As a common software developer with experience in common commercial software (what I call "real world software"), especially in startup settings, I constantly fight resource constraints: memory, compute, and cost.
Recently, I stumbled on something from the academic world that might actually matter to us, common craftsmanship developers in the trenches: a breakthrough by MIT's Ryan Williams. No, it's not some abstract math proof for theorists only. It's a real insight with potential real-world impact on how we write memory-efficient code.
What caught my eye was: "One computer scientist’s 'stunning' proof is the first progress in 50 years on one of the most famous questions in computer science."
WOW.
The core idea is:
You don’t always need linear space to finish a task efficiently.
It took me some time to understand the context of linear space here (thanks Chat-GPT), but essentially, it's this: the memory you need to use to be faster is equal to the input.
If you have 1 million records, you’re expected to use 1 million “slots” in memory to process them efficiently. That’s linear space — one-to-one. More data? More memory. No questions asked.
It’s like trying to be the fastest at checking every name on a list, so you write all of them on sticky notes and plaster them on your walls. Sure, you can find anyone instantly, but now your house is full of notes and you can’t find your cat.
Williams comes along and says:
“Hey… what if we just remembered the important parts, and recomputed the rest when we need it? You’d use fewer sticky notes — and your cat would thank you.”
Before, computer scientists used to believe that:
To run an algorithm efficiently, you needed memory roughly proportional to the size of the input — linear space.
In essence, it sounds obvious: more data means you need more memory to handle it well. Like saying, “If I want to cook for 100 people, I need 100 plates.”
But now, thanks to Ryan Williams, we have proof that this isn’t always true.
Turns out, with the right approach, you can sometimes cook for 100 people using just 10 plates — you just wash and reuse them fast enough that no one notices.
In algorithm terms: you simulate the same result, using way less memory, maybe with a bit more time or clever recomputation. It's not magic. It's just a smarter use of resources — and now it's mathematically backed.
A Kind of Real World Simple Example: Finding the Maximum Value in a List
Let’s say you’re finding the maximum number in a list. Most developers know two ways to do this.
Before (How We Typically Think)
# Load everything in memory
nums = [int(line) for line in open("data.txt")]
max_val = max(nums)
Time: O(n)
Space: O(n)
You load all the numbers into memory, then call max(). Fast and simple, but memory-heavy.
Williams-Inspired Interpretation
Instead of storing everything, why not just keep track of the max as you go?
max_val = float('-inf')
for line in open("data.txt"):
num = int(line)
if num > max_val:
max_val = num
Time: O(n)
Space: O(1)
This simulates the same behavior with way less memory, and its not that slow how we used to think before.
MORE Real World Example: Building a Search Engine
Let’s say you’re building a support dashboard or knowledge base search tool. Normally, you’d build an inverted index like Elasticsearch or Lucene:
Before: Traditional Inverted Index
inverted_index = {}
for doc_id, content in enumerate(docs):
for word in content.split():
inverted_index.setdefault(word, set()).add(doc_id)
Time: Fast lookups
Space: O(n) to store the index
This is memory-heavy. If you have millions of documents, the index might not fit on smaller machines or edge devices.
After: Williams-Inspired Interpretation
What if we simulate the index instead of storing it entirely? We could use space-efficient structures like Bloom Filters or sketches:
class BloomFilter:
def __init__(self, size=10000):
self.size = size
self.bits = [0] * size
def add(self, word):
for h in self._hashes(word):
self.bits[h] = 1
def contains(self, word):
return all(self.bits[h] for h in self._hashes(word))
Each document gets a small filter. At search time, instead of querying a big inverted index, you check which filters "probably" contain your words. You trade exactness for space, but still get fast, usable search.
My two cents: personal insight while digging into this
What really clicked for me while exploring this idea wasn’t just the resource savings — though that’s cool. It was how this way of thinking led me to design software differently.
Instead of just asking “How do I load everything and go fast?”, I started thinking in units of work — batches, chunks, steps. Suddenly, I was building systems that naturally scale better, are easier to retry, and recover more gracefully from failures.
You’re not just writing smarter algorithms — you’re architecting smarter systems and NOW YOU CAN JUSTIFY THAT IS NOT THAT SLOW HOW WE USED TO BELIEVE!
Memory limits become design constraints that actually make your software more resilient.
It’s weird: a theory paper ended up helping me in the system design.
Final Thoughts: Why You Should Care
If you're building for constrained environments or just want more efficient systems, Ryan Williams' result gives you permission to rethink the memory/time trade-offs in your architecture. It’s not just theory — it’s a mindset shift.
And mindset shifts can lead to big wins in the world of startups and real-world software.
Update: I removed a Fibonnaci example that is not the best explanation in this case.
AI Usage:
- To understand the "linear space" concept
- The cover image
- Grammarly for text correction
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