# All of Boris's Comments + Replies

Oops, I mis-stated the result. If we fix a universal Turing machine (equivalently, a programming language), then there exists a constant C so that deciding the halting problem for programs of length less than N can be done by a program of length less than N+C. Pengvado's solution works here.

Unfortunately, as Richard observed, you can't do this with Turing machines, essentially because Turing machines can not inspect their own finite control, unlike the stored program on a von Neumann machine. In fact, it appears that my claim---in Richard's notation, th...

I would drop dead of shock if there were a 500-state Turing machine that solved the halting problem for all the Turing machines up to 50 states.
There exists a constant C so that if you want to solve the halting problem for all Turing machines up to N states, you can use a particular Turing machine with N+C states. Moreover, this constant C is small (definitely less than 100). In other words, there exists a 500-state Turing machine that solves the halting problem for all the Turing machines up to 400 states.

Here's the algorithm: given as input a Turing m...

Eliezer, thank you very much for all of these posts. I believe that this post is an excellent way of presenting them all in a reasonable sequence.

Why doesn't someone make some circular sunglasses that have two polarized disks that you can rotate with respect to each other?

1Skeptityke10y
Well, it isn't quite that, but I made an analogue of it prompted by that exact same thought. Movie 3-d glasses are polarized (the two slightly different images on the screen have orthogonal polarizations, so each image only goes through one lens), so if you can sneak two or more pairs of 3-d glasses out of a movie theater, you can pop the lenses out of one pair, and tape them on the other pair (rotated so that almost all light is canceled out.) The resulting cross-polarized improvised glasses are so dark, that if you made them just right, it is possible to stare straight at the sun and see sunspots. However, this makes them quite useless for most other purposes.
3khafra12y
I was surprised to find out that someone did, but it probably doesn't work very well since nobody seems to retail them. Possible problems could include irregularities in the polarization, like what makes the rainbows in car windows when you're wearing a single polarized lens.

You say "the neural circuitry of anger is a reproductive organ as surely as your liver" and "the evolutionary purpose of anger is to increase inclusive genetic fitness."

I don't believe you have enough evidence to assert these statements. All you know is that "angry ancestors had more kids" but you DON'T know that it's as a result of the anger. It could have happened that, say, the same ancestors that could run faster also happened to have the capacity for anger. As a result of their faster running, they reproduced/survived,...

2ThisIsYourSignal4y
Yes dude! That's showing rigor. And PnrJulius' comment that Boris' comment "seems unlikely" is precisely the soft-serve sludge that rigorous thinkers like Boris here have to slog against day in and day out. Boo Julius, boo. Yay Boris, yay. And then a roar of the crowd for TechnoGuyRob who takes the long pass from Boris and dunks on Julius in a way J's grandbabies gonna feel when he writes "The possibility of an "adaptation" being in fact an exaptatation or even a spandrel is yet another reason to be incredibly careful about purposing teleology into a discussion about evolutionarily-derived mechanisms." It's problematic how stoked this exchange makes me. I'ma say it will not prove adaptive.
7robertzk10y
The possibility of an "adaptation" being in fact an exaptatation or even a spandrel is yet another reason to be incredibly careful about purposing teleology into a discussion about evolutionarily-derived mechanisms.

It's possible that anger was a byproduct of something else which is adaptive (certainly such evolutionary byproducts exist)... but it seems pretty unlikely in this case. Anger is a rather complicated thing that seems to have its own modular brain systems; it doesn't seem to be a byproduct of anything else.