all possible equations and
all possible solutions already "exist".

 

[ehsjr]

But would the theorem still work if it was done in pictures instead of
Roman/Greek letters? Answer that if you're so smart!

Roman/Greek/whatever letters _are_ pictures.
Cosgrove's rule #1: Do _not_ let pictures get in the way of a
good rant. ;-)

Ed

 

[ehsjr]

Ouch!




Flys have more self 'respecks' than that.

Double ouch!!

Ed

 

[TheGlimmerMan]

Well, there is only ONE of me and who "needs" more than one (WinDoze)
desktop?

A rack full of satellite comm gear might. Might need several.

 

[TheGlimmerMan]

...and what INDIVIDUAL would $$pend that kind of money, space and energy
to do ???

Who said anything about an individual?

You? You're just a commoner. You don't get "individual" status.

Done anything noble?

No, really, if you could not see that me talking about VDMs and
hardware control, and then about racks of gear was not about an
individual, then you should probably find some way to give your soul back
to the Hall of Souls, so it can be put to better use.

 

[TheGlimmerMan]

The rules of math are well-suited to the field, because they've been
shown to work well for well over two thousand years now. If you don't
like it, that's fair enough, but it's definitely a private taste of
yours own.

Cheers

Phil Hobbs

The pyramids were built more than 2000 years ago, and Mayan calendars
are older than that as well, and they are down to the second on planetary
positions, and galactic positions as well. Not a small mathematical
feat.

 

[TheGlimmerMan]

Even UTC averages more than 1 leap second per year.

The science community is perfectly aware that the day is only 86,400
seconds long.

It (the year) is 31,557,600 seconds. That's 365.25 times 86,400.

Averages?

Now I now you are smoking Jimson weed. It is right on the money.
Always has been. There are small arguments about crossing points on a
given rotation, but it is pretty easy to look at centuries of time
passage, and center right in on the figure. Just ask Newton.

The Mayan calendar is accurate to the day on a 13,000 year cycle.
Pretty impressive. They describe the passage of three previous cycles
already.

This is our last gig. Is your house in order? Does it even matter?

 

[[email protected]]

The science community is perfectly aware that the day is only 86,400
seconds long.

It (the year) is 31,557,600 seconds. That's 365.25 times 86,400.

Averages?

Now I now you are smoking Jimson weed. It is right on the money.
Always has been. There are small arguments about crossing points on a
given rotation, but it is pretty easy to look at centuries of time
passage, and center right in on the figure. Just ask Newton.

AlwaysWrong is *ALWAYS* wrong. You must be lonely this week, Dimbulb.

The Mayan calendar is accurate to the day on a 13,000 year cycle.
Pretty impressive. They describe the passage of three previous cycles
already.

Clueless.

Try to learn *something* in your life, AlwaysWrong.
http://www.search.com/reference/Leap_second

 

[Martin Brown]

There is a nice graph of the difference and explanation at
http://tycho.usno.navy.mil/leapsec.html

The science community is perfectly aware that the day is only 86,400
seconds long.

It (the year) is 31,557,600 seconds. That's 365.25 times 86,400.

You could legitimately believe that to be true during the period when
the Julian calendar was still in regular use before the Gregorian
calendar reforms. The Julian year is still defined that way, but it is
only used for certain crude computations. You are clueless.

Averages?

Averages - you also have to specify precisely which definition of year
you are referring to - conventionally the tropical year is the civil
definition measured from equinox to equinox and the equation for the
average length of a year is

= 365.2421987 - 0.00000614T days
or
=31556925.97 -0.530496T seconds

Where T is time measured in Julian centuries of 36525 days from 1900

That is about 674 seconds shorter than you claimed. It was this
discreprency that led to the 11 missing days when Pope Gregory finally
had the Christian calendar sorted out.

Sidereal year (fixed star to fixed star) and anomalistic year (perigee
to perigee) are both slightly longer at around 365.26 days.

Sidereal year is experimentally now the easiest to measure to very high
precision and IERS look after the data if anyone is interested:

http://www.iers.org/nn_10406/IERS/EN/Science/EarthRotation/EarthRotation.html?__nnn=true

Now I now you are smoking Jimson weed. It is right on the money.
Always has been. There are small arguments about crossing points on a
given rotation, but it is pretty easy to look at centuries of time
passage, and center right in on the figure. Just ask Newton.

The Mayan calendar is accurate to the day on a 13,000 year cycle.
Pretty impressive. They describe the passage of three previous cycles
already.

This is our last gig. Is your house in order? Does it even matter?

You are certainly B-Ark material. Don't forget to buy some more canned
sausages and bread buns for when the 2012 Mayan calendar rolls over.
Beware the mutant star goat!

Regards,
Martin Brown

 

[Jon Kirwan]

On 25/11/2010 02:06, TheGlimmerMan wrote:

You are certainly B-Ark material. Don't forget to buy some more canned
sausages and bread buns for when the 2012 Mayan calendar rolls over.
Beware the mutant star goat!

Not more than a few weeks ago, I recall seeing some news item
appearing about a recently published paperback book, this
year:

http://www.amazon.com/Calendars-Years-II-Astronomy-Medieval/dp/184217987X

In a separate chapter on the Mayan calendar, I've read that
Dr. Gerardo Aldana (who is a professor at UCSB and
specializes in Maya hieroglyphic history) says that the
process of converting data between the modern and Mayan
calendars may be wrong by 50 years or even perhaps even a
century.

Haven't read the chapter, myself. But it certainly reflects
on any "accuracy" claim for the Mayan calendar.

Jon