A Quote by Kenneth E. Iverson
The properties of executability and universality associated with programming languages can be combined, in a single language, with the well-known properties of mathematical notation which make it such an effective tool of thought.
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Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. [...] The proliferation of programming languages shows no more uniformity than mathematics. Nevertheless, programming languages do bring a different perspective. [...] Because of their application to a broad range of topics, their strict grammar, and their strict interpretation, programming languages can provide new insights into mathematical notation.
I think the most important work that is going on has to do with the search for very general and abstract features of what is sometimes called universal grammar: general properties of language that reflect a kind of biological necessity rather than logical necessity; that is, properties of language that are not logically necessary for such a system but which are essential invariant properties of human language and are known without learning. We know these properties but we don't learn them. We simply use our knowledge of these properties as the basis for learning.
Von Neumann languages do not have useful properties for reasoning about programs. Axiomatic and denotational semantics are precise tools for describing and understanding conventional programs, but they only talk about them and cannot alter their ungainly properties. Unlike von Neumann languages, the language of ordinary algebra is suitable both for stating its laws and for transforming an equation into its solution, all within the "language."
Most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered significant by, say, an applied mathematician.
With the computer and programming languages, mathematics has newly-acquired tools, and its notation should be reviewed in the light of them. The computer may, in effect, be used as a patient, precise, and knowledgeable "native speaker" of mathematical notation.
The upshot is that most philosophers of biology now hold that biological properties supervene on physical properties (where supervenience is taken to include some kind of "in virtue of" relation), and that fitness and other biological properties are not identical with physical properties.
The precision provided (or enforced) by programming languages and their execution can identify lacunas, ambiguities, and other areas of potential confusion in conventional [mathematical] notation.
It is important to distinguish the difficulty of describing and learning a piece of notation from the difficulty of mastering its implications. [...] Indeed, the very suggestiveness of a notation may make it seem harder to learn because of the many properties it suggests for exploration.
Mushrooms provide a vast array of potential medicinal compounds. Many mushrooms - such as portobello, oyster, reishi and maitake - are well-known for these properties, but the lion's mane mushroom, in particular, has drawn the attention of researchers for its notable nerve-regenerative properties.
I hold that space cannot be curved, for the simple reason that it can have no properties. It might as well be said that God has properties. He has not, but only attributes and these are of our own making. Of properties we can only speak when dealing with matter filling the space. To say that in the presence of large bodies space becomes curved is equivalent to stating that something can act upon nothing. I, for one, refuse to subscribe to such a view.
NBC News found that FEMA has redrawn maps even for properties that have repeatedly filed claims for flood losses from previous storms. At least some of the properties are on the secret 'repetitive loss list' that FEMA sends to communities to alert them to problem properties.
Perspective is an Art Mathematical which demonstrates the manner and properties of all radiations direct, broken and reflected.
My time in TNA, I was working extensively in the international side of things - India properties, the U.K. properties, Africa, all of that. So, I know the international business side quite well.
The degree of confirmation assigned to any given hypothesis is sensitive to properties of the entire belief system... simplicity, plausibility, and conservatism are properties that theories have in virtue of their relation to the whole structure of scientific beliefs taken collectively. A measure of conservatism or simplicity would be a metric over global properties of belief systems.
What I'm trying to do is find either existing properties or come up with properties or angles or stories which will create music drama. It's my obsession and most of all I would like to remain working in theatre. I think it's very much alive.
Sometimes the best properties aren't necessarily the biggest properties.
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