S
spinoza1111
It seems deeply implausible to me. Both of my parents taught college
mathematics, and I retain to this day an instinctive distrust of empirical
methods as unreliable and shoddy.
Peter, even if both of your parents taught college mathematics, it's
still possible that you're mathematically jejune, so here is a test/
checklist I'd like you to complete. I will identify just some the
mathematical experiences I had before I had access to any computer
whatsoever. Check the experiences you have also have, and feel free to
add your own. I understand that given your age, there was never a time
when you didn't have access to a computer, so although I think this
nonaccess beneficial, it is not part of this evaluation.
1. Did formal proofs in geometry at high school level
2. Made constructions in geometry using the unmarked straightedge and
compass
3. Figured out the basics of analytic geometry (drawing a graph from
an equation) without taking the class because bored in Religion class
4. Completed Philosophy 210 (Introduction to Logic) including exposure
to pre-20th century formal reasoning (Venn diagrams and Lewis
Carroll's methods). Grade: A
5. Completed Philosophy 310 (Symbolic Logic): propositional logic,
truth tables, lazy evaluation, quantificational logic, model theory.
Grade: A
6. Completed Philosophy 410 (Set Theory): naive set theory and
existential set theory based on Set Theory and Its Logic (Quine). Only
student in class able to prove the validity of induction (proof ran to
five pages) in Quine's system. Grade: A
7. Read Hopcroft and Ullman's Formal Languages and their Relation to
Automata and did a number of exercises.
8. Designed a computer using rubber bands in series, parallel, and
with a half twist (for inversion) but lacked the manual skills to
build it.
9. Mail ordered the Cardiac computer (a hand operated cardboard
device) from Ma Bell and programmed it.
10. Lost my cherry on the same evening astronauts first landed on the
moon. Admittedly not a mathematical experience. Et tu, Brutus?
Your own experiences must not involve an electronic digital computer
as above.