General

Re: Calculus Discussion

baxter — Thu, 30 Dec 2010 18:57:33 GMT

"What Berkley criticized in The Analyst as far as I can see is what later became nonstandard analysis. Which I dislike, but is valid and rigorous."

Or instead of navel-gazing, you can be like the great Leibniz and use infinitesimals with aplomb. While Leibniz and Newton provided tremendous advances in mathematics and physics, Berkeley's pedantic hand-wringing was all for nought: "non-standard analysis can be seen as a belated vindication of Leibniz's mathematical reasoning." - http://en.wikipedia.org/wiki/Gottfried_Leibniz

Re: Calculus Discussion

scineram — Thu, 30 Dec 2010 17:22:09 GMT

However limits are not flawed, so the derivative is fine.

What Berkley criticized in The Analyst as far as I can see is what later became nonstandard analysis. Which I dislike, but is valid and rigorous.

Re: Calculus Discussion

Solid_Choke — Thu, 30 Dec 2010 03:10:29 GMT

I assume you say that because "infinity" and "infinitesimals" are only concepts and not actually numbers, or anything that exists in the real world. I'm fine with that. But how is this a problem with calculus?

The very definition of a derivative contains a limit, so if limits are nonsense then the definition is flawed at its foundation. Anyway, very smart people have had problems with the calculus from its very beginning (for instance, George Berkeley had a pretty interesting critique).

Re: Calculus Discussion

Zangelbert Bingledack — Thu, 30 Dec 2010 01:40:57 GMT

it isn't a problem with calculus (necessarily). Miles Mathis and Player are the ones making that particular claim.

Re: Calculus Discussion

resist272727 — Thu, 30 Dec 2010 01:04:59 GMT

Zangelber Bingledack:
as an aside, you certainly do not need infinitesimals or infinity to do calculus, unless by those words you simply mean "small enough" and "large enough" for a given purpose.

I assume you say that because "infinity" and "infinitesimals" are only concepts and not actually numbers, or anything that exists in the real world. I'm fine with that. But how is this a problem with calculus?

Re: Calculus Discussion

Zangelbert Bingledack — Thu, 30 Dec 2010 00:57:37 GMT

you are quoting my quotation of Miles Mathis. i don't endorse his theories, and even he is not really saying "calculus is straight-up wrong". his argument is apparently more subtle than that, though i have not yet understood it.

as an aside, you certainly do not need infinitesimals or infinity to do calculus, unless by those words you simply mean "small enough" and "large enough" for a given purpose. see the entire discussion at http://mises.org/Community/forums/p/21376/382922.aspx, complete with many visual aids.

Re: Calculus Discussion

resist272727 — Thu, 30 Dec 2010 00:47:20 GMT

Why is anyone saying calculus is wrong? Wrong about what? I'm sorry but this whole thread seems silly.

Re: Calculus Discussion

resist272727 — Thu, 30 Dec 2010 00:43:59 GMT

Zangelbert Bingledack:
"The calculus is true, but its theory is false. It does not work the way anyone has ever thought it does, or for the reason anyone has ever thought it does. It has nothing to do with infinitesimals or limits."-Miles Mathis

How does it have nothing to do with infinitesimals or limits?

Re: Calculus Discussion

Zangelbert Bingledack — Thu, 30 Dec 2010 00:12:05 GMT

to post an outside source when i am making basic logical and semantic observations seems like an appeal to authority. (i cannot speak for Player or Miles Mathis, who attack calculus.)

Re: Calculus Discussion

baxter — Wed, 29 Dec 2010 18:27:08 GMT

"but as regards pure mathematics, i am not too happy with how it takes even the natural numbers as givens (or how it defines them when it does)" - Zanglebert

Zang, before you tackle calculus maybe you should work on figuring out 1+1=2 and then get back to us with your findings. But for those of us not trying to disprove the abacus, this book may be of interest:

http://en.wikipedia.org/wiki/Where_Mathematics_Comes_From

"Much of WMCF deals with the important concepts of infinity and of limit processes, seeking to explain how finite humans living in a finite world could ultimately conceive of the actual infinite. Thus much of WMCF is, in effect, a study of the epistemological foundations of the calculus."

Re: Calculus Discussion

baxter — Wed, 29 Dec 2010 18:22:17 GMT

> I will not agree that calculus is wrong even if perhaps there is indeed proof.

LMAO, it is not "wrong".

Even dogs understand calculus http://abcnews.go.com/Technology/story?id=97628&page=1

Guys, the 1600's are calling, they want their mathematics back. Seriously, I think some of these posters are some kind of Luddite shills sent to discredit this site.

Re: Calculus Discussion

Zangelbert Bingledack — Wed, 29 Dec 2010 09:39:02 GMT

great points, Merlin.

one thing i want to point out is that calculus really cannot all be a big bluff. but what you are saying stands anyway. there could be major inefficiencies, errors, or absurdities in it, but it could still be that these are adjusted in the necessary ways in the fields where "rubber hits road" so to speak.

for instance, even if calculus was built on handwaving and hence only had very limited application, as long as those limited applications were respected it could be useful physically, even highly useful, as it is.

since pure math can be anything the mathematician wants it to be, it seems far better to focus on scientific applications. modern physics is the one where it really doesn't make sense if the physicist begins to talk about physical models. the fudges and equivocations that may be fine in pure math---where after all the mathematician is simply building a system for his own amusement or edification and any future practical applications will have to choose carefully where it applies and doesn't anyway---can become tools for easy cheating in physics. that is, they can be used to support bad theory, even nonsensical theory, such as 4D space-time, 1D strings, and particle wave "dualities".

i cannot attack math very hard, because the pure mathematician can always claim---rightfully---that they don't knwo ro care about practical applications, and they are creating a system that is as rigorous as they need it to be for whatever their purposes are (including just aesthetics). i have to focus my criticism on the misuse of math in other fields, such as economics and physics, where it has done unspeakable damage for the past 80 or so years.

Re: Calculus Discussion

Merlin — Wed, 29 Dec 2010 09:23:07 GMT

Zangelbert Bingledack:

it is puzzling the kneejerk reactions and claims of "logic" from people who have most probably not verified any of the underlying math themselves. this is appeal to authority disguised as an appeal to logic.

This made me think. I’m not mathematician and I rely on the work and conclusions of others in my daily life when it comes to math. Of course, no one can be an expert in more than a very few fields, if only because the body of knowledge is so extensive nowadays.

Now, assume that calculus is indeed a big bluff. How are you going to convince folks? By proof? We are not experts and will rely on the generally accepted mathematical truth, not on checking proofs ourselves. How many here have gone through the proof in those papers? How many can?

By proving it to the established mathematicians? What if they have personal reasons not to espouse your theory? And what of the rest are too dumb to see you proof or have been so much ‘used’ to calculus that they just can’t shake it off?

The reason why I’m thinking along these lines is that I see a perfect parallel with Austrian Economics. People cannot understand as this is not their field of expertise, and economists are either dull or have personal reasons not to endorse it (not saying AE is perfect, of course).

So, if calculus was wrong, would one have any chance of having this revolutionary idea accepted? One thing is certain, going for the masses, as many purport to do with AE, will just not work, as for economics (and even moral standards)people always go to the established experts, and cannot think for themselves, even if they might otherwise be very independent and courageous people, just like I will not agree that calculus is wrong even if perhaps there is indeed proof.

That is why getting libertarianism to the masses will never do it.

Re: Calculus Discussion

I. Ryan — Wed, 29 Dec 2010 02:22:02 GMT

Smiling Dave:

As Newton taught us all, the physical world we live in is contains two things. There are "objects", which have mass, and there are "forces", which do not.

Wilipedia on force:

In physics, a force is any influence that causes a free body to undergo a change in speed, a change in direction, or a change in shape. Force can also be described by intuitive concepts such as a push or pull....

So a force is an "influence". Nice and vague, but there it is. Newton postulated as an axiom that these things called forces exist. We cannot see them, for they are invisible and have no mass. All we can see is the result of their influence.

So that indeed you are correct in saying that all you can see are the magnet, the filings, and some regularity in their motion. But Newton asked himself "What makes that motion happen?" And he answered, after that apple conked him on the head, that there must be some invisible hand pushing those filings and making them move. He called the invisible hands [whose existence he assumed] "forces".

The only reason everyone accepted this very odd way of looking at things is that it works.

As long as we understand that we're not doing anything but modeling how physical objects move, that's fine.

Re: Calculus Discussion

Player — Wed, 29 Dec 2010 02:05:38 GMT

Attention: Straw-man argument (Am I the first person ever to honestly recognize I´m about to do that?)

"The speed of light is a constant within the universe.. However, the velocity of light does change depending on the medium. However, it is not that a photon is slowing down, it is simply interacting with the medium it is traveling in to a degree."

I love physicians, they are like social engineers/politicians, masters of Orwellian-speak. Never give a straight answer in straight terms.

Physicians think the difficulties and challenges lie in calculations and the last steps of their theories. That is, their mathematical world where they rule, choose everything and cheat all they want, finally magically transporting abstract imaginations to the physical world in a second.

They considered it insulting to lower themselves with definitions, and the actual world we live in, things like explaining experiments are beyond them, they have a need to jump back to mathematics, their safe heaven.

You wrote words, but you did not answer the question.

Obviously after your transformation into a physician you think it´s an easy stupid irrelevant question, absurd, "common knowledge", "told to us in schoolbooks".

My objective was to show you the circular reasonings currently used to "deduce" the Earth/Sun distance, which relies in what they want to prove.

The next naive objective of mine was to point out how baseless and unsound is the Hans Bethe theory of the energy source of the Sun, but if you still are at the stage of belief into E=mc^2 and attractive gravity! Then it will take too much time.