tronvillain

DireStraits:
If you can resolve a paradox, it is no longer a paradox. Logic now accords with experience, so there is no conflict between them, and hence no paradox.

Synaesthesia

Tronvillan wrote:
DireStraits,
The error in Zeno’s argument is that as he divided up lengths of space, without stating so explicitly, he correspondingly divided up periods of time. As Zeno’s Paradox is told, the focus upon the division of space with regards to the relative position of the Tortoise and Achilles-thus shifting attention away from the exponentially shrinking timeframe. In your version the premises are different, the periods of time are specifically stated to be constant while those of space are divided recursively.

The objective structure of the situation as Zeno set it out shrinks the timeframes as it shrinks the distances. When the implications of it’s hidden premise are spelled out, it is no longer a paradox.

I hypothesize that the reason we still call it so is (1)Historical accident, analogous to Hofstatder’s example of what is commonly called Fermat’s last Theorem being more of a conjecture and (2) to underline the psychological tension between the seemingly ironclad logical proof and our observations about the universe.

DireStraits

If you can resolve a paradox, it is no longer a paradox. Logic now accords with experience, so there is no conflict between them, and hence no paradox.

DS: Then it would appear that there is no such thing as a paradox!

To form a paradox, one needs two doxa, which seem eminently reaonable, and an at least seemingly reasonable conclusion drawn from them that seem unreasonable, the conclusion forming the paradox.

One might restate Zeno as follows.

Doxa (1) To pass the tortoise, Achilles needs to perform an infinite number of tasks.
Doxa (2) It is impossible to perform an infinite number of tasks.
Paradox: Achilles will never pass the tortoise.

That is a paradox, and will remain for all eternity as a paradox. And I doubt if it will ever be called anything other than a paradox. Perhaps you have a better name for it? Zeno's Resolved Paradox? Zeno's Discredited Paradox? Zeno's Poke in the Eye? Zeno's Demonstration of His Lack of Knowledge of Limits?

DireStraits

The error in Zeno’s argument is that as he divided up lengths of space, without stating so explicitly, he correspondingly divided up periods of time.

DS: Yes, I KNOW how many ways there are to resolve Zeno's Paradox.

But in the situation that you are asked to imagine in the story, Zeno's Paradox DID actually apply. It was applied as a constraint to the actions of the mathematician and the engineer.

As they say in Law School, "Don't fight the hypothetical!"

God! I wish I had never mentioned Zeno at all! Read the story without the allusion to Zeno, and try to get the point. The mathematician and the engineer have different approaches towards the solution of the problem. Why?

copernicus

I work in a company that is largely managed by aerospace engineers, and I have worked with engineers for the past 15 years. I am not an engineer, but a professional linguist. So I am something of an outsider looking in at the engineering culture. Here are my impressions.

The vast majority of engineers seem to be deeply opposed to creationism. If you look at the cars in our parking lots, you will see more Darwin fishes than fundamentalist fishes. Engineers are, by nature, mostly conservative. The quintessential engineer is the Dilbert character (my favorite comic strip). Dilbert is fairly conservative, but he would never put up with the fundamentalist nonsense. (Actually, I believe that Dilbert is a religious figure at work. There are Dilbert icons everywhere, and my boss has pointy hair.)

Now for the engineer vs. scientist conundrum. Engineers and scientists belong to completely different species. (They fill different environmental niches in our society.) Scientists are speculative and formulate theories. They are like people who invent an entirely new cuisine. The engineers write cookbooks. They monkey around with the dishes sometimes, but they seldom step outside the parameters of the cuisine. Scientists want to know what will happen after they do something. Engineers want to know what will happen before they do something.

<rant>
Now here is the problem I have with engineers (since liquid seems to want an honest opinion). I work in Research & Development, which requires a lot of experimentation. There should be a law against allowing engineers to manage R&D. Some engineers are very much open to experimentation, but most seem to abhor it. They don't like surprises, and they don't like to take chances. One engineer, who is a bit of a gadfly at work, put it this way: "Every project in this company must start 'finished'." That is, you don't do anything until you know exactly what will happen, how much it will cost, and whether you know that it will be successful. The only thing that matters is finishing the job on time and within budget. So you are basically done, except for assembling things, before you start the project. There is never enough money to do anything right in the first place and always enough money to fix mistakes after it fails. In our company, the aerospace engineer in charge of the R&D division has said that "R&D means little 'R' and big 'D'."
</rant>

That said, I want to say that I'm glad that our aircraft manufacturing is controlled by engineers, who believe in triple redundant safety and have the gumption to tell finance where to get off. Engineers are too politically conservative, but they are definitely not people who look down on science. Quite the opposite. They are some of the most intelligent and practical people on the planet. And I owe them my job.

[ February 15, 2002: Message edited by: copernicus ]</p>

rabiddog

Since you all seem to be fairly knowledgable in the area of theoretical physics, can someone explain to me how to refute the common argument of the second law of thermodynamics that creationists frequently use to "prove", as they say, that evolution is not possible.
A fellow freethinker

NeilUnreal

Like a lot of earlier posters, I work as an engineer, but my formal training is in science and logic. Scientists seem to be much better than engineers at "listening" to data and using that knowledge to formulate and test hypotheses -- that is, they can quickly pare away irrelevancies and get to the core of a problem. Engineers, on the other hand, seem better at turning processes and architectures into metaphors and then using metaphors from one domain to solve problems in another.

My favorite engineering joke is: A mathematician, a physicist, and an engineer are asked to prove the theorem "All odd numbers greater than one are prime."

The Mathematician: "3, prime; 5, prime; 7, prime. Therefore, by the principle of induction, all odd numbers greater than one are prime."

The Physicist: "3, prime; 5, prime; 7, prime; 9, (pauses) Experimental error. 11 prime, …"

The Engineer "3, prime; 5, prime; 7, prime; 9, (long pause) -- Wait! I can fix that!"

-Neil

Corey Hammer

Actually, that's an easy one. 2LOT basically says that in a closed system heat cannot move from a low concentration (i.e., a cold-er spot) to a high concentration (i.e., a warmer spot) without assistance. It applies only to closed system (e.g., the entire Universe overall), but not open system. Earth is an open system because we receive gads of energy from this big, giant fusion reactor located 93 million miles down a gravity well.

Also, although the Universe is a closed system (unless someone here has discovered interreality rifts and not told us), the Universe is not (yet) uniform and therefore energy distribution is still uneven and some systems can be open.

DireStraits

Since you all seem to be fairly knowledgable in the area of theoretical physics, can someone explain to me how to refute the common argument of the second law of thermodynamics that creationists frequently use to "prove", as they say, that evolution is not possible.

DS: Well, you could preface any argument with the question why chemists and physicists have taken so long in informing biologists that the scientific theory that unifies biology is wrong. Or, if this information has in fact been transmitted to biologists, why there is no evidence of an intellectual fist-fight between these disciplines that would make the Newton/Leibniz altercation seem like an old ladies tea-party.

If that don't work, haul ass over to <a href="http://www.talk.origins." target="_blank">www.talk.origins.</a> There is a click you can do on a search facility they have there.
Do what comes naturally.

Good luck, my fellow!

HRG

Statistician:"3, prime; 5, prime; 7, prime; 9, not prime; 11 prime; 13 prime. OK, we are 95% confident that all odd numbers are prime".

HRG.