97.8% of people instantly believe any oddly specific statistic they read on Twitter.
Don't be susceptible to logical fallacies and subtle manipulations. Spotting and avoiding them is essential to making good decisions in our times.
↓ Here is what to look out for. ↓
1. Argument from repetition.
In Latin, this is called argumentum ad nauseam, that is, an argument that has been repeated until nausea.
Want an example when it worked successfully?
"Ceterum censeo Carthaginem esse delendam."
Cato, the Roman senator closed every one of his speeches with the phrase "Carthage must be destroyed". And so, Carthage was eventually razed and its ruins were sown with salt.
2. Appealing to authority.
Appealing to authority is common, yet hard to spot. Ever heard a scientist claim something stupid about COVID that everyone believed? Then you've seen this in action.
This also means that follower count on Twitter is irrelevant in a debate.
3. "After this, therefore because of this" fallacy.
Ever heard the argument that the COVID vaccine causes COVID, just because there are infections despite several vaccinations? Here you go.
This is called "post hoc ergo propter hoc", and we encounter it almost every day.
4. Conflating correlation with causation.
There is an entire collection of totally random things that correlate, but have nothing to do with each other. Causation implies correlation, but not the other way around.
If it is raining outside, the road is wet. However, if the road is wet, it doesn't mean that it is raining: the neighbor could have been watering their lawn as well.
Politicians love to use this fallacy when jumping to false conclusions.
6. Blinding with science.
Sometime during the 18th century, there was a debate between the great mathematician Euler and the philosopher Diderot.
The topic was whether or not God exists.
Euler opened the debate with the following sentence:
"Monsieur, (a + b^n)/n = x, therefore God exists. Reply!"
Diderot withdrew on the spot, losing the debate immediately. Was Euler right though?
No.
What Euler did was to intimidate his opponent with a scientific but invalid argument.
You can see this method applied in sales and marketing all the time. Don't fall for it.
(This version of the story is from The God Delusion by Richard Dawkins.)
7. Appealing to public opinion.
"Eat shit! A billion flies can't be wrong."
You get the idea.
8. Assaulting someone's character.
"You can't say that killing is wrong, since you have killed before."
However, the two have nothing to do with each other. No argument is invalidated by its source. Yet, we tend to make this mistake all the time.
9. Creating false dilemmas.
"We either build a wall at our borders, or immigrants are going to take all of our jobs."
The goal of this is to present only two options: a highly undesirable one, and the proposer's solution.
In practice, there is always a middle ground.
10. Appealing to tradition.
Just because you've done something in a particular way, it doesn't mean that you were correct.
On the other hand, innovations are not automatically good as well.
+1. Judging the decision by the outcome.
Sometimes, horrible decisions can result in positive outcomes. Suppose that I went to a casino, sat down at the roulette table and put all my money on red 13, and won. Was it a good decision?
No.
This phenomenon is called resulting, and it can be applied to the reverse situation as well: bad outcomes can come from good decisions.
Personally, eliminating resulting has been the best thing to happen to my confidence and self-image.
Are there any other logical fallacies that you think are important? Share it with us!
In my opinion, spotting fallacious arguments is one of the most important skills currently in our modern life. This is how you are manipulated into doing things you don't want.
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Roaming the streets of Königsberg, Euler was working on a simple puzzle: can he cross each of the city's bridges exactly once? The answer was no. And so, graph theory was born.
↓ This is its story. ↓
At the time of Euler, the central part of Königsberg (now Kaliningrad) was split into four parts by the Pregel (now Pregolya) river, with seven bridges between them, as illustrated below.
The question is, can you cross each one exactly once during a single walk?
To answer this question, we don't have to study the particular geography and layout of Königsberg, only the islands and the bridges connecting them.
By stripping away all unnecessary details, we end up with a few nodes connected by edges. This was the first graph.
Differentiation reveals much more than the slope of the tangent plane.
We like to think about it that way, but from a different angle, differentiation is the same as an approximation with a linear function. This allows us to greatly generalize the concept.
Let's see why! ↓
By definition, the derivative of a function at the point 𝑎 is defined by the limit of the difference quotient, representing the rate of change.
In geometric terms, the differential quotient represents the slope of the line between two points of the function's graph.
There are two mistakes people make when building predictive models.
Most models are either too simple to be useful or too complicated to be used. Learning to pick just the right one is a valuable skill that can be applied anywhere.
Here is the basic principle behind it. ↓
Let's see some movie review sentiment analysis to illustrate the point!
Here is a short review snippet: "I had the terrible misfortune of having to view this b-movie in its entirety."
Without a doubt, this review is negative.
Based on this sample, one possible way to capture the sentiment could be just simply looking for the word "horrible".
Reviews containing it are predicted as negative. Otherwise, they are positive.
There is more than one way to think about matrix multiplication.
By definition, it is not easy to understand. However, there are multiple ways of looking at it, each one revealing invaluable insights.
Let's take a look at them!
↓ A thread. ↓
First, let's unravel the definition and visualize what happens.
For instance, the element in the 2nd row and 1st column of the product matrix is created from the 2nd row of the left and 1st column of the right matrices by summing their elementwise product.
To move beyond the definition, let's introduce some notations.
A matrix is built from rows and vectors. These can be viewed as individual vectors.
You can think of them as a horizontal stack of column vectors or a vertical stack of row vectors.