Science and Inquiry discussion
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Science Fun
Kikyosan,I bow to your superior historical knowledge. Archimedes use of infinitesimals is still not clear to me, though. It may be that he understood something about them, but not it seems the abstract mathematical principles.
Ultimately, I you trying to tell me that Newton was not such a genius after all, as the Greeks already knew it all? That seems far fetched to me, particularly as they were obsessed with circular orbits of the planets around the sun.
I'm really sorry about your sarcastic and taunting reply.It is very clear that I never told (nor even thought or infered) that Newton or modern geniuses were not geniuses. How could I? Your conclusion is totally illogical and it displeases me. I was just explaining something whose only aim was to give further and more correct information about Archimedes and the Greeks and their actual knowledge. We're in a science group, and I defend correct information. This should be welcome first, and then a proper and serious discussion may start, with open minds and politeness.
However, this is the "science fun" thread and this is completely off topic here. I won't go on.
John wrote: "Jim,There is no doubt of Archimedes prowess as a mathematician, scientist and engineer. However, the article indicates without evidence that he discovered infinitesimals. I very much doubt that t..."
You're taking a fun article pretty seriously, aren't you? I thought it was kind of cool, but subject to hyperbole like all such.
Jim,You're right, I took it seriously. I'm very much a binary person I suppose: something is right or it's wrong.
Personally, I wouldn't mind having an ancient greek death ray. Imagine how much popcorn you could make.Down playing the greek contributions to mathematics is a bit arogant. They didn't really have the mathematic language that we do. To put it in perspective imagine Pythagoras sitting in his garden doodling with a stick in the dirt. This is how he worked out Pi without arabic numerals. He was surely smarter than me.
J.,If your message was addressed to me, I certainly haven't been "downplaying" Greek mathematics. I try to state the facts as I see them, and arrogance can't come into it as I'm not as smart as any of these people anyway: ancient or modern! So I haven't contributed one iota (nice Greek saying!) to maths understanding. I'm smarter than our Prime Minister Dave Cameron, though!
Newton said something like "if I have been able to see further than anyone else, it's because I have been standing on the shoulders of giant men". And so it has gone on throughout history with some unfortunate periods in Earth history when a lot of material may have needed to have been discovered.
I don't argue that Archimedes was a genius, the equal of anyone we have on Earth today. I have only argued about one aspect of his precise contribution to mathematics. I have already been correctly told off for trying to be too precise.
Finally, to say that the Greeks didn't have the mathematical language of today really puts the cart before the horse. To develop new mathematics you first have to develop new notation and see the need for new language. That's what Newton did in a lot of things (and, yes, I suppose Archimedes before him). In particular both Newton and Leibniz developed precise language and notation for infinitesimals and calculus. I don't know what your hangup with pi is all about, it really doesn't address the infinitesimal issue.
Even as recently as the early 20th century, Einstein needed new mathematics for describing General Relativity. By digging around he already found that the notation existed but in a relatively obscure branch of differential geometry.
I would guess that if the mathematicians hadn't already come up with ways of describing curved space, using co- and contra-variant vectors and tensors, Einstein would have invented in. Of course all that propelled differential geometry into the limelight.
Here's an archive of curious scientific names, sorted by ethimology, puns, wordplays (you can choose on the menu bar). Maybe it's funny only if you are a zoologist, I don't know. I spent some nice time reading these lists with some fellows. :)http://web.archive.org/web/2002102322...
Some animals were named after beloved or hated personalities, others have weirdy sounding names.. and so on.
Campsicnemius charliechaplini Evenhuis, 1996 (dolichopodid fly) "Etymology: This species is named in honor of the great silent movie comedian, Charlie Chaplin, because of the curious tendency of this fly to die with its midlegs in a bandy-legged position."
Boselaphus tragocamelus (Pallas) (nilgai, an Indian antelope) This translates to "ox-deer goat-camel"
Subbuteo (a British table soccer game) named after the small bird of prey Falco subbuteo. Peter Adolph, the game's inventer, wanted to call the game "Hobby", which is the bird's common name.
Thanks, Kikyosan. That was fun to look through. I wish I could pronounce & understand Latin better, though.
John,Pythagoras aproximated a perfect circle by tessellating the trisections of the equal sides of a polygon. He realized that each tessellation brought him closer to a circle, while still giving a side length which he could calculate.
Mathematically, he could do this an infinite number of times without reaching zero.
J.,It is you who is making the step from the procedure of Pythagoras to an understanding of infinity and infinitesimals.
It is not clear that the Greeks themselves knew that the process would converge, for example, to give a value of pi. After all it was only relatively recently, I don't know when, that the concepts of rational numbers versus irrational numbers versus transcendental numbers was understood. The Greeks might easily have thought that there was a "perfect polygon" which computed pi. That would have made pi rational. We don't even know if the Greeks understood the concept of convergence. They may have empirically concluded that the process converges, which may have been good enough at the time.
I mentioned Zeno's paradox. This is an important issue because for Achilles to beat the Tortoise, he needs to complete an infinite number of steps in a finite time. Presumably you don't have a maths degree, but if you did then you would appreciate that this isn't as trivial as it sounds. That's why the ancient Greeks had trouble with the paradox despite Kikyosan's dismissal of the problem.
Obviously the Greeks "engineering and observational" skills could see that Achilles could beat the tortoise, but mathematically they couldn't resolve the paradox. i.e., they didn't understand infinitesimals.
I think in the end, we don't really know how much ancient philosophers knew apart from the basics. Our current scientific and mathematical knowledge is based on traceable standards via the scientific literature. Even if the Greeks had a similar method (which I doubt) a lot of the material has been lost.
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Betsy,You're a spoilsport! Some of us derive a lot of fun from counting the angels on a pinhead!
Jim,Well, pictures of scientists cheering are a bit cheesy, so not not all of the 20 pictures are good!
There was another one in the NASA collection showing the Pluto/Charon pair. I have it on my website http://www.enigmascientific.com/news
I liked them all, cheesy or not. They deserve to cheer after hitting such a small mark so far away.
I'm glad you liked them, but as a scientist myself, I've been in groups cheering on success, but I wouldn't personally want a journalist photographing me doing it. Scientists are people too, is that the message?
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It works until "annoying physics" gets in the way.
That's fun! It's wild how reality bends the ball, too. Very good example.
Jim wrote: "The tree of life is getting a makeover.https://www.sciencenews.org/search?st..."
Thanks for the link. The new tree of life is mind boggling- It certainly blew my mind!
This might be considered a privacy issue, but it's too funny. Windows 10 might just reveal your porn stash to your wife:https://grahamcluley.com/2015/08/wind...
Another good reason not to download porn. My luck it would randomly mix the photos. I could just see my girlfriend considering her reaction to the pics of other women, when suddenly there is a pic Dudley (childhood dog). "What is he into?"
Cracked.com probably isn't the best place to get scientific information (or any, for that matter) but it is entertaining & ...the human body is a ridiculous bundle of evolutionary misfires, and it continually finds ways to surprise us. That's why ... "7 Horrifically Stupid Decisions That Somehow Saved Lives"http://www.cracked.com/article_22666_...
Warning, it is Cracked.com. Profanity & boobs are pretty much to be expected. Generally NSFW unless you are the Sys Admin with your office door (the server room door) closed.
;)
Another Cracked.com photoplasty on 23 wild advances science has come up with lately.http://www.cracked.com/photoplasty_16...
Today is Erwin Rudolf Josef Alexander Schrödinger's birthday (b. 12 August 1887) & I keep stumbling over his cat. Here's the Wikipedia version:https://en.wikipedia.org/wiki/Schr%C3...
but I found "Schrödinger’s Cat, a Feynman Inspired View" more interesting.
https://naturallyinconsistent.wordpre...
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Mice sing just like birds, but we can’t hear them.http://www.washingtonpost.com/news/sp...
Hummingbird tongues are way weirder than we thought.
http://www.washingtonpost.com/news/sp...
5 fun skates & boots (AKA, 5 better ways to die while having fun).http://www.gadgetify.com/skates-boots...
CNN has some 1.5 minute videos on 'Creatures of the Deep'. I stumbled on to one about unknown critters off Hawaii & they're pretty wild. Another is a killer whale who bothers boaters until they pull some fishing line & a bag off him. The videos are not much on content, but pretty cool to watch. http://edition.cnn.com/videos/world/2...
I've been laughing for an hour....http://i.imgur.com/yLamcfC.png
When I was a child I hated this (well, still now, actually): to find a butter cookies can, open it and discover sewing supplies.
only ONCE in my life I did find cookies and it was the best day ever.
Here's an article with a short clip of SpaceX landing. Reusable rockets!!!http://www.popsci.com/missed-spacex-l...
Colorful Orbs in Space: In zero gravity, balls of water create their own universes.http://www.slate.com/articles/video/v...
Drones can be fun, but they're quickly becoming a hazard. They've been in the news more often, but possibly not enough. I had no idea there were people this stupid. Now the insurance companies are getting involved.https://nakedsecurity.sophos.com/2016...
This is awesome - a music video made in zero gee. I'll post an interview on how they made it below in the comments. This was made on a Russian version of NASA's Vomit Comet. 50 seconds of weightlessness at a time, yet it looks seamless. Incredible!http://www.nbcnews.com/tech/innovatio...
How it was done:
http://www.redbull.com/us/en/music/st...
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Science and Inquiry
Books mentioned in this topic
What If?: Serious Scientific Answers to Absurd Hypothetical Questions (other topics)What If?: Serious Scientific Answers to Absurd Hypothetical Questions (other topics)
What If?: Serious Scientific Answers to Absurd Hypothetical Questions (other topics)
mycellium running: how mushrooms can help save the world (other topics)
The Audubon Society Field Guide to North American Mushrooms (other topics)
A post scriptum @John:
Greeks were not only Zeno. Zeno was a philosopher of Parmenides'school (read about School of Elea) who used to "play" with absurd and paradoxes. They used sophisms to contest others' theories. Unfortunately later philosophers were not so creative, so they couldn't break the influence of those sophisms. Infinite became a taboo. But then Archimedes solved it with his mechanical method.
Archimede did use infinitesimals (read about his solids, surfaces, polygons, lines, very illuminating and heuristic). But when Dark Ages came, most of Greek knowledge were consigned to oblivion. Until the Science's rebirth in XVII-XVIII century. (this is valid for too many disciplines, unfortunately)