time and space complexity analysis
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At the beginning of the nineteenth century, communication was slow, even relatively short journeys were uncertain and time-consuming, and people were dependant on the forces of nature for energy; this lecture charts the development of new modes of communication, from the railway to the radio, the telegraph to the telephone, the steamship to the motor-car and examines their efforts on perceptions of time and space.
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Complexity; log, linear, quadratic, exponential algorithms
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According to Musk, some causes of the high costs in space exploration are: The energy to launch a rocket into space is very high, all the calculations have to be right and this is very expensive given the low launch rate. His final analysis is that rockets should be a lot cheaper and presently there are a lot of inefficiencies.
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Algorithm Analysis, Evaluating the Performance, Analysis of Codes: Statement Counts, Another Example (Statement Count Contd.), Comparing Algorithm, Big-O Notation, Big-O to Predict the Time of Execution, Best/Worst/Average Case, Analysis of Recursive Algorithms, Another Example : Towers of Hanoi, A Tabulation for Different Algorithms, Growth Patterns, Application of Algorithm Analysis to Sorting, Selection Sort, Selection Sort Code
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Musk does not recommend space travel to a first time entrepreneur. It is better to start with something that requires low capital.
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In this introductory lecture, Professor Lewin discuses basic units, dimensions, measurements and associated uncertainties, dimensional analysis, and scaling arguments. Further, he explains why a measurement is meaningless without knowledge of its uncertainty, using data collected by Galileo Galilei as an example. He begins to dive into dimensional analysis, reasoning that the time from an object to fall from a certain height is independen...more
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The four-vector is introduced that unifies space-time coordinates x, y, z and t into a single entity whose components get mixed up under Lorentz transformations. The length of this four-vector, called the space-time interval, is shown to be invariant (the same for all observers). Likewise energy and momentum are unified into the energy-momentum four-vector.
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Imagine that interstellar trade is possible at speeds close to the speed of light. It must incorporate the insights of Einstein's special theory of relativity, which teaches us that clocks on board a spaceship moving at high velocity will ensure time at different rates relative to clocks at the point of departure. This means that time travel into the future is possible. Which time-keeping should we use? What would happen to economics if ti...more
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A perennial favorite is the idea of time travel. What would happen if we could go back in time and alter the future a la “Back to the Future”? The great narrative of the history of life has a complexity rife with subplots and twists, many of which we will never uncover. Yet somehow the story of life on Earth began with a prebiotic ooze and ended with the awe-inspiring diversity of life we see today – including us. But like any story, th...more
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The Factor Analysis Model,0 EM for Factor Analysis, Principal Component Analysis (PCA), PCA as a Dimensionality Reduction Algorithm, Applications of PCA, Face Recognition by Using PCA
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The fossil record holds a lot of evolutionary information that can't be seen on shorter time scales, although the more recent fossil record is more complete. Among other things, the fossil record demonstrates that extinctions can open up ecological space for new speciation and radiation, and that life forms tend to begin small and evolve to be bigger over time.
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