How much evidence do you need to be convinced in something that is very implausible is actually the case? Or rather, if you really don’t believe something to be true, how much evidence do you need to push you all the way to near certainty?
Of course, this is a question about probabilities so we aren’t talking about any kind of knowledge that can be gained without evidence. The kind, for example, where we make definitions and then reason according to a set of rules to get some new knowledge.
I probably should have seen this prior to now but there is a lot to read and even good stuff slips through the cracks. It was suggested to a colleague and he presented the work during a journal club. I was impressed by the work.
Visual salience has been a hot term in vision science since the 90s. The salience model identifies local regions in an image that have higher priority than other local regions.
I think a lot about detection and estimation problems. A detection problem is one in which it pays off to identify the presence or absence of a signal amongst some background noise. This is a problem that has applications all over the place. Transmission of data over the internet relies on detection of discrete pulses encoded in an analog signal. Doctors "detect" cancerous masses in images taken with an x-ray or other technology.
Patterns that reduce uncertainty about some aspect of the world are called information. Open your curtains in the morning, see a certain amount of light. Opening your window gives you some information about what time of the morning it is. More light is a pretty reliable way of approximating the time during sunrise.
Speaking generally, it always seems right that more information is a good thing. If getting more information reduces our uncertainty and we want to be more certain, then collect as much information as possible.
The Monty Hall puzzle is entertaining because the result turns out to be counter to intuition. Those are the most entertaining puzzles. The family of puzzles like Monty Hall are so contrived that they don't resemble reality. Reality, especially when chance and probability is involved is not expected to be more intuitive than these puzzles. I like them because they are fun to think about but they also remind me how easy it for intuition to lead to wrong conclusions when not applied under the right circumstances.
The Monty Hall problem is a classic. I like it because it posed with simple language and hides it’s complexity. The first time you hear the puzzle you have a good chance of answering correctly (50⁄50). However, once you start to think about the reason for your answer you might need to grab a beer and get ready to think a little bit. As the story goes, one of the 20th centuries most famous mathematicians, Paul Erdos, needed several days before he was convinced by the truth of the proposed solution.
I had a coffee on campus with a friend in the Engineering department. To him, it was completely obvious that the way that perception should work is that your perceptions should recover exactly what is contained in the distribution of light that strikes the eye. It was an interesting discussion and the following sums up some of our discussion.
The story of colour vision begins in a part of the eye known as the retina.
The Titanic left on it’s maiden voyage on April 10, 1912 from Southampton to New York City. It is one of the most recognizable and iconic disasters of the 20th century. Of the 2,224 passengers and crew that set sail about 1500 of them perished when the ship hit an iceberg in the North Atlantic. The catastrophe led to Engineers rethinking the idea that a combination of hull size and durable steel would result in an unsinkable mass.
The Alamo Draft House is a local theatre company here in Austin. Their bread and butter is putting on the current hits but they also make a solid focus on showing cult hits. Over at the Ritz yesterday they put on the Princess Bride (1987) a love story staring a young Claire Underwood (Robin Wright) in the innocent days before being corrupted by Frank and the dirty lies of the US Senate.
A historical map distributed by the Rand McNally company. Time goes down the map and the relative size of the empire is given by the amount of area that it takes up at any specific time. What strikes me is the historical continuity presented in the map. For example, the Chinese empires rose and fell, but the civilization itself has remained active throughout all of recorded history.
We can also see the emergence of the Roman Empire in classical antiquity and its scale on the map shows the behemoth that it became.