Perplexity is the first generalized AI chatbot I’ve found useful enough to integrate into any part of my daily workflow, much less across multiple domains. It speeds me up enough that I’m planning an increase in my freelancing rate.

Perplexity has three key advantages:

It provides citations, cleanly, in context
It has the persona of a sharp human instead of an intolerable customer service agent.
It is useful (and sufferable) across a wide variety of domains.

The citations are a bigger deal than they sound at first. I could of course google anything ChatGPT tells me and check the results, but that’s costly. I have to spin up a new mental thread (and browser tab), sort through Google’s increasingly shitty results, remember what claim I’m trying to check… the process eats up a lot of working memory at a time when it is scarce. If I wanted to trawl a sea of content farms I would have gone to Google in the first place.

Perplexity’s high quality inline citations solve that . Want to check if a claim is justified? Click the number next to it and look for the relevant quote. Not a perfect substitute for a 30 hour literature search, but a lot of power per minute. I don’t have to spin up a new mental thread, so the whole thing feels much lower friction. Also thus far I’ve never caught it in a hallucination on a question of fact, although if real answers are scarce it will sometimes do the thing where it draws increasingly tenuous connections instead of just telling me no.

I also found perplexity easier to talk to while trying to learn some math and math history. It felt about as useful as my human tutor- better at some things, worse at others.

Test Questions

The real test was which AI do I find myself using, and the answer to that is definitively Perplexity. But just for fun or in case I was wrong, I ran a few questions Perplexity through all major engines to see what they said.

In all cases I used the top free model available. I have Perplexity Pro thanks to a promo, but I haven’t ended up finding Pro to be much of an improvement. I do expect to use the pro-only PDF-analysis tool in the near future.

Comments from me are in italics and [brackets]

How do fractals relate to chaos theory?

I have a project investigating chaos theory as a case study in the development of scientific/mathematical paradigms. This doesn’t require I become a mathematician, but I do need to understand how discoveries relate to each other and generally not be an idiot on the topic. Perplexity is my always available, infinitely patient tutor.

This should have been a challenging role for an AI to fill, because I have a friend who loves explaining math more than almost anything, and did his PhD in a related area. I even feel comfortable looking stupid in front of him. And yet Perplexity still had a value add, because it was never offline and I didn’t feel a need to respect its time the way I would a friend’s.

Perplexity (link to result including citations)

Fractals and chaos theory are closely intertwined concepts in mathematics and physics, with several key connections:

Self-Similarity and Complex Patterns

Fractals are geometric objects that exhibit self-similarity across different scales, meaning smaller parts resemble the whole. This property is often found in chaotic systems, where complex patterns emerge from simple rules.

Visualization of Chaotic Processes

Fractals frequently arise as visual representations of chaotic systems:

The Feigenbaum diagram, which illustrates population dynamics in chaos theory, displays fractal-like structures.
The Mandelbrot set, a famous fractal, is closely related to chaotic processes and can be used to visualize complex number behavior in iterative functions.

Characteristics of Complex Systems

Both fractals and chaos theory deal with complex systems that exhibit:

Non-linear behavior
Sensitivity to initial conditions
Intricate, repeating patterns

Applications in Financial Markets

In financial analysis, fractals and chaos theory are used to understand market behavior:

Fractals can represent underlying patterns in market movements, stripped of emotional “noise” and short-term shocks.
Chaos theory helps explain how markets can appear random but still follow deterministic rules.

[-1 for bringing up markets. That’s a use of both, but lots of things use two things without those things being related ]

Relationship to Complexity Theory

[This seems irrelevant but I think was prompted by context from previous questions]

While chaos and fractals are related, they are distinct concepts:

Chaos theory focuses on deterministic but unpredictable systems.
Fractals are more closely linked to complexity theory and emergent behavior.

Understanding the difference between chaos and fractals is crucial for properly characterizing complex systems like financial markets.

In essence, fractals often emerge as visual representations or outcomes of chaotic systems, providing a way to understand and analyze the complex, non-linear behavior that chaos theory describes. Both concepts contribute to our understanding of intricate, seemingly random phenomena in nature and various scientific fields.

ChatGPT 4o

Fractals as Structures in Chaos: Fractals are often the geometric shapes that emerge from chaotic systems. In chaos theory, systems that appear random and unpredictable (chaotic) can produce complex patterns when visualized. These patterns are often fractal in nature, meaning they exhibit self-similarity at different scales. A classic example is the Mandelbrot set, a fractal that arises from a simple mathematical formula but exhibits infinitely complex boundary patterns.
Sensitivity to Initial Conditions: One of the key aspects of chaos theory is the idea that small changes in the initial conditions of a system can lead to vastly different outcomes, a concept often described as the “butterfly effect.” When you visualize the behavior of chaotic systems, the resulting patterns often reveal fractal characteristics—structures that look similar at various levels of magnification. This sensitivity is mirrored in the recursive, infinite detail of fractals.
Nonlinear Dynamics: Both chaos theory and fractals deal with nonlinear dynamics. In a chaotic system, nonlinear equations govern the evolution of the system, leading to behavior that seems random but is actually deterministic. The complexity and irregularity of fractals reflect the underlying nonlinear processes that produce them.
Scale Invariance: Fractals exhibit scale invariance, meaning their structure looks similar at any magnification level. This property is often found in chaotic systems, where the same patterns or behaviors can appear at different scales of observation, whether in time or space.

In summary, fractals are often the visual and mathematical representations of the complexity inherent in chaotic systems. Chaos theory helps explain the underlying principles that lead to the formation of fractals, and fractals provide a way to visualize and understand the seemingly unpredictable nature of chaos.

Claude

Fractals and chaos theory are interconnected concepts in mathematics that deal with complex systems and their behavior. Here’s a concise overview of their relationship:

Self-similarity: Fractals exhibit self-similarity at different scales, which is often seen in chaotic systems.
Strange attractors: Many chaotic systems produce fractal structures called strange attractors when their behavior is mapped in phase space.
[points to Claude on this one. It’s an important point that the others missed]
Sensitivity to initial conditions: Both fractals and chaotic systems demonstrate extreme sensitivity to initial conditions.
Natural phenomena: Fractals and chaos theory are used to model and explain various natural phenomena that exhibit complex, non-linear behavior.
[again, two things being useful for a third thing doesn’t make them related]
Iterative processes: Both concepts involve iterative processes that can lead to intricate patterns and unpredictable outcomes.
Dimensionality: Fractal dimensions are often used to characterize chaotic attractors.

Would you like me to elaborate on any of these points or discuss a specific aspect of the relationship between fractals and chaos theory?

Google Search AI Summary

Fractal dimension
The fractal dimension of an attractor can indicate how deterministic a system is. A low fractal dimension means the data was generated by a deterministic system, while a high fractal dimension indicates a random system.
Self-similarity
Fractals are infinitely complex patterns that repeat themselves at different scales, which is similar to the principles of chaos theory. Chaos theory studies how small changes in initial conditions can lead to large-scale, unpredictable outcomes.
Geometry of chaos
Fractals are the geometry of chaos, and can be found in nature, such as snowflakes, ferns, and coastlines, as well as in human-made structures, such as architecture, art, and music. For example, the Voyager spacecraft noticed that Jupiter has complicated turbulent vortices that are chaotic geometry, and any geometrical object with that structure is called a fractal.
Visual identity
Fractals are part of the visual identity of chaos theory. For example, the Mandelbrot set is a way of ordering all the Julia sets, which have a fractal-like structure. The Mandelbrot set is infinitely complex, but it also displays self-similarity with regions that look like the outline of the entire set.

What a cool set of random facts with the word “fractal” in them, Google.

How long after antibiotics is bordatello not contagious in cats?

[note: misspelled, the real spelling is Bordatella]

I was supposed to adopt a kitten at the beginning of August. On the day I was supposed to take him home, the breeder found Bordatella in another cat in the home (this is the bacteria that causes kennel cough in dogs and whooping cough in humans; it doesn’t have a common name in cats). It was early in the morning, this was a stressful topic and, due to travel times, I had an hour to figure out if I would take him that day (and risk spreading Bordatella to my existing elderly cat) or wait. Perplexity really hit this one out of the park, but it was a complicated back and forth that doesn’t make for a good example here.

I’m instead going to share this question I asked two weeks later, when I was trying to figure out if it was safe to bring the symptomatic-but-in-treatment kitten home.

ChatGPT was especially bad here. It was factually incorrect and spent 4 paragraphs reminding me to respect authority and eat my vegetables.

Perplexity (link to results including citations)

Based on the search results, there is no specific information about how long Bordetella remains contagious in humans after antibiotic treatment. However, we can draw some relevant insights from the information about Bordetella in cats and humans:

For Bordetella pertussis (whooping cough) in humans, patients treated with antibiotics may be contagious for only 5 to 10 days after starting treatment.
In cats, Bordetella bronchiseptica infections typically cause symptoms that persist for 7-10 days.
Cats infected with Bordetella can shed the bacteria for an extended period, even after clinical signs have resolved. Some cats have been shown to shed the bacteria for at least 19 weeks after initial exposure.
Antibiotics like doxycycline are usually effective in treating Bordetella infections in cats.

While these points don’t provide a definitive answer for humans, they suggest that the contagious period may be reduced to around 5-10 days after starting antibiotic treatment [this is what the source says, although I haven’t verified with other sources]. However, it’s important to note that this is an extrapolation from limited information, and the actual duration may vary depending on the specific Bordetella species and individual factors.

For accurate information about the contagious period of Bordetella in humans after antibiotic treatment, it would be best to consult with a medical professional or refer to guidelines from health authorities.

ChatGPT-4o

Bordetella bronchiseptica, the bacterium responsible for respiratory infections in humans, is less common in humans than in animals but can still be transmitted. The duration of contagiousness after starting antibiotics can vary depending on the individual, the severity of the infection, and the specific antibiotic used.

Generally, with many bacterial infections, including Bordetella, a person is often considered less contagious after 24 to 48 hours of appropriate antibiotic therapy [this is contradicted by the only source I checked, and dangerous. If ChatGPT gave sources maybe I could compare them]. This period allows the antibiotic to reduce the bacterial load to a level where the risk of transmission is significantly lowered.

However, it’s important to follow these guidelines:

Complete the Antibiotic Course: Even if symptoms improve and contagiousness decreases, it’s crucial to finish the entire prescribed antibiotic course to fully eradicate the bacteria.
Follow Medical Advice: Always consult with a healthcare provider to understand the specific recommendations based on your case, as the contagious period can vary.
Hygiene Practices: Continue practicing good hygiene, such as covering your mouth when coughing and washing hands frequently, to minimize the risk of spreading the infection.

If you or someone you know is dealing with Bordetella bronchiseptica, it’s best to consult a healthcare professional for personalized advice on managing the infection and understanding when it is safe to resume normal activities without the risk of spreading the bacteria.

Claude 3.5

The contagious period for Bordetella (also known as kennel cough) in cats typically decreases significantly after starting antibiotic treatment. However, the exact timeline can vary. Here’s a general guideline:

Typically, cats become less contagious within 2-3 days of starting antibiotic treatment.
Most veterinarians recommend keeping infected cats isolated for at least 7-10 days after beginning antibiotics.
The full course of antibiotics (usually 10-14 days) should be completed to ensure the infection is fully cleared.
Some cats may continue shedding the bacteria for several weeks after treatment, even if they no longer show symptoms.

It’s important to note that individual cases may vary, and you should follow your veterinarian’s specific advice. They may recommend a different isolation period based on the severity of the infection and the cat’s response to treatment.

If you need more specific information about your cat’s situation, I recommend consulting with your veterinarian directly. They can provide tailored advice based on your pet’s individual case and current condition.

[This is a better written result than Perplexity but doesn’t cite sources and isn’t reliable enough to trust so doesn’t save me much work]

Google Search AI summary

No AI response, first page of results did not answer the question

Is the Aegis Shield Playful?

This one is kind of goofy; I was considering naming the new kitten Aegis but also wanted a name to signal playfulness. I knew the answer was going to be “no, are you insane?” but Perplexity made it feel cheap to check.

All three engines got the right answer, but Perplexity took a stand and ChatGPT weaseled to avoid telling me no.

Perplexity

The term “playful” is subjective, but the Aegis Shield in gaming contexts often refers to its protective capabilities rather than a playful nature. For instance, in Final Fantasy, it provides strong defense against various status effects, while in Fire Emblem, it is valued for its strategic advantages despite some drawbacks. Overall, the Aegis Shield is more about utility and defense than playfulness.

ChatGPT 4o

The Aegis shield, rooted in Greek mythology, is not typically associated with playfulness. It is more often connected with protection, power, and divine authority. The Aegis was originally described as a protective cloak or shield carried by Zeus and Athena, symbolizing their might and the fear they could instill in their enemies.

However, in a creative or metaphorical sense, you could interpret the Aegis shield as playful if it’s part of a story, game, or artwork that reimagines it in a lighter or more whimsical context. Typically, though, its traditional associations are with seriousness, protection, and strength rather than playfulness.

Claude 3.5

I apologize, but I’m not familiar with a specific item or concept called an “Aegis Shield Playful.” There could be a few possibilities:

If you’re referring to the mythological Aegis shield associated with Zeus and Athena in Greek mythology, it’s not typically described as playful. It’s usually portrayed as a powerful protective device.
If this is related to a video game item, toy, or product, I don’t have specific information about it. Many games or products create their own versions of mythological items, sometimes with unique attributes.
There might be a misunderstanding or typo in the question.

To provide an accurate answer, I would need more context about where you encountered this term or what specific item or concept you’re referring to. Could you provide more details or clarify the context of your question?

[Correct, but miserable to read]

Google Search AI summary

No AI response

Conclusion

I’m jinxing things a little by writing this after 3-4 weeks of work, but Perplexity has genuinely sped up my work in ways no other chatbot has managed. I am both delighted and scared of where we are on the AGI curve.

Acknowledgements and (lack of) COI

This post was financially supported by my Patreon patrons (thanks guys!) but not by any of the companies in question. Unless you count Uber One giving me a Perplexity Pro subscription that didn’t feature in this review. I have friends who work at Anthropic (which produces Claude) and a few other AI orgs, but AFAIK no one at Perplexity.