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How embarrassing.

In practice, any orbits around Lagrangian points L1, L2, or L3 are dynamically unstable, meaning small departures from equilibrium grow over time.[2] As a result, spacecraft in these Lagrangian point orbits must use their propulsion systems to perform orbital station-keeping. Although they are not perfectly stable, a modest effort of station keeping keeps a spacecraft in a desired Lissajous orbit for a long time.

Oh my.

How embarrassing.

Lissajous curves are the family of curves described by [...] parametric equations ...

Go away.

The James Webb Space Telescope will not be in orbit around the Earth, like the Hubble Space Telescope is - it will actually orbit the Sun, 1.5 million kilometers (1 million miles) away from the Earth at what is called the second Lagrange point or L2.

Ah, here we go. Apparently this is a standard term.

What makes science amazing is that we somehow pick hypotheses that not only fit current data but also predict new surprising results.

I am agreeing with you as hard as I can :)

Personally I find it hard to believe that all the information in the universe was deterministically contained at the start. Randomness easily solve this problem.

I'll suggest to you Wolfram's cellular automata work - it's amazing how simple rules can create completely random distributions given enough steps :)

http://mathworld.wolfram.com/E...

We have predictive capacity on climate from century to century and we have historical records going back millions of years to back it up.

I wouldn't be so sure of that. If you went back to 1918, looking for predictions of global average temperature in 2018, I think you'd find the vast majority of those models weren't even close - even the ones with the same central conceits as those that may have gotten it right simply by chance.

This is *especially* true if you believe climate is driven by humans - nobody in 1918 could possibly have predicted the growth in humanity and technology we have had over the past 100 years.

Now, if you wanted to assert that you can predict century to century climate with our historical records, you run into the problem that we don't have that kind of resolution - there are literally centuries upon centuries between data points in our historical proxies - it would be like trying to use a sundial to time a 100m sprint :)

I can perfectly model the behavior of some closed system. Let's say I can model it 1000 times faster than real time.

Sadly, the only way we can model reality faster than real time is by imperfectly modeling behavior :)

This isn't to say that there aren't some models that are close enough for various purposes, but I just can't start a hypothetical with "perfectly model" :)

Unfortunately, most of the time we need to assume the scientists are doing a good job. Even without the statistical issues, people do not have the time to be experts in everything. We need to appeal to experts to help us make decisions. Generally the scientists do a good job of policing themselves.

Let's unpack that a bit.

Yes, most of the time we need to assume scientists are doing a good job. But we should also simultaneously assume that their good job is not perfect, and that they're humans, just like us. Either through honest error, unconscious bias, or conscious bias, they can be wrong - which is where the scientific method comes in, and the concept of a necessary and sufficient falsifiable hypothesis keeps them in check.

As for appealing to the experts to help us make decisions, avoiding this was the entire *reason* for the scientific method :). Put another way, why would we assume that we're all experts at picking out the people who are experts in fields we're not experts in? Why should I believe that I'm capable of discerning which nutritional expert is the right one, if I know nothing about nutrition?

For policing themselves, I'm afraid I'm not nearly as optimistic as you are - especially since much of science has been utterly unscientific for a long time. The incestuous peer review system that has its own internal biases and incentive structures has led to things like the reproducibility crisis in psychology, nutrition, and other fields as well. One could argue, of course, that psychology, by its very nature, is a "soft" science, not really falsifiable, but interesting and "sciencey", but the track record of scientists, especially those playing the academia game of "publish or perish", really isn't that good on the policing side

Essentially, it has been known for a while that the answer is either 4 or 5 or 6 or 7.

This paper identifies a graph that cannot be colored with just 4 colors, so it establishes 5 as the new lower bound.

http://tones.wolfram.com/gener... This has been around 20 years and claims a lot of things

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. More concisely, a prime number p is a positive integer having exactly one positive divisor other than 1, meaning it is a number that cannot be factored. [see Wolfram MathWorld]

Note that when p is set to 1, the test is also true: its only positive integer divisors are itself, p, and 1. (1/1=1 which is both 1 and the current value of p). Wolfram simply ignores this edge case, since for all but esoteric levels of advanced mathematics it is not necessary to go there.

From a historical perspective this makes sense. When at the end of the day's harvest it was time to evenly divide up the bags of grain that had been gathered in, it turned out that it was always the case that if there were certain numbers of bags, there was no way to evenly divide them, no matter how many persons were to receive a portion. Finding a way to fairly dispose of prime numbers of objects was one of the earliest problems in social engineering.

Similarly, the problem of zero is generally ignored except in the rarefied heights where mathematics no longer has value in engineering, finances, and any other applied mathematics that I am aware of. I am of course referring to the fact that division by zero is undefined. In this manner zero does not qualify as a rational number, and since the integers are a subset of rational numbers, zero is not an integer. Nor is it a counting number. At best, zero is an irrational real number, like pi, the sqrt(2), e, etc. But it might actually be better to define it as a hole in the number line ---that's something for the Wolframs out there to noodle over.

Circling back to the original problem, you said:

There is no largest prime number, and primes are a subset of integers. Therefore, we can have a one-to-one correspondence with primes and the integers 1 and greater, giving the ordinal. Given a prime number, therefore, there's a prime that's the ordinal for. Since there is no largest prime number, there's no largest prime whose ordinal is also prime. There is no largest prime number, and primes are a subset of integers. Therefore, we can have a one-to-one correspondence with primes and the integers 1 and greater, giving the ordinal. Given a prime number, therefore, there's a prime that's the ordinal for. Since there is no largest prime number, there's no largest prime whose ordinal is also prime.

This seems to be tightly reasoned. I think it would have been better to say that "primes are a subset of the counting numbers" rather than integers, but that's a mere quibble. Of course you could also call the set of primes a subset of the rational numbers, or the real numbers ---whatever.

However as this thread has been having problems with word usage intended to dazzle with brilliance or possibly baffle with ... . well, I can't immediately accept it what you propose, and I've got other things to think about than puzzling over something that may not have been intended to be meaningful. I will read it over a time or two and let my subconscious play with it. But I also ask whether you can rephrase whatever you may be saying in a more mathematically formal statement.

Does this work because your acceleration is now modelled using the central difference method. This would mean that your acceleration model is no longer subject to first order truncation errors which could be significant if you are actually trying to pick the best speed at any given time by reacting to traffic in your lane.

Not more photons. See https://www.rp-photonics.com/s...
and http://scienceworld.wolfram.co... for their definition.

They get a peak brightness of about 10^19 photons s^-1 mm^-2 mrad^-2 (per 0.1% bandwidth) at 1 MeV photon energy. Peak means at the peak of a 30fs short pulse.

Actually, by your definition, yes. Their x-ray pulses have a rather low number of photons (about a million per shot). However, physicists use a different definition for brightness: http://scienceworld.wolfram.co...
and
https://www.rp-photonics.com/s...

That definition basically translates to "lots of light in one direction and in a narrow spectral range, per unit time" - squeezing the light in every imaginable way to make it as well-defined/focused as possible. This makes your LED lose in a lot of ways: because it's not pulsed, the light is all over the place instead of well collimated (straight like a laser), and oh yours are not x-ray photons - these carry about 10,000x more energy, each.

Their driving laser (Diocles) is another story though: it has more than 1 Joule of optical(!) pulse energy. That's probably more light in one pulse than your LED will generate in its entire life. And that comes in a pulse that's only 33 femtoseconds short, that's 0.000000000000033 seconds. Not even the biggest laser, though.

Uh... no.

Yup. They say "normal math symbols" and then include concatenation. Fucking horse shit.

What has slashdot come to when this type of horse shit gets modded insightful?

https://en.wikipedia.org/wiki/...

http://mathworld.wolfram.com/C...

> If you're even trying to define "normal" in a special way to make something true, then you've already left the realm of normalcy and entered the realm of "alternate facts."

Bad example. Math already has many different kinds of normal. You might think that a 'normal operator' is 'something my calculator has a button for', but instead it's a continuous linear operator N : H -> H that commutes with its hermitian adjoint N*, that is: NN* = N*N on a complex Hilbert space H.

There are also many different axiomatic systems, e.g. ZF vs. ZFC, which are built from different rules and which admit different factual statements. It's not like either one is more 'correct' either. In that example, both accepting and denying the Axiom of Choice leads to strange results.

So if you want to make a point about "alternate facts," you might want to make sure that your knowledge doesn't have big gaps in it. It's fascinating just how many different accounts you have to read these days to get a more complete picture of what's going on these days. So many stories (on *all* sides) like to omit and possibly denigrate whichever parts of a story they find inconvenient. You cannot trust any single source, best to read them all and figure out who is leaving out which bits of the story (and why). Personally, I think that a skeptical reading of the news is a good approach.

I'm not a mathematician, but - from many years ago - I do have a mathematics degree. I'm also not a musician, but I have a very strong interest in many types of music. (But not Disco! Nor Herb Alpert & The Tijuana Brass. But I digress.) And I have a very strong interest in dance: but I'm not a dancer.

Anyway, what you write resonates with me. At my university (Warwick) mathematics students could choose whether to be awarded a BSc (UK - BS in USA?) or a BA. Most chose BSc, but a few of us chose BA. My reasons were partly that I felt that most of the mathematics I chose to study was - although rigorous - in some ways more of an art than a science, and partly because I rather preferred having an "arts" degree to a science degree.

I read Francis Su's address in full, and I recommend it, particularly the sections on the importance of play (not just in mathematics) and beauty. (And if you read Andrew Wiles's account of how he finally saw how to solve the serious difficulty that was preventing his approach to proving "Fermat's Last Theorem", you'll appreciate the joy of creation.)

As an example of beauty in mathematics, I want to cite Muntz's Theorem, also known as the Muntz-Szasz Theorem. I came across this while taking a course in Topology: the set book was "Introduction to Topology and Modern Analysis" by G F Simmons. The appendices weren't included in the course but I read them, with not much understanding. But I was delighted when I read a description, without proof, of Muntz's Theorem. It didn't give me the aesthetic pleasure of the greatest music or dance, but my aesthetic pleasure in seeing this theorem was - and still is - maybe similar to that given by a good relatively minor piece by Beethoven or Chopin.

I think part of its appeal to me is that the theorem is a combination of the expected and the unexpected: if you were asked to guess at the correct form of the theorem, then you might well choose what is actually the theorem, but it's still in some ways a surprise, something which is perhaps also true of some of the greatest music - it can be both familiar and strange.

Think of a "continuous" function, say sin(x), and consider it defined on a restricted interval a <= x <= b.
* The Weierstrass Approximation Theorem says that any "continuous" function defined on a restricted interval a <= x <= b can be approximated as closely as we wish by (carefully chosen) polynomials of a sufficiently high degree.
* Muntz's Theorem says that suppose we don't allow all powers of x in the polynomials, and instead use only a restricted set of powers of x: for example
**maybe (1) only x**0 and x **i where i is a multiple of 3,
** or maybe (2) only x**0 and x **i where i is a prime number,
** or maybe (3) only x**0 and x **i where i is a power of 2:
then Weierstrass's Theorem is still true if and only if the infinite sum of 1/i diverges, where i are the powers of x allowed in the polynomials.
So polynomials of type (1) or (2) are all we need to approximate any continuous function, but for polynomials of type (3) there are some continuous functions which they can't approximate well.

Have you seen this nice little problem? http://mathworld.wolfram.com/C... 1, 2, 4, 8, 16, x. Can you guess x?

well, it's 121 years, but according to this article on Lord Kelvin, he said something like that (not exact - but exactness was not specified). I'm inclined to give him the year.

Are you arguing that it's not possible for our universe to be a simulation? Or rather, that it's not worth seriously considering the possibility that it could be? Because I can't see the basis for that. We've made our own physics simulations, and they do tend to be small-scale and don't incorporate every physical law, but that's basically just a limitation of our knowledge and computing power. Nothing I've seen suggests that it'd be fundamentally impossible to produce a simulation that, from the inside, looks the same as our universe.

Also, a simulated universe doesn't necessarily imply that somebody designed it. For instance, it may be possible to enumerate the set of possible physics rules and then try them out one-by-one. (Please read this blog post for a longer and more convincing version of the previous sentence.)

The archaic ARMv6 architecture CPU in the original Pi is radically different from the ARMv7+NEON of the Pi2 or the ARMv8 of the Pi3. When the Pi2 was released you said the performance advantage of ARMv7 builds optimized for the Pi2 wasn't big enough to justify the complication of having a separate OS image. But after the introduction of the Pi3, as people migrate to newer Pis and the rest of the open source ARM world takes v7 and NEON for granted, don't the scales start to tip in favor of builds for modern processors?

Mathematica devs in particular have said that having to target such disparate architectures in a single binary prevents them from using a high-performance BLAS, which slows many kinds of algorithms down dramatically. And many multimedia codecs have had extensive NEON optimizations but these don't always get enabled at runtime on Pi2/3.

The Wikipedia page is terrible this link is better.
http://mathworld.wolfram.com/C...

Is this not, then, Mathematica?

https://reference.wolfram.com/...

May need a calculus workaround for this. http://mathworld.wolfram.com/C...

A bond consists in its simplest cases of electron pairs (or simply an ionic bond): they neither have heat, nor pressure nor any conceivable volume, hence: they are not covered by "the laws of thermodynamics".

Even ionic bonds require or produce some energy to form or break and you can even look up exactly what the enthalpy of doing so is in standard references such as the CRC Handbook of Chemistry and Physics, but it's beyond obvious that you didn't even bother reading your original post, nor any attention whatsoever to any effort ever to actually cover the physics involved here that has ever happened around you.

I can't even begin to figure out where to start on the whole idea that physics has nothing to do with chemistry that is inherit though unstated in your argument--what the fucking hell do you think physical chemistry is? Chemistry is as much applied physics as engineering, merely at a slightly different level.

The bottom line is every single thing in chemistry requires physics, and thermodynamics--primarily entropy--pretty much dictates if any reaction is likely to happen and under what conditions. You can even calculate enthalpy as a function of entropy...and, since you need the extra help, you do so using a calculation derived using the first and second laws of thermodynamics. (It's so basic Wikipedia doesn't demand a citation when doing just that when giving the formal definition. You can also find the equation elsewhere, such as here.)

I'm not going to bother reading another reply from you, because I doubt you'll bother actually checking your claims, no less actually reading my posts, reading your own previous post(s), or coming up with a coherent explanation of how a goddamn function of thermodynamics is not, in fact, thermodynamics. Thermodynamics hasn't been about only "heat, pressure, volume of gases and the usefulness of either of them in heat engines" (as you put it) for well over a century--and even then it was about energy because heat is thermal energy and engines are machines that convert other types of energy into mechanical energy. Chemical thermodynamics has been around since the 19th century, and it's is what you use to explain the physics of how energy of any sort--including thermal--can be gotten from or needed for a chemical reaction, as well as for explaining the physics involved of how energy can stored in a chemical form.

To put it bluntly? If thermodynamics wasn't involved here, the whole question of how much energy is required to turn CO2 into anything else would be like asking how much beef is in a cup of black coffee. Also, all fuels of any kind would simply not function as such--the very concept of fuel would be meaningless, and not merely because that alone would render life itself impossible. I think we'd kinda notice that one.

Hi, AC. Yes, I understood what I wrote. Where the exponent in a function is a constant (in this case 2), that function is polynomial. An exponential function has the parameter in the exponent. The energy in a collision is not an exponential function of the speed. Sheesh, Slashdot used to be populated with geeks!

You can brush up yourself, at http://mathworld.wolfram.com/ExponentialGrowth.html

Buy him the mathematica program. There is a student desktop price as low as $140 "to use for as long as you're a student." http://www.wolfram.com/mathema... If that is still too much money, there is supposedly a free version of mathematica available for the Raspberry Pi http://www.wolfram.com/raspber... (and I've read of a similar program for Atom-based boards). The Wolfram Language book is available free on line. I suspect a working mathematica could be the best possible gift if he is as bright and motivated as you say. He'll learn a Lisp. He'll get an introduction to Functional Programming (and maybe more). And he'll have a working tool to help him through school and far beyond.

Buy him the mathematica program. There is a student desktop price as low as $140 "to use for as long as you're a student." http://www.wolfram.com/mathema... If that is still too much money, there is supposedly a free version of mathematica available for the Raspberry Pi http://www.wolfram.com/raspber... (and I've read of a similar program for Atom-based boards). The Wolfram Language book is available free on line. I suspect a working mathematica could be the best possible gift if he is as bright and motivated as you say. He'll learn a Lisp. He'll get an introduction to Functional Programming (and maybe more). And he'll have a working tool to help him through school and far beyond.

Sorting may be interesting to you, but it's dry and rather abstract. If you are working in Java or python, graphics is available, and graphical projects are far more interesting to the average high school student. Animation of any kind (processing is ideal) 3d animation (spinning globe, 14 lines in processing) 2d board games (checkers). Note you are creating a board that only allows legal moves, not playing. Earth-moon-sun system (for those captivated by the spinning globe. You can do more mathematics if students like it. For example primes. Tying it to graphics, the prime number spiral: http://mathworld.wolfram.com/P... http://adastraeducation.org/Pr...

This may read like I'm a Julia fan-boy ... I guess I am.

I found out about Julia from the Machine Learning course from Coursera. Not directly, for at that time it was Octave; the advice given there was "trust me, for machine learning, this syntax is better." Indeed for many machine learning algorithms, the basis of understanding it, is vector and matrix operations. The innovation of Matlab which both Octave, which is essentially a gnu, open-source implementation of Matlab, and Julia is making vector valued variables first class (e.g. M*X, M^-1 where M is a matrix and X is a vector) makes things succinct and clear -- btw M^-1 is a representation of the inverse of M, an O^3 order algorithm in 4 characters?

Now yes, Python has numpy, which is close syntactically, but there are yet other comparisons were is not quite so easy, and Julia has an advantage here in that it's so new that devs are still tolerant of syntax changes -- for instance the behavior of {} was changed between Julia 0.3 and 0.4. And so if there's something new on the horizon that needs a re-org, Julia is better able to handle it.

The other thing of course which Julia and Python and R communities are attempting to do is to figure out the best way to extract the optimizations available from LLVM, and owing to it's close ties to and ability to modify to conform to changes of LLVM, Julia also has an advantage. As I've posted before, expect Julia to be able to scale almost linearly on the Xenon Phi (Knight's Landing+) for HPC linear algebra oriented applications -- expect this by Julia 0.5.

Or so Mathworld tells me, http://reference.wolfram.com/l... because x/0 is a Complex Infinity, therefore the answer must symbolic, NaN and so the answer to your question is that, the harm is that your code could be non-deterministic if you do not define what the outcome should be in each case. i.e. Assumptions are dangerous.

Division by zero is a problem only in specific cases:

0 is the only number with this property and, as a result, division by zero is undefined for real numbers and can produce a fatal condition called a "division by zero error" in computer programs.

A real number includes the rationals and irrationals. 0/0 does not represent a "number", therefore it cannot be a rational or an irrational. It's NaN.

That said, there are exceptions:

There are, however, contexts in which division by zero can be considered as defined. For example, division by zero z/0 for z in C^*!=0 in the extended complex plane C-* is defined to be a quantity known as complex infinity. This definition expresses the fact that, for z!=0, lim_(w->0)z/w=infty (i.e., complex infinity). However, even though the formal statement 1/0=infty is permitted in C-*, note that this does not mean that 1=0infty. Zero does not have a multiplicative inverse under any circumstances.

Division by zero is a problem only in specific cases:

0 is the only number with this property and, as a result, division by zero is undefined for real numbers and can produce a fatal condition called a "division by zero error" in computer programs.

A real number includes the rationals and irrationals. 0/0 does not represent a "number", therefore it cannot be a rational or an irrational. It's NaN.

That said, there are exceptions:

There are, however, contexts in which division by zero can be considered as defined. For example, division by zero z/0 for z in C^*!=0 in the extended complex plane C-* is defined to be a quantity known as complex infinity. This definition expresses the fact that, for z!=0, lim_(w->0)z/w=infty (i.e., complex infinity). However, even though the formal statement 1/0=infty is permitted in C-*, note that this does not mean that 1=0infty. Zero does not have a multiplicative inverse under any circumstances.

Fine, I have a better citation than the AC.

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. (More concisely, a prime number p is a positive integer having exactly one positive divisor other than 1.) For example, the only divisors of 13 are 1 and 13, making 13 a prime number, while the number 24 has divisors 1, 2, 3, 4, 6, 8, 12, and 24 (corresponding to the factorization 24=2^33), making 24 not a prime number. Positive integers other than 1 which are not prime are called composite numbers.

Prime numbers are therefore numbers that cannot be factored or, more precisely, are numbers n whose divisors are trivial and given by exactly 1 and n.

While the term "prime number" commonly refers to prime positive integers, other types of primes are also defined, such as the Gaussian primes.

The number 1 is a special case which is considered neither prime nor composite (Wells 1986, p. 31). Although the number 1 used to be considered a prime (Goldbach 1742; Lehmer 1909, 1914; Hardy and Wright 1979, p. 11; Gardner 1984, pp. 86-87; Sloane and Plouffe 1995, p. 33; Hardy 1999, p. 46), it requires special treatment in so many definitions and applications involving primes greater than or equal to 2 that it is usually placed into a class of its own. A good reason not to call 1 a prime number is that if 1 were prime, then the statement of the fundamental theorem of arithmetic would have to be modified since "in exactly one way" would be false because any n=n1. In other words, unique factorization into a product of primes would fail if the primes included 1. A slightly less illuminating but mathematically correct reason is noted by Tietze (1965, p. 2), who states "Why is the number 1 made an exception? This is a problem that schoolboys often argue about, but since it is a question of definition, it is not arguable." As more simply noted by Derbyshire (2004, p. 33), "2 pays its way [as a prime] on balance; 1 doesn't."

With 1 excluded, the smallest prime is therefore 2. However, since 2 is the only even prime (which, ironically, in some sense makes it the "oddest" prime), it is also somewhat special, and the set of all primes excluding 2 is therefore called the "odd primes." Note also that while 2 is considered a prime today, at one time it was not (Tietze 1965, p. 18; Tropfke 1921, p. 96).

Take it up with the many mathematicians who disagree with you. The dictionary actually says virtually the same thing as Wolfram MathWorld. So, your point was?

a positive integer that is not divisible without remainder by any integer except itself and 1, with 1 often excluded

A constant is significantly interesting in some way. Fractions or multiples of a constant (which, granted, are just as invariable as the constant itself) are not interesting in and of themselves, but only in relation to the base constant from which they are derived. Pi is only interesting because it is half of tau.

A circle is the set of points in a plane equidistant from a fixed point. That distance is called the radius. The perimeter of the circle is the circumference. The circle constant should be the ratio between these two. Using the diameter is one of the biggest blunders in the history of mathematics. You have to have extra definitions. You get the superfluous 2 floating around in all equations. It's sloppy.

You had an interesting essay "My Hobby: Hunting for Our Universe" on your blog in 2007 about modeling fundamental Planck scale physics via random networks (this was also mentioned in your NKS books). I didn't see anything written or spoken on that topic later. Did that project ever yield any recognizable physics or was it abandoned?

If

Rx = revenue in year x
R0 = revenue in base year (year 0)
then 20% growth means: Rx = R0 * (1 + .2)^x

represented as:

Rx = R0 * exp[(log(base e)(1 + .2)) * x]

Which is exponential growth as seen at Wolfram where lambda = log(base e)(1.2) (and every mathematician I have ever known). Not sure what you mean when you say exponential growth, but it's not the mathematical definition.

Your soap box is quite misinformed.

Nope, you don't need PL/SQL. It depends on what you want to consider "part of SQL" but there are many clever hacks. If it's cool to store code in the DB itself, then all you need is some sort of WHILE or LOOP and a few lines of code that implement a universal Turing machine (preceded by creating the table and adding all the rows that represent the Turing machine, but that's all still SQL) . If you can construct a Cyclic Tag System, that's Turing complete (you can do that with subset of T-SQL: CTEs and Windowing functions - it's really surprising that's Turing complete but it is).

Remember, it doesn't take much. Combinator logic is a very simple pair of rewrite rules that is Turing complete.

If you love games and group theory then check out

http://www.wolfram.com/broadca...

the whole thing flew off as one piece from some supernova explosion

I didn't read TFA but is it's in the elliptic plane, cruising along in the same general direction as everything, it originated in this solar system.

Presumably, you meant the ecliptic not the elliptic plane .

That said, you are likely correct that the asteroid formed via accretion in the protoplanetary disk, rather than being ejected from a supernova.

Regardless, it's quite an interesting conundrum. I suppose it's possible that high-energy collisions melted the material which would become the asteroid and it coalesced into solid chunk(s) which are unaffected by the high rotation rate.

Ugh, that's what I get for posting before coffee. Yes, the sequence that I was thinking of is circle division by chords, not circle division by lines.

R. Schlafly (1994) obtained U.S. Patent 5373560 on the following two primes (expressed in hexadecimal notation):

        98A3DF52AEAE9799325CB258D767EBD1F4630E9B
        9E21732A4AFB1624BA6DF911466AD8DA960586F4
        A0D5E3C36AF099660BDDC1577E54A9F402334433
        ACB14BCB

and

        93E8965DAFD9DFECFD00B466B68F90EA68AF5DC9
        FED915278D1B3A137471E65596C37FED0C7829FF
        8F8331F81A2700438ECDCC09447DC397C685F397
        294F722BCC484AEDF28BED25AAAB35D35A65DB1F
        D62C9D7BA55844FEB1F9401E671340933EE43C54
        E4DC459400D7AD61248B83A2624835B31FFF2D95
        95A5B90B276E44F9.

Too bad the general public is too apathetic to see how completely retarded patenting a common mathematical symbol is when the dam thing has been in use for THOUSANDS of years prior.

Reference:

* http://mathworld.wolfram.com/P...

Then again, 90%-95% of asbestos (crystotile) used wasn't carcinogenic, and the remaining 5% of asbestos used was only carcinogenic to smokers. http://scienceworld.wolfram.co...

Thanks for the excellent link. It does NOT support your summary. For example: "amphiboles are more potent than chrysotile in the induction of fibrotic lung disease and associated lung cancer" does NOT mean chrysotile is non carcinogenic. Similarly, "Asbestos-induced cancer is found only rarely in nonsmokers" does not support your claim that amphibole asbestos " was only carcinogenic to smokers."

Then again, 90%-95% of asbestos (crystotile) used wasn't carcinogenic, and the remaining 5% of asbestos used was only carcinogenic to smokers.

http://scienceworld.wolfram.co...

There is no such thing as a "real" RNG.

That depends on your definition of "random". For most of us, the generally accepted definition of "produced or obtained by a random process (and therefore completely unpredictable in detail)" (OED 4th ed, and yes I'm aware the definition is self-referential, but contains enough information to resolve itself) is adequate, and there are several hardware RNGs available that are effectively "completely unpredictable in detail" -- they rely on thermal junction noise, for which there is no known model that predicts it in more detail than a frequency distribution.

Yes, there are definitions of "random" that cannot be realised within the constraints of a physical universe bounded by actual physical laws, but such definitions don't seem especially useful to me.

Even most mathematical definitions can be met by hardware RNGs. See, for example, the definition at mathworld.

It will! That's an effect called regression to the mean.

Firmly believing you don't have the flu will, in all likelihood, cure your flu in two days to two weeks!

Or rather, believing in not having the flu will likely cause you to misdiagnose flu symptoms as being something unrelated to flu, thereby curing the flu in no-time.
"I have no flu because those flu-like symptoms have nothing to do with the flu because I have no flu."

I did not know that medicine was about believing...

It's called the placebo effect, and it's quite unreasonably effective.

So, I'll start believing that i do not have the flu. Let's see if this works.

It will! That's an effect called regression to the mean.

Firmly believing you don't have the flu will, in all likelihood, cure your flu in two days to two weeks!

b) it is opaque, in the sense that there is little control on what code is doing what data: many of the functions act actually as black boxes and it is not straightforward to see how to actually get in control of the system and/or understand what is actually being done in order to provide an answer.

You can usually twiddle all the options in a function; the documentation is pretty good for most of the standard libraries. Of course, the demo doesn't look as slick if you have to use 6 lines of optional parameters to get the exact thing you want. Typically, the default options do a pretty good job, and there's a lot less typing for those cases.

Of course, it's also a universal language. You don't have to use the standard libraries; feel free to roll your own. I'm sure an hour later, you'll have a bit more respect for how well the default stuff works.

Are those libs even written in Wolfram?

Yes, and also C/C++ as necessary: Software Engineering of Mathematica.

So, negative 136 celsius then. That is, after all, "twice as cold" as -40 celsius when computed via Kelvin (the only way that makes sense).

I don't know what the nonsense about Kelvin is about.

Wind chill is effectively a measurement of rate of heat transfer from humans. According to Newton's law of cooling, which is a quick and dirty approximation to heat transfer, the rate of heat transfer is proportional to the temperature difference.

If the human body is 37 degrees C and the outside temperature is -40, then the temperature difference is 77 degrees. If the heat transfer rate were to be doubled, this temperature difference should be doubled to 77*2 = 154 degrees. A temperature that is 154 degrees below body temperature would be 37 - 154 = minus 117 degrees C. Wind chill models are more complicated that this, but I don't think anyone's claiming that the wind chill will be anywhere near -117 degrees C.

So I think both you and the weatherman are saying bogus things. I believe the weatherman in the summary is effectively just saying "double the distance below zero" -- which is decidedly dumb -- and you're rambling on some nonsense about Kelvin when you actually need to be calculating heat transfer rates, not temperature.

Ah, wait a minute - the Earth is moving as well as rotating. So the photons reaching Earth are moving (relative to Earth) with a velocity that is the combination of their initial velocity and Earth's orthogonal velocity. Meaning they should appear to be slightly blue-shifted, and coming from a point slightly more in front of the Earth in it's orbit. Unfortunately I can't remember the details of relativistic velocity addition offhand, so I can't calculate the exact angle of the discrepancy.

This is referred to as The Aberation of Light , which is an unfortunate name because light aberration has a different meaning with regards to optical systems.

Given that, then if gravity travels through space at a finite speed then a similar discrepancy should exist, with gravitons hitting the Earth from slighty "in front", and accelerating the planet in it's orbit.

This makes no sense to me.

Let's look at some documentation instead of speculating.

His whole question and narrative is telling. This is obviously someone that has no idea what he is doing nor why. He is also most likely in violation of Wolfram's license agreement on top of his lack of computational knowledge. He should have stopped at web statistics and stayed there.