October 2022

Red Herring Fallacy

It is a logical fallacy used in debates to distract the argument by introducing an irrelevant topic, usually loaded with emotions, into the discussion to divert the opponent.

The name comes from an old method of training dogs in fox hunting. In this process, before the dog (to be trained) leaves in search of the fox that just left by following the scent, the trainer drags a bag of smelly red herrings on the trail. Some dogs will get distracted by the strong smell of the fish and stop following the fox. The trainer then tries and keep the dogs to stay on course.

How is the red herring different from the straw figure fallacy? In some aspects, they seem similar. In the latter case, the original argument is distorted or misrepresented, and the new subject becomes the target. But in the former case, the initial point is completely ignored and is substituted with a new one, which gets attacked.

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Distributional Impacts and Net Energy Metering

While the entry of solar PV into the electricity mix has enabled the system to reduce carbon intensity, it created a new category known as distributed energy resources (DER). It became a complex problem for regulators as, on the one hand, they try to influence its adoption to customers by favourable discounts. But on the other hand, sometimes, it creates strange consequences for the non-adopters of DER.

Net metering is one of the mechanisms to incentivise adopters of (rooftop) solar PV. Burger et al. report a study on the topic in their working paper titled “Quantifying The Distributional Impacts of Rooftop Solar PV Adoption Under Net Energy Metering”. They used data on electricity consumption and income characteristics of 100,170 customers in Chicago, Illinois, which followed the net metering under default tariff.

The net metering scheme enables rooftop PV owners to push the unused electricity into the grid, and for every kWh, they receive the retail price. The question arises, what amount of money should one get back? Ideally, the sender should get the generation cost (energy cost) for every unit send. But it turned out that in the scheme that was in place, customers not only gained the generation cost but also part of the transmission and distribution costs! It happened because the latter were charged not as fixed prices but as volumetric charges (charges proportional to the energy consumed, kWh)!

And who are the adopters of rooftop PV? In the income scale, they were disproportionately more families of the higher income bracket. And naturally, this means when the grid owner recovers their fixed costs, they will charge more from the non-adopters, who are lower income classes, through volumetric charges.

Ironically, perhaps unaware of the underlying economics, the environmental groups also advocate for such schemes to continue in pursuit of increasing renewable penetration.

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Bayesian inference

One of the simpler explanations for Bayesian inference is given by John K. Kruschke in his book, Doing Bayesian Data Analysis. As per the author, Bayesian inference is the reallocation of credibility across possibilities. Let me explain what he meant by that.

Suppose there are four different, mutually exclusive causes for an event. And we don’t know what exactly caused the event to happen. In such cases, we may give equal credibility, 0.25, to each. This forms the prior credibility of the events. Imagine, after some investigations, one of the possibilities is ruled out. The new credibilities are now restricted to the three remainings, with the weightage automatically updated to 0.33. We call the new set posterior.

If you continue the investigation and eliminate one more, the situation becomes as shown below.

Notice the previous posterior is the new prior.

Reference

Doing Bayesian Data Analysis by John K. Kruschke

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Time Travel Paradoxes

Let’s see two paradoxes that can exist if you can time travel.

The first one is the grandfather paradox. Imagine you can time travel, go back to the past, and kill your grandfather before he met your grandmother. That means he did not have children, and you could not be born in the first place (to time travel)!

The second one is the bootstrap paradox. You buy a copy of Hamlet from a bookshop and go back to the time before William Shakespeare has written Hamlet. You give the book to William. He then copies it and claims his own. Years passed, and the book made several copies. One of them enters the same bookshop you originally visited. The question is: who wrote Hamlet?

A direct consequence of these paradoxes could be that there is no time travel possible. Another possibility is that a parallel universe is created as a result, and your existence (and Hamlet’s) is real in one of them.

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Eight Little Speakers

Let’s solve a combination problem. There are eight speakers in a function whose turns come at random. What is the probability for the first three, A, B, and C, to speak such that A speaks before B and B before C?

Focus on A, B and C first and arrange the rest around them. The number of ways to arrange A, B, and C in that order among eight is 8C3. The number of ways of arranging the other five is 5! This means that the number of ways to set the three and five is 8C3 x 5! That forms the numerator. The denominator becomes the total number of ways of arranging eight people to speak, which is 8!

Therefore, the required probability becomes 8C3 x 5! / 8! = (8! x 5!) /(3! x 5! x 8!) = 1/3! = 1/6.

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Another Coin-Tossing Game

Andy and Becky are playing a coin-tossing game. Whoever gets more heads win the game. Andy gets 100 tosses and Becky 101. If they both get the same number, Andy wins. What is the probability that Andy to win the competition?

Let’s do a Monte Carlo on this and find out who.

B<- 100000

results <- replicate(B, {
  Andy <- sum(sample(c(1,0), 100, replace = TRUE, prob = c(0.5,0.5)))
  Becky <- sum(sample(c(1,0), 101, replace = TRUE, prob = c(0.5,0.5)))
  if (Andy >= Becky){
    counter  = 1
  }else{
    counter = 0
  }
})

mean(results)

The answer comes out to be close to 0.5. What happens if they play only 2 and 3 games, respectively?

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Neanderthal mother and a Denisovan father

We have seen that the Neanderthals lived in Western Eurasia and Denisovans in Eastern Eurasia (basically, Denisova cave). The 2018 report by Slon et al. provides the DNA analysis of a bone, Denisova 11, that comes from an individual who had a Neanderthal mother and a Denisovan father!

The previous sequencing had established that the Neanderthals and Denosovals diverged from each other by about 390 kya. It is, therefore, fascinating to note what was found in the Denisova 11 sample. The mitochondrial (mt)DNA showed it was a Neanderthal type, and carbon dating said it was more than 50,000 years old. And what is more: 38.6% of its DNA fragments possessed alleles matching the Neanderthal genome, and 42.3% carried alleles matching the Denisovan genome!

Reference

The genome of the offspring of a Neanderthal mother and a Denisovan father, 2018, Nature, 113

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Post # 365: What Have We Learned in One Year?

We started with the equation of life, Bayes’ theorem, how it mimics the natural learning process, and how even experts can not escape the curse of the base rate fallacy.

We understood the law of large numbers but failed to notice that there was no law of small numbers and continued gambling, hoping to even out, leading to complete ruin.

We have learned mathematically that at the Roulette table, the house always wins, yet we spent countless minutes watching YouTube videos learning strategies to beat the wheel. We also watched financial analysts all day on TV, reasoning on hindsight and glorifying market-beating fund managers, forgetting they were just the survivors of Russian roulette. The same people continue to make us believe in momentum and hot hands.

People gamble and play the lottery, where they are guaranteed to lose, and fail to invest for their retirement, where they are guaranteed to win. Three-quarters of Americans believe in at least one phenomenon that defines the law of physics, including psychic healing (55 per cent), extrasensory perception (41 per cent), haunted houses (37 per cent), and ghosts (32 per cent).

Rationality, by Steven Pinker

We have seen how journalism can mesmerise readers by reporting an 86% increase in myocarditis for the vaccinated, a 300% increase in thrombosis over oral contraceptives, or an 18% risk of colorectal cancer by eating processed meat. We just became easy prey for our inability to make decisions based on risk-benefit trade-offs and the eternal confusion between absolute and relative risks.

We found how the world can make us believe in diseases with causes and designs with a purpose when events were nothing but random processes. We see how careless choice of words and phrases and incorrect teaching lead to myths about evolution.

Even in an era of open data, data science and data journalism, we still need basic statistical principles in order not to be misled by apparent patterns in the numbers.

The Art of Statistics: How to Learn from Data, by David Spiegelhalter

The author was referring to variabilities in the observed rates of events when the population is small, which is the concept behind funnel plots.

We understand that international trade is a win-win for both parties, yet we let free rein to populism and Brexit. We know that the Muslim community in India is on the fastest downhill in the fertility curve, yet we want to believe that the opposite is true and continue believing in one-child policies.

We also know that life is not a zero-sum game and that probability theory is not another useless thing you study in schools and forget later, but it is about how we make decisions and appreciate life. The understanding, or the lack of it, can be a choice between life and death, as we have just witnessed in the global pandemic.

Could everyone have a fact-based worldview one day? Big change is always difficult to imagine. But it is definitely possible, and I think it will happen, for two simple reasons. First: a fact-based worldview is more useful for navigating life, just like an accurate GPS is more useful for finding your way in the city. Second, and probably more important: a fact-based worldview is more comfortable.

Factfulness, by Hans Rosling with Anna Rosling Rönnlund and Ola Rosling

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The Denisovan Story

Another spectacle that emerged from Pääbo’s group was the discovery of Homo Denisovans from a bone sample excavated in Denisova Cave in southern Siberia. They possess the type of hominin mtDNA that shares a common ancestor with modern human and Neanderthal mtDNAs. And the stratigraphy of the location suggested the new samples lived at similar times to Neanderthals.

Where do they stand?

If we define the timelines as a function of pair-wise nucleotide differences of the complete mitochondrial DNA (mtDNA) from modern humans, Denisovans existed about 385 units away from humans. To put it in perspective: the modern humans are between 0 – 100, the Neanderthals at around 202 and the Chimpanzees at 1462.

Interbreeding

The researchers then searched for gene flow (interbreeding) similar to what was found with the Neanderthals using the five samples (San, Yoruba, Papua New Guinean, Han Chinese, and French) from modern humans. This time, there was no overlap between the French and the Han but found ca. 4% match with the Melanesian.

The new representation, combining the findings of the two studies (genome sequencing of Neanderthal and that of Denisovan), is presented below.

Reference: https://commons.wikimedia.org/w/index.php?curid=65505773

References

Krause et al., The complete mitochondrial DNA genome of an unknown hominin from southern Siberia, NATURE, 2010, 464, 894

Reich et al., Genetic history of an archaic hominin group from Denisova Cave in Siberia, NATURE, 2010, 468, 1053

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The Neandertal Affair

The contents of this post are based on Svante Pääbo’s 2010 paper titled “A Draft Sequence of the Neandertal Genome“, published in Science (Green et al., Science, 328, 710, 2010). The study reports genome sequencing of three samples collected from Neandertal bones from Vindija Cave in Croatia, and are carbon dated to be around 38,300 years old.

Based on the existing pieces of evidence, modern humans (Homo Sapiens) and Neandertals (Homo Neanderthalensis) diverged from the common ancestor (Homo Heidelbergensis) around 500,000 – 800,000 years ago. Here is a representation made by Dbachmann of the immediate ancestry of humans and taken from Wiki.

Reference: https://commons.wikimedia.org/w/index.php?curid=65505773#/media/File:Hominini_lineage.svg

The numbers on the Y-axis represent the past years in millions (mya). If you are wondering who appears on the two sub-branches of the branch, Pan, they are Chimpanzee (P. troglodytes) and Bonobo (P. paniscus)!

The earlier analysis of the mitochondrial DNA of Neanderthal, which was the subject of a publication in 1997, showed a lack of relationship between modern humans and Neandertals. That was insufficient to prove that interbreeding never happened, as other parts of genomes also need to be studied. If you are confused about what these are all about – a typical genome of a multicellular animal has two distinct parts: the nuclear genome and the mitochondrial genome. Most genomes (e.g., humans and other cellular life forms) are made of DNA (deoxyribonucleic acid).

The biggest challenge to confirming the interbreeding was the reason for similarities is the fact that these two have a common ancestor within the last million years. So a similarity between the two groups can be within the variability margins of homo sapiens themselves. To reemphasise the point: even if no interbreeding ever happened, the Neanderthals and Sapiens can still have similarities (e.g. humans and chimps have more than 90% similarities in their genomes).

The study compared the Neandertal genomes to five present-day humans: one each from San (Southern) Africa, Yoruba (West Africa), Papua New Guinean, Han Chinese, and French (Western Europe). To cut the long story, they found that the Neandertals are more closely related (by about 3-5%) to present-day non-Africans than to Africans, suggesting some form of interbreeding. The following graphic represents the findings.

Reference: https://commons.wikimedia.org/w/index.php?curid=65505773

Tailpiece

Most of the similarities and differences are academic. And society should not start equating them with friendship, relationships and identities. They are far more complex and, many times, socially constructed.

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