Boring Numbers

 

In this blog we’ve encountered a “boring number” in the story of when the mathematician, Godfrey Hardy, commented to his protegee, the great Srinivasa Ramanujan, that his taxi had an uninteresting number of 1729 (see post on Taxicab Numbers). Ramanujan quickly replied that 1729 is indeed an interesting number as it is the lowest number that can be expressed as the sum of two cubes of positive numbers in two different ways 1³+ 12³ = 1729 and 10³ + 9³ = 1729.

The idea of boring numbers has captured the interest of Philippe Guglielmetti who has searched through the Online Encyclopedia of Integer Sequences, OEIS, for integers that appear the least frequently.

Consider the number 20,067 – it is the lowest integer that does not appear in any of the stored sequences (note the OEIS has over 360,000 sequences).

An article in Scientific America by Manon Bischoff describes Guglielmetti’s effort in more detail.

 

 

Math Vacation: What is the next number in the sequence...? (jamesmacmath.blogspot.com)

2022 - A Good Year for Mathematics

For this post, I refer readers to the summary by Konstantin Kakaes of Quanta Magazine: The Biggest Math Breakthroughs in 2022 | Quanta Magazine.

Also see this video version: https://youtu.be/Nmgl78a02ys

 

Multiple Dimensions of Time - Part 3

                                            

Credit: Pixabay/CC0 Public Domain

In two prior posts, I explored how different authors and physicists have considered the possibility of multiple dimensions of time. See: Multiple Dimensions of Time and Multiple Dimensions of Time - Part 2.

As unusual as this topic may seem, I'm reading more about how many scientists have considered multiple dimensions of time to be a possibility. Just recently, another article was published this past week in which authors Andrzej Dragan et al. develop an extension of special relativity in 1+3 dimensional spacetime to account for superluminal inertial observers and show that such an extension rules out the conventional dynamics of mechanical point-like particles and forces one to use field-theoretic framework.

Update 12/25/2022 - another article posted: https://mindmatters.ai/2022/12/did-physicists-open-a-portal-to-extra-time-dimension-as-claimed-2/

Gunther Kletetschka, physicist - proposes that time has three dimensions and space is only its consequence - this theory could forever change the way we understand the universe https://share.google/wMBNWsoH2nVpGBByO