The other day my family of four had to make a critical decision: what to get for dinner. The options on the table were sushi, fried chicken, Indian, or pizza. We could have done what we’d always done before: each person votes for their top choice and the option with the highest votes wins. But, I had been thinking about how to more accurately model collective preferences, and we decided to give that a whirl. So each of us ranked the 4 options from the most preferred to the least. Here’s how we voted (preserving anonymity to protect the innocent):

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You expect the physical world around you to behave a certain way. If you knock a glass off the table, it will fall to the floor and likely shatter. How do you know this? Primarily from everyday experience, which your brain distills into your intuition. Once you’ve seen enough things fall, you subconsciously generalize that to the intuition that everything falls. Then you encounter a helium balloon, see it rise instead of fall, and you layer on conscious knowledge over your subconscious intuition. You learn about gravity and buoyancy and how to reason about an imbalance between the two causing…

You have precious data. Be it videos of your baby’s first steps or documents you’ve scanned for a paperless life or information you store for users of your startup product. You want to keep this data safe, of course. Safe from permanent loss, temporary unavailability, and unauthorized access.

A typical practice is to *replicate* your data and *spread the replicas* across storage domains that have uncorrelated failures. So, for example, you store a copy of your video in three different cloud storage providers. This is a perfectly reasonable way to keep your data safe. But it has two main drawbacks:

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What is luck? It’s a measure of how much chance you need to achieve a desired outcome, after accounting for any agency you have in affecting the outcome. If you attain the outcome you want, you realize a positive amount of luck i.e. good luck. And the more chance you needed for the outcome, the luckier you were. On the contrary, if the event does not pan out as you would have liked, you realize a negative amount of luck i.e. bad luck. …

You may be familiar with real numbers and their subtypes (rationals, irrationals, integers, etc.). If you need a refresher see “Real Numbers, From The Ground Up”. You may also know that there is an infinite number of real numbers and also an infinite number of each subtype of real numbers. And some of those infinities are equal to others (e.g. # integers = #rationals) while some are larger than others (# irrationals > # rationals). See “Number Of Numbers: Infinite Weirdness” for a discussion of the cardinality of real numbers. What you may not be too familiar with is that…

Would you answer truthfully if you were asked in a survey whether you consume cannabis? Maybe you do like to wind down with an edible after a long day. But the legal contradictions between federal and state laws make you wary. Besides, what will your kids' friends' parents think? The glare of judgment is blinding. Or, what if someone asked you whether you voted for Donald Trump in 2016? What about in 2020? The systematic polling errors in each of those US presidential elections live in infamy. …

How many spatial dimensions do we live in? How many can we directly perceive? Are the two answers the same? If they are different, what effect, if any, do any higher dimensions have on us?

We exist in physical space. In this space, every point or location can be labeled by a set of *coordinates* in a *coordinate* *system*. There can be more than one coordinate system for the same space. But once we choose a system, two points have the same coordinates if and only if they are the same point in space. *The number of independent coordinates needed…*

Keep drawing integers from a random number generator (or a customized lottery machine) until you get a number that is smaller than the previous pick. If your run ends after three or fewer draws (including the last picked smaller number) then you pay $10. Otherwise, you receive $20. Will you accept this bet? Think about it.

Your instincts may tell you it’s a good bet. You need to pick at least two numbers before your run could possibly end. So it seems plausible that the average length of such draws would be larger than three. …

A utopia, in which everyone is a cooperating member of society, cannot exist (at least not for long). Why? Because it is unstable. If everyone plays by the rules, all it takes is one individual to break the rules, gain an advantage over others, and attract more people to break the rules.

Short of utopia, is there something else we can aspire to as a society? Indeed. We can dissuade antisocial behavior. Behaviors can be shaped by incentives. The specific incentives in a society lead to a particular balance of behaviors. That particular mix is not what is optimal for…

Let’s dispel the myth that a single vote does not mathematically make a difference in an election.

If a million ballots are cast in an evenly poised election between two candidates, what are the odds that *your single vote* could decide the election? Almost 0? 1 in 1,000,000? Well, actually it’s close to 1 in 1,000! Admittedly it’s still a small likelihood, but not as small as you thought, right? *If someone gave me a 1 in 1,000 shot at directly choosing an elected official, and all I had to do was to cast a vote, I would take that…*

Mindful Thinker | Software Engineer (Google, Amazon) | Theoretical Physicist (MIT) | Husband, Dad, Dog Dad