exponential function - Feynman's Trick for Approximating \$e^x\$ - Mathematics Stack Exchange
1. e^2.3 ~ 10
2. e^.7 ~ 2
3. e^x ~ 1+x
e = 2.71828...

errors (absolute, relative):
1. +0.0258, 0.26%
2. -0.0138, -0.68%
3. 1 + x approximates e^x on [-.3, .3] with absolute error < .05, and relative error < 5.6% (3.7% for [0, .3]).
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october 2019 by nhaliday
Factorization of polynomials over finite fields - Wikipedia
In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them.

All factorization algorithms, including the case of multivariate polynomials over the rational numbers, reduce the problem to this case; see polynomial factorization. It is also used for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory.

As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article.

...

In the algorithms that follow, the complexities are expressed in terms of number of arithmetic operations in Fq, using classical algorithms for the arithmetic of polynomials.

[ed.: Interesting choice...]

...

Factoring algorithms
Many algorithms for factoring polynomials over finite fields include the following three stages:

Square-free factorization
Distinct-degree factorization
Equal-degree factorization
An important exception is Berlekamp's algorithm, which combines stages 2 and 3.

Berlekamp's algorithm
Main article: Berlekamp's algorithm
The Berlekamp's algorithm is historically important as being the first factorization algorithm, which works well in practice. However, it contains a loop on the elements of the ground field, which implies that it is practicable only over small finite fields. For a fixed ground field, its time complexity is polynomial, but, for general ground fields, the complexity is exponential in the size of the ground field.

[ed.: This actually looks fairly implementable.]
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july 2019 by nhaliday
One week of bugs
If I had to guess, I'd say I probably work around hundreds of bugs in an average week, and thousands in a bad week. It's not unusual for me to run into a hundred new bugs in a single week. But I often get skepticism when I mention that I run into multiple new (to me) bugs per day, and that this is inevitable if we don't change how we write tests. Well, here's a log of one week of bugs, limited to bugs that were new to me that week. After a brief description of the bugs, I'll talk about what we can do to improve the situation. The obvious answer to spend more effort on testing, but everyone already knows we should do that and no one does it. That doesn't mean it's hopeless, though.

...

Here's where I'm supposed to write an appeal to take testing more seriously and put real effort into it. But we all know that's not going to work. It would take 90k LOC of tests to get Julia to be as well tested as a poorly tested prototype (falsely assuming linear complexity in size). That's two person-years of work, not even including time to debug and fix bugs (which probably brings it closer to four of five years). Who's going to do that? No one. Writing tests is like writing documentation. Everyone already knows you should do it. Telling people they should do it adds zero information1.

Given that people aren't going to put any effort into testing, what's the best way to do it?

Property-based testing. Generative testing. Random testing. Concolic Testing (which was done long before the term was coined). Static analysis. Fuzzing. Statistical bug finding. There are lots of options. Some of them are actually the same thing because the terminology we use is inconsistent and buggy. I'm going to arbitrarily pick one to talk about, but they're all worth looking into.

...

There are a lot of great resources out there, but if you're just getting started, I found this description of types of fuzzers to be one of those most helpful (and simplest) things I've read.

John Regehr has a udacity course on software testing. I haven't worked through it yet (Pablo Torres just pointed to it), but given the quality of Dr. Regehr's writing, I expect the course to be good.

For more on my perspective on testing, there's this.

Everything's broken and nobody's upset: https://www.hanselman.com/blog/EverythingsBrokenAndNobodysUpset.aspx
https://news.ycombinator.com/item?id=4531549

https://hypothesis.works/articles/the-purpose-of-hypothesis/
From the perspective of a user, the purpose of Hypothesis is to make it easier for you to write better tests.

From my perspective as the primary author, that is of course also a purpose of Hypothesis. I write a lot of code, it needs testing, and the idea of trying to do that without Hypothesis has become nearly unthinkable.

But, on a large scale, the true purpose of Hypothesis is to drag the world kicking and screaming into a new and terrifying age of high quality software.

Software is everywhere. We have built a civilization on it, and it’s only getting more prevalent as more services move online and embedded and “internet of things” devices become cheaper and more common.

Software is also terrible. It’s buggy, it’s insecure, and it’s rarely well thought out.

This combination is clearly a recipe for disaster.

The state of software testing is even worse. It’s uncontroversial at this point that you should be testing your code, but it’s a rare codebase whose authors could honestly claim that they feel its testing is sufficient.

Much of the problem here is that it’s too hard to write good tests. Tests take up a vast quantity of development time, but they mostly just laboriously encode exactly the same assumptions and fallacies that the authors had when they wrote the code, so they miss exactly the same bugs that you missed when they wrote the code.

Preventing the Collapse of Civilization [video]: https://news.ycombinator.com/item?id=19945452
- Jonathan Blow

NB: DevGAMM is a game industry conference

- loss of technological knowledge (Antikythera mechanism, aqueducts, etc.)
- hardware driving most gains, not software
- software's actually less robust, often poorly designed and overengineered these days
- *list of bugs he's encountered recently*:
https://youtu.be/pW-SOdj4Kkk?t=1387
- knowledge of trivia becomes [ed.: missing the word "valued" here, I think?]more than general, deep knowledge
- does at least acknowledge value of DRY, reusing code, abstraction saving dev time
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may 2019 by nhaliday
Information Processing: Moore's Law and AI
Hint to technocratic planners: invest more in physicists, chemists, and materials scientists. The recent explosion in value from technology has been driven by physical science -- software gets way too much credit. From the former we got a factor of a million or more in compute power, data storage, and bandwidth. From the latter, we gained (perhaps) an order of magnitude or two in effectiveness: how much better are current OSes and programming languages than Unix and C, both of which are ~50 years old now?

...

Of relevance to this discussion: a big chunk of AlphaGo's performance improvement over other Go programs is due to raw compute power (link via Jess Riedel). The vertical axis is ELO score. You can see that without multi-GPU compute, AlphaGo has relatively pedestrian strength.
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may 2019 by nhaliday
Why books don’t work | Andy Matuschak
https://www.spreaker.com/user/10197011/designing-and-developing-new-tools-for-t
https://archive.is/hNIFG
https://archive.is/f9Bwh
hmm: "zettelkasten like note systems have you do a linear search for connections, that gets exponentially more expensive as your note body grows",
https://archive.is/P6PH2
https://archive.is/uD9ls
https://archive.is/Sb9Jq

https://archive.is/cc4zf
I reviewed today my catalogue of 420~ books I have read over the last six years and I am in despair. There are probably 100~ whose contents I can tell you almost nothing about—nothing noteworthy anyway.
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may 2019 by nhaliday
Complexity no Bar to AI - Gwern.net
Critics of AI risk suggest diminishing returns to computing (formalized asymptotically) means AI will be weak; this argument relies on a large number of questionable premises and ignoring additional resources, constant factors, and nonlinear returns to small intelligence advantages, and is highly unlikely. (computer science, transhumanism, AI, R)
created: 1 June 2014; modified: 01 Feb 2018; status: finished; confidence: likely; importance: 10
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april 2018 by nhaliday
The Hanson-Yudkowsky AI-Foom Debate - Machine Intelligence Research Institute
How Deviant Recent AI Progress Lumpiness?: http://www.overcomingbias.com/2018/03/how-deviant-recent-ai-progress-lumpiness.html
I seem to disagree with most people working on artificial intelligence (AI) risk. While with them I expect rapid change once AI is powerful enough to replace most all human workers, I expect this change to be spread across the world, not concentrated in one main localized AI system. The efforts of AI risk folks to design AI systems whose values won’t drift might stop global AI value drift if there is just one main AI system. But doing so in a world of many AI systems at similar abilities levels requires strong global governance of AI systems, which is a tall order anytime soon. Their continued focus on preventing single system drift suggests that they expect a single main AI system.

The main reason that I understand to expect relatively local AI progress is if AI progress is unusually lumpy, i.e., arriving in unusually fewer larger packages rather than in the usual many smaller packages. If one AI team finds a big lump, it might jump way ahead of the other teams.

However, we have a vast literature on the lumpiness of research and innovation more generally, which clearly says that usually most of the value in innovation is found in many small innovations. We have also so far seen this in computer science (CS) and AI. Even if there have been historical examples where much value was found in particular big innovations, such as nuclear weapons or the origin of humans.

Apparently many people associated with AI risk, including the star machine learning (ML) researchers that they often idolize, find it intuitively plausible that AI and ML progress is exceptionally lumpy. Such researchers often say, “My project is ‘huge’, and will soon do it all!” A decade ago my ex-co-blogger Eliezer Yudkowsky and I argued here on this blog about our differing estimates of AI progress lumpiness. He recently offered Alpha Go Zero as evidence of AI lumpiness:

...

In this post, let me give another example (beyond two big lumps in a row) of what could change my mind. I offer a clear observable indicator, for which data should have available now: deviant citation lumpiness in recent ML research. One standard measure of research impact is citations; bigger lumpier developments gain more citations that smaller ones. And it turns out that the lumpiness of citations is remarkably constant across research fields! See this March 3 paper in Science:

I Still Don’t Get Foom: http://www.overcomingbias.com/2014/07/30855.html
All of which makes it look like I’m the one with the problem; everyone else gets it. Even so, I’m gonna try to explain my problem again, in the hope that someone can explain where I’m going wrong. Here goes.

“Intelligence” just means an ability to do mental/calculation tasks, averaged over many tasks. I’ve always found it plausible that machines will continue to do more kinds of mental tasks better, and eventually be better at pretty much all of them. But what I’ve found it hard to accept is a “local explosion.” This is where a single machine, built by a single project using only a tiny fraction of world resources, goes in a short time (e.g., weeks) from being so weak that it is usually beat by a single human with the usual tools, to so powerful that it easily takes over the entire world. Yes, smarter machines may greatly increase overall economic growth rates, and yes such growth may be uneven. But this degree of unevenness seems implausibly extreme. Let me explain.

If we count by economic value, humans now do most of the mental tasks worth doing. Evolution has given us a brain chock-full of useful well-honed modules. And the fact that most mental tasks require the use of many modules is enough to explain why some of us are smarter than others. (There’d be a common “g” factor in task performance even with independent module variation.) Our modules aren’t that different from those of other primates, but because ours are different enough to allow lots of cultural transmission of innovation, we’ve out-competed other primates handily.

We’ve had computers for over seventy years, and have slowly build up libraries of software modules for them. Like brains, computers do mental tasks by combining modules. An important mental task is software innovation: improving these modules, adding new ones, and finding new ways to combine them. Ideas for new modules are sometimes inspired by the modules we see in our brains. When an innovation team finds an improvement, they usually sell access to it, which gives them resources for new projects, and lets others take advantage of their innovation.

...

In Bostrom’s graph above the line for an initially small project and system has a much higher slope, which means that it becomes in a short time vastly better at software innovation. Better than the entire rest of the world put together. And my key question is: how could it plausibly do that? Since the rest of the world is already trying the best it can to usefully innovate, and to abstract to promote such innovation, what exactly gives one small project such a huge advantage to let it innovate so much faster?

...

In fact, most software innovation seems to be driven by hardware advances, instead of innovator creativity. Apparently, good ideas are available but must usually wait until hardware is cheap enough to support them.

Yes, sometimes architectural choices have wider impacts. But I was an artificial intelligence researcher for nine years, ending twenty years ago, and I never saw an architecture choice make a huge difference, relative to other reasonable architecture choices. For most big systems, overall architecture matters a lot less than getting lots of detail right. Researchers have long wandered the space of architectures, mostly rediscovering variations on what others found before.

Some hope that a small project could be much better at innovation because it specializes in that topic, and much better understands new theoretical insights into the basic nature of innovation or intelligence. But I don’t think those are actually topics where one can usefully specialize much, or where we’ll find much useful new theory. To be much better at learning, the project would instead have to be much better at hundreds of specific kinds of learning. Which is very hard to do in a small project.

What does Bostrom say? Alas, not much. He distinguishes several advantages of digital over human minds, but all software shares those advantages. Bostrom also distinguishes five paths: better software, brain emulation (i.e., ems), biological enhancement of humans, brain-computer interfaces, and better human organizations. He doesn’t think interfaces would work, and sees organizations and better biology as only playing supporting roles.

...

Similarly, while you might imagine someday standing in awe in front of a super intelligence that embodies all the power of a new age, superintelligence just isn’t the sort of thing that one project could invent. As “intelligence” is just the name we give to being better at many mental tasks by using many good mental modules, there’s no one place to improve it. So I can’t see a plausible way one project could increase its intelligence vastly faster than could the rest of the world.

Takeoff speeds: https://sideways-view.com/2018/02/24/takeoff-speeds/
Futurists have argued for years about whether the development of AGI will look more like a breakthrough within a small group (“fast takeoff”), or a continuous acceleration distributed across the broader economy or a large firm (“slow takeoff”).

I currently think a slow takeoff is significantly more likely. This post explains some of my reasoning and why I think it matters. Mostly the post lists arguments I often hear for a fast takeoff and explains why I don’t find them compelling.

(Note: this is not a post about whether an intelligence explosion will occur. That seems very likely to me. Quantitatively I expect it to go along these lines. So e.g. while I disagree with many of the claims and assumptions in Intelligence Explosion Microeconomics, I don’t disagree with the central thesis or with most of the arguments.)
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april 2018 by nhaliday
Who We Are | West Hunter
I’m going to review David Reich’s new book, Who We Are and How We Got Here. Extensively: in a sense I’ve already been doing this for a long time. Probably there will be a podcast. The GoFundMe link is here. You can also send money via Paypal (Use the donate button), or bitcoins to 1Jv4cu1wETM5Xs9unjKbDbCrRF2mrjWXr5. In-kind donations, such as orichalcum or mithril, are always appreciated.

This is the book about the application of ancient DNA to prehistory and history.

height difference between northern and southern europeans: https://westhunt.wordpress.com/2018/03/29/who-we-are-1/
mixing, genocide of males, etc.: https://westhunt.wordpress.com/2018/03/29/who-we-are-2-purity-of-essence/
rapid change in polygenic traits (appearance by Kevin Mitchell and funny jab at Brad Delong ("regmonkey")): https://westhunt.wordpress.com/2018/03/30/rapid-change-in-polygenic-traits/
schiz, bipolar, and IQ: https://westhunt.wordpress.com/2018/03/30/rapid-change-in-polygenic-traits/#comment-105605
Dan Graur being dumb: https://westhunt.wordpress.com/2018/04/02/the-usual-suspects/
prediction of neanderthal mixture and why: https://westhunt.wordpress.com/2018/04/03/who-we-are-3-neanderthals/
New Guineans tried to use Denisovan admixture to avoid UN sanctions (by "not being human"): https://westhunt.wordpress.com/2018/04/04/who-we-are-4-denisovans/
also some commentary on decline of Out-of-Africa, including:
"Homo Naledi, a small-brained homonin identified from recently discovered fossils in South Africa, appears to have hung around way later that you’d expect (up to 200,000 years ago, maybe later) than would be the case if modern humans had occupied that area back then. To be blunt, we would have eaten them."

Live Not By Lies: https://westhunt.wordpress.com/2018/04/08/live-not-by-lies/
Next he slams people that suspect that upcoming genetic genetic analysis will, in most cases, confirm traditional stereotypes about race – the way the world actually looks.

The people Reich dumps on are saying perfectly reasonable things. He criticizes Henry Harpending for saying that he’d never seen an African with a hobby. Of course, Henry had actually spent time in Africa, and that’s what he’d seen. The implication is that people in Malthusian farming societies – which Africa was not – were selected to want to work, even where there was no immediate necessity to do so. Thus hobbies, something like a gerbil running in an exercise wheel.

He criticized Nicholas Wade, for saying that different races have different dispositions. Wade’s book wasn’t very good, but of course personality varies by race: Darwin certainly thought so. You can see differences at birth. Cover a baby’s nose with a cloth: Chinese and Navajo babies quietly breathe through their mouth, European and African babies fuss and fight.

Then he attacks Watson, for asking when Reich was going to look at Jewish genetics – the kind that has led to greater-than-average intelligence. Watson was undoubtedly trying to get a rise out of Reich, but it’s a perfectly reasonable question. Ashkenazi Jews are smarter than the average bear and everybody knows it. Selection is the only possible explanation, and the conditions in the Middle ages – white-collar job specialization and a high degree of endogamy, were just what the doctor ordered.

Watson’s a prick, but he’s a great prick, and what he said was correct. Henry was a prince among men, and Nick Wade is a decent guy as well. Reich is totally out of line here: he’s being a dick.

Now Reich may be trying to burnish his anti-racist credentials, which surely need some renewal after having pointing out that race as colloquially used is pretty reasonable, there’s no reason pops can’t be different, people that said otherwise ( like Lewontin, Gould, Montagu, etc. ) were lying, Aryans conquered Europe and India, while we’re tied to the train tracks with scary genetic results coming straight at us. I don’t care: he’s being a weasel, slandering the dead and abusing the obnoxious old genius who laid the foundations of his field. Reich will also get old someday: perhaps he too will someday lose track of all the nonsense he’s supposed to say, or just stop caring. Maybe he already has… I’m pretty sure that Reich does not like lying – which is why he wrote this section of the book (not at all logically necessary for his exposition of the ancient DNA work) but the required complex juggling of lies and truth required to get past the demented gatekeepers of our society may not be his forte. It has been said that if it was discovered that someone in the business was secretly an android, David Reich would be the prime suspect. No Talleyrand he.

https://westhunt.wordpress.com/2018/04/12/who-we-are-6-the-americas/
The population that accounts for the vast majority of Native American ancestry, which we will call Amerinds, came into existence somewhere in northern Asia. It was formed from a mix of Ancient North Eurasians and a population related to the Han Chinese – about 40% ANE and 60% proto-Chinese. Is looks as if most of the paternal ancestry was from the ANE, while almost all of the maternal ancestry was from the proto-Han. [Aryan-Transpacific ?!?] This formation story – ANE boys, East-end girls – is similar to the formation story for the Indo-Europeans.

https://westhunt.wordpress.com/2018/04/18/who-we-are-7-africa/
In some ways, on some questions, learning more from genetics has left us less certain. At this point we really don’t know where anatomically humans originated. Greater genetic variety in sub-Saharan African has been traditionally considered a sign that AMH originated there, but it possible that we originated elsewhere, perhaps in North Africa or the Middle East, and gained extra genetic variation when we moved into sub-Saharan Africa and mixed with various archaic groups that already existed. One consideration is that finding recent archaic admixture in a population may well be a sign that modern humans didn’t arise in that region ( like language substrates) – which makes South Africa and West Africa look less likely. The long-continued existence of homo naledi in South Africa suggests that modern humans may not have been there for all that long – if we had co-existed with homo naledi, they probably wouldn’t lasted long. The oldest known skull that is (probably) AMh was recently found in Morocco, while modern humans remains, already known from about 100,000 years ago in Israel, have recently been found in northern Saudi Arabia.

While work by Nick Patterson suggests that modern humans were formed by a fusion between two long-isolated populations, a bit less than half a million years ago.

So: genomics had made recent history Africa pretty clear. Bantu agriculuralists expanded and replaced hunter-gatherers, farmers and herders from the Middle East settled North Africa, Egypt and northeaat Africa, while Nilotic herdsmen expanded south from the Sudan. There are traces of earlier patterns and peoples, but today, only traces. As for questions back further in time, such as the origins of modern humans – we thought we knew, and now we know we don’t. But that’s progress.

https://westhunt.wordpress.com/2018/04/18/reichs-journey/
David Reich’s professional path must have shaped his perspective on the social sciences. Look at the record. He starts his professional career examining the role of genetics in the elevated prostate cancer risk seen in African-American men. Various social-science fruitcakes oppose him even looking at the question of ancestry ( African vs European). But they were wrong: certain African-origin alleles explain the increased risk. Anthropologists (and human geneticists) were sure (based on nothing) that modern humans hadn’t interbred with Neanderthals – but of course that happened. Anthropologists and archaeologists knew that Gustaf Kossina couldn’t have been right when he said that widespread material culture corresponded to widespread ethnic groups, and that migration was the primary explanation for changes in the archaeological record – but he was right. They knew that the Indo-European languages just couldn’t have been imposed by fire and sword – but Reich’s work proved them wrong. Lots of people – the usual suspects plus Hindu nationalists – were sure that the AIT ( Aryan Invasion Theory) was wrong, but it looks pretty good today.

Some sociologists believed that caste in India was somehow imposed or significantly intensified by the British – but it turns out that most jatis have been almost perfectly endogamous for two thousand years or more…

It may be that Reich doesn’t take these guys too seriously anymore. Why should he?

varnas, jatis, aryan invastion theory: https://westhunt.wordpress.com/2018/04/22/who-we-are-8-india/

europe and EEF+WHG+ANE: https://westhunt.wordpress.com/2018/05/01/who-we-are-9-europe/

https://www.nationalreview.com/2018/03/book-review-david-reich-human-genes-reveal-history/
The massive mixture events that occurred in the recent past to give rise to Europeans and South Asians, to name just two groups, were likely “male mediated.” That’s another way of saying that men on the move took local women as brides or concubines. In the New World there are many examples of this, whether it be among African Americans, where most European ancestry seems to come through men, or in Latin America, where conquistadores famously took local women as paramours. Both of these examples are disquieting, and hint at the deep structural roots of patriarchal inequality and social subjugation that form the backdrop for the emergence of many modern peoples.
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march 2018 by nhaliday
Altruism in a volatile world | Nature
The evolution of altruism—costly self-sacrifice in the service of others—has puzzled biologists1 since The Origin of Species. For half a century, attempts to understand altruism have developed around the concept that altruists may help relatives to have extra offspring in order to spread shared genes2. This theory—known as inclusive fitness—is founded on a simple inequality termed Hamilton’s rule2. However, explanations of altruism have typically not considered the stochasticity of natural environments, which will not necessarily favour genotypes that produce the greatest average reproductive success3,4. Moreover, empirical data across many taxa reveal associations between altruism and environmental stochasticity5,6,7,8, a pattern not predicted by standard interpretations of Hamilton’s rule. Here we derive Hamilton’s rule with explicit stochasticity, leading to new predictions about the evolution of altruism. We show that altruists can increase the long-term success of their genotype by reducing the temporal variability in the number of offspring produced by their relatives. Consequently, costly altruism can evolve even if it has a net negative effect on the average reproductive success of related recipients. The selective pressure on volatility-suppressing altruism is proportional to the coefficient of variation in population fitness, and is therefore diminished by its own success. Our results formalize the hitherto elusive link between bet-hedging and altruism4,9,10,11, and reveal missing fitness effects in the evolution of animal societies.
study  bio  evolution  altruism  kinship  stylized-facts  models  intricacy  random  signal-noise  time  order-disorder  org:nat  EGT  cooperate-defect  population-genetics  moments  expectancy  multiplicative  additive
march 2018 by nhaliday
Variance of product of multiple random variables - Cross Validated
prod_i (var[X_i] + (E[X_i])^2) - prod_i (E[X_i])^2

two variable case: var[X] var[Y] + var[X] (E[Y])^2 + (E[X])^2 var[Y]
nibble  q-n-a  overflow  stats  probability  math  identity  moments  arrows  multiplicative  iidness  dependence-independence
october 2017 by nhaliday
Lecture 14: When's that meteor arriving
- Meteors as a random process
- Limiting approximations
- Derivation of the Exponential distribution
- Derivation of the Poisson distribution
- A "Poisson process"
nibble  org:junk  org:edu  exposition  lecture-notes  physics  mechanics  space  earth  probability  stats  distribution  stochastic-processes  closure  additive  limits  approximation  tidbits  acm  binomial  multiplicative
september 2017 by nhaliday
[1705.03394] That is not dead which can eternal lie: the aestivation hypothesis for resolving Fermi's paradox
If a civilization wants to maximize computation it appears rational to aestivate until the far future in order to exploit the low temperature environment: this can produce a 10^30 multiplier of achievable computation. We hence suggest the "aestivation hypothesis": the reason we are not observing manifestations of alien civilizations is that they are currently (mostly) inactive, patiently waiting for future cosmic eras. This paper analyzes the assumptions going into the hypothesis and how physical law and observational evidence constrain the motivations of aliens compatible with the hypothesis.

http://aleph.se/andart2/space/the-aestivation-hypothesis-popular-outline-and-faq/

simpler explanation (just different math for Drake equation):
Overall the argument is that point estimates should not be shoved into a Drake equation and then multiplied by each, as that requires excess certainty and masks much of the ambiguity of our knowledge about the distributions. Instead, a Bayesian approach should be used, after which the fate of humanity looks much better. Here is one part of the presentation:

Life Versus Dark Energy: How An Advanced Civilization Could Resist the Accelerating Expansion of the Universe: https://arxiv.org/abs/1806.05203
The presence of dark energy in our universe is causing space to expand at an accelerating rate. As a result, over the next approximately 100 billion years, all stars residing beyond the Local Group will fall beyond the cosmic horizon and become not only unobservable, but entirely inaccessible, thus limiting how much energy could one day be extracted from them. Here, we consider the likely response of a highly advanced civilization to this situation. In particular, we argue that in order to maximize its access to useable energy, a sufficiently advanced civilization would chose to expand rapidly outward, build Dyson Spheres or similar structures around encountered stars, and use the energy that is harnessed to accelerate those stars away from the approaching horizon and toward the center of the civilization. We find that such efforts will be most effective for stars with masses in the range of M∼(0.2−1)M⊙, and could lead to the harvesting of stars within a region extending out to several tens of Mpc in radius, potentially increasing the total amount of energy that is available to a future civilization by a factor of several thousand. We also discuss the observable signatures of a civilization elsewhere in the universe that is currently in this state of stellar harvesting.
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may 2017 by nhaliday
[1502.05274] How predictable is technological progress?
Recently it has become clear that many technologies follow a generalized version of Moore's law, i.e. costs tend to drop exponentially, at different rates that depend on the technology. Here we formulate Moore's law as a correlated geometric random walk with drift, and apply it to historical data on 53 technologies. We derive a closed form expression approximating the distribution of forecast errors as a function of time. Based on hind-casting experiments we show that this works well, making it possible to collapse the forecast errors for many different technologies at different time horizons onto the same universal distribution. This is valuable because it allows us to make forecasts for any given technology with a clear understanding of the quality of the forecasts. As a practical demonstration we make distributional forecasts at different time horizons for solar photovoltaic modules, and show how our method can be used to estimate the probability that a given technology will outperform another technology at a given point in the future.

model:
- p_t = unit price of tech
- log(p_t) = y_0 - μt + ∑_{i <= t} n_i
- n_t iid noise process
preprint  study  economics  growth-econ  innovation  discovery  technology  frontier  tetlock  meta:prediction  models  time  definite-planning  stylized-facts  regression  econometrics  magnitude  energy-resources  phys-energy  money  cost-benefit  stats  data-science  🔬  ideas  speedometer  multiplicative  methodology  stochastic-processes  time-series  stock-flow  iteration-recursion  org:mat  street-fighting  the-bones
april 2017 by nhaliday
Beta function - Wikipedia
B(x, y) = int_0^1 t^{x-1}(1-t)^{y-1} dt = Γ(x)Γ(y)/Γ(x+y)
one misc. application: calculating pdf of Erlang distribution (sum of iid exponential r.v.s)
concept  atoms  acm  math  calculation  integral  wiki  reference  identity  AMT  distribution  multiplicative
march 2017 by nhaliday
Discovering Limits to Growth | Do the Math
https://en.wikipedia.org/wiki/The_Limits_to_Growth
https://foundational-research.org/the-future-of-growth-near-zero-growth-rates/
One may of course be skeptical that this general trend will also apply to the growth of our technology and economy at large, as innovation seems to continually postpone our clash with the ceiling, yet it seems inescapable that it must. For in light of what we know about physics, we can conclude that exponential growth of the kinds we see today, in technology in particular and in our economy more generally, must come to an end, and do so relatively soon.
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march 2017 by nhaliday
254A, Supplement 4: Probabilistic models and heuristics for the primes (optional) | What's new
among others, the Cramér model for the primes (basically kinda looks like primality is independently distributed w/ Pr[n is prime] = 1/log n)
gowers  mathtariat  lecture-notes  exposition  math  math.NT  probability  heuristic  models  cartoons  nibble  org:bleg  pseudorandomness  borel-cantelli  concentration-of-measure  multiplicative  truth  guessing
february 2017 by nhaliday
Why does 'everything look correlated on a log-log scale'? - Quora
A correlation on a log log scale is meant to suggest the data follows a power law relationship of the form yy∝x−n.∝x−n.

A low R2R2 is suppose to suggest that the data either actually follows some other distribution like yy∝e−x∝e−xor is simply random noise. The problem is that log log correlation is a necessary but not sufficient condition to prove a power law relationship. While ruling out random noise is fairly easy, ruling out an alternate functional form is much harder- you can reject a power law hypothesis by a log log plot but you cannot prove it by one. As Aaron Brown answer points out, a lot of stuff that looks like it has a power law relationship does not actually follow it in reality. In particular, an exponential or log normal relationship might give similar results over most of the range but will diverge strongly at the tail end .[1] This difference can be difficult to detect if limited data is collected at the tail ends and deviations look like noise.

An example of a log normal distribution plotted on a normal and log-log scale. [2] Note the appearance of a straight line on the right tail that diverges strongly on the left tail. Using a power law relationship in this region will cause serious errors.
q-n-a  qra  data-science  correlation  regression  magnitude  dataviz  street-fighting  gotchas  nibble  plots  multiplicative  additive  power-law
february 2017 by nhaliday
Performance Trends in AI | Otium
Deep learning has revolutionized the world of artificial intelligence. But how much does it improve performance? How have computers gotten better at different tasks over time, since the rise of deep learning?

In games, what the data seems to show is that exponential growth in data and computation power yields exponential improvements in raw performance. In other words, you get out what you put in. Deep learning matters, but only because it provides a way to turn Moore’s Law into corresponding performance improvements, for a wide class of problems. It’s not even clear it’s a discontinuous advance in performance over non-deep-learning systems.

In image recognition, deep learning clearly is a discontinuous advance over other algorithms. But the returns to scale and the improvements over time seem to be flattening out as we approach or surpass human accuracy.

In speech recognition, deep learning is again a discontinuous advance. We are still far away from human accuracy, and in this regime, accuracy seems to be improving linearly over time.

In machine translation, neural nets seem to have made progress over conventional techniques, but it’s not yet clear if that’s a real phenomenon, or what the trends are.

In natural language processing, trends are positive, but deep learning doesn’t generally seem to do better than trendline.

...

The learned agent performs much better than the hard-coded agent, but moves more jerkily and “randomly” and doesn’t know the law of reflection. Similarly, the reports of AlphaGo producing “unusual” Go moves are consistent with an agent that can do pattern-recognition over a broader space than humans can, but which doesn’t find the “laws” or “regularities” that humans do.

Perhaps, contrary to the stereotype that contrasts “mechanical” with “outside-the-box” thinking, reinforcement learners can “think outside the box” but can’t find the box?

http://slatestarcodex.com/2017/08/02/where-the-falling-einstein-meets-the-rising-mouse/
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january 2017 by nhaliday
pr.probability - What is convolution intuitively? - MathOverflow
I remember as a graduate student that Ingrid Daubechies frequently referred to convolution by a bump function as "blurring" - its effect on images is similar to what a short-sighted person experiences when taking off his or her glasses (and, indeed, if one works through the geometric optics, convolution is not a bad first approximation for this effect). I found this to be very helpful, not just for understanding convolution per se, but as a lesson that one should try to use physical intuition to model mathematical concepts whenever one can.

More generally, if one thinks of functions as fuzzy versions of points, then convolution is the fuzzy version of addition (or sometimes multiplication, depending on the context). The probabilistic interpretation is one example of this (where the fuzz is a a probability distribution), but one can also have signed, complex-valued, or vector-valued fuzz, of course.
q-n-a  overflow  math  concept  atoms  intuition  motivation  gowers  visual-understanding  aphorism  soft-question  tidbits  👳  mathtariat  cartoons  ground-up  metabuch  analogy  nibble  yoga  neurons  retrofit  optics  concrete  s:*  multiplicative  fourier
january 2017 by nhaliday
nt.number theory - Is \$x^{2k+1} - 7x^2 + 1\$ irreducible? - MathOverflow
Here is a proof, based on a trick that can be used to prove that x^n+x+1 is irreducible when n≠2 mod 3.
q-n-a  overflow  math  algebra  tidbits  math.NT  contradiction  polynomials  nibble  multiplicative
january 2017 by nhaliday
The Life-Span of Empires
empires die but don't age

The author examined the distribution of imperial lifetimes using a data set that spans more than three millennia and found that it conforms to a memoryless exponential distribution in which the rate of collapse of an empire is independent of its age.

same is true for species apparently
but it's a power law for larger taxa
pdf  study  history  anthropology  civilization  risk  aphorism  regularizer  objektbuch  distribution  stylized-facts  economics  cliometrics  cycles  red-queen  competition  iron-age  mediterranean  new-religion  the-classics  gibbon  leviathan  nihil  cultural-dynamics  great-powers  time  longevity  conquest-empire  multiplicative  power-law  hari-seldon
december 2016 by nhaliday
Standards Drift | West Hunter
We now know that the fraction of Neanderthal ancestry in coding regions has been gradually decreasing with time since the origin admixture, and is now something half as large as it was originally. There were some useful Neanderthal alleles that were favored by selection, and others that deleterious enough to have disappeared completely, but we’re talking about the general trend.

...

I’m thinking of it as standards drift. In a populations, alleles are always being selected for compatibility, for working correctly, conferring high fitness, on a particular average genetic background. Each allele has a spec it needs to meet. That spec doesn’t necessarily stay the same over time: obviously changes in environment will make a difference. Drift should matter too: if a given allele becomes more common, even by chance, the specs will change for other alleles that interact with it. But there’s always a spec.

When two populations split, their specs start to drift apart. There’s no genetic equivalent of that iridium meter bar. Function at the organismal level doesn’t change so much, but there are many slightly different ways of achieving that function.

...

While we’re at it, if there are Pygmies whose genomes are majority ancient Pygmy, their Bantu component is probably slightly incompatible: if left to themselves for a hundred thousand years, they’d probably lose a fair amount of it. Of course they will all be eaten long before that happens.

https://westhunt.wordpress.com/2016/04/08/the-1/
We don’t see people today with Neanderthal Y chromosomes or mtDNA. I keep hearing people argue that this means that mating between Neanderthal males and AMH females must have produced sterile males, or that matings between AMH men and Neanderthal women were all sterile, or whatever.

That is not necessarily the case. A slight disadvantage is all that would be required to totally eliminate Neanderthal Y-chromosomes or mtDNA.

Imagine that a Neanderthal Y-chromosome reduces the bearer’s fitness by 1%, and that the original frequency of Neanderthal Y chromosomes (after admixture) was 2%.

It’s been something like 1500 generations. The expected frequency is 5.67 x 10-9. In real life it would probably have fluctuated to zero, and of course stayed there.

Understand and remember.

https://westhunt.wordpress.com/2017/08/17/mtdna-capers/
The first problem is that there may not have been enough Neanderthals. Selection is not very effective in removing deleterious alleles when their selective disadvantage is < 1/N. For Neanderthals, some analyses indicate the effective population size was around 1000 (others think it was a large but deeply subdivided population), but the effective pop for mtDNA (haploid and only transmitted by females ) was 1/4th that – so, N ~250. Not very big.

The other, general, problem with mtDNA is lack of recombination. In an asexual lineage, mutations accumulate. Muller's ratchet. The only fix is back-mutation, which is very rare, unless the species population size is huge. Sex, on the other hand, reshuffles: a kid can have fewer deleterious mutations than either parent.

So you don’t expect hominid mtDNA to be in great shape, nearly perfectly optimized. That’s closer to true for nuclear genes. Since hominid mtDNA is not too close to optimal, it’s not a huge surprise if population A has noticeably more effective mitochondria than population B.

https://westhunt.wordpress.com/2016/02/18/croatoan/
west-hunter  genetics  evolution  archaics  sapiens  speculation  context  gene-flow  scitariat  gene-drift  multi  aDNA  genomics  archaeology  history  anthropology  critique  explanation  hmm  antiquity  population-genetics  nibble  stylized-facts  methodology  language  selection  ideas  aphorism  rant  africa  lol  population  pop-structure  china  asia  multiplicative  iteration-recursion  magnitude  quantitative-qualitative
november 2016 by nhaliday
Megafaunal Extinctions | West Hunter
When competent human hunters encountered naive fauna, the biggest animals, things like mammoths and toxodons and diprotodons, all went extinct. It is not hard to see why this occurred. Large animals are more worth hunting than rabbits, and easier to catch, while having a far lower reproductive rate. Moreover, humans are not naturally narrow specialists on any one species, so are not limited by the abundance of that species in the way that the lynx population depends on the hare population. Being omnivores, they could manage even when the megafauna as a whole were becoming rare.

There were subtle factors at work as well: the first human colonists in a new land probably didn’t develop ethnic/language splits for some time, which meant that the no-mans-land zones between tribes that can act as natural game preserves didn’t exist in that crucial early period. Such game preserves might have allowed the megafauna to evolve better defenses against humans – but they never got the chance.

It happened in the Americas, in Australia, in New Zealand, in Madagascar, and in sundry islands. There is no reason to think that climate had much to do with it, except in the sense that climatic change may sometimes have helped open up a path to those virgin lands in which the hand of man had never set foot, via melting glaciers or low sea level.

I don’t know the numbers, but certainly a large fraction of archeologists and paleontologists, perhaps a majority, don’t believe that human hunters were responsible, or believe that hunting was only one of several factors. Donald Grayson and David Meltzer, for example. Why do they think this? In part I think it is an aversion to simple explanations, a reversal of Ockham’s razor, which is common in these fields. Of course then I have to explain why they would do such a silly thing, and I can’t. Probably some with these opinions are specialists in a particular geographic area, and do not appreciate the power of looking at multiple extinction events: it’s pretty hard to argue that the climate just happened to change whenever people showed when it happens five or six times.

It might be that belief in specialization is even more of a problem than specialization itself. Lots of time you have to gather insights and information from several fields to make progress on a puzzle. It seems to me that many researchers aren’t willing to learn much outside their field, even when it’s the only route to the answer. But then, maybe they can’t. I remember an anthropologist who could believe in humans rapidly filling up New Zealand, which is about the size of Colorado, but just couldn’t see how they could have managed to fill up a whole continent in a couple of thousand years. Evidently she didn’t understand geometric growth. She is not alone. I have see anthropologists argue [The revolution that wasn’t] that increased human density in ancient Africa was driven by the continent ‘finally getting full’, rather than increased intellectual abilities and resulting greater technological sophistication. That’s truly silly. Look, back in those days, technology changed slowly: you would hardly notice significant change over 50k years. Human populations grow far faster than that, given the chance. Imagine a population with three surviving children per couple, which is nothing special: it would grow by a factor of ten million in a thousand years. The average long-term growth rate was very low, but that is because the rate of increase in human capabilities, which determine the carrying capacity, was very slow – not because rapid population growth is difficult or impossible.

I could explain this to my 11-year old twins in five minutes, but I don’t know that I could ever explain it to Brooks and McBrearty.

https://westhunt.wordpress.com/2012/05/20/megafaunal-extinctions/#comment-3039
Why do people act as if a slightly more habitable Greenland a millennium ago somehow disproves the statement that the world as a whole was cooler then than now? Motivated reasoning: they want a certain conclusion real bad. At this point it’s become an identifying tribal marker, like left-wingers believing in the innocence of Alger Hiss. And of course they’re mostly just repeating nonsense that some flack dreamed up. Many of the same people will mouth drivel about how a Finn and a Zulu could easily be genetically closer two each other than to other co-ethnics, which is never, ever, true.

When you think about it, falsehoods, stupid crap, make the best group identifiers, because anyone might agree with you when you’re obviously right. Signing up to clear nonsense is a better test of group loyalty. A true friend is with you when you’re wrong. Ideally, not just wrong, but barking mad, rolling around in your own vomit wrong. Movement conservatives have learned this lesson well.

https://westhunt.wordpress.com/2013/09/12/younger-dryas-meteorite/
It has been suggested that a large meteorite was responsible for an odd climatic twitch from about 12,800 to 11,500 years ago (the Younger Dryas , a temporary return to glacial conditions in the Northern Hemisphere) and for the extinction of the large mammals of North America. They hypothesize air bursts or impact of a swarm of meteors , centered around the Great Lakes. Probably this is all nonsense.

The topic of the Holocene extinction of megafauna seems to bring out the crazy in people. In my opinion, the people supporting this Younger Dryas impact hypothesis are nuts, and half of their opponents are nuts as well.

...

The problem for that meteorite explanation of North Ammerican megafaunal extinction is that South America had an even more varied set of megafauna (gomphotheriums, toxodonts, macrauchenia, glyptodonts, giant sloths, etc) and they went extinct around the same time (probably a few hundred years later). There’s no way for a hit around the Great Lakes to wipe out stuff in Patagonia, barring a huge, dinosaur-killer type hit that throws tremendous amount of debris into suborbital trajectories. But that would have hit the entire world… Didn’t happen.

https://westhunt.wordpress.com/2012/05/26/redlining/
If you take too many chances in the process of making a living, you’ll get yourself killed before you manage to raise a family. Therefore there is a maximum sustainable risk per calorie acquired from hunting *. If the average member of the species incurs too much risk, more than that sustainable maximum, the species goes extinct. The Neanderthals must have come closer to that red line than anatomically modern humans in Africa, judging from their beat-up skeletons, which resemble those of rodeo riders. They were almost entirely carnivorous, judging from isotopic studies, and that helps us understand all those fractures: they apparently had limited access to edible plants, which entail far lower risks. Tubers and berries seldom break your ribs.

...

Risk per calorie was particularly high among the Neanderthals because they seem to have had no way of storing meat – they had no drying racks or storage pits in frozen ground like those used by their successors. Think of it this way: storage allow more complete usage of a large carcass such as a bison, that might weigh over a thousand pounds – it wouldn’t be easy to eat all of that before it went bad. Higher utilization – using all of the buffalo – drops the risk per calorie.

You might think that they could have chased rabbits or whatever, but that is relatively unrewarding. It works a lot better if you can use nets or snares, but no evidence of such devices has been found among the Neanderthals.

It looks as if the Neanderthals had health insurance: surely someone else fed them while they were recovering from being hurt. You see the same pattern, to a degree, in lions, and it probably existed in sabertooths as well, since they often exhibit significant healed injuries.

...

So we can often understand the pattern, but why were mammoths rapidly wiped out in the Americas while elephants survived in Africa and south Asia? I offer several possible explanations. First, North American mammoths had no evolved behavioral defenses against man – while Old World elephants had had time to acquire such adaptations. That may have made hunting old world elephants far more dangerous, and therefore less attractive. Second, there are areas in Africa that are almost uninhabitable, due to the tsetse fly. They may have acted as natural game preserves, and there are no equivalents in the Americas. Third, the Babel effect: in the early days, paleoIndians likely had not yet split into different ethnic groups with different languages: with less fighting among the early Indians, animals would not have had relatively border regions acting as refugia. Also, with fewer human-caused casualties, paleoindians could have taken more risks in hunting.

https://westhunt.wordpress.com/2013/09/18/hunter-gatherer-fish-and-game-laws/
I don’t think that there are any. But then how did they manage to be one-with-the-land custodians of wildlife? Uh….

Conservation is hard. Even if the population as a whole would be better off if a given prey species persisted in fair numbers, any single individual would benefit from cheating – even from eating the very last mammoth.

More complicated societies, with private property and draconian laws against poaching, do better, but even they don’t show much success in preserving a tasty prey species over the long haul. Considers the aurochs, the wild ancestor of the cow. The Indian version seems to have been wiped out 4-5,000 years ago. The Eurasian version was still common in Roman times, but was rare by the 13th century, surviving only in Poland. Theoretically, only members of the Piast dynasty could hunt aurochsen – but they still went extinct in 1627.

How then did edible species survive in pre-state societies? I can think of several ways in which some species managed to survive … [more]
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november 2016 by nhaliday
Overcoming Bias : Lognormal Jobs
could be the case that exponential tech improvement -> linear job replacement, as long as distribution of jobs across automatability is log-normal (I don't entirely follow the argument)

Paul Christiano has objection (to premise not argument) in the comments
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november 2016 by nhaliday

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