ocfnash

Great point, I agree!

It seems to me that the statement that Wu's experiment holds globally is equivalent to the statement that the universe has an orientation so I now tend to think the universe does not admit one of these orientation-reversing loops.

At first I was surprised that we could apparently draw a global conclusion based on local observations but I've mostly convinced myself now based on the following analogy (which I hope is not misleading).

Imagine we live in a two-dimensional universe and we want to know whether or not it is orientable. E.g., do we live on the surface of a torus or on the surface of a Klein bottle? We have defined a local orientation in the topologically-trivial patch where we live and so are used to speaking of "left-handed" and "right-handed" gloves. The question of whether these words are globally meaningful is exactly the question of whether our universe is orientable.

One day we learn about "colour" and are stunned to discover that all left-handed gloves are red and all right-handed gloves are blue. It seems very unlikely to us that red somehow transitions into blue as we traverse a loop and so we conclude we must live in an orientable universe.

Good question, but no. For example the Klein bottle or real projective plane are closed surfaces containing no boundary.

Incidentally the Mobius strip need not have a edge; you can leave out the boundary circle at the cost of having a non-compact space. This is exactly analogous to the difference between the closed and open intervals: [0, 1] vs (0, 1).

In fact the projective plane can be obtained by taking a disc and glueing its boundary to that of the Mobius strip, which makes the two boundaries "cancel".

I believe it is possible that our universe is not orientable, and so there may exist closed paths which, if followed, reverse orientation upon returning to the starting point. If you were right-handed and traversed such a loop, you would now be left-handed relative to everyone else, everyone would agree your heart was on the "right" side of your body etc.

In fact even Atiyah touches on this idea (though without speculating that it might be a property of our universe). In Mind, Matter and Mathematics, he says:

"When I was a student in Cambridge our mathematical society invited a distinguished professor of philosophy, C.D. Broad, to give us an evening lecture. He chose to talk on a problem which had much exercised Kant, the difference between right-handed gloves and left-handed gloves. After the lecture, over dinner, I diffidently suggested to Broad that, since Kant’s time, we mathematicians had a much better understanding of “handedness”, or chirality as scientists call it. We could even envisage a universe in which a left-handed glove could wander around to distant regions and return to fit your right-hand. "

The poor Maple developer who tried to fix the "bug" is active on MathOverflow and commented briefly on his experience of this in a comment below this answer: https://mathoverflow.net/a/11607

The article finishes with the rather vague and somewhat terrifying assertion that:

"It is estimated that the Airbus A380, comparable in complexity to the Dreamliner, has more than 100 million lines of code."

This is only tangentially-relevant, but I recently read that the earth's mantle is mostly solid! (It does still flow, but as a solid.)

The state of the rock beneath the crust is subject to two competing influences:

* High temperature [promotes liquid state]

* High pressure [promotes solid state]

and apparently the latter influence (mostly) wins.

Of course, when such rock reaches the surface, number 1 wins so we see liquid rock.

Cycling infrastructure in Ireland is woeful but there are great people working to improve it: https://twitter.com/ibikedublin

They're eager for help ;-)

In Ireland, we introduced a tax on plastic bags in 2002 and it had an enormous impact. (Actually we called it a levy: Irish governments never introduce new taxes, but love to introduce new levies!)

One detail works in its favour surprisingly well: once you've paid, the vendor cannot give you a plastic bag. A new transaction must take place as part of every sale "would you like a plastic bag?" and this turned out to apply a substantial friction on their distribution.

I note that each shipwreck record includes a date of loss. I'd be interested to see a histogram of frequency by year.

Indeed, and the name was a deliberate play on the Irish word for play, "súgradh".

I completely agree (though it is some years since I was at school).

Still, as Lockhart points out: at least art and music are recognised as arts. Surely even the ropiest music and art educations at least admit that these arts are:

  1. ends in themselves, because

  2. they are beautiful.

I believe these opinions are entirely absent from most mathematics education.

And I believe this is _the_ https://en.wikipedia.org/wiki/Clifford_Stoll !

In this context I highly recommend Lockhart’s Lament: https://www.maa.org/external_archive/devlin/LockhartsLament....

There seems to be some confusion in this thread between ferroelectric vs ferromagnetic.

These are two distinct physical phenomena. FRAM is based on the former whereas magnetic core memory is based on the latter.

With this in mind, I’m not sure it is really accurate to regard FRAM as a successor to magnetic core memory.

Like most Irish people, I am a huge fan of the EU, and of the many benefits we enjoy thanks to our fellow European citizens, via the EU.

Nevertheless I feel compelled to nitpick at the statement that the EU bailed Ireland out.

I believe the most important components of the so-called bailout instrumented by the IMF, ECB, and EU were that:

  A. Ireland was forced to turn about 65bn euro of private (banking) debt into public debt [for scale: our national debt was 36bn a couple of years before]

  B. The Irish government was allowed to run an _enormous_ budget deficit for many years

I don't know what would have been best for Ireland given the situation, but I'm not delighted about A and B. Even if the terms of the bailout were best for Ireland, all of money received went onto our national debt, which is now well over 200bn euro, and which we must pay back with interest.

For anyone looking for more of Halmos, his book "I want to be a mathematician: an automathography" is worth a look.

Also well worth a look is Serre's "How to write mathematics badly": https://www.youtube.com/watch?v=ECQyFzzBHlo

Possibly a good time to plug moissanite yet again: http://diamondssuck.com

I'm getting rather ridiculous myself at this stage but THEORETICALLY, if the hashes were all done including a long enough salt that was stored independently of the hashes then I believe there would be genuine significant security improvement to hashing.

Getting even more exotic, if the salt were also ENORMOUS, then it could make computing the required ~350 million hashes rather a costly endeavour (even in the event that the salt was obtained together with the hashed challenges).

Anyway.

You have a good point, though I _presume_ the challenge for the three digits of the PIN is made in tandem with the challenge for three characters from the password (making the cracking easy but not perhaps totally hilarious).

Were this not the case, I would have claimed that the number of combinations was 10^3 + k^3 rather than 10^3 x k^3.

If the challenge is indeed made in tandem then the PIN is essentially just a mandatory 4-digit prefix to the password. Still, the fact that only three characters of each part is requested is essentially fatal to the security any hashing scheme, as you say.

Even though this is not as ridiculous as hashing the four PIN challenges independently, which would be crackable with a lookup of amusingly-small size 1000, it still only needs a lookup of size about 700^3 =~ 350 million.

This might be roughly the threshold to annoy rather than to amuse?

Urgh.

They probably do store the unhashed pin/password rather than the quadratically-many 4 x N\choose 3 combinations.

Still, at least an account with known username is guarded with a secret from a space of size 10^3 x k^3, for k =~ 70 or so.

With AIB, that space has size 1000 and for a time, they were revealing a little account information when provided only with the user id: http://olivernash.org/2015/11/18/security-theatre-at-allied-...

To log in to an account for my Irish bank, AIB, you just need:

  * A theoretically-secret 8-decimal-digit id
  * Three digits from a secret 5-decimal-digit PIN

For many years all new online credentials were assigned an 8-decimal-digit id of the form: ddmmyynn where ddmmyy was the account holder birth date and nn was a sequence number.

I don't know how many accounts still have these birth-date-style ids but I have good reason to believe it is a great many.

Also Atiyah supervised Donaldson (albeit jointly with Hitchin), Mirzakhani was supervised by McMullen and others I'm sure.

Yes I do indeed; thank you for the correction!

One corollary of E=mc^2 is that the rest mass of a bound state of fundamental particles will not equal the sum of the rest masses of the individual constituents. For example, the rest mass of a Helium-4 nucleus turns out to be less than the sum of the rest masses of the four nucleons of which it is composed. The difference is only about 0.7% but is famously quite a lot of energy when interpreted using E=mc^2.

It's a lot more fun if we go one level down though: protons are far HEAVIER than the sum of their constituents. Apparently almost 99% of the rest mass of a proton is the binding energy of the zero-rest-mass gluons that hold their three quarks together.

I think it's fun that the vast majority of the mass of ordinary matter, of which we are all constituted, is best explained as gluon binding energy via E=mc^2.

I recently discovered that quite a bit of Ghana is covered in Street View. I feel it provides the most authentic armchair-compatible peek available, at this part of the world that differs so much from my own.

On the plus side, this article gives us another data point supporting Betteridge's law.

SPOILER ALERT ^^

Even at Oxford I only ever heard it used humorously.

My faith in the article's objectivity is called into question by the fact that it reports:

"An American Airlines flight attendant bullied a tired mother of twin babies over her stroller, and then readied himself to punch a passenger who rose to her defense."

Whereas the Guardian's account of what seems to be the same event is:

"Another passenger comes to her defence and threatens to punch the flight attendant, who in turn challenges the passenger to hit him."

https://www.theguardian.com/world/2017/apr/22/american-airli...

Just to advertise this addendum a bit more!

The Kempe-chain proof of the 5-colouring of any planar graph is easy and beautiful.