I can make something almost impossible happen. And so can you.
Let's start by defining what "almost impossible" means. Less than one-in-a-trillion chance? How about less than one in a trillion-trillion chance? One in a trillion-trillion-trillion chance?
Ok, lets take a breath here. What's this trillion-trillion and trillion-etc stuff?
(In my observation, economists say million, billion, trillion, and all their audiences hear is "big number." Innumeracy over scale has bad consequences when applied to public policy.)
One trillion is 1,000,000,000,000. (Yes, I'm using American billions, pretty much like everyone else now does.) This is written as $10^{12}$. A trillion trillion is $10^{12} \times 10^{12} = 10^{24}$ and a trillion-trillion-trillion is $10^{36}$, a one followed by thirty-six zeros.
To put that number in perspective, the age of the Earth is about $4.5$ billion years, or about $1.42 \times 10^{17}$ seconds. That's 142,000 trillion seconds. Note that this is much smaller than a trillion-trillion seconds (it's over one seven-millionth of a trillion-trillion), let alone a trillion-trillion-trillion. If you had seven million planets the same age as the Earth, and you picked at random one specific second in the history in one specific planet you'd would have about a one in a trillion-trillion chance of picking this precise second on this planet. A one in a trillion-trillion-trillion chance is one trillion times smaller than that.
So, something that has a one in a trillion-trillion-trillion chance of happening has to be a very low probability event. Shall we call anything less likely than that "almost impossible"? We shall.
So, here's how I make something almost impossible happen, over and over again, and you can too: shuffle a deck of cards.
Using only 52 cards (no jokers), there are $52! = 52\times 51 \times \ldots \times 2$ possible card shuffles, and $52! \approx 8.1 \times 10^{67}$. That number is $8.1\times 10^{31}$ times bigger than a trillion-trillion-trillion.
And yet, every card shuffle produces an event with 1-in-$8.1 \times 10^{67}$ probability. You and I can generate scores of these "almost impossible" events using a simple deck of cards.
(A little thinking will lead an attentive reader to the solution to this apparent paradox. It's not a paradox. I will post a solution here in a few days, if I remember :-)
-- -- -- --
Just for fun, a simple brain teaser:
Imagine you have two decks of 52 cards (blue and red); what has more possible combinations, shuffling the two decks together and dividing into two piles of 52 cards by separating in the middle of the full shuffled two decks, or shuffling the two decks separately each into its pile?
(Yes, it's obvious for anyone conversant with combinatorics, but apparently not everyone is conversant with combinatorics. Common answer: "it's the same.")
Sunday, January 24, 2016
Friday, January 22, 2016
Cook and teach your children to cook
Cooking has health benefits
If you cook, you control what goes in your food. That's reason enough to do it.
As for all the bad things in food that isn't prepared by you or your family, I recommend the book Salt Sugar and Fat. It describes how the processed food industry, and to a smaller extent restaurants, make choices that are good for business, good for taste, and bad for your health.
Cooking your own food allows for better control of what is ingested, a lesson that should be cultivated in children as early as possible. It also serves as a mechanism for avoiding excesses. For example, making your own french fries reduces the amount of french fries consumed, because of all the trouble it is to make them at home, from scratch, and clean up afterwards.
Cooking is educational
It's a great way to introduce science. Physics, chemistry, arithmetic, measuring, biology, nutrition (duh). Something as simple as making a vinaigrette illustrates different densities (vinegar and oil), solutions (salt in vinegar), immiscible liquids, emulsifiers (mustard), the importance of measuring quantities , acids (vinegar), fats (lipids), salts.
Cooking teaches production engineering. (Well, it is production engineering. Think about it.) Planning, organizing, executing, measuring, controlling, failing and recovering (when in doubt add butter), scaling recipes up and down, dealing with spoilage and leftovers, balancing choices (making baklava takes a lot of time, but sometimes you really want baklava). It can also be used to bring up the matters of cost management. Never too soon to teach kids fiscal prudence.
Cooking creates opportunities to talk about history, culture, and geography. Yes, food itself could be used to introduce these topics, but if you do it in the preparation (and the purchasing) it will be better remembered, and it fills up the time when things are in the oven or fermenting.
(As a side benefit, cooking also educates the parents, as they need to be prepared for teaching the children.)
Cooking develops important traits
Discipline. Like most interactions with the real world, cooking utensils and ingredients are very hard to emotionally blackmail or bargain with.
Patience, carefulness, study habits, observation skills. Because there's a clear payoff at the end, the food, cooking can be used to develop these important life skills. Baking and sauce reductions, for example, teach patience and carefulness. Analyzing recipes and procuring fresh ingredients develop study habits and observation skills.
Plan, Prepare, Work, Clean-up. Many intellectual experiences or intellectual descriptions of physical experiences are too circumscribed. Cooking provides a teaching laboratory for thinking about interaction with the real world: plan the work (and the shopping trip); organize the resources into a mise-en-place; do the work (this is the part that matches most intellectual tasks, the carefully circumscribed activity); clean-up and deal with the consequences.
Rule-following and creativity in balance. This is a very important life lesson, that many people get wrong. There are times when following the rules (the recipe) is essential, especially for beginners. And there are times, usually after a long period of following the recipes so that their rationale is well understood, for deviating and being creative. Creativity is not randomness borne of ignorance, it's willful deviation from rules borne of deep understanding of those rules.
Respect for manual work. Many educated people have a latent bigotry against manual work. Cooking, by integrating the intellectual, the creative, and a lot of physical work, acts as prophylaxis against that bigotry. (Lifting weights and playing a musical instrument partially remove this bigotry as well.)
Cooking is a bonding experience
Humans are, or so I'm told, social animals; apparently, you people like to do things in groups. Cooking presents many opportunities to develop teamwork and leadership skills. And it's extremely meritocratic, as the taste of food doesn't depend on the personal characteristics of those preparing it, other than through the actual cooking.
Family time is good, shared family work much better. Cooperating towards a shared goal creates a stronger bond than just spending time together. Teaching your children to cook is an act of love. It's a lot of work, of course, but that's part of the whole "love" thing.
Cooking has physicality
When things are done in the real world, there's no 'preferences' panel, no 'undo' button. Interacting with physical objects teaches important lessons about reality in a way that no intellectual task (reading, watching, simulating on digital devices) can: things smell, break, are hot, sharp, sticky; sauces separate, soufflés deflate, meat burns, vegetables wilt, frozen desserts melt, cakes crumble, liquids spill.
Also, for small children, cooking provides both opportunity and motivation for developing dexterity and sensory skills. Dragging a finger across the screen of an iPad is not adequate activity to develop motor skills and there are more senses than vision and audition.
Cooking is an important skill to have
Even if all the above benefits were unimportant, which they aren't, cooking is an important skill to have.
You don't have to be a prepper to understand the value of being able to turn ingredients into a meal; you don't have to be a food critic (better yet, a gourmet) to appreciate that a little bit of knowledge about flavor creation and combination can make a lot of difference; and you don't have to be an hypochondriac control freak to be suspicious of the quality of ready-to-eat meals.
Most of all, cooking has a smooth learning curve which makes it one of the easier skills to acquire and maintain, and the results are often delicious and almost always edible.
Cook and teach your children to cook.
If you cook, you control what goes in your food. That's reason enough to do it.
As for all the bad things in food that isn't prepared by you or your family, I recommend the book Salt Sugar and Fat. It describes how the processed food industry, and to a smaller extent restaurants, make choices that are good for business, good for taste, and bad for your health.
Cooking your own food allows for better control of what is ingested, a lesson that should be cultivated in children as early as possible. It also serves as a mechanism for avoiding excesses. For example, making your own french fries reduces the amount of french fries consumed, because of all the trouble it is to make them at home, from scratch, and clean up afterwards.
Cooking is educational
It's a great way to introduce science. Physics, chemistry, arithmetic, measuring, biology, nutrition (duh). Something as simple as making a vinaigrette illustrates different densities (vinegar and oil), solutions (salt in vinegar), immiscible liquids, emulsifiers (mustard), the importance of measuring quantities , acids (vinegar), fats (lipids), salts.
Cooking teaches production engineering. (Well, it is production engineering. Think about it.) Planning, organizing, executing, measuring, controlling, failing and recovering (when in doubt add butter), scaling recipes up and down, dealing with spoilage and leftovers, balancing choices (making baklava takes a lot of time, but sometimes you really want baklava). It can also be used to bring up the matters of cost management. Never too soon to teach kids fiscal prudence.
Cooking creates opportunities to talk about history, culture, and geography. Yes, food itself could be used to introduce these topics, but if you do it in the preparation (and the purchasing) it will be better remembered, and it fills up the time when things are in the oven or fermenting.
(As a side benefit, cooking also educates the parents, as they need to be prepared for teaching the children.)
Cooking develops important traits
Discipline. Like most interactions with the real world, cooking utensils and ingredients are very hard to emotionally blackmail or bargain with.
Patience, carefulness, study habits, observation skills. Because there's a clear payoff at the end, the food, cooking can be used to develop these important life skills. Baking and sauce reductions, for example, teach patience and carefulness. Analyzing recipes and procuring fresh ingredients develop study habits and observation skills.
Plan, Prepare, Work, Clean-up. Many intellectual experiences or intellectual descriptions of physical experiences are too circumscribed. Cooking provides a teaching laboratory for thinking about interaction with the real world: plan the work (and the shopping trip); organize the resources into a mise-en-place; do the work (this is the part that matches most intellectual tasks, the carefully circumscribed activity); clean-up and deal with the consequences.
Rule-following and creativity in balance. This is a very important life lesson, that many people get wrong. There are times when following the rules (the recipe) is essential, especially for beginners. And there are times, usually after a long period of following the recipes so that their rationale is well understood, for deviating and being creative. Creativity is not randomness borne of ignorance, it's willful deviation from rules borne of deep understanding of those rules.
Respect for manual work. Many educated people have a latent bigotry against manual work. Cooking, by integrating the intellectual, the creative, and a lot of physical work, acts as prophylaxis against that bigotry. (Lifting weights and playing a musical instrument partially remove this bigotry as well.)
Cooking is a bonding experience
Humans are, or so I'm told, social animals; apparently, you people like to do things in groups. Cooking presents many opportunities to develop teamwork and leadership skills. And it's extremely meritocratic, as the taste of food doesn't depend on the personal characteristics of those preparing it, other than through the actual cooking.
Family time is good, shared family work much better. Cooperating towards a shared goal creates a stronger bond than just spending time together. Teaching your children to cook is an act of love. It's a lot of work, of course, but that's part of the whole "love" thing.
Cooking has physicality
When things are done in the real world, there's no 'preferences' panel, no 'undo' button. Interacting with physical objects teaches important lessons about reality in a way that no intellectual task (reading, watching, simulating on digital devices) can: things smell, break, are hot, sharp, sticky; sauces separate, soufflés deflate, meat burns, vegetables wilt, frozen desserts melt, cakes crumble, liquids spill.
Also, for small children, cooking provides both opportunity and motivation for developing dexterity and sensory skills. Dragging a finger across the screen of an iPad is not adequate activity to develop motor skills and there are more senses than vision and audition.
Cooking is an important skill to have
Even if all the above benefits were unimportant, which they aren't, cooking is an important skill to have.
You don't have to be a prepper to understand the value of being able to turn ingredients into a meal; you don't have to be a food critic (better yet, a gourmet) to appreciate that a little bit of knowledge about flavor creation and combination can make a lot of difference; and you don't have to be an hypochondriac control freak to be suspicious of the quality of ready-to-eat meals.
Most of all, cooking has a smooth learning curve which makes it one of the easier skills to acquire and maintain, and the results are often delicious and almost always edible.
Cook and teach your children to cook.
Sunday, January 3, 2016
Recognizing, knowing, understanding.
The future needs people who really understand technical material, but I fear what now passes for technical education (including self-education) lacks depth.
Reusing my example of the Heisenberg (physics, not cristal meth) joke, namely,
At the recognition level, Alex associates "Heisenberg" with "science reference" and decides to laugh to appear educated. I find that most people who "love" science are like Alex. I also find people like this in my field of work, effectively LARPing at being experts.
At the knowing level, Blake has some idea that Heisenberg said that you can't measure speed and position together with arbitrary precision. Blake also knows that Heisenberg was talking about electrons or other particles, so applying his "rule" to a car must be hilarious.
At the understanding level, Chris can do what I did and spoil a joke by making calculations. From the linked post:
I think that there's some merit in trying to improve from recognition to knowledge and from knowledge to understanting. So here are a couple of observations on that:
The main problem in most cases, as I see it, is not of ability or opportunity but rather of motivation: if Alex gets social cachet for "loving" science just by recognizing a "science situation," why put in the effort to learn some science (or other technical material)?
There's a trap, however, for people who decide that they want knowledge: because of the identity problem in science popularization, most of the more popular sources are designed for recognition only, not understanding.
I find that books, lectures, etc. from active researchers or practitioners in the technical field (say Leonard Susskind instead of Neil deGrasse Tyson) generally mean better chance of knowledge rather than recognition. Even when non-researchers and non-practitioners are better at showmanship (mistaken for communication skils), it's worth a little effort to get real knowledge from those who understand it and don't treat their readers or audiences as an echo chamber.
(As for television shows, except for a few that are based on books by active researchers, they are to be avoided: they are not reliable sources, not even for the recognition level.)
Problem sets. That's the solution.
Well, to be precise, the step from basic knowledge to understanding has two parts: first, learn the concepts, principles, and tools of the field; second, practice them with incrementally difficult problems.
For the Heisenberg example, some of the elements needed for understanding are:
It then becomes a matter of how much practice and how much effort you're willing to put in: at this level, the difference between amateurs and professionals is that amateurs practice something until they get it right, professionals practice until they can't get it wrong.
Reusing my example of the Heisenberg (physics, not cristal meth) joke, namely,
Police officer: "Sir, do you realize you were going 67.58 MPH?there's a number of levels at which we can understand it.
Werner Heisenberg: "Oh great. Now I'm lost."
At the recognition level, Alex associates "Heisenberg" with "science reference" and decides to laugh to appear educated. I find that most people who "love" science are like Alex. I also find people like this in my field of work, effectively LARPing at being experts.
At the knowing level, Blake has some idea that Heisenberg said that you can't measure speed and position together with arbitrary precision. Blake also knows that Heisenberg was talking about electrons or other particles, so applying his "rule" to a car must be hilarious.
At the understanding level, Chris can do what I did and spoil a joke by making calculations. From the linked post:
A simplified form of Heisenberg's inequality, good enough for our purposes, is
$\qquad \Delta p \, \Delta x \ge h $
Going by orders of magnitude alone, assuming that the mass of Heisenberg plus car is in the order of 1000 kg, and noting that the speed is given to a precision of 0.01 mi/h, an order of magnitude of 10 m/s, with $h \approx 10^{-34}$ Js, we get a $\Delta x$ of the order of
$\qquad \Delta x \approx \frac{ 10^{-34} }{10 000} = 10^{-38}$ m.There are degrees of understanding, from the ability to make use of the uncertainty principle, as above, to deeper understanding of what that means for what the universe is like. But at the most basic level of understanding, you should be able to operationalize knowledge into decision, calculation, program, etc.
I think that there's some merit in trying to improve from recognition to knowledge and from knowledge to understanting. So here are a couple of observations on that:
Recognition to knowledge
The main problem in most cases, as I see it, is not of ability or opportunity but rather of motivation: if Alex gets social cachet for "loving" science just by recognizing a "science situation," why put in the effort to learn some science (or other technical material)?
There's a trap, however, for people who decide that they want knowledge: because of the identity problem in science popularization, most of the more popular sources are designed for recognition only, not understanding.
I find that books, lectures, etc. from active researchers or practitioners in the technical field (say Leonard Susskind instead of Neil deGrasse Tyson) generally mean better chance of knowledge rather than recognition. Even when non-researchers and non-practitioners are better at showmanship (mistaken for communication skils), it's worth a little effort to get real knowledge from those who understand it and don't treat their readers or audiences as an echo chamber.
(As for television shows, except for a few that are based on books by active researchers, they are to be avoided: they are not reliable sources, not even for the recognition level.)
Knowledge to understanding
Problem sets. That's the solution.
Well, to be precise, the step from basic knowledge to understanding has two parts: first, learn the concepts, principles, and tools of the field; second, practice them with incrementally difficult problems.
For the Heisenberg example, some of the elements needed for understanding are:
Concepts: speed, mass, momentum;My rule-of-thumb for learning technical material is $1\%$ from being a passive member of an audience (to a lecture or a video) or a passive reader (reading but not thinking); $9\%$ from actively studying the material (say, working through solved problems, making sure you understand all the steps in an example); and $90\%$ is practicing, in the lingo of academe solving problem sets.
Principles: uncertainty principle;
Tools: order-of-magnitude reasoning.
It then becomes a matter of how much practice and how much effort you're willing to put in: at this level, the difference between amateurs and professionals is that amateurs practice something until they get it right, professionals practice until they can't get it wrong.
Understanding something is so much better than just knowing it, and knowing it so much better than just recognizing it. It worth the effort and the change in attitude required. At least for me it is.
Friday, January 1, 2016
Best books I read in 2015
I read a lot of work-related books, but in this post I'm excluding those.
Best fiction book is a tie between:
The Martian by Andy Weir, for its hard-science attempt. Best description of the book is Andy Ihnatko's (I think, I heard it on a podcast, so I may be wrong): think of it as the 5-minute scene in Apollo 13 when the engineers have to solve the $\mathrm{CO}_{2}$ scrubber problem, except it's an entire book like that. I have quibbles with the science here and there, and its stoichiometry is a bit iffy, but overall -- well, it ties with a Neal Stephenson scifi novel, so that's a major achievement.
Seveneves by Neal Stephenson, for the usual NS reasons: well-researched material, engaging mini-puzzles in the narrative, and interesting story. Plus the second novel that he added at the end, which most writers would have published as a separate book. A number of meta- and meta-meta- references for those of us who like that kind of thing. Despite being 1000-plus pages, I did my usual Stephenson-book thing and read it twice in a row.
Best non-scifi fiction goes to a French book; read the French version, if you can:
Soumission by Michel Houellebec ("Submission" in English), a book that skewers a number of sacred cows of the politically correct, while presenting an… interesting, that's the word, view of Humanities academic life in Europe. Two favorite excerpts, among many:
On peut même, dans une certaine mesure, les persuader de la haute valeur érotique des professeurs d'université (We can, to a certain extent, persuade [marriage brokers] of the high erotic value of university professors - JCS translation).
L'intellectuel en France n'avait pas à être responsable, ce n'était pas dans sa nature (French intellectuals are not expected to be responsible people, that's not in their nature - JCS translation).
Honorable mention in fiction to:
Code of Conduct by Brad Thor, which presents a scary end-of-civilization scenario, unfortunately all-too-possible. Sadly, there are people who actually cheer for that scenario. (I once met someone advocating for a world population of five million. That would be more than a $99.9\%$ reduction, a genocide unparalleled in history.)
Best science book was easier than usual, as I have cut down my reading of science popularization books in favor of reading science textbooks and research papers:
The Science of Interstellar by Kip Thorne is a companion to the movie Interstellar and explains some of the science underlying the story. For those who have the BluRay (like me), the book is a deeper and longer version of the special feature "The Science of Interstellar," with deeper explanations and a few speculative areas. Kip Thorne writes well for a general audience, but he doesn't baby-science the science: despite the accessible prose, thinking is required.
Honorable mention in science to
Dark Matter and the Dinosaurs by Lisa Randall, two concepts that aren't usually put together (as the intro says), is a tour of some new results and some old knowledge in physics written in accessible prose. Like Kip Thorne's book, it requires thinking. (It lost to Thorne because his book had a movie and a documentary attached. :-)
Best nonfiction non-science goes to a combination of two books by the same author:
The 4th-Generation Warfare Handbook and On War by William S. Lind, both illustrate the change in warfare from 3rd-Generation maneuver warfare to 4th-Generation warfare by non-state agents. On War is a book of collected columns and includes quite a few that will jar sensibilities, even considering the topic. The Handbook reads like lecture notes or a textbook for the armed forces or law enforcement, but accessible to the general public. Fair warning: once you learn some of these things, your level of paranoia will increase and your general happiness with the world (hitherto achieved through naïveté) will decrease.
Honorable mention in nonfiction to
The Master Algorithm by Pedro Domingues, a book that will make for many entertaining family dinners for machine learning and artificial intelligence practitioners and researchers. (Because their relatives who read the book will believe that they understand the material to the point where they can debate experts, and that's always entertaining to see.) It covers machine learning at a basic level and makes it easier for non-experts to read articles on automation and decision-support with some understanding of what's going on.
The last book I read in 2015 was a re-read,
Castles of Steel by Robert K Massie, a history of naval combat in World War I. I read it before, of course, when it came out in 2004. Niche appeal to those of us who like to know history (and not from Captain America comic books), have an interest in Europe and Western Civilization, and are nautically-inclined. Despite the topic, little overlap with Dreadnought, by the same author.
Best fiction book is a tie between:
The Martian by Andy Weir, for its hard-science attempt. Best description of the book is Andy Ihnatko's (I think, I heard it on a podcast, so I may be wrong): think of it as the 5-minute scene in Apollo 13 when the engineers have to solve the $\mathrm{CO}_{2}$ scrubber problem, except it's an entire book like that. I have quibbles with the science here and there, and its stoichiometry is a bit iffy, but overall -- well, it ties with a Neal Stephenson scifi novel, so that's a major achievement.
Seveneves by Neal Stephenson, for the usual NS reasons: well-researched material, engaging mini-puzzles in the narrative, and interesting story. Plus the second novel that he added at the end, which most writers would have published as a separate book. A number of meta- and meta-meta- references for those of us who like that kind of thing. Despite being 1000-plus pages, I did my usual Stephenson-book thing and read it twice in a row.
Best non-scifi fiction goes to a French book; read the French version, if you can:
Soumission by Michel Houellebec ("Submission" in English), a book that skewers a number of sacred cows of the politically correct, while presenting an… interesting, that's the word, view of Humanities academic life in Europe. Two favorite excerpts, among many:
On peut même, dans une certaine mesure, les persuader de la haute valeur érotique des professeurs d'université (We can, to a certain extent, persuade [marriage brokers] of the high erotic value of university professors - JCS translation).
L'intellectuel en France n'avait pas à être responsable, ce n'était pas dans sa nature (French intellectuals are not expected to be responsible people, that's not in their nature - JCS translation).
Honorable mention in fiction to:
Code of Conduct by Brad Thor, which presents a scary end-of-civilization scenario, unfortunately all-too-possible. Sadly, there are people who actually cheer for that scenario. (I once met someone advocating for a world population of five million. That would be more than a $99.9\%$ reduction, a genocide unparalleled in history.)
Best science book was easier than usual, as I have cut down my reading of science popularization books in favor of reading science textbooks and research papers:
The Science of Interstellar by Kip Thorne is a companion to the movie Interstellar and explains some of the science underlying the story. For those who have the BluRay (like me), the book is a deeper and longer version of the special feature "The Science of Interstellar," with deeper explanations and a few speculative areas. Kip Thorne writes well for a general audience, but he doesn't baby-science the science: despite the accessible prose, thinking is required.
Honorable mention in science to
Dark Matter and the Dinosaurs by Lisa Randall, two concepts that aren't usually put together (as the intro says), is a tour of some new results and some old knowledge in physics written in accessible prose. Like Kip Thorne's book, it requires thinking. (It lost to Thorne because his book had a movie and a documentary attached. :-)
Best nonfiction non-science goes to a combination of two books by the same author:
The 4th-Generation Warfare Handbook and On War by William S. Lind, both illustrate the change in warfare from 3rd-Generation maneuver warfare to 4th-Generation warfare by non-state agents. On War is a book of collected columns and includes quite a few that will jar sensibilities, even considering the topic. The Handbook reads like lecture notes or a textbook for the armed forces or law enforcement, but accessible to the general public. Fair warning: once you learn some of these things, your level of paranoia will increase and your general happiness with the world (hitherto achieved through naïveté) will decrease.
Honorable mention in nonfiction to
The Master Algorithm by Pedro Domingues, a book that will make for many entertaining family dinners for machine learning and artificial intelligence practitioners and researchers. (Because their relatives who read the book will believe that they understand the material to the point where they can debate experts, and that's always entertaining to see.) It covers machine learning at a basic level and makes it easier for non-experts to read articles on automation and decision-support with some understanding of what's going on.
The last book I read in 2015 was a re-read,
Castles of Steel by Robert K Massie, a history of naval combat in World War I. I read it before, of course, when it came out in 2004. Niche appeal to those of us who like to know history (and not from Captain America comic books), have an interest in Europe and Western Civilization, and are nautically-inclined. Despite the topic, little overlap with Dreadnought, by the same author.
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