## Subtitles section Play video

• This video is based on joke presentation I gave last year.

• I was recently on the phone with an internet service provider whose name shall remain unspoken

• because they promised me their mediocre internet services for one price and then charged me

• another price . And you may not be surprised to hear that price B was greater than price

• A. So I was on the phone to see if I could get B to equal to A.

• Which reminds me of the first of the axioms of Zermelo-Fraenkel set theory.

• For those of you who don't know, Zermelo-Fraenkel set theory is the, how shall I put itpedantry?

• that forms the foundation of modern mathematics.

• And to get a good idea, you only really need to know two things about it:

• it exists (that's a math joke, though I guess so is this whole talk)

• and, using the Zermelo-Fraenkel axioms, the number 2 is written like this , which

• in English readsthe set that contains the set that contains only the set containing

• nothing as well as the set containing nothing”.

• I can see the logicians in the audience are loving this.

• Ok, so the first axiom of Zermelo-Fraenkel set theory says that two sets are equal if

• they have the same elements.

• However, the internet company that shall not be named was providing the same set of services

• for different prices – . So B≠A, but they both contain the same set of servicesthis

• is a violation the first axiom of Zermelo-Fraenkel set theory.

• At this point, perhaps, I should have been worried.

• But I continued nevertheless.

• I again asked for price A.

• And they replied: “The option we offered IS all that we can offer.”

• I was horrified.

• For, you see, the second axiom of Zermelo-Fraenkel set theory implies that a set cannot be a

• member of itself, and yet they had just said that the set of all options they could offer

• was the same as the option they offered, which clearly must be contained in the set of all

• options they could offer.

• And thus they violated the second axiom upon which modern mathematics is built.

• Let me speak to your manager” I said, which is code for “I think your working

• axiomatic system is crap.”

• But, as expected, the manager did not immediately improve the situation.

• Just so we're all on the same page, I simply wanted internet for the promised price A,

• let's say, \$40, but had been charged B, say, \$50 for the same service.

• And I had been told that “\$50 is the best offer they can make.”

• The manager promptly offered me internet, PLUS a home wifi router, for \$45.

• You might think this is an improvement, as did I until I asked if I could have the offer

• of internet plus router, but hold the router, and I was toldNo.”

• The third axiom of Zermelo-Fraenkel set theory was not happy with that.

• Because you're supposed to be able to make a subset out of elements of a set, and have

• that also be a set, but apparently not in the world of ISPs.

• This also violates axiom 6 , by the way.

• The fifth axiom , combining existing sets together into new setswell, I have to

• give it to the internet companies; they've got this down pat: they call itbundling”.

• The violation of the seventh Axiom, the axiom of infinity, is, to be honest, more a criticism

• of modern mathematics than telecommunication companies (though they still violate it).

• Speaking as a physicist, I can tell you that internet service providers and any other physical

• thing in our apparently non-continuous, finite-sized observable universethey can't have

• an infinite amount of anything.

• I can't even say they have an infinite absence of customer service, because that would require

• the possibility of an infinite amount for them to be lacking.

• But there was still something bugging methe manager told me that the offer for \$45 was

• comprised of internet for \$40 a month, plus 5 bucks a month for the router.

• So breaking things down: the possible monthly services provided include {internet for \$40,

• internet for \$50, TV, phone, and wifi router for \$5}.

• Now, it was clear thatinternet for \$40” was an element of the set calledinternet

• plus router”, andinternet plus routerwas an element ofpossible service combinations”,

• whileinternet for \$40”, on its own, was not.

• And yet, the possible service combinations should include all possible combinations of

• services, which Zermelo-Fraenkel would call the power set.

• And thus I realized that the 8th axiom was violated (and, also, the 4th).

• I think at this point we'd hit all 8 axioms, and my internet company violated 7 out of

• 8 – but as all of you doubtless know, the standard Zermelo-Fraenkel axioms often come

• packaged with a 9th axiom.

• And you need only see the name to know this axiom is seriously violated by telecommunications

• companies.

• And so, I almost despaired, except despair can't be constructed without the Axiom schema

• of specification .

• And then I remembered something important: even if all of the axioms I hold dear are

• violated, that doesn't mean there's no logic or reason remaining.

• What's “truein the mathematical world depends on what underlying axioms you take

• to be true.

• So I saidHang on,” and took a deep breath.

• Can I get the 45 dollar option, which consists of internet for \$40 and a router for 5 bucks

• a month, and then just send you back the router so I don't have to pay for it?”

• And you know what the guy from the internet company told me?

• He told me what every scheming mathematician wants to hear from their axioms: “I can't

• tell you you can't do that.”

• The End

• This story is partly based on the truth (I'll leave you to figure out which parts), and

• I first told it at the festival of Bad Ad-Hoc Hypotheses (BAHFest), where the idea is to

• listen to crazy made up scientific theories in the hope that we'll be, well, both entertained,

• and more aware of how science actually works.

• And you can listen to more entertaining stories (science and otherwise) on Audible, this video's

• Audible has the largest selection of audiobooks on the planet, including best-sellers, mysteries,

• memoirs, originals, and science books - I very much enjoyedHow Not To Be Wrong”,

• by Jordan Ellenberg, a more correct but similarly sarcastic book about how to use simple math

• to not be wrong (it has plenty of fascinating stories of big mistakes that have been made

• because people misused math).

• To start listening with a 30-day trial, go to audible.com/minutephysics or text 'minutephysics'

• to 500500 and you can choose 1 audiobook and 2 audible originals each month.

• Again, that's audible.com/minutephysics or text 'minutephysics' to 500500, and

• thanks to Audible for supporting MinutePhysics.

This video is based on joke presentation I gave last year.

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# How ISPs Violate the Laws of Mathematics

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Summer posted on 2021/04/01
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