XP: Written Word/English Language&Reading Material

originally posted by Jonathan Loesberg:
This may be like dark holes, and I will understand the theory without really comprehending it, but how can one infinity be larger than another, since both are infinite.
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Adding to what Mark wrote: Because we cannot do ordinary arithmetic on infinities, Cantor treats them as sets.

The infinite set of integers naturally has infinite members.

How about the infinite set of real numbers? We can't count them, of course, but we can ask whether every member of the set of real numbers can be paired with a member of the set of integers.

The answer is: certainly not!, for the reason already given (that every pair of integers indicates an infinite number of reals).

Thus the two infinities are different in their cardinality.
 
originally posted by Jeff Grossman:
originally posted by Jonathan Loesberg:
This may be like dark holes, and I will understand the theory without really comprehending it, but how can one infinity be larger than another, since both are infinite.
Click to expand...
Adding to what Mark wrote: Because we cannot do ordinary arithmetic on infinities, Cantor treats them as sets.

The infinite set of integers naturally has infinite members.

How about the infinite set of real numbers? We can't count them, of course, but we can ask whether every member of the set of real numbers can be paired with a member of the set of integers.

The answer is: certainly not!, for the reason already given (that every pair of integers indicates an infinite number of reals).

Thus the two infinities are different in their cardinality.
Click to expand...

Well, as I guessed, I understand this without comprehending it. I'm guessing that the problem has to do with the paradox created by introducing cardinality into the concept of infinity. I grant that there are an infinite number of cardinal numbers and an infinite number of real numbers. I'm not sure I grant that cardinal numbers, which is, after all, a linguistically created category, is a subset of real numbers in a meaningful sense, thus making fewer of them, somehow. But I readily grant that this is not a mathematical argument. Still, it gets close to the reason that the problem of whether god can make a stone he cannot lift is not really one that shows that god cannot be omnipotent. The problem is caused by competing taxonomies, not competing realities.
 
All very puzzling. The idea that an infinite number of large things is bigger than an infinite number of small things (if I am paraphrasing correctly) appears linguistically correct but mathematically wrong (to me, but what do I know). It reminds me of the expectation that if you drop a heavier stone and a lighter stone from, say, the leaning Tower of Piza, the heavier stone will hit the ground first.
 
originally posted by Oswaldo Costa:
All very puzzling. The idea that an infinite number of large things is bigger than an infinite number of small things (if I am paraphrasing correctly) appears linguistically correct but mathematically wrong (to me, but what do I know). It reminds me of the expectation that if you drop a heavier stone and a lighter stone from, say, the leaning Tower of Piza, the heavier stone will hit the ground first.
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now you're moving into aerodynamics. unless you first put the leaning tower of Piza into a vacuum.
 
originally posted by Jonathan Loesberg:
originally posted by Jeff Grossman:
originally posted by Jonathan Loesberg:
This may be like dark holes, and I will understand the theory without really comprehending it, but how can one infinity be larger than another, since both are infinite.
Click to expand...
Adding to what Mark wrote: Because we cannot do ordinary arithmetic on infinities, Cantor treats them as sets.

The infinite set of integers naturally has infinite members.

How about the infinite set of real numbers? We can't count them, of course, but we can ask whether every member of the set of real numbers can be paired with a member of the set of integers.

The answer is: certainly not!, for the reason already given (that every pair of integers indicates an infinite number of reals).

Thus the two infinities are different in their cardinality.
Click to expand...

Well, as I guessed, I understand this without comprehending it. I'm guessing that the problem has to do with the paradox created by introducing cardinality into the concept of infinity. I grant that there are an infinite number of cardinal numbers and an infinite number of real numbers. I'm not sure I grant that cardinal numbers, which is, after all, a linguistically created category, is a subset of real numbers in a meaningful sense, thus making fewer of them, somehow. But I readily grant that this is not a mathematical argument. Still, it gets close to the reason that the problem of whether god can make a stone he cannot lift is not really one that shows that god cannot be omnipotent. The problem is caused by competing taxonomies, not competing realities.
Click to expand...
Partly for this reason, Cantor discarded the term infinite, and suggested instead transfinite to describe these quantities.

I haven’t checked but I suspect that there might be an Aleph-two for the number of complex numbers since they are composed of an Aleph-one number of real components combined with another Aleph-one of imaginary components. Apologies if this is too abstruse a discussion.

Mark Lipton
 
originally posted by robert ames:
originally posted by Oswaldo Costa:
All very puzzling. The idea that an infinite number of large things is bigger than an infinite number of small things (if I am paraphrasing correctly) appears linguistically correct but mathematically wrong (to me, but what do I know). It reminds me of the expectation that if you drop a heavier stone and a lighter stone from, say, the leaning Tower of Piza, the heavier stone will hit the ground first.
Click to expand...

now you're moving into aerodynamics. unless you first put the leaning tower of Piza into a vacuum.
Click to expand...

Ok, so let's make them two cannonballs of different weights, since two rocks of different weights are unlikely to have the same shape.
 
originally posted by Jeff Grossman:
Quick: Which weighs more... a pound of feathers or a pound of lead?
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The pound of feathers, of course, because the space between each pair of feathers allows us to add an infinite number of in-between feathers.
 
The cannonballs would have to be of the same size and different weights I suspect, though the differences caused by size with so little space involved wouldn't make the air resistance differential that much. Neither would it for a rock and a cannonball. After all, when Galileo disproved Aristotle, he wasn't operating in a vacuum.
 
originally posted by Jonathan Loesberg:
The cannonballs would have to be of the same size and different weights I suspect, though the differences caused by size with so little space involved wouldn't make the air resistance differential that much. Neither would it for a rock and a cannonball. After all, when Galileo disproved Aristotle, he wasn't operating in a vacuum.
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I don't know if the sizes of what Galileo used are known for sure, but the illustrations I recall seeing in children's books showed cannonballs of different sizes, which makes sense if he wanted spectacle. So, indeed, this presumes that the resistance differential was negligible from such a relatively low height.
 
I come for the wine and stay for the intellectual content (or discontent, as the case may be). Y'all are thinking so deep that you make the Mariana Trench seem like the gutter of the Uber dropoff zone outside of the Spearmint Rhino in Las Vegas. This stuff is inspiring to one stuck in the boonies of the wild west. All this talk of cannonballs and the Tower of Pisa. What if instead of dropping off the leaning side, you just rolled them down the slanted side of the tower? Does gravity abide on a slope, or would one cannonball roll faster than the other? And if the cannonball was made of lead vs feathers (but the same weight), would that be an appropriate way to gauge the aerodynamic characteristics of the two materials?

And that whole thing with the infinite spaces between things that have definite places. As a musician (well, a bass guitarist) I deal with this all the time, particularly when playing to a click track, or maybe a drummer who just graduated cum loudly from Berklee and plays perfectly but doesn't swing (you'd be surprised how many of them there are out there)(or maybe you wouldn't be). They tend to play smack-dab on the beat and it's pretty dull because the rhythm lives between the 1-2-3-4 so I need to place my perception of 1-2-3-4 in in some sort of syncopation to wake things up.

Like when you watch reruns of the Lawrence Welk or Hee-Haw and the audience claps along, they clap ON the beat (1 and 3), but when you watch videos of Sister Rosetta Tharpe or Howlin' Wolf, the audiences (even the ones in England) clap along on the backbeat (2 and 4). Having played a lot of gigs for squares who want to clap on 1 and 3 I've learned to add my own feel to what I play and divert them from this potentially embarrassing predilection. The 1-2-3-4 stays the same, but the emphasis shifts and people find themselves wanting to dance, even if they don't know why. A good bassist can shift the musical pulse and reality and shift things from just being a bunch of notes to being music, even if the song's not all that good. And yes, you can also mess around with the harmonics and chord changes, and even be like James Brown's bands where they always land on the 1 and it still swings because the drums are playing the 2 and 4 but the 1 is always on the root of the chord.

And so it goes with the theoretical stuff above about breaking down the numbers between the numbers. That plays into the way the musicians think of where the beats fall, and how to move them around to make it work for them, instead of against them. And this is further complicated if you're playing in oddball time signatures, like in Brubeck's "Take Five" or Pink Floyd's "Money" which are only in 5/4. If you follow the wacky time signature rabbit hole into the compositions of say, Don Ellis or the modern classical composers who work with unfathomable numbers "because they can" it's almost as worthwhile to have a degree from Cal Tech as it is from Julliard. As you've probably figured out by now, I've matriculated from neither, but it hasn't hurt my career (not much) since I've mainly played in cowboy palaces and blues bars where they string chicken wire in front of the bandstand so we don't get hit by flying bottles. That hasn't happened to me since I was playing in punk clubs in LA back in the good ol' days when we'd be happy to only have bottles thrown at us.

-Eden (instead of music school I was gonna apply to Oxford, but by then I'd fallen into a comma)
 
I think it was mebbe Miles who said that he was focused on playing between the notes. Something like that.

Mark Lipton
 
Miles’ quote was “It’s not the notes you play; it’s the notes you don’t play” giving credit to omission over commission on the bandstand. His final live performances were full of space set into slow-tempo compositions that let the musicians bounce around within the framework, implying the beat and giving them room to play notes that would be considered wrong, but would be resolved with the next notes, kind of like a wine being wonky on its own but tasting pretty good alongside the artichoke. As Delbert McLinton put it, it ain’t what you eat but the way how you chew it.

And to beat a dead horse just a little more (and in case anyone harkens back to the several-page trope earlier in this thread on misheard cliches, this is decidedly not "eat a lead s'more" or "beat a red whore"), my favorite example of shifting the beat around and dropping it seemingly at random within a measure would be the original version of “Whole Lotta Shaking” by Jerry Lee Lewis. The Killer’s pumping piano rhythm is pretty straightforward (compared to say, the more free-form feel developed by Rosco Gordon that inspired Jamaican musicians to come up with ska) but drummer JM Van Eaton played fours on the kick drum while swinging the ride cymbal. The snare vacillates between to two feels, dropping right in the appropriate pocket to fill the gap between Lewis’ feel and the kick drum/ride cymbal dichotomy. The various components of the drum part move around as needed, almost as if Van Eaton’s corpus callous had been severed and two people were playing the same drum pattern under the song.

Interestingly, you hear a similar moving parts in a lot of blues coming out of Chicago around that time, but usually the drums and guitar are pretty much on the beat but its the bass that shifts to unite the disparate performances. Chuck Berry, Muddy Waters, Howlin’ Wolf and the rest of the Chess roster benefited from this lax time feel, thereby intriguing the Rolling Stones to try to make that work. Charlie Watts could get that feel of course, but Bill Wyman never did have the necessary flow. And to wrap this all up, bassist Darryl Jones replaced Wyman in 1993 and among his previous bandleaders for a couple of years was Miles Davis. When Jones auditioned for Davis’ band, Miles asked him to play a slow blues. Darryl started playing, Miles told him to cut the tempo in half, and then to slow it down from there. The Stones are all jingly-jangly compared to the post-Marcus Miller Miles Davis group, but Darryl’s time perception has enhanced Mick and Keith’s ability to keep performing long after their use-by dates have been passed.

-Eden (there’s something that relates to wine in here somewhere. I’ll look around and see if I can find it)
 
originally posted by Eden Mylunsch: there’s something that relates to wine in here somewhere. I’ll look around and see if I can find it
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Eden, no worries. Your writings about the talents and styles of the music artists are of much interest. It makes me wonder what you might think of some of my preferred artists e.g. Mark Knopfler, Bella Fleck, Josh Ritter, Gregory Alan Isakov, Lord Huron, John Mayall, Kenny Burrell, BB King, etc. ... and even the Dire Straits, not to mention the Traveling Wilburys.

Wine!

. . . . . Pete
 
First musician I think of when it comes to wacky time signatures is Robert Fripp. Heck, even the Grateful Dead wasn't adverse this. Estimated Prophet in 7/4, Playing in the Band in 11/4. There's a reason why one song is called The Eleven. Blame the first two on Weir, he loves that shit.

I'd have a hard time seeing the Stones now because Charlie Watts isn't among us anymore. Not taking away anything from Steve Jordan, but Charlie's push/pull of the beat was so ingrained in the band's sound. My favorite Stones show was in 1999 at the San Jose Arena. I had a 6th row seat on the side, stage left. I had a clear sight line to Charlie. Watching him and Keith face off each other was sublime. The engine room.

Speaking of bass guitarists, tonight I'm seeing Hot Tuna play at the Fillmore. Their final electric tour. From 2024 forward, Jack and Jorma are only going to tour as an acoustic duo. It'll be my last chance to hear Jack Casady on electric bass.

Oh, wine. August West (back to the Dead).
 
originally posted by Larry Stein:
First musician I think of when it comes to wacky time signatures is Robert Fripp. Heck, even the Grateful Dead wasn't adverse this. Estimated Prophet in 7/4, Playing in the Band in 11/4. There's a reason why one song is called The Eleven. Blame the first two on Weir, he loves that shit.

I'd have a hard time seeing the Stones now because Charlie Watts isn't among us anymore. Not taking away anything from Steve Jordan, but Charlie's push/pull of the beat was so ingrained in the band's sound. My favorite Stones show was in 1999 at the San Jose Arena. I had a 6th row seat on the side, stage left. I had a clear sight line to Charlie. Watching him and Keith face off each other was sublime. The engine room.

Speaking of bass guitarists, tonight I'm seeing Hot Tuna play at the Fillmore. Their final electric tour. From 2024 forward, Jack and Jorma are only going to tour as an acoustic duo. It'll be my last chance to hear Jack Casady on electric bass.

Oh, wine. August West (back to the Dead).
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Odd time signatures? You’re singing my tune, so to speak. Mummy Was an Asteroid, Daddy was a Small, Non-Stick Kitchen Utensil by Quiet Sun is one of my favorite odd time signature tunes. Not quite Fripp, but Fripp-adjacent.

Mark Lipton
 
I was mystified when my email word processor objected to my speaking of someone who "snuck out of sight" (and I see it is underlined in red here as well). It would never have occurred to me to say the person "sneaked out of sight".

Interesting.

. . . . . . Pete
 
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