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You have all stated that the 10th Amendment forbids the establishment of public education. How?

Not the "establishment of public education" but federal involvement in it. As for "how", see Post #73 (the one right before yours).

Dr. Frank: wherein does the establishment of public education by the states violate the 5th amendment?

Again, it's not "the establishment of public education" which I was talking about, just federal involvement. Anyway, to answer your question, the 5th Amendment reads, in part, that

nor shall private property be taken for public use, without just compensation.

Consider: A single woman with no children has part of her paycheck taken away by the federal government. That government then uses some of the property they took from her to hire a Vice Grand Poohbah of the Department of Education, to fund worthless federal programs with vaguely catchy names like "Head Start", to buy ketchup to give to schoolchildren for lunch, and of course to give lotsa money with mega-strings attached to various State education departments, etc.

Remember, she has no children.

Why was her property taken away by the federal government? For "public use", of course - education of (in this case other peoples') children.

Is she compensated? I don't think so.

Doesn't the actions of State goverments

The Constitution doesn't apply in the same way to State governments, and I certainly wasn't talking about State governments. Best,

"Consider: A single woman with no children has part of her paycheck taken away by the federal government. That government then uses some of the property they took from her to hire a Vice Grand Poohbah of the Department of Education, to fund worthless federal programs with vaguely catchy names like "Head Start", to buy ketchup to give to schoolchildren for lunch, and of course to give lotsa money with mega-strings attached to various State education departments, etc. Remember, she has no children. Why was her property taken away by the federal government? For "public use", of course - education of (in this case other peoples') children."

You are guaranteed representation in the government that taxes you and allocates those taxes. You are not (and cannot be) guaranteed that the programs those taxes are spent for are efficacious. The Founding Fathers envisioned that the public would take care of that themselves through the electoral process. Of course, it will help immensely if the populace is able to read and write, and to think logically, and is able to tell the difference between facts and empty rhetoric. This ability is provided through education. Thus, it is a general good that the public be educated, much as it is a general good that roads be built and maintained, that harbors be dredged, etc. On this basis, governments have established and funded public education. Whether or not it is being run correctly is a different matter, but the public can deal with that by putting elected officials in place (or even running for office themselves) that will make the requisite changes.

Thus, the fact that the woman in your example is childless is immaterial. Education taxes are not tuition payments. If this example held, none of us should pay taxes to support any services we do not use, and all government functions would be funded out of excise taxes and user fees. It was tried before, and it didn't work.

But, in fact, we all pay taxes to support services that don't benefit us directly, but benefit us indirectly. For example: public health. We pay taxes that in part are used to immunize children of families too poor to afford to pay for it themselves. So, I'm paying for some kid that's not my own to get immunized. Why? How does this benefit me? Outside of the spiritual benefits, of course, which may well be the most important.

Because if we have reservoirs of non-immunized children in our cities, we could have outbreaks of communicable diseases that could cause said disease to spread throughout a broad region. This would lead to civil unrest, increases in crime and the money necessary to suppress it, etc. Also, the diseases could directly affect the affluent as well as the poor. Even though the affluent may be immunized, a large pool of infected people can become a breeding ground for new diseases, or for mutated forms of the epidemic disease (think influenza, or AIDS).

"Is she compensated? I don't think so."

I have generally heard this amendment invoked as the basis by which property taken by eminent domain must be paid for at market rate. I've never heard anyone say that it forbids general taxation. Has this theory come before the Supremes?

Again, the theory behind public education means that she is compensated by the production of a better educated population. This means that 1) they can make more informed and intelligent choices in the election of public officials, and 2) our industries are more productive because of a better educated workforce. I confess that I don't know if point 2 is actually invoked in the justification of public education, but I believe it to be true. In any case, this benefits everyone.