This post is the next in a series that dates back several years. In fact, it's been going on so long that I ended up upgrading the title from "50 Years of Science" to "60 Years of Science". And, ignoring the change, this is the seventeenth entry in the series. You can go to sigma5.blogspot.com/2017/04/50-years-of-science-links.html for a post that contains links to all the posts in the series. I will update that post to include a link to this entry as soon as I have posted it.
I take Isaac Asimov's book "The Intelligent Man's Guide to the Physical Sciences" as my baseline for the state of science when he wrote the book (1959 - 60). In this post I am reviewing what he reported then noting what has changed since. For this post I will be reviewing two sections: "Heat" and "Mass and Energy". Both are from the chapter he titled "The Waves".
As he points out, many discussions of "light" are accompanied by a discussion of "heat". A candle, for instance, gives off both light and heat. The quantitative (assigning numbers to things) as opposed to qualitative (generalities such as "it's hot out today") understanding of this subject was completely missing until what he describes as "modern times". If you can't measure it, you can't study it quantitatively.
The observation that kicked off the change from qualitative study to quantitative study was the observation that warming many materials up caused them to expand. Galileo kicked things off in 1603 by plunging a tube of heated air into room temperature water. The water cooled the air, which compressed and drew water up into the tube. He called the device a "thermometer". Unfortunately, the height of the water in the tube could be changed not only by changes in room temperature but also by changes in air pressure (a phenomenon not well understood at the time).
In 1654 the Grand Duke of Tuscany came up with a better design. He sealed the tube. That fixed the problem caused by changes in air pressure. He also switched to a liquid. To magnify the change he placed a large bulb full of the liquid at the bottom of the tube then forced the liquid to expand up a narrow tube. If that sounds familiar, it's because all thermometers were designed that way until the electronic thermometer took over. And that change happened long after Asimov's book came out.
The Duke's design was good enough to permit some serious science to happen. Boyle figured out that human body temperature is (relatively) constant and substantially higher than any ambient temperature people find comfortable. Amontons led the switch from water to mercury as the liquid in the tube. "Mercury thermometers" were ubiquitous until a decade or so ago. They are still pretty easy to find. But, given that electronic thermometers are now cheap and contain no dangerous mercury, I don't expect that to last much longer.
Fahrenheit added a scale. Much of the world, including the US, still lives by his scale. On his scale water freezes at 32 degrees and boils at 212 degrees. On the Celsius scale (invented by a Swedish astronomer named Celsius in 1842) that is part of the Metric System that the rest of the world uses, these numbers are 0 degrees and 100 degrees.
Originally called Centigrade, in 1948 various tiny technical changes were made and the name was changed to Celsius. Given the rampant hostility to science that various groups succeeded in have fomenting, it is unlikely that the US will switch from Fahrenheit to Celsius any time soon.
Temperature is a measure of intensity, not quantity. In 1760 Black started measuring how much heat it took to change the temperature of various materials by a degree. It turns out that this quantity varies a lot. A further source of confusion came from the fact that under certain circumstances you can insert heat and the temperature doesn't change. If you add heat to ice the temperature stops changing when it reaches 0 degrees Celsius (see how much handier the Celsius scale is). Instead, some of the ice melts. There's nothing simple about heat.
What really sent the study of heat into high gear was the invention of the steam engine. The people who bought them didn't just care that they worked. They also cared how much they cost to run. If the same job could be done with less fuel (and fewer people to feed the fuel into the engine) then that was a good thing. But to understand how to make steam engines more efficient scientists had to understand how heat worked.
The first "theory of heat" was that it consisted of something called "caloric". Various materials contained various amounts of caloric, which could flow from here to there, presumably according to a set of rules. But no matter what rules they came up with, one obstacle or another inevitably popped up.
Scientists hunted for alternatives and eventually came up with the idea that heat was the manifestation of some kind of vibration. Thompson studied the way cannon barrels were bored, a process that produces tremendous quantities of heat. He decided that the mechanical friction of hard metal scraping against hard metal was causing some kind of vibration.
Davy then caused two pieces of ice to be rubbed together in a way that produced no caloric and observed that the ice melted. Caloric couldn't explain the result. But again mechanical friction could produce some kind of vibration that could.
Several scientists, most notably Carnot, studied how heat flowed. This later led scientists to crown Carnot as the founder of "thermodynamics", the study of heat and heat flow. Carnot developed a theory that explained how steam engines worked. The theory told scientists and engineers what to do to make them more efficient. It also allowed them to calculate exactly how efficient a steam engine could possibly be made. No actual steam engine is anywhere near as efficient as theory says it can be. But they are now way more efficient than early designs were.
Another pioneer was Joule. He spent 35 years studying how heat behaved in various situations. He developed Joule's Law: A given amount of "work" always produces the same amount of heat. And that meant that heat was just another form of energy. This led to the idea of "conservation of energy". Unfortunately for Joule, it was Helmholtz who formally proposed the idea in 1847. Conservation of Energy means that you can convert energy back and forth from one form to another. But you can neither create nor destroy it.
At roughly the same time it was observed that, with one exception, the conversion of one form of energy to another was never 100% efficient. Every time you did a conversion you got some heat whether you wanted to or not. So the only 100% efficient conversion is from any other form of energy into heat.
A study of the opposite, turning heat into other forms of energy, resulted in the introduction of the concept of "Absolute Zero". (Asimov doesn't talk about it here but that doesn't stop me from talking about it below.) The process of converting heat into other forms of energy involves two reservoirs; a hot reservoir and a cold reservoir. Heat can be turned into other forms of energy by taking some of the contents of the hot reservoir and reducing its temperature to that of the cold reservoir.
It turns out that's what a steam engine does. You heat water and turn it into steam. That's the hot reservoir. The general environment is the cold reservoir. If you process the steam cleverly it's temperature is reduced to that of the cold reservoir and energy is available to turn a flywheel. But the temperature of the cold reservoir imposes a limit on how much of the energy present in the hot steam is available to be converted into the energy of mechanical motion.
The laws of thermodynamics don't let you cool the steam to a temperature below that of the cold reservoir. But it's worse than that. It turns out that as a practical matte, some of the heat goes to warm up the machinery and for other non-productive purposes. The first law of thermodynamics is waggishly stated as "you can't win". The second law is waggishly stated as "you can't even break even". And a similar rendering of the third law yields "you can't even get out of the game".
The part of the theoretically available energy that is actually available is called "free energy". The part that is inevitably lost eventually became associated with the term "entropy". Entropy always goes up. Clausius invented the term in 1850.
At this point scientists knew in general terms how things worked. But they had no idea how the underlying mechanism worked. In 1870 Maxwell and Boltzmann developed the "kinetic theory of gasses". Heat came from the microscopic vibration of each molecule of gas. It turns out that molecules in a liquid can vibrate. Even molecules in a solid can (and do) vibrate. That's where the energy that heat represented was hiding. There was no caloric fluid.
Vibrating molecules can pass on their vibrations to other molecules. The energy contained in a certain rate of vibration depends, among other thins, on the weight of the vibrating molecule. The details are complicated. But the bottom line is that scientists figured out how to make this vibration approach explain all the details of how thermodynamics worked.
The energy involved in melting ice (or turning liquid water into steam) could be explained by the energy necessary to break (thaw, boil) the bonds that make a solid a solid (or a liquid a liquid). The same was true of the freezing (and condensation) processes. Making the bonds freed energy.
And in 1870 Gibbs extended the idea to chemical bonds. Chemical processes could be explained by attributing a certain amount of energy to a chemical bond. The energy was released when the bond formed and absorbed when the bond was broken. That brought chemistry into the thermodynamic fold.
That brings us to the section titled "Mass to Energy". Radioactivity, discovered in 1896, initially presented a challenge. The energies involved were gigantic. Where could that much energy come from? Einstein supplied the answer with his famous "E" equals "M" times the square of the speed of light. "E" is energy. "M" is mass. It turns out that a tiny amount of mass contains a gigantic amount of energy. The square of the speed of light is just a truly enormous constant number. But all it does is tell you exactly how much energy you get when you annihilate a tiny amount of mass.
Doing away with a tiny amount of matter is all it takes to produce the enormous amounts of energy we see coming from radioactive decay. And, of course, if you annihilate a "large" amount of mass, say a pinch of salt's worth, you get enough energy to level a city. Atomic (fission) and Hydrogen (fusion) bombs are just machines for the annihilation of what would otherwise be considered small amounts of mass.
A side effect of all this was the loss of Lavoisier's "conservation of mass" law. It was replace by the "conservation of mass-energy" law. And Einstein's idea soon transitioned from the theoretical to the practical.
Aston was able to experimentally confirm that Einstein's equation was correct. He was able to make measurements involving radioactive decay that were delicate enough to measure the mass loss in some situations. It was the right amount to match the amount of energy that was produced when, of course, you used Einstein's conversion factor.
Before I finish, I want to cover one subject that Asimov didn't. Scientists were able to do complex sets of experiments and calculations to determine how much energy was produced by reducing the temperature of water from say a hundred degrees to zero degrees. (We are using the Celsius scale here where water boils at 100 and freezes at zero.) It turns out the process released 373/273 of the energy theoretically available. Other experiments produced a similar result if you just added 273 to all the temperatures.
That got these scientists to ask themselves "is there such a thing as the lowest possible temperature, an absolute zero?" If there was, it appeared to be -273 degrees. (It's actually 273 and a fraction but I am going to ignore the fraction in order to keep things simple.) That led to the development of the Kelvin temperature scale.
A Kelvin degree is exactly the same as a Celsius degree. But 0 degrees Celsius is the same as 273 degrees Kelvin. 100 degrees Celsius becomes 373 degrees Kelvin. If you convert all temperatures to Kelvin then the ratio of the temperature of the hot reservoir to the temperature of the cold reservoir gives you the answer the question of how much heat energy can be converted to free energy.
Since the environment tends to be at roughly 300 degrees Kelvin (80 degrees Fahrenheit) you have to operate your hot reservoir at 600 degrees Kelvin to have access to even 50% of what's theoretically available. That's about 620 degrees Fahrenheit. This kind of analysis explains why engineers are always trying to increase the "operating temperatures" of things like jet engines.
An operating temperature of 1,100 degrees Celsius, something that the most efficient jet engines can now do, translates to a Kelvin temperature (again ignoring the fraction) of 1,400 degrees. That means that over 70% of the heat energy can theoretically be turned into free energy.
Cars, whose engines don't run anywhere near that hot, are doomed by thermodynamics to have a very low percentage of the heat energy the fuel produces translated into the free energy that can be used to "make the wheels go round and round".
Bottom line: Very little has changed in these areas. These subjects are foundational. And, for the most part, the foundations in these two areas were laid well before Asimov wrote his book. Science has since built on these areas. But for these specific areas, the foundations themselves have seen no changes. And little of a foundational nature has been added in the interval since the book came out.
Saturday, March 28, 2020
Friday, March 20, 2020
Epidemic Explainer
COVAD-19 is all anyone is talking about. There is a lot of misinformation out there. It is easier to sort the wheat from the chaff if you understand the basics. And an important aspect of "the basics" is mathematics. A lot of the people trying to talk about the subject are either poor at mathematics or assume it's something they should stay away from. I am going to take the opposite tack.
The mathematics of how epidemics evolve is the same mathematics as interest (the kind you are charged on your credit card balance) and radioactivity. The generic term for it is "exponential growth". If you understand exponential growth you are a long way toward understanding the process as a whole.
We are used to and intuitively understand additive sequences. If you start with zero and keep adding two to it the result keeps getting bigger. This is an example of "linear growth". If we start with zero and add two every week then after a week our total will be two. After another week it will be four. After still another week it will increase to six. In fact, we can just multiply the number of weeks by two and we will get the result. After 52 weeks, roughly a year, our result will be 104.
Linear sequences grow slowly even if they continue indefinitely. If you wait long enough you can reach any number you want. It's just that if you need to reach a large number it will take a long time. If we have a disease that infects a thousand people per week then it will take seven million weeks to infect everyone in the world. That's over a hundred thousand years. It's also something no one would be concerned with even though a thousand cases per week sounds like a lot.
Now let's change things up. Let's start with a series whose first two elements are one and one. But now let's create the next number in the series by adding the two most recent numbers in the sequence together. You might think that things will go pretty much the same way as the "add two each time" rule. But they don't.
The third number in the series is two (one plus one). The fourth number is three (two (one back) plus one (two back)). This still doesn't sound like it will get out of hand. But 3+2=5 then 5+3=8 then 8+5=13, then 21, then 34, then 55, and so on. And that's only the first ten numbers in the sequence.
And this sequence has a name. It's called the Fibonacci sequence. It doesn't take that long to start generating enormous numbers. The fifty-second number in the sequence is 20,365,011,074. That's more than all the people currently living on earth today. The Fibonacci sequence is an example of exponential growth.
And a fundamental attribute of exponential sequences is that they can grow to truly gigantic numbers even if the starting value is very small. And the Fibonacci sequence is an example of an exponential "growth" sequence. There are also exponential "decay" sequences. A classic example of this is radioactive decay.
Radioactive materials have a characteristic called a "half life". This is the amount of time it takes for half the original material to "decay" into something else. Let's say we have a made up element called "Madeup", which is radioactive. And let's assume its half life is one week. And let's say we have exactly 33,554,432 atoms of pure Madeup at the beginning of our observation period.
Then exactly one week later we will have 16,777,261 atoms of Madeup. (We'll also have the same number of atoms of whatever Madeup decays into as a result of the radioactive decay process.) In two weeks we will have 8,388,608 atoms of Madeup left. And so on. In exactly 25 weeks we will be down to only one atom of Madeup. All the rest will now be something else. That's because 33,554,432 is exactly two raised to the twenty-fifth power. It's the reason I picked it as my starting number. It made the math simple.
So what's this all got to do with COVAD-19 and Epidemics? Plenty. There are a lot of numbers floating around about COVAD-19. At this point it is hard to figure out what the correct numbers are. But we don't need to know the exact numbers to understand the pattern. Let's see what I mean.
There is no exact number for the number of days it takes for COVAD-19 to be transmitted from one person to another. But it seems to be around a week. If it is more than a week then the disease will spread more slowly. If it takes less than a week then the disease will spread more quickly.
The same thing is true of the number of people an infected person turns around and infects. The range most people quote is "two to three people". Again, if the number is higher then the disease will spread more quickly. If it is lower then it will spread more slowly.
But if we start with one infected person. And we assume the transmission time is a week. And we assume that each infected person infects two others. Well, then twenty-three weeks later everyone on earth will be infected. The US Census bureau estimates that the current population of the world is 7.6 billion. That's less than the 8,388,608 number we get by doubling two 23 times.
The first COVAD-19 infection was more than 23 weeks ago and not all of the world has since been infected. So my simple "one week results in two new infections" rule is wrong. Let's see if we can get more real.
The number of people a specific infected person infects varies from zero to a whole lot. A completely correct mathematical model would be very complicated. It would involve statistics and calculus. But there is a "typical" number of infections that gets you to roughly the same place that the super-precise analysis does. And the important thing is that the fewer "average number of new infections" we see, the slower the infection spreads.
The same is true of the transmission time. The actual situation is very complicated. But a single, simple "average transmission time" will get you to pretty much the same place the complex analysis does. And again, the bottom line is the same. If the average transmission time is short then the infection spreads quickly. If the average transmission time long then the infection spreads much more slowly.
And that means we can characterize various changes in terms of their impact on the average number of infections and/or the average transmission time. And, as far as I can tell, nothing much affects the average transmission time. So the whole game is in reducing the average number of new infections.
A few places have taken drastic measures. They have tested lots of people (in some cases everyone). As soon as someone tests positive then they are immediately isolated. This has the effect of driving the average new infection rate to zero (or a small number close to zero).
If we can get the average new infection rate down to 0.5 (two infected people together only infect one new person, on average) then we are talking radioactive decay mathematics. If everybody in the world is infected (this example makes no sense in the real world, but stick with me, anyhow) then after 25 weeks we would be down to one new infection per week. More realistically, if we assume that a million people are currently infected then it would take 20 weeks to drive the world wide new infection rate to 1 per week.
And things go more quickly if we can do better. If we assume that we can drive the average new infection rate to 0.1 (only a 10% chance of an infected person passing the disease on to another person) then a million current infections per week goes to one new infection per week in only six weeks.
That's what health officials are trying to do, drive the average new infection rate as low as possible. If the average new infection rate is greater than one then the number of new cases grows. If it is less than one, then the number of new cases declines. It appears that the average new infection rate is currently less than two but well above one. And, if the best we can do is get it down to just below one, then the disease will linger for a very long time.
It seems to me that an obvious measure to take is to require people to wear face masks while in public. The standard cheapo facemask does NOT completely stop the disease from spreading. The virus can pass through the mask. So an infected person wearing a mask can infect an uninfected person who is also wearing a mask. But face masks drastically reduce the "viral load".
An infected person throws off a lot of virus particles. But a single virus particle does not always succeed in transmitting the virus. In fact, a single particle is almost always unsuccessful. It's a numbers game. If a lot of particles are transmitted from the infected person to the uninfected person then the chances of the uninfected person catching the disease goes way up. Anything that reduces the viral load substantially increases the chances of a transmission failure.
The Chinese found that masks alone were not effective. But I have to believe that they would help. And let's say we adopted an "everybody has to wear a mask while in public' (and here I'm talking about the cheapo masks that are generally available) rule. I think it would help.
And let's say that the average person went through ten masks per month. The world would then need to manufacture eighty billion masks per month indefinitely. That's doable. But nobody is talking about doing that, at least not in the US. So it hasn't happened here. But, even with the low current rate of use of cheapo masks in the US, there is a severe shortage of them.
And there is a mask that is pretty effective. It is something called an N-95 mask. They are more expensive (and harder to use as they must fit tightly to work properly). At this time the thinking is that their use should be restricted to health care workers and others in high risk categories. There is a shortage of them too.
The strategy that is being rolled out instead is "social distancing". The most efficient way to spread the disease is for an infected person to exhale a swarm of virus particles. They then travel a short distance before being inhaled by an uninfected person. COVAD-19 is a lung-based disease so getting a lot of fresh virus particles (a large viral load) into an uninfected person's lungs is what will most effectively transmit the disease.
If the uninfected person is six feet or more away from the infected person the chances of any particular virus particle ending up in that person's lungs is much reduced. Again, its a numbers game. The more hoops you make the virus particles jump through, the fewer make it into the lungs of the uninfected person. Fewer particles (a smaller viral load) means a higher probability of the infection failing to take hold.
The other thing people are doing is cleaning everything. Virus particles can survive in the open air for a while. They can also land on a surface and stick there. Survival time depends on the specifics of the surface. But a wipe with any kind of disinfectant drives the survival rate to infinitesimal. As does the UV component of sunlight. Sunlight hitting free floating virus particles or those lodged on a surface will quickly destroy them.
There is similar thinking behind the "wash your hands", "don't touch your face", and "don't shake hands" admonitions. The idea is that virus particles can end up on your hands. Then you transmit them to your face. Then somehow they get to your lungs from there.
All of these behavioral changes can be helpful. But I think the amount of help they represent is modest. I suspect that abandoning all these practices and replacing them with a "mandatory facemask while in public" rule would be more effective. But then what do I know? And doing both could help and can't hurt.
A very grave concern of many experts is the effect the disease can have on hospitals and the medical system. Italy is seeing large numbers of deaths. Part of the reason is that in a large part of the country the health care system got completely overwhelmed and became unable to care for people.
Like ours, the Italian health care system was sized to handle the normal amount of business, or maybe a little more. What it got was a whole lot more. At that point they ran out of everything: doctors, nurses, medical supplies, intensive care beds, regular care beds, supplies of all kinds, support staff of all kinds, the works.
It is important to react strongly and to react before the crisis hits. Capacity must be "surged" before it is needed. By the time it is needed it's too late. China reacted by building two large hospitals in less than two weeks. Were they full up hospitals? No! But they were capable of handling the patients that weren't acutely sick so that the regular hospitals could focus on the acutely sick.
The US is in the same situation. We currently have enough hospital capacity to handle the need. But we have little "surge" capacity. You need to ramp up in a big way at least three weeks before the wave hits. Remember, if the case load is doubling each week, you will have eight times as many patients to deal with in three weeks.
Let's say that the number of people with the disease who are sick enough to require hospitalization is currently absorbing a quarter or more of your surge capacity. If so, if you don't act immediately, you are guaranteed to be in a world of trouble in three weeks time.
People have been studying epidemics for a long time now. The classic epidemic is the "Spanish Flu" epidemic of 1918-19. It demonstrated all of the characteristics of the current COVAD-19 one. Oh, the average transmission time and the average new infection rate were different from then to now.
But, from a mathematical perspective, they are identical. To model COVAD-19 you just plug the new average transmission time and the average new infection rate into the exact same model and the time line for what is going to happen when pops right out.
And it is important to point out that the actions that are currently being taken are all about "flattening the curve". We know we can slow the rate at which the epidemic grows. This is important. Slower growth gives us more time to prepare. But we need to use that time to actually prepare. So far the time has mostly been squandered.
But let's say we get our act together. Then what? We currently have no way to prevent the disease and only modest ways to treat it. Current treatment consists of supporting the body's natural ability to fight off the disease. Reducing the amount of virus the body has to deal with makes it easier for the body to triumph. It appears that the younger you are the better the body is at fending this particular disease off. That's unusual.
Most of the people who have died so far, at least in the US, have been elderly people and people who have compromised immune systems. I live in King County in Washington State. It has been the epicenter of the early evolution of the disease in the US.
Today the local paper published a graph that broke out the age of the various people who died in my state. 59% of those who died were 80 or older. A further 26% were 70-79. A further 16% were 40-69. No one under 40 has died. (You can find the graph in the March 20, 2020 edition of The Seattle Times.)
But that's all besides the point. Slowing things down does not ultimately reduce the number of people who eventually get the disease. The only current sure-fire protection is to get the disease and live to tell the tale. Once you've had the disease, you can't get it again. Or at least, that's what everybody currently believes. If we wait long enough and let enough people catch the disease then eventually "herd immunity" will kick in.
If almost everyone, say 90%, has already had the disease then the disease will have a hard time finding an uninfected person. And that drives the new infection rate close to zero. The current population of the US is 329 million, according to the US Census bureau. To get to 90% just under 300 million people would have to get the disease.
Our current medical system is in no way ready or able to cope with that. If just 10% of people who get infected require hospitalization, that's 30 million people. If we flatten the curve enough to spread the epidemic over ten years that's still three million hospitalizations per year. That smaller number is still large enough to overwhelm our current medical system.
Right now, the percentage of infected people expected to need hospitalization is higher than 10%. But we are still undertesting so it is likely that we are undercounting the number of people who are infected. So maybe the actual percentage of infected people who need hospitalization is 10% or even less. It would have to be a whole lot less to get the expected number of hospitalizations down to what our system can handle.
Currently Washington State has 1,376 known infections and 74 known fatalities. That's a fatality rate of over 5%. But there are special circumstances that lead many experts to suggest that that number is too high. The early number out of China was 2%. The latest number is 1.4%. Let's say that even that number is too high and the real number is 1%. That means that to get to the point where 90% of the US population has had the disease we can expect 3 million fatalities. That's sobering.
And one hopes that it doesn't come to just having to depend on herd immunity. The two alternatives to be hoped for are an immunization or an effective treatment (or both). If people can get a shot (or take a pill, or whatever) and become instantly immune without having to get the actual disease, that would be ideal. It would mean that we wouldn't have to worry about overwhelming our medical system and a lot of people wouldn't have to die.
But it is important to know that coronaviruses, the group of viruses that COVADS-19 is a member of, also contains the viruses that cause the common cold and the "seasonal" flu. Pharmaceutical companies know that an effective cure for the common cold would be a giant gold mine. So they have vigorously pursued a cure for decades with no luck.
They have had more luck with seasonal flu. They have been successful at creating a flu shot that protects against specific strains of flu. But the flu just mutates into something that the flu shot is ineffective against, necessitating the creation of a new and improved flu shot. So pretty much every year I get the flu even though I always get that year's flu shot. Companies are trying to come up with a "universal" flu shot but have yet to see any success.
There has been more success on the treatment front. Almost nobody dies of the flu or of a cold. Very few people need hospitalization. It looks like it will be easier to come up with something that works on the treatment side. But expect success to be hard to come by. That's what dealing with colds and flus tells us.
So the best thing we can do is to pour resources into medical research. I'm talking doubling (or more) the amount we are currently spending in these areas. That should speed up the process. And, while we are looking for something that is effective against COVAD-19 we might get lucky and find something effective for dealing with colds and/or the flu along the way.
But it is critical to be realistic about how fast some kind of "fix" can be delivered at scale. Here are the steps involved. Step one is for a scientist to find something interesting in the lab. Step two is to do a "safety" test on humans. Step 3, is to do a small scale "effectiveness" test. Step four is to do a large scale effectiveness test. Step five is regulatory approval. Step six is large scale manufacturing. Step seven is large scale implementation.
In normal situations one or more of these individual steps can easily take a year or more. And it doesn't pay to skimp. A drug just failed step three when applied to COVAD-19. Other drugs for other diseases have spectacularly failed step two. Killing ten million people in an attempt to save one million people is a bad idea.
No one knows how long step one will take. If a drug that is already approved for use on humans to treat another medical condition turns out to be effective against COVAD-19 then some of the above steps can be implemented at warp speed. But it will likely take something brand new. And even with a lot of luck and super-fast-track-ing everything, the entire process is likely to take 12-18 months at a minimum.
If you want to know why a lot of knowledgeable people are currently shouting PANIC at the top of their lungs, now you know. And it's not even "just science". Instead, it's "just math".
The mathematics of how epidemics evolve is the same mathematics as interest (the kind you are charged on your credit card balance) and radioactivity. The generic term for it is "exponential growth". If you understand exponential growth you are a long way toward understanding the process as a whole.
We are used to and intuitively understand additive sequences. If you start with zero and keep adding two to it the result keeps getting bigger. This is an example of "linear growth". If we start with zero and add two every week then after a week our total will be two. After another week it will be four. After still another week it will increase to six. In fact, we can just multiply the number of weeks by two and we will get the result. After 52 weeks, roughly a year, our result will be 104.
Linear sequences grow slowly even if they continue indefinitely. If you wait long enough you can reach any number you want. It's just that if you need to reach a large number it will take a long time. If we have a disease that infects a thousand people per week then it will take seven million weeks to infect everyone in the world. That's over a hundred thousand years. It's also something no one would be concerned with even though a thousand cases per week sounds like a lot.
Now let's change things up. Let's start with a series whose first two elements are one and one. But now let's create the next number in the series by adding the two most recent numbers in the sequence together. You might think that things will go pretty much the same way as the "add two each time" rule. But they don't.
The third number in the series is two (one plus one). The fourth number is three (two (one back) plus one (two back)). This still doesn't sound like it will get out of hand. But 3+2=5 then 5+3=8 then 8+5=13, then 21, then 34, then 55, and so on. And that's only the first ten numbers in the sequence.
And this sequence has a name. It's called the Fibonacci sequence. It doesn't take that long to start generating enormous numbers. The fifty-second number in the sequence is 20,365,011,074. That's more than all the people currently living on earth today. The Fibonacci sequence is an example of exponential growth.
And a fundamental attribute of exponential sequences is that they can grow to truly gigantic numbers even if the starting value is very small. And the Fibonacci sequence is an example of an exponential "growth" sequence. There are also exponential "decay" sequences. A classic example of this is radioactive decay.
Radioactive materials have a characteristic called a "half life". This is the amount of time it takes for half the original material to "decay" into something else. Let's say we have a made up element called "Madeup", which is radioactive. And let's assume its half life is one week. And let's say we have exactly 33,554,432 atoms of pure Madeup at the beginning of our observation period.
Then exactly one week later we will have 16,777,261 atoms of Madeup. (We'll also have the same number of atoms of whatever Madeup decays into as a result of the radioactive decay process.) In two weeks we will have 8,388,608 atoms of Madeup left. And so on. In exactly 25 weeks we will be down to only one atom of Madeup. All the rest will now be something else. That's because 33,554,432 is exactly two raised to the twenty-fifth power. It's the reason I picked it as my starting number. It made the math simple.
So what's this all got to do with COVAD-19 and Epidemics? Plenty. There are a lot of numbers floating around about COVAD-19. At this point it is hard to figure out what the correct numbers are. But we don't need to know the exact numbers to understand the pattern. Let's see what I mean.
There is no exact number for the number of days it takes for COVAD-19 to be transmitted from one person to another. But it seems to be around a week. If it is more than a week then the disease will spread more slowly. If it takes less than a week then the disease will spread more quickly.
The same thing is true of the number of people an infected person turns around and infects. The range most people quote is "two to three people". Again, if the number is higher then the disease will spread more quickly. If it is lower then it will spread more slowly.
But if we start with one infected person. And we assume the transmission time is a week. And we assume that each infected person infects two others. Well, then twenty-three weeks later everyone on earth will be infected. The US Census bureau estimates that the current population of the world is 7.6 billion. That's less than the 8,388,608 number we get by doubling two 23 times.
The first COVAD-19 infection was more than 23 weeks ago and not all of the world has since been infected. So my simple "one week results in two new infections" rule is wrong. Let's see if we can get more real.
The number of people a specific infected person infects varies from zero to a whole lot. A completely correct mathematical model would be very complicated. It would involve statistics and calculus. But there is a "typical" number of infections that gets you to roughly the same place that the super-precise analysis does. And the important thing is that the fewer "average number of new infections" we see, the slower the infection spreads.
The same is true of the transmission time. The actual situation is very complicated. But a single, simple "average transmission time" will get you to pretty much the same place the complex analysis does. And again, the bottom line is the same. If the average transmission time is short then the infection spreads quickly. If the average transmission time long then the infection spreads much more slowly.
And that means we can characterize various changes in terms of their impact on the average number of infections and/or the average transmission time. And, as far as I can tell, nothing much affects the average transmission time. So the whole game is in reducing the average number of new infections.
A few places have taken drastic measures. They have tested lots of people (in some cases everyone). As soon as someone tests positive then they are immediately isolated. This has the effect of driving the average new infection rate to zero (or a small number close to zero).
If we can get the average new infection rate down to 0.5 (two infected people together only infect one new person, on average) then we are talking radioactive decay mathematics. If everybody in the world is infected (this example makes no sense in the real world, but stick with me, anyhow) then after 25 weeks we would be down to one new infection per week. More realistically, if we assume that a million people are currently infected then it would take 20 weeks to drive the world wide new infection rate to 1 per week.
And things go more quickly if we can do better. If we assume that we can drive the average new infection rate to 0.1 (only a 10% chance of an infected person passing the disease on to another person) then a million current infections per week goes to one new infection per week in only six weeks.
That's what health officials are trying to do, drive the average new infection rate as low as possible. If the average new infection rate is greater than one then the number of new cases grows. If it is less than one, then the number of new cases declines. It appears that the average new infection rate is currently less than two but well above one. And, if the best we can do is get it down to just below one, then the disease will linger for a very long time.
It seems to me that an obvious measure to take is to require people to wear face masks while in public. The standard cheapo facemask does NOT completely stop the disease from spreading. The virus can pass through the mask. So an infected person wearing a mask can infect an uninfected person who is also wearing a mask. But face masks drastically reduce the "viral load".
An infected person throws off a lot of virus particles. But a single virus particle does not always succeed in transmitting the virus. In fact, a single particle is almost always unsuccessful. It's a numbers game. If a lot of particles are transmitted from the infected person to the uninfected person then the chances of the uninfected person catching the disease goes way up. Anything that reduces the viral load substantially increases the chances of a transmission failure.
The Chinese found that masks alone were not effective. But I have to believe that they would help. And let's say we adopted an "everybody has to wear a mask while in public' (and here I'm talking about the cheapo masks that are generally available) rule. I think it would help.
And let's say that the average person went through ten masks per month. The world would then need to manufacture eighty billion masks per month indefinitely. That's doable. But nobody is talking about doing that, at least not in the US. So it hasn't happened here. But, even with the low current rate of use of cheapo masks in the US, there is a severe shortage of them.
And there is a mask that is pretty effective. It is something called an N-95 mask. They are more expensive (and harder to use as they must fit tightly to work properly). At this time the thinking is that their use should be restricted to health care workers and others in high risk categories. There is a shortage of them too.
The strategy that is being rolled out instead is "social distancing". The most efficient way to spread the disease is for an infected person to exhale a swarm of virus particles. They then travel a short distance before being inhaled by an uninfected person. COVAD-19 is a lung-based disease so getting a lot of fresh virus particles (a large viral load) into an uninfected person's lungs is what will most effectively transmit the disease.
If the uninfected person is six feet or more away from the infected person the chances of any particular virus particle ending up in that person's lungs is much reduced. Again, its a numbers game. The more hoops you make the virus particles jump through, the fewer make it into the lungs of the uninfected person. Fewer particles (a smaller viral load) means a higher probability of the infection failing to take hold.
The other thing people are doing is cleaning everything. Virus particles can survive in the open air for a while. They can also land on a surface and stick there. Survival time depends on the specifics of the surface. But a wipe with any kind of disinfectant drives the survival rate to infinitesimal. As does the UV component of sunlight. Sunlight hitting free floating virus particles or those lodged on a surface will quickly destroy them.
There is similar thinking behind the "wash your hands", "don't touch your face", and "don't shake hands" admonitions. The idea is that virus particles can end up on your hands. Then you transmit them to your face. Then somehow they get to your lungs from there.
All of these behavioral changes can be helpful. But I think the amount of help they represent is modest. I suspect that abandoning all these practices and replacing them with a "mandatory facemask while in public" rule would be more effective. But then what do I know? And doing both could help and can't hurt.
A very grave concern of many experts is the effect the disease can have on hospitals and the medical system. Italy is seeing large numbers of deaths. Part of the reason is that in a large part of the country the health care system got completely overwhelmed and became unable to care for people.
Like ours, the Italian health care system was sized to handle the normal amount of business, or maybe a little more. What it got was a whole lot more. At that point they ran out of everything: doctors, nurses, medical supplies, intensive care beds, regular care beds, supplies of all kinds, support staff of all kinds, the works.
It is important to react strongly and to react before the crisis hits. Capacity must be "surged" before it is needed. By the time it is needed it's too late. China reacted by building two large hospitals in less than two weeks. Were they full up hospitals? No! But they were capable of handling the patients that weren't acutely sick so that the regular hospitals could focus on the acutely sick.
The US is in the same situation. We currently have enough hospital capacity to handle the need. But we have little "surge" capacity. You need to ramp up in a big way at least three weeks before the wave hits. Remember, if the case load is doubling each week, you will have eight times as many patients to deal with in three weeks.
Let's say that the number of people with the disease who are sick enough to require hospitalization is currently absorbing a quarter or more of your surge capacity. If so, if you don't act immediately, you are guaranteed to be in a world of trouble in three weeks time.
People have been studying epidemics for a long time now. The classic epidemic is the "Spanish Flu" epidemic of 1918-19. It demonstrated all of the characteristics of the current COVAD-19 one. Oh, the average transmission time and the average new infection rate were different from then to now.
But, from a mathematical perspective, they are identical. To model COVAD-19 you just plug the new average transmission time and the average new infection rate into the exact same model and the time line for what is going to happen when pops right out.
And it is important to point out that the actions that are currently being taken are all about "flattening the curve". We know we can slow the rate at which the epidemic grows. This is important. Slower growth gives us more time to prepare. But we need to use that time to actually prepare. So far the time has mostly been squandered.
But let's say we get our act together. Then what? We currently have no way to prevent the disease and only modest ways to treat it. Current treatment consists of supporting the body's natural ability to fight off the disease. Reducing the amount of virus the body has to deal with makes it easier for the body to triumph. It appears that the younger you are the better the body is at fending this particular disease off. That's unusual.
Most of the people who have died so far, at least in the US, have been elderly people and people who have compromised immune systems. I live in King County in Washington State. It has been the epicenter of the early evolution of the disease in the US.
Today the local paper published a graph that broke out the age of the various people who died in my state. 59% of those who died were 80 or older. A further 26% were 70-79. A further 16% were 40-69. No one under 40 has died. (You can find the graph in the March 20, 2020 edition of The Seattle Times.)
But that's all besides the point. Slowing things down does not ultimately reduce the number of people who eventually get the disease. The only current sure-fire protection is to get the disease and live to tell the tale. Once you've had the disease, you can't get it again. Or at least, that's what everybody currently believes. If we wait long enough and let enough people catch the disease then eventually "herd immunity" will kick in.
If almost everyone, say 90%, has already had the disease then the disease will have a hard time finding an uninfected person. And that drives the new infection rate close to zero. The current population of the US is 329 million, according to the US Census bureau. To get to 90% just under 300 million people would have to get the disease.
Our current medical system is in no way ready or able to cope with that. If just 10% of people who get infected require hospitalization, that's 30 million people. If we flatten the curve enough to spread the epidemic over ten years that's still three million hospitalizations per year. That smaller number is still large enough to overwhelm our current medical system.
Right now, the percentage of infected people expected to need hospitalization is higher than 10%. But we are still undertesting so it is likely that we are undercounting the number of people who are infected. So maybe the actual percentage of infected people who need hospitalization is 10% or even less. It would have to be a whole lot less to get the expected number of hospitalizations down to what our system can handle.
Currently Washington State has 1,376 known infections and 74 known fatalities. That's a fatality rate of over 5%. But there are special circumstances that lead many experts to suggest that that number is too high. The early number out of China was 2%. The latest number is 1.4%. Let's say that even that number is too high and the real number is 1%. That means that to get to the point where 90% of the US population has had the disease we can expect 3 million fatalities. That's sobering.
And one hopes that it doesn't come to just having to depend on herd immunity. The two alternatives to be hoped for are an immunization or an effective treatment (or both). If people can get a shot (or take a pill, or whatever) and become instantly immune without having to get the actual disease, that would be ideal. It would mean that we wouldn't have to worry about overwhelming our medical system and a lot of people wouldn't have to die.
But it is important to know that coronaviruses, the group of viruses that COVADS-19 is a member of, also contains the viruses that cause the common cold and the "seasonal" flu. Pharmaceutical companies know that an effective cure for the common cold would be a giant gold mine. So they have vigorously pursued a cure for decades with no luck.
They have had more luck with seasonal flu. They have been successful at creating a flu shot that protects against specific strains of flu. But the flu just mutates into something that the flu shot is ineffective against, necessitating the creation of a new and improved flu shot. So pretty much every year I get the flu even though I always get that year's flu shot. Companies are trying to come up with a "universal" flu shot but have yet to see any success.
There has been more success on the treatment front. Almost nobody dies of the flu or of a cold. Very few people need hospitalization. It looks like it will be easier to come up with something that works on the treatment side. But expect success to be hard to come by. That's what dealing with colds and flus tells us.
So the best thing we can do is to pour resources into medical research. I'm talking doubling (or more) the amount we are currently spending in these areas. That should speed up the process. And, while we are looking for something that is effective against COVAD-19 we might get lucky and find something effective for dealing with colds and/or the flu along the way.
But it is critical to be realistic about how fast some kind of "fix" can be delivered at scale. Here are the steps involved. Step one is for a scientist to find something interesting in the lab. Step two is to do a "safety" test on humans. Step 3, is to do a small scale "effectiveness" test. Step four is to do a large scale effectiveness test. Step five is regulatory approval. Step six is large scale manufacturing. Step seven is large scale implementation.
In normal situations one or more of these individual steps can easily take a year or more. And it doesn't pay to skimp. A drug just failed step three when applied to COVAD-19. Other drugs for other diseases have spectacularly failed step two. Killing ten million people in an attempt to save one million people is a bad idea.
No one knows how long step one will take. If a drug that is already approved for use on humans to treat another medical condition turns out to be effective against COVAD-19 then some of the above steps can be implemented at warp speed. But it will likely take something brand new. And even with a lot of luck and super-fast-track-ing everything, the entire process is likely to take 12-18 months at a minimum.
If you want to know why a lot of knowledgeable people are currently shouting PANIC at the top of their lungs, now you know. And it's not even "just science". Instead, it's "just math".
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