Tuesday, 11 July 2017

Using math to investigate possibility of time travel

After some serious number crunching, a UBC researcher has come up with a mathematical model for a viable time machine.
Ben Tippett, a mathematics and physics instructor at UBC's Okanagan campus, recently published a study about the feasibility of time travel. Tippett, whose field of expertise is Einstein's theory of general relativity, studies black holes and science fiction when he's not teaching. Using math and physics, he has created a formula that describes a method for time travel.
"People think of time travel as something as fiction," says Tippett. "And we tend to think it's not possible because we don't actually do it. But, mathematically, it is possible."
Ever since HG Wells published his book Time Machine in 1885, people have been curious about time travel--and scientists have worked to solve or disprove the theory, he says. In 1915 Albert Einstein announced his theory of general relativity, stating that gravitational fields are caused by distortions in the fabric of space and time. More than 100 years later, the LIGO Scientific Collaboration--an international team of physics institutes and research groups--announced the detection of gravitational waves generated by colliding black holes billions of lightyears away, confirming Einstein's theory.
The division of space into three dimensions, with time in a separate dimension by itself, is incorrect, says Tippett. The four dimensions should be imagined simultaneously, where different directions are connected, as a space-time continuum. Using Einstein's theory, Tippett says that the curvature of space-time accounts for the curved orbits of the planets.
In "flat" -- or uncurved -- space-time, planets and stars would move in straight lines. In the vicinity of a massive star, space-time geometry becomes curved and the straight trajectories of nearby planets will follow the curvature and bend around star.
"The time direction of the space-time surface also shows curvature. There is evidence showing the closer to a black hole we get, time moves slower," says Tippett. "My model of a time machine uses the curved space-time -- to bend time into a circle for the passengers, not in a straight line. That circle takes us back in time."
While it is possible to describe this type of time travel using a mathematical equation, Tippett doubts that anyone will ever build a machine to make it work.
"HG Wells popularized the term 'time machine' and he left people with the thought that an explorer would need a 'machine or special box' to actually accomplish time travel," Tippett says. "While is it mathematically feasible, it is not yet possible to build a space-time machine because we need materials--which we call exotic matter--to bend space-time in these impossible ways, but they have yet to be discovered."
For his research, Tippett created a mathematical model of a Traversable Acausal Retrograde Domain in Space-time (TARDIS). He describes it as a bubble of space-time geometry which carries its contents backward and forwards through space and time as it tours a large circular path. The bubble moves through space-time at speeds greater than the speed of light at times, allowing it to move backward in time.
"Studying space-time is both fascinating and problematic. And it's also a fun way to use math and physics," says Tippett. "Experts in my field have been exploring the possibility of mathematical time machines since 1949. And my research presents a new method for doing it."
Tippett's research was recently published in the IOPscience Journal Classical and Quantum Gravity.

Tuesday, 13 June 2017

Top ten facts about maths

1. In 2010 on World Maths Day, 1.13 million students from more than 235 countries set a record correctly answering 479,732,613 questions. 

2. Americans called mathematics ‘math’, arguing that ‘mathematics’ functions as a singular noun so ‘math’ should be singular too. 

3. They have been calling maths ‘math’ for much longer than we have called it ‘maths’. 

4. ‘Mathematics’ is an anagram of ‘me asthmatic’. 

5. The only number in English that is spelled with its letters in alphabetical order is ‘forty’. 

6. The only Shakespeare play to include the word ‘mathematics’ is The Taming Of The Shrew. 

7. Notches on animal bones show that people have been doing mathematics, or at least making computations, since around 30,000BC. 

8. The word ‘hundrath’ in Old Norse, from which our ‘hundred’ derives, meant not 100 but 120. 

9. “Pure mathematics is, in its way, the poetry of logical ideas.” (Albert Einstein). 

10. “Mathematics [is] the subject in which we never know what we are talking about nor whether what we are saying is true.” (Bertrand Russell).

22 amezing....

1. If you write out pi to two decimal places, backwards it spells "pie".

3.14 = PIE.
BuzzFeed / Kelly Oakes / Via Twitter: @TrueFacts
3.14 = PIE.

2. A French word for pie chart is "camembert".

Because of course it is.
Ezergil
Because of course it is.

3. The spiral shapes of sunflowers follow a Fibonacci sequence.

That's where you add the two preceding numbers in the sequence to give you the next one. So it starts 1, 1, 2, 3, 5, 8, 13, 21, etc. The Fibonacci sequence shows up in nature a fair bit.
Irantzu_Arbaizagoitia
That's where you add the two preceding numbers in the sequence to give you the next one. So it starts 1, 1, 2, 3, 5, 8, 13, 21, etc. The Fibonacci sequence shows up in nature a fair bit.

4. The Fibonacci sequence is encoded in the number 1/89.

1/89 = 0.01 + 0.001 + 0.0002 + 0.00003 + 0.000005 + 0.0000008 + 0.00000013 + 0.000000021 + 0.0000000034 etc.
Jupiterimages / Thinkstock
1/89 = 0.01 + 0.001 + 0.0002 + 0.00003 + 0.000005 + 0.0000008 + 0.00000013 + 0.000000021 + 0.0000000034 etc.

5. A pizza that has radius "z" and height "a" has volume Pi × z × z × a.

Because the area of a circle is Pi multiplied by the radius squared (which can be written out as Pi × z × z). Then you multiply by the height to get the total volume.
pizzagifs.tumblr.com
Because the area of a circle is Pi multiplied by the radius squared (which can be written out as Pi × z × z). Then you multiply by the height to get the total volume.

6. The word hundred is derived from the word "hundrath", which actually means 120 and not 100.

Hundrath is Old Norse.
mshch
Hundrath is Old Norse.

7. 111,111,111 × 111,111,111 = 12,345,678,987,654,321.

It also works for smaller numbers: 111 × 111 = 12321.
Via studentbeans.com
It also works for smaller numbers: 111 × 111 = 12321.

8. In a room of just 23 people there’s a 50% chance that two people have the same birthday.

It's called the Birthday Problem. In a room of 75 there's a 99% chance of two people matching.
DimitrovoPhtography/DimitrovoPhtography
It's called the Birthday Problem. In a room of 75 there's a 99% chance of two people matching.

9. Zero is the only number that can't be represented in Roman numerals.

The Latin word "nulla" would have been used instead.
Flickr: wwarby / Creative Commons
The Latin word "nulla" would have been used instead.

10. (6 × 9) + (6 + 9) = 69.

11. We tend to think of odd numbers as male and even numbers as female.

This ancient belief was tested by James Wilkie and Galen Bodenhausen of Northwestern University. In his latest book, Alex Bellos writes: "They showed respondents randomly assigned pictures of the faces of young babies, each next to a three-digit number that was either odd-odd-odd or even-even-even, and asked them to guess the baby’s sex [...] Respondents were about 10 per cent more likely to say that a baby paired with odd numbers was a boy, than if the same baby was paired with even numbers."
crazydiva
This ancient belief was tested by James Wilkie and Galen Bodenhausen of Northwestern University. In his latest book, Alex Bellos writes: "They showed respondents randomly assigned pictures of the faces of young babies, each next to a three-digit number that was either odd-odd-odd or even-even-even, and asked them to guess the baby’s sex [...] Respondents were about 10 per cent more likely to say that a baby paired with odd numbers was a boy, than if the same baby was paired with even numbers."

12. If you shuffle a pack of cards properly, chances are that exact order has never been seen before in the whole history of the universe.

Proof.

13. Zero is an even number.

But people take longer to decide whether it's even or odd because it's not as easy for us to mentally categorise.
daizuoxin / Thinkstock
But people take longer to decide whether it's even or odd because it's not as easy for us to mentally categorise.

14. There's not enough space in the known universe to write out a googolplex on paper.

According to Carl Sagan in the original Cosmos series. A googolplex is 10 to the power of a googol, or 10 to the power of 10 to the power of 100. This website will write it out for you (or start... it won't ever finish because your computer won't have enough memory).

15. The most popular favourite number is 7.

Nearly 3000 people, around 10% of the total asked, chose 7 as their favourite number in an online poll by Alex Bellos. The second most popular was 3.
Flickr: losmininos / Creative Commons
Nearly 3000 people, around 10% of the total asked, chose 7 as their favourite number in an online poll by Alex Bellos. The second most popular was 3.

16. That might be because 7 is "arithmetically unique".

It's the only number below 10 you can't multiply or divide and keep within group. For example, 5 you can multiply by 2 to get 10 (still within the 1-10 group), 6 and 8 you can divide by 2.
Flickr: pagedooley / Creative Commons
It's the only number below 10 you can't multiply or divide and keep within group. For example, 5 you can multiply by 2 to get 10 (still within the 1-10 group), 6 and 8 you can divide by 2.

17. 7 also shows up a lot in human culture.

We have seven deadly sins, and seven wonders of the world. Not to mention colours of the rainbow, pillars of wisdom, seas, dwarves, days in the week...This might be because when these things came about there were celestial bodies visible in the sky (the Sun, the Moon, Venus, Mercury, Mars, Jupiter and Saturn).
headlikeanorange.tumblr.com
We have seven deadly sins, and seven wonders of the world. Not to mention colours of the rainbow, pillars of wisdom, seas, dwarves, days in the week...
This might be because when these things came about there were celestial bodies visible in the sky (the Sun, the Moon, Venus, Mercury, Mars, Jupiter and Saturn).

18. The number 4 is considered unlucky in much of Asia.

That's because the words for "four" in Japanese, Cantonese, Mandarin and Korean (shi, sei, si, sa) sound the same as the words in those languages for death.
Flickr: boklm / Creative Commons
That's because the words for "four" in Japanese, Cantonese, Mandarin and Korean (shi, sei, si, sa) sound the same as the words in those languages for death.

19. .999999... = 1

Here's the proof:If 10N = 9.9999...Then N = .9999....Subtract N from 10N, leaving you with 9N=9.So then N=1. But we already know that N=.9999... as well. So 1=.9999....
Flickr: andrec / Creative Commons
Here's the proof:
If 10N = 9.9999...
Then N = .9999....
Subtract N from 10N, leaving you with 9N=9.
So then N=1. But we already know that N=.9999... as well.
So 1=.9999....

20. Cicadas use prime numbers as an evolutionary strategy.

Cicadas incubate underground for long periods of time – 13 or 17 years – before coming out to mate. 13 and 17 are both prime numbers. It's thought cicadas ended up in these prime number life-cycles because it meant they came into contact with predators on more round numbered life-cycles less often.
Flickr: oakleyoriginals / Creative Commons
Cicadas incubate underground for long periods of time – 13 or 17 years – before coming out to mate. 13 and 17 are both prime numbers. It's thought cicadas ended up in these prime number life-cycles because it meant they came into contact with predators on more round numbered life-cycles less often.

21. 10! seconds is exactly 6 weeks.

10! means 10 factorial. 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3628800 seconds. Which is 42 days, or 6 weeks, exactly.
agafapaperiapunta/agafapaperiapunta
10! means 10 factorial. 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3628800 seconds. Which is 42 days, or 6 weeks, exactly.

22. Take any four digit number, follow these steps, and you'll end up with 6174.

1. Choose a four digit number (the only condition is that it has at least two different digits).2. Arrange the digits of the four digit number in descending then ascending order. 3. Subtract the smaller number from the bigger one. 4. Repeat. Eventually you'll end up at 6174, which is known as Kaprekar's constant. If you then repeat the process you'll just keep getting 6174 over and over again.
stevanovicigor / BuzzFeed
1. Choose a four digit number (the only condition is that it has at least two different digits).
2. Arrange the digits of the four digit number in descending then ascending order.
3. Subtract the smaller number from the bigger one.
4. Repeat.
Eventually you'll end up at 6174, which is known as Kaprekar's constant. If you then repeat the process you'll just keep getting 6174 over and over again.