I’m trying to understand the mechanics here. I get that SpaceX and Nasdaq are in cahoots to get SpaceX bundled with a bunch of other stocks (and that bundle is called QQQ?)
But why must retail investors hold this bundle? If I’m holding now, I can sell it and buy a different bundle right? And if I’m not holding it now, I can just continue not to buy it after SpaceX gets included.
There's trillions of dollars sitting in indexes that are quite literally 'passively' invested. Virtually everything holds this bundle in one way or another. Passive indexing has both outperformed and overtaken active investing - leading a lot of money into VOO/VTI/QQQ/etc that track the S&P500 or some other index ("the market"). For retirement funds like 401ks, retail contributes money every paycheck that gets routed into these indexes. There may not even be much of a choice - your 'plan' may only let you pick some kind of "Target Date Fund" and then the institution picks what it goes into, usually indexes.
If you fully actively managed your own money and picked mostly individual stocks (not broad indexes) then yeah you could change your allocations. But there's a lot of money already in.
QQQ is problematic because it’s influenced by strange back room dealings with Space X, if the article is to be believed.
VTI is different. It literally tracks all public stocks, weighted by market cap so no such manipulation is possible.
If a bunch of people will be forced to buy Space X (QQQ holders), active investors will short the stock in anticipation of market correction and money will flow from those who were forced to buy. I’m sure there are other ways to take advantage of a forced buyer situation.
Total market will be unaffected, assuming efficient market hypothesis / no arbitrage.
QQQ is not in isolation. It’s just a bundle of stocks. Rebalancing that will affect the prices of its constituent stocks, which include some of the highest market cap stocks. Those same stocks are also in many of those other popular market-cap weighted indexes (VTI, VOO, SPY, etc). Price action originating from Nasdaq 100 rebalancing would affect everywhere else those stocks are held. Which is a lot of places.
Except those other indexes won’t have SpaceX. Suggesting any index price moves would be … asymmetric at best.
Now it’s being reported that they’re angling to get SpaceX in the S&P 500 index as well [1]. Maybe if all the indexes get it then it balances out everywhere, who knows. This whole event would be in beyond unprecedented territory.
Are you saying that this forced rebalancing will be large enough to cause a large price drop on other stocks?
Let’s just think about any stock in particular, eg stock ABC. If I am an active investor, I have an opinion on ABC and its net present value. When ABC dips below that value, I buy. Wouldn’t I prepare some cash in anticipation of this large ABC sell off at discounted prices? And thus the ABC price would not move from its fair price.
Bingo. No sane investor holds QQQ because there is no academic theory behind why it should exist. Why is a stock better if it's listed on NASDAQ instead of NYSE? Can any investor answer this question? Doubt it. If you are into factor investing and you like large cap growth, you buy something like VUG. Most people should just stick with SP500 or total market.
However, QQQ had a really good last 15 years and lots of investors hold it because they are chasing returns and because the marketing worked. (The managers of QQQ are legally obligated to spend X% of the fees collected on advertising the ETF, ha ha ha.)
Yeah, I had a milk-up-the-nose moment when I read that Brandolini's Law atomic bomb. I swear when anything finance appears as a topic on HN, the amount of bullshit/misinformation far exceeds the good stuff.
> Why is a stock better if it's listed on NASDAQ instead of NYSE?
The NASDAQ is a stock exchange based in the United States. It’s made up of around 3,500 companies, with a heavy weighting towards companies in the information technology sector.
> If you are into factor investing and you like large cap growth
If you are into factor investing and like large cap tech, you buy something like QQQ.
> No sane investor holds QQQ
The insane can take comfort in their 20% CAGR for the last 10 years on a massive large cap tech expansion.
Yes, you can sell and buy a different index. However, those who buy ETFs want broad market exposure without picking stocks (or ETFs). Also selling and re-buying means you have to pay taxes now - depending on jurisdiction, that is way worse than holding till you are retired and then selling.
SpaceX/Nasdaq want to distort the rules to make more money off the backs of those passive investors.
I also seem to be developing an immune response to several slopisms. But the actual content is useful for outlining tradeoffs if you’re needing to make your Python code go faster.
> Missing @cython.cdivision(True) inserts a zero-division check before every floating-point divide in the inner loop. Millions of branches that are never taken.
I thought never taken branches were essentially free. Does this mean something in the loop is messing with the branch predictor?
They're cheap but not free, especially at the front end of the CPU where it's just a lot more instructions to churn through. What the branch predictor gets you is it turns branches, which would normally cause a pipeline bubble, to be executed like straightline code if they're predicted right. It's a bit like a tracing jit. But you will still have a bunch of extra instructions to, like, compute the branch predicate.
Worse, IMO, is the never taken branch taking up space in branch prediction buffers. Which will cause worse predictions elsewhere (when this branch ip collides with a legitimate ip). Unless I missed a subtlety and never taken branches don’t get assigned any resources until they are taken (which would be pretty smart actually).
From when I was working on optimizing one or two things with Cython years ago, it wasn’t per-se the branch cost that hurt: it was impeding the compiler from various loop optimisations, potentially being the impediment from going all the way to auto-vectorisation.
Yeah if your program has a natural notion of a "frame" (eg most video games), you can do memory management by simply incrementing an integer (bump allocation). At the end of your frame, you reset the integer to zero. You can't really get any faster than that.
An additional benefit of this style of allocation over malloc/free is that you can get a lot of the same type of objects contiguous in memory so that iteration over them is a lot faster because there are fewer cache misses.
Like what you mean when you say “frames per second” in a video game. The image that is finally presented to the user, and then quickly thrown away and rebuilt, again and again to give the illusion of motion.
> Before their papers, mathematicians had assumed that even though the number line might look like a continuous object, if you zoomed in far enough, you’d eventually find gaps.
I'll try to interpret this sentence.
We all have some mental imagery that comes to mind when we think about the number line. Before Cantor and Dedekind, this image was usually a series of infinitely many dots, arranged along a horizontal line. Each dot corresponds to some quantity like sqrt(2), pi, that arises from mathematical manipulation of equations or geometric figures. If we ever find a gap between two dots, we can think of a new dot to place between them (an easy way is to take their average). However, we will also be adding two new gaps. So this mental image also has infinitely many gaps.
Dedekind and Cantor figured out a way to fill all the gaps simultaneously instead of dot by dot. This method created a new sort of infinity that mathematicians were unfamiliar with, and it was vastly larger than the gappy sort of infinity they were used to picturing.
We've known since Zeno that all of our ways of visualizing infinity in finite terms are incomplete and provably incorrect, despite being unavoidable in human thinking. In other words, we knew the "gaps" reflected incomplete reasoning, not real emptiness between "consecutive" numbers. If Dedekind and Cantor only changed how we visualize infinity, I don't understand why it would cause a stir.
> This method created a new sort of infinity that mathematicians were unfamiliar with, and it was vastly larger
I understand that the construction of the reals paved the way for the later revolutionary (and possibly disturbing, for people with strongly held philosophical beliefs about infinity) discovery that one infinity could be larger than another. But in the narrative laid out by the article, that comes later, and to me it's clear (unless I misread it) that the part I quoted is about the construction of the reals, before they worked out ways to compare the cardinality of the reals to the cardinality of the integers and the rationals.
"Knowing" something and proving it mathematically are two different beasts.
Zeno couldn't prove that there were no gaps; he showed that infinity was different from how we understood finite things, bit that's not the same as proving there are no gaps.
Later, mathematicians proved the existence of irrational numbers. These were "gaps" in the rational numbers, but they weren't all the "same" of that makes sense? The square root of 2 and Euler's number are both irrational, but it's not immediately clear how you'd make a set that includes all the numbers like that.
I'm not sure everyone knew that gaps reflected incorrect reasoning. It would have been natural to assume that all infinite sets were qualitatively the same size, since uncountable infinity was not an idea that had been discovered yet. Zeno's own resolution wasn't that his reasoning wrong, but that our perception of the world itself is wrong and the world is static and unchanging.
As for the importance of visualization (of the reals), I don't think you can cleanly separate it from formalism (as constructed in set theory).
I think we all have built in pre-mathematical notions of concepts like number, point, and line. For some, the purpose of mathematics is to reify these pre-mathematical ideas into concrete formalism. These formalisms clarify our mental pictures, so that we can make deeper investigations without being led astray by confused intuitions. Zeno could not take his analysis further, because his mental imagery was not detailed enough.
From clarity we gain the ability to formalize even more of our pre-mathematical notions like infinitesimal, connectedness, and even computation. And so we have a feedback loop of visualization, formalism, visualization.
I think the article was saying that Dedekind and Cantor clarified what we should mean when we talk about the number line, and dispelled confusions that existed before then.
> If Dedekind and Cantor only changed how we visualize infinity, I don't understand why it would cause a stir.
Because scientific progress is explicitly the process of changing the general mental model of how people approach a problem with a more broadly capable and repeatable set of operations
I should have been more specific; I understand why it was a mathematical breakthrough. What I don't understand is why it would have triggered some kind of psychological horror or philosophical crisis. It was a new way of understanding numbers, but it didn't reveal numbers to be acting any differently than we had always assumed.
If anything, it seems like it would have been comforting to finally have mathematical constructions of the real numbers. It had been disturbing that our previous attempts, the rational and algebraic numbers, were known to be insufficient. The construction of the reals finally succeeded where previous attempts had failed.
I would invite you to be more open to the idea that people don’t live in a world where they operate inside a theoretical framework with localized test actions
major breakthroughs tend to cause existential crises because most people don’t have full scope of their work in order to understand where it is broken
Because painting those who objected to these definitions of mathematical infinity as "horrified" and "disturbed" was a form of character assassination, which was not uncommon at the time. The high moderns didn't play.
Extraordinary claims require extraordinary evidence. Can you cite any claims by mathematicians that there were "gaps"? It isn't even true for rational numbers that you can identify an unoccupied "gap".
Yeah, it took me a second, too. By "gaps" they mean numbers that can't be represented in a given construction. So irrational numbers are "gaps" in the rational numbers, and transcendental numbers are "gaps" in the algebraic numbers. Not the best spatial metaphor.
You’re thinking of this with the benefit of dedekind in your schooling - whether or not your calculus class told you about him.
Density - a gapless number line - was neither obvious nor easy to prove; the construction is usually elided even in most undergraduate calculus unless you take actual calculus “real analysis” courses.
The issue is this: for any given number you choose, I claim: you cannot tell me a number “touching” it. I can always find a number between your candidate and the first number. Ergo - the onus is on you to show that the number line is in fact continuous. What it looks like with the naive construction is something with an infinite number of holes.
I think you are getting away from my point, which pertains to what the article said, which is that mathematicians thought there were "gaps". What mathematician? Can I see the original quote?
The linguistic sleight-of-hand is what I challenge. What is this "gap" in which there are no numbers?
- A reader would naturally assume the word refers to a range. But if that is the meaning, then mathematicians never believed there were gaps between numbers.
- Or could "gap" refer to a single number, like sqrt(2)? If so, it obviously is not a gap without a number.
- Or does it refer to gaps between rational numbers? In other words, not all numbers are rational? Mathematicians did in fact believe this, from antiquity even ... but that remains true!
Regarding this naive construction you are referring to: did it precede set theory? What definition of "gap" would explain the article's treatment of it?
I don’t know the answers to all of your questions - but I believe you’d benefit from some mathematical history books around the formalization of the real analysis; I’m not the best person to give you that history.
A couple comments, though - first, all mathematics is linguistics and arguably it is all sleight of hand - that said the word “gaps” that you’ve rightly pointed out is vague is a journalists word standing in for a variety of concepts at different times.
The existence of the irrationals themselves were a secret in ancient greece - and hence known for thousands of years, but the structure of the irrationals has not been well understood until quite recently.
To talk precisely about these gaps, if you’re not a mathematical historian, you have to borrow terminology from the tools that were used to describe and formalize the irrationals -> if former concepts about the lines sound hand-wavy to you, it is because they WERE handwavy. And this handwaviness is about infinity as well, the two are intimately connected. In modern terms, the measure of the rationals across any subset of the (real) number line is zero - that is the meaning of the “gaps”. There is, between any two rationals, a great unending sea where if you were to choose a point completely at random, the odds of that point being another rational is zero.
EDIT: for a light but engaging read about topics like this, David Foster Wallace’s Everything and More is excellent.
I think you will agree that the bulk of your comment employs a post-set-theory nomenclature.
Regarding "if you were to choose a point completely at random, the odds of that point being another rational is zero", I ponder the question of how one might casually "choose" a value with infinite entropy.
Of course a contractor could not decide to unilaterally shut off their missile system, because that would be a contract violation.
A contractor may try to negotiate that unilateral shut off ability with the government, and the government should refuse those terms based on democratic principles, as Luckey said.
But suppose the contractor doesn’t want to give up that power. Is it okay for the government to not only reject the contract, but go a step further and label the contractor as a “supply chain risk?” It’s not clear that this part is still about upholding democratic principles. The term “supply chain risk” seems to have a very specific legal meaning. The government may not have the legal authority to make a supply chain risk designation in this case.
It sounds like the "supply chain risk" designation is just about anyone who works with the DoD not using them, so their code doesn't accidentally make it into any final products through some sub-sub-subcontractor. Since they've made it clear that they don't want to be a defense contractor (and accept the moral problems that go with it), the DoD is just making sure they don't inadvertently become one.
This really reminded me of the first part Flowers for Algernon. The main character undergoes a treatment which improves is intelligence and the story is narrated via a series of diary entries which become successively more fluent and sophisticated.
I read it decades ago, and from time to time I mention it to someone who has not read it and I end up telling them the story.. and I'm usually tearing up before getting to the end. Such a moving piece.
On the contrary, I think it demonstrates an inherent limit to the kind of tasks / datasets that human beings care about.
It's known that large neural networks can even memorize random data. The number of random datasets is unfathomably large, and the weight space of neural networks trained on random data would probably not live in a low dimensional subspace.
It's only the interesting-to-human datasets, as far as I know, that drive the neural network weights to a low dimensional subspace.
But why must retail investors hold this bundle? If I’m holding now, I can sell it and buy a different bundle right? And if I’m not holding it now, I can just continue not to buy it after SpaceX gets included.
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