That is precisely what I posted. Maybe you should try reading it again.



I never declared that Calculus is wrong.

All I said is that Calculus doesn't solve Zeno's paradox.

In other words, mathematicians are wrong when they claim that Calculus solves Zeno's paradox.

Honestly spider,

I thought that James has stated the same thing that you had said... Zeno did not believe that time and space were infinitely divisible. James, much like myself at times, takes the long road to get there, but I had understood him to mean the same thing that you have also said.

You guys agree!!!! Woo-hoo!!! Another first!!!

Anyway, ummmm... as the distance decreases, obviously the time to travel the distance also decreases accordingly. Eventually it would become instantaneous... is that the exact moment that they would be side by side? After that the reversed would happen as far as the calculus goes, right?

I think I have gotten a better understanding here... for a dummy!

Is that also why Zeno suggested that 1/2 and 2x is the same thing when concerning motion?

That has to cause some mathematical issues does it not?

Oh yeah... is there not a problem with the calculus formula to begin with? I mean a value of greater than 1 is impossible to divide into infinite amounts, is it not? For, I have understood that any infinitely divisible value must equate to 0. Is this not true?

I'm not sure what you are saying here. But calculus isn't what mathematicians often claim. If you genuinely look at the formal definition of the calculus limit and what is required to prove that a limit exists, you can clearly see that all that is required to satisty the proof is that certain trends are proven to be true. You never have to actually prove that it ever gets to the limit. It's all about proving trends.

I actually explain all of this in the book that I'm always half-way going to write.

There's a whole chapter devoted to Zeno's paradoxes of motion in my book. That Chapter is called "Zeno and Weierstrass".

Karl Weierstrass is the mathematician who formally defined the mathematical concept of the limit.

By the way, I don't try to claim that Weierstrass is incorrect in any way. He's not. It's just that his formal definition of the calculus limit cannot be used to solve Zeno's dilemma. That's my only point there.

When something is divided into an infinite number of pieces, mustn't their value be of 0?

That's an interesting question Michael. The problem is that it's entirely a philosophical question.

The problem lies in believing that you can achieve an infinite division. But that flies in the face of infinity.

If you chop something into infinitely many pieces, that implies that each piece is zero. Otherwise, you clearly wouldn’t be finished because whatever you have left can be chopped up some more.

However, if you actually did finish, then you face the other dilemma that you’ve actually come to the end of an infinite division. Therefore it must be finite (i.e. it is finished)

The concept of infinity is quite confusing. And modern mathematics doesn’t even have a clear definition for infinity. The whole concept is contextual and understood implicitly.

For example that set of natural numbers is said to be an infinite set (containing an infinite number of elements). This has to be true because if you claim to have a last element all you would need to do is add one to it and you have yet another one. So it’s clear that the set of natural numbers is infinite.

However, it also is a necessary condition that none of it’s elements can be infinite. That is to say that there can be no largest natural number.

This is the same principle as going in the other direction (dividing something up into infinitely many pieces). You can’t claim to have done that and say that all the individual pieces are now each zero.

That would be the very same thing as claiming that an infinite set must contain an largest element.

I’ve solved this problems by making distinctions between differnet kinds of unboundness.

Oh hell’s bells. I guess I just need to write my damn book and then I can just say, “Go read my book”.

I personally have no reason to believe in such a notion as infinite divisibility concerning the measure of time, because of the inherent instantaneous nature of it's reduction.

Instantaneous existence cannot exist.

Well, if it does, it won't have any time to do anything.

By the way,...

Did you pack?

Are we half-way there yet?

Exactly...

I am actually packing things as we speak...

switching ownership of the house...

temporarily staying at my parents' house while I am traveling to different places pursuing employment possibilities...

going through ten years of accumulation...

Thanks fer askin'!

Wow! I didn't realize you were making a permanent move.

I thought this was more like a first date visit?

Ok,... never mind.

I better stick to calculus and physics, I guess I'm really not into the humanities.

Best wishes on your journey!

Lemme clear it all up for you...

A move is imminent...

The destination has yet to be determined...

Travel required to visit prospective employers...

One of which is in Hawaii...

Another was in Seattle...

One trip planned has 3 different objectives...

Sounds like a whole lot of fun!

I'm jealous and envious and all that nasty stuff.

I sincerely do hope you enjoy your journey and find a really great place to live, and a career that you’ll find deeply fulfilling and satisfying.

May I inquire to the type of profession you’re seeking?

Wait,… lemme guess,….

Dean of philosophy at the University of Aloha

Or maybe,….

Secretary of the Restoration and Conservation of Natural Resources of Seattle

Oh wait, I know!,…

The Spiritual Shaman of the Pathos and Logos Artistry Society of British Columbia.

Yep, owl hedge my bets on that last one.

I am humbled James....

I personally had not ever read anything specifically concerning philosophy until recently, within the past 4 to 6 months, I guess. I am hardly estute enough for my own understanding, let alone teaching it...

Actually, I am a high-end professional custom woodworker/custom cabinetmaker, by trade. The position involves that notion.

I just switched my avatar in order to provide a classic example of the type of original work that I do, from concept through completion...

I actually made two of those... my pics show them side by side.

That's cool.

I've done some cabinet making myself. But it was mostly for my own use. I've basically built my cottage myself along with most of my own furniture and cabinetry. But a lot of it was slapped together pretty crudely just to get it done.

I have build curio cabinets and shadowboxes in the past though as a business. I used to call my shop “From the Tree to Thee”. That’s because I made all my own lumber from trees I actually cut down on my own property. Mostly Oak, Cherry, Maple, and White Pine.

I made lots of little jewelry boxes, and shadowboxes, and display cases. My shadowboxes were all curvy like the cabinets in your pictures. And almost never build anything square. All my curio cabinets had angled sides. I liked working with wood glass, and sometimes metals like brass, etc.

Everything I made was my own design. I made a cobbler’s bench coffee table that was a hot seller. And a fold-up desk. It would fold up to about the size of a large rural male box. Fold down the leaves on the sides, and then the drawers could be swung back and it functioned as a pretty nice desk. A great space saver!!!

Here’s a picture of it unfolded.

http://www.csonline.net/designer/ideas/desk.jpg

Later I got into making small curio coffee tables with glass sides and top. Then I put miniature train layouts in them. I called them “Trains Under Glass”.

Unfortunately I don’t have any pictures of those on this computer. But I do still have some unfinished ones out in the wood shop waiting for me to become alive again.

So I’m not totally alien to woodworking. I even built a violin once. Hey! A violin is really just a weird looking wooden cabinet that you put on your shoulder and stroke with a bow.

Seems to me that you’d almost be better off just going into business for yourself.

I actually have a business on the side manufacturing balsa fishing lures. It has taken a backseat in life as a result of some other unexpected situations for the past four years...

It will be coming though... as was planned while it was still in the design process. The entire production line consisting of dedicated pieces of equipment is independantly moveable. Nice margin too...

The problem with wooden things now-a-days is that most customers only care about cost... The ones who do not are a lucrative bunch to deal with, if you can get into that market, which is very, very small. Everybody else buys Chinese garbage...

I will look at that desk...

Cool... excellent job... very innovative...

I know what you mean there. I found that out the hard way. I tried to cater to the average Joe, keeping the price down (which also meant keeping the quality down), at least in terms of a really fine finish. I did try to maintain a high quality of durability in everything I made.

The problem is that the average Joe simply won’t pay for durability. Instead they’ll by the foreign stuff with the high-gloss finish that falls apart. So the profit margin was just too low. That’s why I got out of it.

And dealing with the rich folks can be a high profit margin, but they can sometime be finicky and want to return items for no apparent reason (always at times when I’m at my lowest financially!) So again, it seemed more like a gamble than a business.

However, one thing I did discover is a nice little niche (which I should be taking advantage of right now actually). Here’s the scoup,….

Look in eBay for collectors. It doesn’t matter what they collect. It can be baby dolls, transformers robot figures, Morse code keys, trains… whatever,… it doesn’t matter what the thing is. Just make a nice little display case (or curio cabinet) the custom fits whatever they are collecting. Then advertise those custom made display cases in that same ‘forum’ on eBay. The collectors will gobble them up like hotcakes!!!

Because they have a hard time finding such rare ‘special made’ display cases.

I did that with the Morse code keys. I made a special wooden base to mount the key on. Just the bases alone would sell, because most code keys are made to be screwed down to a wooden base. And then if you have a nice little curio cover to just slip over it so it can be displayed and kept dust free at the same time they eat them up!

But again, it’s not a high profit deal. It’s just that you can get some high volume sells that way. And if you’re clever you can still make a pretty good size mark-up.

The other thing I learned about making money. When it comes to making money, just make the product as easily as you can! Don’t worry about trying to sell the pride of your life. When you make things you are that proud of put them in your own house! Or give them to your friends as gifts!

But when you want to make money just keep the customer satisfied, keep your work to a minimum, and keep the profit margin to the hilt.

Save your best work for yourself, your friends, and your loved ones.

Thanks.

That was my prototype made of white pine. I still have it today. But it looks much richer in oak or cherry.

It’s pretty easy to build too. Actually that desk was very popular and sold quickly at about $250. Everyone says I should have charged more. But that was a pretty good price because it isn’t hard to build actually, and I didn’t put a lot of time in the finishing.

I called it “The Straddle Desk” because once it’s folded open you have to ‘straddle’ the legs to sit at it. It’s not uncomfortable. It’s meant to be almost portable or at least as a space-saver in a small apartment or room. It folds up very easily.

If I ever get a girlfriend owl probably become her slave and have to build lots of those things whilst she sits at the computer selling them on eBay.

You know what them women are like.