Formerly u/CanadaPlus101 on Reddit.

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Cake day: June 12th, 2023

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  • Yeah, that was actually an awkward wording, sorry. What I meant is that given a non-continuous map from the natural numbers to the reals (or any other two sets with infinite but non-matching cardinality), there’s a way to prove it’s not bijective - often the diagonal argument.

    For anyone reading and curious, you take advantage of the fact you can choose an independent modification to the output value of the mapping for each input value. In this case, a common choice is the nth decimal digit of the real number corresponding to the input natural number n. By choosing the unused value for each digit - that is, making a new number that’s different from all the used numbers in that one place, at least - you construct a value that must be unused in the set of possible outputs, which is a contradiction (bijective means it’s a one-to-one pairing between the two ends).

    Actually, you can go even stronger, and do this for surjective functions. All bijective maps are surjective functions, but surjective functions are allowed to map two or more inputs to the same output as long as every input and output is still used. At that point, you literally just define “A is a smaller set than B” as meaning that you can’t surject A into B. It’s a definition that works for all finite quantities, so why not?









  • I mean, the idea of socialism has certainly seen setbacks since the end of the last century, hasn’t it? While gross inequality is still a huge problem, and I hope it will be solved somehow, the Lenin/Stalin version of socialism feels like it has basically lost.

    A good, quick read if you don’t want to dive into books is the article Why Public Property?

    I hadn’t seen this one before, thanks for that. There’s some great examples in here, on the subject of monopolies.

    This phenomenon only continues to be proven true over a century later. The United States today has a far greater concentration of industry than it did during Lenin’s analysis. The small business sector has also consistently been on the decline. This is an observable reality. [Accompanied by a graph]

    Monopolies and particularly oligopolies are having a moment, but the chart only goes back to the 70’s, and implicitly shows total company number going up (why is hard to say, it’s a paywalled article, and they mixed data from two other sources). If you go back further, I think it would look pretty different - the old gilded age ended, Standard Oil was broken up, and some of the giants of the postwar era got knocked down a peg or more. Further, the trend is pretty uneven by sector. Mom and pop shops are dead now, but independently owned franchises and publicly traded whatevers are hella dominant, and contractors (or “contractors”) are everywhere.

    A clear modern example of this would be the smartphone industry. Competition has made cellphone manufacturing more and more complex over time. A cellphone these days is far too complex to be created by a small business. One requires access to enormous factories, machines, and supply chains. According to The Wealth Record, “the net worth of Samsung is pegged at $295 billion.” This is roughly the amount of capital one would need to acquire to even begin to be a serious competitor to Samsung.

    I actually know quite a bit about semiconductor manufacturing. It may be the most capital intensive endeavor of all, but you don’t quite need to be Samsung to do it. If you want to build your own at scale, a fab might be “only” a billion dollars. That’s a lot, but many startups have raised it (for other things), so it’s a different story from being Samsung on day 1.

    If you just want your chip design made, it’s way easier. TSMC exists to build other people’s designs. Companies like Sam Zeloof’s new enterprise exist for small scale printing of your prototypes. Most of the basic design tools can be found open source.

    The network effect has made some genuine monopolies and definitely many oligopolies, but other things are less affected. Individual rich people get rich by chance (if you don’t mind me introducing my own source, which happens to be my favourite one).

    All this to say, I don’t think concentration is going to kill capitalism in the near future, or even come close.


    It is easy to look backwards at prior systems, such as the feudal economic system or the slave economic system, and then figure out how that system developed into the system afterwards. Adam Smith, for example, already explained in detail in his book Wealth of Nations how capitalism developed out of feudalism long before Marx.

    It’s a tangent, so I’ve separated this out, but this is also an interesting claim. The end of feudal economics is an actively researched bit of history, and was far from neat and tidy. IIRC some of those old fealty-type agreements lasted into Marx’s time, if being mere formalities by their end. And I’m not sure why we (correctly) decided slavery was bad after doing it since before recorded history, either.