Kranar

A computable real number is a real number for which a Turing Machine exists that can compute it to any arbitrary precision.

So yes sqrt(2) is computable.

Every BB(n) is computable since every every natutal number can be computed. It's the BB function itself that is not computable in general, not the specific output of that function for a given input.

There is no black hole that is a perfect sphere. That would, at a minimum, require a body with absolutely no angular momentum which isn't in anyway feasible.

Any rotating/spinning black hole will no longer be a perfect sphere.

You don't need the full set of real numbers to do physics, only the computable subset of the real numbers. Using the full reals is mostly done out of simplicity.

Yeah this is a fairly poor article by an otherwise amazing blogger.

With that said the point stands that the likelihood of sending bitcoin to an unintended address due to a typo is very small. It's not as small as the article suggests, but it's still basically impossible (about 1 in 4.3 billion for a single character typo).

Perhaps the irony is that if you do happen to send bitcoin to an unintended address, you have a much greater chance of recovering it if that address belongs to a real person and is in use. If the address is not in use, then for all intents and purposes that bitcoin is lost forever.

If you see "i++" in code and you don't have any context about what "i" is, then what difference does it make if "i" is a member variable, global variable, parameter, etc etc...

If all you see in code is a very tiny 3 character expression, you won't be able to make much of a judgement about it to begin with.

The objection, which I agree with, is to the statement "Any method that works for some programs will fail for others, and in some cases, no method will work."

There is no case where no method whatsoever will work. It's true that for any method, there are cases where it fails but it's not true that there exist cases for which every method fails.

Options exist with no expiration date, but they are not commonly traded. There's nothing in principle unusual about them, at least not more so than most other derivatives.

Perpetual options are a thing, although not mainstream.

No being honest does not mean that and had you said that I'd have no basis upon which to object to your comment.

You refuted an argument about being honest about accepting an award on the basis that the award pays a lot of money and grants one a great deal of popularity.

If your argument didn't involve money and popularity, then why did you choose those two specific criteria as the justification for accepting this award?

I want to be clear, I am not claiming that Dr. Hinton accepted the award in a dishonest manner or that he did it for money, I am simply refuting your position that money is a valid reason to disregard honesty for accepting a prestigious award.

It's not at all obvious, as the article points out it was assumed for 40 years that backpropagation was not an efficient approach for training neural networks.

The argument had to do with honesty while your justification is that money and popularity are worth more than being honest.

Now perhaps Hinton does deserve the award, but certainly it should not be because of the reasons you cite: money and popularity.

The government gets billions back in savings from SpaceX.

The definitions provided appear as though they are constructive, but they are not actually constructive, they are set-theoretic existence claims that quantify over all sequences, in particular over undefinable sets. Specifically, the description that appears constructive doesn't actually define any particular real number, it only defines the universe in which the real numbers live.

Another subtle detail is that while it's true that every real number corresponds to (and can be represented by) a Cauchy sequence of rationals, the very sequence itself might be undefinable.

>When your reviews get removed because the company paid them, you’re just being shown what the company wants you to see.

Glassdoor does not remove reviews for payment.

I think it's the other way around. Tail recursion is a special case of loops. All tail recursive functions can be rewritten as a loop but there exist loops that can not be rewritten as a tail recursive function.

I won't elaborate too much, but consider a situation where the vast majority of of participants just bought a basket of diversified index funds and what the effect would be on the stock market... it would effectively entrench existing companies at their current levels. Regardless of whether Apple or Microsoft or whoever is profitable or not profitable, their relative market cap would basically remain static since people are not buying stocks on the basis of performance but simply buying stocks on the basis of their relative market cap as it existed at some moment in time.

Index funds work because not everyone buys them, they work because the majority of capital is allocated and constantly being rebalanced in a way that tries to reflect the performance of a corporation. It's only in this circumstance that an index fund, or any kind of passive investment, can be of any utility by leveraging the work of those who are actively trying to assess the genuine value of a corporation.

There are good public resources but they are expensive. One of the best resources for learning in depth quantitative techniques that is actually legit as opposed to Youtubers telling you how to squint to see patterns in a bar chart is the ARPM, which provides both a week long course and a year long course:

https://www.arpm.co/

It is a very math heavy course, highly technical and requires a great deal of existing math background. But the truth is that you will not be able to do much quantitative finance without that background anyways, so if what you want is a way to gain that math background then just crack open a textbook and get working.

None of those names have a ligature. Infact Renées is a "deligatured" spelling of Renæes which would be incredibly rare.

You just accept raw strings without doing any kind of validation? The step that performs validation should encode that step in the form of a type.

It's nice that you feel that having one LLM that generates entirely incorrect statements is equally as functional as an LLM that does not, but reality in terms of what LLMs people will actually use in real life and not for the sake of being pedantic over an Internet argument is very much at odds with your sentiment.

How a product happens to currently be implemented using current machine learning techniques is not the same as the set of features that such a product offers and it's absolutely the case that actual researches in this field, those who are not quibbling on the Internet, do take this issue very seriously and devote a great deal of effort towards improving it because they actually care to implement possible solutions.

The feature set, what the product is intended to do based on the motivations of both those who created it and those who consume it, is a broader design/specification goal, independent of how it's technically built.

Being accurate is a feature and it is a bug that can be fixed though.

Given various models, one that always produces statements that are false and another that only sometimes produces false statements, the latter model is preferable and the model which most people intend to use, hence the degree to which a model produces correct statements is absolutely a feature.

And yes, it's absolutely possible to systematically produce models that make fewer and fewer incorrect statements.

Millions of people don't use Go either.

Erlang does not implement CSP, and if you review the very Wikipedia link you presented it should be clear. Erlang implements the Actor model, which is more flexible for distributed, fault-tolerant systems, but lacks CSP's strict formalism and synchronization semantics. The very Wikipedia article you linked to has an entire section on how CSP differs from the Actor model. Similarly Go also does not implement CSP either, although it certainly is influenced by it.

The point of my comment is that to say that Go is basically Erlang style CSP without the weird syntax is not justified as an actual quote nor as a paraphrasing or summary of anything that anyone involved in the design or promotion of Go has ever said. It's best to reserve quotes for situations where someone actually said something or as a way to summarize something for which there are ample references available.

One should not use quotes as a way to present mostly original claims that are presented as if it's some kind of already well established knowledge.

I can't substantiate your claim about Erlang or weird syntax, is that either a proper quote or some kind of paraphrasing because nothing remotely close to it comes up.

There are numerous interviews with Rob Pike about the design of Go from when Go was still being developed, and Erlang doesn't come up in anything that I can find other than this interview from 2010 where someone asks Rob Pike a question involving Erlang and Rob replies by saying he thinks the two languages have a different approach to are fairly different:

https://www.youtube.com/watch?v=3DtUzH3zoFo

It's at the 32 minute mark, but once again this is in response to someone asking a question.

Here are other interviews about Go, and once again in almost every interview I'd say Rob kind of insinuates he was motivated by a dislike of using C++ within Google to write highly parallel services, but not once is Erlang ever mentioned:

https://www.informit.com/articles/article.aspx?p=1623555

https://www.infoq.com/interviews/pike-google-go

https://go.dev/blog/waza-talk

What are they building?

SQLite is a great database for organizing data in desktop applications, including both productivity software and even video games. It's certainly not at all unreasonable for those use cases to have files that are in the low GB and I would much rather use SQLite to process that data instead of bundling MySQL or Postgres into my application.

Yes that's true the terms are confusing but nevertheless it's important. For example having read through some of this book it's still not clear if this book involves parallelism, especially since the book compares itself to Python, which does not involve parallelism without running C extensions.

Yes that's true and I was wrong to say otherwise. A data race can happen with preemptive multithreading on data whose size exceeds what the platform guarantees to access atomically, typically the word size.

A more accurate statement would be that parallelism introduces additional possibilities for data races than those possible from concurrent execution (without parallelism).

Data races are not possible on a single core system.

Parallelism introduces additional hazards such as data races, which are not present in concurrent code that lacks parallelism.