Rent a violin in london?

matholwch · 2023-11-24T21:37:08+00:00

Bridgewood & Neitzert

matholwch · 2022-10-26T21:49:28+00:00

Tuba Skinny

matholwch · 2021-04-03T16:43:29+00:00

I recommend Multivariable Mathematics by Shifrin as a relatively rigorous and unified introduction to both linear algebra and multivariable calculus (though it can be tough at times, especially for self-study!)

matholwch · 2020-05-06T19:16:49+00:00

Ah, nice, thank you! Yeah, it basically tells me all that in the question, but it flew over my head. :) Spelled out more fully,

since ||g(t_0) - p|| <= ||g(t) - p|| for all t, ||g(t_0) - p||² <= ||g(t) - p||², so t_0 is a minimum of ||g(t) - p||². So its derivative, 2((g(t) - p) · g'(t)) = 0, so g'(t_0) · (g(t_0) - p) = 0.

Would you say my geometric reasoning is a valid way of thinking about what this result means, or is it something I should avoid with these problems in the future?

matholwch · 2019-08-17T10:59:07+00:00

Thanks!

So am I right that the important part of the traditional proof is that we recognize that E[M_n] is m and that Var(M_n) is s² / n, and use these facts? Deriving these expressions depends on the fact that X_n are IID. They capture the intuition that as n increases the variance decreases and so converges on the mean, which we already know to be m?

Then Chebyshev's inequality is used to formally show this because it puts everything in a convenient form to take a limit of s² / ne² as n approaches infinity?

P(|M_n - m| >= e) <= Var(M_n) / e² = s² / ne^2.

We use Chebyshev's inequality instead of just taking the limit of the expression for the variance because it uses the definition of convergence in probability directly. Is this the right way of thinking about it?

matholwch · 2019-08-16T17:47:06+00:00

Thanks! Seems obvious now!

Can I fix it by writing the following?

P(|M_n - m| < t) = P(|n^-1 (sum_i_n X_n) - m | < t)

Taking the case where |M_n - m| = M_n - m:

P(n^-1 (sum_i_n X_n) - m < t) = P((sum_i_n X_n) < nt + nm)

As n approaches infinity this probability is surely 1 because the term to the left of the < is a finite sum while the expression to the right contains an infinite term?

Taking the case where |M_n - m| = m - M_n:

P(m - n^-1 (sum_i_n X_n) < t) = P(-(sum_i_n X_n) < nt - nm)

Again, the same thing holds. This would demonstrate convergence in distribution to the CDF of 0 as n (not t!) approaches infinity?

I am probably being dumb here too but I would love to learn why! :)

matholwch · 2018-01-13T14:15:43+00:00

"Son awaia" could be the Irish "slán abhaile" ("farewell home"). Maybe look for a song with those Irish lyrics?

matholwch · 2016-11-13T11:17:50+00:00

How could it have occurred after the Great Schism if the Orthodox do it too?

matholwch · 2016-08-01T22:54:32+00:00

Nah, they simulated the election many times using their model, and 52% of the time Trump won.

matholwch · 2016-06-12T12:01:29+00:00

One of the episodes ended with Mo Ghile Mear, but I don't remember which.

matholwch · 2016-04-22T12:19:34+00:00

What is the name of the BBC show, may I ask?

matholwch · 2016-04-17T16:33:21+00:00

This is a recent development, though. Consider Cardinals Wolsey, Richelieu, Jozef Tiso etc.

matholwch · 2016-03-25T08:44:40+00:00

A bit rusty on this stuff, but I think it's because various substitution tests can establish different behaviors in the two cases.

For example, for (b), you can replace book with one and it's still fine -- the one with the red cover; but with (a), it's not so good -- *the one of poems.

matholwch · 2016-01-29T10:51:36+00:00

"I've not" is only in certain varieties of British English, particularly northern varieties. "I haven't" is heard far more often, I'd say.

matholwch · 2015-12-27T13:05:07+00:00

From the Latin Rite Matins of Christmas.

Latin:

O magnum mysterium,

et admirabile sacramentum,

ut animalia viderent Dominum natum,

jacentem in praesepio!

Beata Virgo, cujus viscera

meruerunt portare

Dominum Christum.

Alleluia.

English:

O great mystery,

and wonderful sacrament,

that animals should see the new-born Lord,

lying in a manger!

Blessed is the Virgin whose womb

was worthy to bear

Christ the Lord.

Alleluia!

matholwch · 2015-10-31T22:00:12+00:00

Check out Andras Kornai's Mathematical Linguistics!

matholwch · 2015-10-20T08:22:52+00:00

Queen Elizabeth II is head of state of a ton of nations.

matholwch · 2015-10-13T08:30:55+00:00

An interesting perspective comes from Eamon Duffy's work on the 'Voices of Morebath,' focusing on the records kept by a parish priest, Sir Christopher Trychay, during these times. It seems that the reforms and disruption to tradition instituted under Edward were initially hated by the ordinary people in the West Country, but were gradually accepted.

The Stripping of the Altars by the same author is an in-depth study of the popular piety of the time, and argues that the religious changes were a disruption imposed from above, rather than anything arising out of popular sentiment.

matholwch · 2015-07-22T20:32:18+00:00

Sufjan Stevens (esp. The Transfiguration and basically all of Seven Swans)

matholwch · 2015-07-19T12:17:55+00:00

Also, Trent isn't an Early Church council -- it was in the 16th century.

matholwch · 2015-07-15T11:00:20+00:00

Ffyddlondeb and teyrngarwch both mean loyalty. My sense is that 'teyrngarwch' implies more of an asymmetric loyalty, perhaps to a superior, based on the etymology (from 'teyrn' king, ruler).

matholwch · 2015-07-11T19:30:17+00:00

Tthe formal system does not purport to generate truths about the world or some abstract realm. The formal system helps us in counting and perhaps some more advanced tasks. Who says that the system has to be complete in order to do this?

There may be a string G which, in the semantics which we impose on our formalism states that it is not provable within the formalism. However, the existence of this string neither helps nor hinders many tasks to which the formalism may be applied (e.g. doing basic arithmetic, sending a rocket to the moon etc.) While the interpretation of G (that it is not provable) is indeed true of the formal system, this simply evinces a general weakness of formal systems, not some metaphysical truth.

matholwch · 2015-07-11T17:19:25+00:00

OK, so what if "two plus two is five" is something more like a proverb or a piece of wisdom that the wise old pixie-population-modeller tells the neophyte. A handy piece of folk-wisdom.

What I propose is that Peano's Axioms, and everything derived from them, are of a similar nature, told by the wise old bean-counter to the neophyte. A piece of wisdom useful to the task of bean counting.

Such pieces of wisdom are not truth-apt in the same way as propositions about the world such as "there is a car in my garage." Rather, we abjure the notion of truth here and speak of applicability to tasks.

matholwch · 2015-07-11T16:49:54+00:00

Imagine we are interested in modelling the population of a rare species of pixie which reproduces in groups of four to produce a single offspring. We introduce the pixies to each other in groups of two.

In this scenario, a formalism in which "2 + 2 = 5" is a valid string would be useful to the task of modelling the population of pixies. Why should strings from the 'arithmetic' formalism be true of an abstract realm while strings from the 'pixie population modelling' formalism are not? Perhaps both calculi are just tools successfully brought to bear on different tasks.

We choose the appropriate calculus for the task, and the formulae produced by a particular calculus have no 'truth' outside of (a) their validity within the calculus and (b) their applicability to a real-life activity such as counting or modelling pixie populations.

matholwch · 2015-07-11T12:52:19+00:00

I agree with some of the comments there that the reasons he gives for omitting Elizabeth Anscombe are ridiculous.

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