Mobile Font Size Problem

This problem relates to my mathematical blog where I've discovered a problem with the font size rendering of LaTeX expressions. It's noticeably smaller than the font size of the surrounding text. I asked Gemini the following question as to how to fix the problem:

In Blogger, my LaTeX mathematical expressions are noticeably smaller than surrounding normal text when viewed in mobile browsers (Chrome, Safari and Brave). However, when viewed in Chrome on my laptop, the LaTeX expressions are larger and similar in size to stringing text. I suspect that this would hold true for other browsers as well although I haven’t tested it out. How can I remedy this problem? 

Figure 1

So far it has failed to solve the problem and I'm thinking that I should try some AI alternatives as Gemini just seems to go around in circles. You'd think that, since Blogger is a Google product, that its AI should be quick to spot a solution but that's proven to be not the case. To be continued. Figure 1 shows the problem. I want the numerals in the LaTeX line: 1, 22, 55, 115, 235, 475, 3389, 13457, 35743 to be larger. It's not a huge problem but it is irritating.

Revanchism

I'd seen the word \( \textbf{revanchism} \) before but forgotten what it meant. Figure 1 shows a dictionary definition of the word. Note the surge in mentions of the word as the 1950's progressed. As can be seen the etymology is quite straightforward. There is the French word for revenge (revanche) with an English suffix (ism) tagged on after the final e is dropped.

Figure 1

The word even has its own Wikipedia entry that begins:

Revanchism (French: revanchisme, from revanche, "revenge") is the political manifestation of the will to reverse the territorial losses which are incurred by a country, frequently after a war or after a social movement. As a term, revanchism originated in 1870s France in the aftermath of the Franco-Prussian War among nationalists who wanted to avenge the French defeat and reclaim the lost territories of Alsace-Lorraine.

The word is linked to \( \textbf{irredentism} \) that the Wikipedia article describes as "the conception that a part of the cultural and ethnic nation remains "unredeemed" outside the borders of its appropriate nation-state." The article contains an interesting map showing the new nations that were created in the aftermath of the First World War. See Figure 2.

Figure 2: link

WordMaster Wizardry

I play a word game on my iPhone called WordMaster and last night I reached the highest score that I've ever achieved in the game. See Figure 1.

Figure 1

I was helped by a phenonomenal point score of 203 for the word BEEFLESS that not only used all seven letters but also fell across a Triple Word Square. This was the highest score that I've ever received for a word. See Figure 2.

Figure 2

I was also aided by another score of 102 for JOUR that also fell on a Triple Word Square. See Figure 3.

Figure 3

There's not much more to say except that I felt I needed to record the accomplishment.

New Router

Recently we acquired a new router (a tp-link TL-WR841HP), currently attached to the router supplied for free by our Internet provider. Here is what Gemini had to say about the TL-WR841HP:

The TP-Link TL-WR841HP is a high-power wireless N router designed to provide extended Wi-Fi coverage and penetration, particularly in environments with obstacles that can weaken standard wireless signals.   

Release Date:

While specific global release dates for all hardware versions can be varied, information suggests the TP-Link TL-WR841HP was initially available around August 2013. Subsequent hardware versions have been released since then.

Specifications:

• Wireless Standards: IEEE 802.11b/g/n   
• Wi-Fi Speed: Up to 300Mbps on the 2.4GHz band   
• Antennas: Two detachable high-gain antennas (often 5dBi or 9dBi depending on the version)  
• Frequency: 2.4 - 2.4835 GHz
• Ethernet Ports: 4 x 10/100Mbps LAN Ports, 1 x 10/100Mbps WAN Port
• Working Modes: Router Mode, Range Extender Mode, Access Point Mode
• Wireless Security: 64/128/152-bit WEP, WPA/WPA2, WPA-PSK/WPA2-PSK   
• WAN Type: Dynamic IP, Static IP, PPPoE, PPTP, L2TP, BigPond
• DHCP: Server, Client, DHCP Client List, Address Reservation   
• Quality of Service (QoS): WMM, Bandwidth Control   
• Port Forwarding: Virtual Server, Port Triggering, UPnP, DMZ
• Dynamic DNS: DynDns, Comexe, NO-IP   
• VPN Pass-Through: PPTP, L2TP, IPSec (ESP Head)   
• Access Control: Parental Control, Local Management Control, Host List, Access Schedule, Rule Management   
• Firewall Security: DoS, SPI Firewall, IP Address Filter, MAC Address Filter, Domain Filter, IP and MAC Address Binding   
• Buttons: WPS/Reset Button, Power On/Off Button, Wi-Fi On/Off Button
• External Power Supply: 12V DC / 1A
• Dimensions (W x D x H): Approximately 9.0 x 7.5 x 1.9 inches (227.5 x 190 x 48.3mm), though this can vary slightly by hardware version.    

Advantages:

• Extended Range and Wall Penetration: The primary advantage of the TL-WR841HP is its high-power design and high-gain antennas, which are intended to provide a stronger signal and better coverage, including the ability to penetrate walls and reduce dead zones.   
• Multiple Operating Modes: It offers flexibility by supporting Router, Range Extender, and Access Point modes, allowing it to be used in various network setups.   
• Easy Setup: The router is generally considered easy to set up, often with the help of a setup assistant or the TP-Link Tether app.   
• Affordable: Compared to more recent and higher-specification routers, the TL-WR841HP is typically an budget-friendly option.
• Detachable Antennas: The detachable antennas allow for potential upgrades to higher gain antennas if needed.   

Disadvantages:

• Limited to 2.4GHz Band: It only operates on the 2.4GHz frequency, which can be congested in many environments, potentially leading to interference and lower speeds. It does not support the faster and less congested 5GHz band.
• Fast Ethernet Ports: The presence of 10/100Mbps Ethernet ports means that wired connections are limited to 100Mbps, which can be a bottleneck for faster internet connections or local network transfers. It lacks Gigabit Ethernet ports.
• Older Wi-Fi Standard: As a Wireless N (802.11n) router, it does not support the newer and faster Wi-Fi standards like Wi-Fi 5 (802.11ac) or Wi-Fi 6 (802.11ax).
• Potential for Overload: Some user feedback suggests that the router can struggle with a large number of connected devices or heavy bandwidth usage, potentially leading to speed drops or instability.
• Inconsistent Performance (based on some user feedback): While designed for high power and range, some users have reported inconsistent performance, including unexpected speed drops or connectivity issues over time, which could be related to firmware, hardware versions, or environmental factors.

Summary of User Feedback Regarding Performance:

User feedback for the TP-Link TL-WR841HP is somewhat mixed but often highlights its strength in providing extended wireless coverage, especially in larger homes or areas with physical obstructions. Many users appreciate the improved signal strength and ability to penetrate walls compared to standard routers. The ease of setup is also frequently mentioned positively.

However, a recurring theme in some user reviews and forum discussions is the potential for performance inconsistency and speed limitations. Some users have reported experiencing significant drops in speed, particularly when multiple devices are connected or under heavy load. Issues with the stability of the connection over time have also been mentioned by some users, occasionally requiring reboots. The limitation to the 2.4GHz band and the 10/100Mbps Ethernet ports are also noted as drawbacks by users with higher internet speeds or those requiring faster local network performance. Despite these criticisms, many users find it to be a cost-effective solution for extending basic internet connectivity over a wider area. 

With a release date of August 2013 this router is clearly OLD but it was the one recommended by the technician and cost about A$50 so it was cheap. It does the job of penetrating those areas of the house where the signal previously struggled to reach and that's what was wanted. The longer 2.4GHz band is what's needed to penetrate the thick walls within the house. Actually the router supplied by the Internet provider does operate in the 5GHz range so that is available if needed.

Figure 1

Figure 1 shows the results of an Internet speed test and we see that data is being downloaded at 26.1Mbps compared to the router's Wi-Fi speed of 300Mbps which is more that 10 times faster. Having a faster router is not really going to make much difference obviously.

Google's NotebookLM

I played around with Google's NotebookLM to create a podcast about psychopaths created from a variety of websites and YouTube videos that I'd linked to as source material. See Figure 1.

Figure 1

Click on this Link to listen to the podcast which is 22 minutes long. It can be downloaded as a 60MB wave file. The site also creates a Study Guide, FAQ, A Briefing Doc and a Timeline. I gathered the source material rather hurriedly and obviously the more time spent in gathering the sources the better. Of course, AI could be used to help in this regard. Overall this was a fun exercise and I'm sure that I'll experiment with NotebookLM further.

ADDENDUM: Another podcast etc. was created for me on the theme of Chess Champions. I used Gemini Deep Research to gather the sources and this was the result (link).

Spreadsheets and AI

I notice that there are several sites offering spreadsheet capabilities in combination with AI so that users need very little knowledge to carry out reasonably challenging tasks like creating pivot tables. One such site that I tried yesterday was quadratic and, after signing up to the site, I copied and pasted some data from the b-table of a sequence in the OEIS. Figure 1 shows what the data looked like.

Figure 1

However, Figure 2 showed what happened when I pasted the data in.

Figure 2

This was extremely annoying and didn't make any sense. I used the site's AI to fix the problem but the fix was tedious and only temporary. The spreadsheet was determined to keep messing up those cells on rows 11 and 12. I liked the site because Python code can be inserted directly into cells but the site obviously has glitches and it's also very slow to load. 

So today I'm trying a different but similar site called Bricks. I carry out the exact same task and see what happens. At first it made a complete mess of it and lumped all the date into cell A1 where I'd pasted it in the first place. At least quadratic had enough sense to put the data into the first column. However, I asked the AI in Bricks to fix the problem and it did. Figure 3 shows the result.

Figure 3

So I was satisfied with that, although I got the message that I only had 99 of 100 trial AI messages left. I hope that's just for the day and not for all time*. To be fair Google Sheets does exactly the same thing as Bricks and then it's very hard to fix without the AI. I'm encouraged to use Bricks again for more complex tasks than the very simple one attempted here.

* It turns out the free plan is as described in Figure 4 with 30 trial AI messages a month, that's only one per day!? The premium plan of $20 per month allows 500 AI queries per month and collaboration with up to 200 team members. This seems very stingy to me.

Figure 4

Gormenghast

I'm currently rereading "Titus Groan", the first novel of the Gormenghast trilogy, and I thought it would interesting to test out Google's Gemini using the following query:

Can you describe the appearance of a fictitious person who appears suddenly and asks for directions. The description should be in the style of the characters that appear in the Gormenghast trilogy.

I was quite impressed with the response. Here it is:

A figure, seemingly extruded from the very fog that clung to the courtyard stones, materialized before me. Not quite a man, not quite a shadow, but a damp, rustling presence. His coat, a patchwork of what might have once been velvet and now resembled desiccated bat wings, draped to the cobbles, trailing a faint, earthy scent. His face, glimpsed beneath a hat woven from what looked like dried reeds and raven feathers, was a landscape of deep, shadowed hollows and jutting, bone-like prominences. One eye, a milky, opalescent orb, stared fixedly, while the other seemed to have retreated into a fold of skin, leaving only a twitching, purplish scar. His hands, gnarled and speckled with a strange, verdigris-like substance, clutched a crumpled, damp parchment. A voice, thin and reedy, like the wind whistling through a broken flute, rasped, "The... the path... to the... the Obsidian Stair? Which... which way?" His lips, cracked and blue, barely moved, as if the words were being forced through a sieve of bone. 

I'd been prompted to do this after reading an article by a writer on technology who had been mightily impressed with AI's ability to write short stories.