We need more research on female hormones’ effects
From Alex Spencer, Burwell, Cambridgeshire, UK
I was very interested to read your feature on how female hormones affect ADHD. I would love you to take a deeper dive into a subject that many women are only learning about from each other: progesterone intolerance (22 August, p 28).
Social media platforms and online forums discussing hormone replacement therapy and hormonal contraception are full of women desperate to feel the benefits of these medications, but when they try them, some discover that progesterone plunges them into the bleakest, darkest depression of their lives. In such treatments, you have to take progesterone with oestrogen to avoid uterine cancer, but when women tell their doctor that their mood is affected, they are often met with a shrug. The only options on offer are lower-dose hormonal coils or taking progesterone vaginally. This doesn’t help many women.
I would love to see some proper, rigorous investigation into this subject, as all the “menopause experts” seem to skate over it.
The implications of getting rid of irrational numbers
From Carl Zetie, Raleigh, North Carolina, US
Physicist Tim Palmer wants to banish irrational numbers from quantum mechanics, but why stop there? Everything we can know about the physical world is ultimately based on a measurement, and any quantity we can measure is either a fraction or a multiple of whatever units we use for our rulers, clocks and scales. We might imagine a 1-metre square and calculate that its diagonal should be 2, but when we come to measure it, we will only ever find a rational number – unless our ruler is subdivided with infinite precision (29 August, p 30).
So is it truly meaningful to say that quantities that appear only in our equations, but never in our measurements, physically exist? Perhaps, in some way analogous to Palmer’s rational quantum mechanics, irrational quantities might appear in the maths, but be excluded “states” in the physical universe.
From Ian Roselman, Leighton Buzzard, Bedfordshire, UK
I find myself hoping that rational quantum mechanics turns out to be right. Could it be that numbers themselves are quantised if they are to have any meaning in reality?
I notice that the estimated maximum number of states of a qubit is 2 400 , and this number is close to 10 120 . This is the scale of the biggest discrepancy in physics: the vacuum catastrophe, the mismatch between the predicted energy of empty space and the amount we actually observe. It is also the result of my simplistic estimate of the number of subatomic particles (real or virtual) that would fit into the known universe. Coincidence? Maybe, but it is fun to speculate.
Key scientific tool may be impaired by solar storms
From Bryn Glover, Kirkby Malzeard, North Yorkshire, UK
As you report, solar storms are injecting random quantities of carbon-14 into our atmosphere to the point where spikes are recorded in tree rings (15 August, p 34). So, to what degree can we rely on carbon-14 dating to determine the age of organic material, given it theoretically depends on a constant supply of the isotope?
More proof needed for AI mathematicians
From Andrew Shead, Tulsa, Oklahoma, US
Terence Tao discusses the recent glut of AI-written proofs of mathematical problems. I would argue that such proofs aren’t true until validated by human mathematicians. Just as a child’s schoolwork doesn’t pass unless they show their working, so an AI proof can’t pass without showing its step-by-step process (15 August, p 38).
Validating proofs is one of the roles of the mathematician. Doing so means making it understandable in stages, which involves a combination of human linguistic explanation, mathematical equations and Lean programming code, with all logical leaps eliminated. Mathematicians must force AI to show its workings, with full citation of the prior work on which it depended.
A fish-friendly way to get omega-3 in your diet
From Erik Foxcroft, St Albans, Hertfordshire, UK
Sam Edge is right to point out that eating fish to get more omega-3 can be harmful to the environment if they aren’t sustainably sourced, and that there are many alternative plant and fungus sources. However, if you want to make sure you are getting enough, you should know that the fish don’t make omega-3 themselves, but get it from eating algae (Letters, 22 August).
Some supplement producers harvest these algae directly and put them into capsules, which look like cod liver oil, but don’t involve killing fish.
Two ways to ensure more action on climate change
From David Flint, London, UK
Peter Brown calls for a global effort to create disincentives for climate-damaging activities, as well as subsidies for the mitigation of adverse impacts. The need for this has been obvious for 30 years, but attempts to take action have been sabotaged by fossil fuel giants and petrostates (Letters, 29 August).
We won’t get the sustainable economy that Peter and I – and, I think, many other Â鶹´«Ã½ readers – want unless we call this out and support parties and politicians who will do what is right for Earth, our shared home.
From Simon Evans, Malvern, Worcestershire, UK
I agree that an out-of-control market economy is responsible for the climate crisis, but I doubt that global markets will be reined in any time soon. Our instinctive urge to compete and to acquire wealth and power, felt at all levels from individual to international, has made our world what it is, both good and bad.
Our amazing ability to innovate and make things happen needs to be channelled towards efforts to reverse the effects of climate change, such as geoengineering. This plays to our strengths: we are very good at doing things and very poor at not doing things.
To deer, cougar presence is claws for concern
From Eric Kvaalen, Les Essarts le Roi, France
Liana Zanette says the presence of cougars creates a “landscape of fear”, and this “is good news all around”. Tell that to the deer (15 August, p 13).
For the record
Gravity affects objects with mass or energy.