The instant that Richard mentioned mathematics and science, Arcturus stopped paying close attention. As he understood it, they were muggle models of explaining the world. A fair effort, but woefully incomplete and inaccurate given their lack of arithmancy and magical theory. Not worth bothering with. He hadn't known about their existence until he started school, and found a couple of Slytherin prefects laughing over a mathematics book that some mudblood boy had brought to Hogwarts with him. Arcturus' sensibilities meant that he wouldn't venture to tell Richard outright what he thought of those muggle theories, any more than he'd have disobeyed the prefects when they eventually gave him the book and sent him to throw it in the lake. But he didn't ask any further technical questions, either.
After his sudden stop, he let the broom continue to drift while Richard spoke to him, flying alongside him. The panic had subsided, and at Richard's soft words he nodded, looking sheepish, and slowly relaxed his grip on the stick and brought himself back to an upright position. 'It was so much faster than I'd ever flown before,' he said, still sounding a little dazed. 'You're right, sir, I oughtn't to have looked down...or to have let it bother me so when I did.'
Arcturus brought the C-Class to a stop, a comfortable static hover, and then watched as Richard demonstrated some flying of his own. That was a clever turn, especially at such a high speed, and then Richard was coming back towards him at a tremendous speed, and if Arcturus had trusted the older wizard's flying abilities a fraction less he might have moved to a considerably safer distance away. His faith wasn't misplaced, and there was no loss of control, no risk of collision, only a perfect, if very peculiarly executed, stop. Safely stopping without relying on the braking spell at all? He'd have thought it impossible if he hadn't just seen the evidence before his own eyes.
He grinned. 'Very well done!' he said approvingly. 'I've never seen a stop like that. Far better than mine – although I did set the bar exceedingly low.' His spirits were beginning to recover, and he couldn't resist a few more words of explanation. 'If I'd been flying my Celeritas, that would have been a perfect emergency brake. I've done it dozens of times. This one-' he gave the side of his broom an affectionate pat, 'just responds very differently. My instincts were off. You should try flying my Celeritas sometime, sir, you'll see.' It was a genuine offer, although he wouldn't be surprised if Richard didn't see the appeal in flying what had to be an antique to him, and turned it down.
Arcturus also wasn't one to give up easily, and now that he'd seen Richard's demonstration, he was even more determined to get things right. 'May I try again?' he asked. 'Reaching that speed and then stopping, I mean? I'll do better this time.' It would be deliberate, and he wouldn't panic, and sometimes the best way to deal with an alarming mistake was to prove to yourself that it wasn't inevitable you'd do it again.