You're still open to errors caused by the runtime environment generating an invalid proof while executing a correct program.

Then run it through the dozen independently-written verifiers I mentioned (in different computer languages) on many OSs and different physical computers. Insert artificial errors in the proofs and make sure they are detected. You have the algorithm and the source code; walk it through a few proofs by hand until you're convinced it does the right thing.

Seriously, at what point would you be satisfied? How do you trust your computer to do anything at all (most of which is far more complex than a 300-line program for verifying mathematical proofs)?

If what this guy is saying is true and our highest levels of math have become so complex that we mere humans can't be counted on to accurately verify mathematical proofs, then how can we be trusted to write code that does the verification of proofs and expect it to be any more accurate?

All you need is a small program that implements the rules of math and verifies that the steps in the proofs follow from those rules, one step at a time. The program would be the same regardless of the math complexity.

For example, all proofs in metamath, no matter how advanced, can be checked with a program that's only a few hundred lines long. Over a dozen versions of this program have been written in as many computer languages, and the likelihood of them all having the same bug is pretty small.

Yeah, it buffers everything locally and transmits when the wake word is triggered. So as long as you don't wake it up, you are fine.

Yes, but once you wake it up, what guarantees it will go back to sleep? Perhaps Amazon could have it behave as if it went to sleep but in actuality still be awake. And not all the time, but only under some circumstances controlled by Amazon, so that packet sniffing wouldn't usually see it.

But, seriously, if we abandoned all the historical baggage, the right length for distance measurement is "the distance light travels in exactly 1 nanosecond in a vacuum", and we should all just switch to that.

Well, that is 11.8 inches, or very close to one foot. So we're essentially back to American units.

"encuentramelo" vs "find it for me"

Maybe not the greatest example. :-) Even though the Spanish "encuentramelo" is one word (vs. 4 words in "find it for me"), it has 5 syllables (vs. only 4 syllables n English).

Honestly, why does anyone care that Facebook has a monopoly on, what, Facebook updates?

Without meaningful competition, they can set ad prices as high as they want. This increases the costs to advertisers, who in turn pass it on to you through higher prices. So in the end you pay for it whether you use Facebook (or one of its numerous former competitors they now own) or not.

You can argue that advertising is evil, and I wouldn't disagree, but the reality is that companies need a way to reach their potential markets.

For the grocery store I go to most often, I print out a chart (on one sheet of paper) that has the things I usually buy sorted by aisle, and I circle what I intend to buy before leaving the house. One quick zig-zag through the aisles and I'm done shopping. Relatively low tech and extremely efficient. I would challenge anyone to beat me by futzing around with an app.

When I need something unusual not on the sheet, at the store I mark where I found it and add it to the chart when I get home. By now it's quite rare that I need to buy something not on the chart.

I miss the instant response of the old fashioned potentiometer volume control on my car radio. Now many of them seem to purposely fade in and out slowly as you turn the knob one way or the other. It seems I always overshoot the volume and have to back it down a little. Does anyone find that a useful feature?

Sort of off topic: anyone remember the silly kids' game of turning the volume all the way down during a newscast or talk show, then flicking it up and down quickly to produce a funny word fragment? Not possible anymore.

(I wonder if the person who invented the fade-in volume control was the same one who invented smooth scrolling... At least you can usually turn that off.)

The point of it flying is to fulfill everyone's fantasy when stuck in traffic jams: push a button to switch to quadcopter mode, soar over the stuck traffic, then go back down to car mode and continue on your way.

When someone accomplishes that, it will market itself and people will be clamoring for them.

As a bonus, it will double as a leaf blower for your lawn in the fall.

People in convertibles might be a little unhappy with these things hovering a few feet over them, though, blowing the car contents all over the place and rupturing eardrums.

I would speculate that if you made the breakdown by wealth/income rather than race, much of the racial difference would disappear.

Why not just make ALL tax returns public information? I am sure half of the public, you know, the half that do not actually pay any income taxes, would be all over that.

In Finland, Sweden, and Norway, all tax returns are public information. In Norway it's been that way since the 1800s.

No company (or President) should be required to make tax returns public. Enforcement is the role of the IRS, not the public at large.

If the IRS is so great at enforcement, how was Mueller able to obtain multiple tax fraud indictments the IRS missed?