from the world's big
10 logical mistakes you make every day — and what to do instead
Do you ever act irrationally? You probably have. Let's take a look at how to fix that.
Most of us like to suppose that we are rational people, going about our days with at least some attempt at using logic and reason. However, logical fallacies and simple mistakes are everywhere. Some wrong ways of thinking are so familiar or so easy to overlook that it is possible you're unaware that there is even a mistake being made.
Here are ten logical fallacies and mistakes you make every day that cause life to be a little more difficult, and how you can avoid making those mistakes again.
The Gambler's Fallacy
When you flip a coin nine times in a row, can you use the results to predict what will happen the tenth time? While many people might try to say "tails has been on a streak" or "heads is overdue," neither of these past events has any effect on the next outcome. Both outcomes still have a 50-50 chance of happening on the next flip. The results of the next coin toss cannot be affected by the results of the last.
What should I do?
Instead of viewing probabilities in the long run, such as the idea that the coin has to have 50 heads and 50 tails results in a set of 100, or that a roulette wheel must hit all numbers at the same rate over a long enough time, look at each bet as separate from all others. The odds never change as a result of the last outcome for a fixed odds, random system.
The Appeal to Authority
Authority figures, but only on law.
Can something be true just because I say it is? Of course not. If your mechanic tells you that you need an oil change, is that true? It probably is. The appeal to authority is one of the subtler fallacies, but one that can still be overcome. Nothing is true just because an authority figure says it is. Instead, something is correct, and the authority figure has determined that fact by using their expertise on the subject.
Determining if the person you are talking to is trying to use raw, irrelevant authority to persuade you or if they actually are an expert on the subject is essential. The difficulty in saying that an authority figure is wrong was studied in the Milgram Experiment. However, it is rarely considered a good excuse to say you were just doing what you were told.
What should I do?
Don't blindly take a statement as true just because an authority figure gave it. My doctor is an authority on medicine and what he tells me about my health is likely to be correct. However, he has less knowledge when it comes to woodworking. On that subject, his authority as a doctor is meaningless. Always assure that an authority figure is qualified and that what they say is likely to be true before taking it as a fact.
The False Dilemma
We've all either heard or made this argument. We must do either A or B, and since A is not what we want then we must do B. However, very often we are facing a false dilemma. A situation where we have more than two choices and are being railroaded into thinking we don't.
What should I do?
When it seems you only have two choices, always make sure there are actually only two options. If a person starts a sentence with the phrase, "The choice is simple," know they are probably about to introduce a false dilemma.
The Post-Hoc Fallacy
Good luck charms, the most common form of this fallacy.
Many people tend to see patterns where they don't exist. This fallacy is when you connect two unrelated events and presume one caused the other. For example, when you flip on a light switch and hear a crash in the next room. Did flipping the switch cause the noise? No, but we often still try to connect events with no relationship. This fallacy is often the basis for good luck charms. "I brought my rabbit's foot with me, and it went well!" you might hear. But, it does not follow that the rabbit's foot caused the outcome.
What should I do?
Remember that coincidences sometimes happen and that sometimes two unrelated events can occur in a way to make them look related. Likewise, remember that one incident seeming to cause another wouldn't prove a relationship anyway; you would need many more tests to demonstrate that.
Affirming the Consequent
The building has collapsed, but do you know why?
This mistake is so easy to make that there can be no doubt that nearly everyone has done it. It is so similar to a valid form of thinking that the mistake can slip right past us.
While it is correct to argue this way:
If A, then B.
However, this is not correct:
If A, then B.
For example, saying "If the cornerstone is removed from the building it will fall over" is fine. But if we see the building has collapsed, it is still possible that another event caused it. The cornerstone might never have moved.
What should I do?
If-then thinking is beneficial and a useful tool, but always be sure that your thinking is going in the right direction. The cause can be used to predict the effect, but the result cannot be used to prove what the cause was. You need more evidence for that.
The Relativist Fallacy
If you believe it hard enough, is this dog really a unicorn?
Can the statement, "Well, it's true for me," ever be correct? It can, but you must use it carefully. While some statements are fully relative, like "I think cilantro tastes horrible," others are fully objective, like "Unicorns do not exist." While it makes sense for a person to say that cilantro tastes terrible to them, it doesn't work to say that unicorns are real for one person and not the next. The existence or non-existence of unicorns is an objective fact not influenced by any belief in that fact.
What should I do?
While some truths, such as ideas on what tastes good, are relative, others, such as what the capital of Canada is, are not. Before you either argue or listen to an argument that somebody is entitled to their own truth, first ask if the fact in question is one that can be relative. If that fact cannot be made true just by believing in it, then they this fallacy may be present.
The Genetic Fallacy
If I am made up of DNA, am I a double helix?
If one thing comes from another, do they have to share traits? This might seem like a convenient bias to have. However, do redwood trees seem to have much in common with their seeds? The genetic fallacy is the assumption that anything with an origin in one thing is highly likely to share traits.
What should I do?
This one is easy to do by accident, but also simple to overcome with a little extra thinking. Remember that things need not have the same traits as their origin. Think of the Volkswagen company; it was founded by the Nazi labor front. Does that make it a Nazi company now? Of course not, we would have to examine its present merits by themselves to determine that. The best thing to do for this fallacy is to try to examine why a thing has the traits it has without using its origin as an end-all answer.
The Inductive Fallacy
Will the sun always come up? It always has!
The sun came up today, does that mean it will come up tomorrow? David Hume showed us in 1748 that inductive arguments can never give us certainty, only probabilities and useful generalizations. The fact that apples always have fallen to the earth doesn't mean it will forever continue to happen. It is simply probable. Here's another example: "Harold is a grandfather. Harold is bald. Therefore, all grandfathers are bald." Inductive thinking makes a broad and highly probably generalization from specific information, but it is assumption, not certainty.
What should I do?
While you don't need to worry about the sun taking a day off tomorrow, it's not because it has never failed to rise. Inductive reasoning can't prove things, but it can be used to help find the best explanation for things. These reasons are better to use in arguments as to why an event will or will not happen than just saying that it has always happened before.
The Slippery Slope
A very slippery slope.
This fallacy is a common one. You have undoubtedly heard somebody say that taking action A is a slippery slope to taking action B, and B is horrible. They argue that we shouldn't take action A because it will, inevitably, lead us to take action B. But is that true? Generally speaking, no.
Now, slippery slope arguments can be good ones if it can be proved that the slope exists. If you can show that taking action A will inevitably lead to me taking action B then you have a good argument. However, most of the time people fail to demonstrate that inevitability.
What should I do?
If you are making the argument, be sure to demonstrate that action A concretely leads to action B. Simply saying "It could happen" doesn't count. You have to either prove it or show that it is much more likely to happen by action A taking place. If you are listening to the argument, always make sure that claimed connections between events are there.
The Masked Man Fallacy
A masked man.
Identical objects share all of the same properties. This rule, called Leibnitz's law, seems simple enough to understand. However, it is very easy to misuse this concept to make bad arguments.
This argument is correct:
1. A is C
2. B is not C
Therefore: A is not B.
However, you can't plug in just any property into the argument and have it work. Think about this one:
The Joker believes that Batman beat him up.
The Joker does not believe that Bruce Wayne beat him up.
Therefore: Batman is not Bruce Wayne.
While physical properties follow Leibnitz's law, attitudes, beliefs, and psychological states don't necessarily do so.
What should I do?
When you are identifying a person, object, or idea be sure to check that the properties you are looking for are non-relative ones.
Here are more tips for making better decisions, from poker pro Liv Boeree:
Andy Samberg and Cristin Milioti get stuck in an infinite wedding time loop.
- Two wedding guests discover they're trapped in an infinite time loop, waking up in Palm Springs over and over and over.
- As the reality of their situation sets in, Nyles and Sarah decide to enjoy the repetitive awakenings.
- The film is perfectly timed for a world sheltering at home during a pandemic.
Richard Feynman once asked a silly question. Two MIT students just answered it.
Here's a fun experiment to try. Go to your pantry and see if you have a box of spaghetti. If you do, take out a noodle. Grab both ends of it and bend it until it breaks in half. How many pieces did it break into? If you got two large pieces and at least one small piece you're not alone.
But science loves a good challenge<p>The mystery remained unsolved until 2005, when French scientists <a href="http://www.lmm.jussieu.fr/~audoly/" target="_blank">Basile Audoly</a> and <a href="http://www.lmm.jussieu.fr/~neukirch/" target="_blank">Sebastien Neukirch </a>won an <a href="https://www.improbable.com/ig/" target="_blank">Ig Nobel Prize</a>, an award given to scientists for real work which is of a less serious nature than the discoveries that win Nobel prizes, for finally determining why this happens. <a href="http://www.lmm.jussieu.fr/spaghetti/audoly_neukirch_fragmentation.pdf" target="_blank">Their paper describing the effect is wonderfully funny to read</a>, as it takes such a banal issue so seriously. </p><p>They demonstrated that when a rod is bent past a certain point, such as when spaghetti is snapped in half by bending it at the ends, a "snapback effect" is created. This causes energy to reverberate from the initial break to other parts of the rod, often leading to a second break elsewhere.</p><p>While this settled the issue of <em>why </em>spaghetti noodles break into three or more pieces, it didn't establish if they always had to break this way. The question of if the snapback could be regulated remained unsettled.</p>
Physicists, being themselves, immediately wanted to try and break pasta into two pieces using this info<p><a href="https://roheiss.wordpress.com/fun/" target="_blank">Ronald Heisser</a> and <a href="https://math.mit.edu/directory/profile.php?pid=1787" target="_blank">Vishal Patil</a>, two graduate students currently at Cornell and MIT respectively, read about Feynman's night of noodle snapping in class and were inspired to try and find what could be done to make sure the pasta always broke in two.</p><p><a href="http://news.mit.edu/2018/mit-mathematicians-solve-age-old-spaghetti-mystery-0813" target="_blank">By placing the noodles in a special machine</a> built for the task and recording the bending with a high-powered camera, the young scientists were able to observe in extreme detail exactly what each change in their snapping method did to the pasta. After breaking more than 500 noodles, they found the solution.</p>
The apparatus the MIT researchers built specifically for the task of snapping hundreds of spaghetti sticks.
(Courtesy of the researchers)
What possible application could this have?<p>The snapback effect is not limited to uncooked pasta noodles and can be applied to rods of all sorts. The discovery of how to cleanly break them in two could be applied to future engineering projects.</p><p>Likewise, knowing how things fragment and fail is always handy to know when you're trying to build things. Carbon Nanotubes, <a href="https://bigthink.com/ideafeed/carbon-nanotube-space-elevator" target="_self">super strong cylinders often hailed as the building material of the future</a>, are also rods which can be better understood thanks to this odd experiment.</p><p>Sometimes big discoveries can be inspired by silly questions. If it hadn't been for Richard Feynman bending noodles seventy years ago, we wouldn't know what we know now about how energy is dispersed through rods and how to control their fracturing. While not all silly questions will lead to such a significant discovery, they can all help us learn.</p>
The multifaceted cerebellum is large — it's just tightly folded.
- A powerful MRI combined with modeling software results in a totally new view of the human cerebellum.
- The so-called 'little brain' is nearly 80% the size of the cerebral cortex when it's unfolded.
- This part of the brain is associated with a lot of things, and a new virtual map is suitably chaotic and complex.
Just under our brain's cortex and close to our brain stem sits the cerebellum, also known as the "little brain." It's an organ many animals have, and we're still learning what it does in humans. It's long been thought to be involved in sensory input and motor control, but recent studies suggests it also plays a role in a lot of other things, including emotion, thought, and pain. After all, about half of the brain's neurons reside there. But it's so small. Except it's not, according to a new study from San Diego State University (SDSU) published in PNAS (Proceedings of the National Academy of Sciences).
A neural crêpe
A new imaging study led by psychology professor and cognitive neuroscientist Martin Sereno of the SDSU MRI Imaging Center reveals that the cerebellum is actually an intricately folded organ that has a surface area equal in size to 78 percent of the cerebral cortex. Sereno, a pioneer in MRI brain imaging, collaborated with other experts from the U.K., Canada, and the Netherlands.
So what does it look like? Unfolded, the cerebellum is reminiscent of a crêpe, according to Sereno, about four inches wide and three feet long.
The team didn't physically unfold a cerebellum in their research. Instead, they worked with brain scans from a 9.4 Tesla MRI machine, and virtually unfolded and mapped the organ. Custom software was developed for the project, based on the open-source FreeSurfer app developed by Sereno and others. Their model allowed the scientists to unpack the virtual cerebellum down to each individual fold, or "folia."
Study's cross-sections of a folded cerebellum
Image source: Sereno, et al.
A complicated map
Sereno tells SDSU NewsCenter that "Until now we only had crude models of what it looked like. We now have a complete map or surface representation of the cerebellum, much like cities, counties, and states."
That map is a bit surprising, too, in that regions associated with different functions are scattered across the organ in peculiar ways, unlike the cortex where it's all pretty orderly. "You get a little chunk of the lip, next to a chunk of the shoulder or face, like jumbled puzzle pieces," says Sereno. This may have to do with the fact that when the cerebellum is folded, its elements line up differently than they do when the organ is unfolded.
It seems the folded structure of the cerebellum is a configuration that facilitates access to information coming from places all over the body. Sereno says, "Now that we have the first high resolution base map of the human cerebellum, there are many possibilities for researchers to start filling in what is certain to be a complex quilt of inputs, from many different parts of the cerebral cortex in more detail than ever before."
This makes sense if the cerebellum is involved in highly complex, advanced cognitive functions, such as handling language or performing abstract reasoning as scientists suspect. "When you think of the cognition required to write a scientific paper or explain a concept," says Sereno, "you have to pull in information from many different sources. And that's just how the cerebellum is set up."
Bigger and bigger
The study also suggests that the large size of their virtual human cerebellum is likely to be related to the sheer number of tasks with which the organ is involved in the complex human brain. The macaque cerebellum that the team analyzed, for example, amounts to just 30 percent the size of the animal's cortex.
"The fact that [the cerebellum] has such a large surface area speaks to the evolution of distinctively human behaviors and cognition," says Sereno. "It has expanded so much that the folding patterns are very complex."
As the study says, "Rather than coordinating sensory signals to execute expert physical movements, parts of the cerebellum may have been extended in humans to help coordinate fictive 'conceptual movements,' such as rapidly mentally rearranging a movement plan — or, in the fullness of time, perhaps even a mathematical equation."
Sereno concludes, "The 'little brain' is quite the jack of all trades. Mapping the cerebellum will be an interesting new frontier for the next decade."
What happens if we consider welfare programs as investments?
- A recently published study suggests that some welfare programs more than pay for themselves.
- It is one of the first major reviews of welfare programs to measure so many by a single metric.
- The findings will likely inform future welfare reform and encourage debate on how to grade success.
Welfare as an investment<p>The <a href="https://scholar.harvard.edu/files/hendren/files/welfare_vnber.pdf" target="_blank">study</a>, carried out by Nathaniel Hendren and Ben Sprung-Keyser of Harvard University, reviews 133 welfare programs through a single lens. The authors measured these programs' "Marginal Value of Public Funds" (MVPF), which is defined as the ratio of the recipients' willingness to pay for a program over its cost.</p><p>A program with an MVPF of one provides precisely as much in net benefits as it costs to deliver those benefits. For an illustration, imagine a program that hands someone a dollar. If getting that dollar doesn't alter their behavior, then the MVPF of that program is one. If it discourages them from working, then the program's cost goes up, as the program causes government tax revenues to fall in addition to costing money upfront. The MVPF goes below one in this case. <br> <br> Lastly, it is possible that getting the dollar causes the recipient to further their education and get a job that pays more taxes in the future, lowering the cost of the program in the long run and raising the MVPF. The value ratio can even hit infinity when a program fully "pays for itself."</p><p> While these are only a few examples, many others exist, and they do work to show you that a high MVPF means that a program "pays for itself," a value of one indicates a program "breaks even," and a value below one shows a program costs more money than the direct cost of the benefits would suggest.</p> After determining the programs' costs using existing literature and the willingness to pay through statistical analysis, 133 programs focusing on social insurance, education and job training, tax and cash transfers, and in-kind transfers were analyzed. The results show that some programs turn a "profit" for the government, mainly when they are focused on children:
This figure shows the MVPF for a variety of polices alongside the typical age of the beneficiaries. Clearly, programs targeted at children have a higher payoff.
Nathaniel Hendren and Ben Sprung-Keyser<p>Programs like child health services and K-12 education spending have infinite MVPF values. The authors argue this is because the programs allow children to live healthier, more productive lives and earn more money, which enables them to pay more taxes later. Programs like the preschool initiatives examined don't manage to do this as well and have a lower "profit" rate despite having decent MVPF ratios.</p><p>On the other hand, things like tuition deductions for older adults don't make back the money they cost. This is likely for several reasons, not the least of which is that there is less time for the benefactor to pay the government back in taxes. Disability insurance was likewise "unprofitable," as those collecting it have a reduced need to work and pay less back in taxes. </p>