K‮ly‬e @khird@qoto.org

Is there a well-known name for the multiplicative equivalent to the absolute value function?

The absolute value function f(x), for real x, is the identity operation f(x) = x for x greater than the additive identity (zero), but it's the additive inverse f(x) = -x for x less than the additive identity.

I'm interested in the function g(x) over the positive reals that is the identity operation for x greater than the *multiplicative* identity (one), but the *multiplicative* inverse x⁻¹ for x less than the multiplicative identity.

I don't need g to take on any particular value for negative x, much less complex x, but I think the most natural extension would be that the function's rotationally symmetrical about the origin (an odd function, so g(-x) = -g(x)).

Taking the current fad for heat pumps one step further, is there a reason we couldn't have other appliances hooked into circuits of cold/hot/return pipes carrying a refrigerant or coolant throughout the house? For example, your refrigerator or water heater would be just a passive heat exchanger with a thermostat to open and close a valve when necessary.

In the case of a refrigerator, this would mean that in summer, the heat gets pumped to the water heater or directly outdoors, rather than getting pumped into your kitchen by the refrigerator and then pumped outdoors by the A/C. And in winter, the waste heat gets pumped into your HVAC to heat the whole house and not just the kitchen.

In the case of the water heater, this would mean that in summer, you're scavenging heat into your water that would be dumped outdoors by a traditional A/C. In winter, you'd be sucking heat in from the outdoors and from your fridge, and only having to run a heating element to make up the difference when necessary.

Diagrams to illustrate are mine. Yes I know the heat exchangers would be counter-current, but I tried to draw them as simply as possible.

Anyone know if it's possible to generate #DNS64 entries locally on #OpenWRT? The service I use (at 2606:4700:4700::64) seems to be misbehaving, but DNS is reported to be fully functional on the Cloudflare status page. It seems like #dnsmasq ought to have all the information it needs to generate an AAAA record corresponding to the A record, so I could just use standard #DNS upstream, but I can't figure out how to do it.