It’s true that, due to its volatility, Bitcoin is currently not a good store of value, at least in the short term. There’s an underlying truth, though, which is that Bitcoin is a potential store of value. In particular, it has all the necessary qualities of a monetary good, among them durability, divisibility, portability, verifiability, and above all scarcity.
Buying Bitcoin right now involves speculating that others will also see this potential, which is why it’s accurate to describe it for the moment as a speculative asset. The reason buying Bitcoin is a smart bet is that its monetary properties are so good that it has the potential to store a significant percentage of the world’s savings. Once that happens, its volatility will be much lower, so it will be a good store of value. And of course its purchasing power in current U.S. dollars will be much, much higher, which is why it’s a good idea to buy some now.
I followed YC from the time it was just a glimmer in pg’s eye (http://www.paulgraham.com/start.html). By the time I went through YC myself, in the Winter 2008, I felt like I was already late to the game. Eventually I realized W08 was still early, early days. (For example, the weekly dinners were generally cooked by pg himself. Also, the benches would see-saw up if someone on the wrong side left their seat—I’m sure some of you fellow old-timers now recall that idiosyncrasy with a strange sense of fondness.)
Congratulations to Y Combinator on 17 amazing years. Here’s to many more years to come!
"Yes, yes, repression, anti-gay prejudice, I know all right-thinking people are supposed to be horrified by such things – but...” -Erik S Raymond
You owe me $100. Please PayPal it expeditiously to don@donhopkins.com.
And if that 10-year-old hateful ESR quote I already provided you with isn't enough for your upwardly mobile goalposts, then here are a couple more recent, even more explicitly vile, hateful, racist, and demeaning ESR quotes. And there are lots more where those came from.
“Unfortunately, this doesn’t cover the BLM crowd, which would have an average IQ of about 85 if it’s statically representative of American blacks as a whole. I’ve never tried to train anyone that dim and wouldn’t want to.” -Erik S Raymond
"In the U.S., blacks are 12% of the population but commit 50% of violent crimes; can anyone honestly think this is unconnected to the fact that they average 15 points of IQ lower than the general population? That stupid people are more violent is a fact independent of skin color." -Eric S Raymond
Did you really mean to carry Eric S Raymond's water so enthusiastically with such aplomb? You're the one who foolishly decided to publicly bet your own money that he couldn't keep his hateful racist mouth shut, and you spectacularly lost that bet, so please pay up.
Thomas Ptacek raised over $30,000 for charity from people who wanted him to stop posting vile ESR quotes to twitter, so consider yourself getting off dirt cheap for only $100 to make me stop posting ESR's own words, after you asked for it.
I’ve been following this project closely (oshams is a friend and I’m an investor in the company), and to echo Darmani’s comment both the product and the pace of development have been extremely impressive. Congrats on the launch!
I haven’t tried everything on this list, mainly due to cost. But you’d be surprised how cheap most of the things on this list are (especially the free ones).
The Tau Manifesto shows how using tau = C/r makes the geometric meaning of Euler’s formula (and hence of Euler’s identity) even clearer. Disclaimer: I am the author of The Tau Manifesto.
I recently enjoyed listening to this interview with someone who knew Grothendieck. It takes a while to get going, but some of the stories are quite gripping.
The article mentions Jean-Pierre Serre, with whom Grothendieck corresponded extensively, and Pierre Deligne, widely regarded as Grothendieck’s greatest student. While investigating Grothendieck recently (inspired by the interview linked in the parent comment), I came across this astonishing anecdote, relating a comment by Serre about Deligne [1]:
“Look, I can take on anyone in Math.” — don’t forget, this guy [Serre] is the youngest Fields medal winner ever, the first Abel prize laureate, etc. — “I can understand the reasoning of the greats, handle them new ideas, you name it.”
“Except for Deligne.” (WHAT ?)
“Deligne is totally out of my league. Above my head.”
“The difference between Deligne and me, is the same difference between me and an average good mathematician.”
I found this anecdote especially astonishing considering that at the time I had never even heard of Deligne. (And most people, of course, haven’t even heard of Grothendieck.)
The article appears to be confusingly written, making reference to a time “before” the Big Bang:
Just before the Big Bang launched the universe onto its ever-expanding course, physicists believe, there was another, more explosive phase of the early universe at play: cosmic inflation, which lasted less than a trillionth of a second.
But cosmic inflation was part of the Big Bang, not something that happened “before” it. According to the current understanding, the Big Bang included the beginning of time itself—in more technical terms, the Universe has no boundary in time (or space)—so asking what happened “before” the Big Bang is akin to asking what’s north of the North Pole.
Isn't the Big Bang only observable as the Cosmic Microwave Background? The Big Bang is the oldest event we can observe, but that doesn't mean nothing was happening before it. It just means we can't observe what was happening.
The travel time for light from that event doesn't seem to tell us very much about how old the Universe is as an n-dimensional space. It only tells us how far back we can observe. We can choose t_0 to be the point in time at which that farthest emitted light was emitted. That doesn't mean there isn't a t_-1, it only means that our axis of positive time starts there because that's all we can observe right now. We know some event happened and before that event we can make no observations, while after that event we can make observations. So everything observable follows from that event. But absence of observations is not evidence of absence.
It's actually sensible to ask what's north of the North Pole because it reveals something about the geometry of the coordinate space. You're considering the North Pole as a fixed boundary where all lines end, whereas the asker considers it as a point that all lines pass through(this is a more correct interpretation). In our polar coordinate system going to that point would result in being somewhere south of north but on the other half of the semicircle. Whether it's sensible to ask that about the universe seems like an open question to me.
The sensible thing to me is to wonder at the question while recognizing that we aren't currently able to answer it sensibly. Maybe we never do.
We can’t observe things before recombination, a couple hundred thousand years after the Big Bang, when electrons bound to nuclei and photons stopped being constantly scattered.
To play the Devil's advocate a bit, I feel like your comment is just arguing about definitions.
Cosmological models of the early universe tend to naturally break up into several phases, e.g. the inflation period, baryogenesis, and (much later) nucleosynthesis.
Given how sketchy our data gets the further back we try to probe, it's certainly not unreasonable to say that "Big Bang" refers to the point at which inflation ended.
Heck, even inflation itself is something that's hotly debated, and the search for evidence of an iflation field is an extremely active area of reseach.
> According to the current understanding...
Feel like you've been misled. What you describe there is a summary of an idea for a model that is particularly beautiful mathematically.
Once we have a solid, evidence-backed model going back so far, I suspect the Quantum Gravity nut will have already been cracked for some time.
The term 'boundary' has a specific mathematical meaning that may or not be appropriate. In particular a ball has a boundary (although a sphere doesn't).
The universe may or may not have a boundary at the big bang. Most straightforward theories seem to suggest it does have one. I believe Hawking has a rather complicated theory where it may not have one, but that involves adding an extra time dimension, which is a bit iffy.
Regardless, even if an infinite (in space) universe simply sprang into existence at a certain moment, that still doesn't mean it makes sense to ask what happened before. It makes sense to ask what happens at the boundary, but there is not necessarily a before to ask about.
Poster is probably using the terms how they are used in Analysis. A sphere is just the surface, i.e. the set of points equidistant from some center. A ball is the entire volume enclosed by said sphere.
To expand on @contravariant's answer a bit, let me take a more hand-wavy intuitive approach.
The surface of a ball, i.e. a sphere, doesn't have boundary for the same reason that the surface of the Earth doesn't. You can't travel along it and eventually reach some kind of edge. That is, no matter where you are on the Earth, you can in principle, move freely along any coordinate direction and still stay on the surface of the Earth.
Thinking of the entire volume of the Earth, however, is akin to considering a 3D ball. Inside the earth, magma/rocks/etc can, in principle, move freely along all 3 axes. However, once we're at the surface, one of our axes of movement is restricted. We can't go further "out" and still stay within the ball (of the Earth).
As @contravariant hints at, the above can be made precise by using the mechanics of topology to get something called a (topological) manifold. If you're at all inclined, I highly recommend taking some time to get familiar with topology. It's an amazingly deep field with applications in almost any field you can think of!
Without going into extreme depth A sphere is a 2D manifold since any point has a neighbourhood that looks more or less like 2D space.
A ball is like a 3D manifold for the same reason, but it also has some points where you don't have a neighbourhood that looks like 3D space but rather one that looks like half of 3D space. That region is the boundary, so to be exact a ball isn't a 3D manifold but a 3D manifold with boundary.
Cosmic inflation did probably occur before the Big Bang. In the eternally inflating cosmos model there is the idea that dark energy that is causing the universe to expand at an accelerating rate is part of an yet to be understood inflaton field. As the rate of inflation in our universe continues to grow, here is a simple question, what happens if the rate of universal expansion exceeds the rate at which light travels. If there is no upper bound to the rate of inflation then at some point no only will normal matter be torn apart but also imagine what happens to a black hole. There are several types of boundaries to the universe. The particle horizon, which is the boundary of the known universe, starts at the CMB (cosmic microwave background.) We know that this is currently viewed as about 46 billion light years from our position is space. But if were to launch a space ship and travel at the speed of light we could never reach the currently known particle horizon. As we travel through space to our destination space is still expanding. This is known as the cosmic event horizon, our best estimate is that this value is currently about 16 billion light years away. However that value shrinks at the rate of inflation increases, long after the big rip destroys all baryon matter around us the only objects that would still exists would be black holes. As the rate of inflation continues to increase eventually the particle horizon and the cosmic horizon approach the boundary of the event horizon of the black hole, and then at some point that rate of expansion exceeds it. This would not immediately result in the black hole tearing itself apart, the rate of inflation still needs to exceed the limit of the gravity. Eventually there will come a point where the rate of inflation hits a tipping point where the singularity is torn apart. As the rate of expansion initially exceeds the speed of light matter a new universe is born as a new dimension of time starts in the new region of space. This new chronology would process similar to our universe but may have different physics. We have no way of knowing at this point.
Well... yes and no. It is confusing, no doubt about it, but in an 'eternal inflation' picture it's practical to start the big bang at the false vacuum collapse.
Not precisely correct, no; there certainly was time before inflation ended, and there may even have been something equivalent to a traditional big bang, but our bubble universe started right then.
Buying Bitcoin right now involves speculating that others will also see this potential, which is why it’s accurate to describe it for the moment as a speculative asset. The reason buying Bitcoin is a smart bet is that its monetary properties are so good that it has the potential to store a significant percentage of the world’s savings. Once that happens, its volatility will be much lower, so it will be a good store of value. And of course its purchasing power in current U.S. dollars will be much, much higher, which is why it’s a good idea to buy some now.