yaks_hairbrush

There's a danger in pedantry -- outsiders can mistake it for "see: there's no consensus that the earth is a sphere!". Having said that, the earth is not an oblate spheroid -- it's very slightly pear-shaped, and has all sorts of mountains and valleys.

To paraphrase Isaac Asimov in his essay The Relativity of Wrong: "The earth is flat" is a pretty good model. "The earth is a sphere" is much better. And "The earth is an oblate spheroid" is just a bit better than that.

So, let us consider the aim of the essay: to debunk the flat earth claim as many ways as possible. I think they did a pretty good job finding data for which the flat earth model is insufficient, but a spherical earth fits quite nicely.

So the ant (allegedly -- I'm eagerly awaiting that source!) saw a dot on the ant in the mirror, and tried to remove the dot on its own forehead. The key point: that looks an awful lot like the identification of the self with the reflected image.

The issue you brought up about the mite is a bit orthogonal to this point. I can give you that the ant was concerned about the possibility of having a mite, and the point still remains that the ant thought it was on its own head only on basis of a reflected image of itself. (Compare to the alternative behavior: the ant tries to get the mite off the reflected image, never making any attempt to remove it from itself.)

I believe Randall Munroe was talking about touching neutron star material, if hypothetically we could stably put it on earth.

I want to know more about that gamma-ray wall...

- Would the CMB be so energetic (from the proton's frame) as to create electron-positron pairs?

- If the particle can't travel more than 100m light-years, what happens to it? Does it slow down? Get destroyed? Is the answer markedly different from our reference frame vs the particle's?

> More oddly still as you approach the size of the observable universe, the required mass density crosses the cosmic mass density, meaning light emitted from Earth cannot gravitationally escape the universe created by the Big Bang

This is true...

> meaning we exist inside of a black hole as big as the observable universe.

This is an unwarranted jump. I'd recommend looking at the reference [0] from Sean Carroll.

[0] http://www.preposterousuniverse.com/blog/2010/04/28/the-univ...

There a germ of the right idea here, but our universe is really more of a black hole backwards. Within the event horizon of a black hole, the singularity is always in the future. Within our universe, we see a singularity in our past.

In short, our universe looks more like a white hole than a black hole.

> Intuitively, that's not "obviously" false to me.

That's fair -- intuitions are pretty personal things. It is "obviously" false to me, and Bertrand Russell fairly well articulated the reason why by calling AC the "multiplicative axiom".

If you have sets A, B with 3 and 5 elements, respectively, the Cartesian product has 15 elements.

So, if we have an infinite series of sets, each with at least one element, I'd expect there to be something in the infinite Cartesian project just by multiplication -- the number of elements should (and I say "should" here to clearly denote my intuition) be in some sense the product of each of the individual numbers of elements. (I avoided the word "cardinality" here explicitly because I'm talking intuitively).

The idea that there's a collection of non-empty sets whose Cartesian product is empty is therefore akin to saying that you can multiply numbers bigger than zero and end up with a zero result.

The factorization of 2 is fine -- factorizations are equivalent if they're off by a unit, and i is a unit.

By the same token, 1+i and 1-i are essentially the same prime, since you can multiply one by a unit to get the other. That's how we can get away with saying 2 is a power.

edit: Just noticed the sibling comment by mrkgnao, which is a very good overview of some of the technical nitty-gritty that goes into this.

Here's a thought: Could we put one of these at the L1 point of the Earth-Sun system to protect against solar storms? If something like the Carrington Event happened to our current society, it would be absolutely devastating.

Bonus: Could we make it big enough to encompass the moon?

Patents represent a deal: You publish specifications, and society will grant you exclusive use for X years. Thankfully, unlike their copyright cousins, patent laws have not seen an increase in X. This serves to prevent knowledge from being locked away as trade secrets.

Beneficial to society? Drug companies have patents, and patents expire. Upon expiration, generics become available because the synthesis of the drugs is public knowledge, which creates a competitive market and lowers the price.

Without patents, the drug companies could (modulo other regulations) keep synthesis of their chemicals a trade secret, which may not be replicable in a reasonable time-frame.

Actually, the big bang bears a pretty striking resemblance to a white hole. That's the time-reversed version of a black hole. Whereas with a black hole, all paths lead toward the singularity at its core, with a white hole, all paths lead away from the singularity.

> I'm not sure how I feel(as an AAPL shareholder) about [giving her time off]

If I were an AAPL shareholder, I'd be very pleased about it. The behavior indicated in the post very much leaves the company at risk of spending possibly hundreds of thousands of dollars on legal counsel and settlement fees/court-ordered payouts.

Getting away with only an apology and some time off is a bargain.

As for your last paragraph, perhaps there's a distinction between necessary stress and unnecessary stress. You seem to be describing necessary stress -- the stress that's intrinsic to working at a company, facing deadlines, negotiating with clients/other departments, etc.

By contrast, this woman describes a pattern of being on the receiving end of personal attacks based on items unrelated to quality/delivery of work. That would be a very different sort of stress from what you're describing.

But where's the NPVIC going to get the 270 EVs from? The blue state contribution is just about maxed out, while swing and red states have no incentive to join it.

A lot of comments here are referencing the National Popular Vote Interstate Compact (NPVIC). If it ever comes to fruition, it would be a rather clever hack to get around needing a constitutional amendment to change/abolish the electoral college.

Don't get too optimistic about it going places, though. We've got three types of states these days: red states, swing states, and blue states. Let's look at incentives:

Blue states are the only ones to go for NPVIC so far, and it's easy to see the incentive: Blue states have twice in the last 20 years seen their candidate get more votes than the other and lose anyway. So far, blue states have contributed 165 electoral votes to the effort, and could maybe contribute another 17 or so (CT, OR, DE).

Swing states are not incentivized to go for NPVIC. Presidential campaigns bring lots of money to swing states. Swing states have contributed 0 EVs so far, and according to Wikipedia three such states are considering it: AZ, PA, MI. I expect each of these to fail. It would be big news if any succeeded.

Red states: They've seen their preferred candidate win while getting outvoted twice in the last 20 years. They currently see the NPVIC as Democrats asking for a rule-change to make it easier for them to win. I could see red states start to go for this if a Republican loses while getting more votes. Until that happens, the red-state contribution to the NPVIC will at or near 0 EV.

Don't know why you were downvoted, you're absolutely correct. At first glance your n and my n are different, with mine (n1) being the input to the function and yours representing the number of digits in a multiplicand (n2). n1 and n2 are linearly related, though, since the exponentiation process increases the number of digits in a linear fashion.

It's also worth noting that since the Fibonacci sequence grows exponentially, the number of digits is the result will be linear in n. Therefore, the memory requirement is actually O(n), and writing the result to the screen will be O(n).

That's log(n) time due to the exponentiation.

There is no constant time implementation. Binet's formula uses exponentiation, which gives us log(n) time.

> why would anyone want to use their high-interest credit card to borrow even a few tens of thousands?

Here are a couple ideas: lawyer fees during a contested divorce and emergency spending from being out of work too long.

It's great that you had it easy. I didn't. When I quit nicotine about two years ago, I got kicked into a deep depression that lasted about 3 months (Worth noting: I had a history with depression). I developed panic attacks (and I had no previous history with those).

On the plus side:

1. I quit and stayed quit.

2. I'm mostly back to my old self. No more depression or panic attacks. Not now, and never again!

3. The whole experience cost me so much that I doubt I'll feel much temptation to use nicotine ever again.

Life expectancy is better today, but life expectancy as a hunter-gatherer was probably better than you think. [0] suggests a modal adult age of 68-78 years for hunter-gatherers. Infant mortality is indeed way down, and that's a big point in our favor (and the biggest driver of the life expectancy difference).

Infectious diseases, though, are very much a product of agricultural society, as is starvation/famine. We might be living through the century (or possibly, have just lived through the century) where our technology finally enables us to fix these two problems caused by our ancestors' conversion to agriculture.

[0] http://www.anth.ucsb.edu/faculty/gurven/papers/GurvenKaplan2...

You're not speaking the same language as your parent commenter. "Generally Recognized As Safe" (GRAS) is an FDA designation, and not a literal phrase. High Fructose Corn Syrup, for example, is GRAS.

Can you provide your email?

I do not agree with your first statement. Mathematics is about developing and studying tools to solve problems. Proofs are only one aspect of that.

The issue of proof is very different from the issue of learning. I thought it was the latter being discussed.

I don't like this attitude at all. Euclid, Archimedes, Newton, Leibniz, Riemann, and many others did a fine job correctly calculating areas, volumes, and so on without need of measure theory.

Why is it so important to avoid the problem laid out by Banach-Tarski on the first go through the concept? We, as a species, did not even realize such a problem existed until about 1920, and yet we still managed to build stuff based on what we knew.

One mechanism by which it's good for the employer is information asymmetry. The employer knows all of the employees' salaries, but the employee does not have this information.

This comment is making the page formatting gross. Those special characters with the strike-throughs make the entire page over-wide, thus requiring horizontal scrolling to read comments.

Don't know about disability.

I would answer "yes" to your second paragraph, excepting possibly residents of Hawaii.

Regarding your third paragraph, we (society) already do tell a segment of the population "tough, you get to live on the street". Why is it so hard to believe society would suddenly find it unpalatable in this case? Basic income is nice, though, because it provides a path out of homelessness, and that's something that's often not present.

Look at the 2-body gravitational system -- let's say Earth-Moon. Let's put our non-rotating reference frame at the barycenter. At any given moment, Earth has a definite position and velocity, and the Moon has a definite position and linear velocity. If we know these positions and velocities (and masses), we can derive anything else we'd like to know about the system. Including its angular momentum.

This would also be true of any system such that the size is large enough to render the quantum spins statistically close to zero.

What is the point you're arguing against? I know perfectly well that conservation of angular momentum is a thing. I know perfectly well that the intrinsic property that we call 'spin' of an electron is really angular momentum. I know that a spinning bucket also has real angular momentum.

So, I'm not sure what you're trying to tell me.

The central point made by colordrops is that angular momentum in a macroscopic object is 100% (accurate to at least ten decimal places) due to synchronicity of linear momenta.