For some shapes, you can tile them in a simple, repetative way.

For example, you can put a load of squares together, and no matter which bit of the tiling you look at, it always has the same pattern.

The same thing happens with triangles.

With 'the hat', whichever bit of tiling you look at, the pattern is always different.

It's the first time this has been done using only a single shape of tile.

Cutting the top length of the rope so they can tie it to the bottom and continue their descent.

The expression "get rid of" sends a chill up my spine as well.

"Hey, Todd. Look, I don't want to be a wet blanket or anything, but last month I lent you twen-..."

"AVADA KEDAVRA! Heh-heh... that's another burden swept under the rug!"

This video explains what I'm talking about:

• Pt1 https://youtu.be/bHIhgxav9LY
• Pt 2 https://youtu.be/oI_X2cMHNe0

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There is no set minimum to be a valid sample. What matters is confidence intervals. Confidence intervals basically mean 'how much of the sample needs to align for it to be significant.'

Imagine you only asked 2 people if America is fascist, and they both said yes. Does this mean everyone thinks America is fascist, or is it just random? You have no confidence.

If you ask 30 people, "is America fascist," and 28 say yes, you can be 95% confident America is fascist.

The larger your sample, the smaller % you need to gain confidence. If you asked 1000 people, and 700 say yes, you can still be pretty confident that America is, in fact, fascist.

Vasopressin enhances aggression. It's linked to the serotonin system in a convoluted way to provide a mechanism for enhancing and suppressing aggressive behaviour.

Generally speaking, the more observations you make (e.g. survey responses), the easier it is to detect an effect. Probably what you heard is that, for the kind of effect sizes one usually sees in whatever context was being discussed, it takes ~30 responses to be reasonably sure (probably a 5% or less chance of being wrong) that the difference observed is caused by a true difference in the population and not mere chance (i.e. you just happened to get a sample where your hypothesis was true, even though it isn't true for the population).

The classic example is pulling coloured balls from a bag. How many balls do you have to pull to get a good idea of what percentage of the balls in the bag are what colour? It depends, of course, on how many balls there are and how the colours are distributed. You have to at least estimate those numbers before you decide what kind of test to do. If there are only ten balls, you could probably just do a census - i.e. look at every ball. If there are 500k balls, you'll only be able to observe a sample. But how big a sample do you need? If you expect the distribution to be ~evenly divided between two colors, you may be able to get away with only 30. If, however, you expect ~25 colours, or that some colours will show up only ~1% of the time, say, you'll need a lot more observations before you can be reasonably confident your sample resembles the population (every ball in the bag).

Bear in mind that most statistical tests assume the sample was drawn randomly. In practice, it is very hard if not impossible to randomly sample humans for a survey. So you generally will want to get more responses to make your statistical tests more powerful (more likely to distinguish a true effect) while keeping your significance level (likelihood that the effect observed is only by chance) reasonably low.

If you could get a truly random sample, you'd need fewer observations to have a good chance that your sample is representative. If it's only mostly random, there's a higher chance that any effect you observe is because of a bias in the sampling. Thus, you will probably want to be more strict in declaring that an observed effect is genuinely present in the population.

But by choosing to reject more findings that could have happened by chance, you make it harder to accept findings that are because of a genuine effect in the population. A real but small effect in the population is not easily distinguishable from a small effect in the sample caused by nonrandom sampling.

Let's say your son has -1$. Imagine it as he owning that dollar to you. If you multiply that debt by 2, the debt is now 2 dollars. If you multiply it by zero, the debt is now cancelled. If you multiply it by -2 the debt turns to credit and now he has 2 dollars.

I still don't understand what you mean - it's the current flowing through the conductor that is going from power station to a residence, not energy in a field

It helps to think of the sign as a direction. Above zero/below zero, credit/debit, above sea level/below sea level, etc. When the sign changes, you change direction.

So, +1 is "take a step," and -1 is "turn around and take a step" which means you move backwards one step.

With --1, you're essentially saying "turn around, then turn around, then take a step," which results in you just spinning about and moving forward just like with +1.

> We don't use magnetic fields to direct energy through utility lines

Sorry, I said electricity when I meant electric energy. Electricity flows through the conductor, energy travels in the field around the wire and can be directed (e.g. from power station to a residence).

Draw him a number line, with 0 in the middle. Show how adding two numbers moves you right, then right again. Show how subtracting two numbers moves you right, then left. Show how adding a negative number moves you left. Then tell him that subtracting a negative number means turning that last operation around once more, meaning you go to the right again. Every minus is a turn.

Edit: if you really want to fry his brain (alternatively inspire him to become a mathematician), tell him that there's also a way to turn away from the number line, and go above or below it.

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NOT THE ELI5 but:
Try to explain him by the number line
https://assets.serlo.org/608fd91b5ab13_80e3137b54975ef440b82f320f15a3473be8e28b.svg

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The magnetosphere is strong because it is huge. It can deflect particles by nudging at them constantly over a distance of several earth diameters. It won't nudge the electrons out of our puny wires that span a tiny fraction of the planet's surface at most.

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I'm sooo going to akshually people with this when the opportunity arises. Or even just out of the blue.

The magnetosphere is very big because the earth is very big, but it isn't really that strong. The magnetic force exerted by the magnetosphere is something like 150-400 times weaker than that of a common magnet. It's just very big, and the charged particles hitting it in space are very small. Even a common magnet would be enough to deflect these particles if you brought it to space, it just wouldn't be very effective in doing so because of how tiny it's range is.

The other part of the question I'm not clear on. We don't use magnetic fields to direct energy through utility lines - that's just current flowing through wires. It does generate a magnetic field, but that's a consequence of electricity passing through the wires, not what is causing it to move.

And yet I’ve used products that did exactly this. Remote control cars use multiple single batteries that are wrapped into one useful mega battery.

Autonomous processes happen by themselves. Cells divide, guts digest, hearts pump.

Reflexes happen in the local nervous system. Eyes blink to protect themselves, hands jerk away from hot stoves, pupils contract or dilate.

Instincts are hardwired into the brain. Hungry - seek food. Horny - seek mate, tired - sleep.

Emotions regulate social behaviour. I like this individual - spend time with it. This is my child - nurture it. This individual wants to hurt me - run away (or kick its ass).

Intellect solves problems. I can't reach this thing, but if I grab a stick, the stick can reach it. That individual is able to eat dirty potatoes by first dipping them in water - imitate it. That animal sure feels scary, but if you look closely you can see it's all a charade - eat it.

Every level is more fine-grained, but also has less control. Your intellect can't control your heart muscle or your cell division, but it can invent a microsocope and figure out how cells divide.

Civilization is arguably yet another level. We can organize in order to solve problems that would be too complex for individual intellects, and the best individuals for a task can devote their lives to it rather than spending a lot of time ensuring their own individual survival.

All of these systems are available to humans. Other animals have them to varying degrees, and even individual becteria have the autonomous processes that keep them alive. Viruses arguably don't even have that, and they're also not alive as such.

The AI singularity is a hypothetical next level, where we've created artificial intelligences so clever that they themselves can design even more clever artificial intelligences without our help.

Good, got it now. Thnx!

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