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 And anything that happened at the speed of light would have too many unknowables attached to begin with—closer to religion than science.

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"closer to religion than science"
This sounds like some of that "common sense" pablum. You know, when some dolt says, "He may be smart but he doesn't have any common sense," to make them feel superior to the smart person. But common sense is stupid. It's observation without scientific backing! It's making assumptions about the world based on basic perceptions! Common sense says that the sun revolves around the Earth. Because you can see the sun moving across the sky. That's common sense. Science is all, "Yes, that is what it looks like! Good perception! But I'm about to blow your mind, baby!" "Common sense" is closer to religion than science ever could be!
    People also love to point out that people who believe in science have faith just like a religious person. They have faith in their theories and whatnot. But obviously that's about as insipid an opinion as somebody could vocalize! Scientific theorems are based on evidence while the main attribute of faith is that it cannot have any evidence to support it. If there's evidence to support a conclusion, there is no room for faith. So shut up with your faith-based arguments against science, stupid people!

Although, really, I get what Merle is getting at. Science always seems to have an event horizon which we can't imagine ever truly being able to understand. In the 1880s, the speed of light must have been bewildering! But they had already developed experiments to begin working with light and methods with which to measure it and observe how it might change based on other variables (the whole point of the Michelson-Morley experiment). I think about this limit in terms of The Big Bang. I can't imagine how it could ever be knowable what was happening on the other side. I don't see theorizing about it as being close to religion though. But then I've been areligious my entire life and so I'm not too fazed by unknowables. Let them be unknowable! I've got turnips to buy!

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 Exists, doesn't exist, what's it got to do with the price of turnips basically.

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"Exists, doesn't exist"
Whether something exists or doesn't exist would seem really important when you get right down to it. But Merle acts rather casually about it and I get it. I once dropped out of a philosophy class in college because my attitude was pretty much this. It felt like everybody in class just believed philosophy was throwing up a new roadblock to anybody else's suggestion on whatever subject was being discussed. It was fucking tiresome. I was just kind of like, "Fine, y'all argue about whether or not what we see is real. I'm going to go get laid. Maybe that won't be real but, man, I'm going to enjoy the hell out of whatever it is!"

"price of turnips"
I guess at some point in Irish history, turnips were so important that if you tried to talk about anything else, people would say, "The head on you and the price of turnips," meaning, well, I don't fucking know what it means. But I guess the price of turnips (and the price of cabbages) was meant to represent some fact that actually matters to the lives of everyday people who don't have the time or luxury to mess with all of this universal hoodoo about natural physical laws and whatnot. So Merle is just pointing out that whether or not Æther exists doesn't mean much to the lives of most people.

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 He had already heard in some dim way about the Æther, though being more on the practical side of things, he couldn't see much use for it.

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"being more on the practical side of things"
At this point in Merle's life, when he's living in Connecticut, he's building machines for Heino Vanderjuice. Later he'll take up an interest in photography, possibly because he's interested in the physical aspects of the machine and how it works at first but later, he becomes quite invested in how many boobies he can see using it. What I mean to say is he's a man of the physical and of what can be seen. Theoretical concepts may as well be magical chants or religious rites. Maybe! I'm projecting and assuming here, I'm sure.

"he couldn't see much use for it"
I think this is a joke! At the time, Æther was supposedly what allowed light to get from one place to another. And without light, you can't see. So not being able to see much use for the thing that enables you to see would, to my mind, be a pretty good joke! Good one, Pynchon!

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 One day Merle had read in the Hartford Courant about a couple of professors at the Case Institute in Cleveland who were planning an experiment to see what effect, if any, the motion of the Earth had on the speed of light through the luminiferous Æther.

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"Hartford Courant"
This Connecticut newspaper is apparently the oldest continuously published newspaper in the United States, beginning its life as the Connecticut Courant in 1764. Merle would have been a reader of this paper as we learned, from his association with Heino Vanderjuice, he was a Connecticut resident. Merle, interested in light and photography, had a mechanical aptitude which he used to help build machines for Professor Vanderjuice back at Yale.

"a couple of professors at the Case Institute in Cleveland"
Physicists Albert Michelson and Edward Morley. The Case Institute wasn't actually known as the Case Institute of Technology until 1947. At the time, it would have been the Case School of Applied Science. But don't be too hard on Pynchon about that. It's not like I would have known any better if I didn't have the Internet to help me understand every single reference Pynchon makes.

"were planning an experiment"
The experiment described in this passage took place between April and July of 1887.

"to see what effect, if any, the motion of the Earth had on the speed of light through the luminiferous Æther"
This experiment is just one of the major changes happening around the liminal space of 1890. Being that Against the Day is one of Pynchon's four great novels he had within him (the others being Mason & Dixon, Gravity's Rainbow, and, well, um, I don't know. Has he done the fourth?! Are the three I named even three of the four?! You'd think I'd do some outside research on shit like this), it takes place at a pivotal place in history (especially the history of Western Civilization, or at least through its perspective, and particularly the American perspective), science, economics, and any other academic subject you can think of.
    While meant to determine motions effect on the speed of light, what the experiment actually presented was strong evidence that Æther didn't exist. So we have the world before 1887 where science simply took for granted that a substance or medium must exist within vacuums and all around us that enables light waves to pass through (as waves through water or sound through air/water), dubbing the mystery substance Æther, and the time after where an entirely new understanding of what light might be and how it works was needed. So just as the Frontier was disappearing, changing the entire landscape of America and our relationship with it and each other, Æther was disappearing as well, turning the physics of light on its head.
    Reading about the failed experiment reminds one of reading Gravity's Rainbow due to all the talk of sine waves and zeroes. I don't think they ever mention beyond the zero though! But beyond this experiment, which was pretty much the nail in the coffin for ether (both physicists themselves ceasing their experimentation into the nature of Æther and concentrating instead on light's properties) and opened up the scientific world for accepting the idea of special relativity. Whatever that is, amirite?! I think that just means light doesn't go faster if a train turns on its headlights because it just phase shifts to red or something (unless it's blue!).

More of my thoughts on this moment in time here!

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 Which usually was how Dally got to hear about her mother, in these bits and pieces.

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I suppose this is fitting, being that her name is Dally. She learns about her mother slowly through Merle's aimless wandering thoughts, mostly focused on his sexual dalliances with her. I'm guessing that's the case because of the whole "she was going to find out in a minute and half anyway" bit of his story. So, yes, I'm making assumptions based on my immaturity.

"bits and pieces"
Glue! I need glue!

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 "What was I doing in Cleveland in the first place?"

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I'm used to Pynchon collapsing scenes by shifting through time and space abruptly without letting the reader know. But I don't remember his characters basically doing the same thing within one dialogue. Maybe this is how conversations with astute and intelligent five year old kids often go. Feels more like Ann Nocenti dialogue in a DC Comic book than Thomas Pynchon! I'm used to her characters not actually listening to each other while talking past them, basically engaging in two monologues instead of one dialogue.

I suppose the point is that Dally, from the time she could talk, was constantly asking questions about her mother and Merle told her whatever he could manage to tell her at the time. And this mini-conversation allows Pynchon to steer the story to that place in time in Cleveland where Merle met Erlys. I'm glad I don't have to blame the conversation being terrible on Pynchon's writing because one of the two people talking is just a little kid and how much sense do they typically make? And Merle is still rattled from his broken heart so we should excuse his inability to answer a direct question from a toddler.

Anyway, we're going to learn why Merle was in Cleveland soon! Is that something we were dying to know? If not, we are now, right?!

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 "And . . ."

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I don't know what information Dally is trying to prompt from Merle after his last bit of dialogue with this "please continue" moment. Fortunately I don't feel all that stupid because Merle's response shows Merle has no idea either.