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earthicuson An ecologist who wants to map everything

Lol, that's a great story; if only that sort of thing was practical, how much more fun life would be :-) I actually had the opportunity to do something similar not too long ago. I'm a beginner learning to program and I had a little puzzle that I got from my grandma ~15 years ago. You have a tower of blocks with symbols on them, and have to arrange the blocks so that all of the symbols on each side are distinct [1]. The problem was small enough that I could just model each symbol as a prime and check uniqueness by seeing of the product was equal to 2 * 3 * 5 * 7 * 11 * 13.

[1] https://imgur.com/vTZotGC

earthicuson iPadOS

The right-click mouse gestures in Maya 3d are one example of solving this problem nicely. If you do it at normal speed, you see & select items on the context menus and submenus. But as you learn the gestures that form from making these selections you can execute them rapidly and the context menus don't need to be displayed. It's a perfect example of training you to use an advanced feature with an easy learning curve, then letting the 'training wheels' come off on a case by case basis, no change in settings needed!

Does anyone happen to know of any other applications that use this kind of UI, or even better, a windows utility that adds this kind of functionality across the OS, building custom context-menus for each application?

earthicuson Ask HN: What are your favorite books or essays written at least 100 years ago?

Also by Maxwell, his semi-pop science lectures on Newtonian physics, 'Matter and Motion'.

https://store.doverpublications.com/0486668959.html

earthicuson Ask HN: What are your favorite books or essays written at least 100 years ago?

Dover editions are fine, imho. Certainly leagues better than the scans you are describing:

https://store.doverpublications.com/048646119x.html

If you want something nicer you could find a old used hardcover from the mid-twentieth century. Sometimes big reference works like this have never actually been used and are in effectively new condition.

earthicuson Calculus Without Limits (1981)

Hmm, I thought they had basically the same meaning! The premise of the book is to replace limits with the method of exhaustion, so I thought the title 'without limits' conveyed that clearer than the somewhat Punny title the book actually uses. From the abstract:

> As the title Calculus Unlimited implies, this text presents an alternative treatment of calculus using the method of exhaustion for the derivative and integral in place of limits. [...] As you will note, this text has a more geometric flavor than the usual analytic treatment of calculus. For example, our definition of completeness is in terms of convexity rather than least upper bounds, and Dedekind cuts are replaced by the notion of a transition point. Who Should Use This Book: This book is for calculus instructors and students interested in trying an alternative to limits. The prerequisites are a knowledge of functions, graphs, high school algebra and trigonometry.

earthicuson Terence Tao – Understanding 1+2+3 =-1/12 Without Complex Analysis

Tao's article certainly requires more background to read, but it gives a much deeper insight than explanations based on Cesaro or Euler/Ramanujan summation, which (as Tao points out in the article), in addition to being very puzzling, are actually mutually inconsistent. His main result is that these classical sums / the zeta function are only the constant term in a certain asymptotic expansion associated with a smoothed version of the original sum. Recognizing the existence of the non-constant terms in that expansion corrects the nonsensical negativeness and logical inconsistency. This is intimately connected to the analytic continuation POV, which is discussed in section 2. It's well worth a read if you have time over a few days. I wrote an overview of the strategy here:

https://www.reddit.com/r/math/comments/cx3qzv/terence_tao_un...

earthicuson Was early modern writing paper expensive? (2018)

Oops, how could I misread 6 sheets per year as 6 sheets per day! o_0 Thanks for pointing out my error, this makes much more sense now.

earthicuson Was early modern writing paper expensive? (2018)

I think you might be making the wrong comparison. We can conclude from your observation that their paper is expensive (relative to ours), or that our paper is dirt cheap! A laborer today might make $120/day so that's $1.60/sheet at early modern prices. While that's expensive compared to our super cheap modern paper, it's perfectly normal to describe things that cost $1.60 as inexpensive, even if you buy quite a few of them. The article says the average englishman used 6 sheets a day, so a modern laborer is spending under $10/day on paper.

earthicuson A Brief Guide to a Few Algebraic Structures

Many of them feature prominently in Stepanov's books, Elements of Programming and From Mathematics to Generic Programming. 'Elements' is a technical monograph, while the other is a more lightweight read, halfway between semi-pop-science and a textbook.

There's also an old textbook by Birkhoff & Bartee called 'Modern Applied Algebra' that i like. It's not super duper computer science-y but might be worth browsing through the table of contents at least.

Edit: I snapped some photos of the table of contents since you can't see it on the amazon page:

https://imgur.com/a/RFIf4CD

earthicuson Discrete Differential Geometry: An Applied Introduction [pdf]

FYI the word 'complex' in mathematics is often used similar to it's usage as an English noun - "a whole made up of interrelated parts", e.g. a building complex, apartment complex, military-industrial complex. A 'simplicial complex' is then, informally, "a whole made up of interrelated simplexes".

earthicuson The Relation Between Mathematics and Physics (1939)

The view that Dirac is putting forth, that the fundamental equations need to be simple, is certainly not the modern one endorsed by theorists today. Since the 70s or 80s, the point of view that has come to dominate is that our most accurate theories (quantum field theories) are what are known as "effective field theories", where the adjective 'effective' refers to the idea that they are only only low-energy approximations to some other more complete theory. In this point of view the complete theory would have more complicated, even non-renormalizable terms that violate conservation laws, but these additional terms are suppressed by powers of something like the plank scale and so are virtually undetectable at low energies. Thus the low energy approximations (the effective field theories) have the simple, renormalizable form that we know. There is a good accessible discussion of this in Weinberg's popular science book 'Dreams of a Final Theory'.

earthicuson Seki Takakazu

One of the books given in the references is actually available in it's entirety [1] and appears to be quite good. Chapter 6 covers Seki, Chapter 7 is about his contemporaries and western influences (or lack there-of), and Chapter 8 is about the 'yenri', which is the Calculus system in question.

[1] https://books.google.com/books?id=J1YNAAAAYAAJ

earthicuson Seki Takakazu

I've heard of this mathematician several times over the years, but have never seen the capabilities and point of view of his calculus-like system actually described. Does anyone know of a more detailed article or book that gives such a description?

earthicuson Adam and Eve – Adobe's Cross-Platform GUI Libraries

I came across this in a talk by Sean Parent (once lead developer of Photoshop). What caught my attention was his assertion that they were able to reduce the GUI code of Photoshop by 600x, from a Million lines of code to less than 2k. It uses a declarative UI, together with what they call the 'Propagator Model' which is an R&D project by Sean Parent & his academic collaborators. An excerpt from one of their papers explains the new ingredient:

> The combination of procedural and declarative program code has found success in, for example, GUI element layout. The most familiar example is perhaps HTML, CSS, and DOM combined with JavaScript. The QTk library [...], XAML [34], and XForms [5] serve as further examples. Some of these systems, along with rule-based systems such as Drools [27], Jess [11], and R++ [14], also support concisely specifying declarative rules for maintaining consistency across values in user interfaces. Property models are distinguished from these systems by not only providing the ability to create rules that assist introducing a valid result but also by providing an explicit model of the dependencies these rules create. Inspecting the state of the model enables generic algorithms (e.g., for widget enablement) for user interface.

http://www.emarcus.org/papers/gpce2009-marcus.pdf

earthicuson 'High likelihood of human civilisation coming to end' by 2050, report finds

I think the claim that Earth is going to turn into Venus or Arrakis is absurd - I haven't heard anyone argue that, but I have heard the claim that it will cause a mass extinction on a geologic scale that could affect humans and our 'pets' as well.

I don't know if it is accurate and based on good science, but I believe that the argument revolves around the timescale that the change is occurring compared to natural climate shifts: that the temperature is increasing so fast there is not enough time for plants and animals to evolve, or even for ecosystems to gradually migrate their locales. For example, one reason you can't simply replace farms with land in, say, the Canadian shield is the lack of good topsoil. According to [1] it takes at least 100 years to form an inch of topsoil in wet, hot climates, and the process is much slower in cold or dry climates. Thus if we render our existing farmland unfit for our existing crops in timescales measured in tens of years, we would have to rely on manually bringing a literal continent's worth of soil north - whatever process was at work during the Cretaceous cannot be relied on to solve this particular problem.

[1] https://www.nrcs.usda.gov/wps/portal/nrcs/detail/wa/soils/?c...

earthicuson SwiftUI

It's very interesting! The 'property model' was apparently a real research project, which adds an additional ingredient over and above most systems in common use:

> The combination of procedural and declarative program code has found success in, for example, GUI element layout. The most familiar example is perhaps HTML, CSS, and DOM combined with JavaScript. The QTk library [12] in Mozart/Oz, Glade [7],XUL [16], XAML [34], and XForms [5] serve as further examples. Some of these systems, along with rule-based systems such as Drools [27], Jess [11], and R++ [14], also support concisely specifying declarative rules for maintaining consistency across values in user interfaces. Property models are distinguished from these systems by not only providing the ability to create rules that assist introducing a valid result but also by providing an explicit model of the dependencies these rules create. Inspecting the state of the model enables generic algorithms (e.g., for widget enablement) for user interface.

http://www.emarcus.org/papers/gpce2009-marcus.pdf

earthicuson SwiftUI

Adobe uses a declarative UI system, and what they call a 'property model', which apparently successfully reduced their UI code by a factor of over 500. The system is available here:

https://stlab.adobe.com/group__asl__overview.html

earthicuson They Fictionalize Nuclear Disasters Like Chernobyl Because They Kill So Few

https://commons.wikimedia.org/wiki/File:Nuclear_power_plant_...

There's a source for the recent data given in the 'description section'.

earthicuson Why isn't 1 a prime number?

Do you mean the example of 1 not being a prime, or the example in the article of Z[root -5] not having unique factorization? You could certainly discover the former, but not the latter as far as I can see. The idea is that the principle should guide you on what the 'right' set of definitions are, so that your theory detects interesting theorems and isn't riddled with edge cases. You might make an analogy to programming, finding good primitive data types and interfaces so that you can implement elegant and efficient algorithms and well structured modules.

Perhaps the key insight of the 'too simple to be simple' principle is that we want the definition to impose both existence & uniqueness of something. In this case proper divisors (divisors strictly less than the number itself e.g. the proper divisors of 6 are 1,2, & 3).

-------------------------------

Let me give a concrete example of how it might be used.

- Uniqueness is captured algebraically here by the notion of a 'subsingleton' set: a subset where any pair of elements are equal. This can happen if (1) the subset has only a single element, or (2) the subset has NO elements (in which case the uniqueness requirement is vacuously true).

- Existence is captured by the notion of a 'singleton' set: a subset with exactly 1 element: any two elements belonging to the set are unique, AND such an element exists.

First lets apply this to the definition of the regular primes: the set of proper divisors of 1 is the empty set. The set of proper divisors of any other prime is the singleton set {1}. Thus the naive definition says 'proper divisors of primes form a subsingleton': it asserts they are unique, but not that they exist. The more sophisticated definition of the primes (which excludes 1) asserts the proper divisors of primes form a singleton: uniqueness and existence.

Now lets try to apply it (somewhat informally) to the fictional example of even numbers and 'even primes'. Examples:

   2 is an even prime, 
   4 = 2*2 not an even prime
   6 is an even prime, 
   8 = 4*2 is not, 
   10 is even prime,
   30 is an even prime is as well, and so on.

Here I have uniqueness of proper divisors (they form a subsingleton), but only because existence of proper divisors fails for every even prime (not just 2)!

Now what happens if we try and factor 60?

   60 = 2*30
   60 = 6*10

It not great surprise that uniqueness of prime factorization fails as well (one of several problems with this informal example). The principle didn't help me find this example, it suggests that if I use the above notion of an 'even prime', i'm not going to get a good set of theorems.

earthicuson Why isn't 1 a prime number?

Very nice article! Also of interest, 1 not being prime can be viewed as a particular example of a more general phenomenon that occurs throughout mathematics, known as the 'Too simple to be simple' principle:

https://ncatlab.org/nlab/show/too+simple+to+be+simple

earthicuson Loop invariants can give you coding superpowers

I've linked [1] to another example of exploiting an invariant that you might find more compelling. The presenter takes a multi-page mess of UI code from Chrome containing something like 8 loops, then solves an even harder version of that problem in ... 2 lines of code, by exploiting an invariant associated with the problem (and a well placed library call!).

[1] https://news.ycombinator.com/item?id=19567671

earthicuson Loop invariants can give you coding superpowers

I don't think the utility of invariants is restricted to proving program correctness, as is suggested by a number of commenters in this thread. Instead, they identify some underlying structure in your problem, and that structure can be exploited to simplify your method of calculation.

Another great example of exploiting a (not-really-loop) invariant to design an algorithm is Sean Parent's implementation of a generic 'gather' algorithm, which takes advantage of the fact that the set of objects below/above the gathering point is unchanged, allowing you to split the problem into two easier sub-problems. Here's his explanation and implementation (video should be linked to 16:50):

https://youtu.be/IzNtM038JuI?t=1009

earthicuson Learning Ada

According to an amazon reviewer [1], Sammet's book Programming Languages: History and Fundamentals (from 1969) already discusses ~120 different languages! And gives code examples in 30 of them.

[1] https://www.amazon.com/Programming-Languages-Fundamentals-Au...

earthicuson Elementary Applied Topology (2014)

The book has an appendix, labeled 'background' which lays out more precisely the formal prerequisites from point-set topology and algebra which you should review. The algebra is surely going to be a bigger obstacle than differential equations.

earthicuson A quantum experiment suggests there’s no such thing as objective reality

How are you interpreting this experiment with DeBroglie-Bohm? This is bumping up into the area where the theory gets into trouble, as photons aren't described by the Schrodinger equation or Dirac equation, and don't have wave functions at all. However in interferometry you might talk about the wave function of a photon if it is not emitted or absorbed.

Re: Locality. The issue is not nearly as simple as you are making it out to be. You are not allowed to naively dispense with locality because locality, described quantitatively by Lorentz invariance, is one of the most well tested physical principles in the history of science. You don't get to ignore observations to conform to your philosophical biases regarding interpretations of your theories.

The principles of special relativity and quantum mechanics are combined in quantum field theory, which is the most accurate and well tested description of the world we currently have. Non-relativistic Quantum Mechanics (where debroglie bohm is nice and simple) is a (0+1) dimensional quantum field theory, whereas our universe is described by (3+1) dimensional quantum field theories like quantum electrodynamics or the standard model. To dispense with locality in a non-naive way requires extending the theory to this more complicated setting, which is an unsolved problem, and an active are of research. According to the wikipedia page, even developing a complete theory of the photon is an active area of research! Whereas developing QED the first time around only took a handful of people 15 years...and they didn't know what the answer was going to turn out to be! I think we can conclude from this that the theory is no longer so simple and easy to grasp.

earthicuson An “acoustic metamaterial” that can cancel 94 percent of sound

For those of you who haven't yet read the article, the cool thing about this new technology is that the material is not a solid plane, but an empty ring that allows air to pass through:

https://www.bu.edu/research/files/2019/02/acoustic-metamater...

earthicuson An “acoustic metamaterial” that can cancel 94 percent of sound

I know nothing about acoustics and its units - the abstract of actual paper says more precisely that it reduces the 'acoustic energy' by 94%, not the power. Can you convert this to a decibel figure? Would you mind explaining what these units mean and how you do the conversions?

earthicuson Kurt Gödel's Letter to John von Neumann (1956) [pdf]

According to [1], the question Goedel raises is equivalent to P vs NP, although clearly not phrased in the same language. The author claimes Goedel's phi(n) is polynomially bounded if and only if P=NP. Do you disagree with that statement?

[1] https://ecommons.cornell.edu/bitstream/handle/1813/6910/89-9...

earthicuson Kurt Gödel's Letter to John von Neumann (1956) [pdf]

Here's a nice article that discusses the historical importance of the letter and the problem Goedel raises:

https://ecommons.cornell.edu/bitstream/handle/1813/6910/89-9...

earthicuson Kurt Gödel's Letter to John von Neumann (1956) [pdf]

My source for learning about the exchange was a biography of von Neumann by Macrae, but i double-checked it and it appears you are correct. I was mis-remembering how much of the correspondence von Neumann was able to contribute at that point. I've corrected my original comment accordingly, thank you.