Frederick's interests

Frederick's posts

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They mention placing it on oil rigs, I wonder if it can be made small enough to fit on life boats.

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A moving, disturbing article.

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A nice visualization to explain the kernel trick used in Support Vector Machines to learn a nonlinear classifying rule by turning it into a linearly separable problem in a higher dimension. It seems that (certain types of) deep learning neural nets achieve a similar thing when they introduce hidden variables to increase the dimensionality of the problem.

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Platonist to Quinean ...to Structuralist?

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I like the question at the end, about whether math is invented or discovered. His answer is slightly evasive. He says that inventing or discovering math is a human activity, and the question needs to be answered about humans as a whole. So it can't be answered within mathematics, it needs some other science, presumably cognitive science. Considering math within cognitive science, I think you can ask how one mathematical thinker discovers the mathematical idea of another human, and decides that they agree. In other words, it is an epistemological or cognitive problem, rather than a metaphysical problem. And it has something to do with fixing the identity criteria for some mathematical object or family of objects (or finding natural identity criteria, for some purpose), which is what homotopy type theory is investigating.

Brouwer talked about mathematical intuitions, attributing them to an ideal creative subject. For me, the ideal subject is like the shared scheme of individuation for mathematical concepts, which exists in history among a community of mathematical thinkers who agree that some things are (provably) true. Among humans working within that scheme, there are many things that are already "known" to the ideal subject, but not to some human who is still learning. A human discovers what is already out there in the scheme, explicitly published or implicit lemmas or folklore. But the community of research mathematicians is pushing the boundaries of the shared scheme all the time. And we are not just talking about new proofs, but also new expositions, that reformulate old knowledge in modern vocabulary. This shifts the landscape of the scheme of individuation over time. Old truths usually aren't made false, they just become special cases of more general truths (and may become less interesting from a modern point of view, or in danger of getting misinterpreted if you are incautiously using the modern vocabulary).

If we allow ourselves to drift back towards metaphysical questions about the nature of things, and we take mathematics as something that happens in the mind or psuchos or soul, we can ask: are souls and their ideas created or discovered, are they constructed in a mortal body or are they already immortally existent only to be discovered? In my own thinking, souls (the seat of mathematical thinking and judgement) are constructed in biology, and one soul cognitively discovers the soul or mind of other humans. And if we look beyond the individual soul, and consider the collective soul of Brouwer's ideal mathematical subject, mathematical truths can certainly look eternal, Platonistically already there to be discovered not invented. But the shared scheme of individuation, and certainly the vocabulary in natural language and notation, of the community of math thinkers shifts gradually over time. Old truths are seldom overturned, they still seem eternal, but they get put in a new position relative to the current scheme, and so their meaning shifts subtly over the centuries or decades.

Brouwer talked about mathematical intuitions, attributing them to an ideal creative subject. For me, the ideal subject is like the shared scheme of individuation for mathematical concepts, which exists in history among a community of mathematical thinkers who agree that some things are (provably) true. Among humans working within that scheme, there are many things that are already "known" to the ideal subject, but not to some human who is still learning. A human discovers what is already out there in the scheme, explicitly published or implicit lemmas or folklore. But the community of research mathematicians is pushing the boundaries of the shared scheme all the time. And we are not just talking about new proofs, but also new expositions, that reformulate old knowledge in modern vocabulary. This shifts the landscape of the scheme of individuation over time. Old truths usually aren't made false, they just become special cases of more general truths (and may become less interesting from a modern point of view, or in danger of getting misinterpreted if you are incautiously using the modern vocabulary).

If we allow ourselves to drift back towards metaphysical questions about the nature of things, and we take mathematics as something that happens in the mind or psuchos or soul, we can ask: are souls and their ideas created or discovered, are they constructed in a mortal body or are they already immortally existent only to be discovered? In my own thinking, souls (the seat of mathematical thinking and judgement) are constructed in biology, and one soul cognitively discovers the soul or mind of other humans. And if we look beyond the individual soul, and consider the collective soul of Brouwer's ideal mathematical subject, mathematical truths can certainly look eternal, Platonistically already there to be discovered not invented. But the shared scheme of individuation, and certainly the vocabulary in natural language and notation, of the community of math thinkers shifts gradually over time. Old truths are seldom overturned, they still seem eternal, but they get put in a new position relative to the current scheme, and so their meaning shifts subtly over the centuries or decades.

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2007, the federal government seizes control of indigenous communities. 2008, Sorry Day.

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Functional Programming Principles in Scala. Study goup, anyone?

Coursera is hosting a course offered by EPFL (the Swiss tech university in Lausanne) starting Nov 7. I am looking for people in Manila who are interested in taking the course and working together in a study group. It is the first course in a 5-part specialization in Scala Programming. Apparently, the course is being led by Martin Odersky, who invented the Scala language at EPFL.

Scala language was designed for scalability, and is used in the development of Apache Spark and Spark Applications.

Coursera is hosting a course offered by EPFL (the Swiss tech university in Lausanne) starting Nov 7. I am looking for people in Manila who are interested in taking the course and working together in a study group. It is the first course in a 5-part specialization in Scala Programming. Apparently, the course is being led by Martin Odersky, who invented the Scala language at EPFL.

Scala language was designed for scalability, and is used in the development of Apache Spark and Spark Applications.

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"The most recent iteration of the IOCs’ business model emerged during the 1990s and was built upon three pillars: maximizing shareholder value based on a strategy that provided benchmarks for financial returns, maximizing bookable reserves and minimizing costs partly based on outsourcing. This model began to face serious challenges as the operating environment changed. It is the accumulation of these challenges, on top of those evident since the 1970s, and the failure of the IOCs to adapt to them that indicates that their old business model is gradually dying.

The [International Oil Companies] have been able to survive over the last quarter of a century, but signs that their business model is faltering have recently begun to show. As well as poor financial performances, the symptoms include growing shareholder disillusion with a business model rooted in assumptions of ever-growing oil demand, oil scarcity and the need to increase bookable reserves, all of which increasingly lack validity."

The [International Oil Companies] have been able to survive over the last quarter of a century, but signs that their business model is faltering have recently begun to show. As well as poor financial performances, the symptoms include growing shareholder disillusion with a business model rooted in assumptions of ever-growing oil demand, oil scarcity and the need to increase bookable reserves, all of which increasingly lack validity."

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https://www.technologyreview.com/s/602344/the-extraordinary-link-between-deep-neural-networks-and-the-nature-of-the-universe/

"The answer is that the universe is governed by a tiny subset of all possible functions. In other words, when the laws of physics are written down mathematically, they can all be described by functions that have a remarkable set of simple properties.

"So deep neural networks don’t have to approximate any possible mathematical function, only a tiny subset of them.

"To put this in perspective, consider the order of a polynomial function, which is the size of its highest exponent. So a quadratic equation like y=x2 has order 2, the equation y=x24 has order 24, and so on.

"Obviously, the number of orders is infinite and yet only a tiny subset of polynomials appear in the laws of physics. “For reasons that are still not fully understood, our universe can be accurately described by polynomial Hamiltonians of low order,” say Lin and Tegmark. Typically, the polynomials that describe laws of physics have orders ranging from 2 to 4."

"The answer is that the universe is governed by a tiny subset of all possible functions. In other words, when the laws of physics are written down mathematically, they can all be described by functions that have a remarkable set of simple properties.

"So deep neural networks don’t have to approximate any possible mathematical function, only a tiny subset of them.

"To put this in perspective, consider the order of a polynomial function, which is the size of its highest exponent. So a quadratic equation like y=x2 has order 2, the equation y=x24 has order 24, and so on.

"Obviously, the number of orders is infinite and yet only a tiny subset of polynomials appear in the laws of physics. “For reasons that are still not fully understood, our universe can be accurately described by polynomial Hamiltonians of low order,” say Lin and Tegmark. Typically, the polynomials that describe laws of physics have orders ranging from 2 to 4."

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