17 OCT 2021 by ideonexus

 Understanding Cause and Effect is Based on Experience

Were a man, such as Adam, created in the full vigor of understanding, without experience, he would never be able to infer motion in the second ball from the motion and impulse of the first. It is not anything that reason sees in the cause, which make us infer the effect. Such an inference, were it possible, would amount to a demonstration, as being founded merely on the comparison of ideas. But no inference from cause to effect amounts to a demonstration, as being founded merely on the compar...
Folksonomies: philosophy empiricism
Folksonomies: philosophy empiricism
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Adam would not know that one billiard ball hitting another would cause a chain reaction.

28 SEP 2021 by ideonexus

 Prime Numbers and Cryptography

Algorithms for finding prime numbers date back at least as far as ancient Greece, where mathematicians used a straightforward approach known as the Sieve of Erastothenes. The Sieve of Erastothenes works as follows: To find all the primes less than n, begin by writing down all the numbers from 1 to n in sequence. Then cross out all the numbers that are multiples of 2, besides itself (4, 6, 8, 10, 12, and so on). Take the next smallest number that hasn’t been crossed out (in this case, 3), an...
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24 SEP 2021 by ideonexus

 Recursive Self-Improvement in Human Civilization

Let’s consider Arabic numerals as compared with Roman numerals. With a positional notation system, such as the one created by Arabic numerals, it’s easier to perform multiplication and division; if you’re competing in a multiplication contest, Arabic numerals provide you with an advantage. But I wouldn’t say that someone using Arabic numerals is smarter than someone using Roman numerals. By analogy, if you’re trying to tighten a bolt and use a wrench, you’ll do better than someone...
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08 NOV 2019 by ideonexus

 Why numbering should start at zero

When dealing with a sequence of length N, the elements of which we wish to distinguish by subscript, the next vexing question is what subscript value to assign to its starting element. Adhering to convention a) yields, when starting with subscript 1, the subscript range 1 ≤ i < N 1; starting with 0, however, gives the nicer range 0 ≤ i < N. So let us let our ordinals start at zero: an element's ordinal (subscript) equals the number of elements preceding it in the sequence. And the ...
Folksonomies: computer science
Folksonomies: computer science
  1  notes
08 NOV 2019 by ideonexus

 Words are More Powerful than Pictures

This “algebraic” flexibility of a word encapsulates the essence of something while leaving unnecessary concretes out. A photo doesn’t and can’t. Further, a word offers enormous flexibility in terms of input/output. It can be spoken, thought, gestured (as in sign language), written, grammatically combined with other words, or stored with very little memory. A photo can’t. Words are altered by syntax and grammatical endings. A photo can’t be modified in this way, other than the temp...
Folksonomies: communication
Folksonomies: communication
  1  notes
02 MAR 2019 by ideonexus

 Scientific Laws Mean That God has No Freedom

he one remaining area that reHgion can now lay claim to is the origin of the universe, but even here science is making progress and should soon provide a definitive answer to how the universe began. I published a book that asked if God created the universe, and that caused something of a stir. People got upset that a scientist should have anything to say on the matter of religion. I have no desire to tell anyone what to believe, but for me asking if God exists is a valid question for science...
Folksonomies: science religion
Folksonomies: science religion
  1  notes
 
04 NOV 2018 by ideonexus

 A Computer Algorithm for Randomization

Back in the early days of computers, one of the more popular methods of generating a sequence of random numbers was to employ the following scheme: 1. Choose a starting number between 0 and 1. 2. Multiply the starting number by 4 ("stretch" it). Subtract 4 times the square of the starting number from the quantity obtained in step 2 ("fold" the interval back on itself in order to keep the final result in the same range). 3.Given a starting number between 0 and 1, we can use the proce-dure...
Folksonomies: algorithms randomization
Folksonomies: algorithms randomization
  1  notes

From John Casti.

04 NOV 2018 by ideonexus

 Probability is Truth-Resembling

The study of mathematical uncertainty is called probability. According to Richard Epstein, "The word 'probability' stems from the Latin probabilis, meaning 'truth-resembling'; thus the word itself literally invites semantic misinterpretation." [1]What Epstein means by "semantic misinterpretation" is that if something is "truthresembling," then it isn't actually truthful; at the same time, the truth is exactly what the something does resemble.
Folksonomies: etymology
Folksonomies: etymology
  1  notes
 
31 OCT 2018 by ideonexus

 How a Nerd Walks Up the Stairs

Your steps should be in a cycle: short, long, long. Long in this case means a double step. Thus, you will cover five stairs in one short-long-long cycle. In addition, you should always start the first cycle on the same foot. Suppose you start on the left foot, then after two cycles you are back on the left foot, having covered ten stairs. While you are walking the stairs in this way, it is clear where you are in the cycle. By the end of the staircase, you will know the number of stairs modulo...
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