0.9999.... = 1 ?

I saw this quick video the other day with the title "Simple proof for $0.999... = 1$" and thought, "can I do this on my own" without watching. The fortunate result was pretty much yes, but my approach was using the concept of limits and was involved compared to the algebra approach shown in the video after I watched it. So I want to document the proof using the algebraic method in the video so I can remember that there are sometimes more straightforward ways to do the same thing. The idea is that we can start with the variable $x$ which we say is:

$$ x = 0.999\cdots $$

Then if we multiply $x$ by $10$, we have

$$ 10x = 10*0.999\cdots$$

which can be rewritten as

$$ 10x = 9 + 0.999\cdots$$

and substituting $x$ back-in on the right hand side,

$$ \begin{aligned} 10x &= 9 + x \\ 10x - x &= 9 \\ 9x &= 9 \\ \therefore x &= 1 \end{aligned} $$

The one thing that I questioned immediately though, is this is a valid mathematical proof or more of a conceptual demonstration of infinite decimal numbers. It most certainly looks to be the latter as discussed on the Wikipedia page. Since I'm not a professional mathematician I can't say why this algebraic approach is most likely not a rigorous proof, but again seems like a nice reminder that there are different ways to convey relations.

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Thoughts on note taking and presentations

Lately I've been thinking a lot about my process of taking notes and preparing presentations. In the last 10 years I've tried to explore many different kinds of techniques and approaches. Like most, I tried to get the most out of MS word and powerpoint throughout the years; I quickly abandoned MS word after writing my masters thesis, which was sheer frustration. As for PowerPoint, this was a more difficult, its not that I didn't want to part-ways with PowerPoint its just there are many "natural operations" that make it a more desirable experience. I guess it comes down to the acroynym, WYSIWYG, which is What You See Is What You Get, where as with something like Beamer $\LaTeX$ , you have WYSIWYW, where the G  is changed to W for "want". 

For presentation format, I find it much less natural to go with WYSIWYW approach since the layout of slides is very much a visual and aesthetic preference so one needs to play around with placement of figures and text to get the best kind of "feel". Also, I have noticed many use PowerPoint slides as a way to put down there research notes and create a record or timeline of their results and analysis. This then becomes the draft for conference presentations and final an outline for research articles. This process flow once again seems very natural and easy, in other words, it doesn't require doing much other than updating your slide deck as you progress. However, this of course this is error prone because it won't track provenance information for graphs or figures you insert and the version control of your slides in PowerPoint is less ideal git, for example. 

So you may ask "I don't see any major issues here? just use PowerPoint"... well that is fair but I think PowerPoint does have some significant issues for individual science and engineering researchers. For one Microsoft still abides by the draconian approach of charging for basic software, its clear the Microsoft isn't making their money from single user office products anymore but from cloud services and enterprise package purchases. But putting that aside, I significantly think the following are some headaches for many:

• The equation editor is cumbersome and frustrating. The only viable workaround is IguanaTeX.
• No support for Zotero or Mendeley reference managers. Adding references to slides in beamer  is easy. 
• The pptx format/standard should be open or more specifically, easy to support. There should be a free MS PowerPoint viewer that allows for PDF export as well.
• "In-file" code generated figures. I've used pythontex in the past to create code generated figures on a beamer slide.
• Version control for individual slides. If you use $\LaTeX$ or Markdown, you can create separate files for each slide and then using git for version control. This makes reverting a specific slide back to a previous version straightforward; although the main issue is you can't do this in a WYSIWYG manner.

There are some other things that can be frustrating with PowerPoint, for example it will crash frequently if the slide deck gets to large. One thing to point out is I don't think Google Slides has done that much of a better job other than they don't charge for the service.

Thus in light of this thinking my approach lately has been to starting exploring new approaches to note taking and presentation making. What I've decided to experiment with is the use of Quarto, which is a document preparation environment. What I like is you can create several different formats all from the same source files. The source files are written in simple markdown and extra capabilities are provided through extended syntax (e.g. code can be placed in an execution environment with {} around the language name). I've started with this mainly for making presentations using the revealjs framework and I'll see how it works. What I like so far is I can begin the presentations more similar to how I might take digital notes and then just use the content I want for slides. One potentially exciting capability of Quarto, is that because it uses Pandoc to export different format documents, it is possible to render a pptx file version of a presentation. I'm hesitant that this will be successful though.

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Nice presentation on AI/ML in materials science

I came across this slide deck from Prof. Shyue Ping Ong at UCSD. He leads a really exciting group that focuses on computational materials science and materials informatics. Many of his papers are outstanding and this particular slide provides a nice review of different use cases for AI/ML. I will note though that in many scenarios trying to replicate or implement similar research is a fairly hefty endevour unless your working with others who have done it before. 

 

A*STAR Webinar on The AI Revolution in Materials Science from Shyue Ping Ong

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