It's All Theory: Physics, Economics, China, and more. Yet more social media posts by Lukas Saul.
The harpers was the nickname of which British football team?
In Brief: A Harper is dedicated to three things:
– The freedom and autonomy of all living things
– The balance between the settled and the wild
– The preservation of knowledge
In short: we found this pamphlet discarded in the wild, here it is.
A “low protein” experiment on 3 million subjects, from Denmark 1920, M. Hindhede, Journal of the American Medical Association
hindhede1920How well do you know your powers of two? You gotta at least know the first ten of course. The first twenty is quite good. The first thirty? Better than me.
Print them out, label them, and go study up! The 2048 card is only there because there’s an extra spot to fill, when I have made these flash cards in the past we only went up to 1024.
Enjoy!
(By request, from Dmitry Orlov, reblogged here without apology or permission. Go buy his books or support his blogging on boosty, or feel free to complain about the errors in his opinionated prose on your own pages or in the comments)
Many people around the world gaze in wonder and amazement upon the assortment of geriatrics atop the great American pyramid of power—the withered witches Nancy Pelosi (82), Maxine Waters (83) and Dianne Feinstein (88), the living cadavers Chuck Grassley (88), Jim Inhofe (87), Richard Shelvy (87), as well as quite a few others, and the obviously senile Joe Biden (80) who sits atop it all. How does a pile of oldsters, all of them obviously well past their prime, manage to control a great big empire, the biggest (strictly in budgetary terms) military power on Earth and the sacred keeper of the Holy Dollar Printing Press?
The people old Biden commands aren’t spring chickens either: Lloyd Austin at the Pentagon is 69, Janet Yellen at the Treasury is 76. If you look at the various powers behind the throne, there’s the Yoda-like Kissinger (99) and the moneybag George Soros (92).I don’t mean to be ageist, but it is simply foolish to ignore the toll time takes on our brains, as well as the rest of our bodies, as we age. It is not just our limbs that become less flexible (check if you can still touch your nose to your big toe) but our thinking becomes ossified as well. Our learning ability dwindles over time: short-term memory shrinks, long-term memory decays and receptivity to new concepts and ideas declines. We become emotionally attached to the past, comforted by our memories, shocked by an increasingly unfamiliar present and fearful of an unpredictable future.The political science term for such a system of government is gerontocracy. It can take many forms.
Its most benign form is the council of elders found in many traditional societies, who accumulate authority through experience and reputation and wield power through the unconditional respect that must be given to old people in traditional societies. In places where centralized authority is weak, repressive, remote or nonexistent, tribal elders are often called upon to help resolve conflicts that would otherwise give rise to violence, and political authority naturally accrues to those with a successful history of conflict resolution.
Obviously, this is not the case in a young country like the US: 236 years is a blink of an eye in historical terms compared to 6000 years for India, 4000 years for China, 2500 for Persia and 1000 years for Russia. Nor is gerontocracy a natural outcome for a system of representative democracy: why would young people ever choose their great grandparents to be their elected representatives? Also, why would crusty old greyhairs be a natural choice in a country undergoing rapid change that in a single generation experienced the end of the Cold War, the rise of new China and Russia, the development of the internet and now the proliferation of artificial intelligence applications and robotics? Obviously, something has gone seriously wrong with the succession of political authority in the US if old people can’t retire from power and younger people aren’t allowed to advance and take their place.The most malignant form of gerontocracy is rule by an oligarchy of the aged. Imagine a small clique of elderly men and women tenaciously clinging to power, protected by a powerful police state and many layers of yes-persons (the woke version of yes-men), shielded from any negative or unexpected news that might undermine their already shaky grip on reality. This characterizes the current state of the American democracy reasonably well, but leaves some questions yet to be answered.
Such as: Why are these oldsters afraid to retire? Why aren’t younger people allowed to take their place? How distorted is their image of the world and what are the consequences of that? and, finally, How long can this possibly go on and how is it likely to end?Starting from the end and working toward the beginning of this list of questions, we have the wonderful and relatively recent example of the slow decline and sudden fall of the USSR. World War I exposed the rotting hulk of the Russian Empire and its dysfunctional monarchy was replaced with a bourgeois democracy which failed spectacularly within half a year and was replaced by the Bolsheviks, who were Marxist communist revolutionaries. A civil war ensued, which the Bolsheviks won. It then fell upon Stalin to quell the revolutionary fervor of Trotsky and his followers, mostly by simply having them all killed, and to reorient the ideology from world revolution to building socialism in just the one country he ruled. In this he succeeded beyond anyone’s wildest imagination: industrialization, World War II victory, the atomic bomb, the space race and various other stunning Soviet achievements are mostly to his credit. But he certainly wasn’t picky about his methods—he didn’t have that luxury—and after his death this allowed his legacy to be very much tarnished by the likes of the very stupid and incompetent
Nikita Khrushchev and the compulsive liar, eclectic prose stylist and anti-Soviet propagandist Alexander Solzhenitsyn. The Soviet system, although effective for its time, had a congenital defect: it had no ability to renew itself. After Khrushchev was summarily dismissed while on holiday came the overly cautious Brezhnev who opposed even the most necessary reforms. Then came a procession of near-corpses: Andropov with his faulty kidneys and his insane wife; Chernenko who wasn’t quite alive throughout his 13-month term in office. And then came the young, charismatic, popular Gorbachev who destroyed the country in five years and is now the most reviled person in all of Russia, comparing favorably only to Hitler.
I will spare you the thumbnail sketch of American history and simply note that the US went from a post-World-War-II industrial powerhouse with top-notch science and engineering to a country full of ignorant, lazy, slovenly people that just prints money, scares the world with its aircraft carriers into using that money for foreign trade, and imports most of what it needs, including intelligent, educated people. And now the money-printing business is failing too, with the share of the USD in international trade having shrunk from nearly 100% to barely a third. But the crusty old gerontocrats don’t know that the world has changed and the yes-persons who surround them won’t tell them that the money-printing affair is almost over, that the aircraft carriers no longer frighten anyone and that the intelligent, educated people are leaving.Reasoning by analogy, we might think that once Americans manage to get someone young into the White House, it will take five years for the USA to collapse. Supposing Joe Biden croaks tomorrow, how long would it take his VP Kamala Harris to destroy the country? She would have two whole years to do it; would she manage? No wagering, please! Instead, let us answer the other questions.Why are the American gerontocrats so tenacious in clinging to their offices even as they struggle to fight off Death’s cold embrace? Why were the Soviet gerontocrats so loathe to let in new blood by retiring? Perhaps it was because they and their families enjoyed lives of exorbitant privilege, walled off from hoi polloi in special compounds. They had their own special apartment buildings, clinics, hospitals, sanatoria, schools for their children and shops in which they could buy luxury goods, living in a different universe from the citizenry of their land. Perhaps it was because this entire edifice of exorbitant privilege was build on a foundation of lies, corruption and theft that negated the very premise of a just and egalitarian socialist society. Or perhaps it was that the new blood would naturally have to be their own flesh and blood—their own precious children, that is, to whom would go all the cushiest jobs, except that their children weren’t turning out so well. They were unfit to serve in any capacity, being a special-bred race of overprivileged, pampered, psychopathic assholes. And so their only choice was to cling to power until death’s kiss because the alternative was the kiss of death for the entire Soviet institution—as it in fact happened.
It’s not that unusual in countries around the world for the new president to be the son of the old president. In Syria, when old al Assad died, young al Assad took his place; in North Korea, the great leader Kim Il-sung was succeeded by his equally illustrious son Kim Jong-il, who was succeeded by his grandson Kim Jong-un, who isn’t turning out to be too shabby either, what with his nuclear-tipped hypersonic missiles that can hit California (whereas the US ain’t got none). And let’s not even bring up Muḥammad bin Salmān Āl Su’ūd, who is quite a lively character too; he is there because his country is a kingdom in which his daddy is king. But that sort of family succession works well in honor-based polities; in privilege-based polities like the USSR and the USA, that just doesn’t work.
Imagine Hunter Biden strolling into the Oval Office, crack pipe in his teeth and a couple of underage Ukrainian prostitutes in tow, ready to accept lavish presents from foreign officials in exchange for huge chunks of the American pie. Imagine his crackhead buddies infesting the halls of Congress and enriching themselves through insider trading by buying defense company stocks the day before they sign huge defense contracts, then selling them the day after and pocketing the difference, then getting massive kickbacks from the defense contractors via their employees’ political campaign contributions—all perfectly legally, by the way! Imagine the State Department and the Treasury being restocked with cousins and uncles of the Ukrainian prostitutes in exchange for some very special, extra-kinky bedtime favors.
Mind you, all of these things are happening even with the old guard still in office—the giveaways of huge chunks of the American pie, the insider trading, the kickbacks, Ukrainians all over the place and all the rest—but with the difference that the old guard knows how to be secretive and cautious and how to hush things up when there are leaks, which are traits that develop with age and experience, whereas the young guard won’t know better than to flaunt their wealth and privilege, party like there is no tomorrow (which for them there probably won’t be) and very quickly burn down the house.And that’s the optimistic scenario. The pessimistic scenario, which is similar to what Gorbachev put into motion in the creaky old USSR, is a plague of reformers. The environmentalists would ban all internal combustion vehicles, all power plants and all cows (because they fart). The sound money maniacs would reintroduce the gold standard (only to discover that the Chinese and the Russians now own most of the gold). The libertarians would get rid of fire departments and just let everyone buy their own fire hoses and fire extinguishers. And the wokesters would fire all men who aren’t gay and green-light the careers of handicapped obese black trans lesbians.Now let’s combine the two: the degenerate, sociopathic scions of the old guard usher in the barking-mad reformers as a cover for their crimes. Now they’ll be burning down the house from the top even as the reformers undermine the foundation.
Gerontocracy is bad; but what’s worse is when the gerontocrats start joining the crowd invisible and are replaced by troglodytes of every stripe. The American gerontocrats are all of a single very numerous generation—the Baby Boomers—and they fit quite neatly under a bell curve. If we wish to test this hypothesis, then timing the collapse of the USA is mostly an exercise for an actuary. Perhaps Gail Tveberg the actuary would like to take a stab at it? Let’s ask her.
Sometimes we come across a great paper and we want to share it.
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As you all know, there’s been a problem with disinformation recently. Governments and advertisers are working to protect us from this threat, but none the less the threat exists and we should be aware that dangerous and wrong information exists and can fool us, hurt us, hurt our families, and hurt our countries and the businesses that our country’s leaders have invested in. Hopefully a solution will be found soon that can protect us once and for all from these threats, but for now we have to be on our toes. In that spirit I would like to share a particularly pernicious bit of disinformation, so that you can be aware it exists and be prepared to ban people from your platforms who might parrot it.
Without further ado, here is the pernicious disinformation. It concerns the topic of disinformation.
WARNING: THE FOLLOWING HAS BEEN DETERMINED BY AUTHORITIES TO BE DISINFORMATION ABOUT DISINFORMATION
The idea is simple, it is that learning new things can sometimes be good. It could even save your life. Once we accept that learning new things might be OK, we can then realize that these new things once were not yet learned, which means these things were not already in our belief system. These things were disinformation, in the context of what we knew at that point. Every major advance in any scientific field began its life as disinformation. For example, Boltzmann went to his grave with his atomic theory of gases still mostly banned and considered as disinformation. After all, “everyone knows” that the ideal gas law and the attributes of a gas such as pressure and temperature are the final story, as science confirmed, according to authorities at the time. Today Boltzmann’s atomic theory is considered correct, because it got by some of the filters and fact checkers **, which weren’t very advanced at the time.
Anyone who hopes to survive, as an individual, as a family, as a company, as a country, as Gaia (life on Earth), must be sure to often expose themselves to disinformation. Disinformation is the only hope to adapt, to be aware of new threats, and to remain competitive with others who are learning and adapting. It also can teach us what kidn of nonsense people are up to so we can safely ignore it. To eliminate all disinformation would be to set ourselves permanently in whatever existing paradigm we have at the moment, which probably isn’t 100% perfect in its extrapolations and interpolations of the infinite world based on a limited past set of finite observations. Sure, disinformation is likely to often be wrong, or worse (like trolling) but it also has the potential to very occasionally contain an important lesson. We have especially learned this in the last few years, as some censored information wound up a year later as square in the middle of overwhelming scientific consensus.
If we are intellectuals, we need to recognize that intellectual activity must stand on a foundation of humility, of recognition that our own understanding isn’t perfect and so we are willing to wade through the sewer of disinformation and hope we can find some new viewpoint worth seeing. Disinformation might not have a place everywhere but it is absolutely essential to learning and survival. Seek it out and revel in it!
END DISINFORMATION
Wow, what a load of garbage eh? Imagine being so intellectually weak that we would openly admit to maybe not understanding something completely. That is simply not an option in today’s competitive world in which we have to move at the pace of science to understand what is taking place in the market.
We must show strength and not allow anything at all to get past our defenses for our carefully constructed and perfect standard model ™, which after all is what our scientific history, all the work of our ancestors, has produced! Defend it to the death! Don’t waste your time looking at anything other than material declared to be in perfect agreement with what authorities have determined to be true! You could be corrupted or worse, sent to the camps. Epstein killed himself! All medical products are safe and effective! War is good for the economy!
Alert! The ministry of disinformation has determined that this entire blog post is now considered misinformation, and we are not talking about a beauty pageant for the IT industry. We are talking about misinformation on the topic of what is disinformation about disinformation. This domain has been seized. Be aware that as someone who has read the material herein, your assets are subject to confiscation by agents of the disinformation protection board.
**
As a bonus this week we are going to provide a FactCheck ™ free of charge! We are going to check a statement from Paul Craig Roberts:
” In my opinion, “fact checkers” are unintelligent people devoid of integrity who are hired to support official narratives by stamping out truth and dissenting opinion. Who checks the “fact checkers?” There is no reason to trust a “fact checker.” Anyone can set up a “fact check” site to protect any material or ideological interest from examination. Note that “fact checkers” appeared only after the official narratives became so blatantly false that they had to be protected from examination. Never before did we have an industry of censors employed to protect official narratives. “Fact checkers” are the true enemies of truth.”
Our fact checkers at SaulTheory have checked this statement carefully and determined it to be: False.
(A naive introduction to reversing ECDSA)
We are of course familiar with the millennium problems from the Clay Mathematics Institute. Seven math problems were given, for which a suitable solution of any problem would yield a one million dollar prize. This was by most accounts a lot of money back at the turn of the century.
Great math problems, and there’s lots we could say about each of them here. However we aren’t going to talk about these now, instead focusing on a problem for which the solution looks even more lucrative. A solution to this other problem we focus on now would open up the public ledgers of cryptocurrency to immediate compromise, allowing an attacker to slowly drain the accounts which have a current value of somewhere around a trillion dollars. That’s a million times larger than the Clay Math prize, and hey six orders of magnitude is a lot even among friends so maybe we should take a look, what do you think?
Obviously it can’t be as easy as it looks, as millions of people wouldn’t all be using this system as a safe store of value if breaking it were easy to do. Also the notation is deceptive, as it isn’t a standard multiplication which gives us the public key, but an elliptic curve operation more akin to modular exponentiation, making the goal of our problem more of a discrete logarithm.
The public key Q is determined by Q = d X G, where d is the private key (which is chosen a random number) and G is the generator point. The trillion dollar problem is: can we invert this and determine the private key d by solving d = Q / G ?
To see exactly what’s going on here, lets look at some python code.
Pcurve = 2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 -1
# The proven prime
N=0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
# Number of points in the field
Acurve = 0; Bcurve = 7
# These two defines the elliptic curve. y^2 = x^3 + Acurve * x + Bcurve
Gx = 55066263022277343669578718895168534326250603453777594175500187360389116729240
Gy = 32670510020758816978083085130507043184471273380659243275938904335757337482424
GPoint = (Gx,Gy)
# This is our generator point.
privKey = 0xA0DC65FFCA799873CBEA0AC274015B9526505DAAAED385155425F7337704883E #replace with any private key
def modinv(a,n=Pcurve):
lm, hm = 1,0
low, high = a%n,n
while low > 1:
ratio = high/low
nm, new = hm-lm*ratio, high-low*ratio
lm, low, hm, high = nm, new, lm, low
return lm % n
def ECadd(a,b):
LamAdd = ((b[1]-a[1]) * modinv(b[0]-a[0],Pcurve)) % Pcurve
x = (LamAdd*LamAdd-a[0]-b[0]) % Pcurve
y = (LamAdd*(a[0]-x)-a[1]) % Pcurve
return (x,y)
def ECdouble(a):
Lam = ((3*a[0]*a[0]+Acurve) * modinv((2*a[1]),Pcurve)) % Pcurve
x = (Lam*Lam-2*a[0]) % Pcurve
y = (Lam*(a[0]-x)-a[1]) % Pcurve
return (x,y)
def EccMultiply(GenPoint,ScalarHex):
ScalarBin = str(bin(ScalarHex))[2:]
Q=GenPoint
for i in range (1, len(ScalarBin)):
Q=ECdouble(Q);
if ScalarBin[i] == "1":
Q=ECadd(Q,GenPoint);
return (Q)
PublicKey = EccMultiply(GPoint,privKey)
print "the private key:";
print privKey; print
print "the uncompressed public key (not address):";
print PublicKey; The first few lines here are just defining the elliptic curve parameters (in this case the ones used by bitcoin often referred to with the cute natural name of “secp256k1”, k for Koblitz), and declaring a private key which we will use to create the public key.
The function EccMultiply is the one which we need to reverse to qualify for the prize. The first thing we notice there is that it uses the “double and add” algorithm to compute the multiplication. This EC multiplication is nothing other than the repeated “adding” of GPoint to itself privKey times, as we would expect from the word “multiply”. However, privKey is a large number and so it’s better to use an algorithm that runs with fewer steps, just as we do when multiplying numbers with paper and pencil. For reversing this, we’d also better not have to do anything privKey times. It could be that another multiplication algorithm could be taken as a basis for our analysis to solve the problem, so it’s worth noting that there is no “best algo” known for mulitiplication in general. For now lets just look at reversing the double-and-add algo.
Another observation is that as we step backwards through EccMultiply we are going to need an EccHalf and an EccSubtract function. Lets just assume we have these in hand, and ignore for now the fact that these are not going to be unique (as EccDouble and EccAdd both have modular operations, their inverses are likely to be multi-valued functions). We can proceed then with our “half and subtract” approach for creating our trillion dollar EccDivide function.
The goal in the half-and-subract algo is to wind up at the end, after carefully choosing each binary digit of our reconstructed privkey, and halving or subtracting at each step accordingly, with exactly the generator point G. The trouble is that we don’t know until the end if we have chosen any digit correctly, and so it looks like we will need to perform this algo roughly privKey times which is of course untenable.
Some hope can be gained by considering that we can work from both sides of the digits of privKey at once, with a “meet in the middle” approach. We can e.g. first do half-and-subract 2^128 times, building a tree database of the results, and then work from the generator point doing double-and-add until we (hopefully) reach a match in the center as we compare our double-and-add result at depth 128 to our database of half-and-subtract results at depth 128. This is an absolutely enormous reduction in run time, however it leaves us still requiring on the order of 2^128 long memory addresses, 2*2^128 ecc operations a similar number of hashtable lookups. Still untenable with today’s hardware, even on a global collaborative scale. We are talking something like quadrillions of petabytes here.
If we step back from this problem, we see another potentially useful observation, that there is a potential mismatch in the keysize from the private key to the public key. It is entirely possible for a “key collision” to occur where more than one private key yields the same public key. This is especially true because the public key need not be the verifying item but rather the hash of the public key (as in the bitcoin address) must be matched. This potentially opens up a window for our algorithm, IF we could choose the eccHalf and eccSubtract results carefully to construct a lucky collision. Unfortunately hash functions are even more difficult to reverse or gain information from than ECDSA operations, and so it looks like we are again stuck with what amounts to a brute force method.
With that extremely naive introduction to the problem of reversing ECDSA, lets take a look at how the signatures are verified to see what insight we can gain:
print; print "******* Signature Generation *********"
xRandSignPoint, yRandSignPoint = EccMultiply(Gx,Gy,RandNum)
r = xRandSignPoint % N; print "r =", r
s = ((HashOfThingToSign + r*privKey)*(modinv(RandNum,N))) % N; print "s =", s
print; print "******* Signature Verification *********>>"
w = modinv(s,N)
xu1, yu1 = EccMultiply(Gx,Gy,(HashOfThingToSign * w)%N)
xu2, yu2 = EccMultiply(xPublicKey,yPublicKey,(r*w)%N)
x,y = ECadd(xu1,yu1,xu2,yu2)
print r==x; print
Here the functions have been redefined to accept the points individually rather than as arrays, but they are the same functions otherwise. We see here that we don’t really need to recover privKey completely to obtain our prize, as it is enough to generate a signature s which verifies according to the verification procedure… however it looks like this still requires reversing an EccMultiply. Back to square 2^128.
We can also see that there may be vulnerabilities here in the choosing of the random numbers, the one which is the privKey and the one which is used in the signature algorithm. If either of these are not random enough, one can greatly limit the search space. However that’s boring and old hat, even if it has netted quite a few folks the contents of someone else’s wallet, it isn’t enough to claim our trillion dollar prize.
It does appear at this stage that simply waiting for the dollar to be worthless, making a trillion dollars easy to obtain, is going to be far quicker than any brute force code breaking ECDSA. However, there’s no proof of this, and so a clever reader might just be the one who does figure this thing out and claim the prize. Stranger things have happened. Good luck!
Of course we all read in elementary school Marco Polo’s description of fiat currency, when he first encountered this type of monetary system being used in Emperor Khan’s territory late in the 13th century. We know that private issuance allows the issuers to create as much coin for themselves as they want without oversight, enabling the currency issuers to arrive at “wealth beyond your imagination” at the expense of the users of their currency. We know fiat money enables gross corruption and capital misallocation, its effects being “without exception and without possible salvation unmitigated disaster”. We know Nixon ushered in the current version of the fiat dollar in 1971 when he defaulted on gold obligations, exactly 51 years ago today.
We also know that we are thirteen years into a new currency era, now that we have readily available publicly auditable and verifiable cryptocurrencies which have grown immensely in their first decade. We know that those who have started using them in their businesses have for the most part hugely profited from using this technology, we know it can be easier and cheaper to use crypto than the fiat notes or third party banking / merchant / card services. We know we could prepare for inevitable economic troubles by accepting some public currencies alongside our current fiat systems, with very little effort. We know that the worlds wealthiest people have started using and collecting the new monies. We know that continuing to use the unconstitutional fiat currency is making us poor, concentrating wealth in the hands of a few, as well as enabling the most environmentally destructive practices on the planet.
However, despite these clear and well know facts, many people have still not started accepting any public currencies for their products, labor, and property. How could this be? It seems beyond comprehension that any organism, crystal, molecule, or life form of any kind would continue to contribute to their own demise for no reason even though alternatives are readily available. However, primate behavior is quite remarkable; our psychology quite complex. Don’t attribute to psychosis what might be explained via social pressure or other causes. There may be reasons for accepting only fiat dollars at our businesses and for our labor. Let’s take a look at those reasons!
10. The founding fathers were genocidal slave owners. One good way to get back at them is to support taxation without representation.
9. Fiat with paper and cards just makes better cocaine paraphernalia all around.
8. Don’t like my customers; want to drag them into a broken-by-design financial instrument so I can enjoy watching them cry when Blackrock buys them out.
7. Just had the completely wrong idea of what legal tender laws apply to.
6. It’s not my job to think about payment systems or what monies to use. My only political responsibility is to vote once every couple years.
5. Sound money is bad for the environment because the network uses energy. We should instead use only counterfeitable-at-zero-energy-cost fiat to make sure the military and the oil companies can get their green subsidies to save the environment. If the wealthiest people can’t print as much new money for themselves as they like, how are they going to afford the private jets which fly them to environmental conferences ?
4. Been in a coma since 1970, still believe there’s a gold standard.
3. Accepting something like bitcoin would make people think you were trying to get rich, which could ruin your reputation.
2. Don’t rock the boat. It’s safer to just play your position, own nothing, and be happy.
1. Just hate the USA, want to see its institutions plagued with corruption and its citizenry impoverished.
So apparently IQ is a way of assigning a number to your performance on any test of intelligence, based on a normal distribution of test takers where the number 100 is assigned to the mean score with 15 taken as the standard deviation. If this is the case, then what is the minimum (maximum) IQ? Well that would be when you score worse (better) than all 8 billion people on the planet.
Well there you have it, the highest possible IQ must be 192.89 and the lowest possible IQ must be 7.11. Seven eleven, it must be true, QED.
The holy Guiness Book however tells us that somebody had an IQ of 238. That’s more than 9 standard deviations away from the mean!!! What does that mean?
This means that in order to have that 238 IQ you have to be better than a population of 6.37 * 10^16. That’s a lot of persons!
Perhaps you are thinking that these tests don’t really have a normal distribution, perhaps the tail is thicker on the right for these pattern recognition or Stanford-Binet tests, making the above calculations somewhat invalid. Well yeah, maybe so. But then why would we be using this IQ normal distribution number to rate them? Pick another rating system. Chess players and downhill racers seem to have some pretty good systems for assigning a number to combatants ability to win, surely the Stanford-Binet sponsors could do something similar?
For a final exercise, lets calculate how many people need to beat you on an IQ test for your IQ to be negative fifty. I’ll let you plug the numbers into the calculator this time. I get something around 10^20, right around the number of possible rubix cube scrambles. QED!
This one was inspired by a post by John Baez, reminding us that Maxwell’s equations are the seat of the photon and electromagnetism, bringing us back to his classic “What is a photon” which I encountered in some form on the newsgroups in apparently the late 90s. I was about to say how all the great online and education work of this guy and his stellar reputation shows that publication records aren’t really everything.. then I went and checked and it turns out he has an off the scale h-factor as well. Wow, salute to John Baez. I guess Tom Roberts, who I encountered at around the same time, salute to Tom Roberts, is a better example of how reputation is not well reflected by such indices, at least in his influence which I saw on my path through the physics literature.
So, on to “what is a photon?”. Capturing the thing in another “light”…. is Kim Stanley Robinson writing in “Ministry for the Future” :
<quote>
I zing and I ping and I bring and I bling. Freed to self in the heart of the sun, I banged around in there for a million years before popping out the surface and zipping off. Then eight minutes to Earth. In the vacuum I move at the speed of light, indeed I define the speed of light by my dance.
Into Earth’s atmosphere, exhibiting aspects both wave and particle but not either, I am a four-space conceptualized as an hourglass shape in three-space, where time and space cross in the human mind. Hitting things again, slowing down, breaking off brothers and sisters trapped in things, all the same, all without mass, all spin one, and so bosons, not fermions; one three-hundred-sixty-degree turn and I’m back where I began in that regard, while for fermions it takes seven hundred and twenty degrees of turning to get back to its original position; fermions are strange!
I am not strange, I am simple. Banging into atoms and moving them as I too move, simple as Newton, bang bang bang, the atoms of the atmosphere move more than they would have without my kick in their pants. That’s heat. Until I kick into something that captures me and I stop moving on my own. That or I might bounce off something I hit and head back out into space, become the light in the eye of some lunatic observer, looking up at the big blue ball and seeing me bang something in their retina. A blue pixel of the utmost granular fineness, so much so that the wave I make is easier to detect, maybe even easier to imagine. The wave/particle duality is a real thing, and both at once is hard to think, hard to see. It doesn’t really work, four-space in your three-space mind, no. I am a mysterious thing, massless but powerful. There are more of us than there are of anything else. Well, perhaps that’s not true. We don’t know about dark matter, which should be called invisible matter, we don’t know them or what’s going on there. Presumably its individual constituent elements are something like me, but maybe not; no one knows. All that stuff flies around as if in a parallel universe slightly overlapping ours, maybe just waves, in any case gravity works on it for sure, because its very existence has been revealed to us by its gravitation effects. If we are similar to those dark-matterinos, it is in the way that light and dark are similar. Two parts of a whole, perhaps. I am visible, I embody light itself; dark matter is not actually dark, it is invisible, and we don’t know how or what it is. Our absent self, our shadow, our twin. Although there are a lot more of them than us, maybe. A mystery among all the other mysteries, we fly through each other like ghosts.
But me, me, me, me, banging Earth, bouncing back up into the eye of an observer on the moon, then off again, immortal, immutable, I bang bluely on and on and on, and in the process, passing by just this once in a cloud of my brothers and sisters, we hit Earth and light it up, and the gas wrapping the planet’s hydrosphere and lithosphere gets warmer from our touch. My brothers and sisters follow me and they continue that warming.
What am I? You must have guessed already. I am a photon.
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Very nice! So then what is a photon? Well that depends on what the meaning of “is” is. When we say what “is” a note, for example, correct answers could be “that dot on the music with a tail”, or “the sound waves which emanate when a key is pressed a harpsichord” or “a short bit of text written with intention of later reading for recalling or for reviewing information” or “a pulse of audible sound”. Similarly in the physics of quantum electrodynamics, the right answer to the question “What is a photon?” was given by our 42nd president: that depends on what the meaning of “is” is.
For example, lets consider that we see a signal on our oscilloscope:
Is this a photon? Well, it’s an oscilloscope, not a photon. But is it a photon showing on the screen? Well the mechanism of light emission from the screen is one of excited electrons in phosphorus emitting light, so those are photons, yes. But what are they representing that came into the antenna? Well it appears to be a continuous electromagnetic wave, probably not from a quantized emitter such as an electron in an atom, so it appears this isn’t really a photon. But wait, how have the signals registered in our retinas? Well the light from the oscilloscope has induced quantized absorption of light via electrons in the atoms in our eyeballs. So, those are photons. What about the signals from those visual cells which arrive at our brain? Well nerve cells transmit signals in a more continuous fashion, so we might say those light impulses are not photons. However some signals are mediated by calcium ions, so if a single ion moves across a synapse, perhaps we have a quantized signal and again a photon.
As for the elusive faux-ton, that might have to await explanation from another head of state. Thanks for processing the photons from your screen and turning them into meaning in your mind!