By using this site, you agree to the Privacy Policy and Terms of Use.
Accept

News Junction

Notification Show More
Font ResizerAa
  • Home
  • World News
    World NewsShow More
    ‘Don’t know what to do’: Johor Bahru’s heritage businesses near RTS station grapple with rising rents, inflation
    ‘Don’t know what to do’: Johor Bahru’s heritage businesses near RTS station grapple with rising rents, inflation
    May 15, 2025
    Jurors view ‘Freak off’ images too graphic to be shown to public
    Jurors view ‘Freak off’ images too graphic to be shown to public
    May 15, 2025
    Gaza hospital attack: Analysis contradicts Israel’s evidence justifying airstrike | World News
    Gaza hospital attack: Analysis contradicts Israel’s evidence justifying airstrike | World News
    May 15, 2025
    For U.S. Defense Industry, These Minerals Really are ‘Critical’
    For U.S. Defense Industry, These Minerals Really are ‘Critical’
    May 14, 2025
    Did the US flinch first in tariff war with China? | Trade War News
    Did the US flinch first in tariff war with China? | Trade War News
    May 14, 2025
  • Business
    BusinessShow More
    Ukraine blows up bridges to consolidate its positions in Russia
    Ukraine blows up bridges to consolidate its positions in Russia
    August 18, 2024
    Commentary: AI phones from Google and Apple will erode trust in everything
    Commentary: AI phones from Google and Apple will erode trust in everything
    August 18, 2024
    The most famous Indian Dishes – Insights Success
    The most famous Indian Dishes – Insights Success
    August 18, 2024
    Life on the road as a female long rides cyclist
    Life on the road as a female long rides cyclist
    August 18, 2024
    UK inflation rises to 2.2%
    UK inflation rises to 2.2%
    August 18, 2024
  • Cryptocurrency
    CryptocurrencyShow More
    Bitwise CIO bats for diversified crypto investment, compares Bitcoin to Google
    Bitwise CIO bats for diversified crypto investment, compares Bitcoin to Google
    May 15, 2025
    The Role of Altcoins in 2025’s Crypto Market
    The Role of Altcoins in 2025’s Crypto Market
    May 15, 2025
    Bitcoin Spread Oscillator Signals Growing Altcoin Momentum – Altseason Entry Signal?
    Bitcoin Spread Oscillator Signals Growing Altcoin Momentum – Altseason Entry Signal?
    May 15, 2025
    Dan Morehead Sees Decades of Bitcoin (BTC) Upside Ahead as Pantera Bets on Broad Crypto Future
    Dan Morehead Sees Decades of Bitcoin (BTC) Upside Ahead as Pantera Bets on Broad Crypto Future
    May 15, 2025
    Price analysis 3/10: SPX, DXY, BTC, ETH, XRP, BNB, SOL, DOGE, ADA, PI
    Price analysis 3/10: SPX, DXY, BTC, ETH, XRP, BNB, SOL, DOGE, ADA, PI
    May 14, 2025
  • Technology
    TechnologyShow More
    How to Improve Your Spotify Recommendations
    How to Improve Your Spotify Recommendations
    August 18, 2024
    X says it’s closing operations in Brazil
    X says it’s closing operations in Brazil
    August 18, 2024
    Supermoon set to rise: Top tips for amateur photographers | Science & Tech News
    Supermoon set to rise: Top tips for amateur photographers | Science & Tech News
    August 18, 2024
    Scientists Want to See Videos of Your Cat for a New Study
    Scientists Want to See Videos of Your Cat for a New Study
    August 18, 2024
    OpenAI’s new voice mode let me talk with my phone, not to it
    OpenAI’s new voice mode let me talk with my phone, not to it
    August 18, 2024
  • Entertainment
  • Sports News
  • People
  • Trend
Reading: The Lawlessness of Large Numbers
Share
Font ResizerAa

News Junction

  • World News
  • Business
  • Technology
  • Cryptocurrency
  • Trend
  • Entertainment
Search
  • Recent Headlines in Entertainment, World News, and Cryptocurrency – NewsJunction
  • World News
  • Business
  • Cryptocurrency
  • Technology
  • Entertainment
  • Sports News
  • People
  • Trend
Have an existing account? Sign In
Follow US
News Junction > Blog > Trend > The Lawlessness of Large Numbers
The Lawlessness of Large Numbers
Trend

The Lawlessness of Large Numbers

Published August 20, 2023
Share
4 Min Read
SHARE

The original version of this story appeared in Quanta Magazine.

So far this year, Quanta has chronicled three major advances in Ramsey theory, the study of how to avoid creating mathematical patterns. The first result put a new cap on how big a set of integers can be without containing three evenly spaced numbers, like {2, 4, 6} or {21, 31, 41}. The second and third similarly put new bounds on the size of networks without clusters of points that are either all connected, or all isolated from each other.

The proofs address what happens as the numbers involved grow infinitely large. Paradoxically, this can sometimes be easier than dealing with pesky real-world quantities.

For example, consider two questions about a fraction with a really big denominator. You might ask what the decimal expansion of, say, 1/42503312127361 is. Or you could ask if this number will get closer to zero as the denominator grows. The first question is a specific question about a real-world quantity, and it’s harder to calculate than the second, which asks how the quantity 1/n will “asymptotically” change as n grows. (It gets closer and closer to 0.)

“This is a problem plaguing all of Ramsey theory,” said William Gasarch, a computer scientist at the University of Maryland. “Ramsey theory is known for having asymptotically very nice results.” But analyzing numbers that are smaller than infinity requires an entirely different mathematical toolbox.

Gasarch has studied questions in Ramsey theory involving finite numbers that are too big for the problem to be solved by brute force. In one project, he took on the finite version of the first of this year’s breakthroughs—a February paper by Zander Kelley, a graduate student at the University of Illinois, Urbana-Champaign, and Raghu Meka of the University of California, Los Angeles. Kelley and Meka found a new upper bound on how many integers between 1 and N you can put into a set while avoiding three-term progressions, or patterns of evenly spaced numbers.

Though Kelley and Meka’s result applies even if N is relatively small, it doesn’t give a particularly useful bound in that case. For very small values of N, you’re better off sticking to very simple methods. If N is, say, 5, just look at all the possible sets of numbers between 1 and N, and pick out the biggest progression-free one: {1, 2, 4, 5}.

But the number of different possible answers grows very quickly and makes it too difficult to employ such a simple strategy. There are more than 1 million sets consisting of numbers between 1 and 20. There are over 1060 using numbers between 1 and 200. Finding the best progression-free set for these cases takes a hefty dose of computing power, even with efficiency-improving strategies. “You need to be able to squeeze a lot of performance out of things,” said James Glenn, a computer scientist at Yale University. In 2008, Gasarch, Glenn, and Clyde Kruskal of the University of Maryland wrote a program to find the biggest progression-free sets up to an N of 187. (Previous work had gotten the answers up to 150, as well as for 157.) Despite a roster of tricks, their program took months to finish, Glenn said.

#Lawlessness #Large #Numbers

TAGGED:Computer ScienceComputinglargeLawlessnessMathmathematicsnumbersquanta magazine
Share This Article
Facebook Twitter Pinterest Whatsapp Whatsapp LinkedIn Email Copy Link Print
Share
What do you think?
Love0
Sad0
Happy0
Sleepy0
Angry0
Dead0
Wink0
Previous Article Adobe co-founder John Warnock dies at 82 Adobe co-founder John Warnock dies at 82
Next Article Russia’s Luna-25 smashes into moon in failure Russia’s Luna-25 smashes into moon in failure
- Advertisement -

Latest Post

Bitwise CIO bats for diversified crypto investment, compares Bitcoin to Google
Bitwise CIO bats for diversified crypto investment, compares Bitcoin to Google
Cryptocurrency
The Role of Altcoins in 2025’s Crypto Market
The Role of Altcoins in 2025’s Crypto Market
Cryptocurrency
‘Don’t know what to do’: Johor Bahru’s heritage businesses near RTS station grapple with rising rents, inflation
‘Don’t know what to do’: Johor Bahru’s heritage businesses near RTS station grapple with rising rents, inflation
World News
Bitcoin Spread Oscillator Signals Growing Altcoin Momentum – Altseason Entry Signal?
Bitcoin Spread Oscillator Signals Growing Altcoin Momentum – Altseason Entry Signal?
Cryptocurrency
Jurors view ‘Freak off’ images too graphic to be shown to public
Jurors view ‘Freak off’ images too graphic to be shown to public
World News
Gaza hospital attack: Analysis contradicts Israel’s evidence justifying airstrike | World News
Gaza hospital attack: Analysis contradicts Israel’s evidence justifying airstrike | World News
World News
- Advertisement -

You Might Also Like

Russia and India Are Racing to Put Landers on the Moon
Trend

Russia and India Are Racing to Put Landers on the Moon

August 18, 2023
Could AI-Generated Porn Help Protect Children?
Trend

Could AI-Generated Porn Help Protect Children?

August 22, 2023
Extra-Juicy QSR Chicken Tenders : Hand-Breaded Chicken Tenders
Trend

Extra-Juicy QSR Chicken Tenders : Hand-Breaded Chicken Tenders

July 9, 2024
Vivo V29e set to launch with 50MP selfie camera and color-changing rear panel for under US0
Trend

Vivo V29e set to launch with 50MP selfie camera and color-changing rear panel for under US$400

August 21, 2023

About Us

NEWS JUNCTION (NewsJunction.xyz) Your trusted destination for global news. Stay informed with our timely and accurate reporting on diverse topics, including politics, technology, science, entertainment, sports, and more. Count on us for unbiased and reliable updates at your fingertips.

Quick Link

  • About
  • Disclaimer
  • Privacy Policy
  • Terms of Use
  • Contact

Top Categories

  • World News
  • Business
  • Technology
  • Entertainment
  • Cryptocurrency
  • Sports News
  • Trend
  • People

Subscribe

Subscribe to our newsletter to get our newest articles instantly!

    © 2023 News Junction.
    • Blog
    • Advertise
    • Contact
    Welcome Back!

    Sign in to your account

    Username or Email Address
    Password

    Lost your password?