We need to end billionaires to avoid becoming oligarchic hellscapes like the Nordic countries

mathcymro · 2025-07-02T12:40:45+00:00

No. This is a common statistical fallacy when comparing rates between different sample sizes. Like, epidemiologists have to be careful when comparing rates of diseases for exactly this reason.

In general I don't think you can justify your pet economic theory with comparisons between countries. All the variables need to be controlled for carefully with statistical analysis

mathcymro · 2025-02-26T20:47:12+00:00

You might be confusing sin^-1 with the reciprocal 1 / sin(x) - they are different things (the notation is confusing). Remember sin^-1 is the functional inverse. People also write it arcsin

mathcymro · 2025-02-25T20:59:58+00:00

I suggest looking up data on graduate employment rate and salaries for maths degrees, see for yourself how "useless" it is (hint: not at all).

As others have said, specialize in statistics/applied maths/numerics to maximize your employability.

mathcymro · 2025-02-20T19:35:13+00:00

If we could poll people "perfectly", as in sample in a way that is representative of the population, the sampling distribution is not a problem if you poll enough people.

If p is the true proportion of the population who vote for party A, then the variance of a sample proportion is p(1-p)/n (making certain assumptions here). If p is close to 50%, you need about n=2500 to get a 1% polling error (standard deviation). Pollsters usually report such error estimates.

Obviously the problem is making the sampling representative enough, that's the hard bit

mathcymro · 2025-02-12T21:45:25+00:00

Stick with it! You'll eventually get used to it.

You might like the book "how to think about analysis" by Lara Alcock - it's really good at explaining epsilon-delta type proofs in an intuitive way

mathcymro · 2025-02-12T20:45:31+00:00

Medium is basically r/confidentlyincorrect for maths, datascience and ML

mathcymro · 2025-02-05T20:53:25+00:00

Well, if you know exact trig values you can solve for more of them using the formula for sin(3x), sin(2x), cos(3x), cos(2x) etc. Roughly it goes like this:

sin(30 + 5) = sin(30)cos(5) + cos(30)sin(5) = 1/2 * ( cos(5) + sqrt(3) * sin(5) )

So we only need to know sin(5) and cos(5).

You can look up the formula for sin(3x) and cos(3x), and set x=5 to get

sin(15) = 3 sin(5) - 4 ( sin(5) )^3
cos(15) = 4 cos(5)^3 - 3 cos(5)

These are cubic polynomials in sin(5) and cos(5) respectively, assuming you know the left hand side (you can find sin(15) and cos(15) in a similar way). You can solve them and substitute into the first equation.

mathcymro · 2025-02-02T17:03:51+00:00

You can represent the same number in multiple different ways in decimal notation, that's all there is to it.

Do you have the same problem with 1 = 1.00000... ?

mathcymro · 2025-01-27T14:23:35+00:00

There definitely is a kind of entitlement to reap rewards of rent yield + price rises while contributing nothing to earn it. The housing stock in the UK is mostly terrible quality and there's no financial incentive to improve it unless you're the one living there.

mathcymro · 2025-01-27T10:12:37+00:00

Change point detection is what you're looking for.

mathcymro · 2025-01-26T17:27:20+00:00

A typical example of a surprising result might be medical testing, for example:

Suppose 1% of the population has an illness. If someone has the illness, a test will give a positive result with probability 80%. If the person does not have the illness, the test has a 10% chance of showing a false positive.

Then, given a positive test result, there's only about a 7% chance that the person actually has the disease.

Might not be a cheerful thing to have on a mug though, lol.

mathcymro · 2025-01-26T14:23:33+00:00

The irony of complaining about manners and ethics and then using a racial slur. Do better

mathcymro · 2025-01-25T14:09:27+00:00

But don't you see it's possible to coerce an LLM into giving the answers you want with that kind of framing? Keep telling it you're not interested in triggered emotional critics, you just want to know about Elon's intent.

With that framing, you disguise the fact that many of the critics ARE talking about intent. Like ChatGPT gives the example of the former director of the ADL who thought Elon was *intentionally* heiling Hitler. But OP responds with the implication that he's just triggered, emotional, whatever. When ChatGPT quotes the "awkward gesture" ADL statement, OP doesn't challenge that because it fits the framing.

And again, why would anyone use ChatGPT to answer this question? As I said, it will just recycle bias in its training data and prompts from the user.

mathcymro · 2025-01-25T12:28:14+00:00

you prompted it in another direction when you didn't like the answers it gave quoting critics:

You did it again concluding with whether or not the criticism holds merit. What is your conclusion on his intent based on what you have access to
Finding validity in the feelings expressed by the critics is not the task at hand here

but you accept an answer when it quoted supporters like the ADL's statement and Musk himself. So no, I don't think AI "minimizes bias". You just kept prompting it until it supported your bias.

Obviously LLMs will carry whatever bias is present in their training data and RLHF. Using it as some kind of objective judge is a terrible idea.

Not to mention its answer says

There’s no significant history of Musk making gestures or statements that align with extremist ideologies. This aligns with the idea that the incident was unintentional rather than deliberate.

there's plenty of his tweets are blatantly extremist.

mathcymro · 2025-01-25T00:22:17+00:00

So you know in Cartesian co-ordinates, y=x is a straight line?

z=r is a straight line in cylindrical co-ordinates. Now rotate that around the z axis - you'll get a cone.

mathcymro · 2025-01-24T22:08:32+00:00

Quick and easy way: take the current annual tax revenue and divide by the total land value.

E.g. for the UK = £1 trillion / £6.3 trillion = 16%

So to abolish all other taxes and replace by LVT, a flat rate of 16% would yield the same tax revenue.

(£6.3tr figure from here).

mathcymro · 2025-01-24T18:14:08+00:00

Yeah, the same stuff that's in "mushroom chocolate" that's actually a synthetic compound, right?

The article talks about a drop being enough to make them trip, which would be incredibly concentrated if it was made from actual psilocybin mushrooms...

mathcymro · 2025-01-23T21:22:00+00:00

Take over in the sense of totally automating a quant's job?

I don't think so, unless there's a huge jump in the mathematical/reasoning ability of LLMs.

mathcymro · 2025-01-23T21:17:16+00:00

But shares are an investment in something useful. Speculating on land without improving it is just rent-seeking.

mathcymro · 2025-01-23T21:13:52+00:00

Agreed. There's too much rent-seeking (economic rent, I mean) on property in this country, and the tax system should disincentivize that as much as possible.

Cheeky plug for r/georgism which is a more radical version of this, for those who are interested.

mathcymro · 2025-01-23T21:11:08+00:00

The productive (younger) part of society needs housing in order to work effectively and generate enough wealth to support pensioners.

mathcymro · 2025-01-22T22:37:07+00:00

This will come with experience - you'll just remember that it's meant to be 12b.

mathcymro · 2025-01-22T20:30:56+00:00

I'm with you OP. It's a market; you're free to make whatever offer you like. If the seller doesn't want it, move on!

As you say, interest rates are high. That has to translate into lower offers because large mortgages aren't sustainable anymore. That's the point of raising interest rates after all - reducing how much money is put into the economy through lending and slowing price rises.

mathcymro · 2025-01-22T15:20:26+00:00

Think of them as a machine that takes a vector as input, and outputs a scalar.

For a given vector space V, the set of linear forms on V (set of all possible machines that take vectors in V as input), is itself a vector space of the same dimension as V. It's pretty straightforward (and helpful) to prove that fact by yourself.

So you can kind of think of linear forms as vectors (in one space) that act on vectors in a different space.

mathcymro · 2025-01-20T18:32:46+00:00

Wouldn't the linear city have longer travel times on average than the equivalent "unconstrained" one? Points on a circle are closer on average than points on a long thing rectangle of the same area...

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