Weekly Roundup 123

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Weekly Roundup 121

Death is such an interesting concept. The medical definition of death is “a permanent cessation of circulatory and respiratory functions” or “a permanent cessation of the functions of the entire brain.” Through this definition it’s clear that when we hear stories about heart attack victims being “dead for an hour” before being revived that this is clearly not true death. Death is, beyond all things, irreversible. But there is a contradiction here: if the person suffering cardiac arrest had not been revived then they would have been dead during the time which the revival efforts were in effect. You can think of this as Schrödinger’s corpse. If I presented you a body and asked you if the person was dead then you could certainly check if there was a pulse or breathing. If I then take the body away and perform a revival procedure with a 50% chance of success then you don’t know whether the body was dead when you checked it because the state it was in might not have been permanent.

This is clearly slightly ridiculous. There has to be a way to define death such that it truly is permanent, no matter how great our technological advancement becomes. This is where the concept of information theoretic death comes from. Information theoretic death occurs when the thermodynamic information in a brain becomes so scrambled that the second law of thermodynamics prevents its recovery. Of course we are far away from the point where we could extract the information from a brain and use it to recover a personality but if such a day does come, then the ultimate limit of our resuscitation will be imposed by information theoretic death.

Until tomorrow, goodnight.

Weekly Roundup 120

I was recently asked that age old question: “Which is more fundamental, physics or mathematics?” I think I’ll try and answer this a slightly differently from the way I answered it before. There I demonstrated the difference regarding the nature of physics as an experimental subject while mathematics deals with absolutes but of course this isn’t a satisfactory argument for a theorist and I also feel my previous argument skirts around the inherent problems that I see with a mathematics decoupled from physics. In order to do this I’m going hop back to the concepts of vector spaces and linear algebra which I covered here.

Now in this weekly roundup I pseudo introduce the idea of a vector space and make the bold claim that “all quadratic equations… add and multiply just like vectors.” Of course vectors are multiplied by either the dot product or the cross product and that isn’t how we’d try and multiply quadratics. If we ignore the cross product for a moment (it is an example of what is known as a bilinear map and isn’t relevant here) we can look at the dot product or more generally, inner products. Vector spaces often get assigned an inner product, this is a function which takes in two vectors and produces a scalar and has to follow certain rules. The dot product is the example often used for regular vectors but so long as the following conditions hold (for a real space):

  • 〈 a b 〉 = 〈 b , a 〉
  • 〈 λb 〉 = λ〈 a , b 〉
  • 〈 a + b  c 〉 = 〈 a , c 〉 + 〈 b , c 〉
  • 〈 a a 〉 ≥ 0

then 〈 a b 〉 will be the inner product. This generality is the brilliance of maths. You can define anything as a vector and assign it to a vector space with a nice inner product so long as you follow certain rules, certain axioms. And this is the importance of physics. These axioms are in fact determined by the physical world, for instance the reason that the seemingly arbitrary rule: 〈 a a 〉 ≥ 0 exists is because the inner product is providing the concept of “length” to a vector. If you give mathematicians free reign (as some people foolishly do) they’ll try and start producing vectors with imaginary length and other non-physical results.

The construction of useful axioms is perhaps the greatest gift that physics provides for maths. Until tomorrow, goodnight.

Weekly Roundup 119

The science journal Nature recently produced a news feature which described an interesting idea. Whether one likes the ethics of it or not, testing medical advancements on mice have been the propulsion for many treatments in the last 50 years. Now in order to make sure tests upon mice have completely controlled variables, the mice often dwell in sterilised environments. The breeding facilities come with autoclaves for regular purification and ventilation and filtration systems for the mice’s air and water. This paper goes into the ritual cleanliness required to meet scientific standards.

However there is the argument to be made, which this Nature feature is making, that the sanitised conditions these rodents live in leaves them with immune systems that are unbelievably flimsy. Now only about 20% of drugs that succeed on mice actually work on human or primate trials, much of this is normally blamed on the biological differences between mice and humans but when you’re testing on a creature with an immune system drastically reduced, we can see that there will be an effect. Overall there many differnces between wild and lab mice such as diet, sunlight exposure or ambient temperature. At least it is possible to repair the laboratory mice’s immune systems by exposing them to wild mice (with an unfortuante number of fatalities along the way).

How much should we try and makes our subjects emulate nature and how much should we try and keep controlled? This is certainly an intersting idea to think about. Until tommorow, goodnight.

Weekly Roundup 118

Maths and physics. It seems like the two can’t really be separated. There is no doubt that advanced maths is need to understand advanced physics but just having the mathematical aptitude doesn’t mean you’ll have the insight to use it practically. If any reader is planning on studying either of these subjects at university, or perhaps a mix of the two, then I would advice they read the syllabus of their preferred university. There have certainly been many times when students have picked incorrectly for their preference but ultimately there is quite a lot of overlap in most universities, especially if the physics course is particularly mathematically rigorous.

Anyway, it is an very fundamental questions: Is any of the mathematics that is performed actually inherent to nature? In other words, is a maths just a human invention to understand the world or not?

Last month a wonderful YouTuber, 3Blue1Brown, uploaded a video about the uncertainty inherent in waves. As a quick sum up, although I recommend the reader watches the video in full, the only way you can be certain of the frequency of a sinusoidal wave is if the wave is infinitely long. If the wave only has a finite length then there will always be some uncertainty in the frequency your measuring.

Two waves
Two waves with slightly different frequencies. My own design on Desmos.

You see, if you were to only take the first full wavelength, you could be excused for thinking these two waves had the same frequency but by the third peak there is notable difference. The only way to be 100% certain that two waves have the same frequency is to travel infinitely far along them checking at each point. So, as no wave is infinitely long, uncertainty is inherent which then proceeds down into the quantum uncertainty that is more familiar.

I remember one of my colleagues stating that it was truly amazing that the ancient Greeks with their trigonometric functions had landed upon a fundamental aspect of  the universe. Of course this isn’t necessarily true it’s just that the mathematics of waves has been built on sine and cosine so when we use waves to model particles all the baggage comes with them.

Anyway, until tomorrow, goodnight.

Weekly Roundup 117

This week an interesting article was published in Nature. It wasn’t a scientific article; in fact it was published in the humanities division but nevertheless is highly relevant to science. It is a paper on discourse analysis, the analysis of communication and language in the vaguest sense. This paper in particular examines how hierarchies exist in people perceived to have knowledge and also within different types of knowledge itself. This is clearly relevant in the realm of science communication and may very well be needed considering a certain movement of anti-intellectualism highlighted by quotes such as “people in [Britain] have had enough of experts,” made by Michael Gove two years ago referring to the Brexit debate. No matter which side of the European Union question you fall on, it is undeniable that phrases like “alternative facts” have certainly become all the rage.

There are certain arguments to be made that politicising science is a source of this social backlash but then again how can scientists be expected to change their results to match people’s expectations? As the paper points out, majority thought does not make Truth. No doubt some readers of this post may be sitting back thinking aloof thoughts along the lines of how reasoned and logical their thoughts are and it’s definitely the other side of the argument who has the problem accepting facts. Well over a year ago I wrote this weekly roundup about a paper showing how easily confirmation bias allows us to be tricked.

Ultimately the majority doesn’t have a monopoly on truth, but neither do scientists in a way. It is undeniable that some forms of truth are more valid then others, for instance I am much quicker to believe a collaboration of atmospheric scientists’ opinions on air pollution as opposed to OPEC’s, yet it’s foolish to think any conclusion is totally absolute, and unscientific to place it beyond question.

Until tomorrow, goodnight.

Weekly Roundup 116

This week science has been filled with considerable sadness as unfortunately Professor Stephen Hawking has died. He passed away on Wednesday 14th of March at age 76. I was actually present at Trinity College Cambridge last year when his 75th birthday celebration was being held. Now Professor Hawking is perhaps one of the most iconic scientists of the modern age and his book, A Brief History of Time, is perhaps one of the most famous and accessible for any layperson wishing to learn about cosmology.  It is this book that brings forth the famous and perhaps apocryphal saying that “each equation in a book halves the number of people who’ll read it.” As a result of no doubt similar advice, Hawking included E = mc2 as the only equation, a perfect choice really.

Perhaps more than all this the most famous thing about Professor Hawking is his suffering with motor neurone disease. I suppose we should all consider ourselves fortunate that Hawking didn’t listen to his original life expectancy of a few years when he was diagnosed at 21 and that the disease progressed much more slowly than expected. Though he never won the Nobel prize in his life, and the award is never given posthumously, there is still one more paper left to be published with Hawking’s name on it. He has spent the last few years working with one of his previous students Professor Malcolm Perry and Harvard physicist Professor Andrew Strominger. The final calculations still need to be performed but it will be likely less than a year until we say Hawking’s last paper was published.

As for what it contains, well we’ll have to wait and see. Until tomorrow, goodnight.