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Activity

Average numbers for the latest posts (max. 50 posts, posted within the last 4 weeks)

4
comments per post
11
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108
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Top posts in the last 50 posts

Most comments: 150

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2013-04-02 18:09:50 (150 comments, 357 reshares, 1025 +1s)Open 

The True Science of Parallel Universes

Most reshares: 357

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2013-04-02 18:09:50 (150 comments, 357 reshares, 1025 +1s)Open 

The True Science of Parallel Universes

Most plusones: 1025

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2013-04-02 18:09:50 (150 comments, 357 reshares, 1025 +1s)Open 

The True Science of Parallel Universes

Latest 50 posts

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2015-06-26 17:19:38 (4 comments, 11 reshares, 96 +1s)Open 

In case you missed it, NEW VIDEO about How To Detect Secret Nuclear Tests by North Korea (or anyone else)

In case you missed it, NEW VIDEO about How To Detect Secret Nuclear Tests by North Korea (or anyone else)___

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2015-05-31 13:42:40 (20 comments, 11 reshares, 129 +1s)Open 

NEW VIDEO! Upside Down Mountains in Real Life

NEW VIDEO! Upside Down Mountains in Real Life___

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2015-01-22 18:28:50 (66 comments, 13 reshares, 253 +1s)Open 

NEW VIDEO! What IS Angular Momentum?

NEW VIDEO! What IS Angular Momentum?___

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2014-12-22 17:15:06 (29 comments, 42 reshares, 264 +1s)Open 

I'm SUPER EXCITED to announce my new video and first Children's Book, Astronomically Correct Twinkle Twinkle, a collaboration with +Zach Weiner of SMBC Comics and illustrator +Chris Jones .

Please watch and share with all science-minded parents you know!

I'm SUPER EXCITED to announce my new video and first Children's Book, Astronomically Correct Twinkle Twinkle, a collaboration with +Zach Weiner of SMBC Comics and illustrator +Chris Jones .

Please watch and share with all science-minded parents you know!___

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2014-12-20 18:28:07 (7 comments, 20 reshares, 136 +1s)Open 

NEW VIDEO! How an Airplane is Made: https://www.youtube.com/watch?v=7rMgpExA4kM

NEW VIDEO! How an Airplane is Made: https://www.youtube.com/watch?v=7rMgpExA4kM___

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2014-10-28 14:12:22 (39 comments, 39 reshares, 318 +1s)Open 

NEW VIDEO! This is Not a Rainbow

NEW VIDEO! This is Not a Rainbow___

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2014-10-20 19:45:30 (87 comments, 96 reshares, 273 +1s)Open 

Why is the Sun Yellow? Why is the Sky Blue?

Why is the Sun Yellow? Why is the Sky Blue?___

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2014-08-26 19:16:43 (40 comments, 32 reshares, 230 +1s)Open 

NEW VIDEO! Why are Stars Star-Shaped?

NEW VIDEO! Why are Stars Star-Shaped?___

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2014-08-20 14:24:52 (19 comments, 21 reshares, 185 +1s)Open 

How long can you balance a pencil on its tip before it falls over? The answer is shorter than you think... (NEW VIDEO!)

How long can you balance a pencil on its tip before it falls over? The answer is shorter than you think... (NEW VIDEO!)___

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2014-08-19 16:37:06 (46 comments, 14 reshares, 164 +1s)Open 

NEW VIDEO: How to Build a Better City

NEW VIDEO: How to Build a Better City___

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2014-08-04 16:14:49 (34 comments, 27 reshares, 142 +1s)Open 

How did Bats make Ebola Deadly? NEW @minuteearth VIDEO Why do Bats Transmit so many Diseases like Ebola?

How did Bats make Ebola Deadly? NEW @minuteearth VIDEO Why do Bats Transmit so many Diseases like Ebola?___

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2014-06-13 20:32:32 (50 comments, 9 reshares, 202 +1s)Open 

Pot Theft (A Radiolab Adventure) - NEW VIDEO collaboration with +Radiolab

Pot Theft (A Radiolab Adventure) - NEW VIDEO collaboration with +Radiolab___

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2014-05-26 15:04:43 (60 comments, 73 reshares, 339 +1s)Open 

Is the Universe Entirely Mathematical? NEW VIDEO with MIT Professor Max Tegmark Is the Universe Entirely Mathematical? Feat. Max Tegmark

Is the Universe Entirely Mathematical? NEW VIDEO with MIT Professor Max Tegmark Is the Universe Entirely Mathematical? Feat. Max Tegmark___

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2014-04-27 15:46:20 (26 comments, 134 reshares, 388 +1s)Open 

This cool trick allows you to see without glasses! (NEW VIDEO!)

This cool trick allows you to see without glasses! (NEW VIDEO!)___

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2014-04-10 15:43:15 (50 comments, 53 reshares, 497 +1s)Open 

This has nothing to do with physics, but I thought it was important so I made a video about it: uprisings in Venezuela. http://youtu.be/kmvAdRntWH8

This has nothing to do with physics, but I thought it was important so I made a video about it: uprisings in Venezuela. http://youtu.be/kmvAdRntWH8___

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2014-03-28 15:22:12 (27 comments, 27 reshares, 176 +1s)Open 

NEW VIDEO! Relativity Isn't Relative

NEW VIDEO! Relativity Isn't Relative___

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2014-03-19 14:08:53 (60 comments, 103 reshares, 296 +1s)Open 

NEW DISCOVERY About the Big Bang! (and a new video explaining that discovery!)

NEW DISCOVERY About the Big Bang! (and a new video explaining that discovery!)___

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2014-03-12 22:52:41 (21 comments, 84 reshares, 201 +1s)Open 

How much mass energy is there in a raisin? Or a mosquito? Or the earth? Find out in the newest lab from MinuteLabs

How much mass energy is there in a raisin? Or a mosquito? Or the earth? Find out in the newest lab from MinuteLabs___

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2014-02-16 01:30:21 (38 comments, 100 reshares, 476 +1s)Open 

How do Modern Light Bulbs Work? NEW VIDEO!

How do Modern Light Bulbs Work? NEW VIDEO!___

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2014-02-14 17:50:43 (24 comments, 30 reshares, 167 +1s)Open 

Are any Animals Truly Monogamous? NEW VIDEO

Are any Animals Truly Monogamous? NEW VIDEO___

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2014-01-22 21:55:54 (2 comments, 10 reshares, 48 +1s)Open 

Excellent

There is a lot of discussion in various online mathematical forums currently about the interpretation, derivation, and significance of Ramanujan's famous (but extremely unintuitive) formula

1+2+3+4+... = -1/12   (1)

or similar divergent series formulae such as

1-1+1-1+... = 1/2 (2)

or

1+2+4+8+... = -1. (3)

One can view this topic from either a pre-rigorous, rigorous, or post-rigorous perspective (see this page of mine for a description of these three terms: http://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-rigour-and-proofs/  ).  The pre-rigorous approach is not particularly satisfactory: here one is taught the basic rules for manipulating finite sums (e.g. how to add or subtract one finite sum from another), and one is permitted to blindly apply these rules to infinite sums.  This approach can give derivations of identities such as (1), but can also lead to derivations of even more blatant absurdities such as 0=1, which of course makes any similar derivation of (1) look quite suspicious.

From a rigorous perspective, one learns in undergraduate analysis classes the notion of a convergent series and a divergent series, with the former having a well defined limit, which enjoys most of the same laws of series that finite series do (particularly if one restricts attention to absolutely convergent series).  In more advanced courses, one can then learn of more exotic summation methods (e.g. Cesaro summation, p-adic summation or Ramanujan summation) which can sometimes (but not always) be applied to certain divergent series, and which obey some (but not all) of the rules that finite series or absolutely convergent series do.  One can then carefully derive, manipulate, and use identities such as (1), so long as it is made precise at any given time what notion of summation is in force.  For instance, (1) is not true if summation is interpreted in the classical sense of convergent series, but it is true for some other notions of summation, such as Ramanujan summation, or a real-variable analogue of that summation that I describe in this post: http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/#comment-265849

From a post-rigorous perspective, I believe that an equation such as (1) should more accurately be rendered as

1+2+3+4+... = -1/12 + ...

where the "..." on the right-hand side denotes terms which could be infinitely large (or divergent) when interpreted classically, but which one wishes to view as "negligible" for one's intended application (or at least "orthogonal" to that application).  For instance, as a rough first approximation (and assuming implicitly that the summation index in these series starts from n=1 rather than n=0), (1), (2), (3) should actually be written as

1+2+3+4+... = -1/12  + 1/2 infinity^2   (1)'

1-1+1-1+... = 1/2 - (-1)^{infinity} /2 (2)'

or

1+2+4+8+... = -1 + 2^{infinity}  (3)'

and more generally

1+x+x^2+x^3+... = 1/(1-x) + x^{infinity}/(x-1)

where the terms involving infinity do not make particularly rigorous sense, but would be considered orthogonal to the application at hand (a physicist would call these quantities unphysical) and so can often be neglected in one's manipulations.  (If one wanted to be even more accurate here, the 1/2 infinity^2 term should really be the integral of x dx from 0 to infinity.)  To rigorously formalise the notion of ignoring certain types of infinite expressions, one needs to use one of the summation methods mentioned above (with different summation methods corresponding to different classes of infinite terms that one is permitted to delete); but the above post-rigorous formulae can still provide clarifying intuition, once one has understood their rigorous counterparts.  For instance, the formulae (1)' and (3)' are now consistent with the left-hand side being positive and diverging to infinity, and the formula (2)' is consistent with the left-hand side being indeterminate in limit, with both 0 and 1 as limit points.  The fact that divergent series often do not behave well with respect to shifting the series can now be traced back to the fact that the infinite terms in the above identities produce some finite remainders when the infinity in those terms is shifted, say to infinity+1.

For a more advanced example, I believe that the "field of one element" should really be called "the field of 1+... elements", where the ... denotes an expression which one believes to be orthogonal to one's application.___Excellent

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2014-01-22 18:02:05 (9 comments, 22 reshares, 150 +1s)Open 

Evolution vs Natural Selection: NEW VIDEO

Evolution vs Natural Selection: NEW VIDEO___

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2014-01-09 23:25:41 (26 comments, 63 reshares, 261 +1s)Open 

Why is the Solar System Flat? NEW VIDEO!

Why is the Solar System Flat? NEW VIDEO!___

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2014-01-06 15:07:06 (45 comments, 63 reshares, 261 +1s)Open 

What should you do when it's really really cold outside? Go swimming, for one...

What should you do when it's really really cold outside? Go swimming, for one...___

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2013-12-17 17:58:43 (9 comments, 28 reshares, 214 +1s)Open 

Why Winter has the Best Full Moons

Why Winter has the Best Full Moons___

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2013-11-25 18:20:49 (20 comments, 66 reshares, 247 +1s)Open 

When we say Mt. Everest is 8850m tall, how do we know what sea level would be beneath the mountain? NEW VIDEO!

When we say Mt. Everest is 8850m tall, how do we know what sea level would be beneath the mountain? NEW VIDEO!___

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2013-10-26 17:31:31 (15 comments, 61 reshares, 253 +1s)Open 

NEW VIDEO! Three Simple Ways to Time Travel

(with help from +Aatish Bhatia )

NEW VIDEO! Three Simple Ways to Time Travel

(with help from +Aatish Bhatia )___

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2013-10-19 16:05:38 (13 comments, 44 reshares, 200 +1s)Open 

Which Came First - the Rain or the Rainforest? NEW VIDEO

Which Came First - the Rain or the Rainforest? NEW VIDEO___

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2013-10-18 16:10:01 (6 comments, 22 reshares, 141 +1s)Open 

Magnetic Levitation!! NEW VIDEO

Magnetic Levitation!! NEW VIDEO___

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2013-10-01 19:47:36 (6 comments, 5 reshares, 179 +1s)Open 

We printed the MinutePhysics logo using the bubble "printer" at the Ontario Science Center

If you squint you can almost make out the Minute Physics logo behind +Henry Reich printed in the bubbles.___We printed the MinutePhysics logo using the bubble "printer" at the Ontario Science Center

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2013-09-23 13:55:04 (13 comments, 51 reshares, 166 +1s)Open 

MAGNETS: How do they work? NEW VIDEO (with +Veritasium)

MAGNETS: How do they work? NEW VIDEO (with +Veritasium)___

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2013-09-18 22:45:56 (23 comments, 43 reshares, 197 +1s)Open 

What is the Biggest Organism on Earth? NEW MinuteEarth Video: The Biggest Organism on Earth

What is the Biggest Organism on Earth? NEW MinuteEarth Video: The Biggest Organism on Earth___

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2013-09-06 16:41:20 (2 comments, 29 reshares, 87 +1s)Open 

Help Free Chopin from copyright! Back the New Musopen kickstarter: http://www.kickstarter.com/projects/Musopen/set-chopin-free

Help Free Chopin from copyright! Back the New Musopen kickstarter: http://www.kickstarter.com/projects/Musopen/set-chopin-free___

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2013-09-05 01:50:49 (13 comments, 18 reshares, 110 +1s)Open 

A game inspired by particle physics is trying to get greenlit on Steam - check out their demo and support them! 

A game inspired by particle physics is trying to get greenlit on Steam - check out their demo and support them! ___

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2013-09-03 21:39:43 (12 comments, 19 reshares, 105 +1s)Open 

John Green continues his excellent video series about health care (and I get to be a case study!)

John Green continues his excellent video series about health care (and I get to be a case study!)___

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2013-08-31 16:35:58 (11 comments, 12 reshares, 127 +1s)Open 

Deep sea, deep sea, have you any fish? (NEW VIDEO)

Deep sea, deep sea, have you any fish? (NEW VIDEO)___

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2013-08-30 03:51:38 (16 comments, 33 reshares, 211 +1s)Open 

Science, Religion, and the Big Bang [MinutePhysics video]

Science, Religion, and the Big Bang [MinutePhysics video]___

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2013-08-29 01:27:25 (10 comments, 2 reshares, 102 +1s)Open 

+Veritasium  has a google+ page!

Took +MinutePhysics on my tour of Sydney today___+Veritasium  has a google+ page!

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2013-08-28 17:54:13 (2 comments, 1 reshares, 24 +1s)Open 

Sweet new MinutePhysics posters are now available! They have a section of the real night sky in the background - how many constellations can you find? http://dft.ba/-darkskyposter

Sweet new MinutePhysics posters are now available! They have a section of the real night sky in the background - how many constellations can you find? http://dft.ba/-darkskyposter___

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2013-07-01 03:45:16 (18 comments, 42 reshares, 176 +1s)Open 

Where is the True North Pole? NEW VIDEO

Where is the True North Pole? NEW VIDEO___

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2013-05-30 15:18:37 (24 comments, 48 reshares, 200 +1s)Open 

We all know what it's like to feel hot and cold things... but are we really sensing Temperature? [NEW VIDEO]

We all know what it's like to feel hot and cold things... but are we really sensing Temperature? [NEW VIDEO]___

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2013-04-18 14:15:52 (24 comments, 56 reshares, 240 +1s)Open 

What's one of the biggest secrets in physics? NEW VIDEO

What's one of the biggest secrets in physics? NEW VIDEO___

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2013-04-02 18:09:50 (150 comments, 357 reshares, 1025 +1s)Open 

The True Science of Parallel Universes

The True Science of Parallel Universes___

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2013-03-08 19:54:53 (22 comments, 80 reshares, 349 +1s)Open 

I'm so thrilled to announce a NEW YOUTUBE CHANNEL!! MinuteEarth, sister channel to MinutePhysics!

I'm so thrilled to announce a NEW YOUTUBE CHANNEL!! MinuteEarth, sister channel to MinutePhysics!___

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2013-02-25 19:47:16 (61 comments, 147 reshares, 469 +1s)Open 

How Big is the Universe? [NEW VIDEO]

How Big is the Universe? [NEW VIDEO]___

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2013-02-16 20:38:30 (22 comments, 131 reshares, 493 +1s)Open 

What is The Universe? NEW VIDEO: What Is The Universe?

What is The Universe? NEW VIDEO: What Is The Universe?___

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2013-02-07 15:50:41 (20 comments, 56 reshares, 147 +1s)Open 

Check out this list of some of the BEST Science Online [in VIDEO form]

Check out this list of some of the BEST Science Online [in VIDEO form]___

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2013-01-25 13:37:26 (36 comments, 101 reshares, 403 +1s)Open 

New Video! What happens when an Immovable Object meets an Unstoppable Force?

New Video! What happens when an Immovable Object meets an Unstoppable Force?___

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2013-01-03 19:13:29 (29 comments, 68 reshares, 277 +1s)Open 

New MinutePhysics video! Another Physics Misconception...

New MinutePhysics video! Another Physics Misconception...___

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2012-12-28 15:36:04 (33 comments, 31 reshares, 162 +1s)Open 

New MinutePhysics video! How do we know the earth is round?

New MinutePhysics video! How do we know the earth is round?___

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