[Outcast (OP)]

The depictions always show the strings vibrating  and floating in a space resembling the dimensions we commonly see, but the experts tell us that the theory requires several extra dimensions to operate coherently. They never tell us why.
Can someone provide a brief description of why standard dimensions are inadequate, and what the extra dimensions provide?
(Please, no moderator responses.)

[evan_au]

String Theory is a candidate for a "Theory of Everything", vying to unite the incompatible aspects of Quantum theory and General Relativity,
- General Relativity (published by Einstein in 1915) has succeeded in every test thrown at it over the past century. It assumes that the universe exists in a 4-dimensional spacetime.
- Quantum theory  (developed by many experimenters and theoreticians during the 20th century) has also been very successful, but it still has many unexplained aspects to the "particle zoo" which researchers discovered.

Physicists see particles like the electron behave like a wave - and there are other "similar" particles, the muon and tau which look like heavier (and unstable) siblings of the electron. Similar family relationships occurs for neutrinos and quarks.
- Physicists would like to explain the relationships between these all these family members by a common underlying theory
- The basic premise of string theory is that all these particles are resonant waves which are quantized -  by being constrained by dimensions of spacetime. The dimensions of Einstein's spacetime are very large, and don't support resonances of the required energy. String Theory hypothesizes that there are additional dimensions that are rolled up in extremely small dimensions, producing high energy resonances (the particle families we observe).
- At this time, this premise cannot be proved.

General Relativity and Quantum theory are compatible on the large scale (matchbox size and larger), but produce awkward infinities on subatomic scales in the vicinity of black holes. So they can't both be right.
- Just as light was shown to be a quantum effect by Einstein & others (thus avoiding some awkward infinities)
- Physicists expect that gravity will also be a quantum effect, & hopefully also avoid some awkward infinities
- But so far, this happy marriage has not happened. String Theory has reproduced the known behavior of General Relativity - but to date this has not made the awkward infinities disappear.
- I will leave resolving this as an exercise for the reader...

See: https://en.wikipedia.org/wiki/Theory_of_everything