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A large part of our civilisation rests on the shoulders of one medieval monk: Thomas Aquinas. Amid the turmoil of life, riddled with wickedness and pain, he would insist that our world is good. And all our success is built on this belief. Note: Before we start, let’s get one thing out of the way: Thomas Aquinas is clearly a Christian thinker, a Saint even. Yet he was also a brilliant philosopher. So even if you consider yourself agnostic or an atheist, stay with me, you will still enjoy his ideas. What is good? Thomas’ argument is rooted in Aristotle’s concept of goodness: Something is good if it fulfills its function. Aristotle had illustrated this idea with a knife. A knife is good to the extent that it cuts well. He made a distinction between an actual knife and its ideal function. That actual thing in your drawer is the existence of a knife. And its ideal function is its essence—what it means to be a knife: to cut well. So everything is separated into its existence and its ideal essence. And this is also true for humans: We have an ideal conception of what the essence of a human […] The post Thomas Aquinas — The world is divine! appeared first on Ralph Ammer.
About 2300 years ago, the great Chinese thinker Xunzi 荀⼦ wrote: “Human nature is bad“. But he wasn’t just having a bad day. The question—Are humans fundamentally good or bad?—is a major fork in the road. How you answer this question profoundly impacts your morals and how you live your life. Previous to Xunzi, another famous scholar had claimed that human nature was inherently good. Mengzi 孟子: Human nature is good The Ox Hill Mengzi had illustrated his idea with a story about a wooded hill. After the trees get chopped down and the sprouts are grazed by animals, the hill appears barren and unfruitful. He compares this hill to someone who can’t bring forth his good character under bad circumstances. For him, goodness is an integral part of every person’s nature. It merely requires the right circumstances to emerge. Goodness will grow forth naturally from every person if no one interferes. Willows and Bowls Someone suggested to Mengzi that a good character had to be forged from a man’s nature like bowls were made from a tree. Mengzi objected that a tree must be violated in order to be turned into useful bowls. He can’t accept the comparison between […] The post Xunzi vs. Mengzi – Are People (No) Good? appeared first on Ralph Ammer.
Should we just live in the moment? In “Matter and Memory” the French philosopher Henri Bergson claims that this is not even possible. 1. Perception is physical First of all: How do we perceive the “current moment” anyway? Bergson suggests that the whole point of perception is action. For example, when some single-cell organism touches an obstacle, it moves away. That is the whole point of perception: to move in the right direction, to find food, to not be food—to survive. Perception serves future action, not insight. Accordingly, our brain is fully embedded in the material world and responds to the movements around it. Bergson refers to such a purely physical reaction as pure perception. Yet he acknowledges that we are more complicated than single-celled organisms. The movements of our environment have to make their way through our complex sensory system with all its twists and turns. And this leaves us more options on how to act. So we don’t just react like a single-celled organism, we can choose from a range of potential movements. But how? We remember. 2. Memory is temporal Bergson distinguishes two kinds of memories: Some memories have become part of our body, they are a […] The post Bergson — Why we live in the past appeared first on Ralph Ammer.
To “animate” means to breathe life into things. In these 5 exercises we make stones come alive. Preparation To get started I suggest this simple setup for you to try at home: Ready? Let’s go! Thinking in time Stop-motion is simple: Take a picture, move the object, take the next picture, move the object, etc. Once you are done, you can play back all those images as a little movie. Tip: You can do the following exercises exactly as shown here or play around with them. Just make sure to have fun! Exercise 1: Timing Turn a stone into a bouncing ball. Start with a stone above the middle of the page and hit the record button. Then move it down a little, take the next frame, move it again, and so on. Once it has reached the bottom, gradually move it up again until it is back to its starting position. Tip: At first you will notice that our steps are too big. As a result the animation plays way too fast! Just start over and make the steps smaller. Another tip: You can make the movement more natural by varying the distances. And you can make the “ball” […] The post A quick beginner’s guide to animation appeared first on Ralph Ammer.
You are awake. You think and you feel. But what is it that is doing all this thinking and feeling? We call it “consciousness” and over 100 years ago the philosopher Edmund Husserl made a bold attempt to uncover its secrets. Subjective experience is private The thing is: Consciousness is not “out there”, it is “in here“. It is personal and subjective. When I say that I like squirrels or that my foot hurts, then you will have to take my word for it. You can’t know what it is like to be me, and I cannot know what it is like to be you. Consciousness can only be observed from the inside, not from the outside. Since we can’t see the world through other peoples’ eyes, their experience remains deeply mysterious to us. Thus we all see the world differently. And this can lead to bitter conflict. Science is based on objective insight One way to overcome such conflict is to take an objective position. We take a neutral view from outside and focus on the things that we can all agree upon. We have learned to see ourselves “from the outside”. In fact, we can build a whole […] The post Edmund Husserl — Consciousness appeared first on Ralph Ammer.
More in programming
I’ve long been interested in new and different platforms. I ran Debian on an Alpha back in the late 1990s and was part of the Alpha port team; then I helped bootstrap Debian on amd64. I’ve got somewhere around 8 Raspberry Pi devices in active use right now, and the free NNCPNET Internet email service … Continue reading ARM is great, ARM is terrible (and so is RISC-V) →
In my first interview out of college I was asked the change counter problem: Given a set of coin denominations, find the minimum number of coins required to make change for a given number. IE for USA coinage and 37 cents, the minimum number is four (quarter, dime, 2 pennies). I implemented the simple greedy algorithm and immediately fell into the trap of the question: the greedy algorithm only works for "well-behaved" denominations. If the coin values were [10, 9, 1], then making 37 cents would take 10 coins in the greedy algorithm but only 4 coins optimally (10+9+9+9). The "smart" answer is to use a dynamic programming algorithm, which I didn't know how to do. So I failed the interview. But you only need dynamic programming if you're writing your own algorithm. It's really easy if you throw it into a constraint solver like MiniZinc and call it a day. int: total; array[int] of int: values = [10, 9, 1]; array[index_set(values)] of var 0..: coins; constraint sum (c in index_set(coins)) (coins[c] * values[c]) == total; solve minimize sum(coins); You can try this online here. It'll give you a prompt to put in total and then give you successively-better solutions: coins = [0, 0, 37]; ---------- coins = [0, 1, 28]; ---------- coins = [0, 2, 19]; ---------- coins = [0, 3, 10]; ---------- coins = [0, 4, 1]; ---------- coins = [1, 3, 0]; ---------- Lots of similar interview questions are this kind of mathematical optimization problem, where we have to find the maximum or minimum of a function corresponding to constraints. They're hard in programming languages because programming languages are too low-level. They are also exactly the problems that constraint solvers were designed to solve. Hard leetcode problems are easy constraint problems.1 Here I'm using MiniZinc, but you could just as easily use Z3 or OR-Tools or whatever your favorite generalized solver is. More examples This was a question in a different interview (which I thankfully passed): Given a list of stock prices through the day, find maximum profit you can get by buying one stock and selling one stock later. It's easy to do in O(n^2) time, or if you are clever, you can do it in O(n). Or you could be not clever at all and just write it as a constraint problem: array[int] of int: prices = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8]; var int: buy; var int: sell; var int: profit = prices[sell] - prices[buy]; constraint sell > buy; constraint profit > 0; solve maximize profit; Reminder, link to trying it online here. While working at that job, one interview question we tested out was: Given a list, determine if three numbers in that list can be added or subtracted to give 0? This is a satisfaction problem, not a constraint problem: we don't need the "best answer", any answer will do. We eventually decided against it for being too tricky for the engineers we were targeting. But it's not tricky in a solver; include "globals.mzn"; array[int] of int: numbers = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8]; array[index_set(numbers)] of var {0, -1, 1}: choices; constraint sum(n in index_set(numbers)) (numbers[n] * choices[n]) = 0; constraint count(choices, -1) + count(choices, 1) = 3; solve satisfy; Okay, one last one, a problem I saw last year at Chipy AlgoSIG. Basically they pick some leetcode problems and we all do them. I failed to solve this one: Given an array of integers heights representing the histogram's bar height where the width of each bar is 1, return the area of the largest rectangle in the histogram. The "proper" solution is a tricky thing involving tracking lots of bookkeeping states, which you can completely bypass by expressing it as constraints: array[int] of int: numbers = [2,1,5,6,2,3]; var 1..length(numbers): x; var 1..length(numbers): dx; var 1..: y; constraint x + dx <= length(numbers); constraint forall (i in x..(x+dx)) (y <= numbers[i]); var int: area = (dx+1)*y; solve maximize area; output ["(\(x)->\(x+dx))*\(y) = \(area)"] There's even a way to automatically visualize the solution (using vis_geost_2d), but I didn't feel like figuring it out in time for the newsletter. Is this better? Now if I actually brought these questions to an interview the interviewee could ruin my day by asking "what's the runtime complexity?" Constraint solvers runtimes are unpredictable and almost always than an ideal bespoke algorithm because they are more expressive, in what I refer to as the capability/tractability tradeoff. But even so, they'll do way better than a bad bespoke algorithm, and I'm not experienced enough in handwriting algorithms to consistently beat a solver. The real advantage of solvers, though, is how well they handle new constraints. Take the stock picking problem above. I can write an O(n²) algorithm in a few minutes and the O(n) algorithm if you give me some time to think. Now change the problem to Maximize the profit by buying and selling up to max_sales stocks, but you can only buy or sell one stock at a given time and you can only hold up to max_hold stocks at a time? That's a way harder problem to write even an inefficient algorithm for! While the constraint problem is only a tiny bit more complicated: include "globals.mzn"; int: max_sales = 3; int: max_hold = 2; array[int] of int: prices = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8]; array [1..max_sales] of var int: buy; array [1..max_sales] of var int: sell; array [index_set(prices)] of var 0..max_hold: stocks_held; var int: profit = sum(s in 1..max_sales) (prices[sell[s]] - prices[buy[s]]); constraint forall (s in 1..max_sales) (sell[s] > buy[s]); constraint profit > 0; constraint forall(i in index_set(prices)) (stocks_held[i] = (count(s in 1..max_sales) (buy[s] <= i) - count(s in 1..max_sales) (sell[s] <= i))); constraint alldifferent(buy ++ sell); solve maximize profit; output ["buy at \(buy)\n", "sell at \(sell)\n", "for \(profit)"]; Most constraint solving examples online are puzzles, like Sudoku or "SEND + MORE = MONEY". Solving leetcode problems would be a more interesting demonstration. And you get more interesting opportunities to teach optimizations, like symmetry breaking. Because my dad will email me if I don't explain this: "leetcode" is slang for "tricky algorithmic interview questions that have little-to-no relevance in the actual job you're interviewing for." It's from leetcode.com. ↩
I’m something of a filesystem geek, I guess. I first wrote about ZFS on Linux 14 years ago, and even before I used ZFS, I had used ext2/3/4, jfs, reiserfs, xfs, and no doubt some others. I’ve also used btrfs. I last posted about it in 2014, when I noted it has some advantages over … Continue reading btrfs on a Raspberry Pi →
Something like a channel changer, for the web. That's what the idea was at first. But it led to a whole new path of discovery that even the site's creators couldn't have predicted. The post Stumbling upon appeared first on The History of the Web.
