4096 byte sectors don’t solve the analog problem—signals are getting weaker, and noise is getting stronger, and only reduced densities or some breakthrough in recording technology are going to change that—but it helps substantially with the error-correcting problem. Due to the way error correcting codes work, larger sectors require relatively less error correcting data to protect against the same size errors. A 4096 byte sector is equivalent to eight 512 byte sectors. With 40 bytes per sector for finding sector starts and 40 bytes for error correcting, protecting against 50 error bits, 4096 bytes requires (8 x 512 + 8 x 40 + 8 x 40) = 4736 bytes; 4096 of data, 640 of overhead. The total protection is against 400 error bits (50 bits per sector, eight sectors), though they have to be spread evenly among all the sectors.

With 4096 byte sectors, only one spacer start is needed, and to achieve a good level of protection, only 100 bytes of error checking data are required, for a total of (1 x 4096 + 1 x 40 + 1 x 100) = 4236 bytes; 4096 of data, 140 of overhead. 100 bytes per sector can correct up to 1000 consecutive error bits; for the forseeable future, this should be “good enough” to achieve the specified error rates. With an overhead of just 140 bytes per sector, about 96% of the disk’s capacity to be used.

With longer block lengths, the error correction capability generally goes up for the same coding overhead, however, it seems rather more complicated than this. First of all, I don’t think each manufacturer uses the same code or coding structure. (They used to just use Reed-Solomon code, though later they tried concatenating it with LDPC code, and now I hear some are switching to pure LDPC with iterative decoding.) But even if we assume they use some non-exotic block code, and use interleaving for bursts, the math still seems very strange: 40 error correction bytes can only correct 50 consecutive bits currently? I think not.

Why is this? Let’s reason about it in a crude way.

It depends on why there is unemployment. It is said that economic policy dictates some buffer stock of unemployed people be maintained to anchor inflation, which is to say that unemployment can be eliminated by inflating. Indeed, at a low enough real interest rate (including negative rate), all work that spans non-zero time becomes “profitable” at wage above zero and there can be no unemployment. So there will be some unstable equilibrium, where there is full employment at just above zero wage and only “unprofitable” work left on the table. For a margin of safety (so as not to overshoot and still leave profitable work at above the lowest wage, which will unanchor the targeted inflation), there will be some unemployment, and therefore always payable yet unprofitable work. If the government offers some delta positive wage, then this excess labor can be used to do the unprofitable work, and we can do away with the technical requirement of excess labor margin and yet get equilibrium without the possibility of overshooting. Effectively, the government inflates the last little bit as needed to pay wages directly … rather than dumping it into the banking system where it will be promptly lent back to the government due to the real interest rate being slightly too high.

Theoretically, this also solves one of the greatest libertarian complaints that the minimum wage causes more unemployment. The theory of minimum wage is that everybody should be able to self-sustain on their wage (which now includes wage from the government as the employer of last resort). Now, by policy, the government can set some minimum wage (but it must be set so low that, it is guaranteed that everybody will definitely spend at least at that wage rate) and pay its own wage at delta below that. Since all of labor now spends at the minimum wage rate, there will be support on the demand side to assure that the full-employment equilibrium is set where the minimum wage cannot be unprofitable. All in all, the government does not compete with the private sector.

Of course there are still practical issues with this. For example, what do you do with lazy workers. So employer of last resort should only be in the sense of employment opportunity of last resort. You should still be fired for substandard work and go without pay at all. Now that’s an incentive to be productive. Another practical issue is churn. Since the government only intervenes at the lower extremum of the wage scale, unemployment higher in wage scale would need to filter down through displacement. I don’t really see a good solution to this. Perhaps there are clever and ethical ways to increase job market liquidity.

The second issue is, if you want, you can always structure your hiring criteria to select the group you want statistically and not violate the letter of the law. In other words, you can find proxies: language ability for national origin perhaps, experience for age, so on and so forth. Unless all forms of discrimination are banned (including things like height, weight, image, etc. — and why not?), there are always correlated variables.

It seems like without genuine bottom-up cooperation, laws won’t amount to much without becoming unreasonably draconian.