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Run DeepSeek R1 Locally to Learn How It 'Thinks'—Here's How

by Bruce LiJanuary 29th, 2025

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Too Long; Didn't Read

It is highly rewarding to see how AI "thinks" aloud step by step, trying alternatives, and self-validate and iterate, by running DeepSeek R1 locally on your computer instead of using their web/phone app. Here are a few examples, as well as instructions on how to run R1 on your computer in the appendix.

featured image - Run DeepSeek R1 Locally to Learn How It 'Thinks'—Here's How

It is highly rewarding to see how AI “thinks” aloud step by step, trying alternatives, and self-validate and iterate, by running DeepSeek R1 locally on your computer instead of using their web/phone app. Here are a few examples that I find intriguing, during my two days of testing. It somehow reminds me of the writing style of Stephen Wolfram in many of his physics education series.

In addition, I added instructions on how to run R1 on your computer in the appendix. I have an “ancient” M1 Pro Macbook Pro with only 16GB memory, and it runs the 8B distilled model (based on LLama) fairly well and fast.

Example 1: Journey to Mars

Question:

if I want to travel to Mars, what will be most energy efficient way to get there?

DeepSeek R1 thinking process

<think>

Okay, so I’m really curious about how to travel to Mars in the most energy-efficient way. I remember reading a bit about rockets and space exploration, but I’m not entirely sure about all the details. Let me try to break this down step by step.

First off, going from Earth to Mars isn’t as simple as just launching a rocket directly there because of the distance involved. I think Mars is about 225 million miles away at its closest point. That’s a huge distance compared to other planets like Venus or Jupiter, so efficiency must be really important here.

I remember hearing that rockets use propellant for thrust and that this process can be quite inefficient, especially in Earth’s atmosphere. So maybe leaving from Earth isn’t the most efficient approach? I’m not sure if there are alternative launch points, but I don’t recall any nearer spaceports or bases. Maybe there’s something about using a different kind of rocket or even a different planet as a starting point?

Wait, the question mentioned something about orbiting the Sun. Mars and Earth both orbit the Sun, so maybe instead of going directly to Mars, we could transfer from an Earth orbit to a Martian orbit. Transfer orbits sound like they require less energy, but I don’t know how that works exactly. I think it’s similar to the Hohmann transfer in celestial mechanics where you use gravitational assists.

Gravitational slingshots? Oh right, when a spacecraft uses the gravity of another planet to speed up or slow down its trajectory. So if we can use Venus or Earth’s gravity to our advantage, maybe we can save energy instead of going straight to Mars. But I’m not sure how effective that is for such a long trip.

I also remember something about electric propulsion systems, like ion thrusters, being more efficient than chemical rockets because they use electricity to ionize propellant and accelerate it with electric fields. They have lower thrust but can operate over longer periods without as much fuel. That sounds promising, but I’m not sure how quickly they can get to Mars compared to traditional methods.

The problem is that even if we use these efficient methods, the overall journey is still a quarter of the way through the Solar System. So maybe we need a combination of both techniques: using chemical rockets for the initial launch but then switching to ion thrusters or another form of electric propulsion once in space. That might save fuel and reduce the amount needed for the long trip.

Another thought I have is about the Martian transfer orbit itself. If we can enter the right kind of orbit around the Sun that intersects with Mars’ orbit, we could potentially arrive there with less energy. But calculating the exact trajectory must be complicated because both planets are moving, so timing and alignment play a huge role.

I also wonder about the cost and feasibility. Even if it’s efficient, getting to Mars might still require an enormous amount of fuel. So maybe we can look into other ways, like using spacecraft that can refuel in space or develop more advanced propulsion systems with higher specific impulse. I think there’s research into nuclear thermal rockets and antimatter drives, but those are speculative.

Wait, the question also mentioned a “Mars transfer orbit.” So instead of going directly to Mars, we might be aiming for an orbit where it can catch up with Mars. That would make sense because it reduces the delta-v required to reach Mars’s orbit from Earth’s. Delta-v is the change in velocity needed to change the trajectory, so using a Hohmann transfer seems like a good strategy.

I’m also curious about the Earth departure point. If we launch from somewhere else on Earth, like a southern hemisphere launch to take advantage of the Earth’s rotational momentum, maybe that could save some energy. I think that’s called a “Hohmann transfer orbit” in a way because it uses the planet’s rotation.

So putting this all together, the most efficient method would involve using chemical rockets for the initial lift-off and then switching to electric propulsion once in space to minimize fuel consumption over the long distance. Additionally, leveraging gravitational assists from other planets could help reduce the energy needed overall.

I’m not entirely sure about the exact numbers or whether this is what’s currently being done or proposed. I think companies like SpaceX are working on Mars transfers and reusable rockets, so maybe they have some insights. It might also depend on the mass of the spacecraft and how much propellant it can carry, especially for long trips.

In summary, to travel to Mars efficiently, a combination of Hohmann transfer orbit, gravitational assists, and electric propulsion seems like the way to go. This approach would minimize the energy expenditure required to cover such a vast distance in the Solar System.

</think>

DeepSeek R1 Answer

To travel to Mars in the most energy-efficient manner, consider the following approach:

1. Hohmann Transfer Orbit: Utilize a transfer orbit that reduces the delta-v required by aligning with Martian orbital mechanics. This involves entering an elliptical orbit around the Sun that intersects with Mars’s orbit, minimizing the energy needed for the transfer.

2. Gravitational Assists: Take advantage of gravitational slingshots from other planets like Venus or Earth to gain speed and redirect trajectory without additional propellant, enhancing efficiency.

3. Electric Propulsion Systems: After initial launch using chemical rockets, switch to ion thrusters or similar electric propulsion systems for the long journey. These systems offer higher specific impulse, allowing sustained operation with less fuel.

4. Optimized Launch Point: Consider launching from a southern hemisphere location to leverage Earth’s rotational momentum, reducing the energy required for lift-off.

5. Combination of Propulsion Methods: Use chemical rockets for the initial ascent and then switch to electric propulsion for interplanetary travel, minimizing overall fuel consumption.

This integrated approach balances the need for initial thrust with efficient long-distance travel, leveraging both traditional and advanced propulsion techniques.

Example 2: Einstein’s famous formula

Question:

prove E = mc²

DeepSeek R1 thinking process

<think>

Alright, so I’m trying to prove that E equals mc squared. Hmm, where do I even start with this? Okay, I know Einstein’s theory of relativity is a big deal in physics, but how did he come up with that equation? Maybe I should break it down into smaller parts.

First, what does E stand for? I think it might be energy. And m could be mass, right? So, energy equals mass times the speed of light squared. That makes sense because the speed of light is a constant in special relativity. But how does that actually work?

I remember that in classical physics, energy and mass were seen as separate concepts. Energy was associated with motion, like kinetic energy, while mass was about inertia and gravitational pull. But Einstein’s theory changed that by showing they are fundamentally connected.

Maybe I can start by reviewing the basics of special relativity. In special relativity, there are two postulates: one about the speed of light being constant in all inertial frames, and another about how space and time are affected by motion. It’s these ideas that lead Einstein to propose the equivalence of mass and energy.

Okay, so if E is energy and m is mass, then the equation E=mc² must come from the idea that mass can be converted into energy and vice versa at the speed of light. But how exactly does that conversion work? I think it has something to do with the equivalence principle, which states that a person in free fall experiences acceleration equivalent to that of a passenger in an accelerating elevator.

Wait, maybe it’s about how mass creates energy due to its motion or gravitational potential. Einstein’s thought experiments probably played a big role here. He imagined what would happen if you were on a beam moving at the speed of light and then accelerated upward. From your perspective, you’d feel weightless, which led him to think that mass and energy are interchangeable.

I’m still not entirely clear on how exactly E=mc² is derived from these concepts. Maybe I should look into the specific steps Einstein took in his thought process. He must have used mathematical relationships between space-time intervals in different inertial frames.

There’s also the idea of invariant quantities, like how certain properties remain constant regardless of the observer’s frame of reference. Energy and mass are two such quantities that can be converted into each other when considering relativistic effects.

But I’m getting a bit lost. Maybe I should try to write down the key postulates of special relativity and see how they lead to E=mc². So, let me jot this down:

1. The speed of light is constant in all inertial frames.

2. The equivalence principle: An observer in an accelerated frame experiences a gravitational field equivalent to being in an inertial frame with acceleration.

Starting from these, Einstein wanted to find a relationship that connects mass and energy. He probably considered how changes in the space-time interval relate to changes in mass and energy.

I think another approach is to consider momentum and force. In relativity, momentum isn’t just mass times velocity anymore; it involves gamma factors. Maybe by manipulating these equations, I can arrive at E=mc².

Alternatively, maybe I should think about the rest mass energy, which is the energy an object has due to its rest mass. This would naturally lead to E=mc² because even when an object isn’t moving, it still possesses energy.

But wait, Einstein didn’t just pull this equation out of thin air. It must have come from years of thinking and calculating how space-time curvature interacts with matter and energy.

I wonder if I can derive it using the equivalence principle directly. If I consider a clock that ticks slower in a gravitational field compared to a far away observer, then there’s a connection between gravitational potential and time dilation. This could relate to mass creating curvature in spacetime, which affects how light travels, thereby influencing energy.

It’s getting complicated, but I think the key idea is that mass influences space-time, and this influence can be quantified as energy. So, E=mc² might be Einstein’s way of expressing this relationship where mass and energy are different manifestations of the same fundamental property.

But to really prove it, I probably need to use mathematical formulations from special relativity. Maybe start with the spacetime interval, then relate it to energy and momentum. From there, perhaps show how changes in space-time due to mass can be equivalent to energy.

I’m still not entirely sure of all the steps, but I’m starting to see that E=mc² isn’t just a random equation; it’s deeply rooted in Einstein’s view of how mass and energy are connected through the constants of nature.

Maybe another angle is to consider nuclear reactions. The release of energy in atomic bombs seems to follow E=mc² because a small amount of mass is converted into a large amount of energy, which matches the equation.

But that’s more of an application than a proof. I need to go back to the foundational principles. Perhaps by using Einstein’s theory of special relativity and its postulates, I can derive the equation from first principles.

I think I’ll try to write out the key equations step by step, starting with the invariant interval in spacetime, then seeing how it relates to energy and mass.

So, the invariant interval is ds² = -c² dt² + dx² + dy² + dz². If an object moves at a certain velocity, this interval remains constant for all observers.

But if the object’s mass changes due to its motion or gravitational potential, then there must be a relationship between that change in mass and the energy involved.

I’m still not clear on the exact steps, but I can see that Einstein needed to find a way to unify these concepts of space-time curvature, mass, and energy into a single equation.

Maybe by considering how an object’s rest frame relates to its motion relative to another observer, I can manipulate the equations to arrive at E=mc².

Overall, it’s clear that proving E=mc² involves deep understanding of special relativity, the equivalence principle, and the nature of mass and energy as different forms of the same entity. It’s a complex derivation, but one that’s foundational in modern physics.

</think>

DeepSeek R1 answer

E = mc² is an equation from Einstein’s theory of special relativity that expresses the relationship between mass (m) and energy (E), where c is the speed of light. Here’s how it can be understood:

1. Postulates of Special Relativity:

- The speed of light in a vacuum is constant for all observers, regardless of their motion or reference frame.

- The equivalence principle: An observer in an accelerated frame experiences the same gravitational effects as an observer in a static gravitational field.

2. Invariance of Space-Time Interval:

The invariant interval in spacetime is given by \( ds² = -c² dt² + dx² + dy² + dz² \). This interval remains constant for all observers, regardless of their frame of reference.

3. Energy and Momentum Relationship:

From the equivalence principle, Einstein concluded that mass and energy are interchangeable forms of the same entity.

This led him to consider how changes in an object’s motion or gravitational potential affect its mass and energy.

4. Derivation Steps:

- By considering a moving object and how its rest frame relates to its motion relative to another observer, Einstein manipulated the equations of special relativity.

- The idea that even at rest, an object possesses energy due to its mass led to the concept of rest mass energy.

- This rest mass energy is proportional to the object’s mass and can be expressed as \( E = mc² \).

5. Application and Implications:

- The equation has profound implications, such as explaining nuclear reactions where a small amount of mass converts into a large amount of energy.

- It underscores the unification of concepts previously seen as separate: mass and energy.

In summary, Einstein’s derivation of E=mc² was rooted in the principles of special relativity, particularly the equivalence principle, leading to the realization that mass and energy are different manifestations of the same fundamental property.