Walking wrap up, 2024

For reasons explained elsewhere, my goal in 2024 was to walk a sphenic number of recorded miles in the vicinity of my 2023 mileage. 

I closed last year with 2,814 miles. This year, I aimed for 2,821 ( = 7 * 13 * 31). I figured if I overshot by a mile, I'd still end with a sphenic number (2,822 = 2 * 17 * 83). And if I overshot that by a mile, I'd land on a semiprime (2,823 = 3 * 941)--not ideal, but whatevs.¹

I was behind schedule in November, but a hiking-focused Thanksgiving trip to Tucson helped put 2,821 back in the realm of obtainable, so I stepped up my miles in December. 

I hit 2,821 on the Atlantic coast of Shackleford Banks, NC, on December 27.

Likewise 2,822...

...and 2,823.

So much for that.

I considered giving myself a new sphenic goal, or a semiprime, or a prime, and then Wikipedia told me that 2,850 is a triangular number. It isn't sphenic (although some triangular numbers are), but I figure a triangular number is in the spirit of the word sphenic--a sphenic number's etymological equilateral cousin, so to speak--so 2,850 became my new goal.²

T_n = n*(n+1)/2
T₇₅ = 2850 = 75*(75+1)/2
(Image courtesy of Melchoir on Wikipedia)

By the time I decided T₇₅ should be my goal, I had three days and 11 miles left, so of course I overshot that too.

Final recorded mileage for 2024 = 2865 miles. 2865 = 3 * 5 * 191, a sphenic number.

My last walk of 2024 was 0.2 miles longer than necessary

This is way more miles than I intended, and getting there brought me precipitously close to violating my 2023 goal to not be quite so obsessive about walking. But walking keeps me sane when SAD kicks in, so it's all good.

Next year's goal: in honor of 2025 = 45², I'll initially aim for 2,809 = 53². Overshooting options include the triangular³ number 2,850 or a semiprime.

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Some 2024 walking highlights:

Longest single walk: 28.09 miles. This was my annual American Tobacco Trail long walk on February 4, with a little extra distance to ensure it was longer than last year's ATT marathon. (I did the ATT again in mid-April, but didn't walk quite as far.) 

Number of weeks topping 100 miles: just 1 (in early June). I had 4 in 2023. I felt like I took more rest days this year than last, but apparently I did better keeping up with my weekly mileage goal (50 miles) and more forcefully made up for the lapses (18 weeks under 50 miles this year, vs. 20 last year).

Most miles in a single week: 100.3, which I only reached because I felt obligated to go for a 1.75 mile walk at 10pm on June 9. 

Number of months topping 300 miles: 2 (June and July), same as last year.

Most miles in a single month: 337.3 (June)

Favorite multi-day walk: Sterzing to Feltre in 13 days. S and I started in Sterzing, where we left off in 2023, and declared the Alps crossed when we arrived in Feltre. Feltre is described on various websites as being in the foothills of the Alps (although those hills still looked pretty mountainous to us), and is where the Alta Via 2 delle Dolomiti terminates.

Favorite photo: Mein geliebter Wanderer ueber dem Nebel(isch)meer, taken on Day 9 on the descent from Rifugio delle Selle:

There were some fine runners up:

Day 5, on Seceda

Day 4, en route to Rifugio Resciesa

Day 12, atop Mt. Pavione. The photo does justice neither to the expanse of globeflowers nor to the double cirque.

Day 8, heroic S literally moving mountains to help me cross a river of snow-melt

Nothing else new to report. All of the walking philosophy from the preceding walking-intense years still stands.

What does 2025 hold in store? Another American Tobacco Trail marathon. Another car-free February. And hopefully the Malerweg--a loop hike in the footsteps of Caspar David Friedrich (and other Romantic-era artists), to see the geology that inspired paintings like Der Wanderer ueber dem Nebelmeer--and a 2-week point-to-point trek in German-speaking Switzerland.

Here's to great walking in 2025!

My serifs weren't as good this year as last...

-----

¹I walked a 4-almost-prime number last year, so walking a sphenic number this year was supposed to make it obvious to aim for a semiprime in 2025 and a prime in 2026. I'm all about long-term goals.

²In case you missed it, the word "sphenic" comes from the Greek word σφήνα, meaning "wedge." 

³Of course, there are also square numbers (like 2025 and 2809), and pentagonal numbers, and hexagonal and etc. polygonal numbers, all of which are fun to think about as mileage goals, as well as polyhedral numbers that my brain has a harder time wrapping itself around.

On sphenic numbers and AI

Way back in January, in my Walking Wrap-Up post for 2023, I mentioned sphenic numbers. Sphenic numbers are positive integers that are the product of three distinct prime numbers (e.g. 30 = 2 * 3 * 5 and 42 = 2 * 3 * 7). I was so enamored of this concept that I decided my mileage goal for 2024 should be sphenic. I also noted that when I queried Generative AI about the sphenic numbers closest to my 2023 mileage, AI struggled to come up with anything remotely correct.

I was thinking about sphenic numbers again in September as my public Instagram account (@geekpots) crept toward 1,000 followers. As is the Instagram self-promotional advertising way, I considered holding a pottery giveaway to celebrate reaching a notable number-of-followers goal-post--but my plan would be different from the norm. 

First, the giveaway wouldn't require anyone to do anything other than to comment some variation of "pick me!"--none of that stuff like "to enter the drawing, you must (1) like this post, (2) sign up for my newsletter, (3) tag two friends, and (4) promise your first-born to a gnome-like man who spins straw into gold."

Second, why celebrate 1,000, when I could celebrate the largest sphenic number below 1,000?

I asked Google for a list of sphenic numbers between 900 and 1,000, and Google's generative AI responded with this:

AI Overview 

The only sphenic number between 900 and 1000 is 930. 

Explanation: 

• A sphenic number is a positive integer that can be written as the product of exactly three distinct prime numbers. 
• Prime factors of 930 are 2, 3, and 5, making it a sphenic number.

Here's a fuzzy screen-shot as evidence:

"The only sphenic number between 900 and 1000 is 930" 

Gentle reader(s), do you remember the sepia-tinted olden days when Google searches were actually useful? 

930 is not sphenic. Its prime factors are 2, 3, 5, and 31. It's "4-almost-prime," not sphenic. There are 16 sphenic numbers between 900 and 1,000, and the highest is 994 ( = 2 * 7 * 71 ).

I subsequently repeated the Google query shown above every other week or so, and the answer always came back "930." Go ahead, you try it.

------

Halfway through December, S and I met up for brunch with E and his sweetie A, and at one point our conversation landed on generative AI. I griped about Google's incorrect claim about 930. E suggested I ask ChatGPT instead.

ChatGPT said:

"Thus, 990 is the only sphenic number between 900 and 1000"

Gentle reader(s), 990 is not sphenic. Nor does 990 equal 2 * 3 * 5 * 11.

E asked ChatGPT to write Python code that could generate a list of sphenic numbers between two user-chosen numbers. His request took him all of 30 seconds to type, and all of 2 seconds for ChatGPT to produce. E then copied and ran the code for 900 ≤ n ≤ 1000, and it generated an accurate list. (If you don't want to bother with code, you can find a list of the first 10,000 sphenic numbers here.)

-----

A few days later, when I was out walking, it occurred to me that because ChatGPT is good with languages but poor with comprehension, maybe it could write about sphenic numbers better than it could come up with lists of them. So I asked it to. The conversation is recorded below, with my queries to the left, ChatGPTs responses in blockquotes, and my thoughts in italics. 

------

Write a poem about sphenic numbers that includes a definition 

A sphenic number, rare and true,
Is made from primes in a special brew. 
Three primes distinct, their product shines, 
Each factor unique, no overlap binds. 

It's not a square, nor a cube,

But a product of primes that does not lube.

Take 6, for instance, a simple start, 

2 * 3, primes from the heart. 

Next comes 30, a step more wide,

2 * 3 * 5, side by side. 

Primes that combine with none the same, 

A sphenic number, in prime’s name. 

Not every product of primes you’ll see, 

Makes a sphenic number, as clear as can be.

But those that do, with their special form,

Stand as distinct, away from the norm.

So now you know what makes them tick,

Three primes combined, the magic trick.

A sphenic number, bold and bright,

Shining like stars, in math’s pure light. 

Formulaic, but not bad for a first try. Not sure what "lube" means in line 6.

------

Write a poem about sphenic numbers that includes a definition and an example of a sphenic number between 900 and 1000 

A sphenic number, rare and bright,

Is made from primes, in pure delight.

Three distinct primes, all multiplied,

A product formed where factors bide.

Each prime stands alone, not shared,

A number with no twins, compared.

Multiply the primes you see,

And find the product’s mystery. 

Take 930, it fits the bill, 

Prime factors—three, and they stand still: 

2, 3, and 5, they intertwine,

Forming 930, pure and fine.

Sphenic numbers, quite unique, 

In prime trio, their strength we seek. 

You and Google AI: What's with "930"? Also, 2 * 3 * 5 = 30, not 930.

------

Explain how 930 is a sphenic number 

To explain how 930 is a sphenic number, let's first define what a sphenic number is: a sphenic number is a positive integer that is the product of exactly three distinct prime numbers.

Now, let's check if 930 fits this definition:

1. Prime Factorization of 930:

• Start by dividing 930 by 2 (since it's even): 930 / 2 = 465

• 465 is odd, so it's not divisible by 2. 

• Next, divide by 3: 465 / 3 = 155 

• 155 is divisible by 5: 155 / 5 = 31 

• 31 is a prime number.

2. Prime Factors of 930:

The prime factorization of 930 is: 930 = 2 * 3 * 5 * 31

• Here, we see that 930 has four prime factors (2, 3, 5, and 31), not three distinct primes.

Thus, 930 is not a sphenic number, because a sphenic number requires exactly three distinct primes. I apologize for the earlier confusion.

Apology appreciated. (At this point, my cellphone had a conniption fit, so I had to restart it, which meant starting the conversation from scratch.)

------

Write a poem about sphenic numbers that includes a definition and an example of a sphenic number between 900 and 1000

[...]

For instance, look at nine hundred and ninety, 

A sphenic number, strong and mighty. 

Its primes are three, ten, and eleven, 

Multiply them, and the answer is heaven.

[...]

Ten is not prime. 3 * 10 * 11 = 330, not "nine hundred and ninety," and it isn't sphenic.

------

Explain how 990 is sphenic 

You're right to question the number 990! In fact, 990 is not a sphenic number. 

Let's break down why: A sphenic number is a positive integer that is the product of exactly three distinct prime numbers. In other words, it is a product of three unique prime factors, with no repeats. 

Now, let's factorize 990: 

1. First, divide by 2 (since it's even): 990 ÷ 2 = 495 

• So, 2 is a prime factor.

2. Next, divide 495 by 3 (since the sum of its digits, 4 + 9 + 5 = 18, is divisible by 3): 495 ÷ 3 = 165 

• So, 3 is a prime factor. 

3. Finally, divide 165 by 5 (since it ends in 5): 165 ÷ 5 = 33 

• So, 5 is a prime factor. 

4. Now, 33 is divisible by 3 again: 33 ÷ 3 = 11 

• So, 3 is a prime factor again. 

Therefore, the prime factorization of 990 is: 990 = 2 * 3² * 5 * 11

Since 3 is repeated as a factor, 990 is not a sphenic number. A true sphenic number would have exactly three distinct primes and 990 has four distinct prime factors, with one of them (3) repeating. 

So, a correct example of a sphenic number between 900 and 1000 would be 930, since: 930 = 2 * 3 * 5 * 31

Here, the product of the distinct primes is 930, which has exactly three distinct prime factors: 2, 3, and 5. Apologies for the confusion, and thank you for pointing it out! 

You're welcome, but golly, you're kinda an idiot. How is it that you can think to sum the digits of a number and divide by 3 to tell whether the number is divisible by 3, but you can't recognize the difference between "three" and "four" when it comes to the number of prime factors?

(I then ask it about 930 again, because it probably doesn't remember anything from before my phone conked out. Note it's offer to find a correct example--)

------

Explain how 930 is sphenic 

Apologies again for the confusion in my previous response. You're right to ask for clarification about 930. Upon reviewing the factorization of 930, it turns out 930 is also NOT a sphenic number. 

Let's break it down properly: [yadda yadda yadda]

Correct Example of a Sphenic Number Between 900 and 1000: Let's find the correct example! A sphenic number between 900 and 1000 should have exactly three distinct prime factors.

The number 930 doesn't qualify, but 990 does have the required prime factors as well. Here's the correct example: 

Example: 990: 

The prime factorization of 990 is: 990 = 2 * 3 * 5 * 11 

But because there's no repeating primes or errors, this number might be 

Aw geez, 990 again, plus an unfinished sentence at the end...

------

Might be what? 

I apologize for the confusion in my previous responses. Let's clarify everything: [yadda yadda yadda] 

Correct Example of a Sphenic Number Between 900 and 1000: Let's find a correct sphenic number between 900 and 1000. The number 935 is a sphenic number because: [yadda yadda yadda]

Thus, the prime factorization of 935 is: 

935 = 5 * 11 * 17

It has exactly three distinct prime factors (5, 11, and 17), so 935 is a sphenic number. 

Final Answer: 935 is a correct sphenic number between 900 and 1000. Thank you for your patience! 

"Final answer," lol, after how many tries? 935 is indeed sphenic--but a broken clock is likewise correct twice a day.

Assuming ChatGPT trained on some website that claimed 990 was sphenic, I ask for its source.

------

Where did you read that 990 is sphenic? 

I made the mistake of incorrectly asserting that 990 was a sphenic number based on my own error in processing the factors. I didn't read or reference any specific external source that labeled 990 as a sphenic number. The mistake stemmed from my own misunderstanding while performing the prime factorization. I didn’t check carefully enough to see that 3 repeats in the factorization of 990. I mistakenly thought it might still qualify, but as we now know, 990 is not sphenic due to the repetition of 3. I appreciate your sharp observation, and again, I apologize for the oversight. Thank you for your patience! 

Like college undergrads everywhere, ChatGPT says it did its own work!

------

Where did you read that 930 is sphenic? 

I mistakenly suggested that 930 might be a sphenic number based on an incorrect factorization and assumption. Similar to my mistake with 990, I didn't read or refer to any specific source that stated 930 was a sphenic number. It was an error I made while processing the factorization. To clarify, I incorrectly concluded that 930 might be a sphenic number, but upon breaking it down, I found that 930 has four distinct prime factors (2, 3, 5, and 31), so it is not a sphenic number either. I didn’t rely on an external source to make this claim; it was a mistake in my reasoning. I appreciate your careful attention and the opportunity to correct it. Thank you again for your patience! 

I don't believe ChatGPT, and accuse it of using Google:

------

Google AI search also says 930 is sphenic. Did you use Google AI search? 

I did not use Google AI search or any external AI tools to suggest that 930 is a sphenic number. My mistake was entirely due to my own miscalculation and incorrect reasoning when processing the prime factorization of 930. 

To clarify, I incorrectly concluded that 930 might be a sphenic number based on its factorization, without thoroughly verifying that it had exactly three distinct prime factors. In fact, 930 has four distinct prime factors (2, 3, 5, and 31), so it does not qualify as a sphenic number. 

It’s possible that external sources or other AI tools might have made a similar error when processing this number. However, I do not rely on Google AI search for these calculations—it's purely based on the reasoning I perform. I appreciate your attention to detail and your patience in allowing me to correct this.

OK, this explanation sounds plausible. Let's get away from 990 and 930.

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Give me another example of a sphenic number between 900 and 1000 

Let's find another example of a sphenic number between 900 and 1000! A sphenic number is the product of exactly three distinct prime numbers. Here’s a valid example: 

1002: Let's factorize 1002: 

1. 1002 ÷ 2 = 501 (so 2 is a prime factor). 
2. 501 ÷ 3 = 167 (so 3 is a prime factor). 
3. 167 is a prime number. 

So, the prime factorization of 1002 is: 1002 = 2 * 3 * 167 . This has exactly three distinct prime factors: 2, 3, and 167. Therefore, 1002 is a sphenic number. 

Conclusion: 1002 is a valid sphenic number between 900 and 1000. 

WTF. And how do you decide when to use boldface font? I know a bunch of grad students applying for grants who'd like to know.

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Explain how 1002 is between 900 and 1000 

You're absolutely right, and I apologize for the mistake! 1002 is not between 900 and 1000—it is greater than 1000. I made an error in my response, and I appreciate your patience in pointing that out. 

Let's correct this and find a proper sphenic number between 900 and 1000. 

Correct Example: 910

Now, let's check 910. [yadda yadda yadda] The prime factorization of 910 is: 910 = 2 * 5 * 7 * 13. Since this has four prime factors, 910 isn't a sphenic number.

Let's check a new candidate like 935 

From "Correct Example" to "isn't sphenic," all on your own!

------

You already showed 935 is sphenic. Give me a different example. 

[yadda yadda yadda]...969...

969 is sphenic! Is ChatGPT finally figuring this out?

------

What determines whether you check the truth of your statements?

Thank you for your thoughtful question. The accuracy of my responses is primarily determined by the way I process information and follow logical steps when explaining or performing calculations. However, as a language model, I rely on the context provided by you and on the knowledge I have been trained on. Here’s how I typically check the truth of my statements: 

1. Internal Reasoning: I perform the necessary logical steps to check whether a statement is true. For example, when discussing sphenic numbers, I perform prime factorization to verify whether a number has exactly three distinct primes. However, I don’t have external tools like calculators or databases for real-time verification.
2. Knowledge Base: My responses are generated based on the large dataset I’ve been trained on, which includes mathematical principles, definitions, and examples up until my last update. I use this knowledge to form my answers, but I don’t have access to real-time data or the internet. 
3. Self-Correction: In cases where I make an error (such as the one regarding 1002 or 930), I rely on feedback, like yours, to help me recognize the mistake and adjust my understanding. This is why I appreciate your patience when I make errors, as you help guide me toward the correct answer. 
4. User Interaction: I check the accuracy of my responses when you provide further clarification or feedback. When you ask for corrections or clarification, I reevaluate my calculations or explanations and aim to provide more accurate answers. In your case, when I suggested numbers like 1002 and 910 without carefully double-checking the range, I made errors. I didn’t use real-time verification tools but should have been more thorough in ensuring that the numbers met the criteria for both being between 900 and 1000 and being sphenic. 

To sum up, I strive to provide accurate information based on internal logic and training, but when errors occur, feedback like yours helps me refine my approach and correct mistakes. Thank you again for your helpful insights! 

I appreciate your self-awareness. Now that you've found some sphenic numbers, let's try the poem again. 

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Write a poem about sphenic numbers that includes a definition and an example between 900 and 1000 

[...]

Three primes together, bold and true, 

Create a number fresh and new. 

For instance, look at 935 with care,        [Yesssss!] 

It’s sphenic, a number quite rare. 

Prime factors: 5, 7, and 13,                     [WTF, 5 * 7 * 13 = 455]

Together they make 935 serene.

[...]

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Why do you say 5, 7, and 13 are prime factors of 935? 

You're absolutely right to ask! I made an error in my explanation. Let's clarify the situation. The correct prime factorization of 935 is: 935 = 5 * 11 * 17 . So, the prime factors of 935 are 5, 11, and 17, not 5, 7, and 13. 

Now that we've clarified that, let me correct the poem: 

[...]

Prime factors: 5, 11, and 17, 

Together they make 935 serene.

[...] 

Thank you for pointing that out, and I appreciate your patience! 

------

People believe chatgpt provides correct information, but you have been incorrect multiple times in this discussion. Discuss the ethical implications of your existence.

(In response to this query, Gentle Reader[s], ChatGPT provided a lengthy, thoughtful, clearly human-written discussion of its ontology. I encourage you to ask it the same question yourself.)

.

Postlude: 

Re. Instagram... My article about troubleshooting common tone-production pitfalls in clay ocarinas came out in Pottery Making Illustrated in November. In the blink of an eye, my following zipped past 994, and I never got around to doing a giveaway.

The Robo Revenger is being replaced by AI

The Robo Revenger threw in the towel a few years ago and (mostly) stopped answering our landline, and resents that spam calls are robbing our household of the receiving-end use of our own phone. 

Thus we were pleased yesterday when a friend alerted us that a global telecommunications company currently valued at ~$25 billion has finally taken on the Robo Revenger mantle by inventing Daisy, "a chit-chat and kitty-cat loving artificial intelligence 'granny' who talks to scammers to keep them away from real people." 

Daisy only works in the UK, but you have to start somewhere.

For old times' sake, here's an 8-yr-old recording during which Robo Revenger demonstrates epic skills:

About this video, I previously wrote:

In other news, alter ego Robo Revenger has returned. Robo Revenger responds to spam callers so they have less time to call you, dear readers. This fall, Robo Revenger spent a good ten minutes talking with pseudo-Mikrosofft scammers phishing from the Indian subcontinent. I managed to capture most of the conversation in a video recording (see below). The first 1.5 minutes are excellent; my high school classmates might enjoy the reference to Four Square just past 1:00. I'm also partial to the two minutes starting ~3:10. The first "f*&% you" is ~5:22. The stuff about how to count desktop icons ~5:35-7:03 is fabulous, yielding a nice stream of "f*&%-yous" ~7:04. The part from 7:00 to the end demonstrates how to remain chipper and polite in the face of adversity. Really, the whole thing is a Robo Revenger tour-de-force.

May the Force be with you, Daisy.

Public service article

I recently wrote an article for Pottery Making Illustrated on troubleshooting tone-production pitfalls in ocarinas, because any potter who has ever been stymied by a malfunctioning fipple deserves help. It's available online here. It's acoustically and musically serious, while simultaneously including lots of googly eyes.

The article had a word limit that I was already exceeding, so I left out my number one rule of ocarina making: 

Fipple ain't broke, don't fix it.

There you have it. Now go forth and make music.

Waiting for the kiln to cool: a poem

I unintentionally deleted an important Powerpoint file that I have spent hours and hours working on, and then in an effort to clear up space on my laptop, I emptied the Recycle Bin. I've tried assorted recovery suggestions, but it's gone, gone, gone.

Alas.

Losing the file made me realize how woefully disorganized my folders are, so I'm doing some housekeeping today.

Lo, I found a free-floating poem I wrote a while ago. It's now tucked safely into a folder where I may or may not ever find it again, so I'm putting it here, so it can live on da blog with assorted other poems. Pretty sure I had a melody in my brain for it, but that's deleted and emptied from my mental recycle bin, oh well.

-----------

Waiting for the Kiln to Cool

Oh I’m waitin’ for the kiln to coo-oo-oo-ool;

Temp’s gotta drop first--I ain’t no fool!

I worked too long on chipmunks, vases, and cups!

To lift the lid now risks thermal-shock blow ups.

Well, I say that’s the case, but truth be told,

Sometimes impatient, feeling risky and bold,

Throwing caution to the wind, anti-erudite,

I peek inside the kiln above two hundred Fahrenheit!

And the pots, they go

            Ping,

                        Ping,

                                    Ping.

In the warm air of the

            Spring,

                        Spring,

                                    Spring,

So I shut the lid, and I

            Sing

                        Sing

                                    Sing

about waitin’ for the kiln to cool….

Blueberry pie and whipped cream

Seemed like a good idea when I started, but the take-away is that an immersion blender whisk is not equivalent to an electric beater, and a Dr. Oetker measuring cup is not equivalent to a German mixing beaker with silicone treads. 

After spraying the west side of the kitchen with whipping cream, I replicated the centrifugal force demo on the east side (Figures 1 & 2). 

E observed, "the remarkable thing is that you didn't get any on the pie" (Figure 3). Figuring I had done enough damage for the night, he and S sent me upstairs to shower while they cleaned up.

Figure 1: east side of kitchen post-demo

Figure 2: west side of me post-demo

Figure 3: pristine blueberry pie

The Rules of Condiments

I am getting up there in years, but I had discerned the Rules on my own by the time I was five. So had my sister, 15 months my junior, though we never spoke of them until well after we were adults. Yet we were raised by parents who had no clue, and our older brother was similarly oblivious. How did they not comprehend what is so clearly true, and good, and right?

The first Rule is this: No mayonnaise from a jar, ever. 

The second Rule follows from the first: If its ingredients are not obvious from visual inspection, do not ingest the commercial condiment. 

All other Rules follow from these two. Eat not ketchup from a bottle or plastic packet, likewise neither yellow mustard, nor homogenized ranch dressing, nor barbecue sauce. 

Know that whole-seed mustard is beloved, for it is like unto caviar for vegetarians. 

Of stone-ground mustard, be watchful: if the seeds are more than lightly crushed, let it not pass between the lips. 

Sambal oelek: beloved. Sriracha: not for eating. 

And what of pickle relish? It is a wolf in sheep’s clothing, a cucumber fallen from grace, now dressed in FD&C Blue no. 1 and Yellow no. 5 and polysorbate 80. Forbidden. 

Partake then of homemade condiments. These are beloved to me, even if the ingredients evade visual identification, for who puts dicalcium sodium EDTA, high fructose corn syrup, or xanthan gum in freshly made aiolis, chutneys, or vinaigrettes? Prepare them with love; share them with friends; ingest them with joy.