As I've mentioned before, I like to hear people discuss complex concepts in mathematics, physics, astronomy and so forth, although I usually start out by following at an inconspicuous distance, and end by losing sight of 'em altogether. This video on the Klein bottle was pretty interesting; however, when the fella began expounding on the concept of a fourth spatial dimension, I admit it felt like those times when I took the Washington Metro to work and found myself surrounded by people talking Farsi or Turkish or some other completely unfamiliar tongue.
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Well ……
ReplyDeleteThere’s a certain amount philosophy associated with mathematics. As one man’s philosophy is another man’s belly laugh, a grain salt should always be handy.
That said, mathematics has no content. Better said, mathematics are purely an invention of the mind that often apply to the real world. But not always, such as in the quantum realm, or relativistic speeds. Or so I understand …. I’m a hairy retired engineer, not a theoretical physicist.
The example I use is to ask someone to show me the number “5”. They generally will write “5” on something, or hold up 5 fingers.
(Don’t use “1” for this demonstration, for reasons I leave to the students to determine.)
I respond with “That’s a graphical representation of the number 5”, or “That’s an example”, followed by, “show me the number 5, in a form that I touch and feel.”
There ain’t no such animal. Mathematics are a concept that have real world applications.
Returning to the video, you see an example of how mathematics (and it’s cousin, geometry) are concepts which sometimes apply to reality. Or rather, that we can use to *describe* reality. Not just the Klein Bottle, but the beaker versus a flat disk being the same thing, or that a beaker has only one side.
Which leads to what we might call “Paco’s Dilemma”, or, “What the heck is the Fourth Dimension?”
Danged if I know. Time it ain’t, not in this context. That’s probably a construct used by the boffins to explain some phenomena that has no real world equivalent.
There may well be more than the 3 dimensions that we can measure in some fashion. Certainly some hypothetical physics postulate them. But science (REAL science, not the money driven “science” pushed by certain charlatans) hasn’t been able to move to a new paradigm where there are real world applications.
The development of nuclear energy is one example of that sort of change; it actually took several decades before practical applications were developed. A lot of pre-conceived notions had to be pushed aside.
But the video is a good example of how such paradigm shifts occur …. …. by the scientific method. I wouldn’t use a Klein Bottle in the kitchen, but there certainly something different about such a shape, and studying it can help us in understanding how the universe is put together.
/nerd psycho-babble
I'm now thinking of buying a Klein bottle; might make a nice conversation piece.
ReplyDeleteWhat you say reminds me of something a teacher told our class one time (I believe, in the sixth or seventh grade). When we write a "1", we're not actually writing a number; we're writing a numeral.
What (or where) is the Fourth Dimension? That's easy. That's where leftist logic lives.
ReplyDeleteI'm now thinking of buying a Klein bottle; might make a nice conversation piece.
ReplyDeleteDoesn't the Weird Science division of Paco Enterprises sell those? Along with the Perpetual Motion Machine, and Fusion Reaction Starter Kit?
Well, yeah, we had a couple gross of those things loaded on pallets and ready to ship, but Raul got to playing with the Perpetual Motion Machine, and one of the spinning blades hit the Fusion Reactor's on switch, then the warehouse got superheated and burned down and...to make a long story short, we wound up with a giant molten Klein blob. When it cools and hardens, I suppose we could sell it as the world's largest 4th dimensional Christmas ornament.
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ReplyDeleteWhat (or where) is the Fourth Dimension? That's easy. That's where leftist logic lives.
Can't argue with THAT, Rebecca.
I really like math but I'm much more engineer oriented.
ReplyDeleteUntil he got to the beaker I was calling bullshit on his "No volume" deal with the klein bottle.
Nothing has a volume without being fully enclosed by his definition, with Saran wrap that beaker or bottle has a volume.
Saying it's 2 mobius strips is really just making a shape to fit a definition. You couldn't cut it into 2 mobius strips. t's a shape that kinda looks like two strips mobii put together.
If you could cut it, you could do it to the beaker too.
Yeah, pure math guys drive me crazy.
It's like Zeno's Paradox, I blame drugs. Or lack thereof maybe.
I like Veeshir's Paradox better, it actually takes reality into account.
You can never get anywhere because...
You're driving to Philly, you're 65 miles away and the speed limit is 65MPH, so you're an hour away.
After about 9 minutes and something, you're 55 miles away and the speed limit goes to 55, so you're still an hour away.
After 10+ minutes..... this keeps happening every 10 miles.
So you're 15 miles away and....construction! 15mph.
An hour and a half or more after first being an hour away you're.... an hour away!
44 minutes later you're 4 miles away and... the road is closed!
So hours after you were first an hour away you're still an hour away.
So you walk at 4mph.
2 minutes later, as you're in Philly, you get shot and you never do make it there.
One of my calc teachers actually had a class discussion on that once, well, except the getting shot part.
We were doing infinite progression functions or something (I forget calc after 20 years of not doing it)
2 minutes later, as you're in Philly, you get shot and you never do make it there.
ReplyDeleteDoes Veeshir's Paradox explain WHY you would want to go to Philly in the first place?
Cheese steaks, the Liberty Bell, Independence Hall, and museums, of course. Gotta do the Rocky Balboa imitation at the top of the steps.
DeleteI'll leave the mathematics to y'all. Your discussion is far beyond me.
ReplyDeleteWould this be the perfect, never ending, whiskey bottle?
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