Ron Lusk

"I don't know how, but you've managed to be both a poet and an engineer." (So said a professor friend of mine.) It's all about language, expression, and experience.

"I don't know how, but you've managed to be both a poet and an engineer." (So said a professor friend of mine.) It's all about language, expression, and experience.

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Ron Lusk commented on a post on Blogger.

Of course, once

"Exit" "I don't understand you"

"Stop" "Why do you want to stop?"

"Cancel" "You seem to be getting agitated. What does 'Cancel' mean to you?"

"Hey, Google" "Call out to your other gods: they will not hear you..."

(conversation from memory, might be embroidered a bit)

I finally tapped her(?) on top of the head and she left.

*in*the Eliza conversation I couldn't find a way out."Exit" "I don't understand you"

"Stop" "Why do you want to stop?"

"Cancel" "You seem to be getting agitated. What does 'Cancel' mean to you?"

"Hey, Google" "Call out to your other gods: they will not hear you..."

(conversation from memory, might be embroidered a bit)

I finally tapped her(?) on top of the head and she left.

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I've seen the work Compassion does in India, and I've seen the need there, over and over and over. Please help.

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Cool. Something to look forward to, however trivial in the grand scheme of things

Get #AndroidNougat and all of its sweet, new features on select #Nexus devices. Updates start rolling out today. http://goo.gl/FSNE8a

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If Eddystone beacons aren’t on your radar, they should be. The technology is giving brands an edge in an omnichannel world. https://goo.gl/lqvPpz

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Beauty and elegance in primes

**Primes with no sevens**

This is a prime number whose decimal digits are all ones. It has 317 ones. It's not the world record. The number with 1031 ones is also known to be prime!

Even larger guys like this are

*suspected*to be prime. Are there infinitely many? Mathematicians believe so, but they can't prove it.

Why do they believe it? The main reason is that they have an estimate of the "probability" that a number with some number of digits is prime. We can use this to guess the answer to this puzzle.

Of course the whole idea of "probability" is a bit weird here. A number is either prime or not: the math gods do not flip coins to decide which numbers are prime!

Nonetheless, treating primes

*as if*they were random turns out to be useful. Mathematicians have made many guesses using this idea, and then proved these guesses are right, using a lot of extra work.

Of course it's subtle. If I wrote down a number with 317 twos in its decimal expansion, you'd instantly know it's not prime - because it would be even.

In the European Congress of Mathematics, a number theorist named James Maynard just announced something cool. There are infinitely many prime numbers with

*no sevens in their decimal expansion!*

And his proof works equally well for any other number: there infinitely many primes without 0 as a digit, or 1, or 2, or 3, or 4, or 5, and so on.

This is big news, but not because mathematicians really care about primes with no sevens in them. It's because proving something like this requires a deep and delicate understanding of "the music of primes" - the way prime numbers are connected to wave patterns. For more on that, here's something easy to read:

https://plus.maths.org/content/missing-7s

Thanks to +Luis Guzman for pointing out this article, and thanks to +David Roberts for finding James Maynard's paper on this subject, which is here:

• James Maynard, Primes with restricted digits, http://arxiv.org/abs/1604.01041.

He shows that if your base b is sufficiently large, you can find infinitely many primes that are lacking a chosen set of digits, where this set can contain up to b^(23/80) of the digits. Unfortunately I don't see how large b must be - he may not have worked this out. If b = 10 counts as sufficiently large, then since 10^(23/80) is about 1.94, this result would let you avoid any one digit in base 10, but not two. In any event, he does prove, separately, that you can find infinitely many primes that avoid any one digit in base 10.

It uses cool techniques, like "decorrelating Diophantine conditions which dictate when the Fourier transform of the primes is large from digital conditions which dictate when the Fourier transform of numbers with restricted digits is large". It also uses ideas from Markov process theory - that is, the theory of random processes - as well as hard-core number theory concepts.

#bigness #spnetwork arXiv:1604.01041 #numberTheory #primes

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HT: +Stephen M. Harris

A truth about ideas in general (though the article is about writing). Always good to be reminded of this pitfall in our thinking.

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We're getting excited for #IPAday this Thursday, 8/4!! It's one of our favorite days of the year, come celebrate! http://goo.gl/o8cU6P

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See! I do know how to give directions!

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