The Half-Life of Facts

The Half-Life of Facts by Samual Arbesman presents an interesting framework for thinking about the updating of our knowledge. He argues there is structure in the time it takes for facts to become outdated. Just like the half-life of uranium, facts become superseded by other facts at a predictable rate.

Read: 1x | First: December 2020

This book got recommended on the Clearer Thinking podcast with Spencer Greenberg. It got introduced as interesting, though not always as sound as presented (i.e. there is more nuance than fitted on the pages).

I enjoyed the book, it helped me think more clearly, and it’s a quick read for those interested in how knowledge develops.

I wrote at the start of the book: “We know 1% of infinity, and that 1% is always getting bigger.

Chapter 1 – The Half-life of Facts

“Facts, in the aggregate, have half-lives: we can measure the amount of time for half of a subject’s knowledge to be overturned.”

Arbesman is using facts in a common-sense way in the book. Things we know to be true (at this moment), as close to ‘ground’ truth as we can currently get.

Mesofacts are facts that change at middle timescale (a few years). Examples are number of chemicals, height of Mount Everest (see chapter 8), height of tallest skyscraper.

Chapter 2 – The Pace of Discovery

We can now measure the speed of discoveries (scientometrics) and in many cases the number of papers published in a field doubles every X years, which showcases exponential (vs linear) growth.

Although, possibly, discoveries are getting harder to make, there are so many more scientists, the speed of discovery is still accelerating.

Chapter 3 – The Asymptote of Truth

Knowledge in a field can also decay exponentially, shrinking by a constant fraction.”

This (and much of this chapter) is based on citations of scientific papers and the decline in that of older papers.

It’s not that when a new theory is brought forth, or an older fact is contradicted, what was previously known is simply a waste, and we must start from scratch. Rather, the accumulation of knowledge can then lead us to a fuller and more accurate picture of the world around us.”

We are currently in the ‘long-tail of discovery’, and by that the author means we may not get block-buster discoveries, but we are ever refining and better understanding and improving them.

Chapter 4 – Moore’s Law of Everything

Processing power grows every year at a constant rate rather than by a constant amount.”

The amount of information we can send to others has grown exponentially, how awesome is that.

This chapter also introduces the idea of several S-curves making up an exponential curve.

Technology, in its broadest sense, is the process by which we modify nature to meet our needs and wants.” and “Science is about understanding the origins, nature, and behavior of the universe and all it contains; engineering is about solving problems by rearranging the stuff of the world to make new things.”

About life expectancy, this chapter mentions Aubrey de Grey from Ending Aging.

Knowledge grows through cumulating, “as there is more technological or scientific knowledge on which to grow, new technologies increase the speed at which they grow.”

This process closely matches population growth. An interesting idea is how this will develop, as population growth slows/stops. Will our interconnectedness still provide us with enough momentum or will the half-life of facts start to grow larger?

Chapter 5 – The Spread of Facts

Knowledge spread slower than we think/hope. Like the idea that spinach has a lot of iron, which isn’t true (but the story about why also is wrong, and that meme has spread even slower).

Information spreads via social networks (and thus also moves in bubbles), and between different networks (e.g. geographies).

The most important ties are thus medium ties, not strong ones (have the same knowledge) nor weak ones (whom you don’t speak to often).

Sometimes errors spread further and quicker because the story is more compelling than the truth/fact. E.g. a frog in a slowly heated to boiling pot will not jump out (wrong!).

Facts do not spread instantaneously, even with modern technology. They weave their way through social networks in mathematically predictable ways.”

To prevent spreading misinformation, have a certain vigilance about what you hear.

Chapter 6 – Hidden Knowledge

Knowledge can be hidden in one domain, and be useful in another domain. So combining domains and ‘throwing people at the problem’ are valid strategies for unearthing facts.

This also holds true for knowledge in the public domain that is lost over time. So ideas, proposed back in the day, were not ‘ripe’ for that time, but could be tested/used/validated now.

Innocentive is mentioned, a crowdsourcing centre for ideas. With the premise being “a long tail of expertise – everyday people in large numbers – has a greater chance of solving a problem than do the experts.”

A cummulative meta-analysis tries to include all trials (not only the latest ones) as to find statistical significance early on. (see page 109)

Another project mentioned is CoPub Discovery (but doesn’t seem to be active anymore?), a paper search engine that matches based on co-occurrence of (similar) words in papers.

Mendeley is a tool that helps with citing papers and saving references to them. And to find related papers.

DEVONthink might also be a good tool to find hidden connections, Mac/iOS only.

… facts are seldom lost. And as long as knowledge is preserved, we have the raw materials for unearthing hidden knowledge.”

Chapter 7 – Fact Phase Transition

At certain thresholds there can be a state change, think water to ice. The changes might themselves not have accelerated, but the end product is very different than X iterations before.

This type of thinking is usually applied to physics but also applies to facts (e.g. number of exoplanets found). And by using this, you can predict (approximately) when we will have an answer about fact/question X.

We are always on the edge of chaos, always learning new things (at least in dynamic societies) and our knowledge (facts) change all the time. Or in other words, we’re always in a critical state.

Chapter 8 – Mount Everest and the Discovery of Error

The height of Mount Everest is a meso-fact (see above), it changes over time as we were getting better at measuring and still changes as the earth is changing.

Revolutions in science have often been preceded by revolutions in measurement.” – Sinan Aral

We have improved our measurements of many things, and by that also our understanding of the world. As we get better at measurements (e.g. brain scans in real-time at more detail) we will continue to learn more.

Error can be measured in two ways, precision (10x same error) and accuracy (10x error around the centre).

Then the book discussed a topic I want to dive deeper into next year, p-values and statistics. This quote from John Maynerd Smith summarizes what we now do “Statistics is the science that lets you do twenty experiments a year and publish one false result in Nature.”

What is important is the discriminating power of a study, of how much it changes our prior to posterior probability of X being true.

Some factors that help falsehoods become significant results:

  • smaller studies
  • smaller effect size
  • more tested hypotheses
  • flexibility in study design, definitions, outcomes, analytical model
  • financial incentives
  • hotter field

I can confidently say that most of these apply to the study of psychedelics for therapy. And one of the things that should (continue to) happen is replication, to be damn sure that something really work.

Only through replication can science be the truly error-correcting enterprise that it is supposed to be.”

This all being said, Arbesman notes that science is not broken. It isn’t perfect, but still moves forward.

One interesting way of looking at this is to make the distinction between the core and the frontier. The former is relatively stable and fixed, the latter is more fluid and full or error. Slowly facts from the frontier make it into the core.

There is a sifting and filtering process that moves knowledge from the frontier to the relatively compact and tiny core of knowledge. We should enjoy this process, rather than despair.”

Chapter 9 – The Human Side of Facts

There is a human side to updating facts. Dan Ariely of Predictably Irrational is mentioned here.

… shifting baseline syndrome… refers to how we become used to whatever state of affairs is true when we are born, or when we first look at a situation.”

An interesting way of defining technology is as “anything that was invented after you were born” – Alan Kay

As facts change, our understanding of them changes slower. I think this matches with the concept of memes, they are similar to genes in many ways, but one way they are different is that it needs to be both transmitted and then received/processed/saved (and then transmitted again).

The beliefs that we have (currently) can prevent us from updating to a newer and better view of reality. Daniel Kahneman referred to this as theory-induced blindness.

Changes in facts thus also follow the phase change bursts and relatively stable periods. I think this can be true, but don’t know if this applies to all fields and institutions (i.e. if a company has good systems they could possibly have continuous change? Netflix maybe?).

The model proposed by Thomas Kuhn about science progressing one funeral at a time doesn’t seem to hold up. Young scientists are just a likely as older ones to accept/reject new ideas.

One thing that could be useful is to stop remembering facts (as we’ve all done to some degree I think) and retrieve (the latest and updated) facts when we need them.

Paradoxically, by not relying on our memories, we become more likely to be up-to-date in our facts, because the newest knowledge is more likely to be online than in our own heads.”

Chapter 10 – At the Edge of What We Know

Science requires an idea to be refutable. It is not good enough for a concept to seem compelling; it must have the potential for a new fact to come along and render it false.”

Are we in an exponential curve or ‘just’ a logistic curve? Some things point towards ever accelerating (e.g. knowledge spreads faster). Other things point towards a slowdown (e.g. population growth is slowing down dramatically).

Facts don’t change arbitrarily. Even though knowledge changes, the astounding thing is that it changes in a regular manner; facts have a half-life and obey mathematical rules. Once we recognize this, we’ll be ready to live in the rapidly changing world around us.”