Like many youth of my generation, I watched the original Star Trek in reruns and Next Generation and Deep Space Nine in real time. I enjoyed the shows but can’t really claim to be a Trekkie. I was already in graduate school when Next Generation began so I could not help but to scrutinize the shows for scientific accuracy. I was impressed that the way they discovered life in a baby universe created in one episode was by detecting localized entropy reduction, which is quite sophisticated scientifically. I bristled each time the star ship was on the brink of total failure and about to explode but the artificial gravity system still didn’t fail. I celebrated the one episode that actually had an artificial gravity failure and people actually floated in space! I thought it was ridiculous that almost every single planet they visited was always at room temperature with a breathable atmosphere. That doesn’t even describe many parts of earth. I mostly let these inaccuracies slide in the interest of story but I could never let go of one thing that always left me feeling somewhat despondent about the human condition, which was that even in a supposed super advanced egalitarian democratic society where material shortages no longer existed, Star Fleet was still an absolute autocracy. Many of the episodes dealt with strictly obeying the chain of command and never disobeying direct orders. A world with a democratic federation of planets, transporters and faster than light travel still believed that autocracy was the most efficient way to run an organization.
For most people throughout history and including today, the difference between autocracy and democracy is mostly abstract. People go to jobs where a boss tells them what to do. Virtually no one questions that corporations should be run autocratically. Authoritarian CEO’s are celebrated. Religion is generally autocratic. It only makes sense that the military backs autocrats given that autocracy is already the governing principle of their enterprise. Julius Caesar crossed the Rubicon and became the Dictator of Rome (he was never actually made Emperor) because he had the biggest army and it was loyal to him, not the Roman Republic. The only real question is how democracies even persist. People may care about freedom but do they really care all that much about democracy?
One outcome of the pandemic is that I have not had any illness (knock on wood), nary a cold nor sniffle, in a year and a half. On the other hand, my skin has fallen apart. I am constantly inflamed and itchy. I have no proof that the two are connected but my working hypothesis is that my immune system is hypersensitive right now because it has had little to do since the spring of 2020. It now overreacts to every mold spore, pollen grain, and speck of dust it runs into. The immune system is extremely complex, perhaps as complex as the brain. Its job is extremely difficult. It needs to recognize threats and eliminate them while not attacking itself. The brain and the immune system are intricately linked. How many people have gotten ill immediately after a final exam or deadline? The immune system was informed by the brain to delay action until the task was completed. The brain probably takes cues form the immune system too. One hypothesis for why asthma and allergies have been on the rise recently is that modern living has eliminated much contact with parasites and infectious agents, making the immune system hypersensitive. I for one, always welcome vaccinations because it gives my immune system something to do. In fact, I think it would be a good idea to get inoculations of all types regularly. I would take a vaccine for tape worm in a heartbeat. We are now slowly exiting from a global experiment in depriving the immune system of stimulation. We have no idea what the consequences will be. That is not to say that quarantine and isolation was not a good idea. Being itchy is clearly better than being infected by a novel virus (or being dead). There can be long term effects of infection too. Long covid is likely to be due to a miscalibrated immune system induced by the infection. Unfortunately, we shall likely never disentangle all the effects of COVID-19. We will not ever truly know what the long term consequences of infection, isolation, and vaccination will be. Most people will come out of this fine but a small fraction will not and we will not know why.
I read an article recently about an anti-vaccination advocate exclaiming at a press conference with the governor of Florida that vaccines against SARS-CoV-2 “change your RNA!” This made me think that most people probably do not know much about RNA and that a little knowledge is a dangerous thing. Now ironically, contrary to what the newspapers say, this statement is kind of true although in a trivial way. The Moderna and Pfizer vaccines insert a little piece of RNA into your cells (or rather cells ingest them) and that RNA gets translated into a SARS-CoV-2 spike protein that gets expressed on the surface of the cells and thereby presented to the immune system. So, yes these particular vaccines (although not all) have changed your RNA by adding new RNA to your cells. However, I don’t think this is what the alarmist was worried about. To claim that something that changes is a bad thing implies that the something is fixed and stable to start with, which is profoundly untrue about RNA.
The central dogma of molecular biology is that genetic information flows from DNA to RNA to proteins. All of your genetic material starts as DNA organized in 23 pairs of chromosomes. Your cells will under various conditions transcribe this DNA into RNA, which is then translated into proteins. The biological machinery that does all of this is extremely complex and not fully understood and part of my research is trying to understand this better. What we do know is that transcription is an extremely noisy and imprecise process at all levels. The molecular steps that transcribe DNA to RNA are stochastic. High resolution images of genes in the process of transcription show that transcription occurs in random bursts. RNA is very short-lived, lasting between minutes to at most a few days. There is machinery in the cell dedicated to degrading RNA. RNA is spliced; it is cut up into pieces and reassembled all the time and this splicing happens more or less randomly. Less than 2% of your DNA codes for proteins but virtually all of the DNA including noncoding parts are continuously being transcribed into small RNA fragments. Your cell is constantly littered with random stray pieces of RNA, and only a small fraction of it gets translated into proteins. Your RNA changes. All. The. Time.
Now, a more plausible alarmist statement (although still untrue) would be to say that vaccines change your DNA, which could be a bad thing. Cancer after all involves DNA mutations. There are viruses (retroviruses) that insert a copy of its RNA code into the host’s DNA. HIV does this for example. In fact, a substantial fraction of the human genome is comprised of viral genetic material. Changing proteins can also be very bad. Prion diseases are basically due to misfolded proteins. So DNA changing is not good, protein changing is not good, but RNA changing? Nothing to see here.
Even though Covid- is going to be with us forever, I actually think on the whole the pandemic turned out better than expected, and I mean that in the technical sense. If we were to rerun the pandemic over and over again, I think our universe will end up with fewer deaths than average. That is not to say we haven’t done anything wrong. We’ve botched up many things of course but given that the human default state is incompetence, we botched less than we could have.
The main mistake in my opinion was the rhetoric on masks in March of 2020. Most of the major Western health agencies recommended against wearing masks at that time because they 1) there was already a shortage of N95 masks for health care workers and 2) they thought that cloth and surgical masks were not effective in keeping one from being infected. Right there is a perfect example of Western solipsism; masks were only thought of as tools for self-protection, rather than as barriers for transmission. If only it was made clear early on that the reason we wear masks is not to protect me from you but to protect you from me. (Although there is evidence that masks do protect the wearer too, see here). This would have changed the rhetoric over masks we are having right now. The anti-maskers would be defending their right to harm others rather than the right to not protect themselves from harm.
The thing we got right was in producing effective vaccines. That was simply astonishing. There had never been a successful mRNA-based drug of any type until the BioNTech and Moderna vaccines. Many things had to go right for the vaccines to work. We needed a genetic sequence (Chinese scientists made it public in January), from that sequence we needed a target (the coronavirus spike protein), we needed to be able to stabilize the spike (research that came out of the NIH vaccine center), we needed to make mRNA less inflammatory (years of work especially at Penn), we needed a way to package that mRNA (work out of MIT), and we needed a sense of urgency to get it done (Western governments). Vaccines don’t always work but we managed to get one in less than a year. So many things had to go right for that to happen. The previous US administration should be taking a victory lap because it was developed under their watch, instead of bashing it.
As I’ve said before, I am skeptical we can predict what will happen next but I am going to predict now that there will not be a variant in the next year that will escape from our current vaccines. We may need booster shots and minor tweaks but the vaccines will continue to work. Part of my belief stems from the work of JC Phillips who argues that the SARS-CoV-2 spike protein is already highly optimized and thus there is not much room for it to change and to become infectious. The virus may mutate to replicate faster within the body but the spike will be relatively stable and thus remain a target for the vaccines. The delta variant wave we’re seeing now is a pandemic of the unvaccinated. I have no idea if those against vaccinations will have a change of heart but at some point everyone will be infected and have some immune protection. (I just hope they approve the vaccine for children before winter). SARS-CoV-2 will continue to circulate just like the way the flu strain from the 1918 pandemic still circulates but it won’t be the danger and menace it is now.
Although cryptocurrencies have been mainstream for quite a while, I still think the popular press has not done a great job explaining the details of how they work. There are several ideas behind a cryptocurrency like Bitcoin but the main one is the concept of a cryptographic hash. In simple terms, a hash is a way to transform an input sequence of characters (i.e. a string) into an output string such that it is hard to recreate the input string from the output string. A transformation with this property is called a one-way function. It is a machine where you get an output from an input but you can’t get the input from the output and there does not exist any other machine that can get the input from the output. A hash is a one-way function where the output has a standard form, e.g. 64 characters long. So if each character is a bit, e.g. 0 or 1, then there are different possible hashes. What makes hashes useful are two properties. The first, as mentioned, is that it is a one-way function and the second is that two different inputs do not give the same hash, called collision avoidance. There have been decades of work on figuring out how to do this and institutions like the US National Institutes of Standards and Technology (NIST) actually publish hash standards like SHA-2.
Hashes are an important part of your life. If a company is responsible, then only the hash of your password is stored on their servers, and when you type your password into a website, it goes through the hashing function and the hash is checked against the stored version. That way, if there is security breach, only the hash list is stolen. If the company is very responsible, then your name and all of your information is also only stored in hash form. Part of the problem with past security breaches is that the companies stored actual information instead of hashed information. However, if you use the same password on different websites then the hash would be same if the same standard was used. Some really careful companies will “salt” your password by adding a random string to it (that is hopefullly stored separately) before hashing. Or they will rehash your hash with salt. If you had a perfect hash, then the only way to break it would be to guess different inputs and see if it matches the desired output. The so-called complex math problem that Bitcoin solves before validating a transaction (and getting a reward) is finding a hash with a certain property but more on this later.
Now, one of the problems with hashing is that you need to deal with inputs of various sizes but you want the output to have a single uniform size. So even though a hash could have enough information capacity (i.e. entropy) to encode all of the world’s information ten times over, it is computationally inconvenient to just feed the complete text of Hamlet directly into a single one-way function. This is where the concept of a Merkle tree becomes important. You start with some one-way function that takes inputs of some fixed length and it scrambles the characters in some way that is not easily reversible. If the input string is too short then you just add extra characters (called padding) but if it is too long you need to do something else. The way a Merkle tree works is to break the text into chunks of uniform size. It then hashes the first chunk, adds that to the next chunk, hash the result and repeat until you have included all the chunks. This repeated recursive hashing is the secret sauce of crypto-currencies.
Bitcoin tried to create a completely decentralized digital currency that could be secure and trusted. For a regular currency like the US dollar, the thing you are most concerned about is that the dollar you receive is not counterfeit. The way that problem is solved is to make the manufacturing process of dollar bills very difficult to reproduce. So the dollar uses special paper with special marks and threads and special fonts and special ink. There are laws against making photocopiers with a higher resolution than the smallest print on a US bill to safeguard against counterfeiting. A problem with digital currencies is that you need to prevent double spending. The way this is historically solved is to have all transactions validated by a central authority.
Bitcoin solves these problems in a decentralized system by using a public ledger, called a blockchain that is time stamped, immutable and verifiable. The block chain keeps track of every Bitcoin transaction. So if you wanted to transfer one Bitcoin to someone else then the blockchain would show that your private Bitcoin ID has one less Bitcoin and the ID of the person you transferred to would have one extra Bitcoin. It is called a blockchain because each transaction (or set of transactions) is recorded into a block, the blocks are sequential, and each block contains a hash of the previous block. To validate a transaction you would need to validate each transaction leading up to the last block to validate that the hash on each block is correct. Thus the blockchain is a Merkle tree ledger where each entry is time stamped, immutable, and verifiable. If you want to change a block you need to change all the blocks before it.
However, the blockchain is not decentralized on its own. How do you prevent two blocks with two different hashes? The way to achieve that goal is to make the hash used in each block have a special form that is hard to find. This underlies the concept of “proof of work”. Bitcoin uses a hash called SHA-256 which consists of a hexadecimal string of 64 characters (i.e. a base 16 number, usually with characters consisting of the digits 0-9 plus letters a-f). Before each block gets added to the chain, it must have a hash that has a set number of zeros at the front. In order to do this, you need to add some random numbers to the block or rearrange it so that the hash changes. This is what Bitcoin miners do. They try different variations of the block until they get a hash that has a certain number of zeros in front and then they race to see who gets it first. The more zeros you need the more guesses you need and thus the harder the computation. If it’s just one zero then one in 16 hashes will have that property and thus on average 16 tries will get you the hash and the right to add to the blockchain. Each time you require an additional zero, the number of possibilities decreases by a factor of 16 so it is 16 times harder to find one. Bitcoin wants to keep the computation time around 15 minutes so as computation speed increases it just adds another zero. The result is an endless arms race. The faster the computers get the harder the hash is to find. The incentive for miners to be fast is that they get some Bitcoins if they are successful in being the first to find a desired hash and earning the right to add a block to the chain.
The actual details for how this works is pretty complicated. All the miners (or Bitcoin nodes) must validate that the proposed block is correct and then they all must agree to add that to the chain. The way it works in a decentralized way is that the code is written so that a node will follow the longest chain. In principle, this is secure because a dishonest miner who wants to change a previous block must change all blocks following it and thus as long as there are more honest miners than dishonest ones, the dishonest ones can never catch up. However, there are issues when two miners simultaneously come up with a hash and they can’t agree on which to follow. This is called a fork and has happened at least once I believe. This gets fixed eventually because honest miners will adopt the longest chain and the chain with the most adherents will grow the fastest. However, in reality there are only a small number of miners that regularly add to the chain so we’re at a point now where a dishonest actor could possibly dominate the honest ones and change the blockchain. Proof of work is also not the only way to add to a blockchain. There are several creative ideas to make it less wasteful or even make all that computation useful and I may write about them in the future. I’m somewhat skeptical about the long term viability of Bitcoin per se but I think the concepts of the blockchain are revolutionary and here to stay.
2021-06-21: some typos fixed and clarifying text added.
Interesting article in the New York Times today about how people to this day still do not know how magician David Berglass did his “Any Card At Any Number” trick. In this trick, a magician asks a person or two to name a card (e.g. Queen of Hearts) and a number (e.g. 37) and then in a variety of ways produce a deck where that card appears at that order in the deck. The supposed standard way to do the trick is for the magician to manipulate the cards in some way but Berglass does his trick by never touching the cards. He can even do the trick impromptu when you visit him by leading you to a deck of cards somewhere in the room or from his pocket that has the card in the correct place. Now, I have no idea how he or anyone does this trick but one way to do the trick is to use “full enumeration”, i.e. hide decks where every possibility is accounted for and then the trick is to remember which deck has that choice. So then the question is how many decks would you need? Well the minimal number of decks is 52 because a particular card could be in one of 52 positions. But how many more decks would you need? The answer is zero. 52 is all you need because for any particular arrangement of cards, each card is in one position. Then all you do is rotate all the cards by one, so the card in the first position is now in the second position for deck 2 and 52 moves to 1 and so on. What the magician can do is to then hide 52 decks and remember the order of each deck. In the article he picked the reporter’s card to within 1 but claimed he may only be able to do it to within 2. That means he’s hiding the decks in groups of 3 and 4 say and then points you to that location and lets you choose which deck.
I sometimes listen to the podcast “How I built this“, where host Guy Raz interviews successful entrepreneurs like Herb Kelleher, who founded Southwest Airlines, Reid Hoffman of Linkedin, Stacy Madison of Stacy’s Pita Chips, and so on. The story arc of each interview is similar – some scrappy undervalued person comes up with a novel idea and then against all odds succeeds by hard work, unrelenting drive, and taking risks. The podcast fully embraces the American myth of the hero entrepreneur although Guy tries to do his best to extend it beyond the stereotypical Silicon Valley one typified by Steve Jobs or Elon Musk. At the end of each interview Guy will ask the subject how much of their success was due to luck and how much due to their ingenuity and diligence. Most are humble or savvy enough to say that some large fraction of the success was luck. While I have no doubt that each successful entrepreneur is bright, hard working, and possesses unique skills, there are countless others who are equally talented and yet did not succeed. Each success story is an example of survivor bias. We sometimes hear about spectacular failures, like the Edsel , but rarely do we hear about the story of “How I almost built this”.
There is a stock market scam where you email blocks of 1024 prospective marks a prediction of what a stock will do that week. For one half, you say the stock will go up and for the other half you say it will go down. Then for the half for which you were correct, you do the same thing and half of them (one quarter of the original) will receive a correct prediction. Finally after ten weeks, one of the original 1024 will have received 10 correct predictions in a row and think that you are either a genius or have inside information and will be primed to sign up for whatever scam you are selling. The lucky (or unlucky) person is fooled because they lack the information that 1023 others did not receive perfect predictions. Obviously, this also works for sports predictions.
While, I think most success is luck there do seem to be outliers. Elon Musk seems to be one. He manages to invent new industries and succeed with regularity. Warren Buffet does seem to be able to beat the market. However, it is for us as a society to decide how winners should be rewarded. In many industries there is a winner-take-all dynamic, where the larger you get the easier it is to crush the competition. Mark Zuckerberg is clearly skilled but Facebook is dominant right now because it is a monopolist; it simply buys up as many competitors as it can. The same goes for Google, Amazon, and AT&T until the government broke it up. Finance works that way too. The bigger a bank or hedge fund gets, the easier it is to succeed. A small fluctuation that propels one firm a little ahead of the rest at the right time will be exponentially amplified. While, I do think it is a positive thing to reward success I don’t think the reward needs to be so disparate. Right now, a very small difference in ability (or none at all) and a lot of luck can be the difference between flying to your house in the Hamptons in a helicopter or selling hotdogs from a cart on Fifth Avenue.
The end of the Covid-19 pandemic is within reach. The vaccines have been a roaring success and former Bell Labs physicist J.C. Phillips predicted it (see here). He argued that the spike protein, which is the business end of the SARS-CoV-2 virus, has been optimized to such a degree in SARS-CoV-2 that even a small perturbation from a vaccine can disrupt it. While the new variants perturb the spike slightly and seem to spread faster, they will not significantly evade the vaccine. However, just because the end is within sight doesn’t mean we should not still be vigilante and not mess this up. Europe has basically scored multiple own goals these past few months with their vaccine rollout (or lack thereof) that is a combination of both gross incompetence and excessive conservatism. The Astra-Zeneca vaccine fiasco was a self-inflicted wound by all parties involved. The vaccine is perfectly fine and any side effects are either not related to the vaccine or of such low probability that it should not be a consideration for halting its use. By artificially slowing vaccine distribution, there is a chance that some new mutation could arise that will evade the vaccine. Europe needs to get its act in gear. The US has steadily ramped up vaccinations and is on course to have all willing adults vaccinated by start of summer. Although there has been a plateauing and even slight rise recently because of relaxation from social distancing in some areas, cases and deaths will drop for good by June everywhere in the US. North America will largely be back to normal by mid-summer. However, it is imperative that we press forward and vaccinate the entire world. We will also all need to get booster shots next fall when we get our flu shots.
Since, the discovery of exoplanets nearly 3 decades ago most astronomers, at least the public facing ones, seem to agree that it is just a matter of time before they find signs of life such as the presence of volatile gases in the atmosphere associated with life like methane or oxygen. I’m an agnostic on the existence of life outside of earth because we don’t have any clue as to how easy or hard it is for life to form. To me, it is equally possible that the visible universe is teeming with life or that we are alone. We simply do not know.
But what would happen if we find life on another planet. How would that change our expected probability for life in the universe? MIT astronomer Sara Seager once made an offhand remark in a podcast that finding another planet with life would make it very likely there were many more. But is this true? Does the existence of another planet with life mean a dramatic increase in the probability of life in the universe. We can find out by doing the calculation.
Suppose you believe that the probability of life on a planet is (i.e. fraction of planets with life) and this probability is uniform across the universe. Then if you search planets, the probability for the number of planets with life you will find is given by a Binomial distribution. The probability that there are planets is given by the expression , where is a factor (the binomial coefficient) such that the sum of from one to is 1. By Bayes Theorem, the posterior probability for (yes, that would be the probability of a probability) is given by
where . As expected, the posterior depends strongly on the prior. A convenient way to express the prior probability is to use a Beta distribution
where is again a normalization constant (the Beta function). The mean of a beta distribution is given by and the variance, which is a measure of uncertainty, is given by . The posterior distribution for after observing planets with life out of will be
where is a normalization factor. This is again a Beta distribution. The Beta distribution is called the conjugate prior for the Binomial because it’s form is preserved in the posterior.
Applying Bayes theorem in equation (*), we see that the mean and variance of the posterior become and , respectively. Now let’s consider how our priors have updated. Suppose our prior was , which gives a uniform distribution for on the range 0 to 1. It has a mean of 1/2 and a variance of 1/12. If we find one planet with life after checking 10,000 planets then our expected becomes 2/10002 with variance . The observation of a single planet has greatly reduced our uncertainty and we now expect about 1 in 5000 planets to have life. Now what happens if we find no planets. Then, our expected only drops to 1 in 10000 and the variance is about the same. So, the difference between finding a planet versus not finding a planet only halves our posterior if we had no prior bias. But suppose we are really skeptical and have a prior with and so our expected probability is zero with zero variance. The observation of a single planet increases our posterior to 1 in 10001 with about the same small variance. However, if we find a single planet out of much fewer observations like 100, then our expected probability for life would be even higher but with more uncertainty. In any case, Sara Seager’s intuition is correct – finding a planet would be a game breaker and not finding one shouldn’t really discourage us that much.
Liberalism, as a philosophy, arose during the European Enlightenment of the 17th century. It’s basic premise is that people should be free to choose how they live, have a government that is accountable to them, and be treated equally under the law. It was the founding principle of the American and French revolutions and the basic premise of western liberal democracies. However, liberalism is inherently conflicted because when I exercise my freedom to do something (e.g. not wear a mask), I infringe on your freedom from the consequence of that thing (e.g. not be infected) and there is no rational resolution to this conflict. This conflict led to the split of liberalism into left and right branches. In the United States, the term liberal is exclusively applied to the left branch, which mostly focuses on the ‘freedom from’ part of liberalism. Those in the right branch, who mostly emphasize the ‘freedom to’ part, refer to themselves as libertarian, classical liberal, or (sometimes and confusingly to me) conservative. (I put neo-liberalism, which is a fundamentalist belief in free markets, into the right camp although it has adherents on both the left and right.) Both of these viewpoints are offspring of the same liberal tradition and here I will use the term liberal in the general sense.
Liberalism has never operated in a vacuum. The conflicts between “freedom to” and “freedom from” have always been settled by prevailing social norms, which in the Western world was traditionally dominated by Christian values. However, neither liberalism nor social norms have ever been sufficient to prevent bad outcomes. Slavery existed and was promoted by liberal Christian states. Genocide of all types and scales have been perpetrated by liberal Christian states. The battle to overcome slavery and to give equal rights to all peoples was a long and hard fought battle over slowly changing social norms rather than laws per se. Thus, while liberalism is the underlying principle behind Western governments, it is only part of the fabric that holds society together. Even though we have just emerged from the Dark Years, Western Liberalism is on its shakiest footing since the Second World War. The end of the Cold War did not bring on a permanent era of liberal democracy but may have spelled it’s eventual demise. What will supplant liberalism is up to us.
It is often perceived that the American Democratic party is a disorganized mess of competing interests under a big tent while the Republicans are much more cohesive but in fact the opposite is true. While the Democrats are often in conflict they are in fact a fairly unified center-left liberal party that strives to advocate for the marginalized. Their conflicts are mostly to do with which groups should be considered marginalized and prioritized. The Republicans on the other hand are a coalition of libertarians and non-liberal conservatives united only by their desire to minimize the influence of the federal government. The libertarians long for unfettered individualism and unregulated capitalism while the conservatives, who do not subscribe to all the tenets of liberalism, wish to halt encroaching secularism and a government that no longer serves their interests.
The unlikely Republican coalition that has held together for four decades is now falling apart. It came together because the more natural association between religious conservatism and a large federal bureaucracy fractured after the Civil Rights movements in the 1960’s when the Democrats no longer prioritized the concerns of the (white) Christian Right. (I will discuss the racial aspects in a future post). The elite pro-business neo-liberal libertarians could coexist with the religious conservatives as long as their concerns did not directly conflict but this is no longer true. The conservative wing of the Republican party have discovered their new found power and that there is an untapped population of disaffected individuals who are inclined to be conservative and also want a larger and more intrusive government that favors them. Prominent conservatives like Adrian Vermeule of Harvard and Senator Josh Hawley are unabashedly anti-liberal.
This puts the neo-liberal elites in a real bind. The Democratic party since Bill Clinton had been moving right with a model of pro-market neo-liberalism but with a safety net. However they were punished time and time again by the neo-liberal right. Instead of partnering with Obama, who was highly favorable towards neoliberalism, they pursued a scorched earth policy against him. Hilary Clinton ran on a pretty moderate safety-net-neo-liberal platform and got vilified as an un-American socialist. Now, both the Republicans and Democrats are trending away from neo-liberalism. The neo-liberals made a strategic blunder. They could have hedged their bets but now have lost influence in both parties.
While the threat of authoritarianism looms large, this is also an opportunity to accept the limits of liberalism and begin to think about what will take its place – something that still respects the basic freedoms afforded by liberalism but acknowledges that it is not sufficient. Conservative intellectuals like Leo Strauss have valid points. There is indeed a danger of liberalism lapsing into total moral relativism or nihilism. Guardrails against such outcomes must be explicitly installed. There is value in preserving (some) traditions, especially ancient ones that are the result of generations of human engagement. There will be no simple solution. No single rule or algorithm. We will need to explicitly delineate what we will accept and what we will not on a case by case basis.
For the past four years, I have been unable to post with any regularity. I have dozens of unfinished posts sitting in my drafts folder. I would start with a thought but then get stuck, which had previously been somewhat unusual for me. Now on this first hopeful day I have had for the past four trying years, I am hoping I will be able to post more regularly again.
Prior to what I will now call the Dark Years, I viewed all of history through an economic lens. I bought into the standard twentieth century leftist academic notion that wars, conflicts, social movements, and cultural changes all have economic underpinnings. But I now realize that this is incorrect or at least incomplete. Economics surely plays a role in history but what really motivates people are stories and stories are what led us to the Dark Years and perhaps to get us out.
Trump became president because he had a story. The insurrectionists who stormed the Capitol had a story. It was a bat shit crazy lunatic story but it was still a story. However, the tragic thing about the Trump story (or rather my story of the Trump story) is that it is an unintentional algorithmically generated story. Trump is the first (and probably not last) purely machine learning president (although he may not consciously know that). Everything he did was based on the feedback he got from his Twitter Tweets and Fox News. His objective function was attention and he would do anything to get more attention. Of the many lessons we will take from the Dark Years, one should be how machine learning and artificial intelligence can go so very wrong. Trump’s candidacy and presidency was based on a simple stochastic greedy algorithm for attention. He would Tweet randomly and follow up on the Tweets that got the most attention. However, the problem with a greedy algorithm (and yes that is a technical term that just happens to coincidentally be apropos) is that once you follow a path it is hard to make a correction. I actually believe that if some of Trump’s earliest Tweets from say 2009-2014 had gone another way, he could have been a different president. Unfortunately, one of his early Tweet themes that garnered a lot of attention was on the Obama birther conspiracy. This lit up both racist Twitter and a counter reaction from liberal Twitter, which led him further to the right and ultimately to the presidency. His innate prejudices biased him towards a darker path and he did go completely unhinged after he lost the election but he is unprincipled and immature enough to change course if he had enough incentive to do so.
Unlike standard machine learning for categorizing images or translating languages, the Trump machine learning algorithm changes the data. Every Tweet alters the audience and the reinforcing feedback between Trump’s Tweets and its reaction can manufacture discontent out of nothing. A person could just happen to follow Trump because they like The Apprentice reality show Trump starred in and be having a bad day because they missed the bus or didn’t get a promotion. Then they see a Trump Tweet, follow the link in it and suddenly they find a conspiracy theory that “explains” why they feel disenchanted. They retweet and this repeats. Trump sees what goes viral and Tweets more on the same topic. This positive feedback loop just generated something out of random noise. The conspiracy theorizing then starts it’s own reinforcing feedback loop and before you know it we have a crazed mob bashing down the Capitol doors with impunity.
Ironically Trump, who craved and idolized power, failed to understand the power he actually had and if he had a better algorithm (or just any strategy at all), he would have been reelected in a landslide. Even before he was elected, Trump had already won over the far right and he could have started moving in any direction he wished. He could have moderated on many issues. Even maintaining his absolute ignorance of how govening actually works, he could have had his wall by having it be part of actual infrastructure and immigration bills. He could have directly addressed the COVID-19 pandemic. He would not have lost much of his base and would have easily gained an extra 10 million votes. Maybe, just maybe if liberal Twitter simply ignored the early incendiary Tweets and only responded to the more productive ones, they could have moved him a bit too. Positive reinforcement is how they train animals after all.
Now that Trump has shown how machine learning can win a presidency, it is only a matter of time before someone harnesses it again and more effectively. I just hope that person is not another narcissistic sociopath.
On some rare days when the sun is shining and I’m enjoying a well made kouign-amann (my favourite comes from b.patisserie in San Francisco but Patisserie Poupon in Baltimore will do the trick), I find a brief respite from my usual depressed state and take delight, if only for a brief moment, in the fact that mathematics completely resolved Zeno’s paradox. To me, it is the quintessential example of how mathematics can fully solve a philosophical problem and it is a shame that most people still don’t seem to know or understand this monumental fact. Although there are probably thousands of articles on Zeno’s paradox on the internet (I haven’t bothered to actually check), I feel like visiting it again today even without a kouign-amann in hand.
I don’t know what the original statement of the paradox is but they all involve motion from one location to another like walking towards a wall or throwing a javelin at a target. When you walk towards a wall, you must first cross half the distance, then half the remaining distance, and so on forever. The paradox is thus: How then can you ever reach the wall, or a javelin reach its target, if it must traverse an infinite number of intervals? This paradox is completely resolved by the concept of the mathematical limit, which Newton used to invent calculus in the seventeenth century. I think understanding the limit is the greatest leap a mathematics student must take in all of mathematics. It took mathematicians two centuries to fully formalize it although we don’t need most of that machinery to resolve Zeno’s paradox. In fact, you need no more than middle school math to solve one of history’s most famous problems.
The solution to Zeno’s paradox stems from the fact that if you move at constant velocity then it takes half the time to cross half the distance and the sum of an infinite number of intervals that are half as long as the previous interval adds up to a finite number. That’s it! It doesn’t take forever to get anywhere because you are adding an infinite number of things that get infinitesimally smaller. The sum of a bunch of terms is called a series and the sum of an infinite number of terms is called an infinite series. The beautiful thing is that we can compute this particular infinite series exactly, which is not true of all series.
Expressed mathematically, the total time it takes for an object traveling at constant velocity to reach its target is
which can be rewritten as
where is the distance and is the velocity. This infinite series is technically called a geometric series because the ratio of two subsequent terms in the series is always the same. The terms are related geometrically like the volumes of n-dimensional cubes when you have halve the length of the sides (e.g. 1-cube (line and volume is length), 2-cube (square and volume is area), 3-cube (good old cube and volume), 4-cube ( hypercube and hypervolume), etc) .
For simplicity we can take . So to compute the time it takes to travel the distance, we must compute:
To solve this sum, the first thing is to notice that we can factor out and obtain
The quantity inside the bracket is just the original series plus 1, i.e.
and thus we can substitute this back into the original expression for and obtain
Now, we simply solve for and I’ll actually go over all the algebraic steps. First multiply both sides by 2 and get
Now, subtract from both sides and you get the beautiful answer that . We then have the amazing fact that
I never get tired of this. In fact this generalizes to any geometric series
for any that is less than 1. The more compact way to express this is
Now, notice that in this formula if you set , you get , which is infinity. Since for any , this tells you that if you try to add up an infinite number of ones, you’ll get infinity. Now if you set you’ll get a negative number. Does this mean that the sum of an infinite number of positive numbers greater than 1 is a negative number? Well no because the series is only defined for , which is called the domain of convergence. If you go outside of the domain, you can still get an answer but it won’t be the answer to your question. You always need to be careful when you add and subtract infinite quantities. Depending on the circumstance it may or may not give you sensible answers. Getting that right is what math is all about.
When I was in graduate school, my friends and I would jokingly classify the utility of research in terms of the order the researcher would be killed after the revolution. So, for physics, if you were working on say galaxy formation in the early universe you would be killed before someone working on the properties of hydrogen at low temperatures, who would be killed before someone working on building a fusion reactor. This was during the cold war and thus the prospect of Stalin and Mao still loomed large. We did not joke this way with fear or disdain but rather with a somewhat bemused acknowledgment that we were afforded the luxury to work on esoteric topics, while much of the world still did not have running water. In those days, the left-right divide was between the small government neoliberals (conservatives in those days who advocated for freer and more deregulated markets) and the bigger government New Deal liberals (those for more government action to address economic inequities). We certainly had fierce debates but they were always rather abstract. We never thought our lives would really change that much.
By the time I had finished and started my academic career, it was clear that the neoliberals had prevailed. The Soviet Union had collapsed, AT&T was broken up, and the Democratic president proclaimed the era of big government was over. Francis Fukuyama wrote “The End of History and the Last Man” arguing that western liberal democracy had triumphed over communism and would be the last form of government. I was skeptical then because I thought we could do better but I really didn’t consider that it could get worse.
But things got worse. We had the bursting of the dot com bubble, 9/11, the endless wars, the great recession, and now perhaps the twilight of democracy as Anne Applebaum laments in her most recent book. We can find blame everywhere – globalization, automation, the rise of China, out of touch elites, the greedy 1%, cynical politicians, the internet, social media, and so forth. Whatever the reason, this is an era where no one is happy and everyone is fearful.
The current divide in the United States is very real and there is fear on both sides. On one side, there is fear that an entire way of life is being taken away – a life of a good secure job, a nuclear family with well defined roles, a nice house, neighbors who share your values and beliefs, a government that mostly stays out of the way but helps when you are in need, the liberty to own a firearm, and a sense of community and shared sacrifice. On the other side, there is the fear that progress is being halted, that a minority will forever suppress a majority, that social, racial, and economic justice will never be achieved, that democracy itself is in peril, and that a better future will always be just out of reach.
What is most frustrating to me is that these points of view are not necessarily mutually exclusive. I don’t know how we can reconcile these differences but my biases and priors incline me to believe that we could alleviate some of the animosity and fear if we addressed income insecurity. While I think income inequality is a real problem, I think a more pressing concern is that a large segment of the population on both sides of the the divide lives continuously on a precipice of economic ruin, which has been made unavoidably apparent by our current predicament. I really think we need to consider a universal basic income. I also think it has to be universal because suspicion of fraud and resentment is a real issue. Everyone gets the check and those with sufficient incomes and wealth simply pay it back in taxes.
Nietzsche famously wrote:
“God is dead. God remains dead. And we have killed him.”
This quote is often used as an example of Nietzsche’s nihilism but it is much more complicated. These words are actually spoken by a madman in Nietzsche’s book The Gay Science. According to philosopher Simon Critchley, the quote is meant to be a descriptive rather than a normative statement. What Nietzshe was getting at is that Christianity is a religion that values provable truth and as a result of this truth seeking, science arose. Science in turn generated skepticism of revealed truth and the concept of God. Thus, the end of Christianity was built into Christianity.
Borrowing from this analysis, science may also have have a built-in mechanism for its own doom. An excellent article in this month’s Technology Review describes the concept of epistemic dependence, where science and technology is so complicated now that no single person can understand all of it. In my own work, I could not reproduce a single experiment of my collaborators. Our collaborations work because we trust each other. I don’t really know how scientists identify new species of insects, or how paleontologists can tell what species a bone fragment belongs to, or all the details of the proof of the Poincare conjecture. However, I do understand how science and math works and trust that the results are based on those methods.
But what about people who are not trained in science? If you tell them that the universe was formed 14 billion years ago in a Big Bang and that 99% of all the stuff in the universe is completely invisible, why would they believe you. Why is that more believable then the earth being formed six thousand years ago in seven days? In both cases, knowledge is transferred to them from an authority. Sure you can say because of science, we live longer, have refrigerators, cell phones, and Netflix so we should believe scientists. On the other hand, a charismatic conman could tell them that they have those things because they were gifted from super advanced aliens. Depending on the sales job and one’s priors, it is not clear to me which would be more convincing.
So perhaps we need more science education? Well, in half a century of focus on science education, science literacy is not really very high in the general public. I doubt many people could explain how a refrigerator works much less the second law of thermodynamics and forget about quantum mechanics. Arthur C. Clarke’s third law that “All sufficiently advanced technology is indistinguishable from magic” is more applicable then ever. While it is true that science has delivered on producing better stuff it does not necessarily make us more fulfilled or happier. I can easily see a future where a large fragment of the population simply turns away from science with full knowledge of what they are doing. That would be the good outcome. The bad one is that people start to turn against science and scientists because someone has convinced them that all of their problems (and none of the good stuff) are due to science and scientists. They would then go and destroy the world as we know it without really intending to. I can see this happening too.
The Nobel Prize in Physiology was awarded for the discovery of Hepatitis C today. The work is clearly deserving of recognition but this is another case where there were definitely more than three people who played an essential role in the work. I really think that the Nobel Prize should change its rules to allow for more winners. Below is my post when one of the winners of this years prize, Michael Houghton, turned down the Gairdner Award in 2013:
The scientific world was set slightly aflutter when Michael Houghton turned down the prestigious Gairdner Award for the the discovery of Hepatitis C. Harvey Alter and Daniel Bradley were the two other recipients. Houghton, who had previously received the Lasker Award with Alter, felt he could not accept one more award because two colleagues Qui-Lim Choo and George Kuo did not receive either of these awards, even though their contributions were equally important.
Hepatitis, which literally means inflammation of the liver, was characterized by Hippocrates and known to be infectious since the 8th century. The disease had been postulated to be viral at the beginning of the 20th century and by the 1960’s two viruses termed Hepatitis A and Hepatitis B had been established. However, there still seemed to be another unidentified infectious agent which was termed Non-A Non-B Hepatitis NANBH.
Michael Hougton, George Kuo and Qui-Lim Choo were all working at the Chiron corporation in the early 1980’s. Houghton started a project to discover the cause of NANBH in 1982 with Choo joining a short time later. They made significant process in generating mouse monoclonal antibodies with some specificity to NANBH infected materials from chimpanzee samples received from Daniel Bradley at the CDC. They used the antibodies to screen cDNA libraries from infected materials but they had not isolated an agent. George Kuo had his own lab at Chiron working on other projects but would interact with Houghton and Choo. Kuo suggested that they try blind cDNA immunoscreening on serum derived from actual NANBH patients. This approach was felt to be too risky but Kuo made a quantitative assessment that showed it was viable. After two years of intensive and heroic screening by the three of them, they identified one clone that was clearly derived from the NANBH genome and not from human or chimp DNA. This was definitive proof that NANBH was a virus, which is now called Hepatitis C. Kuo then developed a prototype of a clinical Hepatitis C antibody detection kit and used it to screen a panel of NANBH blood provided by Harvey Alter of the NIH. Kuo’s test was a resounding success and the blood test that came out of that work has probably saved 300 million or more people from Hepititis C infection.
The question then is who deserves the prizes. Is it Bradley and Alter, who did careful and diligent work obtaining samples or is it Houghton, Choo, and Kuo, who did the heroic experiments that isolated the virus? For completely unknown reasons, the Lasker was awarded to just Houghton and Alter, which primed the pump for more prizes to these two. Now that the Lasker and Gairdner prizes have been cleared, that leaves just the Nobel Prize. The scientific community could get it right this time and award it to Kuo, Choo, and Houghton.
Addendum added 2013-5-2: I should add that many labs from around the world were also trying to isolate the infective agent of NANBH and all failed to identify the correct samples from Alter’s panel. It is not clear how long it would have been and how many more people would have been infected if Kuo, Choo, and Houghton had not succeeded when they did.
I gave a talk at the International Conference on Complex Acute Illness (ICCAI) with the title Forecasting COVID-19. I talked about some recent work with FDA collaborators on scoring a large number of publicly available epidemic COVID-19 projection models and show that they are unable to reliably forecast COVID-19 beyond a few weeks. The slides are here.
I’ve been actively engaged in trying to model the COVID-19 pandemic since April and after 5 months I am pretty confident that models can estimate what is happening at this moment such as the number of people who are currently infected but not counted as a case. Back at the end of April our model predicted that the case ascertainment ratio ( total cases/total infected) was on the order of 1 in 10 that varied drastically between regions and that number has gone up with the advent of more testing so that it may now be on the order of 1 in 4 or possibly higher in some regions. These numbers more or less the anti-body test data.
However, I do not really trust my model to forecast what will happen a month from now much less six months. There are several reasons. One is that while the pandemic is global the dynamics are local and it is difficult if not impossible to get enough data for a detailed fine grained model that captures all the interactions between people. Another is that the data we do have is not completely reliable. Different regions define cases and deaths differently. There is no universally accepted definition for what constitutes a case or a death and the definition can change over time even for the same region. Thus, differences in death rates between regions or months could be due to differences in the biology of the virus, medical care, or how deaths are defined and when they are recorded. Depending on the region or time, a person with a SARS-CoV-2 infection who dies of a cardiac arrest may or may not be counted as a COVID-19 death. Deaths are sometimes not officially recorded for a week or two, particularly if the physician is overwhelmed with cases.
However, the most important reason models have difficulty forecasting the future is that modeling COVID-19 is as much if not more about modeling the behavior of people and government policy than modeling the biology of disease transmission and we are just not very good at predicting what people will do. This was pointed out by economist John Cochrane months ago, which I blogged about (see here). You can see why getting behavior correct is crucial to modeling a pandemic from the classic SIR model
where and are the infected and susceptible fractions of the initial population, respectively. Behavior greatly affects the rate of infection and small errors in amplify exponentially. Suppression and mitigation measures such as social distancing, mask wearing, and vaccines reduce , while super-spreading events increase . The amplification of error is readily apparent near the onset of the pandemic where grows like . If you change by , then the will grow like and thus the ratio is growing (or decaying) exponentially like . The infection rate also appears in the initial reproduction number . From a previous post, I derived approximate expressions for how long a pandemic would last and show that it scales as and thus errors in will produce errors , which could result in errors in how long the pandemic will last, which could be very large if is near one.
The infection rate is different everywhere and constantly changing and while it may be possible to get an estimate of it from the existing data there is no guarantee that previous trends can be extrapolated into the future. So while some of the COVID-19 models do a pretty good job at forecasting out a month or even 6 weeks (e.g. see here), I doubt any will be able to give us a good sense of what things will be like in January.
In order for an infectious disease (e.g. COVID-19) to spread, the infectious agent (e.g. SARS-CoV-2) must jump from one person to another. The rate of this happening depends on the rate that an infectious person will come into contact with a susceptible person multiplied by the rate of the virus making the jump when the two people are nearby. The reproduction number R is obtained from the rate of infection spread times the length of time a person is infectious. If R is above one then a single person will infect more than one person on average and thus the pandemic will grow. If it is below one, then the pandemic will diminish. Herd immunity happens when enough people have been infected that the rate of finding a susceptible person becomes low enough that R drops below one. You can find the math behind this here.
However, a major assumption behind herd immunity is that once a person is infected they can never be infected again and this is not true for many infectious diseases such as other corona-viruses and the flu. There are reports that people can be reinfected by SARS-CoV-2. This is not fully validated but my money is on there being no lasting immunity to SARS-CoV-2 and this means that there is never any herd immunity. COVID-19 will just wax and wane forever.
This doesn’t necessarily mean it will be deadly forever. In all likelihood, each time you are infected your immune response will be more measured and perhaps SARS-CoV-2 will eventually be no worse than the common cold or the seasonal flu. But the fatality rate for first time infection will still be high, especially for the elderly and vulnerable. Those people will need to remain vigilante until there is a vaccine, and there is still no guarantee that a vaccine will work in the field. If we’re lucky and we get a working vaccine, it is likely that vaccine will not have lasting effect and just like the flu we will need to be vaccinated annually or even semi-annually.
The world seems to be in another Covid-19 plateau for new cases. The nations leading the last surge, namely the US, Russia, India, and Brazil are now stabilizing or declining, while some regions in Europe and in particular Spain are trending back up. If the pattern repeats, we will be in this new plateau for a month or two and then trend back up again, just in time for flu season to begin.