Instead of saying mathematics is an attempt to state what is true and is sometimes successful and relevant, I would tend to say that mathematics is a way of saying that the conclusions you are drawing are at least as true as the assumptions that you start with if you do it well. Mathematics does not care if you resolve this by concluding that the conclusion is true or that an assumption is false, either is equally good.
@sfjeff1089 This is an important concept to keep in mind because sometimes learning your assumption space and where you can apply a certain type of math and when you can't is frequently the most important and useful aspect of a certain part of math education you can undertake.
Precision is not Accuracy QM-TIME AM-FM Communication In-form-ation is probabilistic, complicated and messy. Language should be used by Medical Practitioners who have the motto, First do no harm, and in as Diplomatically as possible under the circumstances. Models are not necessary when thorough Accounting is carried out. Reasons are adjusted to, theories are obfuscation if not tested and been accounted in the complete context, not only in abstractions. Etc, etc. Ie QM-TIME Communication includes Quantum-fields Mechanism Holographic Principle Imagery in pure-math relative-timing ratio-rates Perspective.
R.I.P Jim, I worked for him for many years.
Instead of saying mathematics is an attempt to state what is true and is sometimes successful and relevant, I would tend to say that mathematics is a way of saying that the conclusions you are drawing are at least as true as the assumptions that you start with if you do it well. Mathematics does not care if you resolve this by concluding that the conclusion is true or that an assumption is false, either is equally good.
@sfjeff1089 This is an important concept to keep in mind because sometimes learning your assumption space and where you can apply a certain type of math and when you can't is frequently the most important and useful aspect of a certain part of math education you can undertake.
James Mirrlees - Explains why 'free markets' may not always be optimal..
Precision is not Accuracy
QM-TIME AM-FM Communication In-form-ation is probabilistic, complicated and messy.
Language should be used by Medical Practitioners who have the motto, First do no harm, and in as Diplomatically as possible under the circumstances.
Models are not necessary when thorough Accounting is carried out. Reasons are adjusted to, theories are obfuscation if not tested and been accounted in the complete context, not only in abstractions. Etc, etc.
Ie QM-TIME Communication includes Quantum-fields Mechanism Holographic Principle Imagery in pure-math relative-timing ratio-rates Perspective.
R.I.P.