Letters of the Proceedings of Matt Parker

Do you want to be part of a fastidious team who are building something amazing and/or do you like logic circuits and binary computing? I need people from both categories to help with a ridiculous project: to build the biggest domino computer ever.

A “Domino Computer” is exactly that: a computer made out of chains of dominoes. Knocking over one domino sends a signal racing along the chain, just like current flows down a wire, and then interacting lines of dominoes can manipulate the signal in exactly the same way the circuit components do. It’s possible to build the domino equivalent of a transistor, for example.

Here’s a quick video of me demonstrating the concept:

This is a ambitious concept that I’ve been wanting to do for ages. It finally become possible through the support of the Manchester Science Festival. Here’s the event listing on their website:

http://www.manchestersciencefestival.com/whatson/domino-computer

This is a project that I cannot do by myself. I’m going to need a big team of enthusiastic volunteers. I need people who are:

- Good at balancing a lot of dominoes and maybe good at organising other people who are balancing lots of dominoes
- Happy to talk to the general public and communicate maths to them
- Able to co-ordinate ridiculous projects and lead a team
- Masters of logic gates and able to refine a circuit design

You only need to be in one category to help out! We hope to have loads of helpers there on the actual weekend in Manchester (27 and 28 October 2012), fewer people along for the planning weekend (15 and 16 September) and then some people who are only involved online.

For now, I need volunteers in three different categories. You can be involved in as many of the categories as you want! I’ve outlined them below. There are also a few additional aspects of the project that we’re working on (mainly regarding how the public will get to see and interact with the Domino Computer), so there will be more details to follow.

If you’re interested in being involved, please send me an email as an expression of interest: matt@standupmaths.com

We’ll be getting most of the team in place for the planning weekend and then they’re be another push for building volunteers in the lead-up to the actual event.

I can think of so few things that could possibly go wrong…

1] DOMINO BUILDERS
We will need to put a lot of dominoes in very exact positions and we’re working out exactly how to do this. We may use markings on the floor or we may use templates that dominoes can be put in and then the template lifted up and away. Anyhow, if you fancy spending a day or two placing dominoes, then we need people for the 27 and/or 28 October to be in Manchester to help us build this thing. You’ll have the option to come and see my other shows for free and be involved in general Sci Fest fun and drinks as well. No mathsy-knowledge is required to do this.

2] DOMINO COORDINATORS
There will need to be a few people who can help the actual logistics of getting the thing built and running it. Along with a few other side maths-communication projects which will need people to run them. For any of these, you’ll need to understand how the domino circuit works and also be able to help putting dominoes in place. You’ll be needed for the weekend 27/28 October for the final build and preferably the testing weekend inManchester on the 15/16 September as well. Plus the standard bonuses of to coming and see my other shows for free and be involved in general Sci Fest fun and drinks.

3] DOMINO DESIGNERS
I’ve already designed my own circuit for the binary half-adder which is a custom circuit to work well in dominoes and not just stand-alone domino XOR and AND gates put together. However, to scale it up to a full adder, I’ve just mashed the half-adders together and I suspect we could do something a bit smarter if we designed a domino full-adder from scratch. Plus there are all sorts of timing issues with where the domino signal is at different times. One plan is to use a timing-line of dominoes, a bit like a processor clock. TL;DR: there’s still a lot of design work to be done. I plan to form an on-line mailing list where we can discuss ideas and design the circuits. We’ll then have the planning weekend on the 15/16 to try them, and maybe a gathering in London as well. You can be involved in this purely online, but you’re obviously welcome to any of the physical gatherings or the final running at the Manchester Science Festival.

My twitter account “@standupmaths” is the expected mix of mathematics and jokes (with possibly more maths than people initially expect before they slowly acclimatise). But every now and then it is hijacked by myself as I release a flood of tweets to taunt a homeopath. Most likely Dana Ullman.

People often ask why I take my collection of teachers, maths enthusiasts and comedy-fan followers and use them as a digital stick to poke a homeopath. The subject-matter itself comes as no surprise – my views on homeopathy and Alt Med in general are well known – but rather that I would waste my time pestering someone who is so extremely unlikely to change their mind.

My policy on these things is simple; I will not waste my time arguing with people who adamantly believe in homeopathy, biodynamic cosmic energy, astrology, hidden messages in prime numbers, the Moon landing hoax or anything else on the made-up-shit-spectrum except for one tiny exception: If there’s an audience.

Twitter is the perfect combination of ready-made audience and homeopaths who will engage with you despite themselves.

My main conversational partner is Dana Ullman. This is because there are plenty of easy targets in the Land of Hippies but I don’t want to just go after some poor retiree at home who has developed an interest in homeopathy and a website from the late 90s. That would prove nothing. I go after Dana Ullman because he is described as “homeopathy’s foremost spokesman”, is a member of the Advisory Council of the Alternative Medicine Center, is a prolific author and writes for the Huffington Post. Here’s his wikipedia page. And, unlike some other Alt Med people, he doesn’t realise that just shutting-up and never responding is the most-effective defence against skeptics.

I was bored at home on a sick-day yesterday, and as I was curled-up on my sofa I noticed Dana had tweeted a link to some nano-particle research. I’m not going to bore you with a transcript of such an encounter (you may have already had to live through it in real-time), but here’s a rough outline with my chat with him last night:

This is a brilliant Alt Med strategy where they link their therapy (homeopathy) to a legitimate scientific area of research (nano-materials) and then put forward proper scientific papers from that area as proof of their Alt Med methods.

As always, I then ask him how nano-particles can explain such things as “homeopathic dolphin sonar”, or any of the other non-matter things homeopaths claim to be able to dilute with water. The fantastic thing about the Alt Med continuity is that even the most serious practitioners will never break-rank and say how ridiculous the fringe aspects are, and so they all end-up looking silly by association. I have no doubt Dana hates the people who claim to dilute the Berlin Wall as a remedy, but he can’t publicly say so.

The closest he has ever come was probably yesterday, when he decided to call me out as making up the dolphin-sonar people for use as a straw-man argument. Thankfully diluted dolphin-sonar has been sold by Ainsworths – homeopathic suppliers to the Royal Family – and is still readily available online.

This follow-up is a classic move where he completely changes argument-tack (suddenly my made-up straw-man is real and he’s defending it) as well as packing the tweet with several other layers of wrong as a kind of ‘argument chaff’. I consider this burst of logical fallacies as a DoS attack on your brain’s logic systems; there’s suddenly so many incorrect points to counter that you lose track of the original argument.

Tactics aside, the question still remains: why would I engage with these people even given there is an audience in attendance? It’s because while I have no intention of ever changing the arguer’s mind, I do hope to increase general awareness of just how ridiculous some aspects of Alt Med et al are. A lot of people are vaguely aware of homeopathy as a kind of natural herbal thing (much like thinking chiropractors are kinda just a type of physiotherapist) but when they see a leading practitioner trying to defend diluting nano-particles of dolphin-sonar, they see it for the 18th century wishful-thinking it really is.

There is no better way to show people how silly homeopath is than to get the people who believe in it, to discus and defend how it works in a public forum.

So, sorry to everyone who follows me on twitter for maths+jokes and then is suddenly subjected to some member of the pseudo-science community dancing about, trying to justify their wacky beliefs. Just take not of how ridiculous their arguments are and then wait for normal numerical tweets to resume.

And for those of you who follow me for the Alt Med bashing: don’t forget that it’s you guys I’m trying to wean onto maths.

I will spend hours hand-crafting what I believe to be fascinating bit of maths and then gently float it out on twitter only for it to sink without even a ripple. Then someone will notice that multiplication is distributive and the internet will ZOMG itself into a storm.

For example, this was racing across twitter today:

The most common response from the maths-purist is that such trivial bits of maths are “not interesting”. Unfortunately, I think we’re wrong by definition. If thousands of people have been amazed by something and forwarded it to all of their equally-stunned friends, then that trivial bit of maths has fulfilled all the requirements to be classified as definitely interesting.

And why shouldn’t it be. I spend a disproportionate amount of my life researching interesting maths puzzles for the already-maths-excited, why shouldn’t there be a different flavour of recreational maths for those who like their maths a bit more party-trick-esque?

If anything, these “facebook maths tricks” are a chance to explain – hopefully in an equally entertaining/simplified manner – some actual maths. It certainly shouldn’t be an opportunity to reinforce the maths-killjoy image by responding with “ah, I think you’ll fine that only works if you’re less than 100 years old” type pointless pedantry. If any centerians are on facebook, they can certainly defend themselves.

Here’s my explanation attempt from today:

I’m happy to go against the online maths-purist flow when it come to facebook maths. If anything, I’m only annoyed that I’m not good at coming up with them myself…

All the snow this week has reminded me of when I was sitting in a cafe before Christmas 2011 and I spotted the above pentagon-based snowflakes. When normal water freezes at average temperatures and forms snowflakes*, they will always have a hexagonal-based shape. But for some reason, all around us are pentagon, octagon and all sorts of bizarreagon shaped snowflakes. Which I take to represent a complete disregard for maths, physics and chemistry.

At the time, I put the pentagon snowflake up on twitter and started the #snowfake campaign to name-and-shame all those involved in the non-hexagon-based-snowfake trade. Needless to say, the internet joined in.

But like the rest of the internet, it has all been done before. I had first had non-hexagon snowflakes brought to my attention in a talk by Philip Ball, who has already written a blog-post about it as well as being published in Nature on the same day I was sat in the cafe.

Then I was contact by the Campaign for Real Snowflakes who have an impressive collection of snowfakes.

Since then, people have drawn my attention all manner of different snowfakes, including this dispointing effort from Google of all people:

So, the name-and-shaming of #snowfakes is taken care of (but please do keep tweeting examples at me); it’s time to take a positive step of action, and fill the world with mathematically accurate snowflakes.

Make your own:
As always, when in need of a mathematical activity, nrich has the answer. They have great snowflake folding instructions. And a number of people greater than one have drawn my attention to the Star Wars folded snowflakes.

*Yes, I know you can make water do strange things when it freezes when it’s at unusual temperatures and pressures, but I’m only worried about traditional snowflakes here. Don’t get me wrong though, I’m a big fan of other crystals, quasi or otherwise. If I lived on Iota, this would be a whole different campaign.

I gave this man a stern yelling-at. That phone is not his.

Last night I had the misfortune to be on one of the last trains out from London Waterloo, the 00:09 to Guildford. I found a quiet-ish coach and settled in to stop at every station between London and my destination. Plus some other ones I swear only exist when you’re on a night train.

There were the usual fellow passengers, dotted around both the intoxication spectrum and the carriage. So no one took much notice when a rather drunk girl collapsed in a seat for a while and then got up and drifted off, seemingly looking for a toilet. However, she had left her bags behind and never came back for them.

Once we assumed she had alighted from the train, the phone in her bag began ringing incessantly. Assuming it might be her, I eventually answered it and assured a friend of hers that she had been on the train and hopefully got off at the correct stop. I said that if she didn’t come back for her bags, I would hand them in to Guildford Station last-and-found where she could easily collect them.

So I went back to my seat, still many station-stops from Guildford, and resumed my desultory twittering.

One of the other few people in the carriage though, got up and came and sat near the bag. During the casual carriage-banter when I first answered the phone, he had suggested to the whole carriage that we nick the phone. Thus I was already keeping an eye on him when he moved over and then took the phone out of the bag.

I was – to say the minimum – outraged.

So I began initially tell him to put the phone back before escalating to a full yelling-at, during which I had the presence of mind to turn my phone on and video the whole thing. I even asked him first if he minded me photographing him stealing the phone and he was so brazened, he held it up to pose with it. That is the screen-grab at the top of this page.

Spoiler Warning: I’ll post the video soon (although, it does contain a lot of swears: sorry kids) but he did eventually get off at the next stop and leave with the phone.

Naturally, I’ve already re-played the whole thing in my head countless times, but I’m happy that I didn’t resort to physically stopping him, or kicking his bike etc. If someone was defending my lost phone, I wouldn’t want them to risk violence. But I’m kicking myself for not moving sooner or putting the bag somewhere safer. So yeah: lots of yelling, all of it ineffectual.

I did hand the bag in at Guildford, with a note inside explaining what happened and my email address (Always carry a pen kids! (that advice will make up for the swearing)) and today I’ll report it to the Transport Police. I’ve already caused one phone thief to be convicted and sentenced, I’m keen for another.

If you do recognise this dick who would get the last Waterloo to Weybridge train, please get in touch.

Alternative blog-post title: “Maths Man: worst superhero, ever.”

UPDATE: Here’s the video on YouTube.

It was revealed today that O2 has been voluntarily sharing its customers’ phone numbers with every website they visit. This is a serious privacy breach and has worried many of O2’s millions of mobile customers.

When you visit a website, your computer sends a small amount of information to the site to explain what browser you’re using and a few technical details about your computer. It’s very bland data and is useful so websites know if you need the desktop or mobile versions of their site and other technical tweaks. This information your computer sends at the top of its communication with a HTTP (aka “web”) server is known as the “HTTP Header”.

Computers can also add in extra bits of optional information if they think it might be useful or for bespoke arrangements with websites. What O2 are doing is getting a copy of the HTTP Header from your phone as it goes through their mobile internet servers on the way to the website you wish to view, and inserting an extra bit of information which includes your mobile phone number.

This was revealed today when Twitter user @lewispeckover set-up a website which would display all of the HTTP Header information it receives when you accessed the site. O2 users can visit this site on their phones (with wifi turned off) and see their phone number staring back at them.

Try it yourself:
http://lew.io/headers.php

Here’s what I see:

Every site visited on an O2 phone will receive this information and many of them will store this data for long periods of time. I was outraged as this complete disregard for private data by O2 and immediately voiced my concern on Twitter. I had the privilege of being the first person O2 finally responded to, with this message:

O2 in the UK @O2
@standupmaths Hi, we’re investigating this at the moment and will update everyone as soon as we can. Keep an eye on this feed for updates
http://twitter.com/#!/O2/status/162094696552865793

They have since been sending messages to countless people claiming that they are checking with their internal teams about what is going on. I feel sorry for whoever was in charge of their twitter account this morning as it fast become a PR disaster. Beyond that, a lot of customers claim to be reporting O2 to the Information Commissioner’s Office, claiming thsi behaviur is a data protection breach.

Not only do O2 need to fix this problem quickly, they need to explain why they actively chose to share their customers’ personal contact details in the first place. It seems likely that their system to insert phone numbers into HTTP Headers was not supposed to do so for every website visited and this is a technical error. But that raises the grave question of what exactly it was supposed to be doing had it been working correctly.

What has happened is the same as the Post Office writing to every shop you visit, or person you talk to, and sending them your home address. The audacity of what O2’s behaviour can not be allowed to be over-looked because what they did is shrouded in opaque computer-server language.

I’m very much looking forward to how they try to explain what happened to the general public.

Alternative blog-post title: “O2, Where’s Your Header At‽”

UPDATE01: It seems the “x-up-calling-line-id” line in a HTTP Header is nothing new. It was listed as a place to store the “End users phone number” over three years ago.

UPDATE02: Apparent some Tesco Mobile users are also seeing their numbers listed in their HTTP Headers. The problem doesn’t seem to impact BlackBerry phones on O2. We know how possessive Blackberry are over their servers.

UPDATE03: Which? Conversation got in touch with the Information Commissioner’s Office and have a comment from them in their article.

UPDATE04: If you have an O2 phone, you can avoid them messing with your header by changing your “Cellular Data” (or equivalent setting for mobile data) username to “bypass” from whatever it currently is. It worked a treat for me, however it also turns off server-end image compression and so may slow your connection and increase your data use. Idea from here.

The square root of 8053139 has “8053139″ as its first decimal places. It is a so-called Grafting Number.

Mathematicians can be a bit derogatory towards other sciences which are less rigorous, comparing things like biology to stamp-collecting. Actually, every science more theoretical than biology calls it stamp-collecting. The gist of the insult being that all biologists do is document and label things with no underlying logic.

While this is not true of all biology, it’s also not true that maths is free of stamp-collecting aspects. I’m prepared to admit that I’m a bit of stamp-collector of the mathematical world. I love the fact that 3435 = 3^3 + 4^4 + 3^3 + 5^5 and it’s the only such number. Sure it’s only true for Base 10 numbers and it offers no real insight into other numbers, but it’s still fun.

In a similar vein, I noticed something about the number 98 a few months ago, in relation to its square-root.

√98 = 9.899494937…

The first two digits of the square root are “98”. I started wondering if there were any other numbers where the leading digits of the square-root are the same as the digits of the number. It turns out there is a whole family of similar numbers, with a bit of a nice pattern:

√98 = 9.899494937…
√99 = 9.949874371…
√9998 = 99.9899995…
√9999 = 99.99499987…
√999998 = 999.998…
√999999 = 999.9995…

These are all numbers where their root grows out from the number itself, so I took to calling them “Grafting Numbers”. And those are the only numbers where the number appears as the lead digits. But then I noticed something similar about 77 and its own little family of numbers:

√77 = 8.774964387…
√9797 = 98.97979592…
√997997 = 998.997997…
√99979997 = 9998.99979997…

These are all number where the number appears in the square-root starting from the decimal point, which I also declared to be Grafting Numbers.

Now I was curious to see if there were other numbers that appeared somewhere near the start of their own square-root. I decided that “somewhere near the start” was anywhere up to and including the decimal point^[1]. However, these would be harder to find than just square-rooting two digit numbers on a calculator.

Which, frankly, is a good thing.

At university I learned some programming, and I’ve since worked teaching programming to school kids; but it’s been a while since I was fluent in a programming language and I never learned anything useful for mathematics (it was always robotics focused). So one of my resolutions for 2011 was to start learning to programming language “Python”.

Python is a lovely, fun little language and it comes already preinstalled on Macs, ready to run from the Terminal prompt. So away I went, setting myself mathematical challenges and then writing little programmes to solve them. This was a perfect such challenge: I wrote some code to find all the Grafting Numbers less than 10,000,000 (ignoring perfect squares). I’ve put the code below^[2] if you’re interested, but here are the results:

√764 = 27.64054992…
√765 = 27.65863337…
√5711 = 75.57115852…
√5736 = 75.73638492…
√76394 = 276.3946454…
√2798254 = 1672.798254…
√7639321 = 2763.932163…
√8053139 = 2837.8053139…

Now, while this was all good fun, and I was learning some new programming skills, you will notice that all I’m doing is numerical stamp-collecting. I’m hunting down new numbers and giving them labels. Are far as I can find online – and I’m very keen to be corrected if anyone knows better – this type of number has not be named before, but that doesn’t make it interesting in a bigger mathematical context.

What the mathematician in me really wanted now, was some kind of underlying pattern to investigate. Which was why I took a closer look at these Grafting Numbers:

√764 = 27.64054992…
√76394 = 276.3946454…
√7639321 = 2763.932163…

They looked like a new family of numbers where each one appeared in its square-root, proceeded by a “2”. A quick new bit of code found that there are plenty more in the same family:

764
76394
7639321
763932023
76393202251
7639320225003
763932022500210
76393202250020992
7639320225002102784

A little bit of algebraic messing-around^[3] revealed that these numbers are following the decimal places of the irrational number: 3-√5 = 0.763932022500…

Strictly speaking, each of these numbers is a value of ⌈(3-√5)10^(2n+1)⌉

So I decided to call 3-√5 a “grafting constant”. People have pointed out to me that because of the √5 this can be linked to the Golden Ratio: 3-√5 = 2(2-ϕ)

I don’t know if there are other such constants, and I’ve not really had a look at other roots or number bases. An obvious next step might be to look at cube roots in base 10. Feel free to adapt my python code below or write something better!

Programming is such great fun (combined with the greatest levels of frustration) and is such a unique way of using logic. Everyone should learn to program at least once in their lives. There are countless Python resources online, and if you’re looking for some programming challenges to get you started, I recommend Project Euler.

The vast majority of mathematics started because someone noticed something interesting, gave it a name and started playing around to see how it worked. So maybe we should be a bit nicer to biologists after all. A bit.

Matt Parker first talked about Grafting Numbers at the Maths Jam annual weekend, 13 November 2011. He talks about both Grafting Numbers and Maths Jam in this Numberphile video:

[1] If you let go of the decimal point, it’s a long way down. If you have a never-ending sequence of random digits, then you would expect to find any string of digits sooner or later, making all such roots Grafting Numbers. However, this also requires that the number is a Normal Number, meaning that all possible combinations of digits are equally likely. So far, mathematicians haven’t managed to prove that any number is a Normal Number. So I’m not going near it.

[2] Sorry, this code has lost all its formatting. You’ll need to put some indents/tabs in to get it to run as python code. Like this.


# Just looking for ones right at the beginning and alerting to ones that are right at the beginning or lead off form the decimal point.
# Set "mag" to what magnitude number you want to check up to. mag = 7 will give up to 10 million.

while run1 == 1:
run2 = 1
n = n+1
if n % flags == 0:
print 'Checked {0}'.format(n)
root = n ** (1./r) #the r'th root
if n == (int(root)) ** r: #this bit moves it along if n is a perfect square, cube etc
n = n + 1
root = n ** (1./r)
length = len(str(n)) #length of number being tested
lead = len(str(int(root))) #number of leading digits
test = root * (10 ** (length -lead))
pos = -lead
while run2 == 1:
t = int(test)
if n == t:
print 'Found {0} at position {1}'.format(n, pos)
run2 = 0
test = 10*test-(10 ** length)*int(test*(1./(10 ** (length-1))))
pos = pos+1
if pos > interest:
run2 = 0
if n >= end:
print "finished"
run1 = 0


[3] I had a look at the examples so far and to get the grafting constant “g” solved g.10^(2n+1)=[(2+g).10^n]^2

James Grime noticed that 180°(3-√5) is the Golden Angle and did some more involved working out on twitter.

A few days ago, I sent out a throw-away tweet commenting that I’m always careful to write “4 × 4” and not “4 x 4” because the multiplication symbol “×” and the character “x” are different things.

This sparked an unexpected volume of interest in my use of various mathematical symbols in tweets.

Thanks to the power of unicode, almost all electronic devices can display a huge range of symbols beyond the normal letters and numbers we use most frequently. This is particularly useful if you love both maths and typography.

i.e.: you ∈ {love maths} ∩ {love typography}

But while ASCII and its friends might give you the potential to use all manner of symbols, there is no easy way to do it. Twitter gives you the power but not the convenience.

My solution is to keep a document titled “Maths Symbols” on my phone and just copy and paste from there as I need them. After a few requests, I dumped a fistful of these symbols onto twitter for other people to copy, but it was rather desultory collection. I’ve since gone through and put my typographical house in order. They’re now all neatly laid-out, with a space before and after all symbols for ease of selecting. They are vaguely in categories and ordered roughly according to how often I use them. For most of them I’ve noted a name or use for the symbol; many symbols are used different ways in different branches of maths (it was a brave topologist who chase “π” as the symbol for homotopy groups) and so I’ve noted my most common use for them. Your use may vary.

You can download this whole list of maths symbols and greek letters as a text file by right-clicking here. Or else, I’ve put the whole thing at the end of this post for you to just copy+paste. If I’ve missed any characters, put them in the comments below and I’ll keep growing the list.

I should also mention that there are various apps for smart-phones which are effectively glorified lists with simplified copy+paste options. For users of the information-phone: “Character Pad” is good for its easy-of-use while “FancyChars” has an impressive but disorganised range of characters.

In a perfect world though, someone would develop a twitter client which can parse LaTex and convert it to the closest possible unicode text. Unfortunately at the moment: ∄

HERE THEY ARE:
π pi
∞ infinity
ℵ aleph
∆ delta
∑ sigma

× multiplication
÷ division
– subtraction (m dash)
√ square root
± plus and minus
∓ minus and plus

≠ not equal sign
≈ approximately equal
≥ greater than or equal to
≤ less than or equal to
≪ much less than
≫ much greater than
≅ congruent to
~ approximately, similarity
≡ equivalence
≜ equal by definition
∝ proportional to

¬ not
⇒ implies
⇔ equivalent
∀ for all
∃ there exists
∄ there does not exists
∴ therefore
∵ because
→ arrow
↔ double arrow
⇐ back arrow
⇑ up arrow
⇓ down arrow

⊗ circled cross (tensor product)
⊖ circled dash
⊕ circled plus

∈ element of
∉ not element of
∩ and, intersection
∪ or, union
⊆ subset
⊂ strict subset
⊄ not subset
⊇ superset
⊃ strict superset
⊅ not superset
Ø ∅ empty set
Ƥ power set

ℕ natural numbers
ℤ integers
ℚ rationals
ℝ real numbers
ℂ complex numbers
ℍ quaternions (Hamiltonian)
ℙ projective space

∘ composition
∙ dot scalar product
· and

∠ angle
º degrees
∡ measured angle
∢ spherical angle
∟ right angle

‰ per-mille
‱ per-ten-thousand
∇ del
† Hermitian matrix
⌊x⌋ floor brackets
⌈x⌉ ceiling brackets

∂ partial derivative
∫ integral
∬ double integral
∭ triple integral
∮ closed line integral
∯ closed surface integral
∰ closed volume integral
ℒ Laplace transform
ℱ Fourier transform

GREEK ALPHABET: Α α Β β Γ γ Δ δ Ε ε Ζ ζ Η η Θ θ Ι ι Κ κ Λ λ Μ μ Ν ν Ξ ξ Ο ο Π π Ρ ρ Σ σ Τ τ Υ υ Φ φ Χ χ Ψ ψ Ω ω

RANDOMS: ⊥ ⊧ ⊢ ≺ ⋉ ⋊ ≀ ◅ ▻ ↦ ⋈ ∐ … ∤ ■ □ ∎ ▮ ‣ ⊻ ≜ ≝ ≐

SUPERSCRIPTS: ⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁼ ⁽ ⁾ ᵃ ᵇ ᶜ ᵈ ᵉ ᶠ ᵍ ʰ ⁱ ʲ ᵏ ˡ ᵐ ⁿ ᵒ ᵖ ʳ ˢ ᵗ ᵘ ᵛ ʷ ˣ ʸ ᶻ ᴬ ᴮ ᴰ ᴱ ᴳ ᴴ ᴵ ᴶ ᴷ ᴸ ᴹ ᴺ ᴼ ᴾ ᴿ ᵀ ᵁ ⱽ ᵂ ⁿ ʰ ʱ ʲ ʳ ʴ ʵ ʶ ʷ ʸ ˀ ˁ ˠ ˡ ˢ ˣ ˤ ᴬ ᴭ ᴮ ᴯ ᴰ ᴱ ᴲ ᴳ ᴴ ᴵ ᴶ ᴷ ᴸ ᴹ ᴺ ᴻ ᴼ ᴽ ᴾ ᴿ ᵀ ᵁ ᵂ ᵃ ᵄ ᵅ ᵆ ᵇ ᵈ ᵉ ᵊ ᵋ ᵌ ᵍ ᵎ ᵏ ᵐ ᵑ ᵒ ᵓ ᵔ ᵕ ᵖ ᵗ ᵘ ᵙ ᵚ ᵛ ᵜ ᵝ ᵞ ᵟ ᵠ ᵡ ᵸ ᶛ ᶜ ᶝ ᶞ ᶟ ᶠ ᶡ ᶢ ᶣ ᶤ ᶥ ᶦ ᶧ ᶨ ᶩ ᶪ ᶫ ᶬ ᶭ ᶮ ᶯ ᶰ ᶱ ᶲ ᶳ ᶴ ᶵ ᶶ ᶷ ᶸ ᶹ ᶺ ᶻ ᶼ ᶽ ᶾ ᶿ

SUBSCRIPTS: ₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋ ₌ ₍ ₎ ₐ ₑ ₒ ₓ ₔ ᵢ ᵣ ᵤ ᵥ ᵦ ᵧ ᵨ ᵩ ᵪ

FRACTIONS: ½ ↉ ⅓ ⅔ ¼ ¾ ⅕ ⅖ ⅗ ⅘ ⅙ ⅚ ⅐ ⅛ ⅜ ⅝ ⅞ ⅑ ⅒ ⅟

In 16 days I will be 11239 days old, the 1358th time I will be a prime number of days old. Next year I turn 1 bilion seconds old.

Celebrating integer birthdays is so last time interval. Here’s how to locate your more obscure and less frequent Days of Mathematical Celebration:

PRIME BIRTHDAY
http://primebirthday.org/

What started as a conversation between myself and James Grime last year was leaked onto twitter and within a non-prime and non-composite number of days, the website had been built by Edmund Harriss and Dan Hagon. Works brilliantly for anniverseries.

NERDIVERSARY
http://nerdiversary.com/

A much wider spectrum of calculations, this will let you know when your age is a mathematically interesting number of time units as well as when you’d be an integer number of years on different planets in our solar system. As well as mathematically interesting numbers of other-planet years: I’m about to turn 2^7 mercurial years, it seems.

DO IT YOURSELF
http://www.google.com/search?q=pi+cubed+years

I have been waiting a long time for when I’m going to turn π³ (pi cubed) years old. Because I was born at 04:27GMT it will be at 11:28am on the 24 December this year. I’m giving you ample time to organise presents and themed cakes.

What other nerdy time intervals do people celebrate?

I was directed to the following tweet which was put out by @astrologyzone:

How do you reply to something like that? I decided to not even waste my time trying to explain how with huge numbers of natural disasters over the last century, and the fact that for each one there would be multiple different alignments in the astrology-sky, it’s possible to just pick out the occasional coincidence like this.

I decided to go with an old favourite: and just point out a blatantly spurious – but equally valid – correlation of my own.

So I replied with this tweet:

Yes, the first Captain America film was released in 1944 (as a serial) and then there were no further films (ignoring a 1990 straight-to-video effort) until this year’s 2011 Captain America film.

So there you are Susan Miller of Astrology Zone: there is a direct correlation between Captain America films and your NY-earthquake-hurricane combos. And it’s stronger than just “Planets were in Virgo, Libra”, which happens all the time.

I’ll assume that Susan selling her astrology app and tweeting about people’s possible misfortune in New York is only a correlation as well, not causality.