They were on Silpheius 12 the first time it happened.
The Doctor was talking nonstop as they walked through the fields of golden tropho flowers, all about the alteration of helium-3 into beryllium-6 in the presence of certain rare elements in the Silpheius star when he was—rudely, he thought—interrupted.
"Did you know that the volume of the right air sac of the 85-to-the-power-of-1023-th cricket to be hatched on Tryiond is .23 milliliters?" asked Rose suddenly.
The Doctor's mouth stopped its exposition on proton-proton fusion and just hung open for a moment. "Uh, what?" he finally asked.
"You know, you're right. The sun is particularly bright here," commented Rose, looking up at the Silpheius star, as though nothing out of the ordinary had happened.
"You were saying?" prompted the Doctor. "About the cricket?"
"Cricket?" said Rose, confused. "The bug or the sport?"
"Uh," said the Doctor. "Nothing. Never mind."
They kept on walking.
The second time it happened, they were in the TARDIS console room.
The Doctor was in the middle of some rather complex calculations necessary for the recalibration of the left tridimensional phase inducers. Rose was lounging on the jump seat, reading a magazine.
"Did you know that there's a particle of carbon floating through the Zebrar cluster, which is shaped almost exactly like New Zealand? It's traveling at 5.839 meters per Terran hour with a rotational velocity of 63.4 degrees per second," commented Rose. She flipped the page in her magazine.
"Is there?" murmured the Doctor as he adjusted his maths to account for the coefficient of friction on the temporal dampening transponders. "Wait, what?" He turned around to stare at her.
"What?" said Rose, looking up.
"What do you mean, 'what?'" he said in confusion. "What you just said, of course! About carbon and New Zealand and all that."
"I wasn't talking about New Zealand," protested Rose.
"I know you weren't talking about New Zealand," said the Doctor. "You were talking about carbon!"
"Why would I talk about carbon?" asked Rose, raising an eyebrow.
He stared at her. "I don't know why you would talk about carbon," he said.
"Well, then, why do you want me to talk about carbon?"
"I don't!" he protested, tugging on his hair.
"I mean, what is there really to say about carbon?" she asked in a reasonable tone.
"Apparently, that it's shaped like New Zealand!"
She pursed her lips at him. "Y'know, sometimes you are very strange," she said, before turning back to her magazine.
The third time it happened, Rose seemed to notice.
"Did I just tell you about the mineral impurity of the igneous rocks on Vorgren 8?"
"Um, yes. Yes, you did."
Rose chewed on her lip. "That doesn't really seem like something I'd be likely to say."
"No. No, it doesn't."
"Should we, I dunno, check that out or something?"
After a series of tests in the med lab, the Doctor reached a conclusion. "Apparently, it's all an after-effect of looking into the heart of the TARDIS," he explained. "An occupational hazard of seeing all of time and space, if you will."
"Is it a problem, d'you think?"
"Well," he said, drawing out the word while tugging on his ear, "not to be rude or anything, but it's a bit annoying traveling the Universe with someone who's a walking encyclopedia of random bits of knowledge."
Rose crossed her arms. "Oh, really?" she asked, dripping sarcasm. "Can't imagine what that would be like. Do tell!"
The Doctor thought about this and wisely decided not to say anything more.
The fourth time, they were pressed tightly together, hiding in the dark behind a ventilation shaft while Cruslid soldiers roamed the space station searching for them.
The Doctor was just mentally categorizing the advantages of being trapped in this particular (and rather snug) location with his shapely companion when she turned her head to look at him.
Their eyes met.
"Did you know," she whispered, "that the forty-eighth High Priest of S'xiltred Mexcroy prefers a red silk g-string?"
She turned her head back around to keep a look out for the soldiers.
Behind her, the Doctor began to shake with suppressed laughter.
"Did I just tell you about some alien bloke's underpants?" she asked.
After that, silence wasn't really an option. And in the end, there was really nothing left for them to do but run.