It is possible that this is a huge smokescreen to cover up targetted killing, and that the perps are in a big hurry. The idea would be shoot a random bunch of people, amongst whom happened to be some talented academic from Texas A&M, ... I hope my friend Adam Banks is OK. He's a Brit living in Texas, before that he lived in Norway and had one of those ATB skiddoo type things, which probably aren't much fun in TX, ...
At 12 minutes 42 seconds, after showing how rational parameterizations for an ellipse can be constructed from one rational point on the curve, and a straight line, he notes that this can be done for any conic.
I have a feeling that it could be done more generally, for any curves that can be defined as a plane cut by a ruled surface. It seems to me that the only surfaces Euclid considered serously were ruled surfaces: a sphere is not a surface in Euclid's view. This would explain his definition of the circle and semicircle: from Fitzpatrick's edition of Euclid's Elements. Now look at Eucld's definition of a right-lne "A straight line is any line which lies evenly with the points on it", and his definition of a right-angle as "If a right-line is stood upon its end on another right-line, such the angles on either side of the vertical are equal, then those angles are right-angles". Then in a later book, "All right angles are equal. Now think about a right-line AB from point A to point B, and imagine it does not lie evenly with the points on it. Draw a straight line from A to C, and another from C to B. This is a three-sided figure. Now look at Euclid's definition of a triangle: it is a proposition. A triangle has internal angles which sum to two right angles. Now look at Euclid's definition of a circle and a semi-circle.
A ruled surface is the boundary of a cone of light from a point source, so the study of intersections of ruled surfaces is one which can be done just by looking at the action of shadows cast by straight edges onto a screen. Thinking about Plato's "Myth of the Cave" in The Republic, in this context, should give a fruitful way to interpret the notion of Platonic reality. Then read the first chapter of Aristotle's Physics, to see how Aristotle's and Plato's philosophies relate to each other: Aristotle on The Continuum , ... See Rafael's fresco The School of Athens at the Vatican:
Now, by systematically exploring these relationships, one may develop quite a useful body of theory which makes a fairly sound basis for observational astronomy and geodesy. In the latter, you would be interested in ways to locate, say the center of a circle based on observations of an eliptical projection of the circle. Think about relating the readings of sundials and solar and lunar eclipses, at different places, such as at Athens and at Alexandria, ... and collecting the data over several years, then bringing it all together and turning it into a theory about something or other, such as the actual shape of the earth?
This is a reconstruction of Feynman's derivation of Kepler's law from Newton's law. It might be interesting to think about how Kepler's law could have been used to derive Newton's laws, ... with a little help from Euclid, maybe, see All About e and Quaternions Visualised
Now listen to this lecture on Electrical Engineering, by Eric Laithwaite, ...
Now before the people at Cambridge go nuts, watch this beautiful talk, which may sound tongue-in cheek, but isn't. It's totally genuine, and utterly brilliant!
With that in mind, go back and watch the above videos again, and then watch this one:
Some people 'round here need to belt up!
... and study Architecture:
Apparently you don't have to believe in shared simultaneous spaces in a rotating reference frame to be able to do astrophysics! See There's Trouble Down't Dark Satanic Mill!
Helium is thought to be the most abundant element in the Universe. So it is a testament to the competence of the captains of idustry and the free market that the world faces a helium shortage. Something fishy is going on, and I think Bill Clinton knows what it is. See The Quigley Formula.
Helium is found in natural gas, but there are very few extraction plants operating. The biggest was in Qatar and has been shut down. There is another in South Africa:
Here are some ideas about how to make a helium detector, and they also suggest how to start thinking about filtering helium: the thing is, helium atoms are so small and they move so fast at room temperature that they pass through latex, for example much quicker than air, which is why helium balloons need to be made of aluminium foil.
If it is only the helium you need to extract from LNG, then filtering it may the more efficient way to do it.
All I have been able to do today is add a couple of comments to this post which show how we could build some useful hardware, and program it, and use it to develop reliable electronic control systems for industrial robotics.
Please can somebody arrange for me to be able get enough food to eat, without having to spend hours begging for it. I am fed up with starving and eating the garbage people bring me. Why am I not entitled to choose what I eat? Am I just too fucking stupid or something?
Maybe this will give you sime ideas on how to define a $3 Tensor? See Tensor Calculus:
To get a vague idea of the plan, note that the Brachistochrone is a Cycloid, so it enjoys the property that its involute is the same curve as itself. Now note that if we express the "squishing action" at any point of the derivative along the real line, as illustrated in this video (at 9 mins 20 secs) then the rate of change of the involute at that point ought to have some amusing properties, because it sounds to me like a basis for a notion of curvature of some kind. This might turn out to be nicely behaved in some sense, if the straight line along which the circle rolls to generate the brachistochrone were approximated from above and below by a circle rolling along the equator of a sphere as the sphere rotates through 5-space in the quaternion representation. At that point it is a sphere of infinite radius, so you get a straight line at any angle on the surface and it will look like a complex plane, I guess. See Quaternions Visualised for a nice video.
The English poet William Blake wrote somewhere about this finite world being error, "wheels without wheels" and he associated the divine with "wheels within wheels", a point which seems to ave passed by some analysts of Blakes work: Blake's Transformations of Ezekiel's Cheribum Vision in "Jerusalem". These two diagrams seem suggestive of some similar idea, to me, ...
This association is one I read 30 years or so ago, and I can't remember in which of Blakes works it was, nor can Google find it, but I am pretty confident I read it somewhere, maybe "The Marriage of Heaven and Earth". There is a suggestion of this in "Jerusalem", from Edward J. Rose's 'Wheels within Wheels in Blake's "Jerusalem"'
Anyway, to get some ideas for how to calculate derivatives on this weird revolving globe, which Blake thought of as the boundary between the human and the divine, see this video, which explains the Euclidean notion of "comensurable in square only":
Now recall that a solar year and a siderial year differ by one and some fraction of the order of 4/365 of one day, ... why? Because the earth rotates in the same sense, whilst it orbits the sun. But rotating a circle along a line with positive curvature inside the huge circle and rotating it in the other way along the outside, with negative curvature will do what after one full (albeit huge) orbit? ... so that gives the intuition, vague as it is, that I had, about how rotations in space could be used to give a rational model for tensor calcus of some kind, ... But for all I know, that's how Gauss did this stuff in the first place, ... I dunno, I never understood tensor calculus. 🤦
The reason I mention the Brachistochrone is its connection with variational mechanics. See also Tautochrone curve, which is also a cycloid, and so shares this property of being self-involute. This is also the curve used to produce an isochronous pendulum, if you happen to have a gravitational field handy, that is, .... But if you're in free-fall? ... well, I dunno 'bout that. Ask an experimental scientist, ... or Ricci?
So anyway, I love this song!
Because it's about the swarms of little guys you see here, caught up in the Incredibly Big Machine, .... wheels without wheels, ...
... choreographed by some divine comedy, but without individual significance, ... In Spanish we say personas particulares.
Sounds like climate-control fuel additives aren't good for high-tech metallurgy. That's the problem with secret cabals, they don't realise that the world is a connected whole, so you can't do stupid stuff in secret, unless everybody is in on that secret. See Fuck-witted Assholes Plan to Save The World.
... then go back and listen to Diana talking about the LIGO experiment at 4 minutes 42 seconds, ... sounds like someone needs lessons in long distance spittin' ...
This idea is also interesting with regard to sound modelling of the process of computing solutions to differential equations as discussed in Aristotle on The Continuum.
See
These last two videos will give you a motivation for understanding the idea of a conformal mapping of the complex plane:
It looks to me like there might be a kind of duality in the above transformation. It might lend itself to illustration by this view of Fourier transforms. The relevant part of this idea is that of using a parametric formulation of the 2D curve you are calculating the transform of: this gives you two dependent functions, x and y, say, of a third independent variable z. The reason for this is that it is dependencies between x and y which lead to singularities in the derivatives, where the "slope" is infinite. But precisely where these singularities occur on the curve is merely an accident of the chosen basis: the particular orthonormal pair [i,j] which are in some sense arbitrary. This doesn't happen when the derivatives are taken with respect to a separate independent variable, which is orthogonal to i and j. The reason that this works is that you can often quite easily find a relation between the derivatives w.r.t. to the two dependent variables, and since their basis vectors are orthogonal, when one of them is close to 90 degrees, the other is close to zero, and well-behaved there. Now, if you look at the way the Euclidean measure of angle works, the half-turn, it paramaterises the rational points on the curcumference of a circle by units of exactly one right angle, and it does so symetrically about the 45° line, so the values at the parameters above and below the 45° line are reciprocal. See the fourth lecture of Wildberger here: Neil Wildberger on Quaternions and Rational Trigonometry and this video on complex exponential function, from 18 minutes 33 seconds and this video on the idea of the exponential function being the fixed-point of the derivative function.
This is basically the idea behind implicit differentiation which Nancy Pi explains rather beautifully here:
On the summing of infinite series of reciprocals of squares, see this video on how Euler calculated a closed form for the value of the Riemann zeta function at 2.
And here is a more "left-brained" treatment, but still visualisable, just you have to visualise processes of algebraic operations on equations, rather than processes of geometric operations on points, ...
At 8 minutes 35 seconds you see that by starting with the idea of some sort continuum, and deriving operations from the repeated process of division, you can recover basic elements such as the integers 1,2,3,4 and 5, but underlying the idea of each element is the idea of a continuum operated on by operators which have names, ... What are the names, well, they're things like 1,2,3,4 and e. This is what I meant by the phrase "sound modelling of the process of computing [numerical] solutions to differential equations". This is the idea underlying the use of Fast Fourier Transform to efficiently compute products of large integers: in the Fourier space multiplication is convolution, which is a sort of smearing addition operation, in the same way that long multiplication works by adding shifted copies of the multiplicand together. It the linearity of the Fourier basis functions which make this representation possible. See
So this idea of modelling processes of computing numerical solutions 5o differentiial equations gives models of integersas functions like 2^t = e^ln(2t) and that allows us to treat functions and their inverses symetrically, by using a single independent (i.e. orthogonal) variable, and the chain rule is then the connection between the derivative of the function and the derivative of its inverse. Here's a nice explanation of how abstract vector spaces can be used to represent both the functions as operators, and the spaces of things upon which those self-same operators act.
And this gives us the idea of a duality between the different representations of functions as vectors and vectors as functions.
Under this duality, differentiation is an operation which rotates a representation of a function in such a way that the odd components of the function are transformed to even components, and vice versa. In other words, differentiation is a kind of phase-shift. The kinds of vector spaces which have this duality property are called inner product spaces.An Inner Product Space is any Vector Space with an extra scalar field, called a norm which obeys certain symmetries of conjugacy which restrict the way scalar multiplication acts on vector elements to preserve this duality. This scalar field is often the complex plane, but can even be a two-vector of complex vales, as is the case with spin one-half systems in Quantum Mechanics which are represented by spinors with something called Hermitian symmetry to preserve the conjugacy requirements of the inner product space axioms.
The idea I have is that we can model the "whole stack", starting with some species of complex analysis and associated operators for differentiation and integration, down to a successor functional on the integers, as a thing called a Catrtesian Closed Category, starting with just the exponential functor. And this will allow us to build an arbitrarily deeply nested series of inner models for operations on any part of the continuum we can meaningfully carve out. This will allow us to investigate, for example, in what conditions the axiom of infinity plays nicely with the power-set axiom. Cartesian Closed Categories are part of Category Theory, a.k.a. Abstract Nonsense. Here's a nice introduction to the idea of a functor which is one of the principal abstractions:
See Aristotle on The Continuum, which gives some of the very basic theory. Now people of a more practical bent might think this is all a bit Airey-Fairey, so they should have a look at how it applies to industrial robotics. First, see my comments on this video, about we can make a low cost computer which computes these operations:
Those comments will also explain how I think we could quite practicly and feasibly build a machine, at moderate cost, which formally verifies its own operation as it progresses.
Now see how we could build such control systems into industrial robotics and process control systems, including safety-critical areas such as flight control systems for passenger aircraft: See my comments on this video:
I have thought a bit more about the idea of starting at Brachistochrones and Involutes and am now convinced of it, because when I looked up the definition of Evolute, it turns out to be just a generalisation of Euclid's definition of a circular arc to any curve. If you look at a copy of Euclid's Elements in Greek, such as Fitzpatrick's, you will see that in the Greek, a circle is described as a curve where the locus of perpendiculars is a point a constant distance from the curve. In other words, the circle is the degenerate involute of a singularity. This corresponds exactly to Gauss' idea of curvature. See All About e.
But the Daily Twatograph says images that celebrities tweeted are out of date, so there's no problem, ... That will be a relief to Evo Morales, who is the world's first ever indigenous president and a self-proclaimed guardian of La Madre Tierra, so nothing like this could happen in Bolivia, oh no!
La Tierra No Se Vende? They should be outside the Bolivian Embassy in London with that: https://youtu.be/3gcz2pzH5nw
This looks very promising, but I rather doubt that I will get around to watching all of this four part lecture for quite a while. To get an idea about why this le ture is worth paying attention to, see
I wonder if Olya Misik is on some kind of medication. Seriously. But whatever it is, it's nothing compared to the stuff that the FT people who did this piece must be on!
SNC-Lavalin, based in Montreal, is accused of paying C$48m worth of bribes in Libya to Muammar Gaddafi’s family, in order to secure lucrative contracts. The bribery is alleged to have occurred between 2001 and 2011.
On being the Captain: Here is a guide for the perplexed:
It will, for example, explain to you the difference between cybernetics and steerage, ...
but there is a rather unfortunately necessary pre-requisite, which is literacy! Otherwise you mght just think it's about beavers, boots, butchers, and the number forty-two. It's Lewis Carroll's "The Hunting of the Snark".
Before the war, the United States and the United Kingdom had been major material allies of both India and Pakistan, as their primary suppliers of military hardware and foreign developmental aid. During and after the conflict, both India and Pakistan felt betrayed by the perceived lack of support by the western powers for their respective positions; those feelings of betrayal were increased with the imposition of an American and British embargo on military aid to the opposing sides.
Indira Ghandi, daughter of Prime Minister Nehru was elected Prime Minister of India in 1966. The Mountbattens were there
At 32 mins 33 secs you get some idea of how influential the Mountbattens were in India at 33 minutes 42 (2022 seconds) Vijaya Pandit, sister of Nehru, talks about Mountbatten's support for India.
He led the country during the Indo-Pakistan War of 1965. His slogan of "Jai Jawan Jai Kisan" ("Hail the soldier, Hail the farmer") became very popular during the war. The war formally ended with the Tashkent Agreement on 10 January 1966; he died the following day, still in Tashkent, with the cause of his death in dispute and it was reported to be a cardiac arrest but his family was not satisfied with it. Shastri was a Nehru and Congress loyalist. Nehru was his mentor and was fond of Shastri. Although Shastri faced stiff opposition from within his party, his relationship with Nehru aided his ascension to the office of Prime Minister.
Here's Shastri's son Sunil talking about his father
You might think that a terrorist group who abducted up to 100,000 children and who tortures, mutilates and murders tens or hundreds of thousands of people would be known and reviled all over the world, but I'd never heard of them. Why? Just because 99.9% of their victims are black Africans living in DRC and the Congo? Or because they're Christians? Or because they're supported by the CIA?
This is where we are heading. This is the kind of world you make when people only believe in money, not what they actually know. This is what the CIA will eventually become: a bunch of deranged fucking assholes like Pompeo and Bolton, with guns and money, who think they are running the world and part of some fuck-brained biblical crusade fulfilling some fuck-brained prophesy when in fact all they are doing is destroying themselves, and taking millions of others with them.
Assange is not allowed to fraternise. Well, fraternity is overrated, if you ask me. At least his animal rights aren't being abused just so that half-wits can give him bullshit theology lectures.
Here's an interesting lecture on philosophical problems with modern mathematics. What kind of world is it where all mathematics students aren't shown the construction of the Stern-Brocot Tree and its connection with Continued fractions and Farey sequences?
The problem, as Aristotle pointed out quite clearly over a couple of thousand years ago, is that we shouldn't expect to be able to prove anything about a whole from logically prior parts. That's not how logic works. See On Indivisible Lines: page one:
Aristotle wrote something once, somewhere, which was something along the lines of:
What is it that pluralises the one and makes it many?
And his answer was something along the lines of:
That which pluralises the one and makes it many is error and the nature of error.
So, if you want a sound logical basis for mathematics, maybe look at Gauss' error function, and a co-construction of some sort of abstract space and its dual, for example, a normed vector space, whose dual is some sort of Fourier transform, and look for way of building in the steps of that construction by encoding computations into elements of the space. If such computations include iterative proof searches, for example, then you could still hope to produce a coherent whole without needing to know in advance all such questions such as "Is the Riemann hypothesis true", or "Is PA2 consistent". This is what I tried to express here: On Tarski's Definition of Truth "Convention-T". For further discussion, see this post: Logic, in particular this brief note on constructivism, intuitionism and foundations which was the result of an attempt to engage someone in a rational discussion on this subject. The attempt was a failure, I hardly need to add, ...
The idea of starting at a whole and deriving constructions as a process of synthesizing it from elements produced by dividing the whole is inherent in Islamic geometry. See this post: Geometry in Islamic Art, in particular, this video, from 43 seconds:
It's really sad. The same happens with demonstrations. I saw a demonstration here last night, with a few dozen people demonstrating against Evo Morales and the burning of forests. See 2009 Coup D'Etat in Honduras in Bolivia. I can think of half a dozen groups here who might have thought this was something worth faking, including Evo and Alvaro. Because of this, no popular protest is meaningful anymore. We have to find another way. I think it should be through law and the justice system, but this is problematic too. It's really fucking depressing, to be honest.
One way to deal with this problem is to allow scientists to use on-line tools to design complementary research programs. This would work by seeking out vertical dependency loops in the scientific deductions that could be made in different fields, as well as practical or experimental horizontal dependencies which link fields of research by their common requirements for experimental conditions. One example might be geologists exploring sub-sea rock formations, and biologists like Lloyd studying subterranean marine microorganisms. Both would be linked horizontally by the need to have access to undersea drilling apparatus. An example of vertical integration would be people looking for ways to treat nuclear waste, who would be interested in results about bacteria that consume radiation. If funding were decided by a process of optimising the global development of science as a whole, and if funding bodies all cooperated, then much better decisions could be made from the global perspective. See On Connecting People for some ideas about how we could construct systems to help with this optimization process.
Now listen to this description of a Babylonian clay tablet which is thought to be around 3,800 years old. At 11 minutes 49 seconds note how the vertical side of the triangle is unity. Note also the theorem of Euclid which relates the mean proportional of two numbers to the perpendicular height of the right-angled triangle lying in the semi-circle. For some reason, blogger won't let me post this youtube link inline: https://youtu.be/L24GzTaOll0 but here's a snapshot:
Now watch this video and note the connections between decimal and sexagesimal arithmetic which turn up in the Pisano relation, and howLagrange was interested in these when he came to study dynamics and stability of the Solar System.
Now note the proof of Pythagoras' at 1 minute 53 seconds which takes 4 copies of a right triangle and rearranges them like this:
Now look at 9 minutes 30 seconds of this video, on the irrationality of the Golden mean:
Now check out theorems about the squares of primes: for example, that they are all of the form 24n+1.
Then look up this 2100 year old Greek calculating machine found in a shipwreck in the early 1900s, ... Note the numbers of teeth on the gears, ... 10 minutes 13 seconds, ... and how they were used to synthesize intervals as portions of one year.
Now look at this way of synthesizing intervals using Fourier series
But it goes on to connect to ideas about uncountability and computability too. For example, check this cute theorem in the N+1=N video at 23 minutes 30 seconds, then listen to Jade on Cantor's proof of the uncountability of the reals
If every Native American supports him then without any other support at all, Mark Charles' name would be on the ballot in all fifty states, .... and then the fun will begin! For example, he could probably persuade Scott Ritter to run as Vice President, ... and with a kick-ass land reform and agricultural development programme he could get the upport of a large part of the rural population, see IPCC Nonsense, ... As they say "Just do it!"
Over 160 million dollars of farm bailouts went to city slickers. That much money could have started a programme to develop an agricultural land and water supply restoration programme and a new sustainable basis for the US economy. See IPCC Nonsense.
What is much more interesting about this report is how effective the Department of Justice is at fighting white collar crime, ... it isn't. The DoJ doesn't even try!
From 2009:
On cost-benefit analyses of cheating, see "Security Theater". In the following talk about inequality, I would have loved to see some examples of justice and perceived and desired levels of inequality, analysed in Bayesian terms of the sample populations drawn from different demographic classes.
This woman and her boyfriend came to me today to give me a rotten mandarina and two pesos and tell me to never give up on my dream of seeing my daughter one day. And then this stupid idiot tells me that Evo Morales isn't going to jail, and that he's going to be elected as president again. She is very badly mistaken. Evo Morales, and all his accomplices, are going to face trial for the crime of traición de la pátria, under the constitution and statues of the Republic of Bolivia. See 2009 Coup D'Etat in Honduras.
This explains why it is so difficult to learn something that you don't already know.
There is a problem with many analyses of psycho-dynamics of trust based on money. They use money, because it allows some measure of objectivity, but what they don't take into account is that the subjective value of money depends upon many things, such as how much you have, how much you think you are going to need in the future and how much you think you think you are going to actually get in the future. They also depend upon how you value the possible ways in which you could use that money. So in all these behavioural experiments the results are highly suspect, even if you were to take into account the demographics of the sample population in terms of financial wealth and level of education. So what I am saying, in this "long rigmarole of the slave", is this: these observations are not observations about "human nature", they are observations about the behaviour of people under certain highly dubious premisses about the value of money and education. That said, we can still learn from them some of the tricks that people with access to practically unlimited amounts of money can use to manipulate large swathes of a population, and it doesn't bear thinking about!
Here's an Al Jazeera report that was aired during the 2016 Presidential campaign. See in particular from 2 minutes 12 seconds: Environmental activist Berta Cásares was assassinated in her home on March 2016:
A former soldier with the US-trained special forces units of the Honduran military asserted that Caceres' name was on their hitlist months before her assassination. As of February 2017, three of the eight arrested people were linked to the US-trained elite military troops of which two had been trained at Fort Benning, Georgia, USA, the former School of the Americas (SOA), renamed WHINSEC, linked to thousands of murders and human rights violations by its graduates in Latin America.
The problem is, how we are ever going to be able to prosecute these people for these war crimes when we have corrupt, frightened, stupid heads of state like Morales and Maduro desperately holding on to power because they're afraid of doing a couple of decades of jail time. What's the problem, do they think their human rights will be violated somehow? For more on Prison Reform, see this post, ALL THE WAY THROUGH!! Why Climate Scientists Shouldn't Set Policy.
I wrote this weird thing in April 2013, because I was starving and people in Cambridge refused to help me, so I thought the end was nigh. At the time I wrote it, I didn't know Hugo Chavez had died, let alone that there would be an election of some sort in Venezuela within a few weeks. The inflamatory part is in the lyrics to this song, which I altered, see the last few pages of Economics II, about "Predators, preserved by Venezuelan Oil Tar Empty cartridges from a Magnum Tossed, into agricultural lime..." which could also read "Vote cartridges from a[n] MT into agricultural lime, ...."
So after that, maybe George Soros sent someone down to Venezuela wirh a fistfull of dollars to cause a riot over voting machines and Maduro's first act on being elected was to have seven protestors killed, .... shit like that does happen, see Who Owns The Revolution?
On page 8 of Economics II, there is this quote from Aristotle, on what is the efficient cause of any movement of the spirit. Seeing how my life has gone, I have to say that experience bears him out!
As Isaac Newton would have said "I have made the experiment." See Catholic Church.
