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#mathematics

29 posts25 participants4 posts today
Continued thread
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Alexander Knochel

How does this translate to recent claims of a "three sigma" result indicating biomolecules on exoplanets as possibly observed by JWST?

I don't know how the researchers define their significance, and it is probably a complicated procedure analyzing the spectrum, but still -

Let's call the observed result again "R", and the null hypothesis that there are NO biomolecules on the planet "F".

A three sigma result would usually mean

P(R|F)=0.003, or in other words, if there are no biomolecules, the observed result only has a probability of 0.003.

As above, to obtain the *probability that there are biomolecules on the exoplanet* is the backwards claim of P(F|R), and to obtain this number, we again have to do

0.003*P(F)/P(R), meaning that we have to mulitply by the a priori probability that exoplanets are devoid of this biomolecule, and divide by the general probability of observing such spectra. On this admittedly naive level of analysis, it becomes clear that in order to make a statement about the probability of biomolecules on the exoplanet after the recent JWST result, one needs to factor in knowledge or a priori assumptions about the prevalence of such molecules and confounding factors.

End of thread

#Astronomy
#mathematics
#science

Public
Chris Purcell

Here's a stupid #geometry / #astronomy question. Planetary orbits are ellipses (under the obvious simplifying assumptions) which are conic sections. So what's the cone? There are infinitely many cones that fit of course. But is there one that best explains? To put it another way, is there a neat geometric argument that an orbit should be an ellipse, that doesn't require too much physics? #mathematics

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Alexander Knochel

-> Thread on what sigmas in science mean and what they don't mean, and how to correctly talk about and calculate the probability of claims using bayes law:

Apropos of recent events, here's the periodic reminder what "sigmas" mean for the probability of experimental results, because this is almost always presented wrong by popular texts and journalists
#Science
#mathematics

Thread 1/

BBC headline "Telescope finds promising hints of life on distant planet", artists impression of a blue backlit planet. In the article, the author talks about "three sigma" evidence for bio-associated molecules on the exoplanet
Public
pglpm

Happy birthday, Euler, "master of us all"! 🎂 🥇 🎓

- You know the notation "f(x)" for functions? – It was introduced by Euler.

- You know the names "sin(x)" etc for trigonometric functions? – They were introduced by Euler.

- You know the notation "Σ" for summation? – It was introduced by Euler.

- You know the "F = m a" formula? – It was written in this way for the first time by Euler <scholarlycommons.pacific.edu/e>.

- You know *Euler's* formula "exp(ix) = cos(x) + i sin(x)"?

- You know angular momentum and its balance law? Its necessity was definitively demonstrated by Euler <doi.org/10.1007/978-3-642-8664>.

- You know the notion of internal pressure (precursor of "stress")? - Introduced by Euler <scholarlycommons.pacific.edu/e>.

- Not to count his many discoveries in mathematics and works in physics.

- Wrote so many papers that the Prussian Academy kept on publishing them until 8 years after his death.

> "Read Euler, read Euler, he is the master of us all" (Laplace)

Colour painting of Leonhard Euler.
#science#physics#onthisday
Public
💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱

#MathsMonday
#Chinese #Maths #Math #Mathematics
I've seen this video a couple of times, but I never saw any explanation.... so I decided to work it out for myself how they did that! 🙂 Feel free to watch it and see if you can work it out yourself, but if you can't (or don't want to), then here's how this works (scroll down for reveal)...

First some pronumerals, then the steps - a=97, b=94, c=3, d=6
- c=100-a
- d=100-b
- the first 2 digits is a-d
- the last 2 digits is cxd

Public
ABC Feeds

'Faddish and inconsistent' teaching to blame for maths failures, report says
By Conor Duffy

One in three Australian students are failing to reach proficiency in maths, and according to a new report, many teachers lack the confidence to teach it.

abc.net.au/news/2025-04-14/mat

ABC News · Australian kids are failing at maths but a change in teaching styles could add up to successBy Conor Duffy
#Mathematics#SecondaryEducation#Teachers
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Suat Ayöz

I'll be posting the questions from AMS 2025 Daily Epsilon of Math Calendar daily from now on. I should have started earlier (doing it on Blue sky for some time). Hope it will be of interest

Here's the question for April 13th. For those unfamiliar with the calendar, the answer is always the day of the month. Looking for imaginative solutions is the aim.

The mean of: •x and 9 is w • 2x and 15 is y • 3x and 18 is z • w, y, and z is 20
#mathstodon#math#maths
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