Paul Erdős

Paul Erdős, born this day in 1913, was a prolific and eccentric Hungarian mathematician.  He was known both for his social practice of mathematics (he engaged more than 500 collaborators) and for his eccentric lifestyle. He lived out of a suitcase, and traveled the world, staying with other mathematicians, talking shop long into the night, sleeping on the living room sofa. “Property is a nuisance.” He devoted his waking hours to mathematics, even into his later years—indeed, his death came only hours after he solved a geometry problem at a conference in Warsaw.

Erdős asked questions only a mathematician could love (or understand) and proposed problems for others in the most abstract and recondite areas of math, but also in practical questions of approximation, set theory, and probability. Much of his work centered around discrete mathematics, cracking many previously unsolved problems in the field. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics.

Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed. He firmly believed mathematics to be a social activity, living an itinerant lifestyle with the sole purpose of writing mathematical papers with other mathematicians. Erdős’s prolific output with co-authors prompted the creation of the Erdős number, a point of pride for all mathematicians of a certain age. Your Erdős number is 1 if you co-authored a paper with Erdős, 2 if you have co-authored a paper with someone whose Erdős number is 1, 3 if you co-authored a paper with someone whose Erdős number is 2, etc.

[This text was edited from his Wikipedia entry.]

Ancient technology exceeding anything we can do today

It’s a technical argument dependent on engineering and material science, but well worth following in detail because it is some of the solidest evidence we have that human history is in need of a thorough rewrite.

There are drill holes from ancient Egypt into granite that could only have been made with a very sharp, very hard drill under enormous pressure. Granite is so hard that it can only be cut by corrundum or diamond. And spiral scars on the cores that were removed from these holes tell us that with every turn of the core-drill, the blade advanced several millimeters into the stone. The drills that we have today operate at high speed, and with each turn of the drill they go much less than 1 mm into the stone. Hence the conclusion that these drills were made of a very hard mataerial and were backed by several tons of pressure.


Traditional archaeology dates these drill holes to the earliest dynasty or pre-dynastic Egypt, and people at that time did not have iron, let alone diamond drill bits or power tools. They had not yet invented the wheel.

A growing consensus among rebel archaeologists is that an ancient high-tech civilization left us the Pyramids and the megaliths of Machu Picchu and some other examples of precision work with giant pieces of stone. Their technology was lost in a global catastrophe that suddenly ended the last ice age, 12,700 years ago. Civilization rebooted from a few surviving hunter-gatherers, but our surviving myths of floods and a race of gods remind us today of that earlier civilization.

One of my all-time favorite human beings

It is remarkable that mind enters into our awareness of nature on two separate levels. At the highest level, the level of human consciousness, our minds are somehow directly aware of the complicated flow of electrical and chemical patterns in our brains. At the lowest level, the level of single atoms and electrons, the mind of an observer is again involved in the description of events. Between lies the level of molecular biology, where mechanical models are adequate and mind appears to be irrelevant. But I, as a physicist, cannot help suspecting that there is a logical connection between the two ways in which mind appears in my universe. I cannot help thinking that our awareness of our own brains has something to do with the process which we call “observation” in atomic physics.

— Freeman Dyson, 1923 – 2020

My favorite Dyson story is the one that got him started in his career. Twenty years after quantum mechanics, 40 years after relativity, no one had been able to combine the two in a coherent, unified framework. Then, in 1948, there was an embarrassment of riches. Julian Schwinger, a fireplug who spouted equations as if by direct channel from God, told us it was all about particles and sources.

Image result for schwinger source

Richard Feynman, who played the bongo drums and made wisecracks, told us that while we’re not looking, the electron does every possible and impossible thing, and he gave us a cartoon system for keeping track of what all those things are.


Dyson was a 24-year-old grad student, and undeterred by their mutually antagonistic personalities, he befriended both of them, channeled both their thought processes, and published a paper in which he demonstrated that the two theories, though they looked so different on paper, always produced the same predictions.

After that, the rigid hierarchical system of academic physics carved a place for him, and allowed him to do whatever he wanted, so that he never again had to take a test or qualify for a degree. He hung out at Princeton’s Institute for Advanced Study, home to Einstein, Oppenheimer, von Neumann, and Gödel.

He was an original and independent thinker on all subjects. He thought about culture and politics and technology as well as the deep structure of science. He was still writing for the New York Review of Books in his 96th year.

Dyson had a gift for the memorable line and a disarming honesty that admitted the possibility of error. It was, he would say, better to be wrong than to be vague, and much more fun to be contradicted than to be ignored. Dyson was by instinct and reason a pacificist, but he understood the fascination with nuclear weaponry.
Guardian Obit

“The more I examine the universe and the details of its architecture, the more evidence I find that the universe must in some sense have known we were coming,”

What do you make of this?

This material stretches our credulity, and clearly Dr. Wood doesn’t expect to be believed. Nazis landing on the moon in the 1930s? Races of lizard-like aliens maintaining earth bases in Antarctica to this day?

What he documents most convincingly is that there is a sophisticated CIA program of deceit to keep us from knowing the truth about an Alien presence on earth. Maybe Dr Wood is part of that program. Maybe much of what he reports is an elaborate fantasy designed to deceive. But he (and other sources) have convinced me that there is something there worth covering up, and this bare fact is astounding.



We could be SOOO much healthier

Do you know that there’s not a pharmaceutical drug on earth that works for more than seventy percent of the population? Not one drug. Pharma companies consider a drug a success if it’s effective in a much smaller proportion of patients.
— Zia Haider Rahman

Thanks to Sanders and Warren, the Democratic debates are highlighting the huge inefficiencies and inequities in the way we pay for medicine in America. Health care in America costs twice as much per capita as other modern, industrialized countries, and our outcomes are worse than all of them [Harvard Gazette]

But even more important than changing the way we pay for medicine is changing the way we practice medicine, and this is a discussion that has been marginalized.

The gold standard for validating a treatment is the placebo-controlled double-blind study. If you practice medicine that is not based on PCDB studies, you can’t get third party payments and you can’t even get malpracctice insurance.

And yet, we know that PCDB studies are effective validation for only about half of a half of medicaal practice. We’re excluding ¾ of what we know to be effective.

“Placebo-controlled” means that we are focused on the body, not the mind. We are deliberately excluding anything that works through the mind from study, treating it as  an annoying artifact in our scientific study. Medicine that works with the mind as well as the body can be twice as effective. Yet, medical employers assure that doctors’ calendars are so crowded that they have no time to develop a caring relationship with their patients. We make sure our doctors function only as diagnosticians and prescribers, confining them to the part of job that computer algorithms can actually do better. We forbid them to function as healers, or to bring empathy, intuition, and caring to their practice.


The structure of a PCDB study specifies uniformity. Every subject in the study receives the same treatment. We know that choosing the right treatment for each individual patient is half the story, and yet we are not even studying individualized medicine, let alone practicing it. Genetics, personality, and the microbiome make each patient unique; yet every medical intervention in use today has to be validated in a study that treats patients as if they were the same.

Medical technology concept. Medical instruments.

Medicine could be at least four times as effective for the same expense and effort, based on individualized medicine, and considering the mind together with the body. And this is in addition to the low-hanging opportunities to eliminate insurance overhead and administrative costs which are peculiarly American inefficiencies.


Life Immitates Art

When J.S. Bach was challenged by King Frederick to compose on a subject of the King’s devising, he rose to the occasion with a spectacular Offering, applying his inventiveness in 2 fugues, 10 canons, and a four-movement sonata for flute and violin.

One of the pieces he offered is a single line of music  (beginning with a variation on the King’s theme) that is to be played both forward and backward simultaneously, engineered so cleverly that it harmonizes with itself along the way and both begins and ends convincingly.

As we marvel at the mathematical/musical mind that could have created such an invention, consider a virus, whose complete DNA is a perfect palindrome, so that it can be read either forward or backward. “Reading” DNA means translating each triplet of letters (A,T,G,C) into an amino acid and linking them together to make a big, complicated protein molecule that does a particular job. In this virus, the three-letter codes are reversed, and their order is reversed , and the protein is the same, and the protein is not only functional, but adaptive and competitive enough to create a niche for the virus.  Article in Quanta Magazine

Illustration of an RNA sequence, with an arrow pointing from one end to the other, and a sequence of complementary nucleotides, with an arrow pointing the other way.