If it requires a round-trip of human speech through a professor (and thus the requisition of the attention of the entire class) then you can hardly say they are given as many opportunities to test as they'd like. A person of functioning social intelligence certainly has no more than 20 such round-trips available consecutively, and less conservatively even 4 might be pushing it for many.
Give them a computer program to interact with and then you can say they have as many opportunities to test as they'd like.
Utilitarianism is unlikely to rescue anyone from the conundrum (unless it's applied in the most mindless way -- in which case, you might as well not think about it).
There's an obvious social benefit to being secure against being randomly sacrificed for the benefit of others. You're not going to be able to quantify the utility of providing everyone in society this benefit as a general social principle, and weigh the benefit of consistency on that point against the benefit of violating the principle in any given instance, any more easily than you could have decided the issue without any attempt at quantification.
USA Presidents routinely try to signal lower class than they have.
It's important to note that employers are not seeking to maximize employee performance. They're seeking to maximize the difference between the value provided by the employee and the wage provided to the employee.
With that many instances, it's even highly likely that at least one of the specs in the eye will offer a rare opportunity for some poor prisoner to escape his captors, who had intended to subject him to 50 years of torture.
First of all, you might benefit from looking up the beard fallacy.
To address the issue at hand directly, though:
Of course there are sharp discontinuities. Not just one sharp discontinuity, but countless. However, there is not particular voltage at which there is a discontinuity. Rather, increasing the voltage increases the probability of a discontinuity.
I will list a few discontinuities established by torture.
Nightmares. As the electrocution experience becomes more severe, the probability that it will result in a nightmare increases. After 50 years of high voltage, hundreds or even thousands of such nightmares are likely to have occurred. However, 1 second of 1V is unlikely to result in even a single nightmare. The first nightmare is a sharp discontinuity. But furthermore, each additional nightmare is another sharp discontinuity.
Stress responses to associational triggers. The first such stress response is a sharp discontinuity, but so is every other one. But please note that there is a discontinuity for each instance of stress response that follows in your life: each one is its own discontinuity. So, if you will experience 10,500 stress responses, that is 10,500 discontinuities. It's impossible to say beforehand what voltage or how many seconds will make the difference between 10,499 and 10,500, but in theory a probability could be assigned. I think there are already actual studies that have measured the increased stress response after electroshock, over short periods.
Flashbacks. Again, the first flashback is a discontinuity; as is every other flashback. Every time you start crying during a flashback is another discontinuity.
Social problems. The first relationship that fails (e.g., first woman that leaves you) because of the social ramifications of damage to your psyche is a discontinuity. Every time you flee from a social event: another discontinuity. Every fight that you have with your parents as a result of your torture (and the fact that you have become unrecognizable to them) is a discontinuity. Every time you fail to make eye contact is a discontinuity. If not for the torture, you would have made the eye contact, and every failure represents a forked path in your entire future social life.
I could go on, but you can look up the symptoms of PTSD yourself. I hope, however, that I have impressed upon you the fact that life constitutes a series of discrete events, not a continuous plane of quantifiable and summable utility lines. It's "sharp discontinuities" all the way down to elementary particles. Be careful with mathematical models involving a continuum.
Please note that flashbacks, nightmares, stress responses to triggers, and social problems do not result from specs of dust in the eye.
That makes no sense. Just because one thing cost $1, and another thing cost $1000, does not mean that the first thing happening 1001 times is better than the second one happening once.
Preferences logically precede prices. If they didn't, nobody would be able to decide what they were willing to spend on anything in the first place. If utilitarianism requires that you decide the value of things based on their prices, then utilitarians are conformists without values of their own, who derive all of their value judgments from non-utilitarian market participants who actually have values.
(Besides, money that is spent on "overhead" does not magically disappear from the economy. Someone is still being paid to do something with that money, who in turn buys things with the money, and so on. And even if the money does disappear -- say, dollar bills are burnt in a furnace -- it still would not represent a loss of productive capacity in the economy. Taxing money and then completely destroying the money (shrinking the money supply) is sound monetary policy, and it occurs on a regular (cyclical) basis. Your whole argument here is a complete non-starter.)
There's an interesting paper on microtransactions and how human rationality can't really handle decisions about values under a certain amount. The cognitive effort of making a decision outweighs the possible benefits of making the decision.
How much time would you spend making a decision about how to spend a penny? You can't make a decision in zero time, it's not physically possible. Rationally you have to round off the penny, and the spec of dust.
You're misunderstanding. It has nothing to do with time -- it's not a time line. It means the dust motes are infinitesimal, while the torture is finite. A finite sum of infinitesimals is always infinitesimal.
Not that you really need to use a math analogy here. The point is just that there is a qualitative difference between specs of dust and torture. They're incommensurable. You cannot divide torture by spec of dust, because neither one is a number to start with.