However, few of us are likely to consciously apply matrix mathematics in our day to day lives.

If the video game has curved reflecting surfaces, such as a shiny silver goblet, the linear transformation matrix would be more complicated, to stretch or shrink the reflection.

Matrix mathematics simplifies linear algebra, at least in providing a more compact way to deal with groups of equations in linear algebra

Matrix arithmetic helps us calculate the electrical properties of a circuit, with voltage, amperage, resistance, etc.

computer graphics, then touch on science

Speeches using paradigms are not less persuasive, butthose with enthymemes excite more favorable audience reaction

3. In legislation, it is useful to an investigator notonly to know what constitution is advantageous on the basis of pasthistory but also to know the constitutions in effect in other states

Insofar as someone tries tomake dialectic or rhetoric not just mental faculties but sciences, heunwittingly obscures their nature by the change

. As to whatever necessarily exists or will exist or is impossible tobe or to have come about, on these matters there will be no delibera-tion

Further, since all speakers, praising and blam-ing and urging and dissuading and prosecuting and defending, notonly try to show what has been mentioned but that the good or the evilor the honorable or the shameful or the just or the unjust is great orsmall, either speaking of things in themselves or in comparison toeach other, it is clear that it would be necessary also to have prop-ositions about the great and the small and the greater and the lesser,both generally and specifically; for example, [about] what is the greateror lesser good or injustice or justice, and similarly about other qual-ities.87

propositions

Similarly, deliber-ative speakers often advance other facts, but they would never admitthat they are advising things that are not advantageous [to the audi-ence

In the lawcourts there is either accusation [katBgoria] or defense [apologia]; forit is necessary for the disputants to offer one or the other of these

for only it, if true, is irrefutable

Thus,it is necessary for an enthymeme and a paradigm to be concerned withthings that are for the most part capable of being other than they are

In the case of persuasion through proving or seeming toprove something, just as in dialectic there is on the one hand induction[epagDgB] and on the other the syllogism and the apparent syllogism

character is almost, so to speak,the most authoritative form of persuasion

Butrhetoric seems to be able to observe the persuasive about “the given,”so to speak. That, too, is why we say it does not include technicalknowledge of any particular, defined genus [of subjects]

the latter is more characteristic of humans than is use of thebody.

thus an ability to aim at commonly held opinions [endoxa]22isa characteristic of one who also has a similar ability in regard to thetruth

while they explain nothing about artistic proofs

that is the same as if someone made a straight-edge ruler crookedbefore using it.

This is true of Socrates’ argument,found in Appendix I.B, that since a rhetorician “knows” justice hemust necessarily always be just, and his analogy between rhetoric andcookery as sham arts of flattery

flattery