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A thought about burrs

Chandu

I Waxed The Badger.
When honing a razor you do create burrs. What you don't do is create noticeable burrs - it's just a matter of perception and definition. And further - the definition of a burr or wire edge probably actually changes depending on what you're cutting with the blade...
Correct. If we all had scanning electron microscopes we could see the crazy things our stones do to our cutlery.
a 'zero bevel', which is analogous to the edge of a razor.
In the knife world, basically a Scandi grind, though a razor usually has a hollow, but my point is the you lay the blade down to sharpen.
A razor has what, on a knife, one would consider a wire edge. That is why it is so sharp.
Basically, but also an obscene number of pull strokes on some abrasives will create a foil edge which is too thin to be of any use. I don't think barbers ever did that, but I think some razor sharpeners these days cross the line between highly useable and over sharpened because time is not a factor. If you were a barber 100 years ago, once it was ready to shave, you quit honing and earned some money. Today we futz and fiddle the hours away.
 
Correct. If we all had scanning electron microscopes we could see the crazy things our stones do to our cutlery.

In the knife world, basically a Scandi grind, though a razor usually has a hollow, but my point is the you lay the blade down to sharpen.

Basically, but also an obscene number of pull strokes on some abrasives will create a foil edge which is too thin to be of any use. I don't think barbers ever did that, but I think some razor sharpeners these days cross the line between highly useable and over sharpened because time is not a factor. If you were a barber 100 years ago, once it was ready to shave, you quit honing and earned some money. Today we futz and fiddle the hours away.

Yep - techinically it would be a Scandi grind. But analogous to a razor edge in that it's flat against the stone from the beginning of the bevel to the edge. Just a razor has a minute bevel, and a scandi grind/flat bevel on a knife is much wider. I tend to do this sometimes on knives I'm keeping for myself because almost all knife grinds have low spots somewhere, so I can get them out and then re-build the geometry to suit my tastes.
 
Not bad! Not all that jigane is the same, even in the same brand. I have a Takeda sasanoa that’s difficult to get a good ji/ha on, and a bunka and a funayuki thats really easy to get good ji/ha.

Mostly it’s the stone though I think.Alex Gilmore said that when he finds a stone that does the slam dunk on the ji/ha, he sets those aside for the knife guys.

Yeah stones like that are rare as hen's teeth! I don't have many jnats, but my best for it is a Maruoyama Shiro Suita, which is out on loan to someone atm, but when I get it back I'm looking forward to seeing what the diamond balsa will do on top of a really good jnat polish.

Those low grit diamond pastes will pull full mirror on hagane quite quickly, so if they can do that while maintaining the haze on jigane (as they basically did in my initial experiement), then the results after a proper kasumi progression using posh stones should be pretty impressive :).

But yeah as you say - it presumably depends on the cladding too. I've got a couple of yanagi where the banding gets really nicely highlighted with certain stones. Be interesting to see what pastes do to that...
 
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You're right - deburring knives with harder steels and lower angle edges is easier. At least in part because you can more easily play around with using microbevels for deburring.

I remember you got a Maruoyama SS :). You definitely need to get a posh Japanese san-mai knife now... those things are extraordinary for bevel polishing!
Yes i definitely need a nice Japanese knife. The problem is that i am the only "knife" guy in the house.
My wife have not figured out that these stones are expensive yet. They all look the same to her. It is the same reason the shapton gs are so grate, they all look the same😀 Naniwa are clearly missing this important point😉
 
I honed a Boker razor recently. I think these are a little on the soft side compared to some other manufacturers (59-60 hr). I ended up with something that seemed like a micro burr that was visible under a bright overhead light. It looked good under my loupe. Linen and leather did not seem to help. So i decided to just test shave with the razor. The razor felt quite smooth. After the first pass was done i stropped it on linen and leather. Now the edge looked much cleaner. I had no post shave feedback out of the ordinary.
This also seem to happen with some de blades.
 

rbscebu

Girls call me Makaluod
.... a valid point that you were making about how an edge will cut, or not cut, different things. And a well honed razor is absolutely about making sure that it won't cut some things well - your skin being the obvious example as you pointed out.
....
This reminded my of a comment a surgeon (urologists) friend of mine made a few years ago. We were discussing razors and scalpels. From memory he made a comment like "A surgical scalpel should not have a razor type edge. It needs a very fine microscope sawtooth type edge to be comfortable to work with."

I don't know if what he told me is true or not. Just quoting what I remember him saying.
 

Legion

Staff member
This reminded my of a comment a surgeon (urologists) friend of mine made a few years ago. We were discussing razors and scalpels. From memory he made a comment like "A surgical scalpel should not have a razor type edge. It needs a very fine microscope sawtooth type edge to be comfortable to work with."

I don't know if what he told me is true or not. Just quoting what I remember him saying.
This is quite true, for the reasons discussed. Compared to a good SR edge, a scalpel edge isn't very refined at all.

On the other side, where super sharp edges for surgery are required (by cosmetic or eye surgeons, for example) they use shards of obsidian. Glass cleaves to about as sharp an edge as you can get.

 
This reminded my of a comment a surgeon (urologists) friend of mine made a few years ago. We were discussing razors and scalpels. From memory he made a comment like "A surgical scalpel should not have a razor type edge. It needs a very fine microscope sawtooth type edge to be comfortable to work with."

I don't know if what he told me is true or not. Just quoting what I remember him saying.

Just like sharing the test video recorded with the palm of the hand, I understand what the doctor said, because shaving will pay attention to the skin feel to find the edge you want, which is different from the characteristics of the scalpel.
 
This reminded my of a comment a surgeon (urologists) friend of mine made a few years ago. We were discussing razors and scalpels. From memory he made a comment like "A surgical scalpel should not have a razor type edge. It needs a very fine microscope sawtooth type edge to be comfortable to work with."

I don't know if what he told me is true or not. Just quoting what I remember him saying.

Yep, this is exactly the same principle. It's because (as David said above) - though hair is quite fine it's also quite hard. Whereas your skin and flesh in comparison is relatively tough. Those attributes have quite a strong inverse correlation; hard things are brittle, soft things are tough, you don't really get stuff that's both hard and tough.

You also need different types of edge to cut them, which allows you to make a instrument like a razor - with a very refined edge - that will cut one type well but not the other. And it's what allows you to shave in the first place; if your skin was hard like hair, or your hair was soft like skin, then you'd cut yourself up quite badly.
 
Ok, so here are two old posts of mine put together as a deep-dive into the physics of how different edges cut things. It focuses mostly on knife edges to begin with, especially the phenomenon of why very sharp knives aren't very good at cutting tomatoes, but then also explains why that's the same reason you can shave with a straight razor.

---

I did a couple of slightly exaggerated drawings to help anyone new understand this phenomenon...

If you cut down on a tomato at 90 degrees and perfectly straight; you will cut through it, no matter how overly refined your edge is. Like this:

IMG_E2995.JPG



But the majority of the time you're not neatly bisecting a tomato; you're cutting it at an angle, because a tomato is round. And to compound matters you might be using a push or pull cut, rather than chopping straight down. It looks more like this:

IMG_E2994.JPG


Where 'b' is the angle of your edge (sharpening angle). 'a' is 90 degrees minus 'b'. And 'c' is 90 degrees minus the angle you're cutting the tomato at. As soon as 'c' starts getting close to the same as 'a' - that's when you run into problems. And if 'c' is larger than 'a' - you’re really going to struggle if your edge is super slick.

Pretty much all cutting of stuff is the result of friction. If you don't have friction you can't cut anything. A tomato skin is fairly smooth, and if you combine that with a very refined edge you have quite a low coefficient of friction between the two. But that isn't the real kicker here... the really important thing is the 'normal force' exerted by the tomato upwards against your knife.

The normal force is obviously considerably reduced when you're cutting the curved surface of a tomato at an acute angle. And it's also reduced because the pulp is soft. The reason tomatoes are brought up again and again in this test isn't necessarily because the skin is unreasonably tough - the skin of a capsicum or bell pepper is probably tougher, and equally smooth. It's the combination of soft flesh, with skin that is both tough-ish, and smooth, that all together kill the friction generated when cutting it. Try cutting a wet tomato vs a dry one and you'll see the importance of friction.

But unfortunately, apart from making sure it's dry, you can't really change your tomato, so you have to change your knife. You could do this by lowering your sharpening angle, but that might make it less durable, and annoying to maintain. So you do it by finishing the edge at a lower grit, with more teeth, and a higher coefficient of friction...

And now at last you can truly hope to achieve the bruschetta of your dreams, and know the panzanella in the mind of god!

---

So here's the same two diagrams explaining a bit further about friction. It's slightly simplified because in real life there are all sorts of other variables - cutting style would be an important one - but this is the gist (I think)...

IMG-3006.jpg



In the first picture when cutting straight down let's call the Normal force 'N'. When cutting at an angle the Normal Force is reduced - only a certain proportion of N will be acting upwards against our knife, we'll call that 'N1'.

N1 = N sin d. Where 'd' is the angle 'a' minus the angle 'c' from the initial drawing. We can see that if we decrease the sharpening angle 'b' then we increase 'a', hence increase 'd', and subsequently increase the value of N1.

The cutting friction of your knife on the tomato we'll call 'F'. The coefficient of friction between the two surfaces is 'u'.

F = u * N1

So we can increase F to the point that it will cut through the tomato skin either by increasing N1 via a reduction in the edge angle. Or by increasing u via making the surface of our knife rougher, i.e. finishing it at a lower grit - with more 'teeth'.

That's how a less 'sharp' knife can cut things better than a 'sharper' one.

Now let's look at why this kind of sharp is almost the opposite of what you want in a razor. And that's because sharpness is a product of two quite different things; how refined your edge is, and how thin it is. Here's a picture of a knife that I use for trying out new stones. I have made it excessively thin so that it doesn't take me long to raise a burr and get an idea of how a stone performs. To give an idea; this is a closeup shot of a small petty, at the bottom of the picture the blade is about 1.5mm thick.

IMG-2733.jpg



That knife is incredibly sharp. I can get HHT off a fresh, non-glazed, 500 grit stone. It will cut hair because its so thin, but would be awful for shaving in that condition, because the angle of the edge is minute and the coefficient of friction off a 500 grit stone against your skin would be very high... it would cut your face to shreds. I have shaved using this knife very happily, but I finished it at a much higher grit, and you need to take a lot of care because the edge angle is low. It's actually far lower than a razor - the combined edge angle on that knife is no more than 8 degrees I'd guess.

What you want from a razor, for the reasons above, is an edge with a higher angle, and a lower friction coefficient. So it glides smoothly over your skin rather than digging into it, while still cutting the hair on the outside. You do this by working to a very refined edge on a series of increasingly high grit stones / pastes / strops. To create an edge that will effortlessly cut hard/brittle things like hair, but will not tear into soft/tough things like flesh. The same kind of sharpness that is terrible for cutting a tomato skin is also terrible for cutting your own skin. Which is kinda what you want in a razor.

You might however want the same kind sharpness in a yanagiba - for slicing sashimi neatly without tearing the flesh. When slicing sashimi you don't have a tough outer skin to contend with, so don't need to do as much as possible to increase the friction. Which means you might finish sharpening a yanagiba on the kind of stone you use for a razor, but use a much lower grit stone for a gyuto or 'Chef's Knife'.

---

TLDR: Everything about cutting or not cutting anything, is about how friction works.
 
Ok, so here are two old posts of mine put together as a deep-dive into the physics of how different edges cut things. It focuses mostly on knife edges to begin with, especially the phenomenon of why very sharp knives aren't very good at cutting tomatoes, but then also explains why that's the same reason you can shave with a straight razor.

---

I did a couple of slightly exaggerated drawings to help anyone new understand this phenomenon...

If you cut down on a tomato at 90 degrees and perfectly straight; you will cut through it, no matter how overly refined your edge is. Like this:

View attachment 1414527


But the majority of the time you're not neatly bisecting a tomato; you're cutting it at an angle, because a tomato is round. And to compound matters you might be using a push or pull cut, rather than chopping straight down. It looks more like this:

View attachment 1414526

Where 'b' is the angle of your edge (sharpening angle). 'a' is 90 degrees minus 'b'. And 'c' is 90 degrees minus the angle you're cutting the tomato at. As soon as 'c' starts getting close to the same as 'a' - that's when you run into problems. And if 'c' is larger than 'a' - you’re really going to struggle if your edge is super slick.

Pretty much all cutting of stuff is the result of friction. If you don't have friction you can't cut anything. A tomato skin is fairly smooth, and if you combine that with a very refined edge you have quite a low coefficient of friction between the two. But that isn't the real kicker here... the really important thing is the 'normal force' exerted by the tomato upwards against your knife.

The normal force is obviously considerably reduced when you're cutting the curved surface of a tomato at an acute angle. And it's also reduced because the pulp is soft. The reason tomatoes are brought up again and again in this test isn't necessarily because the skin is unreasonably tough - the skin of a capsicum or bell pepper is probably tougher, and equally smooth. It's the combination of soft flesh, with skin that is both tough-ish, and smooth, that all together kill the friction generated when cutting it. Try cutting a wet tomato vs a dry one and you'll see the importance of friction.

But unfortunately, apart from making sure it's dry, you can't really change your tomato, so you have to change your knife. You could do this by lowering your sharpening angle, but that might make it less durable, and annoying to maintain. So you do it by finishing the edge at a lower grit, with more teeth, and a higher coefficient of friction...

And now at last you can truly hope to achieve the bruschetta of your dreams, and know the panzanella in the mind of god!

---

So here's the same two diagrams explaining a bit further about friction. It's slightly simplified because in real life there are all sorts of other variables - cutting style would be an important one - but this is the gist (I think)...

View attachment 1414532


In the first picture when cutting straight down let's call the Normal force 'N'. When cutting at an angle the Normal Force is reduced - only a certain proportion of N will be acting upwards against our knife, we'll call that 'N1'.

N1 = N sin d. Where 'd' is the angle 'a' minus the angle 'c' from the initial drawing. We can see that if we decrease the sharpening angle 'b' then we increase 'a', hence increase 'd', and subsequently increase the value of N1.

The cutting friction of your knife on the tomato we'll call 'F'. The coefficient of friction between the two surfaces is 'u'.

F = u * N1

So we can increase F to the point that it will cut through the tomato skin either by increasing N1 via a reduction in the edge angle. Or by increasing u via making the surface of our knife rougher, i.e. finishing it at a lower grit - with more 'teeth'.

That's how a less 'sharp' knife can cut things better than a 'sharper' one.

Now let's look at why this kind of sharp is almost the opposite of what you want in a razor. And that's because sharpness is a product of two quite different things; how refined your edge is, and how thin it is. Here's a picture of a knife that I use for trying out new stones. I have made it excessively thin so that it doesn't take me long to raise a burr and get an idea of how a stone performs. To give an idea; this is a closeup shot of a small petty, at the bottom of the picture the blade is about 1.5mm thick.

View attachment 1414531


That knife is incredibly sharp. I can get HHT off a fresh, non-glazed, 500 grit stone. It will cut hair because its so thin, but would be awful for shaving in that condition, because the angle of the edge is minute and the coefficient of friction off a 500 grit stone against your skin would be very high... it would cut your face to shreds. I have shaved using this knife very happily, but I finished it at a much higher grit, and you need to take a lot of care because the edge angle is low. It's actually far lower than a razor - the combined edge angle on that knife is no more than 8 degrees I'd guess.

What you want from a razor, for the reasons above, is an edge with a higher angle, and a lower friction coefficient. So it glides smoothly over your skin rather than digging into it, while still cutting the hair on the outside. You do this by working to a very refined edge on a series of increasingly high grit stones / pastes / strops. To create an edge that will effortlessly cut hard/brittle things like hair, but will not tear into soft/tough things like flesh. The same kind of sharpness that is terrible for cutting a tomato skin is also terrible for cutting your own skin. Which is kinda what you want in a razor.

You might however want the same kind sharpness in a yanagiba - for slicing sashimi neatly without tearing the flesh. When slicing sashimi you don't have a tough outer skin to contend with, so don't need to do as much as possible to increase the friction. Which means you might finish sharpening a yanagiba on the kind of stone you use for a razor, but use a much lower grit stone for a gyuto or 'Chef's Knife'.

---

TLDR: Everything about cutting or not cutting anything, is about how friction works.

Thank you for your information, it made me think about the edge I encountered, I can't explain why I didn't cut the toilet paper when I encountered it, but through HHT, when I was cutting toilet paper, I felt a slight vibration when I held it in my left hand, then It may cut the toilet paper, I will deal with the edge again, when the edge slides smoothly without cutting, then I will use HHT again to understand the edge status.
 
Ok, so here are two old posts of mine put together as a deep-dive into the physics of how different edges cut things. It focuses mostly on knife edges to begin with, especially the phenomenon of why very sharp knives aren't very good at cutting tomatoes, but then also explains why that's the same reason you can shave with a straight razor.

---

I did a couple of slightly exaggerated drawings to help anyone new understand this phenomenon...

If you cut down on a tomato at 90 degrees and perfectly straight; you will cut through it, no matter how overly refined your edge is. Like this:

View attachment 1414527


But the majority of the time you're not neatly bisecting a tomato; you're cutting it at an angle, because a tomato is round. And to compound matters you might be using a push or pull cut, rather than chopping straight down. It looks more like this:

View attachment 1414526

Where 'b' is the angle of your edge (sharpening angle). 'a' is 90 degrees minus 'b'. And 'c' is 90 degrees minus the angle you're cutting the tomato at. As soon as 'c' starts getting close to the same as 'a' - that's when you run into problems. And if 'c' is larger than 'a' - you’re really going to struggle if your edge is super slick.

Pretty much all cutting of stuff is the result of friction. If you don't have friction you can't cut anything. A tomato skin is fairly smooth, and if you combine that with a very refined edge you have quite a low coefficient of friction between the two. But that isn't the real kicker here... the really important thing is the 'normal force' exerted by the tomato upwards against your knife.

The normal force is obviously considerably reduced when you're cutting the curved surface of a tomato at an acute angle. And it's also reduced because the pulp is soft. The reason tomatoes are brought up again and again in this test isn't necessarily because the skin is unreasonably tough - the skin of a capsicum or bell pepper is probably tougher, and equally smooth. It's the combination of soft flesh, with skin that is both tough-ish, and smooth, that all together kill the friction generated when cutting it. Try cutting a wet tomato vs a dry one and you'll see the importance of friction.

But unfortunately, apart from making sure it's dry, you can't really change your tomato, so you have to change your knife. You could do this by lowering your sharpening angle, but that might make it less durable, and annoying to maintain. So you do it by finishing the edge at a lower grit, with more teeth, and a higher coefficient of friction...

And now at last you can truly hope to achieve the bruschetta of your dreams, and know the panzanella in the mind of god!

---

So here's the same two diagrams explaining a bit further about friction. It's slightly simplified because in real life there are all sorts of other variables - cutting style would be an important one - but this is the gist (I think)...

View attachment 1414532


In the first picture when cutting straight down let's call the Normal force 'N'. When cutting at an angle the Normal Force is reduced - only a certain proportion of N will be acting upwards against our knife, we'll call that 'N1'.

N1 = N sin d. Where 'd' is the angle 'a' minus the angle 'c' from the initial drawing. We can see that if we decrease the sharpening angle 'b' then we increase 'a', hence increase 'd', and subsequently increase the value of N1.

The cutting friction of your knife on the tomato we'll call 'F'. The coefficient of friction between the two surfaces is 'u'.

F = u * N1

So we can increase F to the point that it will cut through the tomato skin either by increasing N1 via a reduction in the edge angle. Or by increasing u via making the surface of our knife rougher, i.e. finishing it at a lower grit - with more 'teeth'.

That's how a less 'sharp' knife can cut things better than a 'sharper' one.

Now let's look at why this kind of sharp is almost the opposite of what you want in a razor. And that's because sharpness is a product of two quite different things; how refined your edge is, and how thin it is. Here's a picture of a knife that I use for trying out new stones. I have made it excessively thin so that it doesn't take me long to raise a burr and get an idea of how a stone performs. To give an idea; this is a closeup shot of a small petty, at the bottom of the picture the blade is about 1.5mm thick.

View attachment 1414531


That knife is incredibly sharp. I can get HHT off a fresh, non-glazed, 500 grit stone. It will cut hair because its so thin, but would be awful for shaving in that condition, because the angle of the edge is minute and the coefficient of friction off a 500 grit stone against your skin would be very high... it would cut your face to shreds. I have shaved using this knife very happily, but I finished it at a much higher grit, and you need to take a lot of care because the edge angle is low. It's actually far lower than a razor - the combined edge angle on that knife is no more than 8 degrees I'd guess.

What you want from a razor, for the reasons above, is an edge with a higher angle, and a lower friction coefficient. So it glides smoothly over your skin rather than digging into it, while still cutting the hair on the outside. You do this by working to a very refined edge on a series of increasingly high grit stones / pastes / strops. To create an edge that will effortlessly cut hard/brittle things like hair, but will not tear into soft/tough things like flesh. The same kind of sharpness that is terrible for cutting a tomato skin is also terrible for cutting your own skin. Which is kinda what you want in a razor.

You might however want the same kind sharpness in a yanagiba - for slicing sashimi neatly without tearing the flesh. When slicing sashimi you don't have a tough outer skin to contend with, so don't need to do as much as possible to increase the friction. Which means you might finish sharpening a yanagiba on the kind of stone you use for a razor, but use a much lower grit stone for a gyuto or 'Chef's Knife'.

---

TLDR: Everything about cutting or not cutting anything, is about how friction works.
I guess this relates a little to the subject. The type of steel and heat treatment is also really important. I have a Spyderco Serrata in cast dendritic 440C steel. You can cut rope all day and still cut tomato skin afterward with this knife. I have another spyderco knife in M390 steel. This will pass the hanging hair test, but try cutting a tomato after it's been used to cut e.g. rope with. Totally useless. I would gladly shave with a razor made of M390 steel, but regardless of the way the serrata was honed, i would never try to shave with it.

A wider bevel angle will increase the normal force on the bevel planes, and thus increase the cutting resistance from a higher friction force. The edge needs to have a small enough apex width to penetrate the hair, while at the same time be thin enough to keep cutting. The Feather artist club pro super is a good example of this. Even though the apex is more then small enough they tug more then my SR's. They cut skin better then hair in my opinion.

There is also a difference in how the different stones affect the apex of the steel. This is a 1k edge honed on a Morihei stone. The bevel is not affected the same way as other more aggressive cutting stones, like Shapton or Naniwa pro. You do not get these deeper striations on the bevel plane.
I like to think this type of edge cuts differently.

1645636832998.jpeg
 
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I guess this relates a little to the subject. The type of steel and heat treatment is also really important. I have a Spyderco Serrata in cast dendritic 440C steel. You can cut rope all day and still cut tomato skin afterward with this knife. I have another spyderco knife in M390 steel. This will pass the hanging hair test, but try cutting a tomato after it's been used to cut e.g. rope with. Totally useless. I would gladly shave with a razor made of M390 steel, but regardless of the way the serrata was honed, i would never try to shave with it.

A wider bevel angle will increase the normal force on the bevel planes, and thus increase the cutting resistance from a higher friction force. The edge needs to have a small enough apex width to penetrate the hair, while at the same time be thin enough to keep cutting. The Feather artist club pro super is a good example of this. Even though the apex is more then small enough they tug more then my SR's. They cut skin better then hair in my opinion.

There is also a difference in how the different stones affect the apex of the steel. This is a 1k edge honed on a Morihei stone. The bevel is not affected the same way as other more aggressive cutting stones, like Shapton or Naniwa pro. You do not get these deeper striations on the bevel plane.
I like to think this type of edge cuts differently.

View attachment 1414644


These are all very valid points concerning some of the other variables at play...

Though I sharpen various other steels on knives belonging to other people, almost all of our own knives are Aogami 2 + Super, and Shirogami 2. So I don't know a huge amount about how other steels perform over prolonged use. So what you say is very interesting!

Your second and third points are also very interesting; the second probably I guess in more noticeable / important on razor edges than knives. And yep - stones and their finishes are also a massive factor. Especially because the JIS measurement scale isn't standardized or based on abrasive particle size; companies can just interpret it as they wish, and play around with mixing grit sizes and different binders to create what they interpret a '1k' stone should be.

That third point also (I think) ties into why fine grit natural stones work so well as razor finishers. And the resulting shave might be as good or better than much higher 'grit' synthetics... but that's a whole other topic!
 
These are all very valid points concerning some of the other variables at play...

Though I sharpen various other steels on knives belonging to other people, almost all of our own knives are Aogami 2 + Super, and Shirogami 2. So I don't know a huge amount about how other steels perform over prolonged use. So what you say is very interesting!

Your second and third points are also very interesting; the second probably I guess in more noticeable / important on razor edges than knives. And yep - stones and their finishes are also a massive factor. Especially because the JIS measurement scale isn't standardized or based on abrasive particle size; companies can just interpret it as they wish, and play around with mixing grit sizes and different binders to create what they interpret a '1k' stone should be.

That third point also (I think) ties into why fine grit natural stones work so well as razor finishers. And the resulting shave might be as good or better than much higher 'grit' synthetics... but that's a whole other topic!
The Morihei 1k edge is a synthetic edge. There is suppose to be mixed in natural stone particles. It would be interesting to know how they rated these stones. The 4k striations looks quite similar as the 9k.
 
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