Imagine my surprise. You and what's-his-name ought to get along famously. :-)
What does "on my todd" mean? Is it anything like "on the head of a pin?" I wanted to make a joke about whacking on my part, but "todd" is just too obscure. >:->
Thanks! Rich
I read in sci.electronics.design that Terry Given wrote (in ) about 'Wormhole theory', on Wed, 30 Mar 2005:
Just algebra by itself doesn't usually get you the answer. You need one or two transforms as well. They are not easy to comprehend.
-- Regards, John Woodgate, OOO - Own Opinions Only. There are two sides to every question, except 'What is a Moebius strip?' http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
f'(x) = lim h->0 f(x+h)-f(x)/h g'(x) = lim h->0 g(x+h)-g(x)/h
Therefore:
f'(x)/g'(x) = lim h->0 (f(x+h)-f(x))/(g(x+h)-g(x))
if f(x)=g(x)=0 then:
f'(x)/g'(x) = lim h->0 f(x+h)/g(x+h)
Letting h->0, then:
f'(x)/g'(x) = f(x)/g(x)
for the condition f(x)=g(x)=0.
I pat myself on the back, as usual, for this proof as it was one that I invented on my todd. I have yet to see it in any book, although I have been informed after the fact that this approach is known about. I impressed my math proff no end with this one as it was new to him as well. He actually advised me to give up engineering and switch to math instead because of this. Seriously. All the usually proofs of l'Hopital's rule involve the theorem of the mean approach.
And of course, I can never resist pointing out that l'Hopital had nothing to do with the rule. He was a Toff that paid someone to name the rule after him.
Kevin Aylward snipped-for-privacy@anasoft.co.uk
I read in sci.electronics.design that Robert wrote (in ) about 'Wormhole theory', on Tue, 29 Mar 2005:
I can use ANY mathematical concept to derive nonsense. (;-)
-- Regards, John Woodgate, OOO - Own Opinions Only. There are two sides to every question, except 'What is a Moebius strip?' http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
Are you sure it wasn't from your arithmetic teacher? I ask, because my arithmetic teacher was the one that showed me something very much like this about a half a century ago.
But I thank you for presenting it, because I was thinking this very thing as a way to introduce ~~SciGirl~~ to calculus, gently - I just didn't remember the exact formulae.
Thanks! Rich
I read in sci.electronics.design that Robert Monsen wrote (in ) about 'Wormhole theory', on Tue, 29 Mar 2005:
I expect Kevin can explain this better, but it's not ANY acceleration that matters.
In free orbit, you are an inertial observer - the water in your bucket doesn't slosh about. The twin who travels in the spaceship and arrives back younger than his stay-at-home twin cannot be an inertial observer. As he accelerates and decelerates, the water in his bucket does slosh about.
That doesn't violate SR (or GR). Try telling a cop he can't tell you were doing 65 MPH relative to his radar because that would violate SR! (;-) Perhaps you wrote what you didn't mean.
-- Regards, John Woodgate, OOO - Own Opinions Only. There are two sides to every question, except 'What is a Moebius strip?' http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
I read in sci.electronics.design that Rich The Newsgropup Wacko wrote (in ) about 'Wormhole theory', on Wed, 30 Mar 2005:
'on one's own'. Rhyming slang, from 'Tod Sloane', a US horse-jockey.
-- Regards, John Woodgate, OOO - Own Opinions Only. There are two sides to every question, except 'What is a Moebius strip?' http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
"John Woodgate" schreef in bericht news: snipped-for-privacy@jmwa.demon.co.uk...
....and getting better at it, every day ;)
-- Thanks, Frank. (remove 'q' and 'invalid' when replying by email)
I read in sci.electronics.design that Kevin Aylward wrote (in ) about 'Wormhole theory', on Wed, 30 Mar 2005:
It's the justification of de l'Hopital's method that I was taught. It isn't rigorous, which is why it's called 'justification', not 'proof'.
A justification based on Taylor series expansions is in Lowry H V and H A Hayden, 'Advanced [= 'not advanced' in mathematician-speak] Mathematics for technical students - Part 2',pp. 1-2, Longmans, Green and Co (London, 1955) (No ISBN)
That was by no means unusual at the time, and I think it still goes on in France. However, this site:
indicates that you do him an injustice:
Guillaume De l'Hôpital served as a cavalry officer but resigned because of nearsightedness. From that time on he directed his attention to mathematics. L'Hôpital was taught calculus by Johann Bernoulli from the end of 1691 to July 1692.
L'Hôpital was a very competent mathematician and solved the brachystochrone problem. The fact that this problem was solved independently by Newton, Leibniz and Jacob Bernoulli puts l'Hôpital in very good company.
L'Hôpital's fame is based on his book Analyse des infiniment petits pour l'intelligence des lignes courbes (1696) which was the first text-book to be written on the differential calculus. In the introduction L'Hôpital acknowledges his indebtedness to Leibniz, Jacob Bernoulli and Johann Bernoulli but L'Hôpital regarded the foundations provided by him as his own ideas.
In this book is found the rule, now known as L'Hôpital's rule, for finding the limit of a rational function whose numerator and denominator tend to zero at a point.
-- Regards, John Woodgate, OOO - Own Opinions Only. There are two sides to every question, except 'What is a Moebius strip?' http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
I read in sci.electronics.design that Frank Bemelman wrote (in ) about 'Wormhole theory', on Wed, 30 Mar 2005:
Actually, my limited ability comes and goes. If it's in the 'gone' phase, and I have an important problem to solve, it takes about 3 days to come back.
-- Regards, John Woodgate, OOO - Own Opinions Only. There are two sides to every question, except 'What is a Moebius strip?' http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
That's because you didn't invent it!
As soon as I read Johns post, I typed it of the cuff. One don't forget ones rare moments of er.. genius...
Kevin Aylward snipped-for-privacy@anasoft.co.uk
I have seen this approach, but its not as neat as mine is it:-)
Each step can be justified fully rigorously with theorems on limits, or so my proff told me when he examined it.
Maybe:-)
Interesting that this last quote neatly side steps the issue of where the proof came from. I did a search and found this:
"It states that when the limit of f(x)/g(x) is indeterminate, under certain conditions it can be obtained by evaluating the limit of the quotient of the derivatives of f and g (i.e., f¢(x)/g¢(x)). If this result is indeterminate, the procedure can be repeated. It is named for the French mathematician Guillaume de L'Hôpital (1661-1704), who purchased the formula from his teacher the Swiss mathematician Johann Bernoulli (1667-1748)."
So, there you go.
Kevin Aylward snipped-for-privacy@anasoft.co.uk
Heaviside's operational calculus.....
Cheers Terry
Oh yeah, I was astounded too, when I realised calculus can be replaced with algebra. And wondered why nobody ever mentioned it to me in that way.
Cheers Terry
I found this as well
"The well known de l'Hôpital's rule is contained in this calculus book and it is therefore a result of Johann Bernoulli. In fact proof that the work was due to Bernoulli was not obtained until 1922 when a copy of Johann Bernoulli's course made by his nephew Nicolaus(I) Bernoulli was found in Basel. Bernoulli's course is virtually identical with de l'Hôpital's book but it is worth pointing out that de l'Hôpital had corrected a number of errors such as Bernoulli's mistaken belief that the integral of 1/x is finite. After de l'Hôpital's death in 1704 Bernoulli protested strongly that he was the author of de l'Hôpital's calculus book. It appears that the handsome payment de l'Hôpital made to Bernoulli carried with it conditions which prevented him speaking out earlier. However, few believed Johann Bernoulli until the proofs discovered in 1922. "
Kevin Aylward snipped-for-privacy@anasoft.co.uk
Hmm... gothland. Sounds creepy.
What does "the particle can't think" have to do with the uncertainty principle? If the uncertainty principle wasn't true, photons still wouldn't be able to think :)
I read in sci.electronics.design that ~~SciGirl~~ wrote (in ) about 'Wormhole theory', on Wed, 30 Mar 2005:
Besides, we only have one experiment that appears to show that they can't the double-slit experiment, they can't think which slot to go through, so they all go through both.
-- Regards, John Woodgate, OOO - Own Opinions Only. There are two sides to every question, except 'What is a Moebius strip?' http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
I read in sci.electronics.design that Kevin Aylward wrote (in ) about 'Wormhole theory', on Wed, 30 Mar 2005:
I am concerned that this facility for finding obscure information on the web may indicate that you are turning into 'Robert' (aka FB?). (;-)
-- Regards, John Woodgate, OOO - Own Opinions Only. There are two sides to every question, except 'What is a Moebius strip?' http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
...
My moments of genius always come the next day. Once, at a job interview, they gave applicants a test. One of the questions was to write a program that prints out the primes up to 1000. I screwed it up - probably because I don't work well under pressure. It's hard to write spaghetti code in C, but that's about what I accomplished. I didn't get the job. The next day, I wrote a Sieve of Eratosthenes in three lines on the back of an envelope at the bus stop.
Cheers! Rich
This is actually one of my major failings, especially at interviews. I don't work well on the spot. I need time to think things out. Often people claim that solving problems in 5 minutes demonstrates some sort of greatness. It don't at all. In the real world very few things need immediate action, that isn't a copy of what went before. e.g. sorting out Apollo 13. Most *useful* new things take a lot of time and effort to get right.
The best analogy, for interviews, I use is this. Would one expect an experienced musician to be able to write a new song immediately on request? This is what many daft interviewers expect. Why not ask, play me one of your unknown songs that you have previously wrote. This would demonstrate that the person is capable of new things in general.
Just about every time an interviewer asks a question he wants an immediate response from, is because its one of the few that he has already rehearsed, and therefore knows.
Kevin Aylward snipped-for-privacy@anasoft.co.uk
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