Is vaccination better than natural immunity when it comes to Covid-19? Should people who've recovered from Covid-19 get vaccinated nevertheless? Search for real-world scientific studies that contain evidence of vaccination's superiority over natural immunity, and you'll find none. What you'll find is a wealth of scientific literature from around the world that supports the opposite conclusion, that natural immunity is superior to vaccination for Covid-19. There is a single study, however, conducted by the CDC and frequently cited and misinterpreted by the news media. This study is based on data out of Kentucky, so we'll call it the CDC Kentucky Study. The media almost universally misinterprets this study. The media claims that the study shows that vaccination is superior to natural immunity. But it doesn't. Both the CDC and the media claim that the study demonstrates that naturally immune people need to get vaccinated. That claim is a logical fallacy that doesn't follow from the study.
The CDC Kentucky Study actually says nothing about whether natural immunity is superior to vaccination or vice-versa, only that naturally immune people can double their protection by also getting vaccinated. It begs the question, "Can vaccinated people also double their protection by getting infected?" Before you get excited about doubling your protection, note that other much larger-scale and better-conducted studies [#3, #5] show little to no additional benefit to vaccinating the naturally immune. In fact, the CDC Kentucky Study has fundamental flaws that invalidate its results.
In our previous report, Vaccination versus Natural Immunity — Which Provides Better Protection Against Covid-19?, we brought together all of the major real-world population studies comparing vaccine-induced immunity, natural immunity (immunity of people who've recovered from Covid-19), and hybrid immunity (natural immunity + vaccination). By real-world studies, we mean studies of large groups and populations of people. Real-world studies take into account the entire individual and their environment. Theoretical studies, on the other hand, are conducted entirely in-vitro, typically using test tubes of blood serum. Theoretical studies don't take into account the whole individual, nor the entire immune response, nor the real-world environment in which that individual is placed. Theoretical studies are interesting, but they must be backed up by real-world studies to be taken seriously. Vaccines, for example, require real-world clinical trials before they'll be approved; the FDA considers theoretical studies to be insufficient. For those reasons, we emphasize real-world studies.
Our previous report brought together 12 large-scale real-world studies on vaccination versus natural immunity. The overwhelming consensus was that natural immunity is at least equivalent to the best available vaccines, and is likely superior to vaccination in general. You might ask why that contradicts the recommendations of the CDC. You'll find that there's no scientific explanation. When science is pitted against politics and money, politics and money often emerge victorious. A better question would be: "Why do the CDC's recommendations contradict the findings of the worldwide scientific community?" Specifically, we're talking about the CDC's recommendation that all people with previous Covid-19 infection get vaccinated nevertheless. While there are definite monetary/political motivations, are there also valid scientific motivations behind this recommendation? Let's first note that not all worldwide governments advocate for vaccination of recovered people. India, for example, has recommended the precise opposite, so that vaccine is not wasted on the already immune. The European Union allows people who've recently recovered from Covid-19 to obtain a vaccine "passport". So does Israel with their Green Pass system.
DIGGING DEEP — THE CDC KENTUCKY STUDY REVIEWED
This retrospective study followed two groups of individuals who all tested positive for Covid-19 in 2020. Remember that fact: Every person in both groups tested positive for Covid-19 in 2020. Group #1, the Test Group, consisted of everyone — 246 people total — who tested positive again in May or June of 2021. Group #2, the Control Group, was a 2:1 matching group of 492 randomly selected people who did not receive a subsequent positive test result by the end of June 2021. So Group #2 consisted of people who did not test positive again in 2021 by the June 30th cutoff date. No 2021 Covid-19 test was required for Group #2, meaning that many in the Control Group did not actually get tested in May or June of 2021. So this study assumes that all of the Control Group's test results would have come back negative if they had been tested in May or June of 2021. The study looked at the number of people in each group who were fully vaccinated, finding that 20% of Group #1 were fully vaccinated versus 34% of Group #2. Based on this, they concluded that unvaccinated people were more than twice as likely as vaccinated people to acquire their second Covid-19 infection. The study issues the following recommendation: "To reduce their likelihood for future infection, all eligible persons should be offered COVID-19 vaccine, even those with previous SARS-CoV-2 infection." But this recommendation is a logical fallacy. To gain the same level of protection, vaccinated people would have to go out and actively seek Covid-19 infection. Imagine if the CDC had also recommended the following: To reduce their likelihood for future infection, all vaccinated persons should be offered an injection of live COVID-19 virus.
Recall that this study only follows people who had positive Covid-19 tests. Therefore, it has nothing to say about the benefits of vaccination-only versus the benefits of natural-immunity-only. Vaccination, by itself, is considered excellent protection by the CDC and as shown by other studies. Natural infection, by itself, is also considered excellent protection as shown by other studies. So the actual question raised by this study is: Does the combination of natural infection and vaccination provide a level of super-protection? ...a level of protection beyond that provided by vaccination alone or natural immunity alone? The study concludes that it does. But before you get too excited about that prospect, let's take a deeper look at the study.
You may have already noticed the fatal flaw in this study. In any statistical study that compares two groups, it's critical to treat both groups using the same standards. Control Group #2 was not subject to the same Covid-19 testing requirements as Test Group #1. ALL of Group #1 got retested in May or June of 2021. We don't know how many, if any, of Group #2 got retested in May or June of 2021. If the entire Control Group had been retested, as standards would dictate, it's likely that some of them would have tested positive, which means they should have instead been part of Group #1. So Group #2 likely contained people that should have actually been in Group #1. The study itself acknowledges a similar limitation: "Persons who have been vaccinated are possibly less likely to get tested. Therefore, the association of reinfection and lack of vaccination might be overestimated." This limitation is much greater than the CDC acknowledges, because 100% of Group #1 were required to be retested while 0% of Group #2 were required. Best practice would be to rerun the study and only include people in Group #2 who tested positive in 2020, who did not subsequently test positive in January-June 2021, and who tested negative in May/June 2021. It's possible that subjects who meet these three criteria might be insufficient in numbers to conduct a proper study.
A third problem with this study, a potential source of bias, is the random matching of controls to test subjects. Any bias or error in the randomization algorithm could result in something akin to a stacked deck of cards. Better practice would be to run the experiment not once but dozens or hundreds of times, each time randomly selecting a different Control Group. Best practice would be to not randomly select at all, but to expand the Control Group to all eligible subjects. This brings up the question, Why Kentucky? What about the other 49 states? Could this whole study be just an exercise in data mining? ...aka cherry picking your state to provide the desired results? The authors should rerun the study using data from all 50 states and correct at least the one fatal flaw. If the results were to turn out the same using a large data set, that would provide strong evidence that the combination of vaccine and natural infection is super-protective. To their credit, the study authors acknowledge the following: "This is a retrospective study design using data from a single state during a 2-month period; therefore, these findings cannot be used to infer causation. Additional prospective studies with larger populations are warranted to support these findings."
A fourth limitation, noted in the study, is the possibility that some positive test results in May/June 2021 were not actual reinfections but detections of the original infection.
A fifth issue in this study is that it relies exclusively on Covid-19 "NAAT or antigen test results", without confirmation by symptoms. So the study includes asymptomatic people and false positives in both groups. Both groups are supposed to consist only of people with natural immunity. As discussed in our previous report, it's uncertain whether someone who merely tests positive for Covid-19, without accompanying symptoms, should be considered naturally immune. It would be interesting to see what the results would be if only symptomatic cases were counted as positive. Compounding the bias, Group #1 was tested twice to determine initial infection in 2020 and subsequent reinfection in 2021, doubling the possibility of false positives and asymptomatic test results for this group. We don't know how many people would have been excluded from Group #1 if accompanying symptoms had been required on both the front-end test and the back-end test, but it's likely a large percentage of the group would have been dropped from results.
It's worth mentioning that this CDC study is not like other scientific studies. First of all, it's incomplete. The CDC thought the results were so important that they rushed out this early release, pre-publication. The full data set is not made available for outside scrutiny, which means the study fails to meet basic scientific standards. Normally, such a study wouldn't merit serious scientific consideration. Apparently, however, this particular study is very important, because the CDC, primarily based upon this study, is recommending that naturally immune people get vaccinated, a logical fallacy that does not follow from the results of the study. Much of the US media is also citing this study and misinterpreting this study without giving it critical review.
There's a standard disclaimer that accompanies all unpublished and pre-published work on the MedRxiv Preprint Server: "This article is a preprint and has not been peer-reviewed. It reports new medical research that has yet to be evaluated and so should not be used to guide clinical practice." This disclaimer should more-so apply to any self-published articles by the CDC, such as this Kentucky study, that have not been the subject of outside scientific scrutiny by peers. We say "more-so" because the MedRxiv Server includes an active comments section where researchers can get preliminary feedback and review from scientists and the general public. In many cases, the quality and quantity of feedback in the comments section greatly exceeds what one would expect from the typical three peer reviewers. CDC reports, on the other hand, are not peer reviewed, are not tagged by the much-needed disclaimer, and do not have a comments section for scientists to provide feedback. That's why they deserve thorough outside scrutiny before their results are accepted as gospel.
A CASE STUDY IN POOR EXPERIMENTAL DESIGN
It's striking how convoluted the experimental design is in the CDC Kentucky Study, as if the study itself were designed to confuse anyone reading it. The study groups people based on outcomes (Positive May/June 2021 Test versus No Positive May/June 2021 Test) but it also excludes people from the two groups who did not have prior infection from 2020. If they really want to group people based upon outcomes, there should be three outcomes: 1. Positive May/June 2021 Test; 2. Negative May/June 2021 Test; and 3. No May/June 2021 Test. There's no need to exclude anyone from the three groups and there's no need to time-match the three groups. An even better experimental design wouldn't group people based upon outcomes, but would group people based upon prior infection and vaccination status. They could rerun the study with four groups: 1. Prior infection Only; 2. Vaccination Only; 3. Prior Infection + Vaccination; and 4. No Prior Infection & No Vaccination. Since all groups would now be treated equally, they could utilize the same two outcomes as before. The new experimental design would be similar to the design of Delta Study #2 out of Israel.
ARE KENTUCKY PEOPLE REALLY GETTING COVID-19 TWICE?
Let's apply a plausibility test to the CDC Kentucky Study. This study is asking us to believe that 246 people in Kentucky got Covid-19 in 2020, then recovered, then 67 of them got vaccinated, and then all of them got Covid-19 again in 2021. This would indeed be a surprising result, highly newsworthy. With recurrence of Covid-19 being so rare, individuals who get the disease twice often become the subject of news stories. We conducted an internet search looking for confirmation and examined the top 100 Google search results for Kentucky Man Gets Covid Twice and the top 100 for Kentucky Woman Gets Covid Twice looking for anyone who might have been part of this CDC Kentucky Study. The 200 search results yielded a large percentage of links back to and news stories about the CDC Kentucky Study. They yielded news stories about the Hong Kong man who got Covid-19 twice. Our search yielded three potentially relevant news stories. The first was about a Kentucky man who had had Covid-19 twice, but both cases were in 2020, so he was not part of this CDC Kentucky Study. The second story was a CDC article about an outbreak of two reinfections in a Kentucky nursing home. However, both of these reinfections also occurred in 2020, so were not part of this CDC Kentucky Study. The final result yielded one person who was actually part of this study! "Louisville woman gets COVID again after being fully vaccinated". The woman tested positive for Covid-19 in November 2020, got vaccinated in April 2021, then tested positive again in May/June 2021, making her part of Group #1. When she tested positive in November 2020, she was asymptomatic. In June 2021, she had moderate symptoms and was sick for several days.
Through an internet search we found no evidence of a rampant outbreak of reinfections in Kentucky. We found a single 1 out of 246 study participants in Group #1, who had no symptoms when tested in 2020, meaning she was either asymptomatic or a false positive. She would not have been included in this study if a symptomatic requirement had been implemented. What about the other 245 people? Will some, most, or all of them drop out of Group #1 if we implement a symptomatic requirement on both the first and second tests? Most certainly, but we can't know the exact percentage who will drop out without having data on their symptoms.
REAL SCIENCE VERSUS POLITICAL SCIENCE
The CDC Kentucky Study states: "Few real-world epidemiologic studies exist to support the benefit of vaccination for previously infected persons." It looks like the CDC didn't find any such studies, and the only such study we found was this CDC Kentucky Study. So the CDC is relying entirely on this small, fatally flawed, Kentucky study to provide real-world evidence. On the other hand, many large-scale, real-world studies do exist that show natural immunity is indeed powerful protection. It's troubling that the CDC does not cite nor acknowledge the existence of any of these prior natural immunity studies, including the Siren Study [#4], the Cleveland Clinic Study [#5], the Qatar Study [#6], the Curative Study [#7], the Denmark Study [#8], and the Israeli Studies [#2, #3]. They don't even cite Study #9, a theoretical study funded by the USA's National Institutes of Health (NIH) which shows that natural immunity to Covid-19 is long lasting. It's poor scientific practice to predetermine your conclusions before conducting your experiments. It's poorer practice still to deny the existence of studies that contradict your preconceived conclusions. Recommendation: Cite these other studies and stop trying to prove a point. Undertaking a study with a predetermined conclusion in mind, and ignoring all evidence to the contrary, is politics, not science.
In summary, we find that the CDC Kentucky Study is more politics than science, akin to the tobacco industry's studies from years past denying that cigarette smoking causes cancer. The CDC Kentucky Study tries to support a preconceived conclusion using a real-world study, while at the same time denying the existence of numerous real-world studies that support the opposite conclusion. The CDC Kentucky Study has major and fatal flaws, outlined above, that must be corrected before any conclusions can be drawn. The first flaw is the application of two Covid-19 tests to Group #1 but only one test to Group #2. The second flaw is that asymptomatic cases should ideally be excluded on both the front-end and the back-end Covid-19 tests. Excluding asymptomatic cases will also virtually eliminate false positives. The third flaw is randomly selecting subjects for Group #2; it would be better to include all eligible subjects in Group #2. The study should be expanded from one state to all 50 states. Finally, if the study were to be conducted properly and the results were to turn out the same, the CDC should correct the logical fallacy in their recommendation. The study's results don't actually support the recommendation that naturally immune people get vaccinated; they only support the premise that naturally immune people can gain additional protection through vaccination. To set national vaccine policy based upon this fatally flawed and inconclusive study, when the preponderance of scientific evidence suggests otherwise, is irresponsible.
AN ABSURD ANALOGY OR TWO
Vaccination is considered good enough protection. Under our increasingly authoritarion executive branch, vaccinated people are granted the rights to keep their jobs, travel freely, and participate in society. Natural immunity is also good enough protection, demonstrably better than vaccination. But naturally immune people are granted no such rights, not without undergoing unnecessary medical procedures. Can naturally immune people achieve a small gain in immunity by adding a vaccine? That's irrelevant, and it's yet to be demonstrated, but even if it were true, that doesn't change the fact that natural immunity, on its own, is good enough protection, actually better protection than vaccination. That protection applies to both the possibility of getting Covid-19 and the possibility of spreading Covid-19.
Imagine if you, a customer, were to walk into an auto dealership looking for a loan on a new car.
"We'll finance anyone who has a 700 credit rating", the dealer says.
"Great, my credit rating is 800", you reply.
"In that case, we have a special program that will instantly raise your credit rating from 800 to 801. All you have to do is pay us a $100 application fee and fill out this 50-page stack of paperwork".
"That's ok, I'm fine with my 800 credit rating. Can we move on to the auto loan?"
"I'm afraid we can't do that until you pay the application fee and complete the application to raise your score to 801."
"But you said a 700 credit score qualifies me for the loan. So why do I have to do the paperwork and pay the fee? My credit score is 800".
"700 is good enough for people with lower credit ratings. But your credit rating is 800, and 801 is better than 800, so we require 801. And it's a company requirement. I don't make the rules."
You walk away, shaking your head in frustration.
Let's try another scenario. You live in a city with a high crime rate. In fact, it's the murder capital of the world, with killings happening left and right, all around you. There's a huge police force, but they spend all of their time issuing citations for broken taillights and illegal garage sales. The police COULD instead allocate their resources to reducing violent crime, but there's no money to be made in doing so. Misallocation of resources is precisely the problem we face in the Covid-19 pandemic. The government is expending a huge amount of effort to coerce the already immune into getting vaccinated. Pandemic-wise, the payoff in doing so will be zero. Resources would be better expended where they might actually make a difference.
THE LAW OF SMALL NUMBERS
When you're dealing with small numbers, if experimental error shifts a few people from one group to the other, that can alter your conclusions dramatically. You may end up proving the opposite of what you initially thought you had proven, or your statistically significant result might suddenly become statistically insignificant. When you're dealing with small numbers, it's also easy to overstate your results, to make a big deal out of a small deal. When terms like "twice the protection" and "twice as likely" are thrown around, they sound like a big deal, but they're not necessarily so. For example, it's estimated that Americans are four times as likely to be killed by toppling vending machines than by shark attacks, yet people shouldn't needlessly worry about either scenario.
Let's consider a more related example: Preventative Treatment #1 has 98% efficacy. Treatment #2 has 99% efficacy. That means Treatment #1 will reduce your risk of getting infected by 98% while Treatment #2 will reduce it by 99%. If an untreated person in a control group has a 10% chance of getting infected over a given time period, someone taking Treatment #1 would have a 2 in 1000 chance of getting infected and someone taking Treatment #2 would have a 1 in 1000 chance of getting infected. Makers of Treatment #2 could rant and rave about how their treatment provides double the protection of Treatment #1, when in reality they both provide similar protection. If there were any errors in the experiments that determined efficacy, which is always a strong possibility, Treatment #1 might end up being the better choice. If there were major cost differences, availability issues, differences in side effects, or other outside factors, those factors would certainly trump efficacy when choosing a treatment. When there's a choice between medical intervention and no medical intervention, and the end results are expected to be the same, it's wise to avoid the unnecessary medical intervention.
MEDIA COMPLICITY & MISINFORMATION
If we look at the top four Google search results for CDC Kentucky Study, the first result is a media release by the CDC itself entitled "New CDC Study: Vaccination Offers Higher Protection than Previous COVID-19 Infection". This headline is just plain wrong. We all know that's not what the CDC Kentucky study purports to show. If the CDC reports its own study incorrectly, what hope do we have that the rest of the US media will get it right? Investigative journalism seems mostly a thing of the past, now that mainstream media has been replaced by multiple echo chambers for the political parties. Search result #2 comes from the Louisville Courier-Journal entitled "CDC Study of Kentuckians Disputes Rand Paul, Thomas Massie Claims About COVID-19 Immunity". Sorry, Courier-Journal, but that's inaccurate; the study doesn't dispute anyone's claims. Search result #3 comes from the Healio website, a publisher of health journals, entitled "CDC: Study shows COVID-19 vaccines offer better protection than prior infection". Even this publisher of health journals gets it wrong. They double down with the following "Perspective" statement from one of their experts, an MD and Senior scholar from Johns Hopkins Center for Health Security. "The study illustrates the fact that prior immunity, though significant, is not as robust against preventing reinfection than vaccine-induced immunity". This is an inaccurate and misleading statement (not to mention grammatically incorrect). The comparison should be to hybrid immunity, not "vaccine-induced immunity". Search result #4 from Forbes gets it partially right, though their headline is extremely misleading, especially if you miss the "re" part in the reinfections: "CDC: Covid-19 Reinfections for Unvaccinated Over Twice as Likely Compared to Vaccinated". These are just four examples among thousands of media references to the CDC Kentucky Study. Almost none critically review or critically report on the study, most contain misleading claims, and many flat out report the results of the study incorrectly. Search results which challenge the CDC study are nowhere to be found on Google. They may exist somewhere on the internet, but as Google itself has increasingly become a partisan echo chamber, organic search results have become increasingly difficult to obtain on the search engine.
Let's review one more media article in detail. With thousands of media articles to choose from, this one came highly recommended by Google's search engine. It's also important due to its truth-determining status as a fact-checking article. This "fact-checking" article by USA Today states "Based on our research, we rate FALSE the claim that if you have natural immunity from a bout of COVID-19, you don't need the vaccine." This is just one example of the misinformation prevalent in the news media. Let's examine the science backing their "fact-checking". USA Today's "research" consists of gathering opinions from a handful of experts, along with citing the CDC Kentucky Study [#1] and a total of two other scientific studies. Expert opinion is not scientific evidence, so should be discounted and disregarded. As a practical matter, it's easy to find a few experts to state the desired opinion, or even a few thousand experts if you have the time, all opining in unison. Let's look at USA Today's three cited scientific studies instead. The first study is a theoretical investigation of the binding of natural- and vaccine-induced antibodies to virus. The study is interesting, but it's not a real-world study; the authors don't make any bold claims about what their results might mean in the real world; only the fact-checker makes those bold claims. The second study is irrelevant to the question at hand. It concludes that previously uninfected people have 5 times the risk of previously infected people, which tells us that natural immunity is effective, but it says nothing about vaccination; it was conducted entirely before the advent of vaccines. The third study is the CDC Kentucky Study [#1], which also says nothing about whether natural immunity is superior to vaccination or vice-versa, only that naturally immune people can double their protection by also getting vaccinated, which we've seen is a highly suspect claim. The USA Today article does not present a single real-world scientific study that backs their fact-checking, and it conveniently ignores all of the massive real-world studies ([#2], [#3], [#4], [#5], [#6], [#7], [#8]) that would change their fact-checking result to TRUE. Sadly (for science that is), the CDC Kentucky Study also conveniently ignores all of the same massive real-world studies, not citing a single one of them.
Only very weak scientific evidence is presented by the CDC to back their chosen position that previously infected people should get vaccinated. The media provides only weak scientific evidence too but mostly echoes the CDC. So we can only speculate about the real reason behind this complete denial of scientific evidence. One potential reason is convenience. It's easy to track the number of vaccinated people. It's hard to track the number of naturally immune people. In addition to convenience, money and politics are the most likely culprits. $24 a dose, multiplied by 200 million doses, is $4.8 billion dollars. That's the USA's latest order of Pfizer Vaccine. A simple internet search shows a $20-$25 billion-a-year market for Covid-19 vaccines, with forecasts going all the way out to year 2030. Pharmaceutical companies would stand to lose a lot of money if natural immunity were to end the pandemic prematurely.
With an estimated 100+ million people in the US with natural immunity, it's obvious why the government/corporate complex is pursuing them so aggressively to get vaccinated. They're the biggest untapped market for vaccine sales, with young children being a close second. Yet the payoff to society of vaccinating the naturally immune is next to nil. With an ongoing pandemic, it's time to allocate resources elsewhere, and quit trying to coerce people who are already immune into getting vaccinated.
STUDY #1: CDC KENTUCKY STUDY
"Reduced Risk of Reinfection with SARS-CoV-2 After COVID-19 Vaccination — Kentucky, May-June 2021"
Posted 8/6/2021, CDC MMWR Early Release
STUDY #2: ISRAELI STUDY
"Protection of previous SARS-CoV-2 infection is similar to that of BNT162b2 vaccine protection: A three-month nationwide experience from Israel"
Posted 4/20/2021, MedRxiv Preprint Server for Health Sciences
STUDY #3: DELTA STUDY (ISRAEL)
"Comparing SARS-CoV-2 natural immunity to vaccine-induced immunity: reinfections versus breakthrough infections"
Posted 8/25/2021, MedRxiv Preprint Server for Health Sciences
STUDY #4: SIREN STUDY (ENGLAND)
"SARS-CoV-2 Infection Rates of Antibody-Positive Compared with Antibody-Negative Health-Care Workers in England: A Large, Multicentre, Prospective Cohort Study (SIREN)"
Published 4/9/2021, The Lancet
STUDY #5: CLEVELAND CLINIC STUDY (USA)
"Necessity of COVID-19 vaccination in previously infected individuals"
Posted 6/19/2021, MedRxiv Preprint Server for Health Sciences
STUDY #6: QATAR STUDY
"SARS-CoV-2 Antibody-Positivity Protects Against Reinfection for at Least Seven Months with 95% Efficacy"
Published 4/27/2021, The Lancet: EClinicalMedicine
STUDY #7: CURATIVE STUDY (USA)
"Incidence of Severe Acute Respiratory Syndrome Coronavirus-2 infection among previously infected or vaccinated employees"
Posted 7/8/2021, MedRxiv Preprint Server for Health Sciences
STUDY #8: DENMARK STUDY
"Assessment of Protection Against Reinfection with SARS-CoV-2 Among 4 Million PCR-Tested Individuals in Denmark in 2020: A Population-Level Observational Study"
Published 3/17/2021, The Lancet
STUDY #9: LA JOLLA INSTITUTE FOR IMMUNOLOGY STUDY (USA)
"Immunological Memory to SARS-CoV-2 Assessed for up to 8 Months After Infection"
Published 2/5/2021, Science
About the Author — The author has published and peer-reviewed numerous papers for scientific journals, books, and conference proceedings. He holds three degrees in mathematics and computer science, including a PhD from the University of Illinois, where he specialized in genetic algorithms, complex systems, statistical methods, artificial intelligence, and machine learning, and was part of the research team for the Illinois Genetic Algorithms Laboratory. He's worked for companies both big and small. After "retiring" from the corporate world over 20 years ago, he's worked only for himself, those around him, and the benefit of society in general.
Funding / Interests — No funding was sought or received for this research. No conflicts of interest exist.
© Copyright Notice — This article is copyright 2021 by the author with all rights reserved. Permission is granted to share and quote all or part of this writing, as long as proper attribution is made and a link back to this original article is made. Please link back to the following address — www.USABottomLine.com/2/
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