The laws of math

Australia is considering a law that will make it mandatory for all device manufacturers to assist police with decrypting messages sent through their device. This post isn’t about that but about the response by the Prime Minister of Australia, Malcom Turnbull, when he was told that that might be mathematically impossible without also allowing many others access (since it would mean the encryption would have to be weaker):

“The laws of Australia prevail in Australia, I can assure you of that,” he said on Friday. “The laws of mathematics are very commendable, but the only law that applies in Australia is the law of Australia.”

I wonder if he has the same thoughts about gravity?


Via here, we get this:

Insurers would have more leeway to vary prices by age, so that premiums for the oldest customers could be 3.49 times as large as those for younger customers. Today, premiums for the old can be only three times as high as premiums for the young, which is what the Affordable Care Act stipulates. According to sources privy to HHS discussions with insurers, officials would argue that since 3.49 “rounds down” to three, the change would still comply with the statute.

At some level, this is politically stupid since it explicitly raises the rates of older people while reducing it for the young–the opposite of the voting pattern for Trump. For me, the problem is the math–at most 3 times as large means at most 3 times as large, even 3.01 is out, never mind 3.1 or 3.49.

This will be similar to the “Pi Bill” from Indiana which indirectly says that pi is 3.2 (the bill tried to prove a method of squaring the circle, which is impossible, by making it a law).

This is the type of thing which shows why there needs to be a March for Science (it will be on April 22 with satellite marches all over the country).

Math and the American Heritage Education Foundation

Like everyone else, I get a lot of spam in my email boxes. Sometimes they can be fun. Case in point:

Dear Teachers and Citizens,
A unique Social Studies/U.S. History reference text book is now available!
The American Heritage Education Foundation (AHEF) announces a new resource/text that reveals the connection between America’s historical founding ideas and the Bible..
The Miracle of America: The Influence of the Bible on the Founding History and Principles of the United States of America for a People of Every Belief
By Angela E. Kamrath, American Heritage Education Foundation
This would be the group that wrote a history book for Houston strongly based on a work by W. Cleon Skousen, a far right crazy in the mold of the John Birch Society (for example, he believed Eisenhower was a Communist dupe).
It seems their mailing list is about as accurate as their history: they send an email about a high school history book to a college math teacher. Hey, maybe I’ll use it for a probability course?


This is a little crazy:

The study followed just under 11,600 men and women averaging 59 years old across the United Kingdom, surveying them once between 1993 and 1997 and again between 1998 and 2002. At the beginning and end of the 3.6-year period, participants estimated how many fruits (choosing from 11 kinds) and vegetables (choosing from 26) they ate. The changes in amount and variety gave the study its measure of the healthiness of participants’ divorce diets.

By the end of the study, 1.2 percent of men and 1.7 percent of women became separated or divorced. (The study also separately measured participants whose spouses had died.) Among them, the men ate 0.6 fewer grams of fruit per day than their married counterparts did, and with less variety. Divorced and separated women, on the other hand, didn’t change their habits much.

I thought about it and realized how small the numbers were: 1.2% of about half of 11,600 for the number of divorced men is about 50, it turned out to be 52 according to the study. The study also didn’t include a wide variety of people:

We used data from the prospective EPIC-Norfolk study. The EPIC-Norfolk study aimed to quantify the contribution of nutrition and other determinants of chronic diseases in middle and later life. It recruited from age-sex registers of general practices in Norfolk, UK, which is a geographical circumscribed area with little outward migration and a population mainly served by one District General Hospital, as described in detail elsewhere

It also didn’t exactly measure things exactly:

Participants also completed a Food Frequency Questionnaire (FFQ) and detailed Health and Lifestyle Questionnaire in which they reported their occupation, educational level, health status and chronic health conditions (Day et al., 1999). A second health check (HC2), an average of 3.6 years following entry, was attended by 15 786 participants, among whom 12 331 completed a second FFQ.

So, results based on a small number of people from one small region that is 96.5% white that used two surveys to guess at what they ate (ok, it was really a 7 day food diary, but that still has problems) is worthy of an article in a newspaper? Perhaps this is why people don’t trust the results of studies. By the way, I’m not complaining about the study itself–it’s a fine study even if its results are weak.

Happy Pi Day

I was going to wait until 9:26:53 but decided that I’d probably miss the correct second anyway. Happy Pi day



This is fun:

“Gangnam Style,” the K-pop sensation that basically owned 2012, has been viewed so many millions of times that, two years later, YouTube’s view counter literally broke trying to tally it.

The site is upgrading that tool as a result, a spokesperson wrote on YouTube’s Google+ page. That means that in the future, YouTube will be able to accommodate videos with more than 2.147 billion views — which was, previously, the most views YouTube imagined a video could ever receive.

Ok, that’s fun but I really meant this:

But basically, YouTube codes its view count as a signed 32-bit integer, which means (a) it stores numbers as a string of 32 0s and 1s, with one of those slots reserved for determining if it’s a positive or negative number, (b) it can only count up to 2^(32-1), or 2,147,483,648, and (c) if it reaches that point, instead of counting to the next positive number, it will switch into negative integers.

Ok that’s also fun, but really this:

Funnily enough, that’s not a new problem. In fact, it’s been the curse of 2,147,483,647 almost since the number was proven by Leonhard Euler in 1772.

Either someone’s not understanding something here (how does one even prove a number) or there’s something missing. This is implied in the next bit which notes that Euler showed this was a perfect number (a number which is equal to the sum of its proper divisors) back in 1772. Now that’s fun.

Here’s the video if you want to try to break the new counter:

How much?

This is fun:

Anton Purisima v. Au Bon Pain Store, Carepoint Health, Hoboken University Medical Center, Kmart Store 7749, St. Luke’s Emergency Dept., New York City Transit Authority, City of New York, NYC MTA, LaGuardia Airport Administration, Amy Caggiula, Does 1-1000, Case No. 1:14 CV 2755 (S.D.N.Y. filed 4/11/2014).

Civil rights violations, personal injury, discrimination on national origin, retaliation, harassment, fraud, attempted murder, intentional infliction of emotional distress, and conspiracy to defraud. $2,000 decillion ($2,000,000,000,

As they note at Lowering the Bar, this is $2 undecillion. Randall Munroe (of xkcd) has fun with this, putting it in terms of billable hours of a galaxy of Ted Olsons.

I can’t do anything as good as that, but let’s look at water:

  • a liter of water has about 3.34×10^25 molecules (1 liter=1000 grams; 1 mole of water=18.015 grams; 1 mole has 6.0221×10^23 molecules)
  • a cubic meter has 1000 liters, s0 3.34×10^28 molecules
  • a undecillion is 10^36
  • so that’s about 30 million cubic meters of water molecules–or .03 cubic kilometers.

So, not so much.

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