The foundations of morality

Several of my notes assert that it is “natural” to value a nearby person more than a distant one, and a human being more than an animal or an alien. Thus I measure utility with a weight function w(x,t,s) (s=species) that decays as x/t/s move away from here/now/human. Hence my resolution of Pascal’s wager and my rejection of a key assumption of Effective Altruism.

A philosopher may object: what kind of an argument is this? What in the world does “natural” mean?

My answer is that objective moral truths do not exist. If they did, then indeed, it would be hard to see how my own place, time and species could be special. But in fact, we cannot justify moral feelings, we can only explain them, and natural selection is a big part of the explanation. That’s what “natural” means.

[20 November 2022]

Climate change responsibility to poorer nations

At the current COP27 climate summit in Egypt, many people are pointing out how unfair it is that poorer nations are suffering the most while having done very little to bring on the problem. Climate change is the fault of the industrialized West, which is therefore morally obligated to pay “loss and damage” recompense.

I feel the power of this argument. One might quietly wonder, however, about the mathematics. If you consider the total impact of the industrialized West on the poorer nations of the world — a terrifying prospect — you see enormous negatives but enormous positives too, including the doubling of life expectancies. On balance, positive or negative? This question is so fraught, so tied to passions entirely understandable, that it’s hardly surprising it is never brought up for discussion.

[9 November 2022]

Silences in my index cards

As Kate comes near the end of writing Silence: A Literary History, I find myself looking at 53 years of index card notes and mulling over a silence question of my own. There are a number of notes that I think are good, but might be better without their final sentences or paragraphs. These are cases where I present a situation and then spell out the moral explicitly. My older self now wonders, might it have been better if I had left that un-spelled out?

But it’s never a simple call. I dislike aphorisms that are slickly minimalist: it is my aim to be a philosopher, not a poet. Omitting all hints as to the point I am attempting to convey would be going too far.

Of course the poets must think about this issue all the time, and Robert Frost with his rural wisdoms was an interesting case. “Two roads diverged in a yellow wood…,” I like to imagine he mused, is a great start. Now then, should I really spell out “I took the road less traveled by, and that has made all the difference,” or is that too heavy-handed?

[14 October 2022]

Pascal’s wager and my bowl of ice cream

I have marveled that although my life is far past half-way done, this doesn’t bother me much, which seemed irrational. But I’ve also argued, in connection with Pascal’s wager, that we are decoupled from our past and future selves by decreasing weight functions: that the present value of a pound of pleasure a year from now is only a few ounces.

I still hold to this view, and it explains the ice cream effect. If I assess my stage of life by integrating from birth to death without a weight function, then yes, I am 75% finished. With a weight function in there, however, the early and late years drop away. And that is why, throughout life, until near the end, as long as one is healthy, it can feel like the middle.

Living in the here-and-now is like driving at night with headlights shining on the road. A hazard ahead is nearly invisible until you get quite close.

[14 October 2022]

Bad driving incident

The other day on Holywell Street, I backed up without looking properly and put a couple of pedestrians at risk. This was bad driving. I was at fault.

The man gestured to me to lower my window and yelled at me about my bad driving. He was completely right, and I tried to tell him that I agreed and was deeply sorry. However, he was too mad, and he stalked off without hearing my apology.

And then boy was I mad too.

[4 October 2022]

World’s 5th biggest economy

The New York Times points out on the front page today that “Recently, Britain lost its place as the world’s fifth-largest economy to India.”

What an odd statement — not mentioning that India’s population is 20 times greater.

[5 October 2022]

The end of coins

At the Queen’s Lane Coffee House just now I decided to pay for my cappuccino with coins. The server said that was fine, but when I handed them to her, she turned the 20p coin over and around with some curiosity. Evidently she did not recognize it.

[3 October 2022]

Pedantics recapitulates semantics

I enjoy the word prequel, which probably hadn’t even been coined when the first instance I encountered was published: The Magician’s Nephew, in the Narnia series.

Prequel doesn’t come from Latin: it’s a back-formation from sequel, which does. What tickles me is that its derivation aligns thereby with its definition, for a prequel is something constructed backward from something that already exists.

[21 August 2022]

Expansion coefficients of size 10^100,000

Since writing An Applied Mathematician’s Apology I find myself noting more examples of how unquantitative mathematicians may be.

Here’s one. A well-known theorem by Müntz asserts that, for example, the function f(x) = x can be approximated arbitrarily closely for 0< x<1 by linear combinations of the functions 1, x2, x4, x6, … What Müntz’s theorem doesn’t tell you is that to do this, say to 6-digit accuracy, you’ll need 140,000 of those terms with coefficients as large as 10100,000 ! Such approximations would be useless in any conceivable application.

You might think that the discovery that a theorem is useless for any application would be of interest to mathematicians. In fact, most would regard this effect as just a curiosity. It doesn’t touch the essential truth or beauty of the theorem, and indeed, perhaps it enhances it by shining a light on the power of rigorous proof.

(I asked a leading expert in the area whether he knew of this 10100,000 effect. No, he responded, “I am not a numbers man.”)

In other words, a mainstream view among mathematicians is that it is not their business to care whether or not a theorem is capable of being applied. This raises the question, if it is not their business, then whose business is it? Engineers? I imagine most mathematicians would feel that no, one need not go so far as that. It is the business of the numerical analysts, who are, after all, mathematicians of a kind.

[27 July 2022]

Items on our bulletin board

The bulletin board nearest my office has seven color posters on it just now:

(1) Oxford Maths Summer Party
(2) Responsible Bystanders: If you see or hear inappropriate behaviour or language….
(3) The Athena Swan Principles
(4) The University does not tolerate any form of harassment
(5) Her Dark Mathematicals Women’s Coffee (for female and trans students and staff)
(6) Mathematrix (upcoming meetings for minorities/women/LGBTQ+/non-binary)
(7) SECTRA – the LGBTQIA+ Staff Network Pride celebration

Item (1) is an invitation to a party the day after tomorrow. All the others are aimed at special groups of people defined mainly by issues related to gender.

[22 June 2022]